NUREG/CR-6918, Rev. 3

VARSKIN 6

A Computer Code for Skin 

Contamination Dosimetry

Office of Nuclear Regulatory Research
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NUREG/CR-6918, Rev. 3 

VARSKIN 6

A Computer Code for Skin Contamination 

Dosimetry

Office of Nuclear Regulatory Research

Manuscript Completed: December 2017

Date Published: October 2018

Prepared by:

D. M. Hamby

C. D. Mangini

School of Nuclear Science and Engineering

Oregon State University

Corvallis, OR 97331-5902

V. Shaffer, NRC Project Manager

iii

ABSTRACT

The original VARSKIN computer code, an algorithm to calculate skin dose from radioactive skin 

contamination, has been modified on several occasions. VARSKIN is a U.S. NRC computer 

code used by staff members and NRC licensees to calculate occupational dose to the skin 

resulting from exposure to radiation emitted from hot particles or other contamination on or near 

the skin. These assessments are required by 10 CFR 20.1201(c) in which the assigned shallow 

dose equivalent is to the part of the body receiving the highest exposure over a contiguous 10 

cm2 of skin at a tissue depth of 0.007 centimeters (7 mg/cm2).

As with previous versions, five different predefined source configurations are available in 

VARSKIN to allow simulations of point, disk, cylinder, sphere, and slab sources. Improvements 

to the earlier VARSKIN versions included enhanced photon and electron dosimetry models, as 

well as models to account for air gap and cover materials for photon dosimetry. With a simple 

check box activated by the user, VARSKIN 6 gives the user the option to have the code 

automatically include all decay products in dosimetry calculations or to allow the user to 

manually add progeny. Additionally, the option to calculate skin dose using ICRP 107 nuclide 

decay data (ICRP 2008) has been added. Both ICPR 38 (1983) and ICRP 107 (2008) nuclide 

libraries are available at the user’s option and contain data on gamma rays, X rays, beta 

particles, internal conversion electrons, and Auger electrons. Although the user can choose any 

dose-averaging area, the default area for skin dose calculations is 10 square centimeters, to 

conform to regulatory requirements pursuant to Title 10 of the Code of Federal Regulations, 

Section 20.1201(c). Data entry is condensed to a single screen, a variety of unit options are 

provided (including both British and International System (SI) units), and the source strength 

can be entered in units of total activity or distributed in units of activity per unit area or activity 

per unit volume. The output page and the user’s ability to add radionuclides to the library are 

greatly simplified. VARSKIN allows the user to eliminate radionuclides that are not of interest 

and thus build a customized library.

The enhanced photon model, introduced in VARSKIN 4, accounts for photon attenuation, 

charged particle buildup, and electron scatter at all depths in skin. The model allows for 

volumetric sources and clothing/air gaps between source and skin. The electron dosimetry 

model was upgraded in VARSKIN 5 to better account for beta energy loss and particle scatter. 

Dose point kernels are now Monte-Carlo based and results agree very well with EGS and 

MCNP probabilistic simulations.

This document describes the VARSKIN 6 dosimetry code, provides basic operating instructions, 

presents detailed descriptions of dosimetry models, and suggests methods for avoiding misuse 

of those models.

v

TABLE OF CONTENTS

ABSTRACT ................................................................................................................... iii

LIST OF FIGURES........................................................................................................ vii

LIST OF TABLES .......................................................................................................... ix

ACKNOWLEDGMENTS ................................................................................................ xi

ABBREVIATIONS AND ACRONYMS......................................................................... xiii

INTRODUCTION ..................................................................................................... 1-1

VARSKIN 6 USER’S MANUAL............................................................................... 2-1

2.1 Running VARSKIN .......................................................................................................2-1

2.1.1 Hardware and Software Requirements ...........................................................2-1

2.1.2 Source Geometry ...........................................................................................2-1

2.1.3 Adding Radionuclides to the Library ...............................................................2-4

2.1.4 Selecting Radionuclides for the Dose Scenario ..............................................2-7

2.1.5 Geometry Parameters and Multiple Cover Calculator .....................................2-7

2.1.6 Default State...................................................................................................2-8

2.2 Special Options ..........................................................................................................2-12

2.2.1 Calculating Dose ..........................................................................................2-13

2.2.2 Output Window.............................................................................................2-13

2.3 Exiting VARSKIN........................................................................................................2-15

DESCRIPTION OF DOSIMETRY MODELS............................................................ 3-1

3.1 Beta Dosimetry.............................................................................................................3-1

3.1.1 Dose-Point Kernels.........................................................................................3-1

3.1.2 Numerical Integration of Dose-Point Kernels ..................................................3-3

3.1.3 Homogenous Dose-Point Kernels...................................................................3-5

3.1.4 Non-Homogenous Dose-Point Kernels ...........................................................3-7

3.1.5 Beta-Particle Dose-Point Kernels....................................................................3-7

3.1.6 Backscatter Model ..........................................................................................3-9

3.1.7 Scaling Models .............................................................................................3-16

3.2 Photon Dosimetry.......................................................................................................3-21

3.2.1 Off-Axis Scatter Correction ...........................................................................3-25

3.2.2 Integration Methods......................................................................................3-26

3.2.3 Attenuation Coefficients for Cover Materials .................................................3-28

3.2.4 Offset Particle Model ....................................................................................3-29

3.2.5 Off-Axis Calculation of Dose.........................................................................3-29

3.3 Cover Layer and Air Gap Models................................................................................3-32

3.4 Volume Averaged Dose Model ...................................................................................3-34

VALIDATION AND VERIFICATION ........................................................................ 4-1

4.1 Inter-Code Comparisons ..............................................................................................4-1

4.1.1 Point Source Directly on Skin .........................................................................4-1

4.1.2 Point Source on Cover Material ......................................................................4-1

4.1.3 Infinite Plane Electron Source on the Skin ......................................................4-2

4.2 Dosimetry V&V Using Monte Carlo Simulations............................................................4-3
vi

VARSKIN 6 LIMITATIONS...................................................................................... 5-1

5.1 Electron Dosimetry .......................................................................................................5-1

5.1.1 DPK’s and Scaling Model ...............................................................................5-2

5.1.2 Scattering Model.............................................................................................5-2

5.2 Photon Dosimetry.........................................................................................................5-2

5.3 Creation of SADD and Backscatter Data for Progeny Inclusion ....................................5-3

SPECIAL TOPICS................................................................................................... 6-1

6.1 Infinite Sources.............................................................................................................6-1

6.2 Maximum Dose from Multiple Contamination Sources..................................................6-1

6.3 Manipulation of Files for Extended Utility ......................................................................6-2

REFERENCES ........................................................................................................ 7-1

SUPPORTING FIGURES FROM SECTION 4 .................................... A-1

SUPPORTING FIGURES FROM SECTION 5 .................................... B-1

EXAMPLES AND SOLUTIONS USING VARSKIN 6.......................... C-1
vii

LIST OF FIGURES

Figure 1-1 Depiction of Cylindrical Dose Averaging Volume ..............................................1-1

Figure 2-1 Initial View and Main Input Window...................................................................2-2

Figure 2-2 “About VARSKIN 6.0” Window..........................................................................2-2

Figure 2-3 Schematic Representations of the Five Geometry Options ...............................2-3

Figure 2-4a Decay Data Source Window .............................................................................2-6

Figure 2-4b Add Radionuclide Window ................................................................................2-6

Figure 2-5 Slab Source Geometry Parameters ..................................................................2-8

Figure 2-6 Schematic Showing the Cover Material and Air Gap Models ..........................2-10

Figure 2-7 Multiple Cover Calculator Window ..................................................................2-11

Figure 2-8 Schematic Diagram of the Volume-Averaged Dose Model Geometry .............2-13

Figure 2-9 Results Screen for a Typical Calculation.........................................................2-14

Figure 2-10 Results Screen for a Volume-Averaged Calculation........................................2-15

Figure 3-1 Scaled Absorbed Dose Distribution for 0.1 Mev Electrons ................................3-3

Figure 3-2 Scaled Absorbed Dose Distribution for 1.0 Mev Electrons ................................3-3

Figure 3-3 Schematic of Eight-Panel Quadrature Routine..................................................3-5

Figure 3-4 Schematic of EGSnrc Geometry for Determining Point-Source.........................3-6

Figure 3-5 Plot Demonstrating the Wide Range of Densities and Atomic Numbers............3-7

Figure 3-6 Schematic Demonstrating Conditions for Full Source-Water Scattering..........3-11

Figure 3-7 Schematic Demonstrating Conditions for Partial Source Scattering 

Conditions.......................................................................................................3-11

Figure 3-8 Schematic Illustrating Beta Energy Limitations of Side-Scatter Corrections ....3-13

Figure 3-9 Schematic Illustrating Parameters Used for Side Scattering ...........................3-13

Figure 3-10 Schematic Demonstrating Conditions for Full Air-Water Scattering 

Conditions... ...................................................................................................3-15

Figure 3-11 Schematic Demonstrating Conditions for Air-Water Scattering Correction ......3-16

Figure 3-12 Comparison of 1 Mev Electron DPKs..............................................................3-17

Figure 3-13 Example of Depth Scaling on the Homogeneous DPK Curve .........................3-17

Figure 3-14 3D Plot of Depth-Scaling Data ........................................................................3-18

Figure 3-15 Example of Energy Scaling on the Homogeneous DPK Curve 

Presented In Figure 3-13 ................................................................................3-19

Figure 3-16 3D Plot of Energy-Scaling Data.......................................................................3-21

Figure 3-17 ICRU 44 Soft Tissue Mass Attenuation Coefficients........................................3-23

Figure 3-18 ICRU 44 Soft Tissue Mass Energy Absorption Coefficients ............................3-24

Figure 3-19 Off-Axis Correction Factor for off-Axis Angle and Dose-Averaging Area .........3-26

Figure 3-20 Methods for Determining Integration Segments of the Dose-Averaging 

Disk.................................................................................................................3-27

Figure 3-21 Relative Dose for the Number of Segments in a Numerical Integration ...........3-27

Figure 3-22 Dose-Averaging Disk with the Source Point Located on Axis..........................3-29

Figure 3-23 Dose-Averaging Disk Located at Depth H Beneath an Offset Point Source ....3-30
viii

Figure 3-24 Dose-Averaging Disk with the Source Point Located off Axis, on Disk ............3-30

Figure 3-25 Relationship Between the Source-Averaging Disk and One of the Radii .........3-31

Figure 3-26 Dose-Averaging Disk from Above with Source Point Located off Axis, off 

Disk.................................................................................................................3-32

Figure 3-27 Schematic of a Generic Dose Calculation for Cylindrical Geometry ................3-33

Figure 4-1 Horizontal and Vertical Cross-Sectional Views of the MCNP5 Geometry ..........4-4

Figure 4-2 Point Source Geometry of Tissue Volumes.......................................................4-5

Figure 5-1 Backscatter Factors in Air as a Function of Depth in Tissue..............................5-5

Figure 6-1 Input Example for the ICRP38.DAT File............................................................6-2
ix

LIST OF TABLES

Table 2-1 Default Values and Units for Geometry Parameters..........................................2-9

Table 2-2 Suggested Values for Cover Thickness and Density.......................................2-11

Table 3-1 List of Source Materials Used to Develop the Scaling Model ............................3-6

Table 3-2 List of Nuclides Used in Scaling and Scattering Models....................................3-8

Table 3-3 Source Materials Used For Non-Homogeneous Beta Particle DPK Testing ......3-8

Table 3-4 Coefficients for Eq. [3.23]................................................................................3-24

Table 4-1 Comparison of Shallow Dose Estimates for Point Sources ...............................4-1

Table 4-2 Comparison of Shallow Dose Estimates for Various Cover Materials................4-2

Table 4-3 Comparison of Electron Dose with Infinite Plane Source...................................4-3

Table 4-4 Dose vs. Depth for Distributed Disk Sources.....................................................4-3

Table 5-1 Dose from Individual and Combined Parent/Progeny for Sr/Y-90......................5-4

Table 5-2 Dose from Individual and Combined Parent/Progeny for I/Xe-133 ....................5-4

xi

ACKNOWLEDGMENTS

This report was prepared to document work performed by Oregon State University (OSU) for 

the U.S Nuclear Regulatory Commission (NRC) under Contract Nos. NRC-HQ-60-15-C-0011,

NRC-HQ-11-C-04-0011 and NRC-04-08-137. Staff at the Pacific Northwest National Laboratory 

wrote initial versions of VARSKIN (Traub et al. 1987), with later versions amended at Colorado 

State University and then the Center for Nuclear Waste Regulatory Analyses (Durham 1992; 

Durham 2006). The activities reported here, and in previous versions (Hamby et al. 2011; 

Hamby et al. 2014), were performed by the team at OSU on behalf of the NRC Office of Nuclear 

Regulatory Research, Division of System Analysis. This report is a product of OSU and does 

not necessarily reflect the views or regulatory position of the NRC.

The team at OSU is very appreciative of the technical assistance received from D. Neville, L. 

Anspach, N. McDaniel, J. Caffrey, M. Tang, J. Parson, M. Ryan, and S. Marshall in the 

production of previous reports and their findings. We are also grateful to V. Shaffer, S. BushGoddard, M. Saba, and S. Sherbini for their support during development and maintenance of 

the enhanced photon and electron dosimetry models. Beta testers of this and earlier versions of 

VARSKIN include M. Jimenez, E. Dickson, P. Lee, S. Reese, J. Chase, J. Dubeau, K. Sejkora, 

M. Thornhill, R. Struckmeyer, and J. DeCicco.

Authors of earlier versions of the VARSKIN code were indebted to L. Howard for technical 

review and D. Turner for programmatic review of reports. These authors also thanked L. Selvey 

for document preparation; E. Hanson for editorial review; and H. Karagiannis, S. Sherbini, A. 

Roecklein, S. Bush-Goddard, and E. Dickson of the NRC for their support, suggestions, and 

patience during the development of VARSKIN 3. The following people helped develop models 

for VARSKIN 3: J. Chase, B. Plain, M. Wierzbicki, M. Lantz, and K. Krobl. The following people 

provided comments after testing VARSKIN 3: G. Chabot, J. Dwyer, J. Lebda, E. Mercer, 

R. Nimitz, A. Salame-Alfie, M. Stabin, G. Sturchio, B. Tharakan, T. Vandermey, and M. Charles.

xiii

ABBREVIATIONS AND ACRONYMS

2D Two Dimensional

3D Three Dimensional

BSCF Backscatter Correction Factor

CFR Code of Federal Regulations

CPE Charged Particle Equilibrium

CPU Central Processing Unit

CSDA Continuous Slowing Down Approximation

DPK Dose Point Kernel

DSP Depth Scaling Parameter

EDK Energy Deposition Kernel

EGS Electron-Gamma Shower

ESP Energy Scaling Parameter

GUI Graphical User Interface

ICRP Interactional Commission on Radiological Protection

ICRU International Commission on Radiation Units and Measurements

ITS Integrated TIGER Series

KERMA Kinetic Energy Released in Matter

MCNP Monte Carlo N-Particle

NCRP National Council on Radiation Protection and Measurement

NIST National Institute of Standards and Technology

NRC National Research Council (Canada)

NRC Nuclear Regulatory Commission

OSU Oregon State University

RSICC Radiation Safety Information Computational Center

RSO Radiation Safety Officer

SADD Scaled Absorbed Dose Distribution

SI Systeme Internationale

STP Standard Temperature and Pressure

TCPE Transient Charged Particle Equilibrium

V&V Verification and Validation

1-1

INTRODUCTION

The original VARSKIN computer code (Traub, et al., 1987) was intended as a tool for the 

calculation of tissue dose at various depths as the result of skin contamination. The 

contamination was assumed a point or an infinitely thin disk source located directly on the skin. 

Soon after the release of VARSKIN, the industry encountered a “new” type of skin contaminant. 

This contaminant consists of discrete microscopic radioactive particles, called “hot” particles. 

These particles differ radically from uniform skin contamination in that the particles have a 

thickness associated with them, and many of the skin exposures result from particles on the 

outside of protective clothing. These assessments are required by 10 CFR 20.1201(c) in which 

the assigned shallow dose equivalent is to the part of the body receiving the highest exposure 

over a contiguous 10 cm2 of skin at a tissue depth of 0.007 centimeters (7 mg/cm2).

VARSKIN MOD2 (Durham, 1992) contained all the features of the original VARSKIN, with many 

significant additions. Additional features in MOD2 included the modeling of three-dimensional 

sources (cylinders, spheres, and slabs) that accounted for self-shielding, modeling of materials 

placed between the source and skin (including air gaps) that would attenuate beta particles, 

and, in specific cases, modeling hot particle photon doses. VARSKIN MOD2 also used a 

correction for backscatter for one- and two-dimensional beta sources under limited conditions. 

Finally, the VARSKIN MOD2 package incorporated a user interface that greatly simplified data 

entry for calculating skin dose, in addition to providing guidance in the form of help screens.

MOD2 contained a volume-averaged dose model and an offset particle model that have been 

retained in subsequent VARSKIN coding. The volume-averaged model allows the user to 

calculate dose averaged over a volume of tissue defined by a cylinder with a diameter equal to 

that of the dose averaging area and bounded at the top and bottom by two selected skin depths 

(see Figure 1-1). This model is useful for calculations of dose that then can be compared to the 

dose measured by a finite-volume instrument (e.g., a thermoluminescent dosimeter). The offset 

particle model, which allows dose to be calculated for a particle that is not centered over the 

dose area of interest, is useful for calculating dose to a singular given skin area from multiple 

hot particles.

Figure 1-1 Depiction of Cylindrical Dose Averaging Volume

Finally, VARSKIN MOD2 gave the user the ability to select a composite source term, thus 

allowing the calculation of total dose from a mixture of radionuclides instead of requiring the 
1-2

code to be executed separately for each constituent. This feature was altered in VARSKIN 3 

(Durham 2006), allowing the user to select up to twenty radionuclides in a single calculation. 

One drawback of removing this feature in VARSKIN 3 is that the user must explicitly add 

radioactive progeny; we have corrected this shortcoming with the issuance of VARSKIN 6. 

Enhancements that were incorporated into VARSKIN 4 (Hamby et al. 2011) focused on the 

photon dosimetry model. The photon model is fundamentally unchanged in VARSKIN 6 and 

includes charged-particle buildup and subsequent transient equilibrium, along with photon 

attenuation, air and cover attenuation, and the option to model volumetric sources. The 

VARSKIN 5 (Hamby et al. 2014) package provided an updated electron dosimetry model that 

better accounts for charged-particle energy loss as the particle moves through the source, cover 

material, air, and tissue. Likewise, the electron dosimetry model is fundamentally unchanged in 

VARSKIN 6. 

Section 2 of this report describes the content of VARSKIN 6, primarily focused on instructions 

for code execution. Section 3 discusses the technical basis for VARSKIN 6 and describes the 

dosimetry models, while Section 4 contains the results of validation and verification testing. 

Section 5 describes new features of the code and its limitations. Section 6 explains the correct 

method for modeling “infinite” sources and how to hand-calculate the maximum dose to a single 

10-square-centimeter (10 cm2) area from multiple contamination sources. Additionally,

Appendices A and B provide graphical results from photon and electron validation and

verification (V&V), and Appendix C presents four detailed solutions to practical examples using

VARSKIN 6.
2-1

VARSKIN 6 USER’S MANUAL

This section serves as a user’s guide for VARSKIN 6. It includes operating instructions and a 

description of the features of VARSKIN 6.

2.1 Running VARSKIN

Users simply download the VARSKIN folder and double-click the VARSKIN executable icon to 

run the code. There is no need to uninstall previous versions of VARSKIN or install the new 

version. Subsequent versions of VARSKIN will be available on the NRC/RAMP website, as 

necessary. Obtaining new versions is as simple as downloading the new folder and beginning 

execution. Multiple folders, containing different versions of VARSKIN, can be opened and 

operated simultaneously, if the user so chooses.

2.1.1 Hardware and Software Requirements

A personal computer with a Pentium II processor or newer is required. The VARSKIN 6 folder 

requires approximately 25 megabytes of disk space. Over the years, VARSKIN has been tested 

under a variety of Windows® operating systems. An error may occur for international users of 

VARSKIN 6 or users who may have changed their computer settings. This error occurs when 

trying to add a nuclide in the user list from the nuclide library for use. The error relates to using 

comma rather than period as the decimal system; and likewise, the period rather than comma 

as the digit-grouping symbol. If this error occurs, the user should change their computer 

settings in “Change date, time or number formats”.

Operations in VARSKIN 6 are designed to be intuitive. After double-clicking the VARSKIN 

executable icon, the user will see the Main Input window (Figure 2-1). If necessary, the “Help” 

dropdown list provides the user with an “About VARSKIN 6.0” window containing basic code

information and contact numbers (Figure 2-2). The user defines the exposure scenario by 

selecting various boxes, buttons, and data entry fields provided in the input window.

2.1.2 Source Geometry

Although VARSKIN 6 allows the user to enter data in any order, the source geometry should be 

chosen first, because changing the geometry package will cause certain parameters to appear 

and others to be removed. Five geometry packages are available (upper left of window Figure 

2-1): point source, disk source (infinitely thin), cylinder source (thick), spherical source, and slab 

source (rectangular). Source activity is assumed to be evenly distributed throughout the area or 

volume of all source geometries.

The point source geometry (Figure 2-3(A)) is very simple and should be used as an initial 

screening tool for contamination that is confined to an extremely small area of the skin, or for a 

quick calculation to determine whether a regulatory limit is being approached or exceeded. The 

point source geometry does not account for electron self-shielding, so a three-dimensional 

source geometry is best for particulate contamination. The point source model does not require 

any data describing the physical dimensions of the source and will generally yield the highest 

dose rate for a given activity of any of the available source geometries. For electron dosimetry, 

a point source is automatically (due to historical code constraints) modeled as a cylindrical 

source with a thickness of 1 micron, a radius of 1 micron, and a density of 0.001 grams per 
2-2

cubic centimeter (g/cm3). An offset particle model (discussed below) is available for photons in 

the point source geometry. 

Figure 2-1 Initial View and Main Input Window (Source Geometry option box in upper 

left corner) 

Figure 2-2 “About VARSKIN 6.0” Window
2-3

Figure 2-3 Schematic Representations of the Five Geometry Options

The infinitely thin disk source geometry model (Figure 2-3(B)) is simple and is recommended for 

modeling skin contamination events caused by liquid sources. The disk source geometry 

requires the user to enter either the source diameter or the source area at the bottom of the 

Disk Source Irradiation Geometry box. Entering the area of the contamination is useful for 

modeling sources when the area is known. Enter the area of the source in the text box labeled 

“Source Area.” When the user enters the diameter of the source area, VARSKIN 6 calculates 

the area of the two-dimensional (2D) disk with that diameter. Similarly, when the user enters the 

area of the source, VARSKIN 6 calculates the diameter of the disk with the same area. If the 

area of contamination is not circular, entering the area of the actual contamination will generally 

result in a reasonable estimation of skin dose.

The spherical source geometry (Figure 2-3(C)) is perhaps the simplest three-dimensional (3D) 

geometry to use for dose calculations because it requires knowledge of source density and only 

one source dimension, its diameter. The spherical source geometry assumes that the source is 

surrounded by air and touches the skin or cover material only at the bottom point of the sphere. 

For photon dosimetry, it is assumed that the source material is equivalent to air for attenuation 

calculations. Choosing a spherical source will generally overestimate dose compared to a 

similarly sized cylindrical source (same radius and length) with the same total activity. The air 

surrounding the bottom hemisphere does not shield the source particles as efficiently as the 

source material (which would be encountered by the particle in the cylinder or slab models), and 

a larger area of skin will be exposed, resulting in consistently higher doses. 

The cylindrical source model (Figure 2-3(D)) requires knowledge of density and two dimensions, 

the cylinder diameter and its height (thickness). The cylindrical source geometry assumes that 
2-4

the source is surrounded by air and that the entire bottom of the cylinder is in contact with skin 

or cover material. Of the two dimensions describing a cylinder, the calculated dose is much 

more sensitive to changes in the cylinder height as opposed to the cylinder diameter. 

The slab source geometry (Figure 2-3(E)) requires knowledge of density and three physical 

dimensions: the first side length, the second side length, and the slab’s thickness. Generally, as 

with the cylindrical model, slab thickness will have more influence on tissue dose than will lateral 

dimensions. 

The following general rules should govern the choice of geometry package, progressing from 

the most conservative to least conservative dose estimate: 

 If nothing is known about the particle size and shape, use the point source geometry

option. This option is also recommended for a quick comparison to regulatory limits

since the point geometry typically overestimates actual skin dose.

 If the diameter is known, but the thickness cannot be estimated, or if a distributed source

is being modeled (i.e., with a known source strength per unit area), use the

two-dimensional disk source geometry option. If an infinite plane source is desired, a

source area of at least 15 cm2 is generally sufficient.

 If the particle is known to be spherical (few particles are truly spherical), use the

spherical source geometry option.

 If the thickness and the diameter of the source can be estimated, but the shape is

unknown, use the cylindrical source geometry option because this geometry requires

only two dimensions (thickness and diameter) to describe the particle.

 If the particle is known to be rectangular, use the slab or cylinder source geometry

options. The height of the particle should be preserved, and the area of the contact

surface should be selected such that the source volume is preserved. Executing both

slab and cylinder will aid in providing bounding doses.

It is not intended that VARSKIN models be used to simulate large volumetric sources and the 

user is cautioned against using dimensions greater than a few centimeters. For all source 

geometries, dose is averaged over an infinitely thin disk centered below the central axis of the 

source. When using the offset particle model (available only for photon point sources), dose is 

calculated to the disk with its center located at the user-supplied offset distance from the center 

of the source. 

2.1.3 Adding Radionuclides to the Library 

VARSKIN 6 employs two master decay libraries and a user library that contains only those 

radionuclides that have been selected and added by the user. Nuclide decay information is 

obtained from abridged datasets published by the International Commission on Radiological 

Protection (ICRP), namely the ICRP 38 (1983) or ICRP 107 (2008) databases; VARSKIN 6 

defaults to the ICRP 38 database. In VARSKIN, the user selects the nuclear database from 

which to extract decay data when radionuclides are selected from the master library to be added 

to the user library. Additionally, the user will choose between the automatic inclusion of decay 

progeny (designated by “D”), or manual (or none) progeny selection. The user can reference the 

“DaughterList” files in the dat folder to obtain a listing of decay products and branching ratios 

being included by the VARSKIN 6 code when choosing the “D” option.

Radionuclides are added to the VARSKIN user library through the use of a FORTRAN 

executable file entitled SadCalc.exe. The purpose of the program, which is an adaptation of a 
2-5

stand-alone program originally called SADDE Mod 2 (Reece, et al., 1989), and modified by 

Mangini (2012), is to produce data files that contain the information needed to calculate both 

electron and photon doses. In addition to selecting the master library (either ICRP 38 or ICRP 

107, with or without progeny), and the nuclide from that library, the user must specify an 

effective atomic number (Zeff) to characterize the source material in which the radioactivity is 

incorporated. The default value for Zeff is 7.42 (the effective atomic number of water), meaning 

the radioactivity itself is assumed to be dissolved or suspended in water.

When choosing to include decay progeny (“D”), radioactive progeny follows the parent in 

secular equilibrium when selected from the master library. Selecting the non-progeny datasets 

will include parent nuclides only. The selection of decay progeny results in a single calculation 

of dose (one each for electrons and photons) for the parent and progeny incorporating the entire 

decay chain (with branching ratios greater than 1%). Individual doses for each member of the 

chain are not provided. If the user wishes to have this information, the user may select the 

dataset(s) without progeny inclusion and manually selecting each member of the decay series.

If evaluating dose from progeny alone, the user must note its half-life and include the correct 

dose calculation (decay corrected or not) in the dose estimate. For example, in the case of 

137mBa as a stand-alone product of 137Cs decay, the user should report the “Dose (No Decay)” 

result for 137mBa dose; this would force the assumption that 137mBa is continuously supplied by 

the decay of 137Cs (in this example, the branching ratio from 137Cs to 137mBa is 94.6%). However, 

if the “Decay-Corrected Dose” is used, the very short decay time of 137mBa will cause the dose to 

be significantly underestimated. 

When VARSKIN is first executed, a few preselected radionuclides may appear in the user

library. VARSKIN is designed to allow the user to customize the user library so that only the 

nuclides of interest can be maintained for ready use. To add a radionuclide to the user library, 

the user clicks the “Add” button (shown in the upper center of Figure 2-1), after which a new 

window appears to obtain the user’s choice of nuclide decay database and whether decay 

products are to be included (Figure 2-4a). Once this selection is made, another window will 

appear (Figure 2-4b) that displays every radionuclide for which data are available (a total of 838 

radionuclides in ICRP 38 and 1252 radionuclides in ICRP 107). In addition to selecting the 

decay database, the user must specify an effective atomic number (Zeff) to characterize the 

source material in which the radioactivity is incorporated. As stated above, the default value for 

Zeff is 7.42 (the effective atomic number of water). The user then highlights the radionuclide and 

clicks the “Add Radionuclide” button, or simply double-clicks the name of the radionuclide. A 

large number of radionuclides are available in the master library, each of which could be added 

to the VARSKIN user library, each from a different decay database, and each with its own 

effective atomic number (i.e., multiple selections of the same nuclide can be made, but with 

different values of Zeff).

Once the “Add Radionuclide” button is selected (Figure 2-4), calculations are performed 

internally to populate the user library for the selected radionuclide; this can take up to a minute 

or so, depending on the processing power of your computer. In these calculations, data are 

extracted from the appropriate data files .dat, .idx, and .bet (all of which are located in the \dat 

subdirectory of the application directory). If the radionuclide emits electrons, an electron energy 

spectrum is generated for all emissions with yield greater than 0.1%. Photons with energy 

greater than 2 keV and decay yield greater than 1% are also collected from these data files.

The data are processed by SadCalc.exe, and output files that contains the average emitted 

electron energy, electron yield, electron range, the scaled absorbed dose distribution, and the 
2-6

photon energies and yields are generated for the selected nuclide with the extensions “.rad” and 

“.photon” (these can be seen in the \dat folder).

Figure 2-4 (a) Decay Data Source Window and (b) Add Radionuclide Window

When the process of adding the radionuclide is completed, the Main Input window will return, 

and the added radionuclide will be visible in the user list (upper middle) of available 

radionuclides. The nuclide name will indicate the database from which the data were drawn 

(“38” or “107”), the effective atomic number of the source material (e.g., “[7.42]”), and whether 

decay progeny are included (“D” or blank). Each nuclide could be added to the VARSKIN user 

library, and each with its own effective atomic number (i.e., multiple selections of the same 

nuclide can be made, but with different values of Zeff).

Once a radionuclide is added to the library, it is available to be used in all subsequent 

calculations until the user purposefully removes the radionuclide from the library. Note that not 

all the radionuclides emit electrons or photons; some of the radionuclides emit only alpha 

particles, which do not contribute to skin dose. In that case, the user will be notified that the 

radionuclide does not emit these types of radiation, and no library file will be produced. The 

added radionuclide will remain in the user library for subsequent calculations unless the user 

purposefully removes it using the “Remove” button (Figure 2-1) on the Radionuclide Library 

frame; the nuclide data will always remain in the master library.
2-7

In VARSKIN 6, electron energy spectra for beta emitters are obtained from data files located in 

the \dat subdirectory of the VARSKIN folder and contains the maximum energy and the yield 

information for each of a number of energy bins. Index files (.idx) are used to quickly locate 

nuclide information in the very large data files. In addition to beta-emission information, the files 

also contain data on internal conversion or Auger electrons emitted by the radionuclide. The 

graphical user interface (GUI) collects spectral data for a selected radionuclide and writes the 

file sadinput.dat which contains the radionuclide name, the yield, the half-life, the maximum beta 

energy, the beta spectrum, and the energy and yield of any electrons. SadCalc.exe reads this 

file; adds conversion and Auger electrons to the beta spectrum to form a new spectrum that 

includes all electrons; calculates various parameters and writes these data to the file sadout.dat. 

The GUI reads sadout.dat and writes library files with the extensions .rad and .photon. Note that 

sadout.dat and sadinput.dat are internal files and are not normally accessed by the user.

2.1.4 Selecting Radionuclides for the Dose Scenario

Radionuclides in the user library (upper-middle) are selected for a dose calculation by doubleclicking the radionuclide name or by highlighting the desired radionuclide and clicking the 

“Select” button (Figure 2-1). If the nuclide name signifies the inclusion of decay products (“D”), 

doses calculated for that nuclide will include all energy emissions from all of its decay progeny 

(with >1% branching). The default unit of measure for activity is the microcurie (μCi). Users may 

change the activity unit by selecting a different unit from the Activity Units list box. The new unit 

must be chosen before selecting the radionuclide. When a radionuclide is selected, a message 

box will appear asking the user to enter the value of the activity in the chosen units. Once the 

activity is entered, the radionuclide and its activity will be added to the Selected Radionuclide list 

box (lower-middle). A user may select up to 20 radionuclides for a given scenario; nuclides with 

progeny are counted as only one (i.e., the parent) nuclide. If the “D” database is used for a 

given parent nuclide, all decay progeny, regardless of time, are assumed to be in equilibrium 

with the parent. If the user knows this not to be true, the progeny should be selected manually 

(non-starred decay database) so that independent dose values will be calculated for each decay 

product.

For geometry packages other than the point source, the “Use Distributed Source” checkbox will 

appear (see Figure 2-5). The distributed source option allows the user to enter the source 

strength in activity-per-unit-area for a 2D disk source or activity-per-unit-volume for a 3D 

volumetric source. The distributed source option applies only to radionuclides that are chosen 

after the checkbox has been selected. If the distributed source option is unchecked, 

subsequently selected radionuclides will have activities expressed as total inventory instead of 

distributed activity. The user is cautioned to be certain of the activity units in a given dosimetry 

calculation.

2.1.5 Geometry Parameters and Multiple Cover Calculator

The geometry parameter Source Irradiation Geometry box (Figure 2-5, shown on the right 

above the large VARSKIN 6 logo) changes contingent on the particular geometry chosen for the 

calculation (slab geometry in this example). The user can choose the units of each parameter 

from the dropdown lists provided to the right of each input field. The units can be mixed for the 

different parameters; VARSKIN 6 makes the necessary conversions internally. Table 2-1 shows 

the default values for the various parameters.
2-8

2.1.6 Default State 

VARSKIN 6 allows the user to save one default state for easy retrieval at a later time. If the user 

wishes to change the default settings of Table 2-1, the following actions should be taken. From 

the File dropdown menu, if the user selects “Save Default State,” a file is written that contains all 

input parameters for the geometry described at that moment. At a later time, if that geometry is 

to be run again, the user can select “Load Default State,” and all parameter values will return to 

their values at the time the default state was last saved. 

Figure 2-5 Slab Source Geometry Parameters (middle right) 

In the disk geometry package, the user has the option of entering either the source diameter or 

the source area. This feature simplifies data entry for two-dimensional sources where the area 

and the total activity are known. 
2-9

Table 2-1 Default Values and Units for Geometry Parameters

Parameter Default Value

Skin Density Thickness 7 mg/cm2

Air Gap Thickness 0 mm

Air Density (at standard temp & pressure, STP) 0.001293 g/cm3

Cover Thickness 0 mm

Cover Density 0 g/cm3

Source Area (Disk) 0.785 mm2

Source Diameter (Disk) 1 mm

Source Diameter (Cylinder) 1 mm

Source Thickness (Cylinder) 1 mm

Source Diameter (Sphere) 1 mm

Source Thickness (Slab) 1 mm

Source X-Side Length (Slab) 1 mm

Source Y-Side Length (Slab) 1 mm

Source Density (Three-Dimensional Geometries) 1 g/cm3

Source thickness and source density are equally important for calculating skin dose, especially 

for electron dosimetry. It is essential that these parameters are known accurately; otherwise, if 

necessary, their values should be underestimated so that conservative dose calculations will 

result. Modeling a lower source density and thickness decreases the effects of self-shielding, 

which in turn will generally increase shallow skin dose. If source dimensions are unknown, the 

following guidelines will help in choosing appropriate values:

 Diameter (disk and cylinder) and side lengths (slab): For sources of the same activity, 

the dose calculation for most radionuclides is relatively insensitive to these lengths for 

dimensions less than about 2 mm (for undetermined reasons, experience has shown 

that any source diameter less than about 0.2 nm will cause the code to freeze). 

Overestimating source dimensions will generally result in an overestimation of dose, 

unless the source size is larger than the averaging area.

 Thickness (disk and slab) and sphere diameter: The electron dose calculation is very 

sensitive to these dimensions, especially at low energies. Minimizing the value of this 

dimension will provide an overestimate of electron dose. For photons, these dimensions 

are not as critical for the dose calculation.

 Source density (volumetric geometries): For electron dosimetry, users should choose a 

source density that is consistent with the material containing the source. For hot particle 

contaminations, a typical density of stellite (cobalt/chromium alloy) is 8.3 g/cm3, and a 

density of 14 g/cm3 and effective Z of 25.8 is typical for fuel. For photon dose estimates, 
2-10

the source is assumed to be air, with negligible consequence, except for large, dense 

sources and very low-energy photons. 

Users can model the presence of a cover material and/or an air gap. The schematic drawing 

below (Figure 2-6) depicts the cylindrical source geometry to illustrate the cover/air-gap model. 

The required input to describe the cover is material thickness and its corresponding density. 

Both parameters are needed to account for the 1/r2 dependence of the Berger point kernel 

(geometric attenuation) and for the energy loss due to attenuation or residual energy absorption 

(material attenuation). For the air-gap model, only the thickness of the air gap is required for 

input. 

Figure 2-6 Schematic Showing the Cover Material and Air Gap Models 

The physical characteristics of the air gap and cover material can significantly affect the 

calculated skin dose. While the air gap has little consequence for material attenuation, its effect 

on geometric attenuation can be significant for electron dosimetry. The air gap in photon 

dosimetry has the effect of disrupting charged particle equilibrium (CPE) and can appreciably 

influence dose at very shallow depths in tissue. Cover materials influence both the geometric 

and material attenuation. Table 2-2 gives some suggested thickness and density values. 

VARSKIN 6 allows multiple cover materials to be modeled as a composite cover when the user 

clicks on the “Multiple Cover Calculator” button (Figure 2-1). The multiple-cover calculator 

allows the user to combine up to five covers (Figure 2-7). The user must enter a value for two of 

the following three parameters for each layer (while ensuring that the third parameter is blank): 

cover thickness, cover density, and cover density-thickness. The user can choose the units for 

density and thickness, but the value of density-thickness must be entered in mg/cm2. The 

calculator determines the third parameter, combines the different layers, and calculates an 

effective thickness and density of the composite cover. The appropriate input boxes in the 

Source Geometry window are then populated with the composite cover density (mg/cm3) and 

thickness (mm). If the user enters all three parameters, VARSKIN 6 will indicate an error and 

ask the user to enter only two of the three parameters for a given layer. The printout from a 

dose calculation will include the data for each cover layer, as well as the composite cover data. 
2-11

Table 2-2 Suggested Values for Cover Thickness and Density

Material Thickness (mm) Density (g/cm3)

Lab Coat (Plastic) 0.2 0.36

Lab Coat (Cloth) 0.4 0.9

Cotton Glove Liner 0.3 0.3

Surgeon Glove 0.05 0.9

Outer Glove (Thick) 0.45 1.1

Ribbed Outer Glove 0.55 0.9

Plastic Bootie 0.2 0.6

Rubber Shoe Cover 1.2 1

Coveralls 0.7 0.4

To include more than five covers in the composite cover calculation, the user should calculate 

the composite cover thickness and density for the first five covers and then run the calculator 

again entering the first composite cover thickness and density as one of the layers. Accordingly, 

if a composite cover is entered as one of the covers, the layers composing the composite cover 

will not be individually displayed in the printout.

Figure 2-7 Multiple Cover Calculator Window
2-12

For example, suppose each of the items in Table 2-2 (same density and thickness) were 

somehow part of a composite cover. The cover calculator could be used on the first five items 

resulting in a combined thickness of 1.40 mm and a density of 0.759 g/cm3. The final four items 

in Table 2-2 result in a combined thickness of 2.65 mm and a density of 0.791 g/cm3. If we then 

combine those two thicknesses and densities in the calculator, we obtain a final composite 

result of 4.05 mm thickness and 0.78 g/cm3 density. 

2.2 Special Options 

In the “Special Options” box (middle left of Figure 2-1), VARSKIN 6 will display at most three 

options, including: (1) Exclude Photon Dose; (2) Exclude Electron Dose; (3) Perform Volume 

Averaging; and (4) Offset Particle Model. Options 1, 2 and 3 are displayed for every source 

geometry, whereas option 4 is only displayed when the point source geometry is selected. 

The default for options 1 and 2 (boxes unchecked) are to calculate both photon and electron 

dose. The user can, however, select either of these boxes, but not both, to exclude the 

calculation of dose from photons or electrons. A calculated dose of zero will be displayed in the 

dose field as zero (“0.00E+00”), whereas the appropriate field will be blank if the user elects to 

exclude one or the other dose calculations. 

The third special option allows the calculation of dose to be averaged over a user-defined 

volume of tissue described by a cylinder of specific diameter and thickness. The use of the 

volume-averaging dose calculation can be important, for example, in predicting the dose 

averaged between 10 and 15 mg/cm2, as recommended by the International Commission on 

Radiological Protection (1991), for evaluating the dermal effects of skin dose. 

If volume averaging is chosen, the user is prompted (after selecting the “Calculate Doses” 

button) to enter the skin density thicknesses within which to bound the dose calculation (shallow 

and deeper tissue depths defining the cylindrical averaging volume). In this instance, skin 

density thickness must be entered in units of mg/cm2. A range of suggested values for the 

shallow and deep tissue depths is provided based on the physical range of electrons associated 

with the selected radionuclide. Suggested values are from a skin density thickness of 0 mg/cm2

to the maximum penetration depth of the electrons being modeled; however, any non-negative 

value of density thickness can be entered. The user is cautioned, however, to be certain of the 

depths requested; some depths may result in negative values for beta dose. If the user elects to 

exclude the calculation of electron dose, the shallow and deep depths will default to 0 mg/cm2

and 1000 mg/cm2. The VARSKIN model calculates the dose over the averaging area at 10 

discrete layers between the shallow and deep tissue depths (Figure 2-8). Thus, the volumeaveraged dose model requires 10-fold more execution time than that for a single depth. 

The offset particle model, which allows dose to be calculated for a particle that is not centered 

over the dose area of interest, is useful for calculating dose from multiple hot particles. The 

offset particle model is off unless selected by the user. When the “Offset Particle Model” box is 

checked, the user is prompted to enter the offset distance. The offset distance is the lateral 

distance between the point source and the center of the skin averaging area. The value of the 

offset is the only additional input value that is required for the model. The dose result window 

will display the offset value, if this option has been selected. The offset particle model is for 

photon dosimetry only and is described in more detail in Section 3. 
2-13

2.2.1 Calculating Dose

Once the desired geometric parameters and options have been selected, the user initiates the 

calculation by clicking the “Calculate Doses” button (Figure 2-1). A progress bar will appear 

below the VARSKIN 6 logo, which will scroll repeatedly depending on the complexity of the 

calculations. The number of radionuclides to be analyzed and the various options that have 

been selected will impact the calculation time.

Figure 2-8 Schematic Diagram of the Volume-Averaged Dose Model Geometry

VARSKIN 6 calculates dose using compiled FORTRAN programs entitled VarCalc.exe and 

GamCalc.exe. When the user clicks the “Calculate Doses” button, the GUI writes the input data 

in a file called output.dat. VarCalc.exe and GamCalc.exe read output.dat, perform the 

calculations, and then write results to a file entitled results.dat. The GUI reads results.dat and 

displays those results in the output window. Note that output.dat and results.dat are internal files 

and are not intended to be accessed or edited by the user.

2.2.2 Output Window

The Results window for a non-volume-averaged calculation (Figure 2-9) is displayed when the 

dose calculation is complete. The window is separated into three distinct sections: results for 

individual radionuclides (upper left quadrant), combined results for all radionuclides (upper right 

quadrant), and source input data (lower half).

In the individual results section of the initial display, only the results for the first radionuclide are 

shown. The results from other radionuclides are viewed by highlighting the radionuclide of 

interest in the list box (upper left). This will display only the contribution to the dose from the 

selected radionuclide. The combined results section continues to display the total dose for all 

radionuclides. The data in this section cannot be edited and will not change unless a new 

calculation is made. This section of the output window also contains unit selection bubbles, 

which allow the user to select dose results in English or International (SI) units.

The lower half of the results window contains a mirror of the input data entered in the Main Input 

window. The format of this section will change depending on the geometry chosen for the 

calculation. This area of the output also contains buttons that allow the user to perform certain 

functions. Selecting the “Print Results” button prompts the user for a title and then creates an 
2-14

.html file containing the data in the output window. Additionally, the user may save the input 

data to the calculation by closing the output window and selecting “Save” from the “File” 

dropdown list of the Main Input window. 

A slightly different results window will appear for volume-averaged dose calculations (Figure 2-

10). Since the dose could be averaged over different averaging volumes for different 

radionuclides, VARSKIN does not provide a section for combined results of a volume-averaged 

dose calculation. Instead, only the individual results from the highlighted radionuclide is 

displayed at any one time. The upper left section of the volume-averaged results window 

displays values of the shallow and deep skin depths, as well as the total volume over which the 

dose was averaged for the chosen radionuclide. Other radionuclides can be chosen individually 

by highlighting them in the radionuclide list box. As with the other results window, this output 

screen contains unit-selection bubbles allowing the user to select volume-averaged dose results 

in English or SI (Systeme Internationale) units. Again, a summary of the input parameters is 

displayed on the lower half of the screen and the print option (to an .html file) is available. 

Figure 2-9 Results Window for a Typical Calculation 

Calculations of dose and dose rate are carried out in the FORTRAN executable files and sent to 

the GUI for display. Decay-corrected and no decay doses are calculated in the GUI. An error 

was found in VARSKIN 5.2 that resulted in extremely high doses being calculated by the GUI for 

short-lived nuclides. The solution was to limit dose integration (from dose-rate) to no more than 

20 half-lives; this solved the calculation problem. 
2-15

Figure 2-10 Results Window for a Volume-Averaged Calculation

2.3 Exiting VARSKIN

The VARSKIN code is exited from the main window (Figure 2-1), either by clicking the “X” in the 

upper right corner or by selecting “Exit” from the File dropdown menu. Before exiting, the user is 

asked if the current input file is to be saved. When the “Yes” button is clicked, the user is asked 

to create a file name in which the input data will be saved so that the calculation can be 

recreated. Clicking the “No” button will cause the program to end without saving the current 

data. Clicking the “Cancel” button will return the user to the Main Input window. 

Data from a saved file are stored with a .vs6 extension. When a saved file is recalled (by 

selecting “Open” from the File dropdown menu), VARSKIN 6 reads the .vs6 to obtain the data 

for the calculation. These are internal files, should not be edited by the user.

3-1

DESCRIPTION OF DOSIMETRY MODELS

VARSKIN 6 uses updated electron (Mangini 2012; Hamby et al. 2014) and photon (Hamby et al. 

2009) skin dosimetry models, which this chapter describes in detail. In addition, improvements 

to models throughout the VARSKIN series are incorporated and described herein.

3.1 Beta Dosimetry

As with VARSKIN 6, dosimetry codes based on the dose-point kernel (DPK) method rely on the 

numerical integration of a point kernel over the source volume and dose region of interest. 

While this is computationally much faster than a Monte Carlo simulation, accuracy is often 

sacrificed with the point kernel simplification. In one way or another, all DPKs relate the dose at 

a given point to a radiation source at some other point in a homogeneous medium. The 

medium for which the DPK is defined is typically water, as this allows for direct comparison with 

tissue. If the medium is not water, various scaling techniques (discussed later in this section) 

can be used to quantify energy loss along the charged-particle track and to simulate the scatter 

of particle energy.

3.1.1 Dose-Point Kernels

Doses in VARSKIN 6 are calculated through numerical integration methods where dose-point 

kernels are integrated over the entire source volume and dose averaging area. The point kernel 

is given by:

 

10

2

3 90

 g 1.6 10 ( )

 kg sec ( )

sec g

4

J dis MeV x A Y E F

Gy MeV dis

D r

r X cm

cm

 









 

        

                     

      

     

[3.1]

where Fβ(ξ) represents a scaled absorbed dose distribution (Berger 1971; Mangini 2012). The 

parameter ξ represents the density scaled distance (includes distances in the source cover, 

clothing, and air) from the source point to the dose point, written as a ratio normalized to the X90

distance. The distance r is the physical distance between the source point and the dose point.

The development of Monte Carlo electron transport codes over the years has brought with it the 

tabulation of increasingly accurate electron dose-point kernels. The main advantage of Monte 

Carlo-based energy deposition kernels is the ability to account for energy-loss straggling and 

provide more accurate results for r > 0.9X90 (see Figs. 3-1 and 3-2). VARSKIN 6 calculates Fβ(ξ) 

using the Monte Carlo-based energy deposition kernels (I(r)) described below, thereby replacing 

Spencer’s (1955, 1959) moment-based energy dissipation distributions used in the VARSKIN

software through V4.0.

The Monte Carlo transport code, EGSnrc (Ljungberg 2012), was used to determine the radial 

energy distributions (or DPKs) and X90 values at electron energies of 0.01 MeV ≤ E ≤ 8 MeV (32 

total energies). An isotropic mono-energetic point-source was positioned at the center of 

concentric spherical shells of the respective media. For all simulations, the shell thickness was 

5% of the continuous slowing down approximation (CSDA) electron range, as taken from the 

ESTAR software of the National Institute of Standards and Technology (NIST). The last shell 

was at a radius 150% of the CSDA range to ensure complete absorption of the electron energy 
3-2

(excluding radiative-losses). The maximum energy of 8 MeV covers all beta-particle endpoint 

energies published in ICRP Publication 107 (2008). The minimum energy of 0.01 MeV is based 

on the 0.001 MeV lower limit of electron cross-section data available in the Electron Gamma 

Shower (EGS) software. Additionally, the ESTAR CSDA range of a 0.01 MeV electron is only 

0.252 mg cm-2. 

The EGS software was updated by the National Research Council (NRC) of Canada to create 

EGSnrc. The EGSnrc simulations were performed using the EDKnrc user code. The EDKnrc 

code can be used to calculate Energy Deposition Kernels (EDK) for photons or electrons 

(mono-energetic or poly-energetic) forced to interact at the center of a spherical geometry 

(Rogers 2011). The code can output energy deposition kernels in user defined spherical shells. 

The number of particle histories was set to one million and transport parameters were set to 

default settings except that: (1) PEGS data sets used with AE=AP=1 keV; (2) ECUT=PCUT=1 

keV; (3) Rayleigh scattering is turned on; and (4) bremsstrahlung cross sections are set to 

NIST. 

PEGSs data sets are the material cross section data used by EGSnrc. The parameters of AE 

and AP determine the lowest energy for which the cross-section values are defined. Generally, 

when AE and AP are lowered (minimum of 1 keV), the accuracy of the calculation increases; 

however, the computation time increases as well (Kawrakow and Rogers 2000). Electrons with 

energies below AE will not be transported and their energy is assumed to deposit locally. The 

same is true for photons (AP). The parameters ECUT and PCUT are related to AE and AP in 

that when an electron/photon energy falls below ECUT/PCUT, its energy is assumed to deposit 

locally. It is not possible to set ECUT and PCUT below AE and AP, respectively. These two 

parameters represent the Δ value in restricted stopping powers. 

Turning on the Rayleigh scattering parameter allows for the simulation of coherent scattering. 

Raleigh scattering for bremsstrahlung photons may become important below ~1 MeV for high-Z

materials and below 100-200 keV in low-Z materials. The updated NIST database for nuclear 

bremsstrahlung is strongly recommended for electron energies below 1-2 MeV with negligible 

improvements over default Bethe-Heitles cross sections above ~ 50 MeV. Sampling from the 

NIST database is faster at low energies but slower at high energies (Kawrakow and Rogers 

2000). 

Once the energy deposition kernels were determined at CSDA range increments, the X90 values 

for each energy were determined and the kernels re-tabulated with respect to ξ. These kernels 

were then read into SadCalc.exe for use in the SADD (scaled absorbed dose distribution) 

subroutine and SPENS function. As stated previously, the main advantage of Monte Carlobased energy deposition kernels over moment-based kernels is the ability to account for 

energy-loss straggling, thereby improving dose estimations with depth. This is easily seen by 

plotting F(ξ,E0) values determined using both moment-based (VARSKIN 4 and earlier) and 

Monte Carlo-based (VARSKIN 5 and later) methods (Figure 3-1 and 3-2). 
3-3

Figure 3-1 Scaled Absorbed Dose Distributions for 0.1 Mev Electrons 

Figure 3-2 Scaled Absorbed Dose Distributions for 1.0 Mev Electrons 

3.1.2 Numerical Integration of Dose-Point Kernels

DPK codes rely on an accurate and fast numerical integration method to calculate dose from a 

volumetric source to a given dose area. A typical integration process divides the source into 

very small sub-volumes (source points). The dose averaging area is divided into points at which 

the dose rate is to be calculated (dose points). The dose points (60 are used in VARSKIN 6) are 

positioned along the radius of a dose-averaging disk at a specified dose depth (Figure 3-3). 

Since the source geometry (cylindrical is used for this discussion) is symmetric about the doseaveraging area, dose points represent concentric isodose circles that describe the radial dose 

profile at a given depth in skin. 

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

0.00 0.50 1.00 1.50

F(ξ,E0) 

ξ

F(ξ,E0) vs ξ for 0.1 MeV

VARSKIN 5.0

VARSKIN 4.0

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0.00 0.50 1.00 1.50

F(ξ,E0

)

ξ

F(ξ,E0) vs ξ for 1.0 MeV

VARSKIN 5.0

VARSKIN 4.0
3-4

For each of the sixty dose points, a numerical integration is performed over the area of the 

cylindrical source at a given height in the source represented by eight elevations (z), eight radii 

(r’), and eight angular locations (θ). The dose rate at a dose point on an isodose circle of radius 

d’ is evaluated using 

2

0 0 0

( ') ' ( , ', ) ' 

R Z

D d S r B z r dz dr d v



     

 [3.2] 

where B(z,r’,θ) is the dose per disintegration (rad nt-1) from a source point with sourcecoordinates (cylindrical) of z, r’, and θ; R and Z are the source radius and height; and Sv is the 

volumetric source strength (nt cm-3). This procedure is repeated for each dose point beginning 

at the center of the irradiation area and extending to its edge. The dose rate averaged over an 

area at depth in the tissue is then calculated using 

0

2

2 ( ') ' '

R

D d d dd

D

R









[3.3] 

where R is the radius of the dose averaging area. 

The integration starts by choosing one of the eight elevation points ( ) in the source 

(Figure 3-3). At one of these elevations, one of eight concentric circles (radial source-points ) 

is chosen. One of these circles is then subdivided into eight source-points at 45-degree angles 

from each other (angular source-points ). Finally, the dose rate is calculated at each dose 

point from each of these eight source-points at a given elevation and radius. The contribution to 

the dose from the first four points is compared to the contribution of the last four points in a 

given circle. If the relative difference between the two contributions is less than 0.01 percent, 

then convergence of the integral is achieved, and the procedure is repeated at the next radial 

position. If the relative difference between the two contributions is greater than the relative 

error, each of the two contributions is further subdivided into eight additional source-points, and 

the above procedure is repeated for each of the two sets of eight points. This process, known 

as the Newton-Cotes eight-panel quadrature routine, provides a fast and accurate method of 

numerically integrating complex functions such as dose-point kernels (Durham 1992, 2006; 

Hamby 2011). 
3-5

Dose Averaging Area at a Tissue Depth

Dose Points (60)

Radial Source Points (8)

Elevation Source Points (8)

Angular Source Points (8)

Figure 3-3 Schematic of the Eight-Panel Quadrature Routine (redrawn from Durham 2006)

3.1.3 Homogenous Dose-Point Kernels

The Monte Carlo transport code, EGSnrc (Ljungberg 2012), was used to determine the radial 

energy distributions (or DPKs) and X90 values for 7.42 < Z ≤ 94 (Figure 3-5, Table 3-1) at 

electron energies of 0.01 MeV ≤ E ≤ 8 MeV (30 total values). An isotropic mono-energetic pointsource was positioned at the center of concentric spherical shells of the respective media 

(Figure 3-4). For all simulations, the shell thickness was 5% of the CSDA electron range, as 

taken from the ESTAR software provided by NIST. The last shell was at a radius 150% of the 

CSDA range to ensure complete absorption of the electron energy (excluding radiative-losses). 

The maximum energy of 8 MeV covers all beta-particle endpoint energies published in ICRP 

Publication 107 (2008). The minimum energy of 10 keV was chosen considering the 1 keV 

lower limit of electron cross-section data available in EGSnrc. Additionally, the CSDA range of a 

10 keV electron is nominally 2.5 microns in water.

Monte Carlo simulation with the MCNP (Monte Carlo N-Particle) software can be useful to 

determine energy deposition kernels when the Integrated TIGER Series (ITS) software energy 

indexing algorithm is used and when special care is taken for high-resolution measurements 

(LANL 2003). EGSnrc on the other hand, was not only shown to be step-size independent, but it 

is significantly faster at transporting electrons than MCNP. For example, MCNP requires 103 

minutes of central processing unit (CPU) time to measure energy deposition kernels for 1 MeV 

electrons in water (106 particle histories), whereas EGSnrc requires 9 minutes for the same 

simulation. This difference becomes even larger as electron energy and material Z increases. 

For these reasons, EGSnrc is used as the Monte Carlo code of choice for all simulations 

pertaining to the scaling and scattering models.
3-6

Figure 3-4 Schematic of EGSnrc Geometry for Determining Point-Source 

Each shell thickness is 5% of the CSDA electron range. Total spherical radius is 150% of CSDA 

electron range. Simulated electron tracks are represented by the dark dotted lines. 

Table 3-1 List of Source Materials Used to Develop the Scaling Model 

Element Z Density (g cm-3) Element Z Density (g cm-3)

Aluminum 13 2.70 Barium 56 3.59

Titanium 22 4.54 Neodymium 60 7.01

Iron 26 7.87 Gadolinium 64 7.90

Gallium 31 5.91 Ytterbium 70 6.90

Rubidium 37 1.63 Tantalum 73 16.65

Zirconium 40 6.51 Platinum 78 21.45

Ruthenium 44 12.37 Lead 82 11.35

Silver 47 10.50 Actinium 89 10.07

Tin 50 7.31 Plutonium 94 19.84
3-7

Figure 3-5 Plot Demonstrating the Wide Range of Densities and Atomic Numbers 

All materials were solid in nature (except water).

EGSnrc simulations were performed using the EDKnrc user code. This code can be used to 

calculate EDKs for photons or electrons (mono-energetic or poly-energetic) forced to interact at 

the center of a spherical geometry (Rogers 2011). The code can output energy deposition 

kernels in user defined spherical shells.

3.1.4 Non-Homogenous Dose-Point Kernels

Non-homogeneous point-source DPKs also were determined for 7.42 < Z ≤ 94 at 0.01 MeV ≤ E 

≤8 MeV using EGSnrc Monte Carlo simulations using identical transport parameters. The intent 

of calculating non-homogeneous DPKs is to determine how energy is deposited in spherical 

shells of water after a mono-energetic electron has been emitted from the center of a sphere 

composed of some medium other than water.

3.1.5 Beta-Particle Dose-Point Kernels

The end goal of the scaling model is the determination of non-homogeneous DPKs from 

homogeneous DPKs for beta-emitting radionuclides. By determining the depth and energyscaling parameters for all energies between 0.01 and 8 MeV, it is possible to determine the nonhomogeneous beta DPK for any known beta energy spectrum. This is accomplished by 

integrating over the beta energy spectrum for each source Z/thickness using 

max

0

1

( , , ) ( , , , ) ( ) ( , )

E

av

R Z ESP R E Z E N E r E dE

E

      

[3.4]

0.00

5.00

10.00

15.00

20.00

25.00

0 10 20 30 40 50 60 70 80 90 100

Density (g cm-3

)

Atomic Number

Density vs Atomic Number
3-8

where r is the spherical shell radius, Emax is the endpoint energy of the beta spectrum, N(E)dE is 

the fraction of electrons emitted per MeV per disintegration that have energies between E and 

E+dE, and 

max

0

 ( )

E

E E N E dE av 

[3.5]

For example, if the nuclide and source material in question are 60Co and iron, the scaling 

parameters are used to create an n x m array of DPKs for 60Co with source radii ranging from 0 

to a·X90 of iron and the water radii ranging from 0 to b·X90 of water. The parameter a is based on 

complete electron energy absorption in the source material and b is based on complete electron 

energy absorption in water when the source thickness is zero.

Non-homogeneous beta-particle DPKs were determined by incorporating scaling equations into 

SadCalc.exe. The SadCalc.exe routine utilizes ICRP Publication 107 (2008) beta-emission 

spectra to calculate homogeneous water DPKs for each electron present in a given dose 

calculation. Linear interpolation was used to accommodate all source media with 7.42 ≤ Zeff ≤ 

94. 

Non-homogeneous DPKs were calculated for a wide range of electron energies (Table 3-2) and 

source materials (Table 3-3). Stainless steel and uranium oxide were chosen as they represent 

common hot particle materials, and tungsten alloy was chosen to demonstrate the model’s 

ability to handle high-density media.

Table 3-2 List of Nuclides Used in Scaling and Scattering Models

Nuclide E̅ (MeV) X90 (cm)

60Co 0.0958 0.033

90Sr 0.196 0.083

210Bi 0.307 0.212

135I 0.375 0.239

89Sr 0.583 0.321

32P 0.695 0.363

56Mn 0.832 0.634

90Y 0.934 0.533

144Pr 1.217 0.696

Table 3-3 Source Materials Used for Non-Homogeneous Electron DPK Testing

Alloy Zeff Density (g cm-3)

Stainless Steel (SS_302) 25.81 8.06

Tungsten Alloy (Mallory2000) 72.79 18.00

Uranium Oxide 87.88 10.96
3-9

3.1.6 Backscatter Model

A volumetric backscatter model is used in VARSKIN 6 to predict the dose perturbations from 

both source and atmospheric backscattering. The model is applicable for electron-emitting 

radionuclides in a spherical, cylindrical and slab source geometry, and for source materials with 

7.42 < Zeff ≤ 94. Being based on the DPK concept, VARSKIN 6 relies on the numerical 

integration of a point kernel over the source volume and the dose region of interest. The 

medium for which the DPK is defined is typically water, thus allowing for direct comparison with 

tissue. While the electron scattering contribution has been studied extensively for medical 

physics applications, it has been limited to point-source assumptions in the past yet has been 

expanded to volumetric sources for use in VARSKIN 6. In addition to internal source scatter, 

electron scattering must also be considered in the medium surrounding the source (i.e., 

atmospheric scattering).

Inherent to the development of electron DPKs is the assumption of an infinite homogeneous 

medium (water/water interface). The isotropic nature of DPK’s assumes that electrons emitted 

away from the dose point can scatter back toward the dose point in an infinite homogeneous 

water medium and possibly contribute to dose at the point of interest. While scaling methods 

account for the non-homogeneous media that transmit the electrons, an additional adjustment is 

required to correct for the lack of scatter since an atmospheric medium is above the skin rather 

than a modeled water medium (i.e., an air/water interface). In the situation of a source resting 

on the skin, the air above the source (air/water interface) results in less backscatter than would 

have been modeled in developing the DPKs. This scenario is of particular importance for hot 

particle skin dosimetry.

In developing the electron dosimetry model for VARSKIN 5 (Mangini 2012), point-source planar 

dose profiles were determined using EGSnrc Monte Carlo simulations for the scattering media 

of water, air, and source materials with 7.42 < Zeff ≤ 94 at electron energies of 0.01 MeV ≤ E ≤ 8 

MeV. The planar dose volumes were 1 mg cm-2 thick, with a maximum normal depth of 1000 mg 

cm-2. The dose averaging areas were 1 cm2 and 10 cm2, consistent with the monitoring areas 

recommended by ICRP Publication 103 (2007) and NCRP (National Council on Radiation 

Protection & Measurement) Statement No. 9 (2001), respectively. The scattering medium was 

assumed infinite (>> electron range) in both thickness and lateral extent.

In general, a backscatter factor is found by taking the ratio of the planar dose when the 

scattering material is present (non-homogeneous case) to that when water is present 

(homogeneous case). Air scattering corrections often are reported inversely such that they are 

greater than or equal to one (Cross 1991b, 1992c). Regardless, these backscatter factors will 

be dependent on electron energy, the effective atomic number (Z) of the backscattering 

medium, normal depth, and dose averaging area. When applied to an electron-emitting nuclide, 

the backscatter factor for a given dose averaging area takes the form of

max

max

,

0

0

( , , ) ( )

( , )

( , ) ( )

E

A S

E

W

D Z z E N E dE

B Z z

D z E N E dE

 





[3.6]

where z is the normal depth, DW is the dose in the water/water geometry, DA,S is either the dose 

in the air/water geometry or the dose in the source/water geometry, and N(E)dE is the fraction 
3-10

of electrons emitted per MeV per disintegration that have energies between E and E+dE. 

Surface functions were used to determine mono-energetic electron planar dose profile curve fits 

for use in Eq. [3.6]. Once planar dose profile curve fits were determined, they were implemented 

into SadCalc.exe. The ICRP 107 electron-emission spectra were then used to calculate the 

electron backscatter factor of Eq. [3.6]. Linear interpolation was used for all 7.42 < Z ≤ 94.

It is important to remember that it is not possible to determine the absolute volumetric 

backscatter factor using the same procedures as point-sources. This is due to the largely 

different energy-degradation properties of air and water and their impact on the respective dose 

calculations. Therefore, a number of assumptions and estimations were made. 

The method is based on a selective integration process over the entire source volume. Rather 

than applying an overall correction factor to final dose calculations, scattering corrections are 

applied at each step of the numerical integration of dose. If desired, the ‘volumetric’ correction 

factor could then be determined by taking the ratio of overall dose with the applied point-source 

scattering corrections to the overall dose without. Selection criteria are used to determine the 

proper type and amount of scattering correction for which to account. Scattering corrections are 

broken down into three components: source/water interface corrections (for the top and bottom 

of the source), air/water interface corrections (for both the top and the sides of the source), and 

air/source interface corrections (for the sides of the source). 

During the numerical integration process for an ‘infinitely large’ source (dimensions > electron 

range), only source points positioned directly at the source/water interface (i.e., source/skin 

interface) will require the full application of the source/water scattering data (Figure 3-6). Source 

points positioned above this interface (Figure 3-7) require a more advance treatment. In this 

case, there is expected to be an increase in the energy absorption (i.e., dose) from downward 

scattering taking place in the upper portion of the source, as well as a decrease in dose from 

upward scattering in the lower portion of the source. If the contribution from downward 

scattering is greater than the contribution from upward scattering, the dose will be increased for 

that source-point kernel. Likewise, when the upward contribution is greater, the dose will be 

decreased. It can be seen from this argument that when the source point is at the top of the 

source, the application of both air/water and source/water correction results in an effective 

air/source correction. 

Scattering contributions from both upward and downward scattering are determined using Eq. 

[3.7]. The scattering material thicknesses for the top and bottom of the source are given by the 

normal distances from the source-point to the upper- and lower-most points of the source, 

respectively. The source backscatter correction factor (BSCF) is then determined by multiplying 

net scattering effectiveness by the electron source/water scattering correction for point-sources; 

/

( ) Source BSCF SW SE SE top bottom 

top bottom

[3.7] 

where SW is the electron source/water scattering correction for point-sources, SEtop is the 

scattering effectiveness for the top portion of the source, and SEbottom is the scattering 

effectiveness for the bottom portion of the source. The ‘skin depth’ at which the scattering factor 

is determined takes into account the normal density thickness of both the source and tissue 

through which the electron must traverse. 
3-11

Dose Region

Beta-Particle Range Source Point

Figure 3-6 Schematic Demonstrating Conditions for Full Source-Water Scattering

The dimensions of the source (orange) are greater than the range of the electron.

Dose Region

Downward Scattering

Upward Scattering

Source Point Beta-Particle Range

Figure 3-7 Schematic Demonstrating Conditions for Partial Source Scattering Conditions

The lower portion of the source causes upward scattering away from the dose region and 

the upper portion of the source causes downward scattering towards the dose region.

The point-source factors were developed with the assumption that the source medium is infinite 

in both height and lateral extent. As such, application to source points near or on the side of the 

source jeopardizes the accuracy of the results. However, approximations can be made to 

estimate source/scatter corrections for the sides of the source.

When the dimensions of the source are larger than the range of the electron, source points 

toward the center and the top-center of the source have minimal impact on dose. Therefore, 

source-points on both sides and the bottom of the source become more important. It is 
3-12

estimated that scattering contributions from the sides of the source will reach a maximum when 

the scattering media thickness is 1.0 X/X90 and greater. Linear interpolation is used for X/X90

values less than 1.0. 

Unlike source scattering for the top and bottom of the source, during the numerical integration 

process, the direction of the electron needs to be considered when correcting for side scatter. 

Side scattering is accounted for when the electron’s path is directed away from the source and 

travels through air prior to reaching the dose region. The assumption is that an electron emitted 

in the 180 degree opposite direction would be permitted to backscatter off the source’s side and 

still contribute to dose. 

The amount of source material directly above the source point (considered the ‘lateral’ 

dimension in this case) will also have an impact on the scattering effectiveness. If the source 

point is located on the top corner of the source, the probability of a backscattering event toward 

the dose region is greatly decreased. On the other hand, if the source point is at the bottom 

corner of the source, the probability of backscattering event toward the dose region is much 

greater. It is estimated, therefore, that the normal distance to the upper most point of the source 

must be greater than 0.5 X/X90 (or 1⁄2 of the ‘height’ requirement) to have 100% scattering 

effectiveness from the top portion of the source. Therefore, the net scattering correction is 

given by 

_

( )

0.5

top

side op side side

X

Source BSCF SA X X  

[3.8] 

where SA is the electron source/air scattering correction for point-sources (ratio of source/water 

to air/water correction factor), Xside is the normal distance to the side of the source through 

which the electron travels, Xop_side is the normal distance to the opposite side of the source, and 

Xtop is the normal distance to the top of the source. All distances are relative to X90. If Xtop is 

greater than 0.5, the full scattering correction is applied by setting Xtop equal to 0.5. Similarly, if 

Xside or Xop_side are greater than 1.0, they are set equal to 1.0. 

As the energy of the electron decreases and the scattered path angle relative to the air/water 

interface increases, the probability of the scattered beta depositing energy in the dose area 

greatly decreases (Figure 3-8). Conversely, high-energy electrons are expected to have a 

contribution extending to the edge of the dose area when scattered electrons enter the dose 

region at high incident angles. It is assumed that the scattering correction from the top and 

bottom of the source does not accurately account for such contributions due to its inherent 

geometry. Without knowing the angle at which a particular electron scatters and likely enters the 

dose region at each stage of the integration process, it is very difficult to correctly apply this 

additional correction factor. Therefore, the angle of incident (Figure 3-9) is used to estimate the 

frequency at which large angle scattering events occur. The side-scattering correction is only 

applied when the incident angle is greater than 70 degrees and when the density corrected path 

length (includes source and air) to the edge of the dose region, or the maximum scattered 

electron path length, is less than the electron X90 distance. The latter limitation prevents the 

side-scatter correction from being applied to low-energy electrons, where this form of scatter is 

believed unlikely (as explained above). 
3-13

High Energy Scattered Beta Low Energy Source Scattered Beta

Dose Plane

Figure 3-8 Schematic Illustrating Electron Energy Limitations of Side-Scatter Corrections

Both scattering paths assume the same incident angle.

Dose Region

Maximum Scattered Beta Path Incident Beta Path

Source Point

Dose Point

Angle of Incident

Xside Xop_side

Xtop

Figure 3-9 Schematic Illustrating Parameters Used for Side Scattering

As with scattering from the top/bottom of the source, the ‘skin depth’ at which the scattering 

factor is determined takes into account the normal density thickness of both the source and 

tissue through which the electron must traverse.

The application of scattering correction factors is more difficult with an air/water interface than 

with a source/water interface. In order to estimate the scattering effectiveness when source 

material is present between the air/water interface, simple linear interpolation is used. The two 

extreme cases are when there is no source material between the air and water boundaries 

(Figure 3-10) and when the path length from the top or sides of the source is equal to or greater

than the electron range. The scattering effectiveness would be 100% and 0%, respectively. The 
3-14

assumption is that if a backscattered electron can escape the source, there is a chance that a 

dose-contributing scatter event may still occur if water were surrounding the source. This is 

seen as a conservative estimate as an electron that travels 1.8 X/X90 (range estimate, Durham 

2006) out of the top of a source will theoretically not be able to backscatter and contribute to 

skin dose at any depth. 

The overall air BSCF is found using a weighted average. The BSCFs are calculated for all 

surfaces for which the electron can escape and reach air. Scattering contributions from the top 

of the source receive a 50% weight and the remaining 50% is evenly divided among the sides of 

the source. For cylinders and spheres, the shortest distance to the outer surface and the 180 

degree opposite distance represent the two side distances (Figure 3-11). For slabs, four sides 

are used: the normal distances to the x-coordinate sides and the normal distances to the ycoordinate sides. The scattering reductions (for cylinders and spheres) are therefore given by 

1.8

 0.5

1.8

top

top

X

Air BSCF AW





[3.9] 

1.8 0.25

1.8

side

side

X

Air BSCF AW 

[3.10] 

and

_

_

1.8

 0.25

1.8

op side

op side

X

Air BSCF AW





[3.11] 

where AW is electron air/water scattering correction for point-sources, Xtop, Xside, and Xop_side are 

the distances to the top and sides of the source relative to X90. 

Unlike the source scattering corrections, no depth adjustments need to be made for materials 

traversed by the electron prior to entering the dose region. This is because corrections are 

made for scattering events occurring outside the source. The distance to the air/water interface 

is considered negligible in terms of electron energy degradation (assumed to be completely air). 

The overall air scattering correction is found by summing the three components above. 
3-15

Figure 3-10 Schematic Demonstrating Conditions for Full Air-Water Scattering Conditions

All profiles were fit with a 28-parameter Chebyshev Series (LnX-Y, Order 6). While this is a 

complex fit equation, it allowed for all curves to be fit with the same functional form with a high 

goodness of fit (R2 > 0.999). As an example, a second-order Chebyshev is given by,

1 1 2 1 2 Z a bT x cT y dT x eT y fT y       ( ') ( ') ( ') ( ') ( ')

[3.12]

where,

x x Normal Depth cm ' ln( ) ln( ( )) scaled -1 to +1,   y y E MeV ' ln( ( )) scaled -1 to +1,   ( ') cos( * *cos( ')), T x n a x n



and Z is the square root of the dose rate per particle (Gy Bq-1 s

-1

).
3-16

Figure 3-11 Schematic Demonstrating Conditions for Air-Water Scattering Correction 

When the distance to the top and sides of the source are less than 1.8*X90, a partial airscattering correction is applied. 

3.1.7 Scaling Models 

The DPK scaling model consists of two parameters: a depth scaling parameter (DSP) and an 

energy scaling parameter (ESP). Mangini (2016) provides more detail. 

3.1.7.1 Depth Scaling 

The depth-scaling model begins with determining the range of the electron in both the 

homogeneous and non-homogeneous geometries. Given the difficulty of determining an 

absolute electron range, due to energy straggling and a torturous path, the spherical radius at 

which 99.0% energy deposition occurred was chosen as a range estimate. The difference in 

ranges between the homogeneous and non-homogeneous data is therefore attributed to the 

absorption sphere in the non-homogeneous case. For a given absorption radius, the resulting 

difference in ranges is called the depth-scaling parameter,

0 99_ 99_ ( , , , ) DSP R E Z X X   H NH

[3.13] 

where X99_H is the homogeneous electron range, X99_NH is the non-homogeneous electron 

range, ρ and Z are density and effective atomic number, respectively, of the absorption material. 

As an example, consider an iron spherical source (r = 0.022 cm, Z = 26, ρ=7.874 g cm-3) and an 

electron energy of 1 MeV. The radius of the iron source was chosen to be 0.5X90 to allow for 

sufficient electron self-absorption. Due to the presence of the 0.022 cm of iron, the electron 

range in the non-homogeneous shells is 0.120 cm less than the homogeneous range (Figure 3-

12). Therefore, for a 1 MeV electron traversing 0.022 cm of iron, the depth-scaling parameter 

will be 0.120 cm. Shifting the homogeneous DPK data to the left (i.e., degraded electron energy 
3-17

by self-absorption and therefore less skin penetration) by this amount will equate the ranges 

and provide the necessary depth adjustment (Figure 3-13).

Figure 3-12 Comparison of 1 Mev Electron DPKs

Figure 3-13 Example of Depth Scaling on the Homogeneous DPK Curve

The depth-scaling parameter was determined to be 0.120 cm.

When plotted together in three dimensions, the variability of depth scaling with respect to Z is 

difficult to discern, as they all follow the same curvature with little separation (Figure 3-14). The 

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.00 0.10 0.20 0.30 0.40 0.50

Energy Depostion Fraction

Skin Depth (cm)

DPK Comparison

Homogenous

Non-Homogenous

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.00 0.10 0.20 0.30 0.40

Energy Depostion Fraction

Skin Depth (cm)

Depth Scaling

Homogenous

Non-Homogenous

0.120 cm 

difference
3-18

variation in DSPs at small radii is greatest, with essentially no variability at large radii. Each 

curve is linear with a slope near unity. This is expected since density thickness is often used to 

estimate “water equivalent” path length for electrons in non-aqueous media (Cho 2004). The 

small Z dependence, coupled with 18 curve fits, allows for accurate interpolation for any 7.42 < 

Z ≤ 94.

All curve fits for the DSPs took the form: 

2 3

2 3

( ) ( ( ))

(1 )

a bx cx dx ey LN DSP cm

fx gx hx iy

   



   

[3.14] 

where x is LN(E (MeV)) and y is LN(Xx*ρx (g cm-2)). The terms Xx and ρx refer to the radius and 

density of the absorption sphere. The form of Eq. [3.14] was chosen because it was the 

equation that had the largest R2 value (≥0.9999) and was able to fit all 18 plots. The fit 

parameters for each function demonstrated a slight Z dependence.

Figure 3-14 3D Plot of Depth-Scaling Data 

3.1.7.2 Energy Scaling 

The ESP is a direct result of energy conservation at distances within the electron’s maximum 

range, or X99 (neglecting radiative loses beyond this distance). Once the homogeneous curve is 

shifted according to the depth-scaling parameter (Figure 3-13), the total energy deposition is 

found for each case. This is performed by summing the homogeneous DPKs for radii between 

the depth-scaling parameter and the X99 distance,

-5

-4

-3

-2

-1

0

1

2

LN(E (MeV)) -15

-10

-5

0 LN(Xx*x (g cm-2))

-15 -15

-10 -10

-5 -5

0 0

5 5 LN(DSP (cm)) LN(DSP (cm))

Depth Scaling for All Materials
3-19 99

2

4 ( , )0

X

total

DSP

 r r E dr E   

[3.15]

Similarly, the total energy deposition in the non-homogeneous case is found by summing DPKs 

from 0 to X99. The law of energy conservation requires the two to be equal. Therefore, the 

energy-scaling parameter is found by taking the ratio of the non-homogeneous total to the 

homogeneous total, as:

99

99

2

0

0

0

2

0

4 ( , )

( , , , )

4 ( , )

X

NH

X

H

DSP

r r E dr

ESP R E Z

r r E dr

















[3.16]

Applying the resulting ratio to the homogeneous DPK equates the total energy depositions in 

the two geometries. For the iron source example, an energy-scaling parameter of 0.887 is 

computed. Thus, energy conservation is achieved by multiplying the homogeneous curve by the 

energy-scaling parameter of 0.887 (Fig. 3-15).

Figure 3-15 Example of Energy Scaling on the Homogeneous DPK Curve Presented in 

Figure 3-13

The energy-scaling parameter was determined to be 0.887.

As with the case of depth scaling, the natural logarithm of energy was used to decrease 

variability over the range of energies examined. The variability associated with the absorptionsphere radius was minimized by expressing it as a ratio of density thickness to the X90 distance 

in water, Xx*ρx / X90w. The natural logarithm of the depth-scaling parameter multiplied by the 

initial electron energy, LN(ESP*E0), was chosen as the dependent variable. While the quantity 

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.00 0.10 0.20 0.30 0.40

Energy Depostion Fraction

Skin Depth (cm)

Energy Scaling

Homogenous

Non-Homogenous
3-20

of ESP*E0 has no physical meaning, using it as the dependent variable produced better-fitting 

surface plots than simply using ESP. Since E0 is a known quantity, solving for ESP is simple. 

The variability of the ESP curves (Fig. 3-16) with respect to Z is more pronounced than the DSP 

curves (Fig. 3-14). The variation of ESPs becomes quite large as the absorption-sphere radius 

increases. As Z approaches that of water (Zeff of 7.42), the ESP approaches 1.0, as expected. 

As Z increases, the amount of energy reduction following depth scaling increases. Once again, 

this is expected given the lower profile of high-Z non-homogeneous DPK curves for the same 

absorption-sphere radius (with respect to X/X90). Despite this increased variability, interpolation 

within surface plots is not seen as an issue. 

All curve fits for the ESPs took the form: 

2 3 2

2 2

( ) ( * ( ))

(1 )

a bx cx dx ey fy LN E ESP MeV

gx hx iy jy

    



   

[3.17] 

where x is LN(E (MeV)) and y is Xx*ρx / X90w. The terms Xx and ρx refer to the radius and density 

of the absorption sphere. The above equation was chosen because it was the equation that had 

the largest R2 value (≥0.999) and was able to fit all 18 plots. As with the DSPs, fit parameters 

demonstrated a slight Z dependence.

Integration of scaling parameters over a particular electron energy spectrum provides the nonhomogeneous DPK for a given source thickness. Comparisons with EGSnrc non-homogeneous 

DPKs demonstrated excellent agreement over a range of electron energies and high-Z source 

materials by producing nearly identical DPKs for all absorption-sphere radii. In addition, when 

compared to Cross’ (1967, 1968, 1982, 1992a) scaling model and density scaling, the ability to 

account for spectral hardening is clearly shown. This is in large part due to the scaling model’s 

ability to accurately calculate non-homogeneous DPKs at each mono-energetic electron energy 

with a given emission spectrum. 
3-21

Figure 3-16 3D Plot of Energy-Scaling Data 

3.2 Photon Dosimetry

The new photon dosimetry model, first implemented in VARSKIN 4 (Hamby et al. 2011), is an 

improvement to the basic photon model used in the VARSKIN 3 version. The model uses a 

point-kernel method that considers the buildup of CPE, transient CPE, photon attenuation, and 

off-axis scatter. The photon dose model has many of the basic assumptions carried in the beta 

dosimetry model, namely that the source can be a point, disk, cylinder, sphere, or slab and that 

dose is calculated to an averaging disk immediately beneath the skin surface at a depth 

specified by the user. Photon dose is calculated for a specific skin averaging area, also 

specified by the user.

A major problem associated with deterministic photon dosimetry is that of determining the 

amount of charged-particle buildup and electron scatter within shallow depths. Federal law 

(Title 10 of the Code of Federal Regulations (10 CFR) Section 20.1201(b)) states that a dose 

averaging area of 10 cm2is appropriate for skin dosimetry (specifically at the shallow-dose 

equivalent depth of 0.007 cm in tissue (i.e., 7 mg/cm2in unit density material)). Throughout this 

section, the word “depth” is meant to indicate the distance from the skin surface to some point 

directly beneath a point source, normal to the skin surface.

To begin the explanation of the dose model, we assume the simple instance of a volume of 

tissue exposed to a uniform fluence, Φ0, of uncollided photons of energy, E, from a point source 

in a homogeneous medium. When we ignore attenuation and assume that CPE is established, 

the dose to any and every point in that volume of tissue is,

D(E) = Φ0 ∙ E ∙ (

μen

ρ

)

tissue

[3.18]

-5 -4 -3 -2 -1 0

1

2

LN(E (MeV))

2

1.75

1.51.25

1

0.75

0.50.25

Xx*x/X90w

-7 -7

-6 -6

-5 -5

-4 -4

-3 -3

-2 -2

-1 -1

0 0

1 1

2 2

3 3 LN(ESP*E (MeV)) LN(ESP*E (MeV))

Energy Scaling for All Materials
3-22

where (

μen

ρ

)

tissue

 is the energy-dependent mass energy absorption coefficient for tissue. With 

this calculation of dose, we essentially assume that the tissue volume is infinitely thin and that 

interactions occur in two dimensions, normal to a beam of incident photons. The uncollided 

fluence originating from a point source can be determined by, 

Φ0 =

S

4πd2

[3.19] 

where S has units of photons emitted per nuclear transition (i.e., yield), and d is the distance 

between the source and dose locations, in an infinitely large homogeneous volume. Thus, a 

point-kernel tissue dose per transition at distance, d, from a point source can be calculated for 

radionuclides emitting i photons of energy E and yield y, such that, 

Dose [

Gy

nt] =

k[ J∙g

MeV∙kg]

4πd2[cm2]

∙ ∑ [yi

[

photon

nt ] ∙ Ei

[

MeV

photon] ∙ (μen

ρ

)

i,tissue

[

cm2

g

i

]] [3.20] 

where k = 1.602x10−10 [

J∙g

MeV∙kg]. 

If the point source is assumed to rest on the skin surface (with a density interface), and a profile 

of dose with depth in tissue is of interest, Eq. [3.20] must be modified to account for the 

attenuation of photons in tissue, the electronic buildup, and electron scatter at shallow depths 

leading to CPE. First, given that attenuation is occurring as photons travel through tissue, 

photon fluence is decreasing by an attenuation factor (e-d) where  is the energy-dependent 

linear attenuation coefficient for tissue (coefficients are taken from International Commission on 

Radiation Units and Measurements (ICRU) Report 44, 1989). Since tissue typically is assumed 

to be of unit density (1 g/cm3), the value of  (in units of cm-1) is numerically identical to the 

value of  (in units of cm2/g). 

To simplify software coding, analytical expressions are used in VARSKIN 6 (as opposed to 

using “look-up tables”) for a number of dosimetry parameters. An empirical relationship to 

estimate  for tissue as a function of incident photon energy (in MeV) was developed and is 

given below. For energies less than or equal to 0.020 MeV, 

μ

ρ

(E) =

1

0.0000145+3810E

2.5+134400E3

[3.21] 

and for energies from 0.020 to 3 MeV, 

μ

ρ

(E) = e

[−3.22−0.11(lnE)

2+0.5566√E−0.7713lnE+(

0.000721

E

⁄ 2)]

[3.22] 

Figure 3-17 shows a comparison between the ICRU 44 (1989) values of  for soft tissue and 

the functions of Eqs. [3.21] and [3.22]. 
3-23

Figure 3-17 ICRU 44 Soft Tissue Mass Attenuation Coefficients 

The function shown in Eq. [3.23] was also developed to approximate the energy-dependent 

value of en for tissue. That function,

μen

ρ

(E) =

a+clnE+e(lnE)

2+g(lnE)3+i(lnE)4

1+blnE+d(lnE)

2+f(lnE)3+h(lnE)4+j(lnE)5

[3.23]

has a different set of coefficients for energies less than or equal to 0.030 MeV and energies 

from 0.030 to 3 MeV. Table 3-4 provides the coefficients and Figure 3-18 gives the fit of Eq. 

[3.23] to the ICRU 44 (1989) data.

In consideration of CPE, Attix (1986) states that the condition exists if, in an infinitely small 

volume, “...each charged particle of a given type and energy leaving [the volume] is replaced by 

an identical particle of the same energy entering.” For dose at shallow depths to be accurate, 

we must determine the degree (fraction) to which CPE, as a function of depth, has been 

achieved. The VARSKIN 6 estimation of the CPE fraction is based on Monte Carlo simulations 

and the difference between kinetic energy released in matter (KERMA) and energy absorbed 

(dose) as a function of depth.

Since energy transfer (i.e., KERMA) from photons and energy absorption (i.e., dose) from the 

resulting charged particles does not occur in the same location (Johns and Cunningham, 1983), 

there is a “buildup region” in which dose is zero at the skin surface and then increases until a 

depth is reached at which dose and KERMA are essentially equal. The depth at which 

equilibrium occurs is approximately equal to the range of the most energetic electron created by 

the incident photons (Johns and Cunningham, 1983). We determined an energy-dependent 

factor accounting for CPE buildup (fcpe) by Monte Carlo simulation (using MCNP5); this factor is 

the ratio of dose, D, to KERMA, K, for a particular incident photon energy at a given tissue 

depth, such that,

fcpe

(E, d) = D

K

⁄ [3.24]
3-24

Table 3-4 Coefficients for Eq. [3.23] 

Coefficient E ≤ 30 keV E > 30 keV

a 0.02971 0.03072

b 0.7453 0.4972

c 0.01519 0.009879

d 0.2236 0.1825

e 0.0009557 -0.0002386

f 0.03370 0.07303

g -0.0001513 0.0006930

h 0.002545 0.01520

i 0.00006018 0.0003239

j 0.00007744 0.001084

Figure 3-18 ICRU 44 Soft Tissue Mass Energy Absorption Coefficients 

When considering CPE and attenuation, a relationship is achieved with depth in a medium in 

which dose is proportional to KERMA (Attix, 1986); this relationship is referred to as transient 

charged particle equilibrium (TCPE). Dose reaches a maximum “at the depth where the rising 

slope due to buildup of charged particles is balanced by the descending slope due to 

attenuation” (Attix, 1986), and then dose continues to decrease with depth because of 

subsequent attenuation of photons. At the point where TCPE occurs, dose is essentially equal 

to KERMA for low-energy photons and the value of fcpe is equal to unity (1). As photon energy 

increases over about 1 MeV, this assumption of dose and KERMA equality begins to fail, but not 

so significantly that it affects dose estimations at depth appreciably. Based on experience with 

the Monte Carlo simulation of shallow and deep depths, the model used in VARSKIN 6 limits the 

value of fcpe to 1.05 (i.e., it allows dose to exceed KERMA by no more than 5 percent at depth). 
3-25

A function for fcpe that is dependent on initial photon energy is given as,

fcpe(x) =

1

a+bln(x)+c

√x

⁄

[3.25]

where x (in cm) is a function of energy and is equal to the point kernel distance between source 

point and dose point, and the coefficients a, b, and c are functions of energy (in keV) as 

described below:

a = 19.78 + 0.1492 ElnE − 0.008390 E

1.5 + 0.00003624 E2 + 3.343 √ElnE −10.72 E

lnE ⁄ [3.26]

b = 1.217x10−12E

4 −5.673x10−9E3 + 7.942x10−6E2 −0.002028E + 0.3296 [3.27]

c = 9.694x10−13E

4 − 4.861x10−9E3 + 7.765x10−6E2 − 0.001856E + 0.1467 [3.28]

The fcpe factor is used for all materials; any buildup for photon dosimetry in air or thin covers is 

expected to be insignificant as compared to tissue.

3.2.1 Off-Axis Scatter Correction

Estimates of fcpe were determined assuming that the line created between the source and dose 

points was normal to the surface. For a given distance, however, the fractional CPE for point 

kernel calculations, in which the dose point is located off axis and near the edge of the 

averaging disk, will vary because of the escape of energetic particles near the air-tissue 

interface. This loss of energy occurs for more energetic particles, generally from photons of 

energy greater than a few hundred keV. We have accounted for this off-axis scatter of energy 

out of tissue, slowing the buildup of equilibrium, by including an off-axis scatter factor, Foa. The 

factor, taking on values between 0 and 1, is necessary only for point-kernel calculations in which 

the angle between the central axis at the surface and the dose point is greater than 70 degrees 

from normal, and for photon energies greater than 300 keV; otherwise, Foa is set equal to unity 

(1). The off-axis scatter factor is calculated from empirical data obtained through Monte Carlo 

simulation. The factor is represented by,

Foa = (−1.57 + 0.000334 θ

2.5 − 0.0000325 θ3

)(0.93 + 0.1R) [3.29]

where R is the radius (cm) of the dose-averaging disk and  is the off-axis scatter angle (in 

degrees). Figure 3-19 gives a plot of off-axis correction as a function of scatter angle and the 

area of the dose-averaging disk. The considerable dip in the function for a 0.1-cm2 averaging 

area is an artifact of Eq. [3.29] and is not phenomenologically significant.
3-26

Figure 3-19 Off-Axis Correction Factor as a Function of Off-Axis Angle and DoseAveraging Area 

Fully accounting for charged particle buildup and attenuation, Eq. [3.20] now becomes: 

Dose [

Gy

nt ] =

k

4πd2

∙ ∑ [yi

∙ Ei∙ (μen

ρ

)

i,tissue

∙ (fcpe)

i

∙ (Foa)i∙ e−μid

] i

 [3.30] 

3.2.2 Integration Methods 

As stated above, Federal law currently requires the determination of shallow dose to skin 

averaged over an area of 10 cm2 at a depth in tissue of 7 mg/cm2. To determine average photon 

dose at depth from a source at the surface, we must integrate Eq. [3.30] over the averaging 

area. Integrating the exponential, however, results in a solution with imaginary components. 

Therefore, a stepwise numerical integration of Eq. [3.30] is necessary, essentially providing an 

average of the point-kernel dose over combinations of photon emission locations within the 

volume of the radioactive source and dose point locations within an infinitely thin disk of tissue 

at depth, h, from the surface. 

Studies were conducted to determine which numerical integration method achieved 

convergence most rapidly (i.e., dividing the dose-averaging disk into the fewest number of 

segments) for photon dosimetry. The studies investigated three segmenting methods (see 

Fig. 3-20): (1) segments determined by equal radii of the dose-averaging disk, (2) segments 

determined by equal off-axis angles, and (3) segments determined by equal annular area. 
3-27

Figure 3-20 Depiction of Methods for Determining Integration Segments of the DoseAveraging Disk

These studies indicated that segments divided according to equal lengths (radii) along the 

radius of the averaging disk converged with the fewest number of iterations, with segments 

divided by equal annular area requiring the most iterations. Figure 3-21 shows that convergence 

was achieved within about 300 iterations for equal lengths along the radius of a 10-cm2

averaging disk; the VARSKIN 6 numerical integration, therefore, utilizes 300 segments along 

the radius/diameter. Convergence was achieved with fewer segments when analyzing a smaller 

averaging disk.

Figure 3-21 Relative Dose as a Function of the Number of Segments in a Numerical 

Integration

Therefore, given a point source on the skin, the first task in the integration process is to divide 

the dose-averaging disk into N small segments (annuli), j, of uniform incremental radii. If an 

averaging area, A, of radius, R, is at some depth, h, beneath the surface of skin, a method 
3-28

based on the convergence study is used in which values of radii, Rj, of the averaging disk are 

selected such that a radial increment, ∆r, is defined, 

∆r = R

N

[3.31] 

and

Rj = ∑ (j ∙ ∆r)

N

j=0 [3.32] 

If point-kernel dose calculations are conducted where dose is estimated to the midpoint of the 

annulus, each dose must be weighted by wj, the ratio of the annular area to the total area of the 

disk. Given that R0 = 0 and RN = R, the values of wj are determined by, 

wj =

Rj

2−Rj−12

R2

[3.33] 

where j takes on values from 1 to N. We also define rj, which represents the average of the two 

radii describing the annulus in each calculation, such that, 

rj =

Rj−Rj−1

2

[3.34] 

Once all weighting factors are determined, then the dose per nuclear transition for a given point 

source radionuclide with i emissions, averaged over an infinitely thin disk of radius R, at normal 

depth in tissue h and radius rj, is calculated by, 

Ḋ(h, R) [

Gy

nt] = k4π

∙ ∑

wj

dj

2

[∑ [yi∙ Ei∙ (μen

ρ

)

i

∙ (fcpe)

i,j ∙ (Foa)i,j ∙ e−μidj ] i

]

N

j=1 [3.35] 

where dj = √(h2 + rj

2

).

3.2.3 Attenuation Coefficients for Cover Materials 

For the selection of attenuation coefficients in photon dose calculations, the cover materials are 

“forced” to be either latex or cotton. This determination is made by the density entry, i.e., if the 

density is less than or equal to 1.25 g/cm3

, then latex is assumed, but if greater, cotton is 

assumed. These are the two most likely materials used for cover. For photons, cover 

attenuation is relatively minor and this assumption should be insignificant for the dose 

calculation.

We use an empirical function of energy for attenuation coefficients for cotton and latex, namely: 

μ = e(a+b√E∙ln (E)+c√E)

[3.36]

where a = -1.0132, b = 0.31505, and c = -1.6086 for cotton, and a = -1.0286, b = 0.32189, and c 

= -1.6217 for latex. And, coefficients for air were determined from, 

μair = ((a + b

√E

) + (c ∙ ln(E)

E

) + (d

E

) + ( e

E1.5) + (f ∙ ln(E)E2

) + ( g

E2

)) ∗ 0.001168 [3.37]
3-29

where a = 0.027413, b = -0.12826, c = 0.11227, d = 0.060526, e = 0.12508, f = -0.0030978, and 

g = -0.021571. Both of these functions track very well with data from ICRP 44.

3.2.4 Offset Particle Model

The offset particle model allows calculation of skin dose averaged over areas that are not 

directly beneath the contaminant. This model was developed to determine dose to a single 

averaging area resulting from multiple hot particles. The offset particle model is available only 

for photons and the point-source geometry. It requires only one input variable, the distance of 

the offset. For multiple hot-particle irradiations, the dose from each hot particle is calculated 

separately, with the user running VARSKIN once for each source. The offset particle model 

does not calculate the maximum dose to skin from several particles (Section 6.2 outlines the 

iterative process for determining the maximum dose to the dose-averaging area); rather, the 

user must manually add doses from each of the sources to a common dose-averaging disk at 

depth.

3.2.5 Off-Axis Calculation of Dose

The model described thus far is constructed under the assumption that the source of photons is 

a point, located directly above and on axis with the averaging disk, and that there is symmetry in 

dose calculations along a radius of the dose-averaging disk (Fig. 3-22).

Figure 3-22 Dose-Averaging Disk with the Source Point Located on Axis

To extend the model to handle point-kernel calculations for volumetric sources, or for multiple 

point sources, we must consider the case where the point source is off axis yet still over the 

dose-averaging disk (Figs. 3-23 and 3-24) and the case where the point source is completely 

removed from the dose-averaging disk (Figs. 3-25 and 3-26). The implication is simply a 

geometric determination of the distance between source and dose points in each point-kernel 

calculation and an area-weighted factor for the symmetric dose location on the averaging disk.

In the first case, where the point source is off axis yet still over the dose area, there is symmetry 

along a diameter of the dose-averaging disk. The average of the point-kernel doses will be 

determined by a weighting of dose calculated along the diameter. The calculation begins by 

projecting the dose point to the averaging disk, normal to the skin surface (see Figure 3-23).
3-30

Figure 3-23 Dose-Averaging Disk Located at Depth h Beneath an Offset Point Source 

The averaging disk then is divided, as described above, into a series of concentric annuli, about 

the projected dose point, until the radius of the annuli reaches the nearest edge of the averaging 

disk (Fig. 3-24). At this point, the weighting model transitions to a series of arcs passing through 

the averaging disk; these arcs are created by differential radii of two intersecting circles (Fig. 3-

25). The model creates a total of 300 annuli and arcs. Point kernel dose is calculated along the 

diameter in each of the 300 segments defined by the differential annuli and arcs and then 

weighted based on the fractional area of each segment. 

The weight, or fractional area, of each annulus to the total is straightforward, in that, 

wi =

π(ri

2−ri+1

2

)

πR2 =

ri

2−ri+1

2

R2

[3.38] 

Figure 3-24 Dose-Averaging Disk with the Source Point Located off Axis, on Disk 

The weight of each arc is determined by a method considering intersecting circles. In the case 

of Figure 3-25, the area of the “lens” created by the two intersecting circles is given by:

Ai = r2cos−1 (

d

2+r2−R2

2dr ) + R2

cos−1 (

d

2+R2−r2

2dR )
3-31

−

1

2

√(−d + r + R)(d + r − R)(d − r + R)(d + r + R) [3.39]

Figure 3-25 Relationship Between the Source-Averaging Disk and One of the Radii 

The area of the arc formed (Fig. 3-25) by two concentric circles (two radii from the point source) 

that overlap another circle (the averaging disk) is the difference in the area calculations of 

Eq. [3.38]. The arc weight is then the ratio of the arc area to the total area of the averaging disk. 

In the case where the source projection does not fall on the dose-averaging disk (Fig. 3-26), the 

weighting scheme is based solely on arcs.

The numerical integration is conducted from the point source to each of 300 locations along the 

diameter of the averaging disk (or along the radius if the source point is directly on axis with the 

disk). Then, for volumetric sources, point source locations are chosen in equal symmetric 

increments at fifteen point locations in each of the three dimensions within the source volume, 

relative to the averaging-disk diameter. For each volumetric source dose estimate, 

1,000 calculations of dose from each of 15 x 15 x 15 source point locations are executed 

(1 million dose calculations).

The VARSKIN 6 photon dosimetry model accounts for attenuation in cover materials and in air. 

As with the electron dosimetry model, up to five layers above the skin are allowed, with the air 

layer only acceptable just above the skin surface. For photon calculations, the material layers 

are restricted to cotton and/or latex (by way of attenuation coefficient), and the source material 

is assumed to have the same characteristics as air. This latter assumption is not significant for 

very small volumetric sources and for photon energies above about 50 keV. For example, if we 

examine the ratio of air attenuation to lead, tin, copper, aluminum, and water attenuation, the 

greatest difference is obviously at low photon energies with higher-Z materials (i.e., instances of 

higher interaction probability).

Dose-averaging disk

Source

radii
3-32

Figure 3-26 Dose-Averaging Disk from Above with Source Point Located off Axis, off Disk

The data indicate that, for volumetric sources with a maximum linear dimension less than about 

100 microns, the assumption that the source material is similar to air is of no consequence 

whatsoever for photon energies above 10 keV. As the source particle dimensions increase in 

size, an assumption of air for the source material can be quite significant for very low photon 

energies (< 40 keV). The significance, however, is one of conservatism in that more low-energy 

photons than actual will be modeled as striking the skin surface when source dimensions are 

large. Our analysis also shows that, in terms of attenuation, the assumption of air and water 

(tissue) being similar over very short distances (< 5 mm) is a good assumption.

3.3 Cover Layer and Air Gap Models

VARSKIN 6 has the ability to model cover materials and air gaps. The models use the concept 

of effective path length to determine the electron energy lost in either a cover material or air 

before it enters the skin. The path length is not the true path traversed by the electron; rather, it 

is merely a mathematical convenience introduced to provide a measure of the energy lost in 

each layer. To minimize unintended applications of VARSKIN, the air gap is limited to a 

maximum of 20 cm.

Figure 3-27 illustrates the method used to determine path length within the source and within 

the cover material. For the pictured cylindrical source, the known values in the figure are the 

source radius (Rmax), the horizontal distance from the centerline to the source point (SRAD), the 

source thickness (STHICK), the cover thickness (CTHICK), the skin depth (SDEP), the source and 

cover densities ( s and c, respectively), the angular distance from the center of the dose area 

to the dose point (Ps), and the distance from the skin to the plane of the source point (DRAD).
3-33

Figure 3-27 Schematic of a Generic Dose Calculation for Cylindrical Geometry

The quadrature routines are coded to choose values for SRAD, the distance from the centerline to 

the Ps source point; , the angle between SRAD and Ps; and DRAD, the height of the dose point. 

The first quantity to be calculated is r, the physical distance from a source point to a dose point. 

To do this, the square of the projected distance, rp

2

, is calculated using the law of cosines:

rp

2 = Ps2 + Srad

2 − 2PsSradcosθ [3.40]

The quantity r is used in the denominator of the expression in Eq. [3.1] and represents the 

geometric attenuation between the dose point and the source point. This quantity is further 

analyzed to calculate the modified path length used to evaluate the scaled absorbed dose 

distribution.

By the law of similar triangles, the ratio to r of each of the actual distances along r through the 

source, the cover material, and the tissue is the same as the ratios of the thickness of the cover 

material to DRAD, the thickness of tissue layer to DRAD, and the remaining distance along r to 

DRAD respectively, provided that the line connecting the dose point and the source point exits 

through the part of the source that is in contact with the cover material. Thus, the distance 

traveled through the cover material is written as the following:

rc = Cthick ∙ (

r

Drad ⁄ ) [3.41]

The distance traveled through the skin is given by:

rt = Sdep ∙ (

r

Drad ⁄ ) [3.42]

And, the distance traveled through the source is given by:

rs = (Drad − Cthick − Sdep) ∙ (

r

Drad ⁄ ) [3.43]
3-34

For electron dosimetry, the modified path length r1 is then found using the following equation: 

r1 =

(rsρs+rcρc+rtρt

)

ρt

[3.44] 

where the variables ρs, ρc and ρtrepresent the density of the source, the cover material, and

tissue, respectively. The density of tissue is assumed to be equal to that of water (1 g cm-3).

For small-diameter sources, the path between the dose point and the source point may pass 

through the side of the source (e.g., the path may exit the source and pass through air before 

passing into skin). Thus, the quantity in Eq. [3.44] must be further analyzed to determine the 

path length within the source and the path length outside the source but above the level of the 

cover material. The actual path length within the source is multiplied by the source density, and 

the path length outside the source and above the cover material is multiplied by the density of 

the material outside the source, assumed to be air. 

In spherical geometry, the physical distance from source point to dose point is given by: 

rp

2 = Ps2 + Srad

2

sin2φ − 2PsSradsinφcosθ [3.45] 

In slab geometry, the physical distance is given by: 

r = √[(Xsource − Xdose)

2 + (Ysource − Ydose)

2 + (Zsource − Zdose)

2] [3.46] 

Recent investigations [Anspach and Hamby 2017; McDaniel and Hamby 2017; Dubeau et al. 

2018] have shown that the cover and air-gap models for electron dosimetry are too 

conservative, i.e., energy degradation of electrons appears to be too great as the travel through 

material prior to entering the skin. The user is cautioned not to rely on VARSKIN for source 

geometries involving cover materials greater than a few centimeters. 

3.4 Volume Averaged Dose Model 

The volume-averaged dose model (shown schematically in Fig. 2-8) allows the calculation of 

dose averaged over a given tissue volume. This model works with both photons and electrons 

yet is really only meaningful for electron dose calculations. Any two planes of irradiated skin 

can be assigned to bound the skin volume. For sources in contact with the skin, the maximum 

penetration depth for electrons is equal to the X99 distance. Doses averaged over the doseaveraging area are calculated at 10 skin depths between two limits set by the user, and a cubic 

spline (a third-order piecewise polynomial curve fit) is fit to this depth-dose distribution. When 

the user specifies the skin depths corresponding to the volume of interest, VARSKIN 6 

integrates the depth dose function over the region of interest to obtain the volume-averaged 

dose. 
4-1

VALIDATION AND VERIFICATION

To validate the new photon and electron dosimetry models incorporated into VARSKIN 6 and 

previous versions, results were compared to the general-purpose radiation transport codes, 

MCNP5 and EGSnrc. The two software packages are Monte Carlo transport codes that 

simulate interaction and transport of particles in material (Los Alamos National Laboratory, 

2003; Ljungberg et al. 2012). We also compared VARSKIN 5.3 with results from various 

methodologies in the literature [Anspach and Hamby 2017]. Since the unveiling in the late 

1980’s (Traub et al. 1987), VARSKIN results have been examined for comparison sake with 

many different authors. In the sections that follow, we continue to provide inter-comparisons 

with former versions of VARSKIN so that the user can see how dose estimates have changed 

over the years. In addition, the reader will see comparisons with Monte Carlo simulation, as 

well as comparisons with the literature.

4.1 Inter-Code Comparisons

The VARSKIN 6 photon and electron dosimetry models have gone through extensive 

enhancements over the past several years. Comparisons of dose calculated using VARSKIN

3.1, 4, 5.3, and 6.0 for point sources are given below (using ICRP 38 data for historical 

consistency) to demonstrate how the four versions differ in dose estimation for the few 

scenarios considered.

4.1.1 Point Source Directly on Skin

Calculations were made using several versions of VARSKIN for the case of a 60Co point source 

placed directly on the skin (i.e., no material and no air gap between the source and skin). For a 

37-kBq hot particle and a 1-hour exposure time, the electron and photon dose averaged over 

1 cm2 at a depth of 7 mg/cm2 was calculated. Table 4-1 shows the results of this calculation. 

Changes to electron dosimetry indicate a reduction of about 10% at this shallow depth, due 

primarily to changes in the calculation of specific absorbed dose distribution. Photon dose 

estimates changed dramatically because of the inclusion of charged particle buildup and photon 

attenuation.

Table 4-1 Comparison of Shallow Dose Estimates for Point Sources

Nuclide V3.1

 Dose

(mGy)

V4

 Dose

(mGy)

V5.3

 Dose

(mGy)

V6.0

 Dose

(mGy)

V3.1

 Dose

(mGy)

V4

 Dose

(mGy)

V5.3

 Dose

(mGy)

V6.0

 Dose

(mGy)

Co-60 37.6 37.6 34.5 34.5 3.29 0.79 0.79 0.79

4.1.2 Point Source on Cover Material

Dose calculations at 7 mg/cm2 were also performed for 60Co, 137Cs/137mBa, and 90Sr/90Y with 

three different cover material configurations. In each case, a 37-kBq point source and an 

exposure time of 1 hour were assumed with no gap between the layers of cover material. Doses 

were calculated for a 1-cm2 averaging disk. Table 4-2 shows the results of these calculations. 

Changes to electron dosimetry are shown to either increase or decrease, due to model 

enhancements that affect particle track lengths, energy loss, backscatter characteristics, 

conversion electron consideration, etc. Photon dose at shallow depths for the scenario 
4-2

considered decreases by about a factor of two after model enhancement, again, primarily due to 

the consideration of charged particle buildup and photon attenuation.

Table 4-2 Comparison of Shallow Dose Estimates for Various Cover Materials 

Nuclide

Air 

Gap

(cm)

Cover

Material

V3.1

 Dose

(mGy)

V4

 Dose

(mGy)

V5.3

 Dose

(mGy)

V6.0

 Dose

(mGy)

V3.1

 Dose

(mGy)

V4

 Dose

(mGy)

V5.3

 Dose

(mGy)

V6.0

 Dose

(mGy)

Co-60 0.2 M1 1.96 1.96 2.17 2.17 0.571 0.292 0.290 0.292

Cs-137D 0.2 M1 14.0 14.0 13.7 13.5 0.199 0.0969 0.0959 0.0917

Sr-90D 0.2 M1 32.6 32.6 29.1 28.2 0 0 0 0

Co-60 0.2 2M1 0 0 0.0789 0.0789 0.558 0.258 0.257 0.258

Cs-137D 0.2 2M1 4.75 4.75 6.50 6.44 0.181 0.0842 0.0834 0.0797

Sr-90D 0.2 2M1 20.7 20.7 19.5 19.1 0 0 0 0

Co-60 1.0 M1 0.813 0.813 0.813 0.813 0.0797 0.0429 0.0427 0.0429

Cs-137D 1.0 M1 2.79 2.79 2.59 2.53 0.0277 0.0129 0.0128 0.0122

Sr-90D 1.0 M1 5.37 5.37 4.74 0 0 0 0

Co-60 1.0 2M1 0 0 0.0409 0.0409 0.0836 0.0404 0.0402 0.0404

Cs-137D 1.0 2M1 1.40 1.40 1.53 1.49 0.0270 0.0121 0.0121 0.0115

Sr-90D 1.0 2M1 3.95 3.95 3.66 3.51 0 0 0 0

Co-60 1.0 M1 + M2 0 0 0.00838 0.00838 0.0876 0.0400 0.0400 0.0400

Cs-137D 1.0 M1 + M2 0.770 0.770 1.03 1.01 0.0271 0.0120 0.0120 0.0114

Sr-90D 1.0 M1 + M2 3.26 3.26 3.11 3.00 0 0 0 0

Co-60 5.0 M1 + M2 0 0 0.00045 0.00045 0.0045 0.0020 0.0025 0.0025

Cs-137D 5.0 M1 + M2 0.0384 0.0384 0.0521 0.0513 0.0013 0.0006 0.0006 0.0006

Sr-90D 5.0 M1 + M2 0.167 0.167 0.158 0.153 0 0 0 0

Cs-137D includes the progeny 137mBa; Sr-90D includes the progeny 90Y 

M1 — Cover material = thickness of 0.37 mm, density of 0.70 g/cm3

2M1 — Cover material = thickness of 0.74 mm, density of 0.70 g/cm3

M2 — Cover material = thickness of 0.40 mm, density of 1.1 g/cm3 

4.1.3 Infinite Plane Electron Source on the Skin 

Calculations were performed for various nuclides using VARSKIN 4, 5.3, and 6.0 (the electron 

dosimetry model is unchanged between 3.1 and 4) to compare specifically the electron dose 

estimate for a large distributed disk source (simulating an infinite plane) on the skin for an 

exposure period of 1 hour (Table 4-3). The electron dose at a depth of 7 mg/cm2 was calculated 

for a simulated contamination scenario with a concentration of 37 kBq/cm2 on a circular source 

of 100 cm2. A dose-averaging area of 1 cm2 was assumed. Table 4-4 provides additional 

VARSKIN comparisons at various shallow depths in tissue for a source of 90Y.
4-3

Table 4-3 Comparison of Electron Dose with Infinite Plane Source

Nuclide V4 V5.3 V6.0

C-14 11.2 11.1 11.1

P-32 66.3 58.7 58.7

Co-60 37.7 34.5 34.5

I-131 52.4 48.4 48.4

Cs-137 51.2 47.8 47.8

Cs-137D - - 53.5

Sr-90 54.7 49.7 49.7

Y-90 68.3 59.7 59.7

Sr-90D - - 110

Cs-137D includes the progeny 137mBa; Sr-90D includes the progeny 90Y; no dose estimates

are given for V4 and V5.3 since those versions did not automatically include decay progeny.

Table 4-4 Dose vs. Depth for Distributed Disk Sources

Method 4 mg/cm2 7 mg/cm2 10 mg/cm2 40 mg/cm2

VARSKIN 4 79.0 68.3 61.4 40.7

VARSKIN 5.3 65.9 59.7 55.5 38.4

VARSKIN 6.0 65.9 59.7 55.5 38.4

4.2 Dosimetry V&V Using Monte Carlo Simulations

For the simulations, we used MCNP5 for photon comparisons and EGSnrc for electron 

comparisons. With each code, various source geometries were modeled close to the skin. The 

fundamental geometry, illustrated in Fig. 4-1, involves an infinite volume of air located above an 

infinite volume of tissue. Composition of these materials was taken from NIST standards for each 

material. Each of the sources was situated 1 micron above the skin and above the perpendicular 

bisect of the volume of tissue over which the dose is calculated.
4-4

Figure 4-1 Horizontal (left) and Vertical (right) Cross-Sectional Views of the MCNP5 

Geometry 

As illustrated in Fig. 4-2, the dose per particle (photon or electron) was calculated for each of 

the sources at tissue depths of 7, 100, 300, and 1,000 mg/cm2. The density thicknesses of 7, 

300, and 1,000 mg/cm2 correspond to the depth required by 10 CFR Part 20, “Standards for 

Protection against Radiation,” for calculation of dose to the skin, lens of the eye, and the deep 

dose, respectively. Although the value of 100 mg/cm2 does not correspond to a regulatorysignificant density thickness, results at that depth are provided as an indication of accuracy at 

an intermediate, yet shallow, depth. 
4-5

Figure 4-2 Point Source Geometry of Tissue Volumes

At each density thickness, the dose to two volumes of tissue, 0.002 cm3 and 0.02 cm3, was 

calculated. These dimensions correspond to cylindrical volumes within tissue, each having a 

thickness of 20 μm and a cross-sectional area of 1 cm2 and 10 cm2, respectively. The value of 

20 μm was selected to create a volume large enough that uncertainties resulting from low 

numbers of particles interacting in the volume would not be an issue. Sherbini et al. [2008] 

showed that at thicknesses greater than 10 μm, any effects of dose averaging over increasingly 

smaller volumes are avoided.

Energy deposited in the volume of interest was calculated for dose estimation. The number of 

particle histories executed was sufficiently high to maintain statistical errors below 6%, with the 

majority producing an error of approximately 3%. Dose rate was calculated for a simulated 

source strength of 37 kBq, with a yield of 100 percent at a given energy ranging from 0.025 to 3 

MeV. While this is not specific to any particular nuclide, it demonstrates the energy dependence 

of each methodology and shows which models are accurate predictors (as compared to 

MCNP5/EGSnrc) and which are not. Appendix A provides results for photon dosimetry 

comparisons, with Appendix B providing similar results, but for electron dosimetry. The 

appendices are arranged as follows.

For photon dosimetry, V&V focused on seven geometries, including: (1) point source; (2) 1 mm 

diameter 2D disk source; (3) 1 mm diameter by 1 mm height cylindrical source; (4) 1 mm cube 

slab source; (5) 1 mm diameter spherical source; (6) point source with an air gap and a cotton 

cover; and (7) point source that is 1 cm off axis. Dose estimates from VARSKIN 5 as a function 

of photon energy were compared with MCNP5 results at depths of 7, 100, 300, and 1000 

7 mg cm-2

100 mg cm-2

300 mg cm

-2

1000 mg cm-2

20 μm

Air

Tissue

Point Source

10 cm2

1 cm2
4-6

mg/cm2 for each of the geometries considered. VARSKIN 4 was shown to be a very good 

predictor at various tissue depths when the point- and disk-source geometries are modeled. 

VARSKIN 4, however, consistently overpredicts dose (compared to MCNP5) in the cylindrical, 

slab, and spherical geometries at energies greater than about 200 keV. 

For electron dosimetry, results of the V&V exercise are provided in seven geometries: (1) point 

source; (2) 0.5 mm diameter 2D disk source; (3) 1 mm diameter 2D disk source; (4) 5 mm 

diameter 2D disk source; (5) 1 mm diameter by 1 mm height cylindrical source; (6) 1 mm 

diameter spherical source; and (7) 1 mm cube slab source. For each geometry, dose estimates 

from VARSKIN 5 as a function of electron energy were compared with EGSnrc and MCNP5 

results at depths of 7, 100, 300, and 1000 mg/cm2. Additionally, comparisons with four betaemitting nuclides (28Al, 42K, 66Cu, and 138Cs) were conducted to show how the current VARSKIN 

electron dose predictions compare to previous estimates. VARSKIN 5 estimates of dose 

compare very well with EGSnrc and MCNP5, although MCNP5 estimates are slightly higher at 

deeper depths. 

For additional evidence on the efficacy of VARSKIN, the user is directed to two publications in 

which VARSKIN 5.3 results are compared with historic literature on electron skin dosimetry 

[Anspach and Hamby 2017; Dubeau et al. 2018]. 
5-1

VARSKIN 6 LIMITATIONS

VARSKIN 6 calculates skin dose to an infinitely thin disk at depth in tissue for comparison to the 

NRC shallow dose limit of 0.5 gray (Gy) for both point and distributed sources (NRC, 2006). 

VARSKIN 6 can calculate the dose to averaging areas from a minimum of 0.01 cm2to a 

maximum of 100 cm2. Users are cautioned that VARSKIN is designed to calculate the dose to 

skin from skin contamination. Using VARSKIN to perform calculations that are beyond the 

intended application of the code may result in erroneous dose estimates. This section discusses 

the known limitations of VARSKIN 6 and establishes the limits over which the code has been 

tested.

VARSKIN 6 offers the option of dose calculations based on the decay date of ICRP 38 or ICRP 

107. ICRP 38 offers 838 radionuclides in the master library, while ICRP 107 offers more than 

1200.

Dose calculations involving air gaps greater than 20 cm have not been tested and are, 

therefore, not allowed. It is likely that erroneous results may be obtained for large air gaps 

because the code does not account for multiple scattering events in air. These events may 

result in the dose being delivered to an area greater than that determined using VARSKIN 6 and 

can lead to inaccurate results. VARSKIN 6 is limited such that calculations for air gaps greater 

than 20 cm are not possible and a warning message is displayed.

VARSKIN 6 has not been tested extensively for dose-averaging areas other than 1 and 10 cm2. 

However, because of the nature of the calculations performed by VARSKIN, there is no reason 

to believe that doses to areas less than or greater than 10 cm2 will result in errors. A quick and 

limited study of dose results as a function of averaging disk area shows that the code appears 

to be stable and linear in this regard from 0.01 to 100 cm2.

5.1 Electron Dosimetry

The VARSKIN V&V results indicated differences between VARSKIN 5 and EGSnrc for beta 

dosimetry on scenarios involving volumetric sources and intermediate electron energies 

(APPENDIX B). The V&V results for low-energy electrons at shallow depths are similar to the 

results seen at all depths where the electron is reaching its maximum range (even for the pointsources to a certain degree). These larger deviations are apparent at the tail end of the betadose profiles, as well (Mangini, 2012). Either way, it is clear from these results that the accuracy 

of VARSKIN 6 decreases as the electron reaches its maximum depth. In dose calculations for a 

distribution of electrons, this effect is still present since, approaching the deeper depths, the 

deposited energy is occurring at the tail end of the electron range.

VARSKIN 6 has been shown to be reliable for particulate sources that have dimensions less 

than eight times the X99 distance of the radionuclide in tissue. The X99 distance is essentially 

99 percent of the range of beta particles in tissue emitted by nuclides in the source term. When 

the physical size of the source approaches this value, VARSKIN 6 may give unreliable results. A 

user who wants to model sources larger than this limit may wish to begin with smaller sources 

and increase the source size gradually to ensure that spurious results are not being generated. 

Modeling a source of this size is generally not necessary, however, as most of the source does 

not contribute to beta skin dose because of self-shielding. If the source dimensions selected are 

too large, VARSKIN 6 prompts the user with a warning of the potential for inaccurate results. 
5-2

The X99 distance is included on the printout of a calculation to assist the user in determining the 

appropriateness of input source dimensions. 

Also of note, VARSKIN 6 calculates shallow skin dose with the assumption that air is behind the 

source, i.e., an air/water (simulating tissue) interface at the skin surface. Users are reminded to 

use caution when comparing VARSKIN results to other calculations of skin dose that may have 

been executed with water behind the source (i.e., water/water interface). The backscatter 

correction factor used in VARSKIN 6 accounts for this interface difference. 

5.1.1 DPK’s and Scaling Model

DPK’s have always underestimated dose at depths approaching the range of the electron. 

Monte Carlo is the standard and DPK models begin to fail when energy and range straggling 

becomes more and more important at greater depths. The effects of straggling are dominant at 

that part of the electron path. We suspect that the scaling model is not a contributor to the 

discrepancies noted. In fact, the accuracy of the scaling model is highest towards the end of the 

electron path. The interface between the source material and water is where the model has its 

largest deviations. This is likely not the cause, as dose at deeper depths will be dominated by 

electrons traversing very little of the source material (i.e., 0.25 X/X90); the model is extremely 

accurate in this case. 

5.1.2 Scattering Model 

In developing the scattering model, the Monte Carlo (EGSnrc) data used for the model all had a 

standard error less than 5%. Simulations with a greater error were eliminated with a dose 

contribution of zero. However, once the curve fits in SadCalc.exe were developed for the dose 

profiles, the error in the predicted dose values from the curve fits became extremely unreliable 

at very low dose values and the deeper depths. In examining the raw data used to create the 

scattering model and dose profiles, it became apparent that the dose values reached an 

asymptote of about 1x10-12 (Gy per electron). At these dose values the standard error of the 

Monte Carlo simulations begins to exceed 5%. VARSKIN 6 was modified to set all dose 

contributions to zero if the calculation resulted in something less than 1x10-12 Gy/electron. This 

patch is justified since the model begins to fail at such low doses (and the standard error from 

Monte Carlo calculations is very high). When averaging over a beta spectrum, these 

contributions to the BSCF and dose are negligible. Setting dose to zero at these depths is 

executed for both the source scattering profile and the water scattering profile, thereby setting 

the BSCF equal to one (1). Nonetheless, for doses just greater than 1x10-12 Gy/electron, the 

VARSKIN 6 model will be rather inaccurate for dose calculations at depths near the end of the 

electron range. 

5.2 Photon Dosimetry 

The photon dosimetry model assumes that all volume sources are composed of air. This 

assumption results in greater accuracy when modeling larger, less dense sources (e.g., a gas 

cloud). However, when modeling volumetric sources of greater density, VARSKIN 6 is optimized 

for small dimensions (less than about a millimeter). This optimization is the result of a tradeoff 

between attenuation and charge particle buildup within the source itself. The user should 

exercise care when modeling large-volume sources (i.e., if the source is large enough to impact 

self-absorption of photons). 
5-3

5.3 Creation of SADD and Backscatter Data for Progeny Inclusion

When adding a nuclide to the user library (using “ADD”), the SADD routine compiles two SADD 

files, one for each of electron and photon dosimetry (.rad and .photon, respectively). These files 

contain decay data necessary for the dose calculation. The .rad file contains average beta 

energy, half-life, maximum (X90) beta range, yield, electron emission distributions, backscatter 

factors, etc. Likewise, the .photon file contains a list of photon energies (and yield) emitted 

during decay.

When the user elects to include progeny (“D”) in the parent-nuclide dose calculation, the SADD 

calculations are a bit more involved. For photons, the .photon file simply includes a longer list of 

photon energies/yields. For electrons, however, a single SADD file is created for all 

beta/electron emissions from the parent and all of its progeny. This single SADD file contains all 

the same data, but now based on a combination of beta/electron emissions from all nuclides in 

the decay chain. Combining the SADD file in this way simply results in a composite emitted 

electron probability distribution for the chain nuclides. This being the case, dose calculations for 

parent/progeny electrons may be different from the same dose calculated by summing individual 

nuclides (rather than relying on the automatic progeny inclusions). These deviations are shown 

to be the result of the difference in backscatter factors calculated individually, or for the 

combined decay data (because a singular backscatter factor is applied based on average 

electron energy rather than on the probability distribution). One example in which this is most 

prominent is the difference between the sum of 90Sr and its progeny 90Y, versus the combined 

90Sr/90Y calculation by selecting “D”. The difference is generally less than 1% and no more than 

about 3%, varying by nuclide.

The most revealing evidence is a plot of backscatter factors as a function of skin depth for 90Sr, 

90Y, and 90Sr/90Y combined (Fig. 5-1). It is evident that the backscatter factors for the combined 

case are totally driven by the presence of 90Y. This is expected given the higher energy of the 

90Y beta and the method in which the backscatter factors are integrated over the beta spectra in 

the SADD routine (see Section 3.1.6). However, when the source geometry deviates from that 

of a point source, the combined backscatter factor is unable to properly account for the change 

in overall dose contribution for the two radionuclides. For example, Fig 5-1 shows the combined 

backscatter factor being dominated by 90Y. However, in the presence of a volume source or an 

air gap, the path length that a beta traverses prior to entering the dose area will change 

compared to that of a simple point source geometry. If the change in geometry has the effect of 

decreasing the overall path length in tissue, the increase in dose would be more significant for 

the lower energy 90Sr beta at shallow skin depths of interest. The change in dose relative to the 

higher energy 90Y beta will be properly accounted for in the SADD values found in the .rad file. 

However, the impact will be lost on the combined backscatter factor and the 90Y-driven 

correction factor will be slightly off when applied to the added 90Sr dose component. Again, 

however, this discrepancy is at most 3% different and is seen as insignificant in the shallow skin 

dose calculation.

In the two examples that follow, we calculate the shallow skin dose for a millimeter-dimensioned 

cylindrical source. In the first case (Table 5-1) we examine 90Sr, 90Y, and the combined 90Sr/90Y; 

and in the second case (Table 5-2) we examine 133I, 133Xe, 133mXe, the combined 133I with its 

progeny. As can be seen in the tables, the discrepancy with 90Sr/90Y is 3% and there is only a 

rounding difference (in photon dose) for 133I and its progeny. This scenario is worked out in 

Example 4 of Appendix C.
5-4

Table 5-1 Dose from Individual and Combined Parent/Progeny for Sr/Y-90

Nuclide Selection Branching 

Ratio

Relative 

electron 

dose

Relative 

photon 

dose

Sr-90 2.12 -

Y-90 1.000 2.74 -

SUM 4.86 -

Sr-90D* 4.71 -

Difference 3%

*includes dose from Y-90 as calculated in VARSKIN 6.0 with progeny inclusion

Table 5-2 Dose from Individual and Combined Parent/Progeny for I/Xe-133

Nuclide Selection Branching 

Ratio

Relative 

Electron 

Dose

Relative 

Photon 

Dose

I-133 2.77 0.0295

Xe-133 0.971 0.794 0.0270

Xe-133m 0.029 2.33 0.0123

Xe-133 1.000 0.794 0.0107

SUM 3.63 0.0405

I-133D* 3.63 0.0402

Difference 0% 0.9%

*includes dose from Xe-133 and Xe-133m as calculated in VARSKIN 6.0 with progeny inclusion
5-5

Figure 5-1 Backscatter Factors in Air as a Function of Depth in Tissue

6-1

SPECIAL TOPICS

VARSKIN 6 is designed to be very flexible while maintaining a high level of accuracy. However, 

the code can be misused, particularly when modeling infinitely large sources (i.e., sources with 

physical dimensions greater than the X99 distance for the source radionuclides). This section 

describes this possible misuse of VARSKIN and how it can be avoided. This section also 

describes a method to determine the maximum photon dose to an area from multiple hot 

particles.

6.1 Infinite Sources

When modeling infinite or semi-infinite sources (e.g., an enveloping cloud) with VARSKIN 6, the 

tendency is to choose very large dimensions for the source. This approach will result in the 

calculation of a grossly inaccurate dose or a zero dose because the integration routine becomes 

unstable. The correct method is to determine the maximum penetration distance (i.e., the X99

distance) and set the source dimensions as described below.

The X99 distance can be found by running a simple calculation for the radionuclide of interest 

and looking at the printout for the value. The maximum source radius (rmax) and the side 

lengths are then determined using the equation,

rmax = rdos + (

X99

ρmin ⁄ ) ρw [6.1.1]

where rdos is the radius of the dose-averaging area (in cm), is the density of water, and is the 

smallest density of the covering material, source, air (if an air gap is included), or tissue. Using 

the density of the least dense material will ensure that the dose-averaging area includes 

contributions from the entire source. If an air gap is included, using the VARSKIN 6 default 

value for the density of air (0.001293 g/cm3) is appropriate. If no cover material is specified, 

using tissue density (1 g/cm3) is the best choice.

When modeling infinite sources, the use of the cylinder source geometry is recommended. 

When using the cylinder source geometry, the source thickness, ∆tmax, should be determined 

using the equation,

∆tmax =

X99ρw

ρs

[6.1.2]

where ρsis the source density. Source area in this case can be maximized at a value of 100 

cm2to simulate the infinite lateral dimension.

6.2 Maximum Dose from Multiple Contamination Sources

Determining the maximum dose to the dose-averaging area for multiple contaminations requires 

multiple calculations. These calculations require elements that are not available in VARSKIN 6 

but can be accomplished manually, as described below.

Before attempting to run the offset particle model, the user should determine the size of the 

irradiation area directly beneath each of the contaminated areas. Note that the size of sources 

does not need to be the same for each particle. By comparing these areas for each source, it 

may be possible to eliminate one or more of the contaminated areas because there are no 
6-2

associated overlapping fields. However, for contaminated areas with overlapping fields, plot the 

doses and their relative positions leaving plenty of room between the sources for results from 

additional calculations. 

Next, perform VARSKIN 6 calculations using the offset particle model for photons with locations 

midway between any two contaminated areas. For more than two sources that are not in a 

straight line, choose a central location, and calculate the dose at this point using the offset 

particle model. Thus, for three contaminated areas in a triangular formation, perform four 

calculations. Choose the value of the offset as one-half of the distance between any two 

sources, with one additional dose calculation performed in the center of the triangle. 

After performing these calculations, the user must use discretion to determine the most 

probable area of highest dose based on the distribution of dose on the graph paper. After 

determining this area, the user can perform a final calculation for each particle by using the 

offset particle model. The user should not anticipate an accuracy greater than 20 percent. 

6.3 Manipulation of Files for Extended Utility 

The knowledgeable user can modify VARSKIN 6 in a couple of ways for added utility: first, to 

model a mono-energetic electron, and second, to model a water/water interface at the skin 

surface. In the first case, the user should modify the ICRP 38 data (the ICRP38.DAT file in the 

dat folder) for one of the nuclides (this should also work using ICRP 107 data file). We have 

found that 7Be is one of the easiest to modify. Figure 1 shows the first few lines of ICRP38.DAT 

for the original data (left) and modified data (right). 

H-3 12.35y 1 H-3 12.35y 1 

5 1.00000E+02 5.68276E-03 5 1.00000E+02 5.68276E-03

Be-7 53.3d 4 Be-7 53.3d 4 

1 1.03400E+01 4.77605E-01 1 0.00000E+00 0.00000E-00

6 8.04306E-06 4.77550E-01 6 1.00000E+00 0.75000E-00

6 1.18019E-07 4.77605E-01 6 0.00000E+00 0.00000E-00

2 1.63500E-02 5.47500E-05 2 0.00000E+00 0.00000E-00

Be-10 1.6E6y 1 Be-10 1.6E6y 1 

5 1.00000E+02 2.52256E-01 5 1.00000E+02 2.52256E-01

C-11 20.38m 4 C-11 20.38m 4 

4 9.97600E+01 3.85535E-01 4 9.97600E+01 3.85535E-01

3 1.99520E+02 5.11000E-01 3 1.99520E+02 5.11000E-01

2 1.61920E-04 1.83300E-04 2 1.61920E-04 1.83300E-04

2 8.09600E-05 1.83300E-04 2 8.09600E-05 1.83300E-04

Figure 6-1 Input Example for the ICRP38.DAT File 

On examination of the original data (left), we see that 7Be has a half-life of 53.3 days and four 

major emissions per decay. The first in the list is a gamma ray (code 1) with a yield of 10.34% 

and an energy of 0.477605 MeV. The second and third lines show emission of conversion 

electrons (code 6) with very low yields and roughly the same energies as the photon. The final 

emission is a low-energy X-ray (code 2) with a yield of 1.635%. We cannot simply remove three 

of the data lines and indicate that 7Be has only one emission; if we did, indices throughout the 

VARSKIN data files would be in disarray. Therefore, we will set yields and energies to zero 

(data on the right) except for one entry. The modified entry shows the emission of an electron 

with 100% yield and an energy of 0.75 MeV. This will simulate the emission of a mono-energetic 

electron; no other alterations are necessary. 
6-3

The second modification allows the user to change the VARSKIN 6 simulation (normally an 

air/water interface at the skin surface) to model a water/water interface. We accomplish this by 

modifying the .rad file (in the dat folder) for the nuclide of choice. The final 160 lines of data 

written to that file (by SadCalc.exe) are backscatter factors for use in the half-space scenario 

(air/water interface). Manually setting each of these factors to “1” removes consideration of halfspace such that VARSKIN 6 will model a homogeneous water medium (a water/water interface).

Incidentally, the emission codes in the .DAT decay data files are as follows:

(1) gamma ray;

(2) X ray;

(3) annihilation photon;

(4) positron;

(5) electron (beta);

(6) conversion electron;

(7) Auger electron;

And ICRP107.DAT includes these, as well (but they are never accessed):

(8) alpha;

(9) recoil nucleus;

(10) fission fragment; and

(11) neutron

7-1

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Delacroix, D. “Beta Particle and Electron Absorbed Dose Calculations for Skin Surface 

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Atomique. 1986.

Dubeau, J., Hakmana Witharana, S.S., Sun, J., Heinmiller, B.E., Chase, W.J. A Comparison of 

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Durham, J.S. “VARSKIN Mod 2 and SADDE Mod 2: Computer Codes for Assessing Skin Dose 

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7-2

Durham, J.S., and M.W. Lantz. “Determination of Gamma Dose Rates and Charged Particle 

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Regulatory Commission. 2014.

Hamby, D.M., Lodwick, C.J., Palmer, T.S., Reese, S.R., Higley, K.A. “VARSKIN 4: A Computer 

Code for Skin Contamination Dosimetry.” NUREG/CR-6918, Rev 1. Washington, DC: U.S. 

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Publication 38. Oxford, England: Pergamon Press. 1983. 

International Commission on Radiation Protection. “Nuclear Decay Data for Dosimetric 

Calculations.” Publication 107. Ann. ICRP 38 (3). 2008

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Charles C. Thomas. 1983. 

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7-3

Mangini, C.D., and D.M. Hamby. “Scaling Parameters for Hot-Particle Beta Dosimetry”. 

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7-4

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https://www.nrc.gov/docs/ML0209/ML020990362.pdf Last accessed December 2017. 
A-1

SUPPORTING FIGURES FROM SECTION 4

A.1 GEOMETRY 1: POINT SOURCE

Figure A-1 A Point Source Geometry Comparison of VARSKIN 5 (Circles) and MCNP5 

(lines) Predicted Dose Per Initial Photon as a Function of Photon Energy in 

Tissue at a Density Thickness of 7 mg/cm2 and a Tissue Volume Cylinder of 

Area 1 cm2(solid line) and 10 cm2

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

7 mg/cm2
A-2

Figure A-2 A Point Source Geometry Comparison of VARSKIN 5 (circles) and MCNP5 

(lines) Predicted Dose Per Initial Photon as a Function of Photon Energy in 

Tissue at a Density Thickness of 100 mg/cm2 and a Tissue Volume Cylinder of 

Area 1 cm2 (solid line) and 10 cm2 (dashed line), With a Thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

100 mg/cm2
A-3

Figure A-3 A Point Source Geometry Comparison of VARSKIN 5 (circles) and MCNP5 

(lines) Predicted Dose Per Initial Photon as a Function of Photon Energy in 

Tissue at a Density Thickness of 300 mg/cm2 and a Tissue Volume Cylinder of 

Area 1 cm2(solid line) and 10 cm2(dashed line), With a Thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

300 mg/cm2
A-4

Figure A-4 A Point Source Geometry Comparison of VARSKIN 5 (circles) and MCNP5 

(lines) Predicted Dose Per Initial Photon as a Function of Photon Energy in 

Tissue at a Density Thickness of 1000 mg/cm2 and a Tissue Volume Cylinder 

of Area 1 cm2(solid line) and 10 cm2(dashed line), With a Thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

1000 mg/cm2
A-5

A.2 GEOMETRY 2: DISK SOURCE 

Figure A-5 A Disk Source Geometry Comparison of VARSKIN 5 (circles) and MCNP5 

(lines) Predicted Dose Per Initial Photon as a Function of Photon Energy in 

Tissue at a Density Thickness of 7 mg/cm2 and a Tissue Volume Cylinder of 

Area 1 cm2 (solid line) and 10 cm2 (dashed line), With a Thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

7 mg/cm2
A-6

Figure A-6 A Disk Source Geometry Comparison of VARSKIN 5 (circles) and MCNP5 

(Lines) Predicted Dose Per Initial Photon as a Function of Photon Energy in 

Tissue at a Density Thickness of 100 mg/cm2 and a Tissue Volume Cylinder of 

Area 1 cm2 (solid line) and 10 cm2(dashed line), With a Thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

100 mg/cm2
A-7

Figure A-7 A Disk Source Geometry Comparison of VARSKIN 5 (circles) and MCNP5 

(lines) Predicted Dose Per Initial Photon as a Function of Photon Energy in 

Tissue at a Density Thickness of 300 mg/cm2 and a Tissue Volume Cylinder of 

Area 1 cm2 (solid line) and 10 cm2 (dashed line), With a Thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

300 mg/cm2
A-8

Figure A-8 A Disk Source Geometry Comparison of VARSKIN 5 (circles) and MCNP5 

(lines) Predicted Dose Per Initial Photon as a Function of Photon Energy in 

Tissue at a Density Thickness of 1000 mg/cm2 and a Tissue Volume Cylinder 

of Area 1 cm2 (solid line) and 10 cm2 (dashed line), With a Thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

1000 mg/cm2
A-9

A.3 GEOMETRY 3: CYLINDRICAL SOURCE 

Figure A-9 A Cylindrical Source Geometry Comparison of VARSKIN 5 (circles) and 

MCNP5 (lines) Predicted Dose Per Initial Photon as a Function of Photon 

Energy in Tissue at a Density Thickness of 7 mg/cm2 and a Tissue Volume 

Cylinder of Area 1 cm2 (solid line) and 10 cm2 (dashed line), With a Thickness 

of 20 mm

1.E-14

1.E-13

1.E-12

1.E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

7 mg/cm2
A-10

Figure A-10 A Cylindrical Source Geometry Comparison of VARSKIN 5 (circles) and 

MCNP5 (lines) Predicted Dose Per Initial Photon as a Function of Photon 

Energy in Tissue at a Density Thickness of 100 mg/cm2 and a Tissue Volume 

Cylinder of Area 1 cm2 (solid line) and 10 cm2 (dashed line), With a Thickness 

of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

100 mg/cm2
A-11

Figure A-11 A Cylindrical Source Geometry Comparison of VARSKIN 5 (circles) and 

MCNP5 (lines) Predicted Dose Per Initial Photon as a Function of Photon 

Energy in Tissue at a Density Thickness of 300 mg/cm2 and a Tissue Volume 

Cylinder of Area 1 cm2(solid line) and 10 cm2(dashed line), With a Thickness 

of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

300 mg/cm2
A-12

Figure A-12 A Cylindrical Source Geometry Comparison of VARSKIN 5 (circles) and 

MCNP5 (lines) Predicted Dose Per Initial Photon as a Function of Photon 

Energy In Tissue at a Density Thickness of 1000 mg/cm2 and a Tissue Volume 

Cylinder of Area 1 cm2 (solid line) and 10 cm2 (dashed line), With a Thickness 

of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

1000 mg/cm2
A-13

A.4 GEOMETRY 4: SLAB SOURCE

Figure A-13 A Slab Source Geometry Comparison of VARSKIN 5 (circles) and MCNP5 

(lines) Predicted Dose Per Initial Photon as a Function of Photon Energy in 

Tissue at a Density Thickness of 7 mg/cm2 and a Tissue Volume Cylinder of 

Area 1 cm2(solid line) and 10 cm2(dashed line), With a Thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

7 mg/cm2
A-14

Figure A-14 A Slab Source Geometry Comparison of VARSKIN 5 (circles) and MCNP5 

(lines) Predicted Dose Per Initial Photon as a Function of Photon Energy in 

Tissue at a Density Thickness of 100 mg/cm2 and a Tissue Volume Cylinder of 

Area 1 cm2 (solid line) and 10 cm2 (dashed line), With a Thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

100 mg/cm2
A-15

Figure A-15 A Slab Source Geometry Comparison of VARSKIN 5 (circles) and MCNP5 

(lines) Predicted Dose Per Initial Photon as a Function of Photon Energy in 

Tissue at a Density Thickness of 300 mg/cm2 and a Tissue Volume Cylinder of 

Area 1 cm2(solid line) and 10 cm2(dashed line), With a Thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

300 mg/cm2
A-16

Figure A-16 A Slab Source Geometry Comparison of VARSKIN 5 (circles) and MCNP5 

(lines) Predicted Dose Per Initial Photon as a Function of Photon Energy in 

Tissue at a Density Thickness of 1000 mg/cm2 and a Tissue Volume Cylinder 

of Area 1 cm2(solid line) and 10 cm2(dashed line), With a Thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

1000 mg/cm2
A-17

A.5 GEOMETRY 5: SPHERICAL SOURCE

Figure A-17 A Spherical Source Geometry Comparison of VARSKIN 5 (circles) and MCNP5 

(Lines) Predicted Dose Per Initial Photon as a Function of Photon Energy in 

Tissue at a Density Thickness of 7 mg/cm2 and a Tissue Volume Cylinder of 

Area 1 cm2(solid line) and 10 cm2(dashed line), With a Thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

7 mg/cm2
A-18

Figure A-18 A Spherical Source Geometry Comparison of VARSKIN 5 (circles) and MCNP5 

(lines) Predicted Dose Per Initial Photon as a Function of Photon Energy in 

Tissue at a Density Thickness of 100 mg/cm2 and a Tissue Volume Cylinder of 

Area 1 cm2 (solid line) and 10 cm2 (dashed line), With a thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

100 mg/cm2
A-19

Figure A-19 A Spherical Source Geometry Comparison of VARSKIN 5 (circles) and MCNP5 

(lines) Predicted Dose Per Initial Photon as a Function of Photon Energy in 

Tissue at a Density Thickness of 300 mg/cm2 and a Tissue Volume Cylinder of 

Area 1 cm2(solid line) and 10 cm2(dashed line), With a Thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

300 mg/cm2
A-20

Figure A-20 A Spherical Source Geometry Comparison of VARSKIN 5 (circles) and MCNP5 

(lines) Predicted Dose Per Initial Photon as a Function of Photon Energy in 

Tissue at a Density Thickness of 1000 mg/cm2 and a Tissue Volume Cylinder 

of Area 1 cm2 (solid line) and 10 cm2 (dashed line), With a Thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

1000 mg/cm2
A-21

A.6 GEOMETRY 6: POINT SOURCE (with Air Gap And Cotton Cover)

Figure A-21 A Point Source Geometry With a Cotton Cover and a 1 cm Air Gap 

Comparison of VARSKIN 5 (circles) and MCNP5 (lines) Predicted Dose Per 

Initial Photon as a Function of Photon Energy in Tissue at a Density Thickness 

of 7 mg/cm2 and a Tissue Volume Cylinder of Area 1 cm2(solid line) and 10 

cm2(dashed line); Thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

7 mg/cm2
A-22

Figure A-22 A Point Source Geometry With a Cotton Cover and a 1 cm Air Gap 

Comparison of VARSKIN 5 (circles) and MCNP5 (lines) Predicted Dose Per 

Initial Photon as a Function of Photon Energy in Tissue at a Density Thickness 

of 100 mg/cm2 and a Tissue Volume Cylinder of Area 1 cm2(solid line) and 10 

cm2(dashed line); Thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

100 mg/cm2
A-23

Figure A-23 A Point Source Geometry With a Cotton Cover and a 1 cm Air Gap 

Comparison of VARSKIN 5 (circles) and MCNP5 (lines) Predicted Dose Per 

Initial Photon as a Function of Photon Energy in Tissue at a Density Thickness 

of 300 mg/cm2 and a Tissue Volume Cylinder of Area 1 cm2(solid line) and 10 

cm2(dashed line); Thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

300 mg/cm2
A-24

Figure A-24 A Point Source Geometry With a Cotton Cover and a 1 cm Air Gap 

Comparison of VARSKIN 5 (circles) and MCNP5 (lines) Predicted Dose Per 

Initial Photon as a Function of Photon Energy in Tissue at a Density Thickness 

of 1000 mg/cm2 and a Tissue Volume Cylinder of Area 1 cm2 (solid line) and 10 

cm2 (dashed line); Thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

1000 mg/cm2
A-25

A.7 GEOMETRY 7: POINT SOURCE (1 cm off axis)

Figure A-25 A Point Source Geometry 1 cm Off-Axis Comparison of VARSKIN 5 (circles) 

and MCNP5 (lines) Predicted Dose Per Initial Photon as a Function of Photon 

Energy in Tissue at a Density Thickness of 7 mg/cm2 and a Tissue Volume 

Cylinder of Area 1 cm2(solid line) and 10 cm2(dashed line), With a Thickness 

of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

7 mg/cm2
A-26

Figure A-26 A Point Source Geometry 1 cm Off-Axis Comparison of VARSKIN 5 (circles) 

and MCNP5 (lines) Predicted Dose Per Initial Photon as a Function of Photon 

Energy in Tissue at a Density Thickness of 300 mg/cm2 and a Tissue Volume 

Cylinder of Area 1 cm2 (solid line) and 10 cm2 (dashed line), With a Thickness 

of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

300 mg/cm2
A-27

Figure A-27 A Point Source Geometry 1 cm Off-Axis Comparison of VARSKIN 5 (circles) 

and MCNP5 (lines) Predicted Dose Per Initial Photon as a Function of Photon 

Energy in Tissue at a Density Thickness of 1000 mg/cm2 and a Tissue Volume 

Cylinder of Area 1 cm2(solid line) and 10 cm2(dashed line), With a Thickness 

of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

0 500 1000 1500 2000 2500 3000

Photon Dose (Gy/photon)

Photon Energy (keV)

1000 mg/cm2

B-1

SUPPORTING FIGURES FROM SECTION 5

B.1 GEOMETRY 1: POINT SOURCE

Figure B-1 A Point Source Geometry Comparison of VARSKIN 5 (boxes), MCNP5 

(triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a Function 

of Electron Energy in Tissue at a Density Thickness of 7 mg/cm2 and a 20 mm 

Thick Tissue Volume Cylinder of Area 1 cm2 (solid line) and 10 cm2 (dashed 

line) 

1.00E-11

1.00E-10

1.00E-09

0 500 1000 1500 2000 2500 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

7 mg/cm2
B-2

Figure B-2 A Point Source Geometry Comparison of VARSKIN 5 (boxes), MCNP5 

(triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a Function 

of Electron Energy in Tissue at a Density Thickness of 100 mg/cm2 and a 20 

mm Thick Tissue Volume Cylinder of Area 1 cm2 (solid line) and 10 cm2

(dashed line) 

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 500 1000 1500 2000 2500 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

100 mg/cm2
B-3

Figure B-3 A Point Source Geometry Comparison of VARSKIN 5 (boxes), MCNP5 

(triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a Function 

of Electron Energy in Tissue at a Density Thickness of 300 mg/cm2 and a 20 

mm Thick Tissue Volume Cylinder of Area 1 cm2(solid line) and 10 cm2

(dashed line)

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

500 1000 1500 2000 2500 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

300 mg/cm2
B-4

Figure B-4 A Point Source Geometry Comparison of VARSKIN 5 (boxes), MCNP5 

(triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a Function 

of Electron Energy in Tissue at a Density Thickness of 1000 mg/cm2 and a 20 

mm Thick Tissue Volume Cylinder of Area 1 cm2 (solid line) and 10 cm2

(dashed line) 

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

2000 2200 2400 2600 2800 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

1000 mg/cm2
B-5

Figure B-5 A Point Source Geometry Comparison of VARSKIN 5 (boxes) and VARSKIN 4 

(circles) Predicted Dose Per Initial Beta From 28Al as a Function of Density 

Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2 (upper) and 

10 cm2 (lower), With a Thickness of 20 mm 

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

28Al
B-6

Figure B-6 A Point Source Geometry Comparison of VARSKIN 5 (boxes) and VARSKIN 4 

(circles) Predicted Dose Per Initial Beta From 42K as a Function of Density 

Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2 (upper) and 

10 cm2 (lower), With a Thickness of 20 mm 

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

42K
B-7

Figure B-7 A Point Source Geometry Comparison of VARSKIN 5 (boxes) and VARSKIN 4 

(circles) Predicted Dose Per Initial Beta From 66Cu as a Function of Density 

Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2(upper) and 

10 cm2(lower), With a Thickness of 20 mm

Figure B-8 A Point Source Geometry Comparison of VARSKIN 5 (boxes) and VARSKIN 4 

(circles) Predicted Dose Per Initial Beta From 138Cs as a Function of Density 

Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2(upper) and 

10 cm2(lower), With a Thickness of 20 mm

1.00E-15

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

66Cu

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

138Cs
B-8

B.2 GEOMETRY 2: DISK SOURCE (0.5 mm dia) 

Figure B-9 A 0.5 mm Diameter Disk Source Geometry Comparison of VARSKIN 5 (boxes), 

MCNP5 (triangles) And EGSnrc (lines) Predicted Dose Per Initial Electron as a 

Function of Electron Energy in Tissue at a Density Thickness of 7 mg/cm2 and 

a Tissue Volume Cylinder of Area 1 cm2 (solid line) and 10 cm2 (dashed line), 

With a Thickness of 20 mm 

Figure B-10 A 0.5 mm Diameter Disk Source Geometry Comparison of VARSKIN 5 (boxes), 

MCNP5 (triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a 

Function of Electron Energy in Tissue at a Density Thickness of 100 mg/cm2

and a Tissue Volume Cylinder of Area 1 cm2 (solid line) and 10 cm2 (dashed 

line), With a Thickness of 20 mm 

1.00E-11

1.00E-10

1.00E-09

0 500 1000 1500 2000 2500 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

7 mg/cm2

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 500 1000 1500 2000 2500 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

100 mg/cm2
B-9

Figure B-11 A 0.5 mm Diameter Disk Source Geometry Comparison of VARSKIN 5 (boxes), 

MCNP5 (triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a

Function of Electron Energy in Tissue at a Density Thickness of 300 mg/cm2

and a Tissue Volume Cylinder of Area 1 cm2(solid line) and 10 cm2(dashed 

line), With a Thickness of 20 mm

Figure B-12 A 0.5 mm Diameter Disk Source Geometry Comparison of VARSKIN 5 (boxes), 

MCNP5 (triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a

Function of Electron Energy in Tissue at a Density Thickness of 1000 mg/cm2

and a Tissue Volume Cylinder of Area 1 cm2(solid line) and 10 cm2(dashed 

line), With a Thickness of 20 mm

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

500 1000 1500 2000 2500 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

300 mg/cm2

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

2000 2200 2400 2600 2800 3000 3200

Electron Dose (Gy/electron)

Electron Energy (keV)

1000 mg/cm^2
B-10

Figure B-13 A 0.5 mm Diameter Disk Geometry Comparison of VARSKIN 5 (boxes) and 

VARSKIN 4 (circles) Predicted Dose Per Initial Beta From 28Al as a Function of 

Density Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2

(upper) and 10 cm2(lower), With a Thickness of 20 mm

Figure B-14 A 0.5 mm Diameter Disk Geometry Comparison of VARSKIN 5 (boxes) and 

VARSKIN 4 (circles) Predicted Dose Per Initial Beta From 42K as a Function of 

Density Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2

(upper) and 10 cm2(lower), With a Thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

28Al

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

42K
B-11

Figure B-15 A 0.5 mm Diameter Disk Geometry Comparison of VARSKIN 5 (boxes) and 

VARSKIN 4 (circles) Predicted Dose Per Initial Beta From 66Cu as a Function of 

Density Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2

(upper) and 10 cm2(lower), With a Thickness of 20 mm

Figure B-16 A 0.5 mm Diameter Disk Geometry Comparison of VARSKIN 5 (boxes) and 

VARSKIN 4 (circles) Predicted Dose Per Initial Beta From 138Cs as a Function 

of Density Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2

(upper) and 10 cm2(lower), With a Thickness of 20 mm

1.00E-15

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

66Cu

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

138Cs
B-12

B.3 GEOMETRY 3: DISK SOURCE (1 mm dia) 

Figure B-17 A 1 mm Diameter Disk Source Geometry Comparison of VARSKIN 5 (boxes), 

MCNP5 (triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a 

Function of Electron Energy in Tissue at a Density Thickness of 7 mg/cm2 and 

a Tissue Volume Cylinder of Area 1 cm2 (solid line) and 10 cm2 (dashed line), 

With a Thickness of 20 mm 

Figure B-18 A 1 mm Diameter Disk Source Geometry Comparison of VARSKIN 5 (boxes), 

MCNP5 (triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a 

Function of Electron Energy in Tissue at a Density Thickness of 100 mg/cm2

and a Tissue Volume Cylinder of Area 1 cm2 (solid line) and 10 cm2 (dashed 

line), With a Thickness of 20 mm 

1.00E-11

1.00E-10

1.00E-09

0 500 1000 1500 2000 2500 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

7 mg/cm2

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 500 1000 1500 2000 2500 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

100 mg/cm2
B-13

Figure B-19 A 1 mm Diameter Disk Source Geometry Comparison of VARSKIN 5 (boxes), 

MCNP5 (triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a 

Function of Electron Energy in Tissue at a Density Thickness of 300 mg/cm2

and a Tissue Volume Cylinder of Area 1 cm2(solid line) and 10 cm2(dashed 

line), With a Thickness of 20 mm

Figure B-20 A 1 mm Diameter Disk Source Geometry Comparison of VARSKIN 5 (boxes),

MCNP5 (triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a 

Function of Electron Energy in Tissue at a Density Thickness of 1000 mg/cm2

and a Tissue Volume Cylinder of Area 1 cm2(solid line) and 10 cm2(dashed 

line), With a Thickness of 20 mm

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

500 1000 1500 2000 2500 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

300 mg/cm^2

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

2000 2200 2400 2600 2800 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

1000 mg/cm^2
B-14

Figure B-21 A 1 mm Diameter Disk Geometry Comparison of VARSKIN 5 (boxes) and 

VARSKIN 4 (circles) Predicted Dose Per Initial Beta From 28Al as a Function of 

Density Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2

(upper) and 10 cm2 (lower), With a Thickness of 20 mm 

Figure B-22 A 1 mm Diameter Disk Geometry Comparison of VARSKIN 5 (boxes) and 

VARSKIN 4 (circles) Predicted Dose Per Initial Beta From 42K as a Function of 

Density Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2

(upper) and 10 cm2 (lower), With a Thickness of 20 mm 

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000 1200

Log(Gy/electron)

Density Thickness (mg/cm2)

28Al

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000 1200

Log(Gy/electron)

Density Thickness (mg/cm2)

42K
B-15

Figure B-23 A 1 mm Diameter Disk Geometry Comparison of VARSKIN 5 (boxes) and 

VARSKIN 4 (circles) Predicted Dose Per Initial Beta From 66Cu as a Function of 

Density Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2

(upper) and 10 cm2(lower), With a Thickness of 20 mm

Figure B-24 A 1 mm Diameter Disk Geometry Comparison of VARSKIN 5 (boxes) and 

VARSKIN 4 (circles) Predicted Dose Per Initial Beta From 138Cs as a Function 

of Density Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2

(upper) and 10 cm2(lower), With a Thickness of 20 mm

1.00E-15

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000 1200

Log(Gy/electron)

Density Thickness (mg/cm2)

66Cu

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000 1200

Log(Gy/electron)

Density Thickness (mg/cm2)

138Cs
B-16

B.4 GEOMETRY 4: DISK SOURCE (5 mm dia)

Figure B-25 A 5 mm Diameter Disk Source Geometry Comparison of VARSKIN 5 (boxes), 

MCNP5 (triangles) And EGSnrc (lines) Predicted Dose Per Initial Electron as a 

Function of Electron Energy in Tissue at a Density Thickness of 7 mg/cm2 and 

a Tissue Volume Cylinder of Area 1 cm2(solid line) and 10 cm2(dashed line), 

With a Thickness of 20 mm

Figure B-26 A 5 mm Diameter Disk Source Geometry Comparison of VARSKIN 5 (boxes), 

MCNP5 (triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a

Function of Electron Energy in Tissue at a Density Thickness of 100 mg/cm2

and a Tissue Volume Cylinder of Area 1 cm2(solid line) and 10 cm2(dashed 

line), With a Thickness of 20 mm

1.00E-11

1.00E-10

1.00E-09

0 500 1000 1500 2000 2500 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

7 mg/cm2

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 500 1000 1500 2000 2500 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

100 mg/cm2
B-17

Figure B-27 A 5 mm Diameter Disk Source Geometry Comparison of VARSKIN 5 (boxes), 

MCNP5 (triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a 

Function of Electron Energy in Tissue at a Density Thickness of 300 mg/cm2

and a Tissue Volume Cylinder of Area 1 cm2(solid line) and 10 cm2(dashed 

line), With a Thickness of 20 mm

Figure B-28 A 5 mm Diameter Disk Source Geometry Comparison of VARSKIN 5 (boxes), 

MCNP5 (triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a 

Function of Electron Energy In Tissue at a Density Thickness of 1000 mg/cm2

and a Tissue Volume Cylinder of Area 1 cm2(solid line) and 10 cm2(dashed 

line), With a Thickness of 20 mm

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

500 1000 1500 2000 2500 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

300 mg/cm2

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

2000 2200 2400 2600 2800 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

1000 mg/cm2
B-18

Figure B-29 A 5 mm Diameter Disk Geometry Comparison of VARSKIN 5 (boxes) and 

VARSKIN 4 (circles) Predicted Dose Per Initial Beta From 28Al as a Function of 

Density Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2

(upper) and 10 cm2 (lower), With a Thickness of 20 mm 

Figure B-30 A 5 mm Diameter Disk Geometry Comparison of VARSKIN 5 (boxes) and 

VARSKIN 4 (circles) Predicted Dose Per Initial Beta From 42K as a Function of 

Density Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2

(upper) and 10 cm2 (lower), With a Thickness of 20 mm 

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000 1200

Log(Gy/electron)

Density Thickness (mg.cm^2)

28Al

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000 1200

Log(Gy/electron)

Density Thickness (mg.cm^2)

42K
B-19

Figure B-31 A 5 mm Diameter Disk Geometry Comparison of VARSKIN 5 (boxes) and 

VARSKIN 4 (circles) Predicted Dose Per Initial Beta From 66Cu as a Function of 

Density Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2

(upper) and 10 cm2(lower), With a Thickness of 20 mm

Figure B-32 A 5 mm Diameter Disk Geometry Comparison of VARSKIN 5 (boxes) and 

VARSKIN 4 (circles) Predicted Dose Per Initial Beta From 138Cs as a Function 

of Density Thickness In Tissue and a Tissue Volume Cylinder of Area 1 cm2

(upper) and 10 cm2(lower), With a Thickness of 20 mm

1.00E-15

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000 1200

Log(Gy/electron)

Density Thickness (mg.cm^2)

66Cu

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000 1200

Log(Gy/electron)

Density Thickness (mg.cm^2)

138Cs
B-20

B.5 GEOMETRY 5: CYLINDRICAL SOURCE

Figure B-33 A Cylindrical Source Geometry Comparison of VARSKIN 5 (boxes), MCNP5 

(triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a Function 

of Electron Energy in Tissue at a Density Thickness of 7 mg/cm2 and a Tissue 

Volume Cylinder of Area 1 cm2(solid line) and 10 cm2(dashed line), With a

Thickness of 20 mm

Figure B-34 A Cylindrical Source Geometry Comparison of VARSKIN 5 (boxes), MCNP5 

(triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a Function 

of Electron Energy in Tissue at a Density Thickness of 100 mg/cm2 and a 

Tissue Volume Cylinder of Area 1 cm2(solid line) and 10 cm2(dashed line), 

With a Thickness of 20 mm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 500 1000 1500 2000 2500 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

7 mg/cm2

1.00E-12

1.00E-11

1.00E-10

1.00E-09

500 1000 1500 2000 2500 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

100 mg/cm2
B-21

Figure B-35 A Cylindrical Source Geometry Comparison of VARSKIN 5 (boxes), MCNP5 

(triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a Function 

of Electron Energy in Tissue at a Density Thickness of 300 mg/cm2 and a 

Tissue Volume Cylinder of Area 1 cm2(solid line) and 10 cm2(dashed line), 

With a Thickness of 20 mm

Figure B-36 A Cylindrical Source Geometry Comparison of VARSKIN 5 (boxes), MCNP5 

(triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a Function 

of Electron Energy in Tissue at a Density Thickness of 1000 mg/cm2 and a 

Tissue Volume Cylinder of Area 1 cm2(solid line) and 10 cm2(dashed line), 

With a Thickness of 20 mm

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1000 1500 2000 2500 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

300 mg/cm2

1.00E-13

1.00E-12

1.00E-11

1.00E-10

2500 2600 2700 2800 2900 3000

Electron Dose (Gy/electron)

Electron Dose (keV)

1000 mg/cm2
B-22

Figure B-37 A Cylindrical Source Geometry Comparison of VARSKIN 5 (boxes) and 

VARSKIN 4 (circles) Predicted Dose Per Initial Beta From 28Al as a Function of 

Density Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2

(upper) and 10 cm2(lower), With a Thickness of 20 mm

Figure B-38 A Cylindrical Source Geometry Comparison of VARSKIN 5 (boxes) and 

VARSKIN 4 (circles) Predicted Dose Per Initial Beta From 42K as a Function of 

Density Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2

(upper) and 10 cm2(lower), With a Thickness of 20 mm

1.00E-15

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

28Al

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

42K
B-23

Figure B-39 A Cylindrical Source Geometry Comparison of VARSKIN 5 (boxes) and 

VARSKIN 4 (circles) Predicted Dose Per Initial Beta From 66Cu as a Function of 

Density Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2

(upper) and 10 cm2(lower), With a Thickness of 20 mm

Figure B-40 A Cylindrical Source Geometry Comparison of VARSKIN 5 (boxes) and 

VARSKIN 4 (circles) Predicted Dose Per Initial Beta From 138Cs as a Function 

of Density Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2

(upper) and 10 cm2(lower), With a Thickness of 20 mm

1.00E-17

1.00E-16

1.00E-15

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

66Cu

1.00E-15

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

138Cs
B-24

B.6 GEOMETRY 6: SPHERICAL SOURCE 

Figure B-41 A Spherical Source Geometry Comparison of VARSKIN 5 (boxes), MCNP5 

(triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a Function 

of Electron Energy in Tissue at a Density Thickness of 7 mg/cm2 and a Tissue 

Volume Cylinder of Area 1 cm2 (solid line) and 10 cm2 (dashed line), With a 

Thickness of 20 mm 

Figure B-42 A Spherical Source Geometry Comparison of VARSKIN 5 (boxes), MCNP5 

(triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a Function 

of Electron Energy in Tissue at a Density Thickness of 100 mg/cm2 and a 

Tissue Volume Cylinder of Area 1 cm2 (solid line) and 10 cm2 (dashed line), 

With a Thickness of 20 mm 

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 500 1000 1500 2000 2500 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

7 mg/cm2

1.00E-12

1.00E-11

1.00E-10

1.00E-09

500 1000 1500 2000 2500 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

100 mg/cm2
B-25

Figure B-43 A Spherical Source Geometry Comparison of VARSKIN 5 (boxes), MCNP5 

(triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a Function 

of Electron Energy in Tissue at a Density Thickness of 300 mg/cm2 and a

Tissue Volume Cylinder of Area 1 cm2(solid line) and 10 cm2(dashed line), 

With a Thickness of 20 mm

Figure B-44 A Spherical Source Geometry Comparison of VARSKIN 5 (boxes), MCNP5 

(triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a Function 

of Electron Energy in Tissue at a Density Thickness of 1000 mg/cm2 and a 

Tissue Volume Cylinder of Area 1 cm2(solid line) and 10 cm2(dashed line), 

With a Thickness of 20 mm

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1000 1500 2000 2500 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

300 mg/cm2

0.00E+00

5.00E-12

1.00E-11

1.50E-11

2.00E-11

2.50E-11

2400 2500 2600 2700 2800 2900 3000 3100

Electron Dose (Gy/electron)

Electron Energy (keV)

1000 mg/cm2
B-26

Figure B-45 A Spherical Source Geometry Comparison of VARSKIN 5 (boxes) and 

VARSKIN 4 (circles) Predicted Dose Per Initial Beta From 28Al as a Function of 

Density Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2

(upper) and 10 cm2(lower), With a Thickness of 20 mm

Figure B-46 A Spherical Source Geometry Comparison of VARSKIN 5 (boxes) and 

VARSKIN 4 (circles) Predicted Dose Per Initial Beta From 42K as a Function of 

Density Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2

(upper) and 10 cm2(lower), With a Thickness of 20 mm

1.00E-15

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Electron Energy (keV)

28Al

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

42K
B-27

Figure B-47 A Spherical Source Geometry Comparison of VARSKIN 5 (boxes) and 

VARSKIN 4 (circles) Predicted Dose Per Initial Beta From 66Cu as a Function of 

Density Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2

(upper) and 10 cm2(lower), With a Thickness of 20 mm

Figure B-48 A Spherical Source Geometry Comparison of VARSKIN 5 (boxes) and 

VARSKIN 4 (circles) Predicted Dose Per Initial Beta From 138Cs as a Function 

of Density Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2

(upper) and 10 cm2(lower), With a Thickness of 20 mm

1.00E-17

1.00E-16

1.00E-15

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

66Cu

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

138Cs
B-28

B.7 GEOMETRY 7: SLAB SOURCE 

Figure B-49 A Slab Source Geometry Comparison of VARSKIN 5 (boxes), MCNP5 

(triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a Function 

of Electron Energy in Tissue at a Density Thickness of 7 mg/cm2 and a Tissue 

Volume Cylinder of Area 1 cm2 (solid line) and 10 cm2 (dashed line), With a 

Thickness of 20 mm 

Figure B-50 A Slab Source Geometry Comparison of VARSKIN 5 (boxes), MCNP5 

(triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a Function 

of Electron Energy in Tissue at a Density Thickness of 100 mg/cm2 and a 

Tissue Volume Cylinder of Area 1 cm2 (solid line) and 10 cm2 (dashed line), 

With a Thickness of 20 mm 

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 500 1000 1500 2000 2500 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

7 mg/cm2

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

500 1000 1500 2000 2500 3000

Energy Dose (Gy/electron)

Electron Energy (keV)

100 mg/cm2
B-29

Figure B-51 A Slab Source Geometry Comparison of VARSKIN 5 (boxes), MCNP5 

(triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a Function 

of Electron Energy in Tissue at a Density Thickness of 300 mg/cm2 and a 

Tissue Volume Cylinder of Area 1 cm2(solid line) and 10 cm2(dashed line), 

With a Thickness of 20 mm

Figure B-52 A Slab Source Geometry Comparison of VARSKIN 5 (boxes), MCNP5 

(triangles) and EGSnrc (lines) Predicted Dose Per Initial Electron as a Function 

of Electron Energy in Tissue at a Density Thickness of 1000 mg/cm2 and a 

Tissue Volume Cylinder of Area 1 cm2(solid line) and 10 cm2(dashed line), 

With a Thickness of 20 mm

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1000 1500 2000 2500 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

300 mg/cm2

1.00E-13

1.00E-12

1.00E-11

1.00E-10

2500 2600 2700 2800 2900 3000

Electron Dose (Gy/electron)

Electron Dose (keV)

1000 mg/cm2
B-30

Figure B-53 A Slab Source Geometry Comparison of VARSKIN 5 (boxes) and VARSKIN 4 

(circles) Predicted Dose Per Initial Beta From 28Al as a Function of Density 

Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2 (upper) and 

10 cm2 (lower), With a Thickness of 20 mm 

Figure B-54 A Slab Source Geometry Comparison of VARSKIN 5 (boxes) and VARSKIN 4 

(circles) Predicted Dose Per Initial Beta From 42K as a Function of Density 

Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2 (upper) and 

10 cm2 (lower), With a Thickness of 20 mm 

1.00E-15

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

28Al

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

42K
B-31

Figure B-55 A Slab Source Geometry Comparison of VARSKIN 5 (boxes) and VARSKIN 4 

(circles) Predicted Dose Per Initial Beta From 66Cu as a Function of Density 

Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2 (upper) and 

10 cm2 (lower), With a Thickness of 20 mm 

Figure B-56 A Slab Source Geometry Comparison of VARSKIN 5 (boxes) and VARSKIN 4 

(circles) Predicted Dose Per Initial Beta From 138Cs as a Function of Density 

Thickness in Tissue and a Tissue Volume Cylinder of Area 1 cm2 (upper) and 

10 cm2 (lower), With a Thickness of 20 mm 

1.00E-17

1.00E-16

1.00E-15

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

66Cu

1.00E-15

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

138Cs

C-1

EXAMPLES AND SOLUTIONS USING VARSKIN 6

EXAMPLES AND SOLUTIONS USING THE VARSKIN 6 MODELS

This appendix describes three different practical applications of VARSKIN using an 

example/solution format. Each example describes a situation followed by a solution that 

involves the use of VARSKIN 6 to estimate skin dose at 7 mg/cm2 and dose at a depth of 1000 

mg/cm2. The purpose of these examples is to lead a new user of VARSKIN through several 

calculations that highlight many of its features. Because VARSKIN is a flexible tool, there are 

always several ways to calculate the dose for a given example. The solutions presented here 

reflect the recommendations that are provided throughout the user’s manual. With some 

experience, most VARSKIN users will not need to perform all of the steps described in the 

solution in an actual situation. It is suggested that the user complete all three examples in the 

order in which they are presented to develop familiarity with VARSKIN. The examples given 

below all utilize the ICRP 38 (no decay progeny) database. 

It is important to note that, even though we use VARSKIN 6 to calculate dose at depths other 

than 7 mg/cm2, these values do not ensure compliance with requirements of 10 CFR 20. The 

examples herein simply change the tissue depth from 7 mg/cm2 to some different value without 

changing other pertinent parameters of the dose averaging calculation. We want to stress here 

that when, in the following scenarios, the depth is changed from 7 mg/cm2 to 1000 mg/cm2, for 

example, we are not attempting to calculate deep dose equivalent, but simply demonstrating the 

utility of the code for estimating energy absorption at various depths in tissue. 

Example 1: Radiopharmaceutical Technician in Nuclear Medicine 

At a research hospital, a doctor prescribes a 5-milliliter (mL) administration from a stock solution 

containing 370 kiloBequerels per milliliter (kBq/mL) of rhenium-186 (186Re) for a clinical research 

study at 1 p.m. that day. Around 12:30 p.m., a lab technician loads the dose under the hood. 

Subsequently, a fellow employee bumps into her, and the needle slips out of its container. The 

entire 5 mL of the solution is spilled on the arm of her cloth lab coat in a circular shape with an 

area of approximately 50 square centimeters (cm2). She is unaware of the accident and 

continues with her work until the end of the day. Around 5 p.m., a routine survey for 

contamination is performed, and the contamination is discovered. 

Solution 1: Radiopharmaceutical Technician in Nuclear Medicine 

The point source geometry is suggested as a starting point to estimate the magnitude of the 

dose and to collect some other useful information. Run VARSKIN 6 and check the user 

“Radionuclide Library.” If 186Re does not appear in the “Radionuclide Library” window, add 186Re 

by selecting the “Add” button, selecting the ICRP 38 bubble with “OK”, and double-clicking 186Re 

in the Add Radionuclide to Library window (with an effective Z of equivalent-water, Z = 7.42). 

Enter the Exposure Time as 4.5 and change the time unit to hours using the drop-down menu or 

the down-arrow key. Because the point source geometry is being used, it is necessary to 

calculate the source strength by multiplying the concentration of the stock solution (370 kBq/mL) 

by the size of the administration (5 mL) to get a total source strength of 1.85 MBq. Be sure that 

the source strength units are set to MBq, then double-click the 186Re library entry. When 

VARSKIN asks for the source strength, enter 1.85. The other defaults will establish a dose 

calculation at 7 mg/cm2 and a dose-averaging disk of 10 cm2. All other entries should retain their 
C-2

default values. Click “Calculate Doses.” After the calculation is performed, the VARSKIN 6 NonVolume Averaged Results window will appear. 

The results window shows two groups of nine dose or dose-rate values (the group to the left is 

for nuclide-specific doses and the group to the right is total (over all nuclides) dose). Since only 

one nuclide has been selected, the two groups will display the same dose values. For each of 

electron, photon, and total, the initial dose rate, the dose with no decay, and the decaycorrected dose are displayed. As described earlier, the dose with no decay is provided so that 

the user can assume either that the source has a very long half-life or that the radionuclide is in 

secular equilibrium with its parent. Note that 186Re has a relatively short half-life; therefore, the 

decay-corrected dose is the appropriate dose for the current calculation. Looking at either the 

VARSKIN results window or the results printout (by clicking the “Print Results” button) will show 

that the decay-corrected total dose is 1.31 Gray (Gy) (1.31 Gy from electrons and 0.673 

milliGy (mGy) from photons), a total dose that exceeds regulatory limits. To calculate the dose 

at a 1 cm depth, for example, return to the main VARSKIN window (i.e., close the results 

window), change the value of the Skin Thickness or Skin Density Thickness to 1,000 milligrams 

per square centimeter (mg/cm2), and click “Calculate Doses.” The VARSKIN results screen now 

displays a decay-corrected beta dose of 0 (zero) and a photon dose of 0.0712 mGy. 

The total shallow dose calculated using the point geometry was above regulatory limits. 

However, the situation described in this example will obviously be more accurately modeled 

using the disk or cylinder geometries. A more realistic, yet conservative approach would be to 

use the disk geometry and calculate the dose as if all of the contamination were directly on the 

skin. Return to the main VARSKIN window and choose “Disk” in the Source Geometry frame. 

Confirm the Exposure Time of 4.5 hours. Next, enter the Source Area as 50 cm2 (do not forget 

to change the units from the default setting). Note that the Source Diameter is automatically 

calculated to be 7.98 cm (this value will be needed for the next model). Change the Skin 

Thickness or Skin Density Thickness back to the shallow depth of 7 mg/cm2 and click “Calculate 

Doses.” The results screen shows a decay-corrected electron dose of 0.262 Gy and a photon 

dose of 0.149 mGy. While the total dose is still quite high, it is now below regulatory limits. 

Even more realism can be introduced by using the cylinder model to simulate contamination that 

is uniformly distributed throughout the thickness of the lab coat. In this case, the lab coat is 

assumed to soak up the contamination instead of acting as a protective cover material. The data 

in Table 2-2 for a cloth lab coat give a thickness of 0.4 millimeters (mm) and a density of 

0.9 g/cm3. After returning to the main VARSKIN window, choose “Cylinder” in the Source 

Geometry frame. Confirm the exposure time of 4.5 hours. Paying close attention to each unit’s 

entry, confirm the Source Diameter as 7.98 cm (from the disk calculation), and establish a 

Source Thickness of 0.4 mm (the thickness of the lab coat) and a Source Density of 0.9 g/cm3

(the density of the lab coat). Click “Calculate Doses”; after a longer calculational period (due to 

the geometric complexity), the VARSKIN results screen then will display 0.169 Gy and 0.126 

mGy as the decay-corrected electron and photon doses, respectively. 

It is interesting to see what the beta dose would be if the lab coat was impervious to the liquid 

contamination, and the contamination resided as an infinitely thin layer of contamination on the 

plastic. In this case, the plastic lab coat acts as a cover material instead of defining the size and 

density of the source. To perform this calculation, return to the main VARSKIN window and 

change the Source Geometry to a “Disk” source. Confirm the Exposure Time of 4.5 hours and 

the source area of 50 cm2. Enter a Cover Thickness of 0.2 mm with a density of 0.36 g/cm3. 

After the user clicks “Calculate Doses,” the VARSKIN results screen will display decaycorrected doses of 0.186 Gy for electrons and 0.124 mGy for photons. It can be concluded that, 
C-3

based on the above calculations, a thicker, absorbent lab coat will give more protection than a 

thin, impervious material. 

Example 2: Radiation Worker in Reactor Containment 

A worker damages his outer glove while working inside containment during an outage at a 

nuclear reactor. His outer glove is removed, leaving only a surgeon’s glove. The worker 

proceeds to the step-off pad, which takes about 15 minutes. During the exit survey, 

contamination is detected on the surgeon’s glove, and the glove is removed and taken to the 

laboratory for analysis. The laboratory report concludes that the contamination is a stellite hot 

particle with the following characteristics: 

 Radioactive contaminant: 60Co

 Source strength: 92.5 MBq

 Particle thickness and density: 50 m; 8.3 g/cm3

 Particle size: 80 microns x 70 microns

 Stellite assumed atomic number (cobalt-chromium alloy): 25.5

 Glove thickness: 0.3 mm

 Glove density: 0.6 g/cm3

Solution 2: Radiation Worker in Reactor Containment 

First, we will use the point source geometry to estimate the magnitude of the dose and to collect 

some other useful information. Start or “Reset” (from the File drop-down menu) VARSKIN 6. If 

Co-60 does not appear in the Radionuclide Library frame, add Co-60 by selecting the “Add” key, 

selecting the ICRP 38 bubble with “OK”, and double-clicking “Co-60” in the Add Radionuclide to 

Library window (with an effective Z of 25.5). Enter an Exposure Time of 15 minutes. Doubleclick “Co-60” in the Radionuclide Library and enter 92.5 MBq. Enter a Cover Thickness of 0.3 

mm and a Cover Density of 0.6 g/cm3. After you click “Calculate Doses,” the VARSKIN results 

window will display an electron dose of 0.325 Gy, a photon dose of 0.105 Gy, and a total dose 

of 0.431 Gy, a value approaching the regulatory limit. Thus, a more realistic calculation is 

desirable. In addition, there is a photon component to the dose, so a dose calculation at 1 cm is 

warranted. 

Using the cylinder model will result in a more realistic calculation because the effects of selfshielding of the beta particles will be considered. As described in Section 2.1.2, the slab and 

cylinder models can be used for a particle that is known to be rectangular. Return to the main 

VARSKIN window and choose the “Cylinder” source geometry. Confirm 15 minutes as the 

Exposure Time, 0.3 mm as the Cover Thickness, and 0.6 g/cm3 as the Cover Density. Enter 50 

m as the Source Thickness. The diameter of a disk source, with the same area as the 

rectangular source, is found by: 

d = 2√X ∙ Y⁄π = 2√80 μm ∙ 70 μm

π

⁄ = 84 μm

Enter 84 m for the Source Diameter and 8.3 g/cm3 for the Source Density, and then click 

“Calculate Doses.” After a short time, the VARSKIN results screen will display an electron dose 

of 0.131 Gy, a photon dose of 0.106 Gy, and a total dose of 0.237 Gy. Including the effects of 

self-shielding greatly reduced the electron dose and resulted in a dose that is now below 

regulatory limits. To investigate the dosimetric influence of tissue depth, calculate dose at 1 cm 
C-4

by returning to the main window, and changing the Skin Thickness or Skin Density Thickness to 

1,000 mg/cm2. Click “Calculate Doses.” The VARSKIN results screen will display a dose at 1 

cm of 0.0324 Gy, all from photons. 

Example 3: Contaminated Metal in a University Laboratory Hood 

During a radiation survey of a fume hood, a new Radiation Safety Officer (RSO) at a university 

discovers a contaminated aluminum plate inside the hood. Upon further investigation, it is found 

that the plate was used to hold beakers of solution containing carbon-14 (14C) for use in 

radiobiology experiments. The RSO decides that the plate should be disposed of as low-level 

radioactive waste and that the activity of 14C on the plate must be determined. The plate is 

15.24 centimeters (cm) by 15.24 cm and is uniformly contaminated over the entire surface. The 

RSO uses a calibrated circular detector with an area of 50 cm2 and a window thickness of 

3 mg/cm2 to measure a dose rate of 1.90 mGy/hr on contact and 0.60 mGy/hr at a distance of 

2.54 cm. The RSO uses these dose-rate measurements and VARSKIN results to estimate the 

activity of 14C on the plate. VARKSIN must be configured to mimic the measurements. 

Solution 3: Contaminated Metal in a University Laboratory Hood 

The solution to this example demonstrates a method in which VARSKIN 6 might be used for 

applications other than skin contamination events; users are cautioned not to relying too heavily 

on such calculations. In this situation, the Skin Averaging Area will be set to 50 cm2 to 

correspond to the area of the probe, the Skin Density Thickness will be set to 3 mg/cm2 to 

correspond to the thickness of the probe window, and the Source Area will be set to 232 cm2 to 

correspond to the area of the contaminated plate. An initial source strength of 1 MBq/cm2 will be 

used for the calculation, and the results then scaled to the measurements obtained by the RSO. 

Both of the measurements can be modeled because the air gap in Example 3 is smaller than 

5 cm. 

For this solution, first “Reset” VARSKIN 6 and choose the “Disk” geometry. If the Radionuclide 

Library does not contain 14C, add it by clicking “Add”, selecting the ICRP 38 bubble with “OK”, 

and double-clicking “C-14” in the Add Radionuclide to Library screen (with an effective Z of 

7.42). From the main VARSKIN window, click the “Use Distributed Source” checkbox. Notice 

that the default unit for activity has changed; set that to “MBq/cm2”. Double-click “C-14” and set 

the source strength to 1 MBq/cm2. Set the Skin Averaging Area to 50 cm2, the Skin Thickness 

or Skin Density Thickness to 3 mg/cm2, and the Source Area to 232 cm2. For this example, 

dose rate is of interest, so the irradiation time can remain at the default value of 60 minutes. 

Click “Calculate Doses”; the VARSKIN results window will appear, displaying an initial electron 

dose rate of 1,210 mGy/hr, with no photon dose. The activity concentration on the plate then 

can be found using, 

[Aact]

[Acal]

=

Ḋmeas

Ḋ

cal
C-5

Therefore, the activity concentration on the plate is given by:

(1

MBq⁄

cm2) (1.90 mGy

hr

⁄ )

1,210 mGy

hr

⁄

= 0.00157 MBq⁄

cm2

Multiplying the activity concentration by the area of the plate (232 cm2) results in a total activity 

of 0.364 MBq.

The measurement at a distance of 2.54 cm can be used to verify this result. Close the results 

window and return to the main window; enter an Air Gap Thickness of 2.54 cm and change the 

activity to 0.364 MBq. After you click “Calculating Doses,” the VARSKIN results window will 

display an initial electron dose rate of 0.602 mGy/hr, compared to the measurement of 0.60 

mGy/hr with the calibrated detector.

Example 4: Use of Decay Databases and Automatic Progeny Selection

This example is not specific to a particular contamination scenario but is provided here to 

demonstrate the internal calculations of VARSKIN 6 as it automatically includes decay progeny 

in the calculation of skin dose, and to give the user an appreciation of the possible differences 

between the two ICRP decay databases. The simulation itself is quite simply modeled as an 

infinite plane source of 144Ce on the skin surface. The shallow skin dose is calculated at a depth 

of 7 mg/cm2, normalized to an activity of 1 Bq for a 1 sec exposure, resulting in a dose 

prediction per decay of 144Ce. The calculation is executed using ICRP 38 data in the first case, 

and then using ICRP 107 data in the second case. The photon and electron data are provided 

explicitly so that the user can better understand the origin of differences in the dose predictions.

Cerium-144 (144Ce) decays by 

- emission (see Fig. C-1), with a half-life of about 285 days, 

through several energetic routes to praseodymium-144 (144Pr). One of the 144Ce decay routes 

stops at the metastable state 144mPr (~1% yield), with a half-life of about 7 minutes. 

Praseodymium-144 then decays again by 

- decay, with a half-life of about 17 minutes, to 

neodymium-144 (144Nd). They’re not all shown in the figure, but a large number of gamma-ray 

photons, conversion electrons, characteristic X rays, and Auger electrons are also emitted 

during these decay processes. The emission data, as extracted by VARSKIN 6, are provided in 

Tables C-1 and C-2 (divided by (a) photons and (b) electrons) according to both ICRP 38 and 

ICRP 107, respectively. It is evident from the data that we can expect differences in the dose 

calculations using the two datasets.
C-6

Figure C-1 The Decay Scheme of 144Ce to Stable 144Nd

Table C-1a ICRP 38 Photon Emission Data for the Decay of 144Ce to Stable 144Nd 

Branching Photon Photon Photon Photon 

Nuclide Ratio Yield (%) Energy (MeV) Nuclide Yield (%) Energy (MeV) 

144Ce 1.6416 0.0801199 144Ce(D) 1.6416 0.0801199 

10.8 0.13353 10.8 0.13353 

5.40195 0.0360263 5.40195 0.0360263 

2.95756 0.0355502 2.95756 0.0355502 

1.06958 0.0407484 1.06958 0.0407484 

144Pr 0.9822 1.48 0.69649 1.45366 0.69649 

144mPr 0.0178 15.7456 0.0360263 0.280272 0.0360263

8.62071 0.0355502 0.153449 0.0355502 

3.11763 0.0407484 0.05549381 0.0407484 

1.25177 0.0417924 0.02228151 0.0417924 

1.60605 0.0406532 0.02858769 0.0406532 

4.53392 0.00503329 0.08070377 0.00503329 

1.63137 0.00548929 0.02903838 0.00548929 

144Pr 0.999 1.48 0.69649 0.02631766 0.69649 

144Ce(D) represents the combined “nuclide” in VARSKIN 6 having selected the option to include progeny. 
C-7

Table C-2b ICRP 38 Electron Emission Data for the Decay of 144Ce to Stable 144Nd

Half-life Electron Electron Avg Electron

Nuclide (hours) Yield (%) Energy (MeV) X90 (cm)

144Ce 6823.2 1.57344 0.09230879 0.02774469

144Pr 0.288 1.0006 1.2079 0.695699

144mPr 0.12 3.37682 0.617 0.004115152

144Ce(D) 6823.2 1.57344 0.654206 0.682593

144Ce(D) represents the combined “nuclide” in VARSKIN 6 having selected the option to include progeny.

Table C-3a ICRP 107 Photon Emission Data for the Decay of 144Ce to Stable 144Nd

Branching Photon Photon Photon Photon

Nuclide Ratio Yield (%) Energy (MeV) Nuclide Yield (%) Energy (MeV)

144Ce 1.36407 0.08012 144Ce(D) 1.36407 0.08012

11.09 0.133515 11.09 0.133515

4.40559 0.0360557 4.40559 0.0360557

2.41237 0.0355671 2.41237 0.0355671

144Pr 0.99023 1.342 0.69651 1.32889 0.69651

144Ce(D) represents the combined “nuclide” in VARSKIN 6 having selected the option to include progeny.

Table C-3b ICRP 107 Electron Emission Data for the Decay of 144Ce to Stable 144Nd

Half-life Electron Electron Avg Electron

Nuclide (hours) Yield (%) Energy (MeV) X90 (cm)

144Ce 6837.84 2.34621 0.09170876 0.0285164

144Pr 0.288 1.00107 1.20882 0.696917

144mPr 0.12 10.231 0.296957 0.004116936

144Ce(D) 6837.84 2.34621 0.654899 0.682717

144Ce(D) represents the combined “nuclide” in VARSKIN 6 having selected the option to include progeny.

Solution 4: Use of Decay Databases and Automatic Progeny Selection

This example begins with the selection of scenario, along with the manual selection of parent 

and progeny nuclides using the ICRP 38 decay database. We follow up with the selection of 

automatic decay progeny inclusion and a comparison of shallow skin dose predictions.

For this solution, first “Reset” VARSKIN 6 and choose the “Disk” geometry. Select an Exposure 

Time of 1 second, Activity Units of “Bq”, and set the Source Area to 100 cm2(this will 

approximate an infinite plane source for a dose averaging area of 10 cm2). All other inputs 

should remain as they are, in the default state.

On examination of the decay scheme for 144Ce, we see that its decay progeny includes 144Pr 

and 144mPr. Therefore, if those nuclides must be in your Radionuclide Library. If the 

Radionuclide Library does not contain 144Ce from the ICRP 38 library, add it by clicking “Add”, 
C-8

selecting the “ICRP 38” bubble, pressing “OK”, and then double-clicking “Ce-144” in the Add 

Radionuclide to Library screen (for simplicity, we’ll use the default effective Z of 7.42). Next, do 

the same for “Pr-144” and “Pr-144m”. Additionally, to add 144Ce with its decay progeny, click 

“Add” and select the “ICRP 38D” bubble, press “OK” and then double-click “Ce-144”. Then, to 

include those nuclides in the dose calculation for this scenario, double-click “Ce-144” in your 

Radionuclide Library and enter an activity to 1 Bq (repeat for 144Pr, 144mPr, and 144Ce(D)). 

Recheck the input window to see that all parameters contain the appropriate values, including 

the four nuclides listed in the Selected Radionuclides box, and then click “Calculate Doses” to 

generate the VARSKIN results. With the results (Table C-3), we will compare a manual 

calculation of the total dose (SUM in Table C-3) and compare that with the automatic calculation 

using the progeny option (144Ce(D) in Table C-3). We calculate the SUM using, 

D = DCe + (BRPrDPr) + (BRmDm) + (BRmBRPr∗DPr)

D = 2.40x10−9 + (0.9822 ∙ 4.58x10−9) + (0.0178 ∙ 5.55x10−13) + (0.0178 ∙ 0.999 ∙ 4.58x10−9)

D = 6.98x10−9 mGy/nt

Table C-3 Dose Results from VARSKIN 6 with Progeny Using the ICRP 38 Decay 

Database 

Branching Electron Dose Photon Dose 

Nuclide Ratio (mGy/nt) (mGy/nt) 

144Ce 2.40x10-9 3.63x10-12

144Pr 0.9822 4.58x10-9 7.78x10-13

144mPr 0.0178 5.55x10-13 1.42x10-11

144Pr* 0.999 4.58x10-9 7.78x10-13

SUM 6.98x10-9 4.66x10-12

144Ce(D) 6.93x10-9 4.66x10-12

Difference -0.7% 0%

144Ce(D) represents the combined “nuclide” in VARSKIN 6 having selected the option to include progeny. 

*this entry represents 144Pr as the decay product of 144mPr.

The “discrepancy” (percent difference) in the dose calculations is shown to be within the 

tolerance of rounding (within 1%). To execute VARSKIN 6 with the ICRP 107 decay database, 

simply “Add” the proper nuclides in the same fashion as above, except this time selecting the 

“ICRP 107” and “ICRP 107D” bubbles, where appropriate. ICRP 107 does not provide 

branching for 144mPr, therefore, the metastable state of 144Pr is not included in the calculation. 

Dose results for the ICRP 107 comparison are given in Table C-4. Electron and photon dose 

estimates with comparing manual to automatic progeny selection give results within rounding. 
C-9

Table C-4 Dose results from VARSKIN 6 with progeny using the ICRP 107 decay 

database

Branching Electron Dose Photon Dose

Nuclide Ratio (mGy/nt) (mGy/nt)

144Ce 2.44x10-9 3.27x10-12

144Pr 0.99023 4.58x10-9 7.05x10-13

SUM 6.98x10-9 3.97x10-12

144Ce(D) 6.93x10-9 3.97x10-12

Difference -0.7% 0.0%

144Ce(D) represents the combined “nuclide” in VARSKIN 6 having selected the option to include progeny.



NUREG/CR-6918, Rev. 3

Vered Anzenberg Shaffer

Division of System Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-001

Division of System Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-001

The original VARSKIN computer code, an algorithm to calculate skin dose from radioactive skin contamination, has 

been modified on several occasions. VARSKIN is a U.S. NRC computer code used by staff members and NRC 

licensees to calculate occupational dose to the skin resulting from exposure to radiation emitted from hot particles or 

other contamination on or near the skin. These assessments are required by 10 CFR 20.1201(c) in which the 

assigned shallow dose equivalent is to the part of the body receiving the highest exposure over a contiguous 10 cm2

of skin at a tissue depth of 0.007 centimeters (7 mg/cm2).

This user manual describes the updates to VARSKIN 6.0, in addition to aiding the user in installing VARSKIN 6.0.

Dose, Internal Dosimetry, RAMP, Dosimetry Computer Codes

October 2018

Technical

VARSKIN 6

A Computer Code for Skin Contamination Dosimetry



NUREG/CR-6918, Rev. 3 VARSKIN 6

A Computer Code for Skin Contamination Dosimetry

October 2018