NUREG/CR-6918

VARSKIN 3: A Computer Code 

for Assessing Skin Dose

From Skin Dose Contamination 

\

Center for Nuclear Waste Regulatory Analyses

U.S. Nuclear Regulatory Commission

Office of Nuclear Regulatory Research

Washington, DC 20555-0001
AVAILABILITY NOTICE
 

 

 

 NUREG/CR-6918

 

VARSKIN 3: A Computer Code

for Assessing Skin Dose

From Skin Dose Contamination

Manuscript Completed: October 2006

Date Published: October 2006

Prepared by

J.S. Durham

Center for Nuclear Waste Regulatory Analyses

Southwest Research Institute

6220 Culebra Road

San Antonio, TX 78238-5166

H. Karagiannis, NRC Project Manager

Prepared for

Division of Fuel, Engineering and Radiological Research 

Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Job Code Y6266
iii

ABSTRACT

The computer code VARSKIN Mod 2, which calculates skin dose from radioactive skin

contamination, has been significantly modified. The new code, VARSKIN 3, operates in a

Windows® environment and is designed to be significantly easier to learn and use than

VARSKIN Mod 2. Six different predefined source configurations are available: point, disk,

cylinder, sphere, slab, and syringe. Improvements in VARSKIN 3 include a backscatter

correction for three-dimensional sources, an upgraded photon dose model, air gap and cover

material models. The default area for skin dose calculations has been changed to 10 cm2

 to

conform to regulatory requirement pursuant to 10 CFR 20.1201(c), but the area can be changed

by the user. Data entry for the code has been condensed to a single screen, and the user does

not need to enter the data in any particular order. A variety of unit options are provided,

including both English and System Internationale units, and the source strength can be entered

in units of activity or distributed in units of activity per area or activity per volume. The output

page also has been simplified. In addition, adding radionuclides to the library has been greatly

simplified. Previously, users added radionuclides to the library using SADDE Mod 2, the

companion code to VARSKIN Mod 2. SADDE Mod 2 required the user to supply basic nuclear

data so that radionuclides could be added to the VARSKIN Mod 2 library. In addition, SADDE

Mod 2 did not include the contribution to dose from beta particles below a

radionuclide-dependent cutoff energy, which affected the accuracy of the dose calculations at

skin depths below 7 mg/cm2

 for high-energy-beta sources. In VARSKIN 3, the user merely

needs to select the radionuclide name for the radionuclide to be added to the library. The

library file also contains data on photons, internal conversion electrons, and Auger electrons. 

VARSKIN 3 also allows the user to build a customized library, eliminating radionuclides that are

not of interest. Finally, an extensive, context-sensitive help file is available to provide guidance

and to offer new users a tutorial in the use of VARSKIN 3. The help file contains all of the

information in this document. This document describes the revised code, provides installation

and operation instructions, provides detailed descriptions of the models used, and suggests

methods for avoiding misuse of the code.

v

FOREWORD

The VARSKIN code is a tool for assessing doses from skin contamination, including hot

particles. Although the original code was developed for use by the NRC staff to calculate skin

dose for regulatory requirements, both the industry and academia have been interested in 

using the code. 

VARSKIN 3, the third update to the VARSKIN series, operates in a Windows environment and is

designed to be significantly easier to learn and use than its predecessor, VARSKIN Mod 2. In

the following years after the release of VARSKIN Mod 2, users have identified several errors

and suggested improvements. VARSKIN 3 addresses these errors and improves upon the

users’ needs and requirements.

This report describes the upgrades of VARSKIN 3 and includes a user’s guide. Section 1

includes the introduction and describes the evolution of the VARSKIN series. Section 2

describes the contents of the VARSKIN 3 code package and includes instructions for installing

and running the code on a personal computer. Section 3 discusses the technical basis for

VARSKIN 3 and describes the models incorporated in the code. Section 4 contains the results

of validation and verification testing for VARSKIN 3. Section 5 of this report describes the

problems of and suggested improvements for VARSKIN Mod 2 that were included in VARSKIN

3 as well as new features of the code and its limitations. Section 6 explains the correct method

for modeling "infinite" sources and how to calculate the maximum dose to 10 cm2

 from multiple

contaminations. Appendix A contains the technical basis for the photon dose model. Finally,

Appendix B provides three detailed solutions to practical examples using VARSKIN 3.

This report will support strategies that ensure the protection of public health and safety and the

environment by utilizing regulatory programs and applied research effectively to anticipate and

resolve safety issues.

_____________________________

Brian W. Sheron, Director

Office of Nuclear Regulatory Research

vii

CONTENTS

Section Page

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

FOREWORD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

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

2 VARSKIN 3 USER’S MANUAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

2.1 Installing Varskin 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

2.2 Running Varskin 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

2.2.1 Source Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2

2.2.2 Adding Radionuclides to the Library . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6

2.2.3 Selecting Radionuclides From the User Library . . . . . . . . . . . . . . . . . 2-8

2.2.4 Geometry Parameters and Multiple Cover Calculator . . . . . . . . . . . . . 2-9

2.2.5 Special Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-13

2.2.6 Calculating Doses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-16

2.2.7 Output Screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-16

2.2.8 Exiting Varskin 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-19

3 DESCRIPTION OF CALCULATIONAL MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1

3.1 Beta Dose Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1

3.2 Backscatter Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4

3.3 Cover Layer and Air Gap Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9

3.4 Volume-Averaged Dose Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-11

3.5 Offset Particle Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-12

3.6 Photon Dose Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-12

3.7 Syringe Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-13

3.8 Adding Radionuclides to the Varskin 3 Library . . . . . . . . . . . . . . . . . . . . . . . 3-14

4 VALIDATION AND VERIFICATION OF VARSKIN 3 . . . . . . . . . . . . . . . . . . . . . . . . . 4-1

4.1 Point Source on Skin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1

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

4.3 Distributed Contamination on Skin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2
viii

CONTENTS

Section Page

5 CHANGES TO VARSKIN MOD 2 AND NEW FEATURES AND LIMITATIONS

OF VARSKIN 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1

5.1 Corrections to Errors in VARSKIN Mod 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1

5.2 New Features in Varskin 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4

5.3 Limitations of Varskin 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-5

6 SPECIAL TOPICS FOR ACCURATE USE OF VARSKIN 3 . . . . . . . . . . . . . . . . . . . . 6-1

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

6.2 Maximum Dose to 10 cm2

 From Multiple Contaminations . . . . . . . . . . . . . . . 6-1

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

APPENDIXES

A DATA FROM MICHAEL W. LANTZ FOR THE PHOTON DOSE MODEL . . . . . . . . . A-1

B EXAMPLES AND SOLUTIONS USING VARSKIN 3 . . . . . . . . . . . . . . . . . . . . . . . . . B-1
ix

FIGURES

Figure Page

1-1 Schematic of the Volume-Averaged Dose Model . . . . . . . . . . . . . . . . . . . . . . 1-2

2-1 Opening Screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2

2-2 Source Geometry Screen (Slab Source Screen Shown) . . . . . . . . . . . . . . . . 2-3

2-3 Source Geometry Option Box From the Source Geometry 

Screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3

2-4 Schematic Representations of the Six Geometry Options . . . . . . . . . . . . . . . 2-4

2-5 Radionuclide Library List Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6

2-6 Add Radionuclide Screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7

2-7 Slab Source Geometry Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-9

2-8 Schematic Showing the Cover Material and Air Gap Models . . . . . . . . . . . . 2-11

2-9 Composite Cover Calculator Screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12

2-10 Special Options Subscreen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-13

2-11 Schematic Diagram of the Volume-Averaged Dose Model Geometry . . . . . 2-15

2-12 Schematic Diagram of the Offset Particle Model . . . . . . . . . . . . . . . . . . . . . 2-15

2-13 Logic Flow Diagram for Varskin 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-17

2-14 Results Screen for a Typical Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-18

2-15 Results Screen for a Volume-Averaged Calculation . . . . . . . . . . . . . . . . . . . 2-19

2-16 Exit Screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-20

3-1 Schematic Representation of a Dose Calculation for a Symmetric Source . . 3-2

3-2 Backscatter Correction Factor for Infinitely Thin and Point Sources . . . . . . . . 3-4

3-3 Geometry Used for MCNP Calculations for the Backscatter Model . . . . . . . . 3-5

3-4 Ratio of Flux in Water to Flux in Air for Pm-147 . . . . . . . . . . . . . . . . . . . . . . . 3-6

3-5 Ratio of Flux in Water to Flux in Air for Sr-90 . . . . . . . . . . . . . . . . . . . . . . . . . 3-7

3-6 Ratio of Flux in Water to Flux in Air for Tl-204 . . . . . . . . . . . . . . . . . . . . . . . . 3-7

3-7 Ratio of Flux in Water to Flux in Air for Y-90 . . . . . . . . . . . . . . . . . . . . . . . . . . 3-8

3-8 Combined Data for the Four Radionuclides . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9

3-9 Schematic Drawing of a Generic Dose Calculation Performed by

Varskin 3 for the Cylinder Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10

xi

TABLES

Table Page

2-1 Default Values and Units for Geometry Parameters . . . . . . . . . . . . . . . . . . . 2-10

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

3-1 Radioactive Characteristics of the Sources Modeled for the Backscatter

Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6

4-1 Comparison of Calculated Skin Dose Rates for a 1-μCi Hot Particle

on the Skin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1

4-2 Comparison of the Chabot Method and Varskin 3 for 1-μCi Hot Particle

Point Source on Cover Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2

4-3 Comparison of Calculated Beta Skin Doses for Distributed Contamination

of 1 μCi/cm2

 Averaged Over 100 cm2 on the Skin . . . . . . . . . . . . . . . . . . . . . 4-3

4-4 70-μm Depth Dose Coefficients in rad-cm2

/μCi/h . . . . . . . . . . . . . . . . . . . . . . 4-3

4-5 Dose Coefficients Versus Depth for Y-90 Averaged Over 0.01 cm2

 in

rad-cm2

/μCi/h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4

5-1 Specific Gamma Ray Constant Γ, as a Function of Cutoff Energy

for Co-57 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-6

xiii

ACKNOWLEDGMENTS

This report was prepared to document work performed by the Center for Nuclear Waste

Regulatory Analyses (CNWRA) for the U.S. Nuclear Regulatory Commission (NRC) under

Purchase Order No. NRC–DR–04–05–086 and at Colorado State University under Contract

No. NRC–04–02–055. The activities reported here were performed on behalf of the NRC Office

of Nuclear Regulatory Research, Division of Fuel, Engineering and Radiological Research. This

report is an independent product of CNWRA and does not necessarily reflect the views or

regulatory position of NRC. 

The author thanks L. Howard for technical review and D. Turner for programmatic review of this

report. The author also thanks L. Selvey for document preparation; E. Hanson for editorial

review of the document; H. Karagiannis, S. Sherbini, A. Roecklein, S. Bush-Goddard, and

E. Dickson of NRC for their support, suggestions, and patience during the development of

Varskin 3; the following people who helped develop models for Varskin 3: J. Chase (Ontario

Power Generation), B.D. Plain (Ontario Power Generation), M. Wierzbicki (Ontario Power

Generation), M. Lantz (Arizona Public Service Company), K. Krobl (Colorado State University),

and the following people who provided comments after testing Varskin 3: G. Chabot (University

of Massachusetts at Lowell), J. Dwyer (NRC), J. Lebda (First Energy Nuclear Operating

Company), E. Mercer (Maine Yankee Atomic Power Station), R. Nimitz (NRC), A. Salame-Alfie

(New York State Department of Health), M.G. Stabin (Vanderbilt University), G.M. Sturchio

(Mayo Clinic), B.K. Tharakan (NRC), T.J. Vandermey (Detroit Edison), and M.W. Charles

[University of Birmingham (England)].

QUALITY OF DATA, ANALYSES, AND CODE DEVELOPMENT

DATA: No CNWRA-generated original data are contained in this report.

ANALYSES AND CODES: CNWRA computer analysis results are used in this report. 

VARSKIN Version 2.2 was acquired and is controlled under the Technical Operating Procedure

(TOP)–18, Development and Control of Scientific and Engineering Software. The final version

of Varskin 3 Version 3 will also be controlled under TOP–18.

1-1

1 INTRODUCTION

The original VARSKIN computer code (Traub, et al., 1987) was intended for calculation of skin

dose from contamination directly on the skin. The contamination was assumed to be a point or

infinitely thin disk source directly on the skin. Soon after the release of VARSKIN, a “new” type

of skin contaminant was encountered in the industry. This contaminant consisted 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 exposures result from particles on the outside of protective clothing.

Using VARSKIN for calculating skin doses from hot particles or other contaminants on the skin

or outside of a cover material such as protective clothing had three primary drawbacks. First,

VARSKIN modeled the contaminant as having no thickness; thus, source self-shielding was

not taken into account in the calculation. For example, hot particles containing weak

beta-emitting radionuclides (such as Co-60), VARSKIN greatly overestimated calculated skin

doses from particles that were thicker than about 1 μm. Second, VARSKIN did not model a

cover material (e.g., protective clothing) that may exist between the source and skin, again

leading to an overestimate of skin dose from skin contamination. Finally, it has been shown that

the gamma component of a mixed beta/gamma-emitting 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 mg/cm2

, the authors of VARSKIN correctly concluded that the photon dose would not be

significant compared to the beta dose under these exposure conditions, and no photon dose

model was included. Because of these and other shortcomings of the code, an upgrade of

VARSKIN was needed in order to provide accurate skin dose calculations under a variety of

exposure conditions.

The upgraded computer code VARSKIN Mod 2 (Durham, 1992) contained all of the features of

the original VARSKIN with numerous significant additions. Additional features in VARSKIN

Mod 2 included modeling of three-dimensional sources (cylinders, spheres, and slabs) that

included self-shielding of the sources, modeling of materials placed between the source and

skin (including air gaps) that attenuate the beta particles, and modeling of hot particle photon

doses in certain cases. VARSKIN Mod 2 also used a correction for backscatter for one- and

two-dimensional 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 dose model allowed the user to calculate the 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 as shown in Figure 1-1. This

model can be used to calculate the dose averaged between two depths in tissue, which is

useful when characterizing the dose measured by a finite-volume dosimeter such as 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

particular skin area from multiple hot particles not centered on that area.
1-2

Figure 1-1. Schematic of the Volume-Averaged Dose Model

Finally, VARSKIN Mod 2 included the capability to use composite source terms that allowed a

user to calculate the total dose from a mixture of beta-emitters instead of having to run the code

separately for each radionuclide in the mix. This feature has been removed in Varskin 3. 

Instead, the number of radionuclides that can be included in a single calculation has been

increased to 20. Note that one implication of removing the feature in Varskin 3 is that

radioactive progeny of radionuclides must be added explicitly by the user.

Section 2 of this report describes the contents of the Varskin 3 code package, including

instructions for installing and running the code on a personal computer. Section 3 discusses the

technical basis for Varskin 3 and describes the models incorporated in the code. Section 4

contains the results of validation and verification testing for Varskin 3. Section 5 of this report

describes the problems and suggestions for improvement of VARSKIN Mod 2 that were

included in Varskin 3 as well as new features of the code and its limitations. Section 6 explains

the correct method for modeling “infinite” sources and how to calculate the maximum dose to

10 cm2

 from multiple contaminations. Appendix A contains the technical basis for the photon

dose model. Finally, three detailed solutions to practical examples using Varskin 3 are provided

in Appendix B.
2-1

2 VARSKIN 3 USER'S MANUAL

This section serves as a user’s guide for Varskin 3. It includes installation instructions,

operating instructions, and a description of the features of Varskin 3.

2.1 Installing Varskin 3

The installation files for Varskin 3 are located on the disk provided from the Radiation Shielding

Information and Computational Center (RSICC) at www.rsicc.oral.gov. To install Varskin 3,

place the CD–ROM in the disk drive and execute the setup.exe file.

During installation, the user is asked to choose file locations for the program. The default file

locations are recommended. However, any disk with a designated drive letter (e.g., c:/) is

suitable to use for installation of the program.

Important Note: If a previously installed version of Varskin exists on your computer, then the

older version must be uninstalled before the newer version is installed. Not uninstalling

previous versions may result in more than one installation of Varskin appearing in the Start

Menu, causing confusion for the user. Upgrades to Varskin 3 may be made available, as

necessary. In the event the upgrades are available from a web site, then you must have

previously installed Varskin 3 from RSICC or from NRC staff to use the upgrade. Upgrades to

Varskin 3 will include only updated executable files. If Varskin 3 has not been installed from an

installation disk, then the code will not be registered with Windows, the required data files will

not exist, and the directory structure that is created when Varskin 3 is installed will not exist. 

Therefore, the user must install Varskin 3 from an installation disk before upgrades are installed. 

Simply download the upgraded executable file(s) into the subdirectory where Varskin 3 was

installed. When asked if the existing files should be replaced, choose “Yes.”

Note to Computer Administrators: Varskin 3 is designed to pass information between the

Visual Basic Graphical User Interface (GUI) and the FORTRAN computation engines by writing

files to the drive on which it is installed. Therefore, users of the computer on which it is installed

must have permission to write to the directory in which Varskin 3 is installed. To enable this, an

administrator must set the permissions on the Varskin 3 directory to “everyone.” Varskin 3 is

not designed for installation on a network. Attempts to install Varskin 3 on a network have

been unsuccessful.

Hardware and Software Requirements: A personal computer with an 80386 processor or

newer is required. The code requires 4 MB of disk space. Varskin 3 has been tested under

Windows XP and 2000. It is anticipated that the code will also operate under Windows 9X

and NT.

2.2 Running Varskin 3

To run Varskin 3 in Windows XP after installation, go to

Start > Programs > Varskin 3 > Varskin 3
2-2

 Figure 2-1. Opening Screen

Operations within Varskin 3 are designed to be intuitive. The opening screen provides the user

with contact information and basic code information. The only options on this screen are to exit

the program or to begin a calculation. The opening screen is shown in Figure 2-1.

2.2.1 Source Geometry

The Source Geometry Screen is shown in Figure 2-2. This screen contains all of the input

information that is needed to perform a dose calculation. Although Varskin 3 allows the user to

enter data in any order, the geometry package must be chosen first because changing the

geometry package will reset all of the geometry parameters to their default values. Six

geometry packages are available: point source, (infinitely thin) disk source, cylinder source

(thick), spherical source, slab source (rectangular), and syringe source. When the geometry

package is changed, the required input parameters also change. In addition, if

geometry-dependent units for the source strength have been chosen, a warning message will

appear that informs the user that some of the selected radionuclides will be unselected. The

source geometry option box is pictured in Figure 2-3.

The point source geometry is very simple to use, but should only be used for non-particulate

contamination that is confined to a very small area of the skin or for a quick calculation to

determine whether a regulatory limit has been potentially exceeded. The point source geometry

does not account for self-shielding of the source 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. Varskin 3 models a point source as a

cylinder source with a thickness of 1 μm, a radius of 1 μm, and a density of 0.001 g/cm3

. The

point source geometry is shown schematically in Figure 2-4(A).
2-3

Figure 2-2. Source Geometry Screen (Slab Source Screen Shown)

Figure 2-3. Source Geometry Option Box From the Source Geometry Screen
2-4

Figure 2-4. Schematic Representations of the Six Geometry Options

The disk source geometry model is simple and is recommended for modeling liquid skin

contamination events. The disk source geometry requires the user to enter either the source

diameter or the source area in the appropriate contamination 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 3 automatically calculates the area of the circle with that diameter. Similarly,

when the user enters the area of the source, Varskin 3 automatically calculates the diameter

of a circle with the same area. Varskin 3 models a disk source as a cylinder with a thickness of

1 μm and a density of 0.001 g/cm3

. The disk source geometry is shown schematically in

Figure 2-4(B). If the area of contamination is not circular, entering the area of the actual

contamination will generally result in a reasonable estimation of the dose.

The sphere source geometry is perhaps the simplest three-dimensional geometry to use for

dose calculations because it requires knowledge of only one source dimension: the source

diameter. The sphere source geometry assumes that the source is surrounded by air and

touches the skin or cover material only at the bottom-most point on the sphere surface. 

Choosing the sphere source geometry will generally overestimate the dose compared to a

similarly sized cylinder source with the same 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 and slab models), and a larger area of skin

will be irradiated resulting in consistently higher doses. The sphere source geometry is shown

schematically in Figure 2-4(C). The cylinder source geometry is recommended for sources that

are not spherical.
2-5

The cylinder model requires knowledge of two dimensions: the cylinder diameter and the

cylinder thickness. The cylinder source geometry assumes that the source is surrounded by air

but that the entire bottom of the cylinder is in contact with skin or cover material. This geometry

requires the same amount of time to execute as the spherical model but generally offers a more

accurate dose calculation. Of the two cylinder source dimensions, the calculated dose is much

more sensitive to changes in the cylinder thickness than in the cylinder diameter. Because the

cylinder source geometry allows the user to specify the thickness of the source (compared to

the sphere source geometry), calculations using cylinder source geometry are more accurate

than those using the sphere source geometry. The cylinder source geometry is shown

schematically in Figure 2-4(D).

The slab source geometry requires knowledge of three physical dimensions: the x-side length,

the y-side length, and the thickness. The slab source geometry requires two to five times more

execution time than the cylinder and sphere geometries, and the accuracy of the calculation is

significantly lower. As evidenced by the Varskin 3 Validation Test Plan and Report, results of

calculations using the slab geometry differed by as much as 35 percent from the results

obtained using the other five geometries when modeling the same source. This discrepancy is

the result of a fundamental difference between the mathematical approach used for the slab

geometry compared to the other geometry packages when modeling similar sources. These

differences are described in more detail in Section 4. The slab geometry should only be used

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

the offset particle model is needed). The slab source geometry is shown schematically in

Figure 2-4(E).

The syringe source geometry is a specialized geometry that calculates dose from a syringe or

other cylindrical object for which the dose to the side of the cylinders is needed. The user

needs to supply the syringe outer diameter, the syringe wall thickness, and the volume and

density of the source. The syringe material density is assumed to be that of polyethylene

(1.1 g/cm3

). Varskin 3 calculates the source length based on the input data, then models the

syringe source as a cylinder with a thickness equal to the inner diameter of the source and a

diameter such that the volume of the source is preserved. Because the dimensions of the

syringe source geometry are larger than 1 mm, photon doses are not calculated for the syringe

source geometry. The syringe source geometry is shown schematically in Figure 2-4(F).

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

highest dose estimates to lower dose estimates:

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

option. This option is also recommended for a quick screen against regulatory limits

since the point geometry typically overestimates the 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 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 sphere source geometry option.
2-6

Figure 2-5. Radionuclide Library List Box

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

unknown, use the cylinder source geometry option because this geometry requires only

two dimensions (thickness and radius) to describe the particle.

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

thickness of the particle should be preserved, and the area of the contact surface should

be selected such that the source volume is preserved. This option requires less time to

run than the slab source geometry option and is more accurate.

• If the source is a syringe, use the syringe source geometry.

For all source geometries, doses are calculated to a circular area centered below the central

axis of the source. When using the offset particle model, dose is calculated to circular area with

the center located at the offset distance from the center of the source.

2.2.2 Adding Radionuclides to the Library

Varskin 3 employs two radionuclide libraries: a code library (supplied on the installation disk)

that contains data for all radionuclides available to the user, and a user library that contains only

those radionuclides that the user adds to it. When Varskin 3 is first installed, no radionuclides

will appear in the user library. Varskin 3 is designed to allow the user to customize the

radionuclide library so that only those radionuclides of interest to the user appear in the library. 

To add a radionuclide to the user library, the user clicks on the “Add” button (shown in

Figure 2-5), and a new screen appears that displays every radionuclide for which data is

available (a total of 838 radionuclides), as shown in Figure 2-6. Radionuclides are added to the

library by highlighting the radionuclide and clicking on “Add Radionuclide” or simply double

clicking on the name of the radionuclide. A scrolling status bar will appear indicating that

calculations are being performed to compile the input file for the selected radionuclide. The

status bar may scroll several times depending on the speed of the computer processor and the

availability of computer resources. When the process of adding the radionuclide is completed,
2-7

Figure 2-6. Add Radionuclide Screen

the Source Geometry screen will return, and the added radionuclide will be visible in the 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 on the

Radionuclide Library frame.

When the “Add Radionuclide” button shown in Figure 2-5 is clicked, the following events occur

in a separate executable file. First, data are extracted from the data files ICRP38.dat,

ICRP38.idx, and ICRP.bet, which are located in the \dat subdirectory of the application

directory. If the radionuclide emits beta radiation, the beta spectrum is generated for one or

more beta decay paths. If the radionuclide does not emit beta radiation, a tritium beta spectrum

is generated with a yield of 0.001. Next, internal conversion and Auger electrons are added to

the beta spectrum. Finally, photon energy and yield data are collected from the data files, and

the average photon energy and total photon yield is calculated. 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 average photon energy, the specific gamma ray constant, and the photon yield

is generated with the extension “.dat.” As discussed in Section 3.1, the X99 distance is used as

the range of the beta particles.

The radionuclide library file will contain all known electrons and any photons with energies

above the user-selected photon minimum energy and yield. The user may accept the default

value of 2 keV for the Photon Minimum Energy (keV) text box or specify a different value by

entering the cutoff energy in keV. The cutoff energy is the minimum energy for photons to be

included in photon dose calculations. The user may also accept the default value of 1.0 percent

for the Photon Minimum Yield (%) text box or specify a different value by entering the minimum

yield in percent.
2-8

As discussed in Section 5.3, the choice of the minimum photon energy and yield can have

significant effects on the accuracy of photon dose calculations. The limited photon dose model

used in Varskin 3 calculates dose based on the specific photon dose constant, which includes a

contribution from all photons included in its calculation. Thus, the photon dose model does not

adjust the photon doses for absorption in the skin. When calculating skin dose at depths of

7 mg/cm2

, photons with energies as low as 2 keV contribute to skin dose. However, when the

target is deeper tissue (for example, when calculating deep dose), only higher-energy photons

(above 35 keV) will contribute to the dose. Because low-energy photons are not attenuated, the

deep dose could be overestimated if a cutoff energy lower than 35 keV is chosen. Therefore,

using a specific photon dose constant that includes low-energy photons to calculate deep dose

will overestimate that dose. On the other hand, using a specific photon dose constant that does

not include low-energy photons when calculating shallow dose will underestimate that dose. It

is recommended that three files be created for radionuclides that emit low-energy photons: one

for shallow dose (70 mg/cm2

), one for eye dose (300 mg/cm2), and one for deep dose

(1,000 mg/cm2

). Recommended values for the cutoff energies are 2 keV (shallow), 20 keV

(eye), and 35 keV (deep). Multiple library files are created by giving each file a unique name

(i.e., Cs-137, Cs-137e, and Cs-137d).

To create multiple library entries for a single radionuclide, choose “Add” radionuclide in the

Radionuclide Library frame on the Source Geometry screen. When the Add Radionuclide to

Library screen appears, select the radionuclide by clicking on the name once. For shallow

dose, set the Photon Minimum Energy to 2 keV, then click on Add Radionuclide. A library file

will be created in the \dat subdirectory using the name of the radionuclide. To create another

library file with a different cutoff energy, choose Add in the Source Geometry screen and select

the same radionuclide. For eye dose, set the photon minimum energy to 20 keV and double

click on radionuclide name. After the scrollbar appears, the user will be informed that the library

file already exists and the user is prompted if the user wants to cancel. Select “No,” then enter

a new name for the library file. For example, adding an “e” after the radionuclide name can

indicate the particular file is to be used for the dose to the eye. This process can be repeated

for deep dose by changing the photon minimum energy to 35 keV and appending a “d” to the

library file name.

Radionuclides can be removed from the user library by highlighting the appropriate radionuclide

and clicking on the “Remove” button. The “Add” button can also be used to replace

radionuclides in the library by naming an added radionuclide with the same name as that of an

existing library entry. Thus, a library file that calculates shallow dose and another library file that

calculated deep dose from the same radionculide can exist in the user library.

In Varskin 3, radioactive progeny are not included in the user library file. The user must create

a user library file for each radioactive progeny. Radioactive progeny are not included regardless

of the half-life of the progeny.

2.2.3 Selecting Radionuclides From the User Library

Radionuclides can be selected for a calculation by double clicking on the name of the

radionuclide or by highlighting the desired radionuclide and clicking the “Select” button (shown

in Figure 2-5). The default unit of measure for activity is μCi. Users may change the activity

unit by selecting a different unit from the Activity Units list box. The new unit must be chosen

prior to selecting the radionuclide. When a radionuclide is selected, a message box will appear
2-9

Figure 2-7. Slab Source Geometry Parameters

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. Up to

20 radionuclides may be selected for a given calculation.

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

appear as shown in Figure 2-5. The distributed source option allows the user to enter the

source strength in activity/cm2

 for the disk source geometry or activity/cm3 for three-dimensional

source geometries. The distributed source option only applies to radionuclides that are selected

after the checkbox is checked. If the distributed source option is unchecked, subsequently

selected radionuclides will have activities in terms of total inventory instead of distributed

activity.

2.2.4 Geometry Parameters and Multiple Cover Calculator

The geometry parameters box (shown in Figure 2-7 for the slab geometry) changes depending

on the particular geometry chosen for the calculation. Clicking on the arrow next to the units of

the parameter and choosing from the drop-down list will choose the units for that particular

parameter. It is also possible to intermix different units for the different parameters. Varskin 3

makes the necessary conversions internally. The default values for the various parameters are

shown in Table 2-1.

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.

The results of a sensitivity analysis show that (i) the most sensitive source dimension for

calculating dose is the source thickness and (ii) the dose will vary greatly for small variations in

the value of this parameter. Similarly, the source density is an equally sensitive parameter. It is

essential that these parameters are known accurately or that an underestimate of their values 
2-10

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

Parameter Default Value

Skin Density Thickness 7 mg/cm2

Air Gap Thickness 0 mm

Cover Thickness 0 mm

Cover Density 0 g/cm3

Source Area (Disk) 0.785 mm2

Source Diameter (Disk) 1 mm

Source Diameter (Sphere) 1 μm

Source Thickness (Disk, Slab) 1 μm

Source X-Side Length (Slab) 1 μm

Source Y-Side Length (Slab) 1 μm

Source Volume (Syringe) 1 cm3

Syringe Wall Thickness (Syringe) 1 μm

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

Source Diameter (Syringe) 1 cm

be made. Underestimating the source thickness or density will generally result in the calculation

of larger doses. The following guidelines will help in choosing appropriate values for source

dimensions and density:

(1) Diameter (disk and cylinder); x-side and y-side lengths (slab): The dose calculation for

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

below 2 mm for sources with the same activity. Overestimating the size of the source

will generally result in an overestimation of the dose unless the source size is larger than

the averaging area.

(2) Thickness (disk and slab) and sphere diameter: The dose calculation for all

radionuclides is very sensitive to this dimension, especially for low-energy-beta-emitting

radionuclides. Minimizing the value of this dimension will provide an overestimate of

the dose.

(3) Source Density (three-dimensional geometry models): 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

, and a density of

14 g/cm3

 is typical for fuel.
2-11

Figure 2-8. Schematic Showing the Cover Material and Air Gap Models

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

the two models is shown in Figure 2-8, which depicts the cylinder geometry, although the two

models are available for any of the source geometries. The required input for the cover material

model is the thickness of the material and its corresponding density. Note that 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 in the material (material attenuation). 

For the air gap model, only the thickness of the air gap is required for input. Varskin 3 uses a

default value of 0.001293 g/cm3

 for air density.

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

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

geometric attenuation can be dramatic. Cover materials affect both the geometric and material

attenuation. Some suggested thickness and density values are given in Table 2-2.

Varskin 3 allows multiple cover materials to be modeled as a composite cover by clicking on the

“Multiple Cover Calculator” button. The multiple-cover calculator allows the user to add up to

five covers together as shown in Figure 2-9 and is the only way for the user to enter multiple

covers. The user must enter two of the following three parameters for each layer: Cover

Thickness, Cover Density, and Cover Density Thickness. The user can choose the units for

density and thickness, but the density thickness must be entered in g/cm2

. The calculator

calculates the third parameter, adds the different layers together, and calculates the thickness

and effective density of the composite cover. The composite cover density in mg/cm3

 and

thickness in cm are then automatically entered in the appropriate boxes in the Source Geometry

screen. If the user enters all three parameters, Varskin 3 will recalculate the density thickness

from the density and thickness data prior to determining the characteristics of the composite

cover. The printout from a dose calculation will include the data from each cover layer as well

as the composite cover data.
2-12

Figure 2-9. Composite Cover Calculator Screen

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

Material Thickness (mm) Density (g/cm3

)

Lab Coat (Plastic) 0.1 0.036

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 
2-13

Figure 2-10. Special Options Subscreen

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. 

However, 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.

2.2.5 Special Options

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

calculation, as shown in Figure 2-10. The first special option, which is available for all geometry

packages except the syringe geometry package, 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 choose to uncheck the box so the photon dose will not be calculated. The

photon dose calculation will not noticeably increase the overall calculation time. If the option to

include the photon dose is chosen 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. Note that the syringe geometry package does not include a

photon dose calculation.

The Varskin 3 photon dose model assumes that the source is small enough to be considered a

point source and that any covering material is similar to tissue or water. Thus, the photon dose

is only calculated for sources with dimensions smaller than 1 mm, and the photon dose is not

calculated for the syringe source. The Varskin 3 photon dose model, which is described in

detail in Section 2, is an extension of a model published by Lantz and Lambert (1990) that was

the basis for the VARSKIN Mod 2 photon dose model. The Varskin 3 photon dose model is

applied to irradiation areas up to 10 cm2

. For larger areas, the user will be informed that the

photon dose will not be calculated even if the photon dose option is selected.
2-14

Photon doses are calculated as if the source was a point source, and the model includes effects

due to the incomplete establishment of electronic equilibrium at shallow depths. Electronic

equilibrium is established at different depths depending on the average energy of the photon (or

photons) emitted by the source. At shallow depths, before electronic equilibrium is established,

the photon dose is lower than the dose would be if electronic equilibrium is established.

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

dose, usually by several orders of magnitude. A significant exception to this concerns Co-60

and other low-energy beta emitters. A cover material can easily shield the relatively

low-energy-beta particles from this radionuclide without significantly attenuating the photon

dose. In this case, the photon dose will account for 100 percent of the calculated skin dose. 

Durham and Lantz (1991) published measurements verifying this phenomenon.

Despite upgrades to the photon dose model, Varskin 3 is primarily a beta dose calculation tool. 

The photon dose model is intended for use in estimating the photon dose from a particle. It is

not intended for use with distributed contamination. Calculations of photon doses for distributed

sources should be performed using a code designed to calculate photon dose.

The second special option (Figure 2-10) allows the dose to be averaged over a volume of tissue

defined by two different skin depths and the area of irradiation instead of the dose at one given

depth. An example of the use of the volume-averaged dose is evaluating the dose between

10 mg/cm2

 and 15 mg/cm2 as recommended by the International Commission on Radiological

Protection (1991) to evaluate the dermal effects of skin dose. Volume averaging greatly

increases the calculation time to as long as several minutes for each selected radionuclide.

If volume averaging is chosen, the user is prompted to enter the skin density thicknesses

associated with the top and bottom of the volume. The units of skin density thickness must be

entered in mg/cm2

. The range of possible values for the top and bottom of the volume are also

provided to the user and range from a skin density thickness of 0 mg/cm2

 to the maximum

penetration depth of the beta particles. Entering a value for the bottom of the volume that is

greater than the maximum penetration depth will result in an error message, and the user will be

asked to enter a different value. Varskin 3 calculates the dose averaged over the dose

averaging area at 50 depths between the top and bottom of the volume, as shown schematically

in Figure 2-11. Thus, the volume-averaged dose model requires up to 50 times more execution

time than that for a single depth. Calculation times in excess of 20 minutes on a pentium-class

computer are possible.

When the slab 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 (Figure 2-10) over the dose area of interest, is useful for calculating

dose from multiple hot particles. The default for this option is to not use the offset particle

model. When the offset particle box is checked, the user is prompted to enter the offset

distance. The offset distance is the horizontal distance between the center of the slab source

and the center of the dose area, as shown in Figure 2-12. Note that the x-side length and the

y-side length must be equal when using the offset particle model or an error message will be

displayed. The value of the offset is the only additional input value that is required for the

model, and the calculation is completed in roughly the same amount of time as a centered

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

the offset value if this option is selected.
2-15

Figure 2-11. Schematic Diagram of the Volume-Averaged Dose Model Geometry

Figure 2-12. Schematic Diagram of the Offset Particle Model
2-16

The offset particle model can be used to calculate the dose from multiple hot particles. Use of

the offset particle model is discussed in Section 6.2

2.2.6 Calculating Doses

When the desired geometrical parameters and options are selected, the calculation is initiated

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

at least once and possibly many times depending on the complexity of the calculations. The

calculation time is greatly affected by the number of radionuclides used in the calculation and

the various options that are selected. Volume-averaged doses require a particularly long time

to complete.

Varskin 3 calculates doses using a compiled FORTRAN program entitled Varcalc.exe. The

main program that collects the input data and displays the output data is written in Visual Basic. 

When the user clicks the “Calculate Doses” button, the Visual Basic program writes the input

data in a file called Output.dat. Varcalc reads Output.dat, performs the calculations in the

background, and then writes the results to a file entitled Results.dat. The Visual Basic code

reads Results.dat, performs some additional calculations, and displays the results of the

calculation. The logic flow diagram for Varskin 3 is depicted in Figure 2-13. Note that

output.dat and results.dat are internal files and are not intended to be used or edited by

the user.

2.2.7 Output Screen

The output screen for a nonvolume-averaged calculation is displayed immediately after a

calculation is completed, as shown in Figure 2-14. The screen is separated into three distinct

sections: results for individual radionuclides (upper left quadrant of the screen), combined

results for all radionuclides (upper right quadrant of the screen), and source input data/code

navigation (bottom half of the screen).

In the individual results section, only the results for the first radionuclide are shown initially. The

results from other radionuclides are displayed by highlighting the radionuclide of interest from

the list in the list box. Only the contribution to the dose from the selected radionuclide will be

displayed on this screen.

The combined results section displays the combined results for all radionuclides added

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

is initiated. This section of the output screen also contains a button that toggles the results

between English and System Internationale (SI) units. The dose results on the output screen

are displayed in either English or SI units depending on the choice of activity units for the last

radionuclide entered. If the activity of the last radionuclide was entered in SI or metric units, the

results will be displayed in SI units. Similarly, if the activity of the last radionuclide was entered

in English units, the results will be displayed in English units. Clicking on the button labeled

“SI Units” will switch the results from English units to SI units. Similarly, clicking on the button

labeled “English Units” (when SI units are displayed) will switch the results from SI units to

English units. The units will change for the calculated doses only; the input data will be

displayed in the same units that were entered on the Source Geometry screen.
2-17

Figure 2-13. Logic Flow Diagram for Varskin 3
2-18

Figure 2-14. Results Screen for a Typical Calculation

The bottom half of the output screen contains a mirror of the input data that was 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 on the “Print Results” button will send a hard copy of

all results to the default windows printer. Varskin 3 will not allow the user to change the default

printer. In addition, the program will fail if a printer is not installed when the “Print Results”

button is clicked. 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 3 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 clicking on the “Return to Geometry Screen” button and using

the file operations buttons as described above. This button can also be used to change a

parameter in the current calculation or to start a new calculation. Finally, the “Exit Program”

button allows the user to end Varskin 3.

A slightly different screen will appear for volume-averaged dose calculations. Because the dose

can be averaged over different averaging volumes for different radionuclides, Varskin 3 does

not provide a section for combined results of a volume-averaged dose calculation. Instead, only

the results from the individual radionuclides are displayed, as shown in Figure 2-15. In this

figure, the last unit entered was an SI unit, so the results are displayed in SI units. Only the

results for the highlighted radionuclide are displayed. The upper left section of the

volume-averaged results screen displays values of the top and bottom of the volume as well as

the total volume over which the dose was averaged for the chosen radionuclide. Highlighting

the name on the radionuclide list box allows other radionuclides to be chosen. The units may

be toggled between English and SI by clicking on the “English Units” button when SI units are

displayed or
2-19

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

by clicking on the “SI Units” button when English units are displayed. A summary of the input

parameters is displayed on the bottom half of the screen.

2.2.8 Exiting Varskin 3

There are several ways to exit Varskin 3. On the opening screen (Figure 2-1), clicking on the

X box in the upper right corner of the screen will immediately cause the code to stop and exit. 

On the Source Geometry screen (Figure 2-2), clicking on either the X box in the upper right

corner or the “End” button will result in a prompt to the user asking if the input data should be

saved to a file, as shown in Figure 2-16. Similarly, the same outcome will result from the

results screen by clicking on the X box in the upper right corner or the “Exit Program” button

(Figures 2-14 and 2-15). The user is then asked if the file is to be saved. When the “Yes”

button is clicked, the user is asked to create a file in which the input data will be saved so that

the calculation can be recreated. Clicking on the “No” button will end the calculation and cause

the program to end. Clicking on the “Cancel” button will return the user to the previous screen. 

Data from a saved file are stored with a .vs3 extension. When a saved file is opened, Varskin 3

reads the .vs3 to obtain the data for the calculation. This file is an internal file and is not

intended to be used or edited by the user.
2-20

Figure 2-16. Exit Screen
3-1

3 DESCRIPTION OF CALCULATIONAL MODELS

Varskin 3 includes upgrades to several models that are described in detail in this chapter. In

addition, improvements to models that were used in VARSKIN Mod 2 were incorporated into

Varskin 3 and are also described here. First, the calculational methodology used in Varskin 3

is described.

3.1 Beta Dose Calculations

Varskin 3 calculates beta dose using essentially the same method used in VARSKIN Mod 2. In

general, Varskin 3 performs a five-dimensional integration of the source volume and the target

area. With the exception of the slab model, the integration is simplified significantly because the

dose is symmetric for a circular target area centered under the source.

Varskin 3 calculates the beta dose rate by performing a numerical integration of the Berger

point kernel (Berger, 1971). This kernel is mathematically written as

B

k E YF X

r X (r) (r / )

( ) = β β

πρ

1 99

2

99

(3-1a)

where

B(r) = the dose at the dose point from a source at a source point

r = the distance between a source point and the dose point

k = a unit conversion constant

Eβ = the average beta energy for the radionuclide

Y = the beta yield per disintegration

Fβ(r1/X99) = the scaled absorbed dose distribution 

r1 = the modified path length between a source point and the dose point

ρ = the density of the irradiated medium (assumed to be unity for tissue)

The following equation gives an example of the units that might be included in Eq. (3-1a)

( ) (3-1b)

( )[ ]

[ ] [ ]

B r rad

h dis

k rad q

MeV h

Y

dis

F r X frac

g

cm

r cm X cm ⋅

⎡

⎣

⎢ ⎤

⎦

⎥ =

⋅

⋅

⎡

⎣

⎢ ⎤

⎦

⎥

∗ ⎡

⎣

⎢ ⎤

⎦

⎥

∗

⎡

⎣

⎢ ⎤

⎦

⎥

1

1 99

3

2 2

99

β

π ρ

/

where dis stands for disintegration.

The X99 distance is defined as the radius of a sphere of water surrounding a point source of beta

radiation in which 99 percent of the beta energy is deposited. In Varskin 3, the range of the

beta particles is chosen as the X99 distance, where X99 is equal to 1.8 times the X90 distance

cited in the reference (Berger, 1971). Varskin 3 calculates Fβ(r1/X99) for a selected radionuclide

when the radionuclide is added to the library, as described later in this section.

For the purpose of illustrating a dose calculation for a symmetrical source, the following

discussion describes a simplified dose calculation for the cylinder geometry shown in
3-2

Figure 3-1. Schematic Representation of a Dose Calculation for a Symmetric Source

Figure 3-1. Varskin 3 chooses a point located at the center of the irradiation area (dose point). 

The code then divides the sources into very small subvolumes (source points). The number of

source points ranges from 512 to over 1081 depending on a number of factors. The contribution

from each source point to the dose point is evaluated using Eq. (3-1) and the contributions are

summed. The total contribution (in dose/dis) is multiplied by the source strength (in dis) to get

the dose to the dose point. This procedure is repeated for each of 60 dose points beginning at

the center of the irradiation area and extending to its edge. These dose points represent

isodose curves within the irradiation area. Finally, the curves are average over the irradiation

area to determine the total dose to the area.

A more detailed description is now presented. The integration is performed by choosing

60 dose points [points at which the dose rate is to be calculated, shown as (–) (Figure 3-1),

beginning at the source centerline and proceeding radially outward from the centerline at the

skin depth level. Since the source is symmetric, dose points represent concentric isodose

circles that describe the radial dose rate profile at a given depth in skin. For each dose point,

an integration is performed over the area of the disk-shaped source at a given height in the

source represented by one of the eight elevation points (+) by choosing eight concentric circles

located at radially equidistant positions on the source (denoted by *). One of these circles

defined by a radial dose point (*) is chosen, subdivided into eight source points at equiangular

locations (angular source points, x), and the dose rate at the dose point from each of these

eight source points is calculated. The contribution to the dose from the first four points is then

compared to the contribution to the last four points. If the relative difference between the two

contributions is less than 0.0001, then convergence of the integral for the circle is considered to

be achieved, and this 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

subdivided into eight source points, and the above procedure is repeated for each of the two

sets. This process, known as the Newton-Cotes eight-panel quadrature routine, provides a fast

and accurate method of numerically integrating complex functions such as the Berger kernel.
3-3

Varskin 3 calculates dose for each of the dose points (!) pictured in Figure 3-1. Once a dose

rate value from each radial source point (*) is determined, the first four radial values are

summed and compared to the sum of the last four radial values. These two groups of radial

points are checked for convergence, and the above procedure is followed until convergence is

reached for all radial points in the source.

The dose at a dose point is calculated using the quadrature integration routine according to

the equation

&

D d S B r z r dz dr d () (,,)

R Thickness

= v ′′ ′ ∫ ∫ ∫

0 0 0

2π

θ θ (3-2)

where Sv is the volumetric source strength and z is the depth in the cylinder. A similar equation

can be written for spherical and slab geometries. These equations are

&

D d S B r r dr d d ( ) ( , , ) sin V

R

= ′′ ′ ∫ ∫ ∫

0 0

2

0

π π

θφ θ θ φ (3-3)

in spherical geometry where and are the azimuthal and polar angles, respectively, and θ φ

&() (,,)

max

max

max

max

D d S B x y z dzdy dx V

Thickness

y

y

x

x

= ∫ ∫ ∫ − − 0

(3-4)

in slab geometry.

The dose rate at the next dose point is then calculated until values are obtained at all 60 dose

points. If the dose rate profile defined by these 60 points as a function of target radius d' is

denoted D(d'), then the dose rate averaged over an area in the skin is calculated using

the equation

D

D d d dd

R Avg

R

=

′′ ′ ∫ 2

0

2

π

π

( ) (3-5)

The 60 dose points are not chosen linearly from the center of the irradiation area to its outer

radius. Instead, the 60 dose points are chosen such that more points are chosen where the

dose profile is changing the most. Typically this occurs at the edge of the source. Increasing

the number of dose points in the area where the dose is changing the most increases the

accuracy of Varskin 3 calculations. The distribution of dose points is chosen automatically

within Varskin 3.

When modeling a three-dimensional source, two types of attenuation must be addressed: 

attenuation due to the presence of the source material and attenuation due to geometry

(i.e., 1/r2

 attenuation). The Varskin 3 code determines the attenuation within the source material

by calculating the path lengths within the source, outside the source but above the skin, in the
3-4

Figure 3-2. Backscatter Correction Factor for Infinitely Thin and Point Sources

cover material (if any), and in the skin. Each of the path lengths is then modified by multiplying

the path length by the ratio of the density of the material to the density of water. The individual

modified path lengths are then added to obtain the total modified path length, r1, in Eq. (3-1).

3.2 Backscatter Model

In VARSKIN Mod 2, a backscatter model was introduced that has the effect of reducing the

calculated dose from point and thin disk sources. The backscatter correction was needed

because the Berger kernel (Berger, 1971) used in the dose calculation assumes that the source

is located in an infinite medium. Thus, the dose includes the contribution from beta particles

that were emitted away from the skin and subsequently scattered back toward the skin to

contribute to skin dose. Thus, when the Berger point kernel is used to calculate skin dose from

an infinitely thick (point or disk) source, the calculated dose will be an overestimate of the skin

dose. Depending on the maximum energy of the beta spectrum, the overestimate can be as

high as 40 percent (Cross, et al., 1992). VARSKIN Mod 2 applies an energy-depth-dependent

backscatter correction to doses calculated for point and disk sources. The backscatter factor is

the ratio of the dose from a source in an infinite medium to that from a finite source. An infinite

source is one where the dimensions of the source are larger than the X99 distance of the

beta-energy spectrum. A backscatter correction for three-dimensional sources was not included

in VARSKIN Mod 2.

The backscatter correction in VARSKIN Mod 2 was based on data calculated by Cross, et al.

(1992) for point and disk sources and dose calculations averaged over 1 cm2

. The backscatter

correction as a function of X99 distance is shown in Figure 3-2 (redrawn from Durham, 1992). 

The backscatter correction reduces the calculated dose by dividing the calculated dose by the

correction factor. In Varskin 3, the backscatter model extended to areas of up to 10 cm2

 and

includes a correction for three-dimensional sources that have dimensions that are less than the

X99 distance in the source material. This section describes the model and the calculations that

were performed to develop the model.
3-5

Figure 3-3. Geometry Used for MCNP Calculations for the Backscatter Model

A backscatter correction is needed for three-dimensional sources that have dimensions that are

smaller than the range of the beta particles emitted by the source. The range of a beta source

is not a discrete value because of electron straggling effects. In Varskin 3, the range is equated

to the X99 distance, which is the radius of a sphere of water surrounding a point source of beta

radiation in which 99 percent of the beta energy is deposited.

Calculations for the backscatter model were performed using the Monte Carlo Transport Code

MCNP4c2 (RSICC, 2001). The source was modeled as a uniformly distributed cylinder source

with the thickness equal to the diameter. For the infinite-medium model, the source was

surrounded by water (see Figure 3-3a). For the air-skin interface model, the region above the

source was modeled as air (see Figure 3-3b). Note that the tissue in Figure 3-3 extends to the

top of the source for both cases. The source was modeled in this fashion because only the

effect of backscatter on the ratio of the doses was of interest. If the sides of the source were

not covered in the air-skin interface model, the beta particles emanating from the sides of the

source would affect the dose ratios for reasons other than backscatter because a larger area

would be irradiated. The source material was iron with a density of 7.86 g/cm3

, and the

thickness of the disk was varied between 1 μm (the diameter of the point source in Varskin 3

calculations) and the X99 distance for the radionuclide.

Four different radionuclides were used as sources that emitted very low-, low-, intermediate-,

and high-energy beta particles. The radioactive attributes of each of the four sources are

provided in Table 3-1. Spectra for the four radionuclides were obtained from the computer code

NUCDECAY (RSICC, 1995).

For each data point, one million particles were generated in the source with a uniform emission

angle for each simulated geometry. The simulations calculated energy flux through a circular 
3-6

Figure 3-4. Ratio of Flux in Water to Flux in Air for Pm-147

Table 3-1. Radioactive Characteristics of the Sources Modeled for the

Backscatter Correction

Nuclide

Average Energy

(keV)

Maximum Energy

(keV) Range in Iron (μm)

Pm-147 62 225 38

Sr-90 196 546 182

Tl-204 244 763 297

Y-90 935 2,280 1,190

disk located 70 μm below the bottom of the source sorted into 15 different energy bins. The

dose was determined from the flux by multiplying the flux in each bin by the average stopping

power for that energy bin and summing the results. Values for mass stopping power were

obtained from the National Institute of Standards and Technology (NIST) website (Berger, et al.,

2006). The calculated quantity of interest was the ratio of the flux in the infinite medium model

to the flux in the air-interface model.

Figure 3-4 displays the (i) ratio of flux in the infinite medium to the flux in air and (ii) ratio of dose

in the infinite medium to dose in the finite medium as a function of the source size expressed as

a percent of the X99 distance for Pm-147. With the exception of very shallow depths, the ratio of

fluxes and ratio of doses are essentially the same. This trend was observed for all four

radionuclides. Since the VARSKIN Mod 2 model is sufficient for small particles, the remaining

figures show only the ratio of fluxes as a function of the X99 distance. Figures 3-5 through 3-7

contain the ratio of fluxes as a function of the size of the particle-expressed fraction of the X99

distance for Sr-90, Tl-204, and Y-90, respectively. A common trait of all four figures is a steadily 
3-7

Figure 3-5. Ratio of Flux in Water to Flux in Air for Sr-90

Figure 3-6. Ratio of Flux in Water to Flux in Air for Tl-204
3-8

Figure 3-7. Ratio of Flux in Water to Flux in Air for Y-90

diminishing correction factor with depth in the source. The correction approaches unity as the

size of the source approaches the range of the beta particles (the X99 distance). When the

source size is expressed as the fraction of the X99 distance, all four figures are similar with the

exception of sources with sizes less than 5 percent of the X99 distance. The backscatter

correction associated with these extremely small sources is similar to the backscatter correction

applied to infinitely thin sources in VARSKIN Mod 2. Thus, the backscatter correction applied to

sources with a thickness of less than 5 percent of the X99 distance is the same backscatter

correction applied to point and disk sources. It should be noted that the point source

backscatter correction model provides correction factors that are consistent with the

current calculations.

The data in Figure 3-8 are obtained by taking the data from Figures 3-4 through 3-7 and

consolidating them for all sources greater in size than 5 percent of the X99 distance. Several

attempts were made to fit the data using curve-fitting techniques available in Microsoft Excel®. 

The curve-fitting technique that resulted in the highest R2

 value was the logarithmic fit with an R2

value of 0.98. The trend line represents the Backscatter Correction Factor (BCF) as a function

of the fraction of X99 distance. The equation for the backscatter correction factor is

BCF t X = − 1018 0 060 source 99 . . ln( / ) ∆ (3-6)

where ∆tsource is the source thickness (or diameter for spheres).

In VARSKIN Mod 2 and Varskin 3, the backscatter correction factor is applied to the calculated

dose for three-dimensional sources with a thickness that is less than the X99 distance in the

source material. If the source thickness is less than 5 percent of the X99 distance in the source

material, then the point backscatter correction factor is applied. For sources with a thickness

that is greater than the X99 distance, no backscatter correction is applied because the source is

“infinitely thick” and the Berger kernel is accurate for these sources.
3-9

Figure 3-8. Combined Data for the Four Radionuclides

The VARSKIN Mod 2 backscatter correction model also accounted for material located between

the source and the skin depth of interest. The current calculations support this model. The

VARSKIN Mod 2 model for infinitely thin sources has been incorporated in Varskin 3, and for

sources with a thickness of less than 5 percent of the X99 distance, the backscatter correction

factor changes when the source is not in contact with the skin. The presence of covering

material does not significantly affect the backscatter correction for three-dimensional sources

because of the small magnitude of the correction. Therefore, the backscatter correction factor

does not change with depth for sources with a thickness greater than 5 percent of the X99

distance in the source material.

A backscatter correction model has been developed for three-dimensional sources that can be

used in the Varskin 3 skin dose code. For sources with a thickness of less than 5 percent of the

X99 distance in the source material, the model uses a correction factor that is consistent with the

backscatter model used in VARSKIN Mod 2. For sources with a thickness between 5 and

100 percent of the X99 distance, a new correction factor is applied as a function of the X99

distance that follows a logarithmic distribution. Sources that are thicker than the X99 distance

are infinite sources, and no correction to the Berger kernel is required.

3.3 Cover Layer and Air Gap Models

Both cover materials and air gaps can be modeled using Varskin 3. The models use the

concept of path length to determine the energy lost in either a cover material or air. 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. In order to

prevent unintended applications of Varskin 3, the air gap is limited to a maximum of 5 cm.

The method used to determine path length within the source and within the cover material can

be illustrated using Figure 3-9. 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 
3-10

Figure 3-9. Schematic Drawing of a Generic Dose Calculation Performed by Varskin 3 for

the Cylinder Geometry

point (SRAD), the source thickness (STHICK), the cover thickness (CTHICK), the skin depth (SDEP), the

source and cover densities (ρs and ρc, 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). The quadrature routines 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. To

do this, the square of the projected distance, rp

2

, is calculated using the law of cosines:

r P S PS p s RAD s RAD

2 22 = + −× × × 2 cosθ (3-7)

The quantity r is used in the denominator of the expression in Eq. (3-1) and represents the

geometric attenuation between the dose point and the source point. The value of r can then be

determined using the Pythagorean theorem

r rD = + p RAD

2 2 (3-8)

This quantity is further analyzed to calculate the modified path length used to evaluate the

scaled absorbed dose distribution as discussed next.

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

r C rD c THICK RAD = × / (3-9)
3-11

The distance traveled through the skin is given by

r S rD t DEP RAD = × / (3-10)

Finally, the distance traveled through the source is given by

r D C S rD s RAD THICK DEP RAD = − −× ( )/ (3-11)

The modified path length r1 is then found from the equation

rr r r 1 = ( )/ ss cc tt t ρ + ρ + ρ ρ (3-12)

where ρt

 is the density of tissue, assumed to be equal to the density of water (1 g/cm3).

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. (3-12) must be further analyzed to determine the

path length within the source and the path length outside the source, but above the

cover-material level. The actual path length within the source is multiplied by the source

density, and the path length outside the source and above the cover material is multiplied by the

density of the material outside the source, assumed to be air.

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

r PS PS p s RAD S RAD

2 22 2 = + × −× × × × sin sin cos φ φθ 2 (3-13)

and in slab geometry the actual distance is given by the equation

rx x y y z z = −+−+− [ ] ( source dose source dose source dose ) ( ) ( ) 222 1 2/

(3-14)

The remaining equations apply to both spherical and slab geometries.

3.4 Volume-Averaged Dose Model

The volume-averaged dose model (shown schematically in Figure 2-11) allows the calculation

of doses averaged over volumes of skin. Any two planes of irradiated skin bound the volume

(i.e., any two planes between zero skin depth and the skin depth that corresponds to the

maximum penetration of beta particles emitted by the source). For sources in contact with the

skin, the maximum penetration depth is equal to the X99 distance. Doses averaged over the

dose-averaging area are calculated at 50 skin depths between these two limits, and a cubic

spline (a third-order piecewise polynomial curve fit) is fit to this depth-dose distribution. When

the user enters the skin depths corresponding to the volume of interest, Varskin 3 integrates the

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

volume-averaged dose model requires roughly 50 times the execution time as a single depth
3-12

calculation to establish the depth dose function. Calculation times as long as 5 minutes

are possible.

3.5 Offset Particle Model

The offset particle model (shown schematically in Figure 2-12) allows calculation of skin dose

averaged over areas that are not directly below the contaminant. This model was developed to

calculate doses from multiple hot particles. The offset particle model is available only for the

slab geometry.

The offset particle model requires only one input variable, the distance of the offset. When

performing the calculations for the model, Varskin 3 requires that the offset is in the x direction. 

Since this requirement implies a symmetrical source, the x- and y-side lengths must be equal. If

the user invokes the offset particle model with a source that does not have equal x- and y-side

lengths, Varskin 3 will request that the user re-enter the x- and y-side lengths. Varskin 3 also

provides the user with the x-side length that corresponds to a source of equivalent area should

the user wish to maintain the area of the source.

For multiple particle irradiations, doses from each particle must be calculated separately,

running Varskin 3 once for each particle. The offset particle model does not calculate the

maximum dose to skin from several particles (the iterative process for determining the maximum

dose to the dose-averaging area is outlined in Section 6.2).

3.6 Photon Dose Model

Photon doses calculated by Varskin 3 use an expanded version of a simplified model developed

by Lantz and Lambert (1990). Durham and Lantz (1991) verified the original photon dose model

experimentally. The photon dose model assumes that the source is a point source and that any

material between the source and skin is nearly tissue-equivalent. Therefore, the largest

dimension of any source has been arbitrarily limited to a maximum of 1 mm. The photon dose

is calculated (provided that the radionuclide emits photon radiation) for skin areas of up

to 10 cm2

. The method used to develop the photon dose model is described in Appendix A.

It is important to note that the photon dose is calculated assuming that the source can be

represented as a point source, regardless of the geometry package that is chosen by the user. 

If a three-dimensional source geometry is chosen, the photon source is assumed to be located

at the bottom center of the source. Thus, if the radius of the source is changed, the photon

dose will remain the same for the same amount of activity.

Two pieces of information are used to calculate the photon dose: the specific photon dose

constant and the average photon energy. The specific photon dose constant is used to

determine photon doses when electronic equilibrium is fully established. The average photon

energy is used to determine the extent to which electronic equilibrium is established.
3-13

The specific photon dose constant, in units of rad-cm2

/mCi/h is calculated for the radionuclides

using the following equation modified from Attix (1986)

Γ [ ] rad cm

mCi h

P E MeV m

kg i

i

n

i

en

Ei tissue

−

−

⎡

⎣

⎢ ⎤

⎦

⎥ = ⎛

⎝

⎜ ⎞

⎠

⎟ ⎡

⎣

⎢ ⎤

⎦

⎥

⎡

⎣

⎢

⎢

⎤

⎦

⎥ = ⎥ ∑

2

1

2

1938 μ

ρ ,

(3-15)

where Pi

 is the probability of the emission of a photon having an energy Ei and (μen/ρ)Ei,tissue is the

mass energy absorption coefficient in soft tissue for the photon. Data for (μen/ρ)Ei,tissue were

obtained from a NIST website (Hubbell and Seltzer, 2006) and based on ICRU–44 (International

Commission on Radiation Units and Measurements, 1989). Data for Ei

 and Pi were obtained

from the NUCDECAY data files (RSICC, 1995).

The average photon energy in keV is calculated using the equation

[ ]

[ ]

E MeV

P E MeV

P avg

i i

i

i

i

=

∑

∑ (3-16)

In Varskin 3, the specific photon dose constant and the average photon energy are included in

the library file for the chosen radionuclide. The user can choose to eliminate low-energy

photons by choosing a suitable cutoff energy when creating the radionuclide library file. The

gamma dose model does not account for absorption in the skin. At skin depths of 7 mg/cm2

,

photon energies as low as 2 keV contribute to the dose. However, at skin depths of

1,000 mg/cm2

, photons below 35 keV do not contribute to the dose. It is important that the user

choose a cutoff energy that is appropriate for the depth at which the dose is being calculated. 

If a low cutoff energy is chosen for a deep skin depth, the dose may be overestimated. If a high

cutoff energy is chosen for a shallow skin depth, the dose may be underestimated. 

Recommended cutoff energies for photons is 2 keV for shallow dose, 20 keV for eye dose, and

35 keV for deep dose equivalent.

3.7 Syringe Model

The syringe model in Varskin 3 employs a major approximation to an actual syringe and, in this

respect, has several limitations. In the syringe model, Varskin 3 converts the syringe to a

cylinder in which the diameter of the syringe is set equal to the thickness of the cylinder. The

diameter of the cylinder is calculated by setting the volume of the cylinder equal to the volume of

the syringe. The dose is then calculated at the bottom of the cylinder. This approximation has

significant impacts for syringes that are long and narrow. Doses calculated for long, narrow

syringes will probably be inaccurate. In addition, since the dimensions of the syringe are

greater than 1 mm, photon doses will not be calculated. To calculate beta doses, the syringe

model collects values from the user for the source volume, V; source density, ρs; the syringe

wall thickness, wT; and the outer diameter of the syringe, ODsyr. As with all geometry packages,

the user has the option to include an air gap thickness and the thickness and density of a cover

material, ∆tcov and ρcov, respectively. The syringe wall material is assumed to be polyethylene

with a density of 0.92 g/cm3

. Varskin 3 approximates the dose from a syringe source by using

the cylinder geometry with input values modified to approximate the size of the syringe as

described in the following discussion.
3-14

First, Varskin 3 calculates the diameter of the syringe source, ds, using the following equation

d OD w s syr T = − 2 (3-17)

Varskin 3 constructs a cylinder with a thickness, ∆tcyl, equal to the diameter of the syringe

source. While maintaining the volume of the source, the radius of the constructed cylinder, rcyl,

is determined using the equation

r

V

r t cyl

cyl

= π ∆ (3-18)

Finally, Varskin 3 calculates the total cover thickness and effective density that includes any

cover material and the thickness of the syringe wall. The total cover thickness, ∆ttot, is

calculated according to

∆ ∆ t wt tot T = cov (3-19)

and the effective density, ρcov, is found from the equation

ρ ρ e

T

tot

t g cm w

t = ∆ + ×

∆

cov cov 0 92 . / 3

(3-20)

3.8 Adding Radionuclides to the Varskin 3 Library

Adding radionuclides to the Varskin 3 library is accomplished using a FORTRAN executable file

entitled Sadcalc.exe. The purpose of the program, which is an adaptation of a stand-alone

program formerly called SADDE Mod 2 (Reece, et al., 1989) is to produce a data file that

contains the information needed to calculate both beta and photon doses in Varskin 3. For beta

doses, the data file includes four of the variables that are shown in Eq. (3-1) for a chosen

radionuclide. These variables include the average beta energy, Eβ; the beta yield, Yβ; the X99

distance (which is used to establish the range of the beta particles); and the scaled absorbed

dose distribution, Fβ(r/X99). These data are calculated using the method described by Berger

(1971), which is not repeated here. The X99 distance is used in this document and has been

adapted from the X90 concept introduced by Berger (1971) in order to simplify the concepts. 

The relation between X90 and X99 is given by the equation

X99 = 1.8 X90 (3-21)

In Varskin 3, the beta spectrum is obtained from the data file ICRP38.BET, which is located in

the \dat subdirectory of Varskin 3 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 the values

in ICRP.DAT. A file that is associated with the beta spectra 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 file ICRP.DAT also includes photon data and the GUI in Varskin 3

calculates the specific photon dose constant and the average photon energy as described in

Section 4.6. The GUI collects the beta spectrum for a selected radionuclide and writes a file
3-15

entitled SadInput.dat that 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 Eβ, Yβ, the X99 distance, and Fβ(r/X99); 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.

The FORTRAN program Sadcalc.exe runs independently of the GUI, and no information is

passed from Sadcalc.exe to the GUI when the executable is running. In order for the GUI to

detect when the executable is finished running, Sadcalc.exe writes a small file entitled “ping”

when it has finished writing sadout.dat. While the executable is running, the GUI executes a

“do loop” that continuously checks for the presence of ping while updating a scroll bar at the

same time. When the GUI detects ping, the do loop is exited, and the GUI continues with the

subsequent calculations and operations.

A total of 838 radionuclides are available to add to the Varskin 3 library. 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

that 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. If the radionuclide

emits photons and/or electrons but no beta particles, then the following occurs. First, a tritium

spectrum is generated with a yield of 0.001. Any electrons are added to the tritium spectrum,

and the photon parameters are calculated for the library file. Sadcalc.exe then calculates 

Fß(r/X99) for the tritium spectrum and any electrons. This procedure is necessary because

Sadcalc.exe requires that a beta spectrum be present to calculate the scaled absorbed dose

distribution. Tritium was chosen because of its extremely low energy, and the low yield was

chosen to minimize the impact of dose from the tritium spectrum. The presence of the tritium

spectrum will calculate a small beta dose in the rare case of dose calculations at extremely

shallow depths (i.e., depths less than 2 mg/cm2

) for radionuclides that do not emit beta particles.

4-1

4 VALIDATION AND VERIFICATION OF VARSKIN 3

A validation plan and report was developed and implemented to demonstrate that Varskin 3

operates as expected and compares well with other methods. The validation plan and report is

available on the Varskin 3 distribution disk. The portion of the validation plan and report that

compares Varskin 3 results to other techniques is reproduced in this section.

4.1 Point Source on Skin

In this test, calculations were completed for the case of a point source directly on the skin

(i.e., no material and no air gap between the source and skin). For a 1-μCi hot particle on the

skin, the beta dose rate to 1 cm2

 at 7 mg/cm2 was calculated using Varskin 3. For Co-60, a

comparison of beta and gamma dose rates given by Chabot, et al. (1988) to those predicted by

Varskin 3 was made. The results are shown in Table 4-1. There is reasonable agreement

among the beta dose rates with those calculated using Varskin 3. The Varskin 3 results were

slightly lower because of the backscatter correction that is discussed in Section 3.2. The

difference in the photon dose calculation reflects the inclusion of charged particle equilibrium

effects in Varskin 3.

4.2 Point Source on Cover Material

The model of Chabot, et al. (1988) was used in this test. The types of cover materials

modeled were 

• One layer of cotton coveralls with a thickness of 0.37 mm and density of 0.7 g/cm3

• Two layers of cotton coveralls with a thickness double that of the above thickness

• One layer of coveralls plus one layer of plastic suit material, the latter with a thickness

of 0.4 mm and a density of 1.1 g/cm3

The calculations were completed for the isotopes Co-60, Cs-137, Ba-137m, and Sr-90/Y-90,

assuming a point source of 1 μCi each and no self-absorption. Air gaps of 0.2 and 1.0 cm were

used for the first two clothing types, and 1.0 and 5.0 cm were used for the third. It was assumed

that there was no air gap between the layers of protection clothing. Photon doses were

calculated using the analytical expression in Chabot, et al. (1988), assuming no attenuation in

clothing, no scatter, and a conversion from exposure to dose of 1 rem/R for photons.

Table 4-1. Comparison of Calculated Skin Dose Rates for a 1-μCi Hot Particle on

the Skin

Beta Dose Rate (rad/h) Photon Dose Rate (rad/h)

Nuclide Varskin 3

Chabot,

et al.*

Difference

(%) Varskin 3

Chabot,

et al.*

Difference

(%)

Co-60 3.76 4.33 !15 0.329 0.364 !11

*Chabot, G.E., K.W. Skrable, and C.S. French. “When Hot Particles Are Not on the Skin.” Radiation Protection

Management. Vol. 5, No. 6. pp. 31–42. 1988.
4-2

The results of these calculations and the same calculations completed with Varskin 3 are shown

in Table 4-2. In general, there is reasonable agreement between the two calculations for both

the beta and photon dose rate calculations. The largest differences occur for the case of

Cs-137, Ba-137m on two layers of cotton coveralls.

4.3 Distributed Contamination on Skin

The third set of calculations was for the case of distributed contamination on the skin. A

concentration of 1 mCi/cm2

 over a circular area of 100 cm2 was assumed, and the beta dose

rate to 1 cm2

 of skin centered under the contamination was calculated. The calculations were

completed with Varskin 3, and the results were compared to values published by Rohloff and

Heinzelmann (1986) and by Kocher and Eckerman (1987). The results from Varskin 3 and

Rohloff and Heinzelmann (1986) (shown in Table 4-3) agree quite well because both methods

account for the lack of backscatter from an infinitely thin source. Results using the Kocher and

Eckerman (1987) method are somewhat higher because the method overestimates backscatter

from air.

Table 4-2. Comparison of the Chabot Method and Varskin 3 for 1-μCi Hot Particle Point Source on

Cover Material

Beta Dose Rate (rem/h) Photon Dose Rate (rem/h)

Nuclide

Air Gap 

(cm) Clothing

Chabot,

et al.* Varskin 3

Difference

(%)

Chabot,

et al.* Varskin 3

Difference

(%)

Co-60 0.2 1B† 0.203 0.196 !3 0.077 0.0721 !6

1.0 1B 0.080 0.078 !1 0.011 0.010 !9

0.2 2B 0.002 0 — 0.067 0.063 !6

1.0 2B 0.004 0 — 0.010 0.0094 !6

1.0 B+P ‡ 0 0 — 0.010 0.0096 !4

5.0 B+P 0 0 — 0.0005 0.0005 0

Cs-137/

Ba-137m

0.2 1B 1.33 1.40 +5 0.019 0.019 0

1.0 1B 0.295 0.279 !5 0.0027 0.0027 0

0.2 2B 0.357 0.475 +33 0.0167 0.0177 0

1.0 2B 0.121 0.140 +16 0.0025 0.0025 0

1.0 B+P 0.067 0.077 +15 0.0025 0.0025 0

5.0 B+P 0.0035 0.0038 +9 0.0001 0.0001 0

Sr-90/

Y-90

0.2 1B 3.534 3.26 !8

1.0 1B 0.596 0.531 !11

0.2 2B 2.245 2.069 !8

1.0 2B 0.409 0.395 !3

1.0 B+P 0.337 0.326 !3

5.0 B+P 0.018 0.0167 !7

*Chabot, G.E., K.W. Skrable, and C.S. French. “When Hot Particles Are Not on the Skin.” Radiation Protection

Management. Vol. 5, No. 6. pp. 31–42. 1988.

†B—Cover material = thickness of 0.37 mm, density of 0.7 g/cm3.

‡P—Cover material = thickness of 0.4 mm, density of 1.1 g/cm3.
4-3

Table 4-3. Comparison of Calculated Beta Skin Doses for Distributed Contamination of

1 μCi/cm2

 Averaged Over 100 cm2 on the Skin

Beta Dose Rate (rad/h)

Nuclide Varskin 3

Rohloff and

Heinzelmann*

Kocher and

Eckerman†

Co-60 3.77 3.24 4.18

Cs-137 5.12 — 5.91

Sr-90 12.43 12.06 15.61

*Rohloff, F. and M. Heinzelmann. “Calculation of Dose Rates for Skin Contamination by Beta Radiation.” 

Radiation Protection Dosimetry. Vol. 14. pp. 279–287. 1986.

†Kocher, D.C. and K.F. Eckerman. “Electron Dose-Rate Conversion Factors for External Exposure of the Skin

From Uniformly Deposited Activity on the Body Surface.” Health Physics. Vol. 53. pp.135–141. 1987.

Next, results of Varskin 3 calculations were compared to the results of calculations using the

following references:

• Delacroix (1986)

• Kocher and Eckerman (1987)

• Piechowski (1988)

These three papers give maximum dose rates from a source modeled as an infinitely thin,

uniformly contaminated (1 μCi/cm2

) plane surface. Doses were calculated at different depths in

the skin. The Varskin 3 input data were

• Disk geometry

• 2-cm diameter

• 3.14-μCi activity

Tables 4-4 and 4-5 show that the results are in good agreement although the Varskin 3 results

are lower because of the backscatter correction as discussed in Section 3.2.

Table 4-4. 70-μm Depth Dose Coefficients in rad-cm2

/μCi/h

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

Varskin 3 1.12 6.63 5.25 5.46 6.84

Delacroix* 1.07 9.15 6.42 6.99 9.18

Kocher and

Eckermann†

1.22 8.87 6.34 6.76 8.87

Piechowski‡ 1.2 7.0 6.0 5.9 7.5

*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.

†Kocher, D.C. and K.F. Eckerman. “Electron Dose-Rate Conversion Factors for External Exposure of the Skin

from Uniformly Deposited Activity on the Body Surface.” Health Physics. Vol. 53. pp.135–141. 1987.

‡Piechowski, J. “Dosimetry and Therapy of Skin Contaminations (in French).” CEA–R–5441. Paris, France: 

Commissariat à l'Energie Atomique. 1988.
4-4

Table 4-5. Dose Coefficients Versus Depth for Y-90 Averaged Over 0.01 cm2 in 

rad-cm2

/μCi/h

Method 40 μm 70 μm 100 μm 400 μm

Varskin 3 7.94 6.86 6.17 4.09

Delacroix* 10.46 9.18 8.37 5.24

Kocher and

Eckerman†

10.14 8.87 — 5.07

*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.

†Kocher, D.C. and K.F. Eckerman. “Electron Dose-Rate Conversion Factors for External Exposure of the Skin

From Uniformly Deposited Activity on the Body Surface.” Health Physics. Vol. 53. pp.135–141. 1987.
1

Chase, J. “pdf Version of Report.” Email communication (September 15) to J. Durham, Colorado State University,

Ft. Collins, Colorado. Toronto, Ontario, Canada: Ontario Power Generation, Inc. 2004.

5-1

5 CHANGES TO VARSKIN MOD 2 AND NEW FEATURES AND LIMITATIONS

OF VARSKIN 3

This section describes the problems that were identified in VARSKIN Mod 2, fixes incorporated

in Varskin 3, and the new features that are included in Varskin 3. It also provides information on

the limitations of Varskin 3.

5.1 Corrections to Errors in VARSKIN Mod 2

In the years since the release of VARSKIN Mod 2, several errors have been identified and

industry users have made many suggestions for improvement. VARSKIN Mod 2 calculated the

dose averaged over 1 cm2

 of skin as the default value. The U.S. Nuclear Regulatory

Commission (NRC) has proposed a new uniform skin dose limit that requires determining the

dose averaged over an area of 10 cm2

 for comparison against the 50 rad limit for both point and

distributed sources (NRC, 2002). Varskin 3 calculates the dose to 10 cm2

 as a default for

comparison to the 50 rad limit. Varskin 3 also contains the capability of calculating the dose to

areas other than 10 cm2

 to evaluate exposures to other areas.

VARSKIN Mod 2 was designed to operate efficiently on a personal computer containing an

80286 processor; this required several simplifications in the calculational methodology to be

incorporated into the code to allow the dose calculations to be completed in a reasonable length

of time. These simplifications did not significantly affect the accuracy of doses at a depth of

7 mg/cm2

 averaged over 1 cm2 for which the code was designed. However, the accuracy of the

code when applied to dose calculations averaged over significantly smaller or larger areas or

when applied to irradiated volumes can be affected by the simplifications. In addition, the user

interface in VARSKIN Mod 2 requires the user to enter radionuclide data sequentially even

when the source and target geometry remained the same for each radionuclide. With the

advent of powerful personal computers and the windowing capabilities of current operating

systems, calculational simplifications are no longer necessary and sequential data entry can be

avoided. Varskin 3 uses improved algorithms for calculating skin dose that take advantage of

the increased power of modern personal computers and that improve the overall accuracy of

the calculations.

Personnel at Ontario Power Generation, Inc., performed extensive testing of VARSKIN Mod 2. 

This testing covered many atypical applications of the code, and several errors were identified. 

A communication summarizing the errors and their impact on dose calculations was sent in

20041

. Errors associated with the following items have been identified, and the solution

incorporated in Varskin 3 is identified. Errors were also identified in SADDE Mod 2. SADDE

Mod 2 is a companion computer code to VARSKIN Mod 2 that allows radionuclides to be added

to the VARSKIN Mod 2 radionuclide library. SADDE Mod 2 was developed shortly after

VARSKIN Mod 2.

• Source Density: The source density for point and two-dimensional calculations is

defined by the last calculation using a three-dimensional geometry and is not reset to

0.001 g/cm3

 as intended. In VARSKIN Mod 2 and Varskin 3, point and
5-2

two-dimensional disk sources are modeled as cylindrical sources with very small

(~1 μm) dimensions, when appropriate, and a negligible density of 0.001 g/cm3

.

Solution: The source density is reset to 0.001 g/cm3

 when point and disk source

geometries are used for calculations.

• Backscatter Correction: The backscatter correction is only included for point and

two-dimensional geometries when the dose is averaged over 1 cm2

.

Solution: The backscatter correction model has been expanded to include

three-dimensional sources and is applied regardless of the dose-averaging area.

• Low Results for Small Sources: The cylinder source geometry used for point, disk,

and cylinder source geometries omits the dose contribution from a center cylinder with

a 0.27-μm radius, where the cylinder height is the source height. This omission

results in a relatively large dose contribution being ignored in calculations involving

very small sources, significantly reducing the calculated dose. In VARSKIN Mod 2,

the minimum distance between a source point and a target point was chosen to be

0.27 μm based on the average distance that an electron travels between interactions. 

In the sphere model, the dose contribution from a 0.27-μm radius sphere was

also omitted.

Solution: Varskin 3 was revised so that the minimum distance between the source

and target was reduced from 0.27 μm to a value of 0.01 μm.

• Incorrect Results for Very Shallow Skin Depths: Results of calculations at very

shallow skin depths for sources directly on the skin were found to be unreliable.

Solution: Varskin 3 uses 60 radial-dose-calculation points on the target area instead

of 26 points used in VARSKIN Mod 2. Once the 60-point distribution is calculated, the

distribution is evaluated at 10,000 points to increase the reliability of the calculation.

• Incorrect Volume-Averaged Dose Results for Sources on Skin: The volume-averaging

results were found to oscillate for sources directly on the skin. The recommended

correction of placing a 1-μm layer of unit density cover between the source and skin

only worked for radionuclides whose beta energy was less than or equal to that of

Co-60 (318 keV).

Solution: Varskin 3 evaluates the dose at 50 depths for volume averaging instead

of 20 depths. Once the 50-point depth-dose distribution is calculated, the distribution

is evaluated over 10,000 points to increase the accuracy and eliminate

oscillating results.

• Volume-Averaged Dose Backscatter Correction Factor: A single backscatter

correction factor is used at all skin depths for volume-averaged doses in VARSKIN

Mod 2. The backscatter correction factor is chosen when the skin depth is entered on

the input screen.
5-3

Solution: Varskin 3 calculates the backscatter correction factor at each of the

50 depths in the volume-averaged dose distribution.

• Incorrect Charged Particle Equilibrium (CPE) Correction for Photon Dose

Calculations: A programming error in the photon dose CPE correction was identified

that allows unreliable calculations if clothing is present with a density much different

than that of water and for large air gaps.

Solution: The programming error was corrected in Varskin 3.

• Mixtures of Radionuclides and Multiple Decay Paths: SADDE Mod 2 was found to

incorrectly add mixtures of radionuclides and perform poorly with single radionuclides

that have multiple decay paths with widely varying energies. This is caused in part by

using a beta-screening model in SADDE Mod 2 that greatly affects low-energy beta

particles when they are added to high-energy beta particles.

Solution: In Varskin 3, the capability of adding multiple radionuclides was eliminated,

and a more accurate method of building library files was incorporated.

• Double Yield Problems in Doses With Single Radionuclides: SADDE Mod 2 was

found to contain a programming error that resulted in the yield of a beta decay being

applied twice. For yields that differ significantly from 1, the yield is either

underestimated or overestimated.

Solution: The programming error was corrected in Varskin 3.

• Incorrect Dose Calculation for Small Target Areas, Low Energy Betas, and Large

Sources: For large three-dimensional sources emitting low-energy betas, the

calculated results were found to be incorrect. Specifically, the dose to a small target

area at a very shallow skin depth from a S–35 cylinder source with a diameter of

34,000 μm and a thickness of 200 μm (the source density-thickness is comparable to

the range of the beta particles) was found to be in error.

Action: The integration limits for these unique calculations were investigated, and the

error was corrected for all geometry packages in Varskin 3. 

• “Ringing” of Spline Function for Small Sources: For small sources on the skin or with

a very thin cover or air gap, the dose rate decreases very rapidly with a small increase

in radial distance, causing the spline interpolation function to oscillate or “ring.” 

Ringing causes doses at the edge of the irradiation area.

Action: Ringing was found to be caused by using a linear fit of data that is changing

very rapidly. Varskin 3 transforms the data to a log scale prior to applying the spline

fit, thus eliminating this problem.
2

Chase, J. “pdf Version of Report.” Email communication (September 15) to J. Durham, Colorado State University, Ft. Collins,

Colorado. Toronto, Ontario, Canada: Ontario Power Generation, Inc. 2004.

5-4

5.2 New Features in Varskin 3

In addition, the Chase communication2 recommended investigation of several areas for

improvement to the code. The action taken in Varskin 3 is provided for each of the suggestions.

1. Anomalies in Radial Dose Distributions: The radial dose distribution exhibited

unexpectedly large dips and peaks.

Action: The Relative Error has been changed from 0.001 in VARSKIN Mod 2 to

0.0001 in Varskin 3 to minimize the problem, and the user can no longer change this

parameter. The relative error is the parameter that determines when the numerical

integration routine has converged. This correction was possible because of the high

speed of modern computers.

2. Improved Photon Dose Model: The photon dose model in VARSKIN Mod 2 was

limited to a dose area of 1 cm2

. The photon dose model is inadequate for determining

both shallow dose and deep dose at the newly recommended dose-averaging area of

10 cm2

.

Action: An improved photon dose model that calculates the photon dose to any area

smaller than 10 cm2

 was incorporated into Varskin 3. The new model is based on

data provided by Lantz as shown in Appendix A.

3. More Accurate Beta Spectrum Information: The specific absorbed dose distributions

used by VARSKIN Mod 2 were calculated from basic nuclear data.

Action: In Varskin 3, beta spectra are obtained from abridged ICRP–38 (International

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

data files. This improves the reliability of the library files in Varskin 3 and results in

more reliable dose calculations.

4. Poor Results From Internal Conversion and Auger Electrons at High Energies: 

Internal conversion and Auger electrons are treated correctly in SADDE Mod 2 only

when they have energies much less than the maximum beta energy and have

relatively small yields. This is caused by using a cubic spline to fit data that is

rapidly changing, resulting in an oscillation or “ringing” of the fit. Ringing leads to

inaccurate results.

Action: Varskin 3 performs a log transformation prior to applying the cubic spline to fit

the data, thus eliminating the ringing.

Users of VARSKIN Mod 2 in the nuclear power industry and in the field of medical isotopes

have also suggested improvements to the code. The most common suggestion is to make a

version that is Windows® compatible to allow the user to enter data more efficiently. The

second most common suggestion is to make adding radionuclides to the library easier. 
5-5

With the release of the operating system Windows XP®, the Microsoft Corporation has

significantly reduced its support of DOS. VARSKIN Mod 2 operates under the DOS operating

system, and when DOS is eventually eliminated from Windows, operation of VARSKIN Mod 2

will no longer be possible. Therefore, Varskin 3 was written to operate under the Windows

operating system.

The input data file for VARSKIN Mod 2, BETADATA.DAT, is no longer used in Varskin 3. Each

user builds a library that contains only the radionuclides of interest to that user. The new data

files contain physical data for the average energy, maximum energy, and yield based on data

generated by the computer code NUCDECAY (RSICC, 1995), which uses data published in

ICRP–38 (International Commission on Radiological Protection, 1983). Further information in

the library files includes data for photon dose calculations and contributions from internal

conversion and Auger electrons.

5.3 Limitations of Varskin 3

Varskin 3 is designed to calculate the dose to skin from skin contamination. Users may try to

use Varskin 3 to perform calculations that are beyond the intended application of the code. This

section discusses the known limitations of Varskin 3 and establishes the limits over which

Varskin 3 has been tested.

The first item of note is not a limitation of Varskin 3, but a code design decision, and involves

the treatment of radioactive progeny. In Varskin 3, radioactive progeny are not included with the

parent radionuclide and must be entered explicitly.

Varskin 3 has been shown to be reliable for all particulate sources that have dimensions that

are smaller than eight times the X99 distance of the radionuclide in tissue, depending on the

area of irradiation, especially for relatively small irradiation area. The X99 distance, which is

described in detail later, is essentially the range of the beta particles and appears on the

printout. When a source becomes larger than this value, Varskin 3 may give results that are

unreliable. It is suggested that a user who wishes to model sources larger than this limit begin

with smaller sources and increase the source size gradually to ensure that spurious results are

not being generated. However, modeling a source of this size is generally not necessary as

most of the source does not contribute to skin dose. When modeling a gas cloud the size of the

cloud should not be larger that eight times the X99 distance in the gas. Varskin 3 prompts the

user with a warning if the potential for inaccurate results is modeled by choosing a source that is

too large. The X99 distance is included on the printout of a calculation.

Varskin 3 has not been tested extensively for dose averaging areas greater than 10 cm2

. 

However, because of the nature of the calculations performed by Varskin 3, there is no reason

to believe that doses to areas greater than 10 cm2

 will result in errors. It is suggested that the

user begin with a calculation averaged over 10 cm2

 and gradually increase the dose-averaging

area to ensure that spurious results are not obtained.

Beta doses involving air gaps greater than 5 cm have not been extensively tested. It is likely

that erroneous results may be obtained for large air gaps because Varskin 3 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 3, and can lead to inaccurate results. 
5-6

Varskin 3 will not perform calculations for air gaps greater than 5 cm and a warning message

is displayed.

The photon dose model in Varskin 3 must be used with caution because it has limitations and

may be improved in the future. The photon dose model in Varskin 3 treats the source as a point

source, regardless of the actual geometry or size. The photon dose is only a function of the

radionuclide, the materials between the source and skin, the skin depth, and the target area. 

Therefore, the photon dose from a Co-60 source to an area of 10 cm2

 at a skin depth of

7 mg/cm!2

 with no cover or air gap will be the same regardless of the source geometry or size. 

In addition, the photon dose model is inappropriate for air gaps larger than 5 cm. Although

Varskin 3 will not calculate the photon dose for air gaps larger than 5 cm, the user can enter a

larger cover thickness with the density of air that could lead to inappropriate results. Varskin will

not calculate the photon dose from any source with a dimension greater than 1 mm. In addition,

Varskin 3 will not calculate photon dose from a syringe source.

Another limitation of the photon dose model, as discussed in more detail in Section 3.6, is that

the photon dose is based on the specific gamma ray exposure constant, Γ, that is calculated

when a radionuclide is added to the Varskin 3 library. The value of Γ is strongly dependent on

the energy of the photons that are included when it is calculated. Thus, the choice of the

photon cutoff energy is a critical parameter when adding radionuclides to the library. In

addition, the photon energy cutoff that is appropriate for calculating skin dose is generally not

appropriate for calculating deep dose because the range of photons that contribute to skin dose

may not be large enough to contribute to deep dose. For many radionuclides, it may be

appropriate to create three different library files for a radionuclide: one for skin dose, one for

eye dose, and one for deep dose as discussed in Section 3.6. The recommended photon cutoff

energies are 2 keV, 20 keV, and 35 keV, for the shallow dose, eye dose, and deep dose,

respectively.

Table 5-1 demonstrates the strong dependence of Γ on the cutoff energy using Co-57 as an

example by comparing calculated values of Γ to the value published in the Radiological Health

Handbook (U.S. Department of Health, Education, and Welfare, Public Health Service,

Consumer Protection and Environmental Health Service, 1970). These data show that the

cutoff energy is a critical parameter when determining the photon dose.

Table 5-1. Specific Gamma Ray Constant Γ, As a Function of Cutoff Energy for Co-57

Cut-Off Energy (keV) Γ(R-cm2

/mCi/h)

2 14.98 

10 1.00 

20 0.556

100 0.556

Published Value* 0.9 

*U.S. Department of Health, Education, and Welfare, Public Health Service, Consumer Protection and Environmental

Health Service. Radiological Health Handbook. Rockville, Maryland: U.S. Department of Health, Education, and

Welfare, Public Health Service, Consumer Protection and Environmental Health Service. 1970.
6-1

6 SPECIAL TOPICS FOR ACCURATE USE OF VARSKIN 3

Varskin 3 is designed to be very flexible while maintaining a high level of accuracy. However,

Varskin 3 can be misused, particularly when modeling infinitely large sources (sources with all

dimensions greater than the X99 distance for these radionuclides). This section describes this

possible misuse of Varskin 3 and how to avoid it. 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 3, the

tendency is to choose very large dimensions for the source. This approach will result in the

calculation of grossly inaccurate doses or zero doses 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 x- and y-side

length are then determined using the equation

rrX max min dos w = + (/) 99 ρ ρ (6-1)

where rdos is the radius of the dose-averaging area (in cm), ρw is the density of water, and ρmin 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 used, use the Varskin 3 default

value for the density of air (0.001293 g/cm3

). If no cover material is used, use the density

of tissue.

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

∆t X max w s = / 99 ρ ρ (6-2)

where ρs is the source density.

6.2 Maximum Dose to 10 cm2 From Multiple Contaminations

Determining the maximum dose to the dose-averaging area for multiple contaminations requires

multiple calculations and cannot be performed quickly. The calculations also require elements

that are not available in Varskin 3 but that can be accomplished with some graph paper and a

calculator or a spreadsheet program.

Before attempting to run the offset particle model (Section 2.5), determine the size of the

irradiation area directly beneath each of the contaminated areas. Note that the size of sources

do not need to be the same for each particle. By comparing these areas for each source, it may

be possible to eliminate one or more of the contaminated areas because there are no

overlapping fields associated with them. For contaminated areas with overlapping fields, the
6-2

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, choosing the value of the offset 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, a final calculation for each particle using the offset particle model can be

performed. An accuracy of greater than 20 percent should not be anticipated.
7-1

7 REFERENCES

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

John Wiley and 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> (14 February 2006).

Chabot, G.E., K.W. Skrable, and C.S. French. “When Hot Particles Are Not on the Skin.” 

Radiation Protection Management. Vol. 5, No. 6. pp. 31–42. 1988.

Cross, W.G., N.O. Freedman, and P.Y. Wong. “Tables of Beta-Ray Dose Distributions in

Water.” AECL 10521, CA9200298. Chalk River, Ontario, Canada: Chalk River Laboratories,

Dosimetric Research Branch. 1992.

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.

Durham, J.S. NUREG/CR–5873, PNL–7913, “VARSKIN Mod 2 and SADDE Mod 2: Computer

Codes for Assessing Skin Dose From Skin Contamination.” Washington, DC: NRC. 1992.

Durham, J.S. and M.W. Lantz. “Determination of Gamma Dose Rates and Charged Particle

Equilibrium From Hot Particles.” Radiation Protection Management. Vol. 8, No. 3. pp. 35–41. 

1991.

Hubbell, J.H. and S.M. Seltzer. “Tables of X-Ray Mass Attenuation Coefficients and Mass

Energy-Absorption Coefficients.” Radiation Research. Vol. 136. p. 147. 1993.

<http://physics.nist.gov/PhysRefData/XrayMassCoef/cover.html> (14 February 2006).

International Commission on Radiation Units and Measurements. “Tissue Substitutes in

Radiation Dosimetry and Measurement.” ICRU Report 44. Bethesda, Maryland: International

Commission on Radiation Units and Measurements. 1989.

International Commission on Radiological Protection. “The Biological Basis for Dose Limitation

in the Skin.” Publication 59, Oxford, England: Pergamon Press. 1991.

–––––. “Radionuclide Transformations.” Publication 38. Oxford, England: Pergamon Press. 

1983.

Kocher, D.C. and K.F. Eckerman. “Electron Dose-Rate Conversion Factors for External

Exposure of the Skin From Uniformly Deposited Activity on the Body Surface.” Health Physics. 

Vol. 53. pp.135–141. 1987.
7-2

Lantz, M.W. and M.W. Lambert. “Charged Particle Equilibrium Corrections for the Gamma

Component of Hot Particle Skin Doses.” Radiation Protection Management. Vol. 7, No. 5. 

pp. 38–48. 1990.

NRC. News Release No. 02-039. http://www.nrc.gov/reading-rm/doccollections/news/2002/02-039.html. April 2, 2002. Last Accessed March 2006.

Piechowski, J. “Dosimetry and Therapy of Skin Contaminations (in French).” CEA–R–5441. 

Paris, France: Commissariat à l'Energie Atomique. 1988.

Reece, W.D., S.D. Miller, and J.S. Durham. NUREG/CR–5276, “SADDE (Scaled Absorbed

Dose Distribution Evaluator), A Code to Generate Input for VARSKIN.” Washington, DC: NRC.

1989.

Rohloff, F. and M. Heinzelmann. “Calculation of Dose Rates for Skin Contamination by Beta

Radiation.” Radiation Protection Dosimetry. Vol. 14. pp. 279–287. 1986.

RSICC. “MCNP4c2, Coupled Neutron, Electron Gamma 3-D Time-Dependent Monte Carlo

Transport Calculations.” CCC–701. Oak Ridge, Tennessee: RSICC. 2001.

–––––. NUCDECAY: Nuclear Decay Data for Radiation Dosimetry Calculations for ICRP and

MIRD.” CCC–701. Oak Ridge, Tennessee: RSICC. 1995.

Traub, R.J., W.D. Reece, R.I. Scherpelz, and L.A. Sigalla. NUREG/CR–4418, “Dose

Calculation for Contamination of the Skin Using the Computer Code VARSKIN.” Washington,

DC: NRC. 1987.

U.S. Department of Health, Education, and Welfare, Public Health Service, Consumer

Protection and Environmental Health Service. Radiological Health Handbook. Rockville,

Maryland: U.S. Department of Health, Education, and Welfare, Public Health Service,

Consumer Protection and Environmental Health Service. 1970.
APPENDIX A

A–1

DATA FROM MICHAEL W. LANTZ FOR THE PHOTON DOSE MODEL

This appendix contains graphs of the data generated by Michael W. Lantz, Arizona Public

Service Company, that was used for the photon dose model incorporated in Varskin 3. The

methodology for generating the data is provided in Lantz and Lambert (1990) but modified as

follows. The photon model was expanded to include a dose-averaging area of 10 cm2

 instead

of 1 cm2

 used in the original publication. This area applies to both the calculated photon dose

and the charged particle equilibrium (CPE) correction. The equation for the uncorrected photon

dose rate averaged over 10 cm2

 in mrad/h per μCi as a function of depth, h, in cm is given by

I ln h 1.784 ln h [ ] ( ) ( ) 2 22 = +− πΓ (A–1)

where Γ is the specific photon dose constant, in units of rad-cm2/μCi/h. The dose rate with the

CPE correction included as a function of photon energy, Ep, and depth is given by 

ICPE correction = { [ ( ) ]} −

+ ∑ −− +

π(R R )

h r 1 exp 139exp 0.00209E h r 1

2

2

2

2 2

0

1.784

p

Γ 2 2 (A–2)

where R2 and R1 are radii of concentric circles within the circular dose averaging area on either

side of r. The quantity (1–CPE fraction) as a function of photon energy was determined from

these two equations by subtracting the ratio of Eq. (A–2) to Eq. (A–1) from 1 for a given depth

and energy. Figure A–1 shows the family of curves generated for depths below 0.02 cm for

photon energies ranging from 200 keV to 1400 keV. Figure A–2 shows the same data obtained

for depths greater than 0.02 cm. Note that the trend line through each curve is of the form

y aexp bx = −( ) (A–3)

The values of a and b for depths that are less than 0.02 cm as a function of energy are plotted

in Figures (A–3) and (A–4), respectively. It is possible to fit the data to a function, which is

shown on each figure. Figures (A–5) and (A–6) contain plots of a and b for depths that are

greater than 0.02 cm, and similar functions are again obtained. It is now possible to write two

sets of equations that describe the CPE correction for depths less than and greater than

0.02 cm that are a function of photon energy. These equations are

Fraction a bh CPE =− − 1 exp( ) (A–4)

where

a 0.117 0.000272E ,b 170exp 0.001465E =+ = − n n ( ) (A–5)

for d < 0.02 cm and

a 0.0458 0.000267E ,b 147exp 0.00166E =+ = − n n ( ) (A–6)

for d > 0.02 cm. As an example, the CPE fraction as a function of photon energy for a depth of

0.007 cm is shown in Figure (A–7).
A–2

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.350

0.400

0.450

0.000 0.005 0.010 0.015 0.020

Depth (cm)

1 - CPE Fraction

200 keV

300 keV

400 keV

500 keV

600 keV

700 keV

800 keV

900 keV

1,000 keV

1,100 keV

1,200 keV

1,250 keV

1,300 keV

1,400 keV

y = 0.5061e-22.217x

y = 0.4753e-25.546x

y = 0.46e-27.407x

y = 0.4449e-29.38x

y = 0.4151e-33.786x

y = 0.3859e-38.887x

y = 0.3573e-44.832x

y = 0.3294e-51.768x

y = 0.3023e-59.923x

y = 0.276e-69.555x

y = 0.2508e-80.957x

y = 0.2266e-94.526x

y = 0.2036e-110.75x

y = 0.1818e-130.22x

Figure A–1. 1–CPE Fraction as a Function of Depth for 14 Photon

Energies. The Depth for These Data Range From 0.007 cm to 0.02 cm.

Reference

Lantz, M.W. and M.W. Lambert. “Charged Particle Equilibrium Corrections for the Gamma

Component of Hot Particle Skin Doses.” Radiation Protection Management. Vol. 7, No. 5. 

pp. 38–48. 1990.
A–3

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.010 0.020 0.030 0.040 0.050

Depth (cm)

1-CPE Fraction

200 keV

300 keV

400 keV

500 keV

600 keV

700 keV

800 keV

900 keV

1,000 keV

1,100 keV

1,200 keV

1,250 keV

1,300 keV

1,400 keV

y = 0.4334e-14.696x

y = 0.4001e-17.182x

y = 0.3836e-18.594x

y = 0.3675e-20.107x

y = 0.3361e-23.543x

y = 0.3059e-27.605x

y = 0.2768e-32.442x

y = 0.2491e-38.203x

y = 0.2228e-45.113x

y = 0.1981e-53.436x

y = 0.1750e-63.472x

y = 0.1537e-75.626x

y = 0.1341e-90.397x

y = 0.1163e-108.4251x

Figure A–2. 1– CPE Fraction as a Function of Depth for 14 Photon

Energies. The Depth for These Data Range From 0.02 cm to 0.05 cm,

Although the Actual Data Extend to Depths of 0.514 cm.

a = 0.000272E + 0.117

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 200 400 600 800 1000 1200 1400 1600

Energy (keV)

a

Figure A–3. The Parameter a as a Function of Energy for Depths

Below 0.02 cm
A–4

b = 170e-0.001465E

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Energy (keV)

b

Figure A–4. The Parameter b as a Function of Energy for Depths

Below 0.02 cm

a = 0.000267E + 0.0458

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0 200 400 600 800 1000 1200 1400 1600

Energy (keV)

a

Figure A–5. The Parameter a as a Function of Energy for Depths Greater

Than 0.02 cm
A–5

b = 147e-0.00166E

0

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600

Energy (keV)

b

Figure A–6. The Parameter b as a Function of Energy for Depths Greater

Than 0.02 cm

0

0.2

0.4

0.6

0.8

1

0 500 1000 1500 2000 2500

Average Energy (keV)

CPE Fraction

Figure A–7. CPE Fraction as a Function of Energy for a Depth of 0.007 cm

APPENDIX B

B–1

EXAMPLES AND SOLUTIONS USING VARSKIN 3

This appendix describes three different practical applications of Varskin 3 using a

example/solution format. Each example describes a situation followed by a solution that

involves using Varskin 3 to calculate 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 the features of Varskin 3. Because Varskin 3 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 3 users will not need to perform all of the steps that are described in the solution in an

actual situation. It is suggested that all three examples be completed in the order they are

presented to develop familiarity with Varskin 3.

Example 1: Radiopharmaceutical Technician in Nuclear Medicine

At a research hospital, a doctor prescribed a 5 ml dose from a stock solution containing

10 μCi/ml of rhenium (Re)-186 for a clinical research study at 1:00 p.m. that day. Around

12:30 p.m., a lab technician was loading the dose under the hood, a fellow employee bumped

into her, and the needle slipped out of the container. The entire 5 ml of the dose was spilled on

the arm of her cloth lab coat in a uniform circular shape about 50 cm2

 in area. She was

unaware of the accident and continued with her work until the end of the day around 5:00 p.m. 

Before she left work, a routine survey for contamination was performed and the contamination

was discovered. 

Solution 1: Radiopharmaceutical Technician in Nuclear Medicine

First, use the point source geometry to estimate the magnitude of the dose and to collect some

other useful information. Start Varskin 3 and proceed to the Source Geometry screen. If

Re-186 does not appear in the Radionuclide Library frame, Add Re-186 by selecting the “Add”

button and double-clicking on Re-186 on the Add Radionuclide to Library screen. Enter the

Exposure Time as 4.5 and change the unit to hours (hr) 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 dose (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 on the Re-186 library entry. When Varskin 3 asks for a source

strength, enter 50. All other entries should retain their default values. Click on “Calculate

Doses” and shortly the Varskin 3 Results screen will appear. Print the results of the calculation.

The Varskin 3 Results screen displays nine dose or dose rate 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 assumes that either the source has a very long half life or

that the radionuclide is in secular equilibrium with its parent. The printout provides additional

information about the source, including the half life of Re-186, the average photon energy, and

the specific photon dose constant. Note that Re-186 has a relatively short half life; therefore,

the decay-corrected dose is the appropriate dose for the current calculation. Looking at either

the Varskin 3 Results screen or the printout will show that the decay-corrected total dose is

136 rad, a value that exceeds regulatory limits. The results also indicate that there is a gamma

component to the dose, so a deep dose calculation is warranted. Next, generate a library file

for deep dose (see the discussion in section 2.2.2 for details) by returning to the Source
B–2

Geometry screen and selecting Add on the Radionuclide Library frame. Change the Photon

Minimum Energy (keV) to 35 and double click on Re-186. When prompted to cancel, select

“No” then choose the name Re-186d as the name of the library file. Add Re-186d to the list of

selected radionuclides, set the activity to 50 μCi, and click on “Calculate Doses.” From the

results screen, print out the results. Compare the two values for the Specific Photon Dose

Constants to see that the choice of cutoff energy does not affect its value because Re-186 does

not emit any photons with energies below 35 keV that have a yield above 1 percent. Therefore,

the entry for Re-186d can be removed from the Selected Radionuclides frame by highlighting

the name and clicking on “Remove.” Re-186d can also be permanently removed from the

Radionuclide Library by clicking on “Remove.”

Because the photon dose model in Varskin 3 treats photon sources as point sources, it is not

possible to use the disk or cylinder models to calculate photon dose. The point source

calculation is the only way to estimate the photon dose in this example. To calculate the deep

dose, return to the Source Geometry screen, change the value of the Skin Thickness or Skin

Density Thickness to 1,000 mg/cm2

, and click on “Calculate Doses.” The Varskin 3 Results

screen displays a decay-corrected photon dose of 9.67 mrad.

The beta dose calculated using the point geometry was above regulatory limits. However, it

should be obvious that the situation described in this example will be more accurately modeled

using the disk or cylinder geometries. A more realistic 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 Source Geometry screen and choose “Disk” in the Source Geometry frame. You must

now re-enter the exposure time as 4.5 hr. Next, enter the Source Area as 50 cm2

. Note that the

Source Diameter is automatically calculated to be 7.98 cm (this value will be needed for the next

model). After clicking on “Calculate Doses,” an error may appear that warns the user that the

photon dose model only applies to sources with dimensions less than 1 mm and asks if the user

wishes to proceed. If “Yes” is clicked, the calculation continues and the results screen shows a

decay-corrected dose of 27.1 rad. 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 mm and a density of 0.9 g/cm3

. 

After returning to the Source Geometry screen, choose “Cylinder” in the Source Geometry

frame. Previously-entered geometry data will return to the default values, so the Exposure Time

must be re-entered as 4.5 hours. Enter the Source Diameter as 7.98 cm (from the disk

calculation) and enter the Source Thickness as 0.4 mm (the thickness of the lab coat), and

enter the Source Density as 0.9 g/cm3

 (the density of the lab coat). Click on “Calculate Doses”

and after a short delay the Varskin 3 Results screen will display 16.6 rad as the decay-corrected

beta dose.

It is interesting to look at 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 Source Geometry

screen and change the geometry to the “Disk” source. Enter the Exposure Time as 4.5 hr, then

enter the source area as 50 cm2

. Enter a Cover Thickness of 0.2 mm and a density of
B–3

0.36 g/cm3

. After clicking on “Calculate Doses” the Varskin 3 Results screen will display a total

decay-corrected dose of 19.5 rad. It can be concluded that, based on the above calculations,

using a thicker, absorbent lab coat will give more protection than a thin, impervious material.

Example 2: Radiation Worker in Reactor Containment

A worker damages his outer glove while working inside containment during an outage at a

nuclear reactor. His outer glove is removed, leaving only a surgeon’s glove. The worker

proceeds to the step-off pad, which takes about 15 minutes. During the exit survey,

contamination is detected on the surgeon’s glove and the glove is removed and taken to the

laboratory for analysis. The laboratory report concludes that the contamination is a stellite hot

particle with the following characteristics:

• Radioactive contaminant: cobalt (Co)-60

• Source strength: 2.5 mCi

• Particle thickness: 50 μm

• Particle size: 80 μm × 70 μm

• Glove thickness: 0.3 mm

• Glove density: 0.6 g/cm3

The density of the particle is assumed to be 8.3 g/cm3.

Solution 2: Radiation Worker in Reactor Containment

First, use the point source geometry to estimate the magnitude of the dose and to collect some

other useful information. Start Varskin 3 and proceed to the Source Geometry screen. If Co-60

does not appear in the Radionuclide Library frame, add Co-60 by selecting the “Add” key and

double-clicking on Co-60 on the Add Radionuclide to Library screen. Enter an Exposure Time

of 15 minutes. Double-click on Co-60 in the Radionuclide Library and enter 2.5 mCi. Enter a

Cover Thickness of 0.3 mm and a Cover Density of 0.6 g/cm3

. After clicking on “Calculate

Doses,” the Varskin 3 Results screen will display a photon dose of 18.9 rad and a total dose

rate of 51.3 rad, which is above 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 taken into effect. As described in section 2.2, the cylinder

model should be used for a particle that is known to be rectangular. Because the source does

not have any dimensions larger than 1 mm, Varskin 3 will allow the cylinder model to calculate

both shallow dose and deep dose. Return to the Source Geometry screen and choose the

“Cylinder” source geometry. Enter 15 min as the Exposure Time, 50 μm as the Source

Thickness, 0.3 mm as the Cover Thickness, and 0.6 g/cm3

 as the Cover Density. The diameter

of a source with the same area as the rectangular source is found from Eq. (B–1)

d xY m m m =⋅ ⋅ =⋅ ⋅ = 2 2 80 70 84 ( / / π μ μπ μ ) ( ) (B–1)

Enter 84 μm for the Source Diameter and 8.3 g/cm3 for the Source Density, then click on
B–4

“Calculate Doses.” The Varskin 3 Results screen will display a photon dose of 18.9 rad and a

total dose of 27.2 rad. Including the effects of self shielding greatly reduced the beta dose and

resulted in a dose that is below regulatory limits. To calculate deep dose, simply return to the

Source Geometry screen, change the Skin Thickness or Skin Density Thickness to 1,000

mg/cm2

, and click on “Calculate Doses.” The Varskin 3 Results screen will display a deep dose

of 3.38 rad.

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 an aluminum plate inside the hood that is contaminated. Upon further investigation it

was found that the plate was used to hold beakers of solution containing carbon (C)-14 for use

in radiobiology experiments. The RSO decides that the plate should be disposed as low level

radioactive waste and that the activity of C-14 on the plate must be determined. The plate is

6 in. by 6 in. and is uniformly contaminated over the entire surface. The RSO uses a calibrated

circular Geiger-Muller “pancake” probe with an area of 50 cm2

 and a window thickness of

3 mg/cm2

 to measure a dose rate of 190 mrad/h on contact and 60 mrad/h 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 3 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 3.

For this solution, choose the Disk geometry. If the Radionuclide Library dose not contain C-14,

add it by clicking on Add and double-clicking on C-14 in the Add Radionuclide to Library screen. 

C-14 does not emit photons so it is not necessary to change the photon minimum energy. From

the Source Geometry screen, click the “Use Distributed Source” checkbox. Notice that the

default unit for activity is now μCi/cm2

. Double click on 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 in2. For this example the dose rate is of

interest so the irradiation time can remain at the default value of 60 min. Click on “Calculate

Doses” and shortly the Varskin 3 Results screen will appear displaying an initial dose rate of

4.68 rad/h [4,680 mrad/h]. The activity concentration on the plate can be found from the

following equation

(B–2) [ ]

[ ]

A

A

D

D

ACT

CAL

MEAS

CAL

=

•

•
B–5

Therefore the activity concentration on the plate is given by Eq. (B–3)

(1 190 4680 0 04 ) ( ) (B–3) 2 2 μ μ Ci cm mrad h mrad h Ci cm / // / . / ∗ =

Multiplying the activity concentration by the area of the plate (6 in × 6 in = 232 cm2) results in a

total activity of 9.3 μCi.

The measurement at a distance of 1 in. can be used to verify this result. Return to the Source

Geometry screen and enter an Air Gap Thickness of 1 in. After clicking on “Calculating Doses”

the Varskin 3 Results screen will display an initial dose rate of 1.43 rad/h. Comparing this dose

rate to the measured dose rate gives an activity concentration of 

(1 60 1430 0 04 ) ( ) (B–4) 2 2 μ μ Ci cm mrad h mrad h Ci cm / // / . / ∗ =

From this value the total activity of the plate is calculated to be 9.3 μCi. Thus, the two

measurements result in a consistent determination of the activity on the plate.