VARSKIN 5: A 

Computer Code for 

Skin Contamination 

Dosimetry

Office of Nuclear Regulatory Research

NUREG/CR-6918

Revision 2
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VARSKIN 5: A 

Computer Code for 

Skin Contamination 

Dosimetry

Manuscript Completed: October 2013

Date Published: July 2014

Prepared by: 

D. M. Hamby, C. D. Mangini, J. A. Caffrey, M. Tang

Department of Nuclear Engineering and Radiation Health Physics

Oregon State University

Corvallis, OR 97331-5902

M. Saba, NRC Project Manager

S. Sherbini, NRC Technical Monitor

Office of Nuclear Regulatory Research

NUREG/CR-6918

Revision 2

iii

ABSTRACT

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

contamination, has been modified on several occasions. This program is a rewrite of the U.S. 

NRC computer program VARSKIN 4 which is 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 VARSKIN 4, five different predefined source configurations are available in VARSKIN 5

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

earlier VARSKIN 3 and 4 included an enhanced photon dosimetry model, as well as models to 

account for air gap and cover materials for photon dosimetry. The new VARSKIN 5 version has 

been updated to better predict beta dosimetry in shallow skin targets. Although the user can 

choose any dose-averaging area, the default area for skin dose calculations in VARSKIN 5 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. A library file contains data on gamma rays, x-rays, beta 

particles, internal conversion electrons, and Auger electrons. VARSKIN 5 allows the user to 

eliminate radionuclides that are not of interest and thus build a customized library. Finally, an 

extensive, context-sensitive help file is made available for VARSKIN 5 to provide guidance and 

to offer new users a tutorial in the use of the skin dosimetry software.

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 beta dosimetry model 

has been upgraded in VARSKIN 5 to better account for beta energy loss and particle scatter. 

Dose point kernels are now Monte Carlo based and the code agrees very well with the EGSnrc 

Monte Carlo code.

This document describes the VARSKIN code, provides basic operating instructions, presents

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

models.

v

CONTENTS

Page

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

FIGURES.................................................................................................................................. vii

TABLES.....................................................................................................................................ix

AKNOWLEDGMENTS ...............................................................................................................xi

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

1 INTRODUCTION.............................................................................................................1

2 VARSKIN 5 USER’S MANUAL........................................................................................3

2.1 Running VARSKIN 5............................................................................................3

2.1.1 Hardware and Software Requirements ............... ..................................3 

2.1.2 Source Geometry .....................................................................................3

2.1.3 Adding Radionuclides to the Library .........................................................7

2.1.4 Selecting Radionuclides from the User Library .........................................8

2.1.5 Geometry Parameters and Multiple Cover Calculator...............................9

2.1.6 Default State ............................................................................................9

2.2 Special Options..................................................................................................13

2.2.1 Calculating Doses ..................................................................................14

2.2.2 Output Screen ........................................................................................15

2.3 Exiting VARSKIN 5 ............................................................................................18

3 DESCRIPTION OF DOSIMETRY MODELS ..................................................................19

3.1 Beta Dosimetry ..................................................................................................19

3.1.1 Dose-Point Kernels ................................................................................19

3.1.2 Numerical Integration of Dose-Point Kernels ..........................................23

3.1.3 Homogeneous Dose-Point Kernels.........................................................25

3.1.4 Non-homogeneous Dose-Point Kernels .................................................27

3.1.5 Beta-Particle Dose-Point Kernels ...........................................................27

3.2 Backscatter Model .............................................................................................29

3.3 Scaling Models ...... ..........................................................................................37

3.3.1 Depth Scaling .... ...................................................................................37

3.3.2 Energy Scaling ......................................................................................39

3.4 Cover Layer and Air Gap Models .......................................................................42

3.5 Volume-Averaged Dose Model ..........................................................................44

3.6 Offset Particle Model..........................................................................................44

3.7 Adding Radionuclides to the VARSKIN 5 Library ...............................................44

3.8 Photon Dosimetry ..............................................................................................45

3.9 Attenuation Coefficients for Cover Materials ......................................................52

3.10 Off-Axis Calculation of Dose ..............................................................................53
vi

CONTENTS (continued)

Page

4 VALIDATION AND VERIFICATION ..............................................................................57

4.1 Comparison with A General Monte Carlo N-Particle Transport Code (MCNP) ..57

4.2 Shallow Dose Comparisons ..............................................................................59

4.2.1 Point Source on the Skin........................................................................59

4.2.2 Point Source on Cover Material..............................................................60

4.2.3 Distributed Beta Contamination on Skin .................................................62

5 VARSKIN LIMITATIONS ...............................................................................63

5.1 Beta Dosimetry .................................................................................................63

5.1.1 DPK's and Scaling Model ......................................................................64

5.1.2 Scattering Model ...................................................................................64

5.2 Photon Dosimetry .............................................................................................65

6 SPECIAL TOPICS FOR ACCURATE USE OF VARSKIN .............................................67

6.1 Infinite Sources ..................................................................................................67

6.2 Maximum Dose from Multiple Contamination Sources .......................................67

7 REFERENCES..............................................................................................................69

APPENDICES

Appendix A Supporting Figures from Section 5.....................................................................A-1

Appendix B Figures for the Supporting Photon Dosimetry V&V....................................... B-1

Appendix C Examples and Solutions Using VARSKIN 5.. .....................................................C-1
vii

FIGURES

Figure 1-1 Depiction of cylindrical dose averaging volume....................................................2

Figure 2-1 Initial view and main input screen ........................................................................3

Figure 2-2 About Varskin 5.0 screen ....................................................................................4

Figure 2-3 Schematic representations of the five geometry options ......................................5

Figure 2-4 Add Radionuclide screen .....................................................................................8

Figure 2-5 Slab source geometry parameters .......................................................................9

Figure 2-6 Schematic showing the cover material and air gap models ................................11

Figure 2-7 Composite cover calculator screen ....................................................................13

Figure 2-8 Schematic diagram of the volume-averaged dose model geometry ...................14

Figure 2-9 General logic flow diagram ................................................................................16

Figure 2-10 Results screen for a typical calculation ..............................................................17

Figure 2-11 Results screen for a volume-averaged calculation .............................................18

Figure 3-1 Scaled absorbed dose distributions for 0.1 MeV electrons in an infinite 

homogeneous waste medium ............................................................................23

Figure 3-2 Scaled absorbed dose distribution for 1.0 MeV electrons in an infinite 

homogeneous water medium.............................................................................23

Figure 3-3 Schematic representation of the eight-panel quadrature routine used to 

calculate dose for a symmetric source (redrawn from Durham 2006).................25

Figure 3-4 Schematic of EGSnrc geometry for determining point-source radial DPK’s........26

Figure 3-5 Plot demonstrating the wide range of densities and atomic numbers used in 

development of the scaling model......................................................................27

Figure 3-6 Schematic demonstrating conditions in which full source-water scattering 

corrections are applied.......................................................................................31

Figure 3-7 Schematic demonstrating conditions in which partial source-water scattering 

corrections are applied..... .................................................................................32

Figure 3-8 Schematic illustrating beta energy limitations of side-scatter corrections...........34

Figure 3-9 Schematic illustrating parameters used to determine the amount of 

side-scatter correction applied to high-energy beta-particles emitted from 

large sources.....................................................................................................34

Figure 3-10 Schematic demonstrating conditions in which a full air-water scattering 

corrections are applied......................................................................................36

Figure 3-11 Schematic demonstrating conditions in which air-water scattering 

corrections are applied.......................................................................................37

Figure 3-12 Comparison of 1 MeV electron DPK’s for the homogeneous water case and 

the case when the electron traverses iron source material of thickness 

0.0222 cm.........................................................................................................38

Figure 3-13 Example of depth scaling on the homogeneous DPK curve .............................38

Figure 3-14 TableCurve 3D plot of depth-scaling data for all source materials used in 

scaling model....................................................................................................39

Figure 3-15 Example of energy scaling on the homogeneous DPK curve presented in 

Figure 3-14........................................................................................................40
viii

FIGURES (continued)

Page

Figure 3-16 TableCurve 3D plot of energy-scaling data for all source materials in scaling 

model...............................................................................................................41

Figure 3-17 Schematic of a generic dose calculation performed by VARSKIN 4 for the 

cylinder geometry...............................................................................................42

Figure 3-18 ICRU 44 soft tissue mass attenuation coefficients compared to the empirical 

functions ............................................................................................................47

Figure 3-19 ICRU 44 soft tissue mass energy absorption coefficients compared to the 

functions of Eqs. [3.8.5] and [3.8.6] ...................................................................48

Figure 3-20 Off-axis correction factor as a function of off-axis angle and dose-averaging 

area ...................................................................................................................50

Figure 3-21 Depiction of methods for determining integration segments of the 

dose-averaging disk...........................................................................................51

Figure 3-22 Relative dose as a function of the number of segments in a numerical 

integration (iterations), by method......................................................................51

Figure 3-23 Dose-averaging disk with the source point located on axis ................................53

Figure 3-24 Dose-averaging disk located at depth h beneath an offset point source.............54

Figure 3-25 Dose-averaging disk with the source point located off axis, yet still over the 

averaging disk....................................................................................................54

Figure 3-26 Relationship between the source-averaging disk and one of the radii for dose 

calculation..........................................................................................................55

Figure 3-27 Dose-averaging disk from above with the source point located off axis, far 

enough removed to be off the averaging disk.....................................................56

Figure 4-1 Horizontal and vertical cross-sectional views of the MCNP5 geometry ..............57

Figure 4-2 Illustration of the point source geometry of the tissue volumes of interest at 

various density thicknesses in tissue..................................................................58
ix

TABLES

Table 2-1 Default Values and Units for Geometry Parameters...........................................11

Table 2-2 Suggested Values for Cover Thickness and Density..........................................12

Table 3-1 List of source materials used to develop the scaling model................................26

Table 3-2 List of nuclides used in scaling and scattering models .......................................28

Table 3-3 Source materials used for non-homogeneous beta particle DPK testing...........28

Table 3-4 Coefficients for Eq. [3.8.6] .................................................................................47

Table 4-1 Comparison between Beta and Photon Shallow Dose Calculations from 

VARSKIN 3.1, 4, and 5 for a 1-μCi Point Source of Co-60 Exposing the 

Skin for 1 Hr.......................................................................................................60

Table 4-2 Comparison between VARSKIN 3.1, 4 and 5 of the Shallow Dose for 

Various Cover Material Configurations...............................................................61

Table 4-3 Comparison between VARSKIN 3.1, 4 and 5 of the Beta Dose (mGy) for 

a 1-hr Exposure to Distributed Contamination on the Skin .................................62

Table 4-4 Dose (mGy) for Various 1 μCi/cm2 Distributed Disk Sources and a 1-hr 

Exposure Time (dose calculated at a depth of 7 mg/cm2 and averaged 

over 1 cm2)........................................................................................................62

Table 4-5 Dose (mGy) vs. Depth for a 1 μCi/cm2 Distributed Disk Source of Y-90 

and a 1-hr Exposure Time (dose averaged over 1 cm2).....................................62

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-11-C-04-0011

and NRC-04-08-137. Staff at the Pacific Northwest National Laboratory wrote initial versions of 

VARSKIN; later versions were written at Colorado State University and then the Center for 

Nuclear Waste Regulatory Analyses. The activities reported here were performed 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.

We are appreciative of the technical assistance received from J. Parson, M. Ryan, and S. 

Marshall in the production of this and the previous report and their findings. Our beta testers for 

various versions of VARSKIN included J. Chase, J. Dubeau, K. Sejkora, M. Thornhill, R.

Struckmeyer, and J. DeCicco. We are also grateful to S. Bush-Goddard, M. Saba, and S. 

Sherbini for their support during the development process of the enhanced photon and beta 

dosimetry models. 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

ABREVIATIONS AND ACRONYMS

2D Two Dimensional

3D Three Dimensional

BSCF Back Scatter 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 Radiation Protection

ICRU International Committee on Radiation Units and Measures

KERMA Kinetic Energy Released in Matter

MCNP Monte Carlo N-Particle

NCRP National Commission on Radiation Protection

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 Specific Absorbed Dose Distribution

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 to be 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.

Originally, there were a few drawbacks to using VARSKIN to calculate skin doses from hot 

particles or other contaminants on the skin or outside of a cover material such as protective 

clothing. Formerly, VARSKIN modeled the contaminant as having no thickness; thus, the 

calculation did not account for source self-shielding. For example, for hot particles containing 

weak beta-emitting radionuclides (e.g., cobalt-60 (Co-60)), VARSKIN greatly overestimated 

calculated skin doses from particles that were thicker than about 1 micrometer (μm). Second, 

VARSKIN did not have the capability of modeling a cover material (e.g., protective clothing) that 

might exist between the source and skin, again leading to an overestimation of skin dose from 

skin contamination. Finally, it was shown that the gamma component of a mixed beta/gammaemitting hot particle becomes increasingly important as the skin depth and the thickness of 

cover material increase (Durham and Lantz, 1991). Because VARSKIN did not model a cover 

material or allow skin depths other than 7 milligrams per square centimeter (mg/cm2

), the code’s 

original authors concluded that the photon dose would not be significant compared to the beta 

dose under these exposure conditions, and thus they did not include the photon dose model. 

Because of these and other shortcomings of the code, an upgrade of VARSKIN was needed to 

provide skin dose calculations under a variety of exposure conditions.

VARSKIN Mod 2 (Durham, 1992) contained all the features of the original VARSKIN, with many 

significant additions. Additional features in VARSKIN Mod 2 included the modeling of threedimensional 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 Mod 2 also 

used a correction for backscatter for one- and two-dimensional beta sources under limited 

conditions. Finally, the VARSKIN Mod 2 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.

The upgraded code also contained a volume-averaged dose model and an offset particle model. 

The volume-averaged model allowed 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 can then be compared to the dose measured by a finitevolume 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.
2

Figure 1-1 Depiction of cylindrical dose averaging volume

Finally, VARSKIN Mod 2 gave the user the ability to select a composite source term, thus 

allowing the calculation of total dose from a mixture of beta-emitters instead of requiring the 

code to be run separately for each radionuclide in the mix. This feature was removed in 

VARSKIN 3 (Durham 2006), and instead, the maximum number of radionuclides included in a 

single calculation was increased to 20. One drawback of removing this feature in VARSKIN 3 is 

that the user must explicitly add radioactive progeny. The VARSKIN 3 photon dose model, 

which has been improved in VARSKIN 4, was an extension of a model published by Lantz and 

Lambert (1990) that was the basis for the VARSKIN Mod 2 photon dose model. A syringe 

model was included in VARSKIN 3, but was deactivated in VARSKIN 4. That model employed 

a major approximation to an actual syringe and, in that respect, had several limitations.

Enhancements that initiated VARSKIN 4 focused on the photon dosimetry model. This model 

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

attenuation, air and cover materials, and volumetric sources. In VARSKIN 3, only point photon 

sources could be modeled, charged particle equilibrium (CPE) and attenuation were not 

considered, and cover materials were not modeled. The VARSKIN 5 package provides an 

upgraded beta dosimetry model that better accounts for charged-particle energy loss as the 

particle moves through the source, cover material, air, and tissue.

Section 2 of this report describes the contents of the VARSKIN 5 code package, including 

instructions for code execution. Section 3 discusses the technical basis for VARSKIN 5 and 

describes the dosimetry models incorporated in the code, while Section 4 contains the results of 

validation and verification testing. Section 5 describes the problems and suggestions for 

improving VARSKIN Mod 2 and VARSKIN 3 that were included in VARSKIN 5, as well as 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-squarecentimeter (10 cm2

) area from multiple contamination sources. Additionally, Appendix A 

provides a graphical display of the results from Section 4, and Appendix B presents three 

detailed solutions to practical examples using VARSKIN 5.
3

2 VARSKIN 5 USER’S MANUAL

This section serves as a user’s guide for VARSKIN 5. It includes operating instructions and a 

description of the features of VARSKIN 5.

2.1 Running VARSKIN 5

Users must download and unzip the VARSKIN 5 folder and double-click the V5 icon to execute 

the VARSKIN code. There is no need to uninstall previous versions of VARSKIN. Upgrades to 

VARSKIN 5 will be made available, as necessary. Obtaining upgrades is as simple as 

downloading the new zipped folder and beginning execution.

2.1.1 Hardware and Software Requirements: A personal computer with a Pentium II 

processor or newer is required. The code requires approximately 10 megabytes of disk space. 

VARSKIN has been tested under a variety of Windows® operating systems.

Operations within VARSKIN 5 are designed to be intuitive. After double-clicking the V5 icon, the 

user will see the Main Input screen (Figure 2-1). If necessary, the “About Varskin 5.0” screen 

provides the user with contact information and basic code information (Figure 2-2).

Figure 2-1 Initial view and main input screen (Source Geometry option box in upper left corner)

2.1.2 Source Geometry. The Source Geometry selection box is shown in the initial view 

“Varskin 5.0” screen in Figure 2-1. This screen contains all of the input information that is 

needed to perform a dose calculation. Although VARSKIN 5 allows the user to enter data in any 

order, the geometry package must be chosen first because changing the geometry package 

will cause certain parameters to appear and others to be removed. Five geometry packages 

are available: point source, disk source (infinitely thin), cylinder source (thick), spherical source, 

and slab source (rectangular).
4

Figure 2-2 “About Varskin 5.0” screen

The point source geometry (Figure 2-3(A)) is very simple to use 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 beta self-shielding, so a three-dimensional source 

geometry should be used for particulate contamination. The point source model does not 

require any data for the physical description of the source and will generally yield the highest 

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

VARSKIN 5 models a point source as a cylindrical source with a thickness of 1 μm, a radius of

1 μm, and a density of 0.001 grams per cubic centimeter (g/cm3

). The offset particle model is 

available only when using the point source geometry.
5

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 5 calculates 

the area of the 2D disk with that diameter. Similarly, when the user enters the area of the 

source, VARSKIN 5 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 

geometry to use for dose calculations because it requires knowledge of 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. 
6

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 two dimensions, the cylinder 

diameter and its height. The cylindrical source geometry assumes that 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 cylinder dimensions, 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 three physical dimensions: the 

first side length, the second side length, and the slab’s thickness. As evidenced by the previous 

VARSKIN Validation Test Plan and Report, results of beta dose calculations using the slab 

geometry differ by as much as 35 percent from the results obtained using the other four

geometries when modeling the same source. This discrepancy is the result of a fundamental 

difference between the mathematical approach used for the slab geometry and the other 

geometry packages when modeling similar sources. The slab geometry should be used only 

when skin dose from multiple, discrete particles is needed, as described in Section 6 (i.e., when 

the offset particle model is used).

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 the particle is known to be spherical (few particles are truly spherical) and is not 

imbedded in another material, 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 (height and radius) to describe the particle.

• If the particle is known to be rectangular, use the cylinder source geometry option. 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.
7

For all source geometries, doses are calculated to an infinitely thin disk centered below the 

central axis of the source. When using the offset particle model, 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 5 employs two radionuclide libraries,

a master library (supplied with the code) that contains data for all radionuclides available to the 

user, and a user library that contains only those radionuclides that are selected and added by 

the user (drawn from the master library). Beta energy emission spectra are obtained from an 

abridged ICRP–38 (International Commission on Radiological Protection, 1983) dataset using 

NUCDECAY (RSICC, 1995) data files.

When VARSKIN 5 is first executed, a few preselected radionuclides may appear in the user 

library. VARSKIN 5 is designed to allow the user to customize the radionuclide 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), and a new 

screen appears (Figure 2-4) that displays every radionuclide for which data are available (a total 

of 838 radionuclides). Radionuclides are added to the user library by highlighting the 

radionuclide and clicking the “Add Radionuclide” button, or simply double-clicking the name of 

the radionuclide. In building the user library, one can specify a minimum photon energy and 

minimum photon yield (photons per disintegration) to limit calculation times, if necessary. These 

defaults are set at 2 kiloelectronvolts (keV) and 1 percent, respectively. In addition to selecting 

the nuclide from the master library, the user must specify an effective atomic number (Zeff) to 

characterize the source material in which the source is incorporated. The default value for Zeff is 

7.42 (the effective atomic number of water). A total of 838 radionuclides are available in the 

master library, each of which 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). Computational speeds are generally not an issue; therefore, users are 

advised to use the default settings when building their library.

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 few 

seconds depending on processing power. In these calculations, data are extracted from the 

data files ICRP38.dat, ICRP38.idx, and ICRP.bet (all of which are located in the \dat 

subdirectory of the application directory). If the radionuclide emits beta radiation or 

conversion/Auger electrons, an electron energy spectrum is generated for all beta decay routes

and other electron emissions. Photon energy and yield data are then collected from the data 

files.

These data are processed by the FORTRAN executable file Sadcalc.exe, and an output file that 

contains the average beta spectrum energy, the electron and beta yield, the X99 distance, the 

scaled absorbed dose distribution, the photon energies, and the photon yields is generated with 

the extension “.dat.” As discussed in Section 3, the X99 distance is used as the range of the 

beta particles.
8

Figure 2-4 Add Radionuclide screen

When the process of adding the radionuclide is completed, the Source Geometry screen will 

return, and the added radionuclide will be visible in the user list of available radionuclides. 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.

In VARSKIN 5, radioactive progeny do not follow their parent in the dose calculations. To have

the code consider progeny, the user must create a user library file for each radioactive decay 

product. Radioactive decay products are not included, regardless of the half-life of the progeny. 

If evaluating dose from progeny alone, the user must be cautious and be aware of the half-lives 

of both parent and progeny 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. If the “Decay-Corrected

Dose” is used, the very short decay time of 137mBa will cause the dose to be significantly 

underestimated, assuming that 137mBa is continuously supplied by the decay of 137Cs.

2.1.4 Selecting Radionuclides from the User Library. Radionuclides can be selected for a

dose calculation by double-clicking the radionuclide name or by highlighting the desired 

radionuclide and clicking the “Select” button (Figure 2-1). The default unit of measure for 

activity is microcuries (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. A user may select up to 20 radionuclides for 

a given calculation.
9

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

appear (Figure 2-1). The distributed source option allows the user to enter the source strength 

in activity-per-unit-area for the disk sources or activity-per-unit-volume for volumetric sources. 

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. 

Beta energy emission spectra are obtained from an abridged ICRP–38 (International 

Commission on Radiological Protection, 1983) dataset using NUCDECAY (RSICC, 1995) data 

files.

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 VARSKIN 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 drop-down lists provided 

to the right of each input field. The units can be mixed for the different parameters; VARSKIN 5

makes the necessary conversions internally. Table 2-1 shows the default values for the various 

parameters.

2.1.6 Default State. VARSKIN 5 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 drop-down 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 (right)
10

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

source area. The units for the radius will be used when the area of the source is displayed. 

This feature simplifies data entry for two-dimensional sources where the area and the total 

activity are known.

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

for beta dosimetry. It is essential that these parameters are known accurately; otherwise, their 

values should be underestimated so that conservative dose calculations will result. If source 

dimensions are unknown, the following guidelines will help in choosing appropriate values:

• Diameter (disk and cylinder) and side lengths (slab): The dose calculation for most 

radionuclides is relatively insensitive with respect to these dimensions for sizes below 

2 millimeters (mm) with sources of the same activity. 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 beta dose calculation for all 

radionuclides is very sensitive to these dimensions, especially for low-energy beta 

emitters. Minimizing the value of this dimension will provide an overestimate of beta 

dose. For photons, these dimensions are not as critical for the dose calculation.

• Source density (three-dimensional geometry models): For beta dosimetry, users should 

choose a source density that is consistent with the material containing the source. For 

hot particle contaminations, a typical density for stellite (Co-60) is 8.3 g/cm3

, a density of 

14 g/cm3

, and an effective Z of 25.81 is typical for fuel. For photon dose estimates, the

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

sources and low-energy photons.
11

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 (@ 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 μm

Source Diameter (Sphere) 1 mm

Source Thickness (Slab) 1 μm

Source X-Side Length (Slab) 1 μm

Source Y-Side Length (Slab) 1 μm

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

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/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 (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
12

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 beta dosimetry. The air gap in photon dosimetry 

has the effect of disrupting 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 5 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): covert, cover density, and cover density thickness. The user can choose the units for 

density and thickness, but the 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 screen are then populated with the composite cover density (mg/cm3

) and thickness 

(in cm). If the user enters all the three parameters, VARSKIN 5 will indicate an error and ask the 

user to enter only two of the three parameters for a given layer. The print out from a dose 

calculation will include the data for each cover layer, as well as the composite cover data.

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 must calculate the 

composite cover thickness and density for the first five covers. The user must then run the 

calculator again and enter the first composite cover thickness and density as one of the layers. 
13

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

composite cover will not be individually displayed on the printout.

Figure 2-7 Composite cover calculator screen

2.2 Special Options

Depending on the geometry package selected, special options are available that affect the 

calculation. The first special option, available for all packages, is to include the photon dose in 

the calculation. The default for this option is to calculate the photon dose, which includes x-rays 

and gamma rays; the user can, however, de-select this box so the photon dose will not be 

calculated. If the photon dose option is included when the “Calculate Doses” button is clicked, 

the photon dose will be calculated for all selected radionuclides. If the radionuclide does not 

emit photons, a dose of zero will be displayed.

In most cases, the calculated photon skin dose will be negligible relative to the beta skin dose. 

A noteworthy exception to this is evident when modeling Co-60 or other low-energy beta 

emitters with significant photons. A cover material can easily shield low-energy beta particles 

without appreciably affecting photon dose. In this case, the photon dose will account for the 

majority of the calculated skin dose.

The second special option allows the calculation of dose to be averaged over a volume of tissue 

defined by a cylinder of specific diameter and thickness. The use of the volume-averaged dose 

calculation can be important, for example, in evaluating the dose between 10 mg/cm2 and 

15 mg/cm2

, as recommended by the International Commission on Radiological Protection 

(1991), for evaluating the dermal effects of skin dose.
14

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

button) to enter the skin density thicknesses associated with the boundaries (shallow and 

deeper tissue depths defining the cylindrical averaging volume). 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 beta particles associated with the selected 

radionuclide(s). Suggested values are from a skin density thickness of 0 mg/cm2 to the 

maximum penetration depth of the beta particle(s) being modeled; however, any nonnegative 

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

depths requested; some depths may result in negative values for beta dose. The VARSKIN 5

model calculates the average dose over the averaging area at 10 discrete depths between the 

shallow and deep tissue depths (Figure 2-8). Thus, the volume-averaged dose model requires

10 times more execution time than that for a single depth.

Figure 2-8 Schematic diagram of the volume-averaged dose model geometry

When the point source geometry is selected, the “Offset Particle Model” checkbox appears in 

the Special Options frame. 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 normally not accessed 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 dose area. The value of the offset is the only additional input value that is required for the 

model. The results screen (including the volume-averaged dose results screen) will display the 

offset value, if this option has been selected. Section 6.2 describes in more detail the use of the 

offset particle model.

2.2.1 Calculating Doses. Once the desired geometrical 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 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.
15

VARSKIN 5 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 the results of the calculation. Figure 2-9 depicts the logic flow diagram. 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 Screen. The Results screen for a non-volume-averaged calculation (Figure 2-

10) is displayed immediately after the dose calculation is completed. The screen 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 displayed by highlighting the radionuclide of 

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

the selected radionuclide. The combined results section displays 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 screen 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 screen contains a mirror of the input data entered in the Source 

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

the calculation. This section of the output screen also contains buttons that allow the user to 

perform certain functions. Clicking the “Print Results” button will send a hard copy of all results 

to the default Windows printer. VARSKIN 5 will not allow the user to change the default printer. 

Additionally, the program will fail if a printer is not installed when the “Print Results” button is 

selected. The user will be asked to supply a title for the printed output, and then the output file 

will be sent to the printer. VARSKIN 5 does not allow the user to save the output as a computer 

file; the only record of the calculation is the printout. However, the user may save the input data 

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

list. Selecting “Exit” from that dropdown list, which also gives the user the option to save the 

input, allows the user to end VARSKIN 5.
16

Figure 2-9 General logic flow diagram
17

Figure 2-10 Results screen for a typical calculation

A slightly different screen will appear for volume-averaged dose calculations (Figure 2-11). 

Because the dose can be averaged over different averaging volumes for different radionuclides, 

VARSKIN 5 does not provide a section for combined results of a volume-averaged dose

calculation. Instead, only the results from the highlighted radionuclide are displayed. The upper 

left section of the volume-averaged results screen 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 screen, this output screen contains unit-selection 

bubbles allowing the user to select volume-averaged dose results in English or SI units. Again, 

a summary of the input parameters is displayed on the lower half of the screen.
18

Figure 2-11 Results screen for a volume-averaged calculation

2.3 Exiting VARSKIN 5

The VARSKIN 5 code is exited from the main screen (Figure 2-1), either by clicking the “X” in 

the upper right corner or by selecting “Exit” from the File drop-down 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 screen. 

Data from a saved file are stored with a .vs3 extension. When a saved file is recalled (by 

selecting “Open” from the File drop-down menu), VARSKIN 5 reads the .vs3 to obtain the data 

for the calculation. These are internal files, not intended to be used or edited by the user.
19

3 DESCRIPTION OF DOSIMETRY MODELS

VARSKIN 5 includes enhancements to the beta and photon skin dosimetry models which this 

chapter describes in detail. In addition, improvements to models throughout the VARSKIN 

series are incorporated in VARSKIN 5 and are also described here.

3.1 Beta Dosimetry

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 Monte Carlo simulation, accuracy is often sacrificed. In one 

way or another, all DPK’s relate the dose at a given point to a radiation source at some other 

point in the same medium. The medium for which the DPK is defined is typically homogeneous 

water, as this allows for direct comparison with tissue. If the medium is not water, various 

scaling techniques (discussed in the sections that follow) 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 5.0 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 AY E F

Gy MeV dis D r

r X cm

cm

β β

β

β ξ β

π ρ

−        ⋅⋅⋅ ⋅                 =       ⋅ ⋅    



[3.1.1]

where Fβ(ξ) is the Berger (1971) scaled absorbed dose distribution. 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 with respect to the X90 distance. The distance r

is the physical distance between the source point and the dose point. Berger’s scaled absorbed 

dose distribution is based on Spencer’s (1955, 1959) energy dissipation distribution, as detailed 

below.

Spencer (1955) used the moments method to numerically solve the electron transport equation 

in the steady state. His calculations were based on the following assumptions: (1) the electrons 

are in a homogeneous medium, extending in all directions around the source to a distance 

greater than the electron range; (2) range straggling due to large single-energy losses occurring 

in both the radiative and inelastic collisions are neglected; and (3) the electrons lose their 

energy continuously until their kinetic energy is completely exhausted. The last assumption 

yields the following expression for the residual range, r0,

0

0

0

,

E

dE

r dE

dr

= ∫ [3.1.2]
20

where E is the kinetic energy of an electron as it slows down, E0 is the initial electron energy, 

and dE/dr is the average rate of energy loss, i.e., stopping power. Residual range was later 

called the ‘continuous slowing down approximation’ (CSDA) range.

Once the ‘residual range moments’ for electron flux, I0(r/r0), were determined, Spencer (1955) 

calculated the energy dissipation distribution, I(r), where r is the radial distance from an isotropic 

point-source at the center of a spherical volume. These two terms can be related using

0

0 0

0 0

1 ( ) ( / ).

r

dE I r dr I r r

r dr

  =     ∫ [3.1.3]

Equation [3.1.3] assumes that each electron contributing to the flux, I0(r/r0), at r/r0 dissipates 

energy at the average rate dE/dr per unit path length traversed. Spencer (1959) re-wrote the 

energy dissipation distribution such that it was a scaled, dimensionless function, J(μ),

0

0

( ) (, ) , ( /)E

I r J E

dE dr μ = [3.1.4]

where μ is the scaled distance of r/r0, (dE/dr)Eo is the stopping power at E0, and I(r)dr is the 

average energy per electron dissipated in the spherical shell between r and r+dr. Spencer 

(1959) tabulated J(μ,E0) for mono-energetic electron energies ranging from 0.025 to 10 MeV for 

scaled distance of μ at increments of 0.025μ up to 0.975μ. 

Berger (1971) used Spencer’s data to tabulate a ‘scaled absorbed-dose distribution’, F, for a 

number of radionuclides and monenergtic electrons in water. His tabulated kernels spanned 75 

common beta-emitting radionuclide and monenergetic electron energies ranging from 0.025 to 4 

MeV. Berger re-wrote Spencer’s dimensionless energy dissipation distribution as

0

2 0

0 0 (, ) 4 ( , ), ( /)E

E J μE r r E

dE dr = π Φ [3.1.5]

where Φ(r,E0) is the ‘specific absorbed fraction' and represents the fraction of energy deposited 

per gram at a distance r from a point-source. The quantity 4πρr2Φ(r, E0)dr is the fraction of 

emitted energy that is absorbed in a spherical shell of radius r, thickness dr, density ρ, and is 

normalized such that 

2

0

0

4 ( , ) 1. πρ r r E dr

∞

Φ = ∫ [3.1.6]

As with Spencer (1959), Berger (1971) used a scaled distance when tabulating his data. Rather 

than using the CSDA range, he used the radial distance at which 90% of the emitted electron 

energy was deposited, X90. His dimensionless scaled distance was written as ξ = r/X90. 

For mono-energetic electrons, Berger defined the relationship between the scaled absorbeddose distribution and the specific absorbed fraction as:
21

2 2

0 0 90 0 ( , ) 4 ( , ) 4 ( , ). dr F E r rE rX rE

d ξ πρ πρ ξ

=Φ = Φ [3.1.7]

When a distribution of electron energies is considered, the specific absorbed fraction is given by

max

0

1 ( ) (, ) ,

E

av

E N E x E dE

E

Φ = β ∫ Φ [3.1.8]

where

max

0

 () .

E

E E N E dE av = ∫ [3.1.9]

The scaled absorbed dose distribution is then

2 2

90 ( ) 4 ( ) 4 ( ), dr F r r rX r

d ββ β ξ πρ πρ ξ

=Φ = Φ [3.1.10]

where X90 is determined from the beta-particle energy distribution.

Berger estimated his tabulated F(ξ,E0) values to have an accuracy of 4% or better at distance r 

≤ 0.9X90 from the source. For r > 0.9X90, the results are expected to be less accurate and to 

underestimate the absorbed dose. Similar results were expected for Fβ(ξ) with an accuracy of 

4% or better at a distance r ≤ X90 from the source. 

In VARSKIN 4, Spencer’s energy dissipation distributions were coded into the SPENS function 

of SADCALC.f for a range of electron energies and radii. When called upon by the SADD 

subroutine, the SPENS function calculated the mono-energetic electron scaled absorbed dose 

distribution (F(ξ,E0)) using Spencer’s data with Eqs. [3.1.4] and [3.1.5]. The subroutine then 

used Eqs. [3.1.8] – [3.1.10] to calculate Fβ(ξ) for the beta-particle.

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

tabulation of increasingly accurate electron and beta dose-point kernels. Energy deposition 

measurements in spherical shells of water centered on an isotropic point-source provide the 

physical information needed to reproduce the moment-based kernels used in VARSKIN 4. The 

main advantage of Monte Carlo-based energy deposition kernels over moment-based kernels is 

the ability to account for energy-loss straggling and provide more accurate results for r > 0.9X90. 

VARSKIN 5 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 in the SPENS function.

The Monte Carlo transport code, EGSnrc, was used to determine the radial energy distributions 

(or DPK’s) and X90 values at electron energies of 0.01 MeV ≤ E ≤ 8 MeV (32 total energies). 
22

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 CSDA 

electron range, as taken from ESTAR 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 (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 

EGSnrc. In addition, the ESTAR CSDA range of a 0.01 MeV electron is only 0.252 mg cm-2

.

The EGSnrc simulations were performed using the EDKnrc user code. The NRC (National 

Research Council, Canada) user code EDKnrc can be used to calculate Energy Deposition 

Kernels (EDK) for photons or electrons (mono-energetic or polyenergtic) 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 (CPU) increases as well (Kawrakow and Rogers 2000). 

Electrons with energies below AE will not be transported and their energy will be 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 were re-tabulated with respect to ξ. These 

kernels were then read into SADCALC.f for use in the SADD subroutine and SPENS function. 

As stated previously, the main advantage of Monte Carlo-based 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 Monte Carlo-based (VARSKIN 5) methods (Figure 3-1 and 3-2). 
23

Figure 3-1. Scaled absorbed dose distributions for 0.1 MeV electrons in an infinite homogeneous 

water medium. VARSKIN 4.0 uses moment-based methods and VARSKIN 5.0 used Monte Carlobased methods.

Figure 3-2. Scaled absorbed dose distributions for 1.0 MeV electrons in an infinite homogeneous 

water medium. VARSKIN 4.0 uses moment-based methods and VARSKIN 5.0 used Monte Carlobased methods.

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 5) are positioned along the 

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
24

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 dose-averaging area, 

dose points represent concentric isodose circles that describe the radial dose profile at a given 

depth in skin. 

For each of the 60 dose points, a numerical integration is performed over the area of the 

cylindrical source at a given height in the source represented by 8 elevations (z), 8 radii (r’), and 

8 angular locations (θ). The dose rate at a dose point on an isodose circle of radius d’ is 

evaluated using 

2

0 00 ( ') ' ( , ', ) ' ,

R Z

D d S r B z r dz dr d v

π

= θ θ ∫ ∫∫ 

[3.1.11]

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

π

π = ∫ 

[3.1.12]

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 for the circle is considered to be 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).

. 
25

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 representation of the eight-panel quadrature routine used to calculate 

dose for a symmetric source (redrawn from Durham 2006).

3.1.3 Homogeneous Dose-Point Kernels. The Monte Carlo transport code, EGSnrc

(Ljungberg 2012), was used to determine the radial energy distributions (or DPK’s) 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 point-source 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 

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 (excluding radiativelosses). 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 MCNP can be useful to determine energy deposition kernels when 

the ITS energy indexing algorithm is used and when special care is taken for high-resolution 

measurements. 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 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.
26

Figure 3-4. Schematic of EGSnrc geometry for determining point-source radial DPK’s. 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.

Material selection covered a wide range of densities and atomic numbers.

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
27

Figure 3-5. Plot demonstrating the wide range of densities and atomic numbers used in 

development of the scaling model. All materials were solid in nature (except water).

EGSnrc simulations were performed using the EDKnrc user code. The NRC (National 

Research Council, Canada) user code EDKnrc can be used to calculate Energy Deposition 

Kernels (EDK) for photons or electrons (mono-energetic or polyenergtic) 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-Homogeneous Dose-Point Kernels. Non-homogeneous point-source DPK’s 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 

DPK’s is to determine how energy is deposited in water spherical shells 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 energy-scaling parameters for all energies 

between 0.01 and 8 MeV, it is possible to determine the non-homogeneous 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

Φ = β ρ ρ ∫ Φ [3.1.13]

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
28

where r is the DSP-adjusted spherical shell radius, Emax is the endpoint energy of the beta 

spectrum, N(E)dE is the fraction of beta-particles emitted per MeV per disintegration that have 

energies between E and E+dE, and 

max

0

 () .

E

E E N E dE av = ∫ [3.1.14]

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 DPK’s 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 will be 

based on complete beta-energy absorption in the source material and b will be based on 

complete beta-energy absorption in water when the source thickness is zero.

Non-homogeneous beta-particle DPK’s were determined by incorporating scaling equations into 

SADCALC. The SADCALC routine utilizes ICRP Publication 107 (2008) beta-particle spectra to 

calculate homogeneous water DPK’s for each beta-particle present in a given dose calculation. 

Linear interpolation was used to accommodate all source media with 7.42 ≤ Zeff ≤ 94. 

Non-homogeneous DPK’s were calculated for a wide range of beta 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 E� (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 beta-particle 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
29

3.2 Backscatter Model

A volumetric backscatter model has been developed for VARSKIN 5 to predict the dose 

perturbations from both source and atmospheric backscattering. The model is applicable for 

beta-emitting radionuclides in a spherical, cylindrical and slab source geometry, and for source 

materials with 7.42 < Zeff ≤ 94. Being based on the dose-point-kernel (DPK) concept, VARSKIN 

5 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 5. 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 beta DPK’s is the assumption of an infinite homogeneous 

medium. While scaling methods are used to account for the non-homogeneous media which 

transmit the beta-particles, an additional adjustment is required to correct for the lack of 

atmospheric scattering in the non-existent water medium. For example, when a DPK is applied 

to a point-source on an air-water interface, the isotropic nature of DPK’s assumes that betas 

emitted away from the source point have the ability to backscatter in an infinite homogeneous 

water medium and possibly contribute to the energy deposition at the dose point of interest. 

This scenario is of particular importance for hot particle skin dosimetry.

In developing the new beta dosimetry model for VARSKIN 5, 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 Statement No. 9 (2001), respectively. 

The scattering medium was assumed infinite (>> electron range) in both thickness and lateral 

extent. Pertinent details of EGSnrc can be found in Mangini (2012).

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 are often inversely reported such that they are 

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

be dependent on electron energy, backscattering medium Z, normal depth, and dose averaging 

area. 
30

When applied to a beta-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 Zz

D z E N E dE

β =

∫

∫

[3.2.1]

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 

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

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

for use in Eq. [3.2.1]. Once planar dose profile curve fits were determined, they were 

implemented into SADCALC. The ICRP 107 beta spectra were then used to calculate the betaparticle backscatter factor of Eq. [3.2.1]. 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 attenuation properties of air and water and their impact on the respective dose 

calculations. Therefore, a number of assumptions and estimations must be 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 > range of 

beta-particle), only source points positioned directly at the source-water interface (i.e., sourceskin 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.
31

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

[3.2.2]. 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 beta-particle source-water scattering correction for pointsources;

/ ( ), top bottom top bottom Source BSCF SW SE SE = − [3.2.2]

where SW is the beta-particle 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 beta-particle must traverse. 

Dose Region

Beta-Particle 

Range

Source Point

Figure 3-6. Schematic demonstrating conditions in which full source-water scattering corrections 

are applied. The dimensions of the source (orange) are greater than the range of the beta-particle.
32

Dose Region

Downward 

Scattering

Upward 

Scattering

Source Point Beta-Particle 

Range

Figure 3-7. Schematic demonstrating conditions in which partial source-water scattering 

corrections are applied. 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 in order 

to estimate source-scatter corrections for the sides of the source.

When the dimensions of the source are larger than the range of the beta, source points toward 

the center and the top-center of the source have minimal impact on dose. Therefore, sourcepoints on both sides and the bottom of the source become more important. It is 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 beta-particle needs to be considered when correcting for side 

scatter. Side scattering should only be accounted for when the beta-particle’s path is directed 

away from the source and travels through air prior to reaching the dose region. The assumption 

is that a beta-particle emitted in the 180 degree opposite direction would be permitted to 

backscatter off of 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 very 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 

very bottom corner of the source, the probability of backscattering event toward the dose region 

is much greater. 
33

It is estimated 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) in order 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 = − [3.2.3]

where SA is the beta-particle source-air scattering correction for point-sources (ratio of sourcewater to air-water correction factor), Xside is the normal distance to the side of the source that 

the beta travels through, 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 in terms of X/X90. If Xtop is 

greater than 0.5, 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 beta-particle decreases and the scattered path angle relative to the airwater interface increases, the probability of the scattered beta depositing energy in the dose 

area greatly decreases (Figure 3-8). Conversely, high-energy betas are expected to have a 

contribution extending to the very edge of the dose area when scattered beta-particles 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 beta backscatters 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 beta 

path length, is less than the beta-particle X90 distance. The latter limitation prevents the sidescatter correction from being applied to low-energy beta-particles, where this form of scatter is 

believed unlikely (as explained above). 

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 beta-particle must traverse.
34

High Energy 

Scattered Beta

Low Energy 

Source Scattered Beta

Dose Plane

Figure 3-8. Schematic illustrating beta 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 to determine the amount of side-scatter 

correction applied to high-energy beta-particles emitted from large sources.

The application of air-water interface scattering correction factors is more difficult 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. 
35

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 out of the top or sides of the source is equal 

to or greater than the range of the beta. The scattering effectiveness would be 100% and 0%, 

respectively. The assumption is that if a backscattered beta-particle 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 a beta-particle 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 dose at any depth.

The overall air BSCF is found using a weighted average. The BSCF’s are calculated for all 

surfaces for which the beta-particle 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 y-coordinate sides. The scattering reductions (for cylinders and spheres) are therefore 

given by

1.8

 0.5 , 1.8

top

top

X

Air BSCF AW − = [3.2.4]

1.8 0.25 , 1.8

side

side

X Air BSCF AW − = [3.2.5]

and

_

_

1.8

 0.25 , 1.8

op side

op side

X

Air BSCF AW − = [3.2.6]

where AW is beta-particle air-water scattering correction for point-sources, Xtop, Xside, and Xop_side

are the distances to the top and sides of the source in terms of X/X90. 

Unlike the source scattering corrections, no depth adjustments need to be made for materials 

traversed by the beta-particle prior to entering the dose region. This is due to the fact that 

corrections are being made for scattering events occurring outside the source. The distance to 

the air-water interface is considered negligible in terms of beta attenuation (assumed to be 

completely air). The overall air scattering correction is found by summing the three components 

above.
36

Figure 3-10. Schematic demonstrating conditions in which a full air-water scattering corrections 

are applied.

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 and a high 

goodness of fit (R2 > 0.999). As an example, a second-order Chebyshev is given by,

11 21 2 Z a bT x cT y dT x eT y fT y =+ + + + + ( ') ( ') ( ') ( ') ( '), [3.2.7]

where,

x x Normal Depth cm ' ln( ) ln( ( )) scaled -1 to +1, = =

y y E MeV ' ln( ( )) scaled -1 to +1, = =

( ') cos( * *cos( ')), Tx na x n =

and Z is the square root of the dose rate per particle (Gy Bq-1 s-1

).
37

Figure 3-11. Schematic demonstrating conditions in which air-water scattering corrections are 

applied. When the distance to the top and sides of the source are less than 1.8*X90, a partial airscattering correction is applied.

3.3 Scaling Models

The DPK scaling model consists of two parameters: a depth-scaling parameter (DSP) and an 

energy-scaling parameter (ESP).

3.3.1 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 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 ρ = − H NH [3.3.1]

where X99_H is the homogeneous electron range, X99_NH is the non-homogeneous electron 

range, ρ and Z are the absorption material density and atomic number, respectively.

As an example, consider an iron spherical source (r = 0.0222 cm, Z = 26, ρ=7.874 g cm-3

) and 

an electron energy of 1 MeV. The radius of the iron sphere was chosen to be 0.5X90 to allow for 

sufficient electron self-absorption. Due to the presence of the 0.0222 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 0.0222 cm of iron, the depth-scaling parameter 
38

will be 0.120 cm. Shifting the homogeneous DPK data to the left by this amount will equate the 

ranges and provide the necessary depth adjustment (Figure 3-13).

Figure 3-12. Comparison of 1 MeV electron DPK’s for the homogeneous water case and the case 

when the electron traverses iron source material of thickness 0.0222 cm.

Figure 3-13. Example of depth scaling on the homogeneous DPK curve. The depth-scaling 

parameter was determined to be 0.120 cm.

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
39

When plotted together, the variability with respect to Z is difficult to discern as they all follow the 

same curvature with little separation (Figure 3-14). The variation in DSP’s 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 DSP’s took the form of

2 3

2 3

( ) ( ( )) , (1 )a bx cx dx ey LN DSP cm

fx gx hx iy

++ + + = ++ + +

[3.3.2]

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. [3.3.2] 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. TableCurve 3D plot of depth-scaling data for all source materials used in scaling 

model.

3.3.2 Energy Scaling. The energy-scaling parameter 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 

-5

-4

-3

-2

-1

0

1

2

LN(E (MeV))

-15

-10

-5

0

LN(Xx*ρx (g cm-2))

-15 -15

-10 -10

-5 -5

0 0

5 5

LN(DSP (cm))

LN(DSP (cm))

Depth Scaling for All Materials
40

(Figure 3-13), the total energy deposition is found for each case. This is performed by summing 

the homogeneous DPK’s for radii between the depth-scaling parameter and the X99 distance,

99

2

0 4 (, ) .

X

total

DSP

πρ r r E dr E Φ = ∫ [3.3.3]

Similarly, the total energy deposition in the non-homogeneous case is found by summing DPK’s 

from 0 to X99. The law of energy conservation requires the two be equal. Therefore, the energyscaling parameter is found by taking the ratio of the non-homogeneous total to the 

homogeneous total,

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

πρ

ρ

πρ

Φ

=

Φ

∫

∫

[3.3.4]

Applying the resulting ratio to the homogeneous DPK equates the total energy depositions in 

the two geometries. For the example, an energy-scaling parameter of 0.887 is computed. 

Thus, energy conservation is achieved by multiplying the homogeneous curve by the energyscaling parameter of 0.887 (Fig 3.3.4).

Figure 3-15. Example of energy scaling on the homogeneous DPK curve presented in Figure 3-14.

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 absorption0

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
41

sphere 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 

of ESP*E0 has no physical meaning, using it as the dependent variable produced tighter fitting 

surface plots than simply using ESP. Since E0 is a known quantity, solving for ESP is simple.

The variability of the ESP curves (Figure 3-16) with respect to Z is more pronounced than the 

DSP curves. The variation of ESP’s 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 ESP’s took the form:

23 2

2 2

( ) ( * ( )) (1 )

a bx cx dx ey fy LN E ESP MeV

gx hx iy jy

++ + ++ = + + ++

[3.3.5]

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 DSP’s, fit 

parameters demonstrated a slight Z dependence.

Figure 3-16. TableCurve 3D plot of energy-scaling data for all source materials in scaling model.

-5

-4

-3

-2

-1

0

1

2

LN(E (MeV))

2

1.75

1.5

1.25

1

0.75

0.5

0.25

Xx*ρx/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
42

Integration of scaling parameters over a particular beta spectrum provides the nonhomogeneous DPK for a given source thickness. Comparisons with EGSnrc non-homogeneous 

DPKs demonstrated excellent agreement over a range of beta-particle energies and high-Z

source materials by producing nearly identical DPK’s 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 DPK’s at each mono-energetic 

electron energy of a given beta-particle spectrum.

3.4 Cover Layer and Air Gap Models

Cover materials and air gaps can be modeled using VARSKIN. The models use the concept of 

effective path length to determine the beta 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 beta particle; it is merely a 

mathematical convenience introduced to provide a measure of the energy lost in each layer. To 

prevent unintended applications of VARSKIN, the air gap is limited to a maximum of 5 cm.

Figure 3-17 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).

Figure 3-17 Schematic of a generic dose calculation performed by

VARSKIN 4 for the cylinder geometry

The quadrature routines are coded to choose values for SRAD; the distance from the centerline to 

the Ps source point; θ, 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. 
43

To do this, the square of the projected distance, rp

2

, is calculated using the law of cosines:

rp

2 = Ps2 + Srad

2 − 2PsSradcosθ [3.4.1]

The quantity r is used in the denominator of the expression in Eq. [3.1.1] 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 � � [3.4.2]

The distance traveled through the skin is given by:

rt = Sdep ∙ �r

Drad � � [3.4.3]

Finally, the distance traveled through the source is given by:

rs = �Drad − Cthick − Sdep� ∙ �r

Drad � � [3.4.4]

For beta dosimetry, the modified path length r1 is then found using the following equation:

r1 = (rsρs+rcρc+rtρt)

ρt

[3.4.5]

where ρt is the density of tissue, 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 sources and pass through air before 

passing into skin). Thus, the quantity in Eq. [3.4.5] 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.
44

In spherical geometry, the physical distance from source point to dose point is given by:

rp

2 = Ps2 + Srad

2 sin2φ − 2PsSradsinφcosθ [3.4.6]

In slab geometry, the physical distance is given by:

r = �[(Xsource − Xdose)2 + (Ysource − Ydose)2 + (Zsource − Zdose)2] [3.4.7]

3.5 Volume-Averaged Dose Model

The volume-averaged dose model (shown schematically in Figure 2-8) allows the calculation of 

dose averaged over a given tissue volume. 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 beta particles is equal to the X99 distance. Doses averaged over the dose-averaging area 

are calculated at 10 skin depths between two limits set by the user, and a cubic spline (a thirdorder 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 integrates the depth 

dose function over the region of interest to obtain the volume-averaged dose.

3.6 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 the point-source geometry. It requires only one input variable, the distance of the offset. For 

multiple particle irradiations, the dose from each particle must be calculated separately, with the 

user running VARSKIN once for each particle. 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.

3.7 Adding Radionuclides to the VARSKIN 5 Library

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 

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 

beta and photon doses. In addition to selecting the nuclide from the master library, the user 

must specify an effective atomic number (Zeff) to characterize the source material in which the 

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

In VARSKIN, beta energy spectra are obtained from the data file ICRP38.BET, which is 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 defined in the file ENERGY.DAT (also located 

in the \dat subdirectory). The beta yield for the radionuclide is determined by summing each of 
45

the values in ICRP.DAT. A file that is associated with the beta spectrum is ICRP.IDX, an index 

file (also located in the \dat subdirectory) used to quickly locate data in the large ICRP.DAT file. 

Also included in ICRP.DAT is information on any internal conversion or Auger electrons emitted 

by the radionuclide. The GUI collects the beta spectrum for a selected radionuclide and writes a 

file entitled 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 any electrons to the beta spectrum to form a new spectrum 

that includes internal conversion and Auger electrons; calculates,, the distance, and ; and then 

writes these data to the file sadout.dat. The GUI reads sadout.dat, adds the photon data, and 

writes the library file with the extension .rad. The user enters the name of the file when 

prompted by the GUI. Note that sadout.dat and sadinput.dat are internal files and are not 

intended to be used or modified by the user.

A total of 838 radionuclides are available in the master library, each of which 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 of the 838 

radionuclides emit beta particles, 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.

3.8 Photon Dosimetry

The photon dose model first implemented in VARSKIN 4 and unchanged in VARSKIN 5, is an 

improvement to the basic photon model used in VARSKIN 3. The photon model uses a point 

kernel method that considers the buildup of CPE, transient CPE, photon attenuation, and offaxis 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 surface of skin 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 cm2 is appropriate for skin dosimetry (specifically at the shallow-dose 

equivalent depth of 0.007 cm in tissue (i.e., 7 mg/cm2 in unit density material)). Skin dosimetry 

also involves the calculation or determination of the lens-dose equivalent (at a depth of 0.3 cm) 

and the deep-dose equivalent (at a depth of 1 cm) in tissue. 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,
46

D(E) = Φ0 ∙ E ∙ �

μen

ρ �

tissue

[3.8.1]

where �

μen

ρ �

tissue

is the energy-dependent mass energy absorption coefficient for tissue. With 

this calculation of dose, we essentially assume that the 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 [3.8.2]

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, given that,

Dose �

Gy

nt� = k� J∙g

MeV∙kg�

4πd2[cm2] ∙ ∑ �yi �

photon

nt � ∙ Ei � MeVphoton� ∙ �

μen

ρ �

i,tissue

�

cm2

g i �� [3.8.3]

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. [3.8.3] 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 the factor where μ 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 numerical value of μ (in units of cm-1) is identical to the numerical value of 

μ/ρ (in units of cm2

/g).

To simplify software coding, analytical expressions are used in VARSKIN 5 (as opposed to 

using “look-up tables”) for a number of dosimetry parameters. An empirical relationship to 

estimate μ/ρ for tissue as a function of incident photon energy (in megaelectronvolts (MeV)) was 

developed and is given below. For energies less than or equal to 20 keV,

μ

ρ

(E) = 1

0.0000145+3810E2.5+134400E3, [3.8.4]

and for energies from 20 keV to 3 MeV,

μ

ρ

(E) = e

�−3.22−0.11(lnE)2+0.5566√E−0.7713lnE+�0.000721

E

� 2��

. [3.8.5]
47

Figure 3-18 shows a comparison between the ICRU 44 (1989) values of μ/ρ for soft tissue and

the functions of Eqs. [3.8.4] and [3.8.5].

Figure 3-18. ICRU 44 soft tissue mass attenuation coefficients

compared to the empirical functions

The function of Eq. [3.8.6] was also developed as part of the VARSKIN 4 enhancements to 

approximate the energy-dependent value of μen/ρ 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 , [3.8.6]

has a different set of coefficients for energies less than or equal to 30 keV and energies from

30 keV to 3 MeV. Table 3-4 provides the coefficients and Figure 3-19 gives the fit of Eq. [3.8.6] 

to the ICRU 44 (1989) data.

Table 3-4. Coefficients for Eq. [3.8.6]

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
48

Figure 3-19 ICRU 44 soft tissue mass energy absorption coefficients compared 

to the functions of Eqs. [3.8.5] and [3.8.6]

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, 

the CPE as a function of depth must be determined. The VARSKIN determination of CPE is 

based on Monte Carlo simulations and the difference between energy released (KERMA) and 

energy absorbed (dose).

Since energy transfer (KERMA) from photons and energy absorption (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 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 (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� [3.8.7]

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 
49

increases over about 1 MeV, this assumption of dose and KERMA equality begins to fail, but not 

so significantly that it affects deep-dose estimations appreciably. Based on experience with the 

Monte Carlo simulation of shallow and deep depths, the model used in VARSKIN 4 limits the 

value of fcpe to 1.05 (i.e., it allows dose to exceed KERMA by a maximum of 5 percent at 

depth).

A function for fcpe that is dependent on initial photon energy is given as,

fcpe(x) = 1

a+bln(x)+c

√x � , [3.8.8]

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 E1.5 + 0.00003624 E2 + 3.343 √ElnE − 10.72 E

lnE � [3.8.9]

b = 1.217x10−12E4 − 5.673x10−9E3 + 7.942x10−6E2 − 0.002028E + 0.3296 [3.8.10]

c = 9.694x10−13E4 − 4.861x10−9E3 + 7.765x10−6E2 − 0.001856E + 0.1467 [3.8.11]

The fcpe factor is used for all materials; any buildup in air or thin covers is expected to be 

insignificant as compared to tissue.

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 θ2.5 − 0.0000325 θ3)(0.93 + 0.1R), [3.8.12]

where R is the radius of the dose-averaging disk and θ is the off-axis scatter angle (in degrees). 

Figure 3-20 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. [3.8.12] and is not phenomenologically significant.
50

Figure 3-20. Off-axis correction factor as a function of off-axis angle and

dose-averaging area. Averaging disks of 0.1, 1, 5, and 10 cm2 are shown.

Fully accounting for charged particle buildup and attenuation, Eq. [3.8.3] now becomes:

Dose �

Gy

nt � = k4πd2 ∙ ∑ �yi ∙ Ei ∙ �

μen

ρ �

i,tissue

∙ �fcpe�

i ∙ (Foa)i ∙ e−μid� i . [3.8.13]

As stated above, Federal law requires the determination of average dose to skin over an 

averaging area (e.g., 10 cm2

) at some depth in tissue (e.g., 7 mg/cm2). To determine average 

dose at depth from a source at the surface, we must integrate Eq. [3.8.13] over the averaging 

area. Integrating the exponential, however, results in a solution with imaginary components. 

Therefore, a stepwise numerical integration of Eq. [3.8.13] 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.

The authors conducted convergence studies to determine which numerical integration method 

achieved convergence most rapidly for photon dosimetry (i.e., dividing the dose-averaging disk 

into the fewest number of segments). The studies investigated three segmenting methods (see 

Figure 3-21): (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.
51

Figure 3-21. Depiction of methods for determining integration

segments of the dose-averaging 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 3-22 shows that

convergence was achieved within about 300 iterations for equal lengths along the radius of a 

10-cm2 averaging disk; the VARSKIN 4 numerical integration, therefore, utilizes 300 segments 

along the radius/diameter. Convergence was achieved with fewer segments when analyzing a 

smaller averaging disk.

Figure 3-22. Relative dose as a function of the number of segments in

a numerical integration (iterations), by method

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
52

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 [3.8.14]

and

Rj = ∑ (j ∙ ∆r) N

j=0 . [3.8.15]

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 area of the annulus created by, and 

, 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−1 2

R2 , [3.8.16]

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 . [3.8.17]

Once all values of 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 , [3.8.18]

where dj = ��h2 + rj

2�.

3.9 Attenuation Coefficients for Cover Materials

For photon dose calculations, the cover materials (and associated attenuation coefficients) are

“forced” to be either latex or cotton. This determination is made by the density entry, i.e., if the 

density is less than 1.25 g/cm3

, then latex is assumed, if greater, cotton is assumed. These are 

the two most likely materials used for cover. It is noted that the cover attenuation is minor and 

this decision should be insignificant for the dose calculation.

An empirical function of energy was used for attenuation coefficients for cotton and latex, 

namely:

μcotton/latex = e(a+b√E∙ln(E)+c√E) [3.9.1]
53

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. 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 [3.9.2]

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.

3.10 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 (Figure 3-23).

Figure 3-23. 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. 3.10.2 and 3.10.3) and the case where the point source is 

completely removed from the dose-averaging disk (Figs. 3.10.4 and 3.10.5). 

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 
54

determined by a weighting of doses calculated along the diameter. The calculation begins by 

projecting the dose point to the averaging disk, normal to the skin surface (see Figure 3-24).

Figure 3-24. 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 (Figure 3-25). 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 

(Figure 3-26). 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.

Figure 3-25. Dose-averaging disk with the source point located off axis, yet

still over the averaging disk
55

The weight (fractional area) of each annulus to the total is straightforward, in that,

wi = π�ri

2−ri+12 �

πR2 = ri

2−ri+12

R2 . [3.10.1]

The weight of each arc is determined by a method considering intersecting circles. In the case 

of Figure 3-26, the area of the “lens” created by the two intersecting circles is given by:

Ai = r2cos−1 �

d2+r2−R2

2dr � + R2cos−1 �

d2+R2−r2

2dR �

− 1

2 �(−d + r + R)(d + r − R)(d − r + R)(d + r + R). [3.10.2]

Figure 3-26. Relationship between the source-averaging disk and one of the radii

for dose calculation. A “lens” is created by the intersection of the two circles.

The area of the arc formed (Figure 3-26) 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. [3.10.1]. 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 

(Figure 3-27), 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 15 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).

Dose-averaging 

Source

radii
56

The new VARSKIN 4 photon dosimetry model accounts for attenuation in cover materials and 

air. As with the beta 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 other material 

layers are restricted to cotton and/or latex, 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).

Figure 3-27. Dose-averaging disk from above with the source

point located off axis, far enough removed to be off the averaging 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 between 10 keV and 3 MeV. 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 (e.g., energies less than about 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. The analysis of attenuation also shows that the 

assumption of air and water (tissue) being similar, in terms of attenuation, over very short 

distances (i.e., less than 5 mm) is a good assumption.
57

4 VALIDATION AND VERIFICATION

To validate the new photon and beta dosimetry models incorporated into VARSKIN, results

were compared to the general purpose radiation transport codes, MCNP5 and EGSnrc. The 

two software packages are Monte Carlo transport codes which simulate movement and 

interaction of particles in material (Los Alamos National Laboratory, 2003; Ljungberg et al. 

2012).

4.1 Comparison with A General Monte Carlo N-Particle Transport Code (MCNP)

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 Figure 4-1, involves an infinite volume of air located above 

an infinite volume of tissue. Composition of these materials was taken from National Institute of 

Standards and Technology standards for each material. Each of the sources was situated 1 μm 

above the skin and above the perpendicular bisect of the volume of tissue over which the dose 

is calculated.

Figure 4-1. Horizontal (left) and vertical (right) cross-sectional views of the

MCNP5 geometry

As illustrated in Figure 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 doses to the skin, lens of the eye, and the deep 

dose, respectively. Although the value of 100 mg/cm2 does not correspond to a 

regulatorsignificant density thickness, results at that depth are provided as an indication of 

accuracy at an intermediate, yet shallow, depth.
58

Figure 4-2. Illustration of the point source geometry of the tissue volumes of interest at various

density thicknesses in tissue

At each density thickness, the dose to two volumes of tissue, 2x10-3 cm3 and 2x10-2 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 for use 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 percent, 

with the majority producing an error of approximately 3 percent. Dose rate was calculated for a

simulated source strength of 1 μCi, with a yield of 100 percent at a given energy ranging from 

25 keV to 3 MeV. While this is not specific to any particular nuclide, it demonstrates the energy 

dependence of each methodology and also shows which current models are accurate predictors 

(as compared to MCNP5/EGSnrc) and which are not.

Appendix A provides results for beta dosimetry comparisons, with Appendix B providing similar 

results, but for photon dosimetry. The appendices are arranged as follows.

7 mg cm-2

100 mg cm-2

300 mg cm-2

1000 mg cm-2

20 μm

Air

Tissue

Point Source

10 cm

2

1 cm

2
59

For beta 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 

beta 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 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 electron energy were compared with MCNP5 results at depths of 7, 100, 300, and 1000 

mg/cm2 for each of the geometries considered. VARSKIN is shown to be a very good predictor 

at various tissue depths when the point- and disk-source geometries are modeled. VARSKIN 

consistently overpredicts dose (compared to MCNP5) in the cylindrical, slab, and spherical 

geometries at energies greater than about 200 keV.

4.2 Shallow Dose Comparisons

VARSKIN 4 was released after an enhancement to the photon dosimetry model (without 

changes to the beta dosimetry model), and VARSKIN 5 includes enhancements to the beta 

dosimetry model (without photon dosimetry changes). Comparisons of dose calculated using 

VARSKIN 3.1, 4 and 5 are given below to demonstrate how the three versions differ in dose 

estimation for the few scenarios considered.

4.2.1 Point Source on the Skin. In this test, calculations were completed 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 1-μCi hot particle and a 1-hour exposure time, the beta 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 beta 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.
60

Table 4-1. Comparison between Beta and Photon Shallow Dose Calculations from

VARSKIN 3.1, 4, and 5 for a 1-μCi Point Source of Co-60 Exposing the Skin for 1 Hr

Nuclide V3.1

β Dose

(mGy)

V4

β Dose

(mGy)

V5

β Dose

(mGy)

V3.1

γ Dose

(mGy)

V4

γ Dose

(mGy)

V5

γ Dose

(mGy)

Co-60 37.6 37.6 34.5 3.29 0.79 0.79

4.2.2 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 1-μCi point source and an exposure time of 1 hour were assumed with no air gap 

between the layers of cover material. Doses were calculated for a 1-cm2 averaging disk. Table 

4-2 shows the results of this calculation. Changes to beta dosimetry are shown to either 

increase or decrease, due to model enhancements that impact particle track lengths, energy 

loss, backscatter characteristics, conversion electron consideration, etc. Photon dose at 

shallow depths for the scenario considered decreases by about a factor 2 after model 

enhancement, again, primarily due to the consideration of charged particle buildup and photon 

attenuation.
61

Table 4-2. Comparison between VARSKIN 3.1, 4 and 5 of the Shallow Dose 

for Various Cover Material Configurations

Nuclide

Air 

Gap

(cm)

Cover

Material

V3.1

β Dose

(mGy)

V4

β Dose

(mGy)

V5

β Dose

(mGy)

V3.1

γ Dose

(mGy)

V4

γ Dose

(mGy)

V5

γ Dose

(mGy)

Co-60 0.2 M1 1.96 1.96 1.69 0.571 0.292 0.292

Cs-137/

Ba-137m

0.2 M1 14.0 14.0 12.1 0.199 0.0969 0.0969

Sr/Y-90 0.2 M1 32.6 32.6 27.0 0 0 0

Co-60 0.2 M1 + M1 0 0 0.0643 0.558 0.258 0.258

Cs-137/ 

Ba-137m

0.2 M1 + M1 4.75 4.75 5.91 0.181 0.0842 0.0842

Sr/Y-90 0.2 M1 + M1 20.7 20.7 18.6 0 0 0

Co-60 1.0 M1 0.813 0.813 0.634 0.0797 0.0429 0.0429

Cs-137/ 

Ba-137m

1.0 M1 2.79 2.79 2.25 0.0277 0.0129 0.0129

Sr/Y-90 1.0 M1 5.37 5.37 4.35 0 0 0

Co-60 1.0 M1 + M1 0 0 0.0335 0.0836 0.0404 0.0404

Cs-137/ 

Ba-137m

1.0 M1 + M1 1.40 1.40 1.35 0.0270 0.0121 0.0121

Sr/Y-90 1.0 M1 + M1 3.95 3.95 3.42 0 0 0

Co-60 1.0 M1 + M2 0 0 0.00704 0.0876 0.0400 0.0400

Cs-137/ 

Ba-137m

1.0 M1 + M2 0.770 0.770 0.939 0.0271 0.0120 0.0120

Sr/Y-90 1.0 M1 + M2 3.26 3.26 2.96 0 0 0

Co-60 5.0 M1 + M2 0 0 0.00038 0.00453 0.00205 0.00205

Cs-137/ 

Ba-137m

5.0 M1 + M2 0.0384 0.0384 0.0476 0.00138 0.00061 0.00061

Sr/Y-90 5.0 M1 + M2 0.167 0.167 0.151 0 0 0

M1—Cover material = thickness of 0.37 mm, density of 0.70 g/cm3.

M2—Cover material = thickness of 0.40 mm, density of 1.1 g/cm3

.
62

4.2.3 Distributed Beta Contamination on Skin. 

Calculations were performed for the same three nuclides using VARSKIN 3.1, 4 and 5 to 

compare specifically the beta dose estimate for a distributed disk source on the skin over an 

exposure period of 1 hour (Table 4-3). The beta dose at a depth of 7 mg/cm2 was calculated for 

a simulated contamination scenario with a concentration of 1 μCi/cm2 distributed over a circular 

area of 100 cm2

. A dose-averaging area of 1 cm2 was assumed. The results were compared to 

values published by Rohloff and Heinzelmann (1986) and by Kocher and Eckerman (1987). 

The results from VARSKIN and published values are somewhat different than expected, 

however, comparisons with Monte Carlo simulation (Appendix B) are shown to be quite good.

Additional comparisons were made for shallow beta dosimetry assuming a 1-hour exposure 

from a source modeled as an infinitely thin, uniformly contaminated (1 μCi/cm2

) two-dimensional 

disk with a diameter of 2 cm. Doses were calculated at different depths in the skin and 

compared to similar values in the literature. Tables 4-4 and 4-5 show that the results are in fair

agreement, although the VARSKIN results are lower than the published values.

Table 4-3. Comparison between VARSKIN 3.1, 4 and 5 of the

Beta Dose (mGy) for a 1-hr Exposure to Distributed Contamination on the Skin

Nuclide V3.1 V4 V5 Rohloff et al.

(1986)

Kocher et al.

(1987)

Co-60 37.7 37.7 34.5 32.4 41.8

Cs-137 51.2 51.2 47.6 - 59.1

Sr/Y-90 123.4 123.4 104.2 121 156

Table 4-4. Dose (mGy) for Various 1 μCi/cm2 Distributed Disk Sources and a 1-hr 

Exposure Time (dose calculated at a depth of 7 mg/cm2 and averaged over 1 cm2

)

Method C-14 P-32 I-131 Sr-90 Y-90

VARSKIN 3.1 11.2 66.3 52.5 54.7 68.2

VARSKIN 4 11.2 66.3 52.5 54.7 68.2

VARSKIN 5 11.1 58.6 48.4 49.7 59.4

Delacroix (1986) 10.7 91.5 64.2 69.9 91.8

Kocher and Eckerman (1987) 12.2 88.7 63.4 67.6 88.7

Piechowski (1988) 12 70 60 59 75

Table 4-5. Dose (mGy) vs. Depth for a 1 μCi/cm2 Distributed Disk Source of Y-90 and a 

1-hr Exposure Time (dose averaged over 1 cm2

)

Method 4 mg/cm2 7 mg/cm2 10 mg/cm2 40 mg/cm2

VARSKIN 3.1 79.0 68.2 61.4 40.7

VARSKIN 4 79.0 68.2 61.4 40.7

VARSKIN 5 65.7 59.4 55.3 38.2

Delacroix (1986) 104.6 91.8 83.7 52.4

Kocher and Eckerman (1987) 101.4 88.7 — 50.7
63

5 VARSKIN LIMITATIONS

VARSKIN calculates skin dose to an infinitely thin disk at depth in tissue for comparison to the 

NRC limit of 0.5 gray (Gy) for both point and distributed sources (NRC, 2006). VARSKIN can 

calculate the dose to averaging areas from a minimum of 0.01 cm2 to 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 and establishes the limits over which the code has been tested.

The first item of note is not a limitation, but a code design decision, and involves the treatment 

of radioactive progeny. In VARSKIN, radioactive progeny are not included with the parent 

radionuclide and must be entered explicitly, i.e., selecting 137Cs gives you only that nuclide, 

137mBa is not included unless it is specifically called. The user is additionally cautioned to 

consider the half-life of the progeny when selecting the appropriate dose contribution (decaycorrected or not) from daughter products. As an example, for the case of 144Ce and its 

daughter, 144Pr (with a short half-life), the dose result from the daughter product must be taken 

from the non-decay corrected calculation. If the user takes the decay-corrected dose in this 

case, the dose would be significantly underestimated. The limitation that must be recognized by 

the user in this case is that VARSKIN uses the decay characteristics of each nuclide, whether 

that nuclide is in secular equilibrium with a parent, or not.

Dose calculations involving air gaps greater than 5 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 and can lead to 

inaccurate results. VARSKIN is limited such that calculations for air gaps greater than 5 cm are 

not possible and a warning message is displayed.

VARSKIN 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 Beta Dosimetry

VARSKIN 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 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. 
64

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 prompts the user with a warning of the potential for inaccurate results. The 

X99 distance is included on the printout of a calculation to assist the user in determining the 

appropriateness of input source dimensions.

The VARSKIN 5 V&V results indicate discrepancies between VARSKIN 5 and EGSnrc for beta 

dosimetry on scenarios involving volumetric sources and intermediate electron energies. 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 point-sources to a 

certain degree). These larger deviations are apparent at the tail end of the beta-dose profiles,

as well (Mangini, 2012). Either way, it is clear from these results that the accuracy of 

VARSKIN5 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.

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 

percent error less than 5%. Simulations with a greater error were eliminated with a dose 

contribution of zero. However, once the curve fits in SADCALC 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%. The VARSKIN 5 code 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 model will be rather inaccurate for dose calculations at the end of the electron range.
65

5.2 Photon Dosimetry

The photon dosimetry model assumes that all volume sources are made of air. This 

assumption results in greater accuracy when modeling larger, less dense sources (a gas cloud, 

for example). However, when modeling volumetric sources of greater density, VARSKIN 4 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. Care should 

be exercised when modeling large-volume sources.

67

6 SPECIAL TOPICS FOR ACCURATE USE OF VARSKIN

VARSKIN 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 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, 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 accordingly.

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 default value 

for the density of air (0.001293 g/cm3

) is appropriate. If no cover material is specified, using 

tissue density 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 ρs is the source density.

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

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 
68

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 no overlapping 

fields are associated with them. For contaminated areas with overlapping fields, the doses and 

their relative positions should then be plotted on a sheet of graph paper, leaving plenty of room 

between the sources for results from additional calculations.

Next, calculations using the offset particle model should be performed for locations midway 

between any two contaminated areas. For more than two sources that are not in a straight line, 

a central location should be chosen, and the dose at this point should be calculated using the 

offset particle model. Thus, for three contaminated areas in a triangular formation, a total of four 

calculations should be performed. The value of the offset should be chosen to be one-half of 

the distance between any two sources, with one additional dose calculation performed in the 

center of the triangle.

After these calculations have been performed, it is left to the user’s 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. An accuracy of greater than 20 percent should not be anticipated.
69

7 REFERENCES

Attix, F.H. Introduction to Radiological Physics and Radiation Dosimetry. New York, NY: John 

Wiley & Sons. 1986.

Berger, M.J. “Distribution of Absorbed Dose Around Point Sources of Electrons and Beta 

Particles in Water and Other Media.” Medical Internal Radiation Dose Committee, Pamphlet 

No. 7. Journal of Nuclear Medicine. Vol. 12, Supplement No. 5. pp. 5–22. 1971.

Berger, M.J., J.S. Coursey, M.A. Zucker, and J. Change. “Stopping-Power and Range Tables 

for Electrons, Protons, and Helium Ions.” ESTAR, PSTAR, and ASTAR databases. 

Washington, DC: National Institute of Standards and Technology. 

<http://physics.nist.gov/PhysRefData/Star/Text/contents.html> (February 14, 2006).

Cross, W.G., N.O. Freedman, and P.Y. Wong. “Tables of Beta-Ray Dose Distributions in 

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Delacroix, D. “Beta Particle and Electron Absorbed Dose Calculations for Skin Surface 

Contaminations” (in French). DCES/SPR/SRI/86–656. Paris, France: Commissariat à 

l’Energie Atomique. 1986.

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APPENDIX A

Supporting Figures from Section 5

A-1

GEOMETRY 1:

POINT SOURCE

Figure A.1.1. 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 μm thick tissue volume cylinder of area 1 cm2 (solid line) and 10 cm2 (dashed line).

Figure A.1.2. 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 μm 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

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
A-2

Figure A.1.3. 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 μm thick tissue volume cylinder of area 1 cm2 (solid line) and 10 cm2 (dashed line).

Figure A.1.4. 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 μm 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

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

2000 2200 2400 2600 2800 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

1000 mg/cm2
A-3

Figure A.1.5. 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 μm

Figure A.1.6. 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 μm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1.00E-08

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
A-4

Figure A.1.7. 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 μm

Figure A.1.8. 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 μm

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

1.00E-08

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

138Cs
A-5

GEOMETRY 2:

DISK SOURCE (0.5 mm dia)

Figure A.2.1. 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 μm

Figure A.2.2. 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 

μm

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
A-6

Figure A.2.3. 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 

μm

Figure A.2.4. 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 

μm

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

1.00E-09

2000 2200 2400 2600 2800 3000 3200

Electron Dose (Gy/electron)

Electron Energy (keV)

1000 mg/cm^2
A-7

Figure A.2.5. 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 μm

Figure A.2.6. 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 μm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1.00E-08

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
A-8

Figure A.2.7. 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 μm

Figure A.2.8. 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 μm

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

1.00E-08

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

138Cs
A-9

GEOMETRY 3:

DISK SOURCE (1 mm dia)

Figure A.3.1. 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 μm

Figure A.3.2. 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 

μm

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
A-10

Figure A.3.3. 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 

μm

Figure A.3.4. 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 

μm

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

1.00E-09

2000 2200 2400 2600 2800 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

1000 mg/cm^2
A-11

Figure A.3.5. 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 μm

Figure A.3.6. 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 μm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1.00E-08

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
A-12

Figure A.3.7. 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 μm

Figure A.3.8. 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 μm

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

1.00E-08

0 200 400 600 800 1000 1200

Log(Gy/electron)

Density Thickness (mg/cm2)

138Cs
A-13

GEOMETRY 4:

DISK SOURCE (5 mm dia)

Figure A.4.1. 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 μm

Figure A.4.2. 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 

μm

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
A-14

Figure A.4.3. 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 

μm

Figure A.4.4. 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 

μm

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

1.00E-09

2000 2200 2400 2600 2800 3000

Electron Dose (Gy/electron)

Electron Energy (keV)

1000 mg/cm2
A-15

Figure A.4.5. 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 μm

Figure A.4.6. 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 μm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1.00E-08

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
A-16

Figure A.4.7. 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 μm

Figure A.4.8. 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 μm

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

1.00E-08

0 200 400 600 800 1000 1200

Log(Gy/electron)

Density Thickness (mg.cm^2)

138Cs
A-17

GEOMETRY 5:

CYLINDRICAL SOURCE

Figure A.5.1. 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 μm

Figure A.5.2. 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 μm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1.00E-08

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
A-18

Figure A.5.3. 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 μm

Figure A.5.4. 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 μm

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

1.00E-09

2500 2600 2700 2800 2900 3000

Electron Dose (Gy/electron)

Electron Dose (keV)

1000 mg/cm2
A-19

Figure A.5.5. 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 μm

Figure A.5.6. 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 μm

1.00E-15

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1.00E-08

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

1.00E-08

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

42K
A-20

Figure A.5.7. 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 μm

Figure A.5.8. 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 μm

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

1.00E-08

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
A-21

GEOMETRY 6:

SPHERICAL SOURCE

Figure A.6.1. 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 μm

Figure A.6.2. 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 μm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1.00E-08

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
A-22

Figure A.6.3. 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 μm

Figure A.6.4. 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 μm

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
A-23

Figure A.6.5. 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 μm

Figure A.6.6. 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 μm

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

1.00E-08

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

42K
A-24

Figure A.6.7. 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 μm

Figure A.6.8. 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 μm

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

1.00E-08

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

1.00E-08

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

138Cs
A-25

GEOMETRY 7:

SLAB SOURCE

Figure A.7.1. 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 μm

Figure A.7.2. 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 μm

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1.00E-08

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
A-26

Figure A.7.3. 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 μm

Figure A.7.4. 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 μm

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
A-27

Figure A.7.5. 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 μm

Figure A.7.6. 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 μm

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

1.00E-08

0 200 400 600 800 1000

Electron Dose (Gy/electron)

Density Thickness (mg/cm2)

42K
A-28

Figure A.7.7. 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 μm

Figure A.7.8. 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 μm

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

1.00E-08

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
APPENDIX B

Figures for the Supporting Photon Dosimetry V&V

B-1

GEOMETRY 1: POINT SOURCE

Figure B.1.1. 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 (dashed line), with a thickness of 20 μm

Figure B.1.2. A point source geometry comparison of VARSKIN 5 (circles) and MCNP5 (lines) predicted dose per 

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

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
B-2

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 μm

Figure B.1.3. 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 μm

Figure B.1.4. 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 μm

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

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-3

GEOMETRY 2: DISK SOURCE

Figure B.2.1. 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 μm

Figure B.2.2. A disk source geometry comparison of VARSKIN 5 (circles) and MCNP5 (lines) predicted dose per 

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

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
B-4

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 μm

Figure B.2.3. 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 μm

Figure B.2.4. 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 μm

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

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-5

GEOMETRY 3: CYLINDRICAL SOURCE

Figure B.3.1. 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 μm

Figure B.3.2. A cylindrical source geometry comparison of VARSKIN 5 (circles) and MCNP5 (lines) predicted dose 

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

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
B-6

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 μm

Figure B.3.3. 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 μm

Figure B.3.4. A cylindrical source geometry comparison of VARSKIN 5 (circles) and MCNP5 (lines) predicted dose 

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

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-7

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 μm

GEOMETRY 4: SLAB SOURCE

Figure B.4.1. 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 μm

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
B-8

Figure B.4.2. 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 μm

Figure B.4.3. 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 μm

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

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
B-9

Figure B.4.4. 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 μm

GEOMETRY 5: SPHERICAL SOURCE

Figure B.5.1. A spherical source geometry comparison of VARSKIN 5 (circles) and MCNP5 (lines) predicted dose 

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

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
B-10

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 μm

Figure B.5.2. 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 μm

Figure B.5.3. A spherical source geometry comparison of VARSKIN 5 (circles) and MCNP5 (lines) predicted dose 

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

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
B-11

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 μm

Figure B.5.4. 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 μm

GEOMETRY 6: POINT SOURCE (with Air Gap And Cotton Cover)

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-12

Figure B.6.1. 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 μm

Figure B.6.2. 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 μm

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

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
B-13

Figure B.6.3. 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 μm

Figure B.6.4. 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 μm

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

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-14

GEOMETRY 7: POINT SOURCE (1 cm off axis)

Figure B.7.1. 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 μm

Figure B.7.2. 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 100 mg/cm2 and a 

tissue volume cylinder of area 1 cm2 (solid line) and 10 cm2 (dashed line), with a thickness of 20 μm

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

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
B-15

Figure B.7.3. 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 μm

Figure B.7.4. 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 μm

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

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

APPENDIX C

Examples and Solutions Using VARSKIN 5

C-1

EXAMPLES AND SOLUTIONS USING VARSKIN 5

This appendix describes three different practical applications of VARSKIN 5 using an

example/solution format. Each example describes a situation followed by a solution that 

involves the use of VARSKIN to estimate skin dose and deep-dose equivalent. 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.

Example 1: Radiopharmaceutical Technician in Nuclear Medicine

At a research hospital, a doctor prescribes a 5-milliliter (mL) administration from a stock solution 

containing 10 microcuries per milliliter (μCi/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 5 and check the user 

“Radionuclide Library.” If 186Re does not appear in the “Radionuclide Library” window, add 186Re

by selecting the “Add” button 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 (10 μCi/mL) by the size of the administration 

(5 mL) to get a total source strength of 50 μCi. Be sure that the source strength units are set to 

μCi, then double-click the 186Re library entry. When VARSKIN asks for the source strength, 

enter 50. 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 default values. Click “Calculate Doses.” 

After the calculation is performed, the VARSKIN Non-Volume 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 

beta, photon, and total, the initial dose rate, the dose with no decay, and the decay-corrected 

dose are displayed. The dose with no decay is provided so that the user can assume that either 

the source has a very long half-life or that the radionuclide is in secular equilibrium with its 
C-2

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 beta and 0.673 milliGy (mGy) from photons), a 

value that exceeds regulatory limits. To calculate the deep dose, 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 (don’t 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 beta dose of 0.262 Gy and a photon dose 

of 0.149 mGy. While the 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 0.149

mGy as the decay-corrected beta 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 beta and 0.124 mGy for photons. It can be concluded that, 

based on the above calculations, a thicker, absorbent lab coat will give more protection than a 

thin, impervious material.
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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: 2.5 mCi

• Particle thickness and density: 50 μm; 8.3 g/cm3

• Particle size: 80 μm x 70 μm

• 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 5. If 

Co-60 does not appear in the Radionuclide Library frame, add Co-60 by selecting the “Add” key 

and double-clicking “Co-60” in the Add Radionuclide to Library window (with an effective Z of 

7.42). Enter an Exposure Time of 15 minutes. Double-click “Co-60” in the Radionuclide Library,

and enter 2.5 millicuries (mCi). 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 a beta 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 gamma 

component to the dose, so a deep-dose calculation is needed.

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 2.2, the cylinder 

model should 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 

μm 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 μm 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 a beta dose of 

0.130 Gy, a photon dose of 0.105 Gy, and a total dose of 0.235 Gy. Including the effects of 

self-shielding greatly reduced the beta dose and resulted in a dose that is now below regulatory 

limits. To calculate deep dose, simply return to the main window, change the Skin Thickness or 

Skin Density Thickness to 1,000 mg/cm2

, and click “Calculate Doses.” The VARSKIN results 

screen will display a deep dose of 0.0325 Gy, all from photons.
C-4

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 

6 inches (in.) by 6 in. 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 1 in.

Solution 3: Contaminated Metal in a University Laboratory Hood

The solution to this example demonstrates a method of using VARSKIN 5 for applications other 

than skin contamination events. 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 36 in2 to 

correspond to the area of the contaminated plate. A source strength of 1 μCi/cm2 will be used 

for the calculation, and the results of the calculation will be 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, the limit for air gaps in VARSKIN 5.

For this solution, first “Reset” VARSKIN and choose the “Disk” geometry. If the Radionuclide 

Library does not contain 14C, add it by clicking “Add” 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 “μCi/cm2

”. Double-click “C-14” and set the source strength to 1 μCi/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 36 in.

2

. For this example, the 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 beta dose rate of 0.0447 Gy/hr, with 

no photon dose. The activity concentration on the plate then can be found using,

[Aact]

[Acal] = Ḋ

meas

Ḋ

cal

.

Therefore, the activity concentration on the plate is given by:

�1 μCi�

cm2� �1.90 mGy

hr � �

44.70 mGy

hr �

= 0.0425 μCi�

cm2

Multiplying the activity concentration by the area of the plate (6 in. x 6 in. = 232 cm2

) results in a 

total activity of 9.86 μCi.
C-5

The measurement at a distance of 1 inch can be used to verify this result. Close the results

window and return to the main window; enter an Air Gap Thickness of 1 inch and change the 

activity to 9.86 μCi. After you click “Calculating Doses,” the VARSKIN results window will 

display an initial beta dose rate of 0.604 mGy/hr, compared to the measurement of 0.60 mGy/hr 

with the calibrated detector.




UNITED STATES 

NUCLEAR REGULATORY COMMISSION

WASHINGTON, DC 20555-0001

--------------------

OFFICIAL BUSINESS
NUREG/CR-6918

Revision 2

VARSKIN 5: A Computer Code for Skin Contamination Dosimetry