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AN ABSTRACT OF THE THESIS OF

Kevin A. Makinson for the degree of Master of Science in Radiation Health Physics presented

on July 2, 2009.

Title: Tissue Weighting Factors for Radiation Protection: Derivation and Parametric Analysis.

Abstract approved:

___________________________________________________________________________

David M. Hamby

Tissue weighting factors, wT, used to convert equivalent dose to effective dose,

account for differences in radiosensitivity of various organs in the human body and allow

users to compare individual organ detriment to whole body risk. They are explicitly

calculated in ICRP 26, 60, and 103, although the methods of calculation, as well as the

weighting factors themselves, vary greatly between reports. The ICRP 26 report bases its

weighting factors solely on fatal cancer risk for eleven organs, whereas ICRP 60 and 103 use

detriment (with unique definitions in each report) to calculate the tissue weighting factors

for twenty‐two and twenty‐eight organs, respectively. Each new report introduces levels of

uncertainty into the calculation of wT, which ultimately may reduce the significance of

individual weighting factors. A review of the three calculational methods used in ICRP 26,

60, and 103 is covered, as well as an examination of the uncertainties introduced by each

weighting factor parameter utilized in ICRP 103 and the total uncertainties of the various wT

values. Finally, the effective dose is calculated for several exposure scenarios using the ICRP

26 and 60 methodologies for comparison to ICRP 103 effective dose calculation and

uncertainties thereof.

©Copyright by Kevin A. Makinson

July 2, 2009

All Rights Reserved

Tissue Weighting Factors for Radiation Protection: Derivation and Parametric Analysis

by Kevin A. Makinson

A THESIS

submitted to

Oregon State University

in partial fulfillment of the requirements for the

degree of

Master of Science

Presented July 2, 2009 Commencement June 2010

Master of Science thesis of Kevin A. Makinson presented on July 2, 2009.

APPROVED:

___________________________________________________________________________

Major Professor, representing Radiation Health Physics

___________________________________________________________________________

Head of the Department of Nuclear Engineering and Radiation Health Physics

___________________________________________________________________________

Dean of the Graduate School

I understand that my thesis will become part of the permanent collection of Oregon State University libraries. My signature below authorizes release of my thesis to any reader upon request.

___________________________________________________________________________

Kevin A. Makinson, Author

ACKNOWLEDGEMENTS

I would like to express my sincerest appreciation to my family for their continued

support of my academic, athletic, and musical dreams. I would not be writing this without

their love and support. My advisor, Dr. David Hamby, deserves respect for his guidance on

this project, as well as in life. I would also like to thank the rest of my committee members

for agreeing to support me in this endeavor: Dr. Kathy Higley, my first contact at Oregon

State; Dr. John Edwards, my “psychology advisor,” and fellow musician; and Dr. Paul

Vincent, my Graduate Council Representative.

TABLE OF CONTENTS

Page

1 Chapter 1 – Introduction ................................................................................................... 1

1.1 The International Commission on Radiological Protection ....................................... 1

1.2 Effective Dose Scenario ............................................................................................. 3

1.3 10.CFR.20 Proposed Revisions .................................................................................. 4

2 Chapter 2 – Literature Review ........................................................................................... 6

2.1 Pre ICRP 2 .................................................................................................................. 6

2.2 ICRP 2 ......................................................................................................................... 7

2.2.1 Relevant Terminology Used in ICRP 2 ............................................................... 7

2.2.2 Maximum Permissible Body Burden ................................................................. 8

2.2.3 Maximum Permissible Concentration ............................................................. 10

2.3 Linear Energy Transfer ............................................................................................. 12

2.4 Absorbed Dose ........................................................................................................ 13

2.5 ICRP 26 ..................................................................................................................... 14

2.5.1 Quality Factor .................................................................................................. 14

2.5.2 Tissue Weighting Factor and Detriment .......................................................... 16

2.6 ICRP 60 ..................................................................................................................... 19

2.6.1 Radiation Weighting Factor ............................................................................. 19


2.7 ICRP 103 ................................................................................................................... 27

2.7.1 Radiation Weighting Factor ............................................................................. 27


3 Chapter 3 – Methods ....................................................................................................... 35

3.1 ICRP 103 ................................................................................................................... 35

3.2 Uncertainty Analysis ................................................................................................ 36

3.2.1 Cancer Incidence Risk ...................................................................................... 40

3.2.2 Heritable Effects (Gonads)............................................................................... 46

TABLE OF CONTENTS (Continued)

Page

3.2.3 Lethality Fraction (k) .......................................................................................... 49

3.2.4 Minimum Weight for Quality of Life (qmin) ........................................................ 51

3.2.5 Relative Length of Life Lost................................................................................ 52

4 Chapter 4 –Results ............................................................................................................. 56

4.1 Uncertainty Analysis Output ‐ Parameters ................................................................ 56

4.2 Uncertainty Analysis Output ‐ Figures ....................................................................... 56

5 Chapter 5 – Discussion ...................................................................................................... 59

5.1 Skin ............................................................................................................................ 59

5.2 Normalization ............................................................................................................ 62

5.3 ICRP 103 Tissue Weighting Factor Comparison ......................................................... 63

5.4 ICRP 60 Tissue Weighting Factor Comparison ........................................................... 65

5.5 ICRP 26 Tissue Weighting Factor Comparison ........................................................... 66

5.6 Tissue Weighting Factor Comparison Summary........................................................ 68

6 Chapter 6 – Conclusion ...................................................................................................... 70

Bibliography ............................................................................................................................... 73

APPENDICIES .............................................................................................................................. 77

Appendix A – Steps in the development of the tissue weighting system, taken from (ICRP, 2007) ........................................................................................................................... 78

Appendix B – A summary of all input parameters in the uncertainty analysis ..................... 80

Appendix C – Relative detriment plots generated by Crystal Ball ......................................... 84

LIST OF FIGURES Figure Page

2.1 A comparison of Equation (1.17) and the step function described in Table 2.1 .... 21

2.2 Equation (1.24) expressed graphically .................................................................... 29

3.1 An example of a uniform distribution generated by Crystal Ball ............................ 37

3.2 An example of a triangular distribution generated by Crystal Ball ......................... 37

3.3 An example of a normal distribution generated by Crystal Ball ............................. 38

3.4 Normal‐probit plot line fit ....................................................................................... 39

3.5 Log‐probit plot line fit ............................................................................................. 39

3.6 The combined distribution from several uniform distributions used in the calculation of heritable risk ..................................................................................... 49

3.7 Number of years of life lost due to cancer in the esophagus ................................. 53

4.1 Crystal Ball graphical output for the results of the uncertainty analysis on the bone relative detriment .......................................................................................... 57

4.2 Crystal Ball graphical output for the results of the uncertainty analysis on the skin relative detriment ............................................................................................ 58

5.1 Input log‐normal distribution for skin incidence risk with GM of 1000 and GSD of 3 .......................................................................................................................... 60

5.2 Input triangular distribution for skin lethality fraction with bounds of 0 and 1 and a most likely value of 0.002.............................................................................. 61

5.3 Input uniform distribution for skin years of life lost with bounds of 0 and 30 ....... 62

LIST OF FIGURES (Continued) Figure Page

5.4 Box‐plot of the ICRP 103 uncertainty analysis data, with the deterministic tissue weighting factors from the various documents highlighted. The box represents the middle two quartiles of the data.. .................................................. 68

LIST OF TABLES

Table Page

1.1 The inputs of Equation (1.1), the tissue weighting factors, dose, and radiation weighting factors ...................................................................................................... 3

1.2 The outputs of Equation (1.1), the effective dose using weighting factors from ICRP 26, 60 and 103 .................................................................................................. 4

2.1 ICRP 2 RBE values ...................................................................................................... 8

2.2 Unrestricted LET, quality factor relationship .......................................................... 15

2.3 ICRP 26 quality factors ............................................................................................ 16

2.4 The ICRP 26 calculation of radiation weighting factors .......................................... 18

2.5 ICRP 60 radiation weighting factors ........................................................................ 20

2.6 ICRP 60 calculation of lethality fraction .................................................................. 22

2.7 The ICRP 60 calculation of relative life lost ............................................................. 24

2.8 ICRP 60 parameter values used in the calculation of detriment ............................ 25

2.9 ICRP 60 calculation of tissue weighting factors for various organs ........................ 26

2.10 ICRP 103 radiation weighting factors ...................................................................... 28

2.11 A summary of the terms used to define detriment in ICRP 60 and 103 ................. 29

2.12 ICRP 103 detriment parameters ............................................................................. 31

LIST OF TABLES (Continued)

Table Page

2.13 The ICRP 103 calculation of tissue weighting factors ............................................. 32

2.14 A summary of tissue weighting factors in ICRP 26, 60, and 103 ............................. 33

3.1 Relative and absolute LAR from BEIR VII (National Research Council, 2006) ......... 44

3.2 ICRP 103 nominal risks taken as the GM; GSD estimates obtained from BEIR VII confidence intervals ........................................................................................... 45

3.3 Current estimates of genetic risk from continuing exposure to low‐LET, low dose or chronic irradiation (UNSCEAR, 2001) with an assumed doubling dose of 1 Gy. .................................................................................................................... 48

3.4 Risk coefficients (per 10,000) for the reproductive and the total population obtained up to two generations when the population sustains radiation exposure generation after generation. ................................................................... 48

3.5 Lethality fractions and confidence intervals from USCS 2001‐2005 ...................... 50

3.6 Uniform distributions fit to the ICRP 103 reported lethality fraction using the confidence interval percentages from Table 3.5 .................................................... 51

3.7 Triangular distribution parameters defined for two sites ...................................... 51

3.8 Triangular distribution parameters defined for qmin ............................................... 52

3.9 Log‐normal distribution parameters for years of life lost calculation .................... 54

3.10 Non‐log‐normal distributions for years of life lost parameter ............................... 55

LIST OF TABLES (Continued)

Table Page

4.1 Log‐normal distribution parameters for the results of the uncertainty analysis ... 56

5.1 The normalization of the geometric means from the uncertainty analysis ........... 63

5.2 A comparison of the ICRP 103 tissue weighting factors and the uncertainty analysis .................................................................................................................... 64



5.5 A comparison of the renormalized ICRP 26 tissue weighting factors and the uncertainty analysis ................................................................................................ 67

LIST OF APPENDIX FIGURES

Figure Page

C.1 Crystal Ball graphical output for the results of the uncertainty analysis on the esophagus relative detriment ................................................................................. 84

C.2 Crystal Ball graphical output for the results of the uncertainty analysis on the stomach relative detriment .................................................................................... 84

C.3 Crystal Ball graphical output for the results of the uncertainty analysis on the colon relative detriment ......................................................................................... 85

C.4 Crystal Ball graphical output for the results of the uncertainty analysis on the liver relative detriment ........................................................................................... 85

C.5 Crystal Ball graphical output for the results of the uncertainty analysis on the lung relative detriment ........................................................................................... 86

C.6 Crystal Ball graphical output for the results of the uncertainty analysis on the bone relative detriment .......................................................................................... 86

C.7 Crystal Ball graphical output for the results of the uncertainty analysis on the skin relative detriment ............................................................................................ 87

C.8 Crystal Ball graphical output for the results of the uncertainty analysis on the breast relative detriment ........................................................................................ 87

C.9 Crystal Ball graphical output for the results of the uncertainty analysis on the ovary relative detriment ......................................................................................... 88

C.10 Crystal Ball graphical output for the results of the uncertainty analysis on the bladder relative detriment ...................................................................................... 88

LIST OF APPENDIX FIGURES (Continued)

Figure Page

C.11 Crystal Ball graphical output for the results of the uncertainty analysis on the thyroid relative detriment ...................................................................................... 89

C.12 Crystal Ball graphical output for the results of the uncertainty analysis on the gonads relative detriment ....................................................................................... 90

C.13 Crystal Ball graphical output for the results of the uncertainty analysis on the remainder relative detriment ................................................................................. 90

LIST OF APPENDIX TABLES

Table Page

B.1 Nominal risk input parameters used in the uncertainty analysis ........................... 80

B.2 Lethality fraction input parameters used in the uncertainty analysis .................... 81

B.3 Minimum lethality weight input parameters used in the uncertainty analysis ...... 82

B.4 Relative length of life lost input parameters used in the uncertainty analysis ...... 83

LIST OF ACRONYMS

Acronym Definition

ALARA As Low As Reasonably Achievable

ALI

Annual Limit of Intake

BEIR Biological Effects of Ionizing Radiation

CFR Code of Federal Regulations

DAC Derived Air Concentration

DDREF Dose and Dose Rate Effectiveness Factor

EC Commission of the European Communities (‘European Commission’)

EPA

Environmental Protection Agency

ESU Electrostatic Unit

IAEA International Atomic Energy Agency

ICRP International Commission on Radiological Protection

ICRU International Commission on Radiation Units and Measurements

IEC International Electrotechnical Commission

ILO International Labor Organization

IRPA International Radiation Protection Association

ISO International Standards Organization

IXRPC International X‐Ray and Radium Protection Committee

LET Linear Energy Transfer

LSS Life Span Study

MPBB Maximum Permissible Body Burden

LIST OF ACRONYMS (Continued)

MPCa Maximum Permissible Concentration in air

MPCw Maximum Permissible Concentration in water

MPD Maximum Permissible Dose

NRC Nuclear Regulatory Committee

OECD/NEA

Nuclear Agency of the Commissions of Economic Co‐operation and Development

STP Standard Temperature and Pressure

RBE Relative Biological Effectiveness

REB Roentgen Equivalent Biological

REM Roentgen Equivalent Man

REP Roentgen Equivalent Physical

UNEP United Nations Environment Program

UNSCEAR United Nations Scientific Committee on the Effects of Atomic Radiation

WHO World Health Organization

Tissue Weighting Factors for Radiation Protection: Derivation and Parametric Analysis

1 Chapter 1 – Introduction

Tissue weighting factors are mandated for use in the field of radiation protection to

convert equivalent dose to effective dose. The International Commission on Radiological

Protection (ICRP) is the international body that provides the method of calculation for these

weighting factors and recommends their use. With the recent proposal in the United States

to update 10.CFR.20 to incorporate the newest weighting factor calculations from the ICRP,

it is necessary to address the two objectives of this work:

• to understand the meaning of the tissue weighting factor; and

• given their inherent uncertainties, determine how the weighting factors have

changed over the past 30 years.

1.1 The International Commission on Radiological Protection

The International Commission on Radiological Protection (ICRP) was established in

1928 by the Second International Congress of Radiology. At the time, it bore the name,

“The International X‐Ray and Radium Protection Committee” (IXRPC). It wasn’t until 1950

that the committee reorganized into its present form to more effectively cover the

expanding field of radiation protection (ICRP, 2007).

Although the Commission still has a special relationship with the Congress of

Radiology, it now works closely with its sister organization, the International Commission on

Radiation Units and Measurements (ICRU), and has official relationships with the United

Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR), the World

Health Organization (WHO) and the International Atomic Energy Agency (IAEA). It also

Page: 2 works closely with the International Labor Organization (ILO), the United Nations

Environment Program (UNEP), and other United Nation’s bodies. The group collaborates

with the Commission of the European Communities (‘European Commission’, EC), the

Nuclear Agency of the Commissions of Economic Co‐operation and Development

(OECD/NEA), the International Standards Organization (ISO), the International

Electrotechnical Commission (IEC) and the International Radiation Protection Association

(IRPA) (ICRP, 2007).

The primary goal of the recommendations of the ICRP, as stated in ICRP Publication

103 (2007) is to:

“Contribute to an appropriate level of protection for people and the environment against the detrimental effects of radiation exposure without unduly limiting the desirable human actions that may be associated with such exposure” (ICRP, 2007).

The ICRP does not, however, have regulatory authority in the United States, nor any

other country; rather, it provides recommendations agreed upon by the international

community with the intent of influencing national laws. In the United States, these laws can

be found in the Code of Federal Regulations (CFR) and are enforced by governmental

organizations such as the Nuclear Regulatory Commission (NRC) and the Environmental

Protection Agency (EPA).

The ICRP released several documents which are especially pertinent to this work.

ICRP 2 lists permissible radionuclide intake limits. ICRP 26 simplifies this method and is the

first to define tissue weighting factors, determined from fatal cancer risk. ICRP 60 and 103

update the weighting factors by incorporating new parameters into the calculation.

Page: 3 1.2 Effective Dose Scenario

According to US regulation, the effective dose (dose of record) is calculated using the

ICRP 26 tissue weighting factors. If ICRP 60 or 103 weighting factors were used instead, the

reported effective dose could change appreciably. For example, assuming a radiation

worker received an internal dose (see Table 1.1) of 5 rad to the thyroid from electrons, 1 rad

to the bone from alpha particles, 2 rad to the breast from photons, and a whole body dose

of 0.5 rad from photons, we would obtain the effective dose using:

( )( )( ) ( )( )( ), ,,E T thyroid thyroid T bone bone RR e

H w D w w D w α−⎡ ⎤

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

, , , , T breast breast R T WB WB Rw D w w D wγ γ

⎡ ⎤= + +⎣ ⎦⎣ ⎦⎡ ⎤ ⎡ ⎤+⎣ ⎦ ⎣ ⎦

(1.1)

where:

• wT is the tissue weighting factor [unitless];

• D is the equivalent dose to a particular organ [rem] and;

• wR is the radiation weighting factor [unitless].

Table 1.1 The inputs of Equation (1.1), the tissue weighting factors, dose, and radiation weighting factors

wT

Site ICRP 26 ICRP 60 ICRP 103 D[rad] wR Thyroid 0.03 0.05 0.04 5 1 Bone 0.03 0.01 0.01 1 20 Breast 0.15 0.05 0.12 2 1 Whole body 1.00 1.00 1.00 0.5 1

The effective dose (Table 1.2) recorded for this individual, depending on whether

ICRP 26, 60, or 103 tissue weighting factors were used, would vary from 1.55 rem, to 1.05

rem, to 1.14 rem, respectively.

Page: 4

Table 1.2 The outputs of Equation (1.1), the effective dose using weighting factors from

ICRP 26, 60 and 103

Effective dose (rem)

Organ ICRP 26 ICRP 60 ICRP 103 Thyroid 0.15 0.25 0.20 Bone 0.60 0.20 0.20 Breast 0.30 0.10 0.24 Whole Body 0.50 0.50 0.50 Total: 1.55 1.05 1.14

Between ICRP 26 and 103, there is about a 35% difference in the reported effective

dose and between ICRP 26 and 60 there is about a 50% difference. As observed from this

simulation, depending on the methodology used, there can be large differences in the

reported effective dose. This could be of particular concern if, for example, a regulation was

exceeded using the ICRP 26 methodology, but not the ICRP 103 methodology. It is therefore

necessary to investigate the uncertainties involved in this calculation.

1.3 10.CFR.20 Proposed Revisions

For several years, there has been discussion in the US regarding the update of

10.CRF.20 to align with the international community. As of April 9, 2009, the NRC had

approved plans to begin revising 10.CFR.20 (Vietti‐Cook, 2009) to be in alignment with ICRP

103. The regulation that will require the most attention is the annual occupational dose to a

radiation worker. The ICRP 103 Committee recommends 2 rem, while the US currently has a

limit of 5 rem. The 5 rem limit was derived based on placing radiation workers at the same

level of risk as the average US industrial worker in the 1950’s. Since then, however, industry

worldwide has attained higher levels of safety, while the dose limit remains the same for

Page: 5 nuclear workers. The 2 rem limit would simply bring the estimated risk from radiation

exposure (using the linear no‐threshold hypothesis) in line with other US industries of today.

Among the many other quantities suggested for update are the tissue weighting

factors. The tissue weighting factors currently used in 10.CFR.20 are specified in the

“definitions” section and are based on the ICRP 26 values. The NRC is currently proposing to

keep the definitions of the weighting factors in the “definitions” section, but to move the

numeric values from that section to an appendix of 10.CFR.20 (Borchardt, 2008). The

possibility of adding an appendix for radiation and tissue weighting factors would allow for

greater ease in updating the document in the future.

As explained in Section 1.2, the effective dose can change appreciably depending on

the methodology used. However, the weighting factors themselves may not be statistically

different from one another. This work will explore the differences in tissue weighting

factors over the years in comparison to an uncertainty analysis of the ICRP 103 data.

Page: 6 2 Chapter 2 – Literature Review

For the past 50 years, the ICRP has released publications addressing a multitude of

topics in the field of radiation protection. The current series began in 1959 with ICRP

Publication 1. Since then, the ICRP has released over 100 publications in the series. For the

sake of simplicity, the titles have been shortened; for example, ICRP Publication 1 is

commonly referred to as ICRP 1. The reports summarized below (chronologically) are ICRP

2, 26, 60, and 103, which all pertain to radiation protection methodology.

2.1 Pre ICRP 2

In 1928, the first report published by the IXRPC focused on the protection of medical

professionals by limiting their work with radioactive sources (IXRPC, 1928). These

recommendations were qualitative in nature and primarily concerned with the avoidance of

threshold doses. At the time, there was no official system of dose quantification; hence no

dose limits could be defined. In 1934, the IXRPC defined a threshold limit of what can be

estimated today as about ten times the current annual occupational dose limit (ICRP, 2007;

IXRPC, 1934).

In the years following, due to epidemiological evidence of excess disease among

American radiologists, and the first reports of excess leukemia in the Japanese atomic bomb

survivors, support for a radiation risk threshold diminished and the ICRP released

supplemental material to their earlier 1951 report (ICRP, 1955). The 1955 report was the

first by the ICRP to officially recognize the possibility of stochastic effects following radiation

exposure (ICRP, 2007). A stochastic (or probabilistic) effect is one where the risk (e.g., of

fatal cancer) appears to have a random outcome, and the probability of which increases

Page: 7 proportionally with dose. Conversely, a non‐stochastic, or deterministic effect, is one in

which there are no discernable effects below a certain dose threshold.

At the time, the ICRP advised that “every effort [should] be made to reduce

exposures to all types of ionizing radiation to the lowest possible level” (ICRP, 1955). This

statement has become the cornerstone of radiation protection and, as the years have

passed, gradually transformed: from “as low as practicable” in the first report (ICRP

Publication 1, (ICRP, 1959), to “as low as readily achievable” (ICRP, 1966), and finally, as it is

known today, “as low as reasonably achievable” (ALARA) (ICRP, 1973).

2.2 ICRP 2

The second publication in the current ICRP series, commonly referred to as ICRP 2,

was also released as the third issue of the Health Physics journal in 1960.

2.2.1 Relevant Terminology Used in ICRP 2

The rem was defined in ICRP 2 as the dose in tissue which results in biological

damage equivalent to that produced per rad of X‐radiation (of about 200 kV) having a linear

energy transfer (LET) (see Section 2.3) in water of 3.5 keV/µm.

Before the creation of quality factors and radiation weighting factors (see sections

2.5.1, 2.5.2, 2.6.1, and 2.6.2), the relative biological effectiveness (RBE) factor was used. To

convert from rad to rem, one would simply multiply the absorbed dose by the RBE value

(Table 2.1). The resulting value would be called the RBE dose, or simply the dose expressed

in rem. To determine the RBE of a particular radiation, one would take the inverse ratio of

the absorbed dose producing the same degree of a defined biological end point as 250 kVp

(peak voltage) x‐rays or cobalt‐60 photons. For example, given that the RBE for cobalt‐60

Page: 8 photons is defined as 1, and 100 rads of radiation from cobalt‐60 photons produced an

increase in cancer mortality equivalent to 10 rads of 5 MeV alpha radiation, the RBE for the

alpha radiation would therefore be 10.

Table 2.1 ICRP 2 RBE values

Radiation RBE

γ, β‐, β+, e‐ 1

Low energy β‐, β+, e‐ (if Emax≤ 0.03 MeV) 1.7

Alpha 10

Recoil Atoms 20

At the time, internal dose limitations were expressed by two main quantities:

“maximum permissible body burden” (MPBB or q), and “maximum permissible

concentration” specified for air and water (MPCa and MPCw, respectively).

2.2.2 Maximum Permissible Body Burden

The maximum permissible body burden (MPBB) was defined by the ICRP 2 Task

Group as the internal activity (in μCi) of a particular radionuclide that results in a maximum

permissible dose (MPD) to the whole body, or to one or more organs in the body (ICRP,

1960). For radionuclides that do not localize in the bone, MPDs of 0.1 rem per week were

used for gonads and total body, 0.6 rem per week for the skin and thyroid, and 0.3 rem for

all other soft tissues. The method of calculating the non‐bone localizing MPBB was as

follows:

Page: 9

[ ][ ]

4 6 52

ergs rad100 g Rg rad week

μCint ergs secs MeV3.7 10 1.6 10 6.05 10 ntμCi MeV week

mq

x x x f ε−

⎡ ⎤ ⎡ ⎤⋅ ⋅⎢ ⎥ ⎢ ⎥⋅ ⎣ ⎦⎣ ⎦=⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥ ⋅ ⋅ ⋅ ⋅⎢ ⎥ ⎢ ⎥ ⎣ ⎦⎢ ⎥ ⎣ ⎦ ⎣ ⎦⎣ ⎦

(1.2)

or

[ ][ ]3

2

week MeV μCi rad2.8 10 g Rnt rad g week

μCiMeV

nt

x mq

f ε

− ⎡ ⎤⋅ ⋅ ⎡ ⎤⋅⎢ ⎥ ⎢ ⎥⋅ ⋅ ⎣ ⎦⎣ ⎦=⎡ ⎤⋅ ⎣ ⎦

(1.3)

where:

• m is the reference organ mass [g];

• R is the MPD per week limitation [rad/week];

• 2f is the reference organ body burden fraction [unitless]; and

• ε is the effective absorbed energy per disintegration of a given radionuclide

[MeV/nt].

In the case of radionuclides that do localize in the bone, such as 90Sr and 239Pu, the

MPBB was determined from a direct comparison with 0.1 μCi of 226Ra (ICRP, 1960). These

special cases for MPBB were calculated as follows:

[ ] [ ] ( )2

2 2

MeVμCi 0.1 0.99 110ntμCiMeV

nt

RaRa Raq fq

f f

ε

εε

⎡ ⎤⎣ ⎦= ⋅ =⎡ ⎤⎣ ⎦

⋅ (1.4)

or

Page: 10

[ ]2

MeV11 μCi ntμCiMeV

ntq

f ε

⎡ ⎤⎣ ⎦=

⎡ ⎤⎣ ⎦

(1.5)

where:

• = 0.1 [µCi] the MPBB for 226Ra, used for comparison to other radionuclides; Raq

• 2Raf =0.99, the fraction of radium in the body that resides in the skeleton;

• 2f is the fraction of the radionuclide in the body that resides in the skeleton;

• MeV110 ntRaε ⎡= ⎣

⎤⎦ , the effective absorbed energy per disintegration of radium;

• ε is the effective absorbed energy per disintegration of a radionuclide, or

( )MeVntEF RBE n⎡ ⎤ ⋅⎣ ⎦ ⋅∑ ; and

• n is the relative damage factor, which was 1 if the radionuclide was a daughter of

radium, and 5 in all other cases.

The MPBB was the predecessor to the annual limit of intake (ALI), described in ICRP 30

(1982a). The MPBBs for 240 different radionuclides were calculated in ICRP 2 and listed in

over 200 pages of tables. The MPBB provided the health physicist with a look‐up value

utilized for determining internal dose limitations. To date, the US still requires several of

these calculations to be performed by health physicists in nuclear power plants as specified

in 10.CFR.50 Appendix I (Borchardt, 2008).

2.2.3 Maximum Permissible Concentration

The maximum permissible concentration (MPC) was simply the concentration in air

or water that would result in the MPBB, given a certain breathing rate or water

Page: 11 consumption rate. The calculation of the MPC was somewhat more complicated than the

calculation of MPBB.

For example, if the radionuclide considered was the parent of a chain of k daughters

and the stomach was the critical tissue, the corresponding formulas for MPCa and MPCw

were:

( )[ ]

( )

103

3a /24

0 01

0

μCi MeV2.5 10cm g ntμCiMPC cm MeV 1

nt

hik ir

a i j ii hj

h p hpp h

x m g

efλ

ε λλ λ λ

−

−

= ==

=≠

⎡ ⎤⋅ ⋅⎢ ⎥⋅ ⋅⎣ ⎦⎡ ⎤ =⎢ ⎥⎣ ⎦ ⎛ ⎞ −⎡ ⎤ ⋅ ⋅⎜ ⎟⎢ ⎥⎣ ⎦ ⎝ ⎠ −∑ ∑∏

∏

(1.6)

and:

( )[ ]

( )

63

3 /24

0 01

0

μCi MeV2.2 10cm g ntμCiMPC cm MeV 1

nt

hw ik ir

w i j ii hj

h p hpp h

x m g

efλ

ε λλ λ λ

−

−

= ==

=≠

⎡ ⎤⋅⋅⎢ ⎥⋅ ⋅⎣ ⎦⎡ ⎤ =⎢ ⎥⎣ ⎦ ⎛ ⎞ −⎡ ⎤ ⋅ ⋅⎜ ⎟⎢ ⎥⎣ ⎦ ⎝ ⎠ −

∑ ∑∏∏

(1.7)

where:

• m is the reference organ mass [g];

• λj, p, h is the effective decay constant for various radionuclides j, p, h in the decay

chain [s‐1];

• k is the number of daughters in the decay chain [unitless];

• ε i is the effective absorbed energy per disintegration for radionuclide, i [MeV/nt];

• af is the inhalation fraction that is retained in the critical organ [unitless]; and

• wf is the ingestion fraction that is retained in the critical organ [unitless].

Page: 12 A list of all MPC equations used in ICRP 2 was considered beyond the scope of this work, and

thus was omitted. A list of all MPC equations used and complete derivations can be found

in ICRP 2 on pages 16‐39 (ICRP, 1960).

Just as the MPBB was the predecessor to the ALI, MPC was the predecessor to the

derived air concentration (DAC), also defined in ICRP 30 (1982a).

The MPC’s for 240 different radionuclides were calculated in ICRP 2 and listed,

together with MPBB’s, in over 200 pages of tables. The MPC’s provided health physicists

with a look‐up value utilized for the determination of air and water concentrations that

correspond to the MPBB for a given radionuclide.

2.3 Linear Energy Transfer

The restricted LET was defined in ICRU Report 19 (1971) as:

dELdΔ

Δ

⎛ ⎞= ⎜ ⎟⎝ ⎠l

(1.8)

where Δ is a specified energy cutoff in electronvolts and dE is the energy lost by a

charged particle traversing a distance dl in a medium.

The unrestricted linear energy transfer (LET) was defined in ICRU Report 16 (1970)

as:

dELd∞ = l

(1.9)

Δ = ∞ ). or the restricted LET with no energy cutoff (i.e.,

Page: 13

Photons and electrons are considered to be of “low LET” due to their energy

deposition over a relatively long path length. Alpha particles and other heavy charged

particles deposit their energy in a very short distance, and thus are considered to be of “high

LET.”

2.4 Absorbed Dose

Absorbed dose, D, was defined in ICRU Report 19 (1971) as,

dDdmε

= (1.10)

where dε is the mean energy imparted by ionizing radiation to the matter in a

volume element of mass . The special unit, as the ICRP refers to non‐SI units, for

absorbed dose is the rad, where 1 rad was defined as 100 ergs g‐1 or 0.01 J kg‐1. The SI unit,

introduced later, is the Gray (Gy), where 1 Gy was defined as 1 J kg‐1 or 100 rad.

dm

The unit for absorbed dose is the rad, which corresponds to the energy absorption of

ionizing radiation of 100 ergs per gram in any medium. Its predecessor was the rep or

“roentgen equivalent physical.” There is widespread belief that the rad is an acronym for

“radiation absorbed dose.” This seems reasonable because several other radiation

protection units at the time were acronyms (e.g., rem, rep, reb). This is not the case,

however, as was specifically addressed by Dr. Lauriston Taylor, Chairman Emeritus of the

ICRU in a 1990 issue of ICRU News, “The term rad was simply suggested as a word by itself.

Since then it has frequently been improperly referred to as an abbreviation for ‘radiation

absorbed dose.’ This is simply incorrect” (Taylor, 1990).

Page: 14 2.5 ICRP 26

ICRP 26 was published in 1977 as an update to the ICRP 2 radiation dosimetry

methodology. It contained several very useful tools that are still used today in radiation

protection, as specified in 10.CFR.20. Among them were the concepts of detriment, the

quality factor, and the tissue weighting factor.

As is the case in ICRP 26, an informative way to describe radiation dose is through

the use of “detriment.” For effects on health, if pi, the probability of suffering the effect i, is

small and the severity of the effect is expressed by a weighting factor gi, then the detriment

to health, G, in a group of P persons is given by:

i ii

G P p g= ∑ (1.11)

Generally speaking, the detriment to a population is defined as the mathematical

“expectation” of the harm incurred from radiation exposure (ICRP, 1977). The ICRP uses

detriment to quantify the risk of radiation exposure.

2.5.1 Quality Factor

The first measure of detriment introduced in ICRP 26 was the dose equivalent. The

dose equivalent (H) was defined (ICRU, 1970) as:

H DQN= (1.12)

or the absorbed dose weighted by the modifying factors of Q, the quality factor (see Table

2.3), and N, the product of all other modifying factors specified by the Commission. The

Page: 15 value of N could, for example, account for the absorbed dose rate and fractionation effects

on detriment. However, in most cases, N is assigned a value of 1.

The special unit for dose equivalent is the rem, “roentgen equivalent man.” The rem

replaced the reb, “roentgen equivalent biological” resulting from a confusion of speech from

its creator, Herbert M. Parker, in the 1950s (Kathren & Parker, 1986). It was reported that

“during one of his early presentations of the new unit, Parker was suffering from a cold,

which led to difficulty in differentiating it from the rep. Accordingly, the name of the unit

was changed to rem” to avoid future confusion. The rem has since been replaced by the SI

unit, the Sievert (Sv), where 1 Sv is equivalent to 100 rem. According to NIST (2008), the use

of the rem today is “strongly discouraged,” in an attempt to standardize dose units.

Quality factors, or Q‐values, replaced the RBE factors of ICRP 2. Quality factors were

defined as a function of the unrestricted LET, L∞, in water (Table 2.2).

Table 2.2 Unrestricted LET, quality factor relationship

L∞ in water (keV/μm) Q 3.5 (and less) 1 7 2 23 5 53 10 175 (and above) 20

Because the distribution of LET is not always known, an approximation of average

LET per radiation type was recommended by the ICRP (Table 2.3).

Page: 16

Table 2.3 ICRP 26 quality factors

Radiation Quality Factor (Q) X rays, γ rays, and electrons 1 Neutrons, protons, and singly‐charged particles of rest mass greater than one atomic mass unit of unknown energy

10

α particles and multiply‐charged particles (and particles of unknown charge) of unknown energy

20

The quality factor values in Table 2.3 were based on an extrapolation from higher

absorbed doses at which deleterious effects could be directly assessed. Therefore, the Q‐

values were also not necessarily representative of RBE values for other observed effects,

such as stochastic effects at low absorbed doses, and non‐stochastic effects at larger

absorbed doses.

Oftentimes, to estimate the dose equivalent for the entire residence time of a

radionuclide in the human body, the “committed” dose equivalent, H50, is used:

0

0

50

50 ( )t y

tH H t dt

+= ∫ (1.13)

where ( )H t is the relevant dose‐equivalent rate, t0 is the time of intake, and the integration

time is 50 years.

2.5.2 Tissue Weighting Factor and Detriment

An interesting quantity recommended for the regulation of dose‐equivalent limits

was the weighted committed dose equivalent, or the doubly weighted committed absorbed

dose. This limit was defined in ICRP 26 as the product of the dose equivalent and a tissue

weighting factor, wT, summed over all tissues, T, being below the annual dose‐equivalent

limit, Hwb,L, where:

Page: 17

,T T wb LT

w H H≤∑ (1.14)

It is a common misconception that ICRP 26 introduced the quantity of “effective

dose equivalent.” This is not the case. It was not until several years later (1982) that this

quantity made its first appearance in ICRP 33 (ICRP, 1982b). The effective dose equivalent,

HE, was defined as the dose equivalent multiplied by a tissue weighting factor, wT, summed

over all tissues, T, or:

E TT

H w TH= ⋅∑ (1.15)

The unit for effective dose equivalent was the same as dose equivalent, i.e., the Sievert or

rem.

The ICRP 26 methodology for quantifying detriment to a given organ or tissue relies

on the risk of fatal cancer, only. The risk is normalized and rounded to yield a tissue

weighting factor (Table 2.4).

Page: 18

Table 2.4 The ICRP 26 calculation of radiation weighting factors

Organ Risk (fatal cancer per Sv)

% Total wt

Gonads 4.00E‐03 0.242 0.25

Red Bone Marrow 2.00E‐03 0.121 0.12

Bone Surface 5.00E‐04 0.030 0.03

Lung 2.00E‐03 0.121 0.12

Thyroid 5.00E‐04 0.030 0.03

Breast 2.50E‐03 0.152 0.15

Other 5.00E‐03 0.303 0.30

Total: 1.65E‐02 1.000 1.00

The ICRP 26 report was vague about the origin of the values of fatal cancer risk in Table 2.4,

although it is suspected that the values are from BEIR I (National Research Council &

National Academy of Sciences, 1972). The ICRP 30 (ICRP, 1982a) Committee used ICRP 26

methodology to calculate limits for the intake of radionuclides by workers.

The ICRP clearly prescribes the correct (and incorrect) uses of effective dose

equivalent, in that:

• HE is calculated using reference values for a reference person or group (not for an

individual);

• HE is to be used for the planning of prospective situations;

• HE is not to be used for retrospective dose and risk assessments of exposure of

individuals; and

• HE is not to be used for epidemiological studies.

Page: 19 The ICRP states that when it is inappropriate to use effective dose equivalent, an RBE‐

weighted dose, RBExD [Sv or rem] should be used in its place.

2.6 ICRP 60

The ICRP 60 report was published in 1991 as an update to ICRP 26. It contained

several revisions to ICRP 26, including enhancements to the radiation weighting factor and

tissue weighting factor methods.

2.6.1 Radiation Weighting Factor

The ICRP 60 method updated the definition of dose equivalent in two ways. First,

the Commission changed dose equivalent to “equivalent dose”; second, at this time, they

call the quality factor the “radiation weighting factor.” Equivalent dose is defined in ICRP 60

as the absorbed dose multiplied by a radiation weighting factor (Table 2.5), or:

, ,T R R T RH w D= ⋅ (1.16)

where:

• wR is the radiation weighting factor [unitless];

• DT,R is the absorbed dose averaged over a tissue, T, from radiation, R [Gy or rad]; and

• HT,R is the equivalent dose, to tissue T, from radiation, R [Sv or rem].

Page: 20

Table 2.5 ICRP 60 radiation weighting factors

Radiation Energies Radiation Weighting Factors

X‐Rays, γ rays, and electrons All energies 1 Neutrons <10 keV 5 10‐100 keV 10 100 keV‐2 MeV 20 2‐20 MeV 10 >20 MeV 5 Protons <20 MeV 5

Alpha particles, fission fragments, heavy nuclei

20

Due to the significant variation of secondary radiation with neutron energy, the

biological effectiveness of neutrons incident on the human body is strongly dependent on

their energy. For energies below 100 keV, significant fractions of the absorbed dose are

deposited by secondary photons via the H(n, γ) reaction, thereby reducing the biological

effectiveness. The maximum weighting factor occurs between 100 keV and 2 MeV and has a

value of 20. This weighting factor is not an experimentally determined value; rather, it is a

representative value accounting for the broad range of RBE values from animal testing data

using reactor generated neutrons of around 1 MeV. It was thus decided (ICRP, 1991) that a

step function, dependent on energy, provided a more accurate measure of neutron

detriment than the single value used in ICRP 26.

To provide consistency in calculations, a smooth curve was fit (ICRP, 1991) to the

step function for neutrons (Figure 2.1). The mathematical relationship for neutron radiation

weighting factors (as a function of energy in MeV) is:

(1.17) ( )( )2ln 2 /6( ) 5 17 E

Rw E e−= +

Page: 21

0

5

10

15

20

25

1.E‐08 1.E‐06 1.E‐04 1.E‐02 1.E+00 1.E+02 1.E+04

Radiation Weighting

Factor

Neutron Energy (MeV)

Neutron Radiation Weighting Factors: ICRP 60

Smoot Fit

Step Function

Figure 2.1 A comparison of Equation (1.17) and the step function described in Table 2.1


As in ICRP 26 (1977), the determination of the tissue weighting factors in ICRP 60 is

based on organ detriment. However, unlike the 1977 definition, detriment to organs or

tissues was defined in ICRP 60 (1991) as the product of fatal cancer risk, severe genetic

effects (for gonads only), the relative non‐fatal contribution, and the relative length of life

lost.

“Fatal cancer risk” is simply defined as the number of fatal cancers per Sievert, per

10,000 persons. These data were obtained primarily from the Japanese atomic bomb

survivor Life Span Study (LSS) cohort, summarized in BEIR V (National Research Council,

1990).

Page: 22

“Severe genetic effects” were defined in ICRP 60 as the incidence probability of

genetic effects due to radiation exposure over all generations per person in the total

population. This was found by the ICRP (1991) to be 0.014 Gy‐1. The ICRP points out that

“because some of the mulifactorial diseases are less detrimental… this probability should

not be added as such without some weighting for the severity of the effects.” The ICRP

admits that “this weighting is necessarily somewhat arbitrary.” And, it was decided

therefore to reduce the risk of genetic effects by a factor of about 1/3, to 0.01 Gy‐1 (ICRP,

1991).

The “relative non‐fatal contribution” to detriment is a function of the probability of

fatal cancers and the lethality fraction for cancer in a given organ. The lethality fraction, k,

was determined from the available lethality data at the time (Table 2.6).

Table 2.6 ICRP 60 calculation of lethality fraction

Organ 5 year Lethality

20 year Lethality

Proposed Lethality, k

Bladder 0.22 0.58 0.50 Breast 0.24 0.62 0.50 Colon 0.45 0.62 0.55 Liver 0.95 0.98 0.95 Lung 0.87 0.96 0.95 Esophagus 0.92 0.97 0.95

Ovary 0.62 0.74 0.70 Stomach 0.85 0.90 0.90 Thyroid 0.06 0.15 0.10

Using the lethality fraction, the non‐fatal contribution was calculated as follows. For

a given tissue, there are F fatal cancers in a given population (i.e., the probability of fatal

cancer). The total probability of cancers, T, in the population, is therefore defined as:

Page: 23

FTk

= (1.18)

The probability of non‐fatal cancers, N, is therefore:

( ) F1N T F kk

= − = − (1.19)

The weighted detriment, D, is then defined (so far) as the sum of the fatal cancer probability

and the lethality fraction multiplied by the probability of non‐fatal cancers:

(1 ) FD F kN F k kk

⎛ ⎞= + = + − ⋅⎜ ⎟⎝ ⎠

(1.20)

or

( )2D F k= − (1.21)

where (2‐k) is now defined as the relative non‐fatal contribution.

The relative length of life lost is a dimensionless ratio of two values, l , defined as

the organ‐specific length of life lost per fatal cancer, and l , the average length of life lost

due to any fatal cancer. The ICRP (1991) defined l as 15 years; this value was obtained by

dividing the expected years of life lost summed over all cancers, by the total number of fatal

cancers. Values of (see l Table 2.7) for bladder, bone marrow, breast, colon, lung,

esophagus, ovary, stomach and remainder were obtained from Land and Sinclair (1991).

Values of for bone surface, liver, skin and thyroid could not be determined in 1991 and l

Page: 24

were arbitrarily set to 15, making the ratio ll equal to unity. The value of l for gonads

was also uncertain and was arbitrarily set to 20 years.

Table 2.7 The ICRP 60 calculation of relative life lost

Organ Life Lost (years): l Relative Life lost: ll

Bladder 9.8 0.65

Bone Marrow 30.9 2.06

Bone Surface 15.0* 1.00

Breast 18.2 1.21

Colon 12.5 0.83

Liver 15.0* 1.00

Lung 13.5 0.90

Esophagus 11.5 0.77

Ovary 16.8 1.12

Skin 15.0* 1.00

Stomach 12.4 0.83

Thyroid 15.0* 1.00

Remainder 13.7 0.91

Gonads 20.0* 1.33

* values were arbitrarily chosen l

( )

After accounting for the relative life lost, the total detriment, D, to a tissue is calculated

using:

2 lD F k l= − (1.22)

Using the data in Tables 2.6 and 2.7, the relative contribution of detriment can be calculated

(Table 2.8).

Page: 25

Table 2.8 ICRP 60 parameter values used in the calculation of detriment

Probability of fatal cancer (10,000

people/Sv)

Severe genetic effects (10,000

people/Sv)

Relative length of life lost

( )ll

Relative non‐fatal

contribution (2‐k)

Detriment (D)

Bladder 30 0.65 1.5 29.25

Bone Marrow 50 2.06 1.01 104.0

Bone Surface 5 1.00 1.30 6.5

Breast 20 1.21 1.50 36.3

Colon 85 0.83 1.45 102.3

Liver 15 1.00 1.05 15.8

Lung 85 0.90 1.05 80.3

Esophagus 30 0.77 1.05 24.3

Ovary 10 1.12 1.30 14.6

Skin 2 1.00 2.00 4.0

Stomach 110 0.83 1.10 100.4

Thyroid 8 1.00 1.90 15.2

Remainder 50 0.91 1.29 58.7

Gonads 100 1.33 133.3

Total Detriment: 724.9

It was determined that there was insufficient data in 1991 to use probability of

cancer incidence for determining detriment. Instead, probability of fatal cancer was used.

The relative organ contribution to total detriment (see Table 2.9) was generated by

determining the fractional contribution of organ detriment to total detriment. Taking into

account the uncertainties involved in the generation of detriment factors, the ICRP decided

that the relative organ contributions could be rounded and grouped into a “simple system of

weights of adequate accuracy” that “would use no more than four groups of weights and

require no more than about a factor of 2 rounding between the relative contributions and

the assigned weight” (ICRP, 1991). The possible values for weights were selected in such a

way as to limit the amount of manipulation involved in forcing the weights to sum to unity.

Page: 26 The possible weighting factors selected were: 0.01, 0.05, 0.12, and 0.20. The tissue

weighting factors (wT) decided upon by ICRP 60 (ICRP, 1991) are summarized in Table 2.9.

Table 2.9 ICRP 60 calculation of tissue weighting factors for various organs

Organ Relative Contribution

wT

(from ICRP 60) Bladder 0.040 0.05

Bone Marrow 0.144 0.12

Bone Surface 0.009 0.01

Breast 0.050 0.05

Colon 0.141 0.12

Liver 0.022 0.05

Lung 0.111 0.12

Esophagus 0.033 0.05

Ovary** 0.020 ‐‐

Skin 0.006 0.01

Stomach 0.139 0.12

Thyroid 0.021 0.05

Remainder* 0.081 0.05

Gonads** 0.184 0.2

Total 1.000 1

*Remainder is composed of 10 tissues: adrenals, brain, upper large intestine, small intestine, kidney, muscle, pancreas, spleen, thymus, and uterus. ** Detriment for gonads and ovaries were summed to yield one wt

The weighting factor for the remainder tissues was divided equally between 10

tissues yielding a wT of 0.005 for each; which is purposefully lower than the lowest wT for

other tissues.

For simplicity sake, effective dose equivalent (HE) was shortened to effective dose (E)

in ICRP 60. According to the Commission, “[effective dose equivalent] is unnecessarily

Page: 27

T TT

E w H

complicated, especially in more complex combinations such as collective committed

effective dose equivalent (ICRP, 1991).” Effective dose was defined as:

= ⋅∑ (1.23)

where wT is the tissue weighting factor and HT is the equivalent dose.

2.7 ICRP 103

The ICRP 103 report was released in 2007 as an update to ICRP 60. The overall

estimates of deterministic and stochastic effects remain fundamentally the same. Even the

ICRP admits, “The overall estimates of cancer risk attributable to radiation exposure have

not changed appreciably in the past 16 years” (ICRP, 2007).

2.7.1 Radiation Weighting Factor

The ICRP 103 radiation weighting factors (Table 2.10) are fairly similar to the ICRP 60

factors (Table 2.5), in that photons and electrons are given a weighting factor of 1. Protons’

and other charged particles’ (not including electrons or muons) weights were reduced from

5 to 2. For neutrons, aside from the use of a continuous function (as opposed to a step

function as was utilized in ICRP 60), the two most significant changes are the decrease of wR

in the low‐energy range (which accounts for the large contribution of secondary photons to

the absorbed dose in the human body), and the decrease of wR at energies above 100 MeV

(ICRP, 2007). It was noted by the ICRP that most neutron doses involve a range of energies

and the use of a continuous function was based on practical considerations and does not

imply greater precision.

Page: 28

Table 2.10 ICRP 103 radiation weighting factors

Radiation Type Radiation weighting factor, wR Photons 1 Electrons and muons 1 Protons and charged particles 2 Alpha particles, fission fragments, heavy ions 20 Neutrons A continuous function of neutron

energy (see Equation (1.24) and Figure 2.2) ranging from 2 to 20

The energy dependent radiation weighting factor for neutrons (see Figure 2.2) can

be found by using the empirically derived, continuous Equation (1.24) as a function of

neutron energy, En:

(1.24)

[ ]

[ ]

[ ]

2

2

2

ln( ) /6

ln(2 ) /6

ln(0.04 ) /6

2.5 18.2 , 1 MeV

( ) 5.0 17.0 , 1 MeV 50 MeV

2.5 3.25 , 50 MeV

n

n

n

En

ER n n

En

e E

w E e E

e E

−

−

−

⎧ + <⎪⎪= + ≤ ≤⎨⎪

+ >⎪⎩

For energies above 1 MeV, very little animal data was available to determine the

biological effectiveness of neutrons; however, the scant data that were available show a

clear decrease in RBE with increasing neutron energy. At energies above 50 MeV, it was

decided (ICRP, 2007) that the weighting factor should asymptotically approach a value close

to that of protons due to their similar behavior at higher energies.

Page: 29

0

5

10

15

20

25

1E‐06 1E‐04 1E‐02 1E+00 1E+02 1E+04Radiation Weighting

Factor

Neutron Energy (MeV‐1)

Neutron Radiation Weighting Factors: ICRP 103

Figure 2.2 Equation (1.24) expressed graphically


Although most of the calculation of the ICRP 103 tissue weighting factors will be

covered in this section, Appendix A presents an enlightening step‐by‐step procedure,

written by the ICRP 103 committee, for calculating tissue weighting factors. For the

following calculations, it is useful to reference Table 2.11 for a comparison of terminology

used in ICRP 60 and 103.

Table 2.11 A summary of the terms used to define detriment in ICRP 60 and 103

ICRP 60 Terminology ICRP 103 Terminology Definition F

,F TR Fatal risk

(1 ) FN kk

= − , , ( (1 ))T F TR R k q k= + −NF Nonfatal risk

ll Tl Relative length of life lost

FTk

= IR Nominal risk for fatal and non fatal cancers

Page: 30

, ,( )T F T T NF T TD R q R l

As with ICRP 60, tissue weighting factors are based on detriment to a tissue, T.

Detriment is defined by ICRP 103 as:

= +

min min(1 )Tq q q k

(1.25)

where qT is based on lethality and subjective quality of life accounting for pain and suffering

due to cancer in a tissue, T, and is defined as:

= + − ⋅ (1.26)

The value of qmin is defined as the minimum weight for non‐lethal cancers and attempts to

adjust for pain and suffering for different cancer types. The values assigned to qmin were 0

for skin, 0.2 for thyroid and 0.1 for all other organs. In most cases the weighted detriment

was not terribly sensitive to the value chosen (ICRP, 2007). The qmin adjustment primarily

has an impact on cancers in tissues that have a low lethality rate, such as the skin.

The ICRP assigned a qmin value of 0 to skin cancer because, “radiogenic skin cancer is

almost exclusively of basal cell type which is usually associated with very little pain, suffering

or treatment sequelae” (ICRP, 2007). They assigned a qmin value of 0.2 to thyroid cancer

because they believed that cancer of the thyroid was significantly more painful than other

cancers, although they never specified the origin of this belief. There was little conclusive

evidence to support different qmin values for other organs, therefore the rest of the organs

received a qmin value of 0.1.

Detriment estimates were based on cancer incidence in ICRP 103, whereas cancer

mortality was the basis for tissue weighting factors in ICRP 60. Since that time, however,

Page: 31

T

there has been more progress made on the data analysis of the Life Span Study (ICRP, 2007),

such that the ICRP felt comfortable using incidence data to determine detriment.

Table 2.12 ICRP 103 detriment parameters

Site Nominal risk based on

incidence(RI)(per 10,000)

Lethality (k)

Non‐fatal weight (qT)

Relative life lost ( l )

Absolute Detriment

(DT)

Esophagus 15.1 0.93 0.935 0.87 13.1 Stomach 79.1 0.83 0.846 0.88 67.8 Colon 65.4 0.48 0.530 0.97 48.0 Liver 30.3 0.95 0.959 0.88 26.6 Lung 114.2 0.89 0.901 0.80 90.4 Bone 7 0.45 0.505 1.00 5.1 Skin 1000 0.002 0.002 1.00 4.0 Breast 112.1 0.29 0.365 1.29 79.0 Ovary 10.6 0.57 0.609 1.12 9.9 Bladder 43.4 0.29 0.357 0.71 16.8 Thyroid 32.5 0.07 0.253 1.29 12.9 Bone Marrow 41.9 0.67 0.702 1.63 61.6 Other Solid* 143.8 0.49 0.541 1.03 113.4 Gonads 20 0.80 0.820 1.32 25.4

Total: 574.1

* Other Solid is a grouping of 14 tissues: Adrenals, Extrathoracic (ET) region, Gall bladder, Heart, Kidneys, Lymphatic nodes, Muscle, Oral mucosa, Pancreas, Prostate, Small intestine, Spleen, Thymus, and Uterus/cervix.

Utilizing the values presented in Table 2.12 and Equation (1.25), the relative

detriment was calculated (Table 2.13). Similar to ICRP 26 and 60, the possible values for

weights were selected in such a way as to limit the amount of manipulation involved in

forcing the weights to sum to unity. The possible weighting factors selected were: 0.01,

0.04, 0.08, and 0.12.

Page: 32

Table 2.13 The ICRP 103 calculation of tissue weighting factors

Site Absolute Detriment

(DT)

Relative Detriment

wT

Esophagus 13.1 0.023 0.04 Stomach 67.8 0.118 0.12 Colon 48.0 0.084 0.12 Liver 26.6 0.046 0.04 Lung 90.4 0.157 0.12 Bone 5.1 0.009 0.01 Skin 4.0 0.007 0.01 Breast 79.0 0.138 0.12 Ovary* 9.9 0.017 ‐‐ Bladder 16.8 0.029 0.04 Thyroid 12.9 0.022 0.04 Brain ‐‐ ‐‐ 0.01 Salivary glands ‐‐ ‐‐ 0.01 Bone Marrow 61.6 0.107 0.12 Remainder 113.4 0.198 0.12 Gonads* 25.4 0.044 0.08 Total: 574.1 1.000 1.00

*Gonad and ovary data were summed to yield one weighing factor for the combined organs

The wT for the reminder tissues was divided equally between 14 tissues yielding a wT

of 0.0086 for each; which is purposefully lower than the lowest wT for other tissues. While

not specifically quantifiable, cancer risk to the salivary glands and the brain are thought to

be greater than that of the other tissues in the remainder category, and thus were ascribed

a value of 0.1 (ICRP, 2007).

In summary, Table 2.14 is provided to track the evolution of tissue weighting factors

over 30 years from 1977 (ICRP 26) to 2007 (ICRP 103).

Page: 33

Table 2.14 A summary of tissue weighting factors in ICRP 26, 60, and 103

Organ ICRP 26 ICRP 60 ICRP 103

Gonads 0.25 0.2 0.08 Bone marrow 0.12 0.12 0.12 Lung 0.12 0.12 0.12 Breast 0.15 0.05 0.12 Thyroid 0.03 0.05 0.04 Bone Surfaces 0.03 0.01 0.01 Remainder 0.3 0.05 0.12 Colon 0.12 0.12 Stomach 0.12 0.12 Bladder 0.05 0.04 Liver 0.05 0.04 Esophagus 0.05 0.04 Skin 0.01 0.01 Salivary glands 0.01 Brain 0.01

The weighting factors stayed fairly consistent between the publications with a few

exceptions. The weighting factor for gonads changed significantly from 0.20 in ICRP 60 to

0.08 in ICRP 103. This primarily is due to genetic risk being estimated for only two

generations into the future. The ICRP (2007) points out that, “the equilibrium value used in

Publication 60 is judged to be of limited scientific validity because of the unsupported

assumptions necessary on selection coefficients, mutation component, and population

changes over hundreds of years“ (ICRP, 2007).

The weighting factor for breast dropped by a factor of three (0.15 to 0.05) between

ICRP 26 and 60. This is most likely due to advances in cancer therapy resulting in a drop in

the lethality of breast cancer between 1977 and 1991. The weighting factor, however,

Page: 34 jumped up to 0.12 in ICRP 103. This is due to ICRP 103’s method of using cancer incidence

risk instead of cancer mortality risk in the detriment calculation.

The bone surface weighting factor also dropped by a factor of three (0.03 to 0.01)

between ICRP 26 and 60. This is due to the publication of BEIR IV (1988) on the effects of

radium and other internally deposited alpha emitters. The ICRP 60 and 103 reports both use

the data from BEIR IV in their calculation of detriment to bone surface; ICRP 26 does not.

The deterministic values of the tissue weighting factors are difficult to compare

unless an estimate of uncertainty is determined. Chapter 3 explains the process of

determining the uncertainty of the ICRP 103 relative detriment calculation; Chapter 4

presents the results of that analysis, while Chapter 5 compares the tissue weighting factors

from each publication to the uncertainty analysis.

Page: 35

3 Chapter 3 – Methods

In order to compare the tissue weighting factors of ICRP 103 to the weighting

factors of ICRP 26 and 60, and to determine the significance of any changes, one first needs

to calculate the uncertainties in the newly developed ICRP 103 relative detriment

calculation. The method of assessing uncertainty is similar to that used by Hamby (1993), in

an estimation of atmospheric tritium dose. The goal of this uncertainty analysis is to

quantify the uncertainties in the ICRP 103 relative detriment calculations. Crystal Ball

uncertainty and sensitivity analysis software* was utilized (as a plug‐in to Microsoft Excel)

for this task.

3.1 ICRP 103

The report of ICRP 103 estimates relative detriment due to cancer in a specific organ

from three primary factors: nominal risk based on incidence, a non‐fatal weighting factor

(including the probability of lethality), and relative life lost due to radiogenic cancer death.

Each factor carries an associated uncertainty, distributions of which have been captured

herein. These probability distributions can be deduced, given the availability of data

appropriate for the estimate. If the original data set is not available, or if parameter values

were chosen arbitrarily by the Commission, one can use similar data to determine trends,

functional forms, and variances of the known distribution. For example, if the ICRP used US

cancer incidence data from 2005, but one only has access to US cancer incidence data from

2002, an appropriate assumption would be that the distributions of the 2002 and 2005 data

are sufficiently similar to use one distribution in estimating the other. It therefore can also

be assumed that the variance of the 2002 data is reasonably similar to the variance of the

* By Oracle; online at: http://www.oracle.com/crystalball/

http://www.oracle.com/crystalball/

Page: 36 2005 data such that the same geometric standard deviation (GSD) (or some other

multiplicative expression of variance, depending on the distribution) can be applied to the

2005 data.

To carry the example further, if the 2002 cancer incidence of a particular organ was

fit to a log‐normal distribution with a GSD of 1.5, a geometric mean (GM) of 20 (per 10,000),

and the ICRP reported a cancer incidence of 15 (without sufficient information to locate the

original data), one would take 15 as the new GM of a lognormal distribution and apply a

GSD of 1.5. Applying this method and using original data sets where available, probability

distributions for each parameter were generated for the three primary factors in the ICRP

103 detriment calculation to determine the final uncertainties in the relative organ

detriment.

3.2 Uncertainty Analysis

Each parameter in an uncertainty analysis is defined by a probability distribution of

possible values. The choice of distribution is based on one’s knowledge of the parameter

and the values appropriate for the calculation. For example, if the variable of interest is a

fraction, but nothing else is known, a uniform distribution (Figure 3.1) would be fit with

bounds of 0 and 1.

Page: 37

Figure 3.1 An example of a uniform distribution generated by Crystal Ball

If the most likely value of the variable on interest is 0.5, a more informative,

triangular distribution (Figure 3.2), could be assigned.

Figure 3.2 An example of a triangular distribution generated by Crystal Ball

If additional information is available to indicate that the data are normally

distributed, with a mean of 0.5 and a standard deviation of 0.2, a normal distribution (Figure

3.3) would be assigned.

Page: 38

Figure 3.3 An example of a normal distribution generated by Crystal Ball

Unfortunately, not all of the ICRP 103 original data were available to determine

information of distribution shape. If it were, standard statistical tests could be implemented

to determine an appropriate distribution and a measure of goodness‐of‐fit.

Oftentimes, confidence intervals are reported alongside deterministic parameter

estimates. This information can be utilized to determine how data are distributed. For

example, in order to determine if data are normally distributed, one can plot the mean and

confidence intervals on a normal‐probability (often referred to as normal‐probit) plot

(Figure 3.4). If a straight line can be fit to the points, then the data are normally distributed.

One could then use the fit line to determine the standard deviation as the average distance

from the mean at the 16th and 84th percent.

Page: 39

Figure 3.4 Normal‐probit plot line fit

If the plot does not form a straight line on a normal‐probit plot, another functional

fit must be determined. To determine if data are log‐normally distributed, the median and

confidence intervals can be plotted on a log‐probit plot (Figure 3.5); if the points form a

straight line, the data are log‐normally distributed. If the data do not fit a normal or a log‐

normal distribution, other methods must be employed to determine an appropriate

probability distribution to describe the data.

Figure 3.5 Log‐probit plot line fit

Page: 40

To determine a geometric standard deviation (GSD) from a log‐probit plot, the

multiplicative difference between the 84th and 16th percentiles (represented by F(84%) and

F(16%), respectively) and the geometric mean are averaged, expressed below:

(84%)

2 2 (16%)F GM GSD

GM F+ =

⋅ ⋅ (2.1)

Oftentimes, 95% confidence intervals are given. In that case, the GSD can be determined as

follows. Given:

(2.2) 1.96 (97.5%)GM GSD F⋅ =

1.96 (2.5%)GM FGSD

= (2.3)

Rearrangement of the above equations provides the GSD from knowledge of the median

and confidence interval, expressed as:

1.96 1.961 (97.5%)2 (2.5%)

F GGSDGM F

M⎡ ⎤⎛ ⎞⎛ ⎞= +⎢ ⎥⎜ ⎟⎜ ⎟⎝ ⎠⎢ ⎥⎝ ⎠⎣ ⎦

(2.4)

3.2.1 Cancer Incidence Risk

The nominal organ risk coefficients utilized in ICRP 103 were taken from BEIR VII

(2006). BEIR VII is a compilation of several studies (including the Life Span Study), and

represents the most up to date, detailed analysis of the biological effects of radiation.

Instead of quantifying risk by cancer mortality, ICRP 103 uses a measure of incidence

rate, defined by BEIR VII (2006) as “new cases of cancer occurring among previously

Page: 41 unaffected individuals.” The ICRP 103 report uses BEIR VII’s measure of the risk from the

incidence, or the “probability that an individual develops cancer over a specified interval of

time, given that the individual is alive and disease free at the start of the time period

(National Research Council, 2006).”

To accurately measure the increase in cancer risk from radiation exposure, one must

account for the base rate of a particular cancer. If we allow λE(t) and λU(t) to describe the

incidence rates of the exposed (E) and unexposed (U) groups, respectively, and if disease

occurrence is unrelated to exposure, it is expected that λE(t)=λU(t). A lack of equality

indicates an association between cancer occurrence and radiation exposure.

BEIR VII uses two measures of this discrepancy between incidence rates, excess

absolute risk (EAR) and excess relative risk (ERR). The first measure, EAR, is defined as the

difference between the incidence rates of the exposed and unexposed groups, or:

( ) ( ) ( )E UEAR t t tλ λ= − (2.5)

Excess absolute risk describes the additive increase in incidence rate associated with

exposure. For example, if the EAR is constant (EAR=a), then the effect of exposure is to

increase the incidence rate by the constant amount, a, for all time periods.

The second common measure of discrepancy is the relative risk (RR), defined as the

quotient of incidence rates between exposed and unexposed groups, or:

( )( )( )

E

U

tRR tt

λλ

= (2.6)

Page: 42 The relative risk describes the multiplicative increase in incidence rate associated with

exposure. When RR is constant (RR=r) the effect of exposure is to alter incidence rate by a

factor of r.

The ERR is often a more useful quantity than the RR and is defined as the percent

increase of cancer risk from exposed populations, or:

( ) ( ) 1ERR t RR t= − (2.7)

For example, if the relative risk from a particular cancer was 1.3, the ERR(t) would indicate a

30% increase in risk from exposure.

To model risk from radiation exposure, BEIR VII uses lifetime attributable risk (LAR),

which is an approximation of the risk of exposure‐induced death (REID), the measure used

by UNSCEAR (2000) to estimate the probability that an individual will die from (or develop)

cancer associated with the exposure. The LAR for a person receiving a dose D at age e is

expressed as:

100 ( )( , ) ( , , )

( )a

S aLAR D e M D e aS e

=∑ (2.8)

where:

• M(D, e, a) is the EAR or ERR depending on whether the LAR is expressed as absolute

or relative risk;

• a denotes the attained age in years, or e+L;

• L is the risk‐free latent period (L=5 for solid cancers and L=2 for leukemia); and

Page: 43

• ( )( )

S aS e

is the probability of surviving to age a conditional on survival to age e.

Unfortunately, the LAR cannot be observed directly from the LSS data set. Because

the atomic bomb survivors were exposed to high doses, and BEIR VII presents the risk from

low‐dose exposures, the risk is extrapolated using the linear no threshold (LNT) model of

radiation risk (except for leukemia, which uses a linear‐quadratic model). The LNT model

does not account for the effects of dose rate (although the linear‐quadratic model does). It

is known that higher dose rates are more harmful than low dose rates due to the body’s

ability to repair itself over time. It was calculated by BEIR VII that a dose and dose rate

effectiveness factor (DDREF) of 1.5 should be used to account for this discrepancy (see

Annex 10B, BEIR VII for the complete derivation). The ICRP (2007) used this model, but

rounded their DDREF to 2 in an attempt to communicate that the DDREF is a “board

judgment which embodies elements of both subjectivity and probabilistic uncertainty.”

Table 3.1 appears in BEIR VII as a summary of the LAR based on relative and

absolute risk transport.

Page: 44

Table 3.1 Relative and absolute LAR from BEIR VII (National Research Council, 2006)

Males Females Cancer Site LAR based

on Relative Risk

Transport

LAR based on

Absolute risk

Transport

Combined and

Adjusted by DDREF (subjective 95% CI)

LAR based on

Relative Risk

Transport

LAR based on

Absolute risk

Transport

Combined and

Adjusted by DDREF (subjective 95% CI)

Incidence Stomach 25 280 34

(3, 350) 32 330 43

(5, 390) Colon 260 180 160

(66, 360) 160 110 96

(34, 270) Liver 23 150 27

(4, 180) 9 85 12

(1, 130) Lung 250 190 140

(50, 380) 740 370 300

(120, 780) Breast ‐‐ ‐‐ 510

(not used) 460 310

(160, 610) Prostate 190 6 44

(0, 1860) ‐‐ ‐‐

Ovary 66 47 40 (9, 170)

Bladder 160 120 98 (29, 330)

160 100 94 (30, 290)

Other 470 350 290 (120, 680)

490 320 290 (120, 680)

Thyroid 32 No model 21 (5, 90)

160 No model 100 (25, 440)

Leukemia ‐‐ ‐‐ 800* (400, 1590)

‐‐ ‐‐ 1310* (690, 2490)

*No DDREF adjustment was made for leukemia

The absolute and relative LAR were log‐averaged and weighted by EAR and ERR,

respectively, to yield the combined and adjusted (by DDREF) risk values, which reflects the

excess cancer risk across all populations. The BEIR VII committee weighted EAR:ERR as

0.3:0.7 for all organs except for thyroid and lung, which used 0.0:1.0 and 0.7:0.3,

respectively. The ICRP 103 committee reasoned that “only for lung, breast, and thyroid was

it considered that there was sufficient information to justify a representative [EAR:ERR ratio]

Page: 45 other than 0.5:0.5.” The ICRP used a 1.0:0.0 EAR:ERR ratio for breast and bone marrow, a

0.0:1.0 ratio for thyroid and skin, and a 0.7:0.3 ratio for lung.

By plotting the confidence intervals on log‐probit plots, it was observed that all

averages (except bone) corresponded to a log‐normal distribution. The GSD’s were

obtained from these distributions (Table 3.2) and applied to the ICRP 103 estimates with the

same GSD and a GM of the reported ICRP 103 nominal risk value.

Table 3.2 ICRP 103 nominal risks taken as the GM; GSD estimates obtained from BEIR VII confidence intervals

Organ Distribution Type GM GSD Stomach Log‐Normal 79.1 2.40 Colon Log‐Normal 65.4 1.50 Liver Log‐Normal 30.3 2.20 Lung Log‐Normal 114.2 1.40 Breast Log‐Normal 112.1 1.41 Ovary Log‐Normal 10.6 1.41 Bladder Log‐Normal 43.4 2.35 Thyroid Log‐Normal 32.5 2.89 Bone Marrow* Log‐Normal 41.9 2.35 Bone** Normal 7.0 1.80 Skin Log‐normal 1000 3 Esophagus Log‐normal 15.1 3 Remainder Log‐Normal 143.8 1.85

*Leukemia risk from BEIR VII was used ** Normal mean and standard deviation are reported

The ICRP 103 report points out that “nominal risk estimates for bone and skin are

those used in Publication 60 (1991).” In accordance with ICRP 60, bone risk was taken from

BEIR IV (National Research Council, 1988), reported as 133 ± 36 (bone sarcomas/106 person‐

rad). The uncertainty of the bone risk was assumed to be normally distributed based on

BEIR IV’s presentation of an additive standard error. This assumed standard deviation was

then changed to a percentage of the mean (133 ± 27%) and applied to ICRP 103’s value of

Page: 46 the mean (7 per 10,000), and a normal distribution was assumed with a standard deviation

of 1.8 (i.e., 27% of 7).

Skin distribution estimates proved to be more difficult. The ICRP (2007) references

ICRP 60, which references ICRP 59 (1992), which references a compilation of several studies

on skin cancer from the 1970’s but reports no uncertainty. To fit a distribution by extension,

it was assumed the skin was most likely log‐normally distributed based on all other organ

incidence risks (except bone) being log‐normally distributed. The largest GSD complied for

any organ risk was just under 3, so a conservative estimate of a GM of 1000 and a GSD of 3

was assigned to skin cancer incidence risk.

Esophagus risk was also not reported in BEIR VII. The same method was applied

from above and a GM of 15.1 and a GSD of 3 was applied to the esophagus incidence risk.

3.2.2 Heritable Effects (Gonads)

The three primary disease classes that the ICRP uses to determine the heritable

effects of radiation are Mendelian diseases, chronic diseases and congenital abnormalities.

The risk per unit dose is calculated for each disease class and summed to obtain the total

risk of heritable effects per unit radiation dose.

To calculate the risk per unit dose for a particular disease class, Equation (2.9) is

utilized (ICRP, 2007):

1Risk per unit dose = P MC PCRF

DD⋅ ⋅ ⋅ (2.9)

where:

• P is the baseline frequency of the genetic disease class;

Page: 47

• DD is the doubling dose, or radiation dose required to produce as many mutations

as those that arise spontaneously in one generation;

• MC is the mutation component, or a relative measure of the relationship between

change in mutation rate and increase in disease frequency, or (ΔP/P)/(Δm/m) where

m is the spontaneous mutation rate; and

• PCRF is the potential recoverability correction factor for different classes of

mutation. PRCF allows for differing degrees of recoverability of mutations in live

births, i.e., the fraction of mutations that is compatible with embryonic/fetal

development.

It was decided that an in‐depth analysis of the uncertainties involved in the genetics of

the above variables is beyond the scope of this work. For more information see Appendix

A.6 of ICRP 103 (2007), pages 217‐241. For the purpose of this paper, the uncertainties

reported in ICRP 103 were deemed sufficient. Genetic risk (see Table 3.3) from continuing

exposure to low‐LET, low dose radiation is reported in the 2001 report by the United

Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR). The ICRP uses

the genetic risk per Gy to the second generation in their calculation of gonadal risk (Table

3.3).

Page: 48 Table 3.3 Current estimates of genetic risk from continuing exposure to low‐LET, low dose or

chronic irradiation (UNSCEAR, 2001) with an assumed doubling dose of 1 Gy. Disease Class: Baseline Frequency

(per 10,000 live births):Risk per Gy

(per 10,000 progeny): 1st Generation 2nd Generation Mendelian Autosomal dominant and

X‐linked 165 ~7.5 to ~15 ~13 to ~25

Autosomal Recessive 75 0 0 Multifactorial Chronic 6,500 ~2.5 to ~12 ~2.5 to ~12 Congenital abnormalities 600 ~20 ~24 to ~30

The above estimates apply only to the reproductive population. The estimate of

genetic risk to an entire population will be lower because the “genetic damage sustained by

germ cells of individuals who are beyond the reproductive period, or who are not

procreating for any reason, poses no genetic risk (ICRP, 2007).” Given that the average life

expectancy is about 75 years, and the mean reproductive age is 30 years, the dose received

by a person at 30 years of age should be 40% (30/75) of the total dose (ICRP, 2007).

Table 3.4 Risk coefficients (per 10,000) for the reproductive and the total population obtained up to two generations when the population sustains radiation exposure generation

after generation.

Disease Class Reproductive Population Total Population Range Average Average

Mendelian Diseases 13 to 25 19 8 Chronic Disease 3 to 12 8 3 Congenital Abnormalities

24 to 30 27 11

Total 54 22

The ranges given in Table 3.4 were multiplied by 40%, to account for the differences

in total population and reproductive population, and used as the bounds for uniform

Page: 49 distributions. These distributions were then averaged to yield the combined distribution

(Figure 3.6).

Figure 3.6 The combined distribution from several uniform distributions used in the calculation of heritable risk

Although the distribution appears normal, the beta distribution was the best fit with

a mean of 21.4 and variance of 3.46. The beta distribution was not used in the final

uncertainty calculation, as it is only an approximation of the average of three uniform

distributions, which were utilized instead.

3.2.3 Lethality Fraction (k)

The ICRP 103 Committee states that it used “national cancer statistics” to determine

the lethality fraction of various cancers. Because the exact data set that ICRP used for its

calculation was not available, the United States Cancer Statistics document (National

Page: 50 Program of Cancer Registries (NPCR), 2001) was used in its place. Utilizing the USCS, the

follow data were obtained:

Table 3.5 Lethality fractions and confidence intervals from USCS 2001‐2005

Site Lethality Fraction

LCI UCI 2*LCI % 2*UCI%

Esophagus 0.88 0.88 0.90 100.0% 102.3% Stomach 0.57 0.58 0.58 101.4% 102.4% Colon excluding Rectum 0.42 0.42 0.42 99.6% 100.4% Liver and I.H. Bile Duct 0.89 0.89 0.89 99.8% 100.0% Lung and Bronchus 0.78 0.78 0.78 100.1% 100.2% Bones and Joints 0.44 0.44 0.50 100.0% 112.5% Male and Female Breast 0.21 0.21 0.21 100.1% 100.4% Ovary 0.69 0.69 0.69 99.7% 100.3% Testis 0.06 0.04 0.05 67.9% 98.2% Urinary Bladder 0.20 0.20 0.20 98.2% 99.5% Thyroid 0.06 0.06 0.06 101.1% 100.0% Leukemias 0.60 0.60 0.60 100.8% 100.5%

The conservative assumption was made that the confidence intervals represented

only one standard deviation. Therefore, twice the distance from the mean (reported

lethality fraction) was used to obtain the upper and lower CI columns. The lower and upper

confidence interval percentages were applied to the lethality fractions from ICRP 103 to fit

uniform distributions to the data set, with occasional numeric manipulation to account for

inconsistencies in the data (Table 3.6).

Page: 51

Table 3.6 Uniform distributions fit to the ICRP 103 reported lethality fraction using the confidence interval percentages from Table 3.5

Site Lethality Fraction Lower Bound Upper Bound

Esophagus 0.93 0.92 0.95 Stomach 0.83 0.82 0.86 Colon 0.48 0.47 0.49 Liver 0.95 0.94 0.96 Lung 0.89 0.88 0.89 Bone 0.45 0.44 0.47 Breast 0.29 0.28 0.30 Ovary 0.57 0.56 0.58 Bladder 0.29 0.28 0.30 Thyroid 0.07 0.06 0.08 Bone Marrow 0.67 0.66 0.68 Gonads 0.80 0.56 0.81

For the statistics that were not available in the USCS archives, a much broader

uncertainty measure was used; triangular distributions were fit with bounds of 0 and 1, and

a most likely value equal to the ICRP 103 reported value (Table 3.7).

Table 3.7 Triangular distribution parameters defined for two sites

Site Lethality Fraction (most likely value)

Lower Bound Upper Bound

Skin 0.002 0 1 Remainder 0.49 0 1

3.2.4 Minimum Weight for Quality of Life (qmin)

Because qmin is a purely subjective quantity, measuring the pain and suffering

brought on by a particular cancer, not much information can be concluded about its

parametric uncertainty. The ICRP selected only three possible values for qmin: 0, 0.1, and

0.2. It appears most reasonable to select triangular distributions with a most likely value

Page: 52 taken as the ICRP 103 reported value (Table 3.8), and lower bound of 0. The upper bound

was set at 0.3 in to give qmin=0.2 a non‐zero likelihood.

Table 3.8 Triangular distribution parameters defined for qmin

Site qmin (likeliest value)

Lower Bound

Upper Bound

Esophagus 0.1 0 0.3 Stomach 0.1 0 0.3 Colon 0.1 0 0.3 Liver 0.1 0 0.3 Lung 0.1 0 0.3 Bone 0.1 0 0.3 Skin 0.0 0 0.3 Breast 0.1 0 0.3 Ovary 0.1 0 0.3 Bladder 0.1 0 0.3 Thyroid 0.2 0 0.3 Bone Marrow 0.1 0 0.3 Gonads 0.1 0 0.3 Remainder 0.1 0 0.3

3.2.5 Relative Length of Life Lost

To determine the relative uncertainty related to the length of life lost due to the

development of a cancer, it was assumed that all death occurs at the average age of death

in the US, 77.5 years of age. Therefore, if death from cancer occurs at age 77.5 or later, 0

years of life is lost as a result of the cancer. Conversely, if death from cancer occurs at age

0, 77.5 years of life is lost. Given this assumption, cancer mortality data by age, presented

in ICRP 103 Tables A.4.10‐A4.17, were used to determine the number of years of life lost

due to a given cancer. Thyroid data were not available in ICRP 103; the USCS 2001‐2005

data were used as a surrogate. These years of life lost were normalized to sum to unity,

yielding the probability of losing a certain number of years of life given that cancer has

already developed. The probabilities were then multiplied by the years of life lost for that

Page: 53 particular probability and plotted versus years of life lost to determine the distribution

shape (see Figure 3.7 as an example).

0.000.200.400.600.801.001.201.401.601.80

0 10 20 30 40 50 60 70 80 90

Years Lost*P

roba

bility (years)

Esophagus Life Lost

Years Lost (years)

Figure 3.7 Number of years of life lost due to cancer in the esophagus

These data were graphed on a log‐probit plot and it was concluded that they were

log‐normally distributed. From this analysis, the data in Table 3.9 were obtained.

Page: 54

Table 3.9 Log‐normal distribution parameters for years of life lost calculation

Site Years of Life lost GSD

Esophagus 13.05 1.71 Stomach 13.20 1.82 Colon 14.55 1.77 Liver 13.20 1.81 Lung 12.00 1.69 Breast 19.35 1.66 Ovary 16.80 1.72 Bladder 10.65 1.76 Thyroid* 19.35 1.76 Bone Marrow 24.45 2.31 Gonads** 19.80 1.72 Average 15.00 1.86

*Thyroid data from USCS 2001‐2005 **Ovary GSD was used because gonads and ovaries are eventually combined in the detriment calculation

The ICRP points out that data were not available for the calculation of years of life

lost for bone and skin. The ICRP (2007) uses the average life lost for both organs as a result.

For this reason, a uniform distribution was fit with bounds of 0 and 30 years to reflect this

assumption (Table 3.10). It is unclear where the “remainder” life lost calculation originated.

However, since the ICRP reports a value of 15.45, it appears that the number is more certain

than the bone and skin life lost values. For this reason, a triangular distribution was fit for

the remainder category with bounds of 0 and 30 years.

Page: 55

Table 3.10 Non‐log‐normal distributions for years of life lost parameter

Site Distribution Likeliest Lower Bound Upper Bound Remainder Triangular 15.45 0 30

Bone Uniform ‐‐ 0 30

Skin Uniform ‐‐ 0 30

A summary of all input parameters used in the uncertainty analysis can be found in

Appendix B.

Page: 56 4 Chapter 4 –Results

Crystal Ball, along with the input parameters in Chapter 3 were used to perform the

ICRP 103 relative detriment calculation. The results of the uncertainty analysis follow.

4.1 Uncertainty Analysis Output ‐ Parameters

The following table is a summary of the deterministic relative uncertainty calculation

by ICRP 103 and the uncertainty analysis described in Chapter 3.

Table 4.1 Log‐normal distribution parameters for the results of the uncertainty analysis

Organ Distribution Mean* Standard Deviation** 2.50% 97.50% Esophagus Log‐normal 0.008 4.38 0.000 0.145 Stomach Log‐normal 0.045 3.37 0.004 0.487 Colon Log‐normal 0.032 3.07 0.004 0.288 Liver Log‐Normal 0.017 3.58 0.001 0.207 Lung Log‐normal 0.06 2.86 0.008 0.471 Bone Log‐normal 0.003 2.83 0.000 0.023 Skin*** ‐‐ 0.349 0.272 0.000 0.893 Breast Log‐normal 0.053 2.83 0.007 0.407 Ovary Log‐normal 0.006 3.08 0.001 0.054 Bladder Log‐normal 0.011 3.7 0.001 0.143 Thyroid Log‐normal 0.007 3.89 0.000 0.100

Bone Marrow Log‐normal 0.04 4.25 0.002 0.682 Gonads Log‐normal 0.017 2.8 0.002 0.128

Remainder Log‐normal 0.062 3.35 0.006 0.663 * For log‐normal distributions, GM is displayed, otherwise arithmetic mean is displayed ** For log‐normal distributions, GSD is displayed, otherwise standard deviation is displayed *** No fit was available for skin data; mean and standard deviation reflect only the spread of data

4.2 Uncertainty Analysis Output ‐ Figures

Appendix C displays uncertainty plots of the relative detriment generated by Crystal

Ball. Each figure (except skin) was fit to a log‐normal distribution with parameters given in

Table 4.1.

Page: 57

Figure 4.1 Crystal Ball graphical output for the results of the uncertainty analysis on the bone relative detriment

The bone relative detriment uncertainty (Figure 4.1) was fit to a log‐normal

distribution with a GM of 0.003 and a GSD of 2.83. The above figure is similar in appearance

and fit to all other (except skin) relative detriment uncertainty plots (see Appendix C).

Page: 58

Figure 4.2 Crystal Ball graphical output for the results of the uncertainty analysis on the skin relative detriment

The skin relative detriment uncertainty (Figure 4.2) could not be successfully fit to any

of the continuous distributions† available in Crystal Ball. The statistical mean and standard

deviation were determined as 0.349 and 0.272, respectfully. These values are suspect due to

the predictability of all other distributions, and the significantly lower deterministic relative

uncertainty of 0.007. See Section 5.1 for more details.

The results presented in Chapter 4 are discussed in Chapter 5 and compared with the

tissue weighting factors in ICRP 26, 60, and 103.

† Available continuous distributions in Crystal Ball: beta, betaPERT, exponential, gamma, logistic, lognormal, max extreme, normal, Pareto, student’s t, triangular, uniform, Weibull

Page: 59 5 Chapter 5 – Discussion

Although it is enlightening to understand the origin of the relative organ detriment

calculation, this quantity is not used for radiation protection purposes; tissue weighting

factors are, however. To transfer from relative detriment to tissue weighting factors, a

significant amount of subjective manipulation is involved. Historically, four, fairly arbitrary

values are chosen and each relative detriment is grouped into these categories. The relative

detriments aren’t necessarily assigned the closest weighting factor, they are decided based

on what is necessary to sum to one, as long as the weighting factor is within “about a factor

of two,” of the relative detriment. This seems reasonable in that the uncertainties (GSD)

determined herein are greater than 2 for each of the 14 organs analyzed.

5.1 Skin

The results of the uncertainty analysis give a skin relative detriment distribution mean

as 0.35 with a standard deviation of 0.27. No distribution fit the shape of the data, which is

suspect, especially when all other organ relative detriments fit well into log‐normal

distributions.

The inputs are responsible for the behavior of the output. The ICRP (2007) reported

an incidence risk of 1000 Sv‐1 (per 10,000) for skin cancers. No uncertainty was located for

these data; a log‐normal distribution was assumed, based on the prevalence of the

distribution for other cancer risks. A conservative estimate for the GSD of 3 was ascribed

due to 3 being larger than all other GSDs. These two assumptions left a relatively large

distribution (Figure 5.1).

Page: 60

Figure 5.1 Input log‐normal distribution for skin incidence risk with GM of 1000 and GSD of 3

In an uncertainty analysis, it may be acceptable if there is significant uncertainty in

one parameter, as long as it is not the most sensitive parameter of the model. The risk of

incidence for skin cancer (Figure 5.1), however, is a very sensitive parameter, spans two

orders of magnitudes, and is considerably larger than incidence risks from other cancers.

Uncertainties for the skin lethality fraction were difficult to determine. Because the

lethality fraction is bounded by 0 and 1, and a likely value was reported, 0.002, a triangular

distribution (Figure 5.2) was fit for the lethality fraction.

Page: 61

Figure 5.2 Input triangular distribution for skin lethality fraction with bounds of 0 and 1 and a most likely value of 0.002

All other lethality fraction uncertainties were input as uniform distributions with

bounds relatively close to the expected value. In this case, the triangular distribution

communicates much more uncertainty through to the relative detriment estimate.

For years of life lost, not even a deterministic value was available for ICRP 103 to

display. The ICRP 103 Committee admitted that there was insufficient data to report

anything other than the average years of life lost for this parameter. Due to this lack of

data, a uniform distribution was assumed with bounds of 0 and 30 years (Figure 5.3).

Page: 62

Figure 5.3 Input uniform distribution for skin years of life lost with bounds of 0 and 30

5.2 Normalization

One of the most interesting aspects of tissue weighting factors is their necessity to

sum to unity, and therefore their dependence on one another. Before the relative

detriments from the uncertainty analysis could be normalized, the results from the skin

needed to be manipulate to preserve the integrity of the data. The results show detriment

to the skin as 0.35, whereas the largest detriment to any other organ is for the stomach

(0.047), nearly an order of magnitude smaller than the detriment calculated for the skin. If

the relative detriments were normalized without addressing this issue, the skin detriment

would dominate the normalization, making all other organs appear less sensitive, and the

skin appear even more sensitive.

One can observe that the skin and bone have about the same deterministic relative

detriments, 0.007 and 0.009, respectively (Table 2.13). Skin and bone were also assigned

Page: 63 the same weighting factor (0.01) in both ICRP 60 and 103, suggesting that they have

relatively similar sensitivities to radiation. The GM for bone from the uncertainty analysis

was 0.003; to follow the trend of the detriments, skin was assigned an unnormalized relative

detriment of 0.002. This prevents skin from dominating the normalization (Table 5.1).

Table 5.1 The normalization of the geometric means from the uncertainty analysis

Organ GM of Relative Detriment Normalized GM

Skin 0.002 0.006 Bone 0.003 0.008 Ovary 0.006 0.017 Thyroid 0.007 0.019 Esophagus 0.008 0.022 Bladder 0.011 0.030 Liver 0.017 0.047 Gonads 0.017 0.047 Colon 0.032 0.088 Bone Marrow 0.04 0.110 Stomach 0.045 0.124 Breast 0.053 0.146 Lung 0.06 0.165 Remainder 0.062 0.171 Sum 0.363 1.000

5.3 ICRP 103 Tissue Weighting Factor Comparison

A comparison of the tissue weighting factors utilized in ICRP 103 and the GM and GSD

results from the uncertainty analysis (Table 5.2) are provided.

Page: 64 Table 5.2 A comparison of the ICRP 103 tissue weighting factors and the uncertainty analysis

Organ ICRP 103 wT

Normalized GM

(Uncertainty Analysis)

GSD (Uncertainty Analysis)

wT Within 1 GSD of GM?

Esophagus 0.04 0.022 4.38 TRUE Stomach 0.12 0.124 3.73 TRUE Colon 0.12 0.088 3.07 TRUE Liver 0.04 0.047 3.58 TRUE Lung 0.12 0.165 2.86 TRUE Bone 0.01 0.008 2.83 TRUE Skin 0.01 ‐‐ ‐‐ Breast 0.12 0.146 2.83 TRUE Bladder 0.04 0.030 3.70 TRUE Thyroid 0.04 0.019 3.89 TRUE Bone Marrow 0.12 0.110 4.25 TRUE Remainder 0.12 0.171 3.35 TRUE Gonads* 0.08 0.063 2.80 TRUE Salivary Glands 0.01 ‐‐ ‐‐ ‐‐ Brain 0.01 ‐‐ ‐‐ ‐‐

*Gonads includes risk to ovaries

It is useful to observe how many geometric standard deviations the weighting

factors lie away from the geometric mean. As observed above, all tissue weighting factors

from ICRP 103 are within one GSD of the normalized median.

The weighting factors for the salivary glands and the brain could not be compared

with the uncertainty analysis because the weighting factors were chosen (ICRP, 2007) based

on the subjective belief that there was slightly more risk to those organs than the ones in

the “remainder” category.

As explained earlier, there was not enough data available to accurately quantify the

uncertainty in the relative detriment to the skin; hence, no comparison could be made to

the tissue weighting factor presented in ICRP 103.

Page: 65 5.4 ICRP 60 Tissue Weighting Factor Comparison

One fundamental question this paper sought to answer was, “Given their inherent

uncertainties, have the tissue weighting factors changed in the last 30 years?” To answer

this question involves comparing the results of the uncertainty analysis with the tissue

weighting factors of ICRP 60 and 26.

Table 5.3, below, compares tissue weighting factors derived in ICRP 60 and the

normalized GM and GSD from the ICRP 103 uncertainty analysis.

Table 5.3 A comparison of the ICRP 60 tissue weighting factors and the uncertainty analysis

Organ ICRP 60 wT

Normalized GM





Esophagus 0.05 0.022 4.38 TRUE Stomach 0.12 0.124 3.73 TRUE Colon 0.12 0.088 3.07 TRUE Liver 0.05 0.047 3.58 TRUE Lung 0.12 0.165 2.86 TRUE Bone 0.01 0.008 2.83 TRUE Skin 0.01 ‐‐ ‐‐ Breast 0.05 0.146 2.83 FALSE TRUE Bladder 0.05 0.030 3.70 TRUE Thyroid 0.05 0.019 3.89 TRUE Bone Marrow 0.12 0.110 4.25 TRUE Remainder 0.05 0.171 3.35 FALSE TRUE Gonads* 0.20 0.063 2.80 FALSE TRUE *Gonads reflects gonads and ovaries

All organs are still within two GSDs of the GM. The ICRP 60 weighting factor for

gonads is farther than one GSD from the GM, even though the ICRP 103 weighting factor

was relatively close to the GM. This is reasonable since the ICRP changed the way they

calculated the heritable risk to gonads from the risk to all generations in ICRP 60, to the risk

to only the first two generations in 103.

Page: 66 It is also not surprising that the remainder category is beyond 1 GSD from the

normalized GM. The ICRP 60 remainder category includes fewer tissues than the ICRP 103’s

remainder category. To maintain approximately the same level of sensitivity, the remainder

category had to be given more weight in ICRP 103 to include more organs.

Although skin uncertainty data was not available, ICRP 103 did not update the

method of calculating skin cancer risk. The ICRP 59 methodology was used in ICRP 103 as

well as in ICRP 60; hence there was no change from ICRP 60 to 103.

Brain and salivary were not singled out in ICRP 60. They were expressed as part of

the remainder category. No comparison could be made between the salivary glands and

brain weighting factors due to the purely subjective nature of those particular weighting

factors in ICRP 103.

5.5 ICRP 26 Tissue Weighting Factor Comparison

Table 5.4, below, compares tissue weighting factors derived in ICRP 26 and the GM

and GSD from the ICRP 103 uncertainty analysis.

Table 5.4 A comparison of the ICRP 26 tissue weighting factors and the uncertainty analysis

Organ ICRP 26 wT

Normalized GM





Lung 0.12 0.165 2.86 TRUE Bone 0.03 0.008 2.83 FALSE TRUE Breast 0.15 0.146 2.83 TRUE Thyroid 0.03 0.019 3.89 TRUE Bone Marrow 0.12 0.11 4.25 TRUE Remainder 0.30 0.171 3.35 TRUE Gonads* 0.25 0.063 2.80 FALSE TRUE Total: 1.00 0.626 *Gonads reflects gonads and ovaries

Page: 67 As expected, the gonads weighting factor did lie outside of one GSD of the GM, due

to the change in the heritable risk calculation in ICRP 103. It is however, surprising that the

bone surface weighting factor changed significantly (by a factor of 3) from ICRP 26 to 60.

This could perhaps be a reflection of the progress made in internal dosimetry methods for

alpha emitters since 1977. Specifically, BEIR IV (1988) was not available to the ICRP 26

Committee, but was utilized by the 60 and 103 Committees.

It is interesting that the ICRP 26 breast weighting factor is within 1 GSD of the ICRP

103 normalized GM, while the ICRP 60 breast weighting factor lies outside this range. This is

due to the decrease in lethality over the years, but the approximately constant incidence

rate.

Because ICRP calculates risk to only six organs plus a remainder category, the

normalized GM from the ICRP 103 uncertainty analysis can be renormalized to account for

the seven sites defined ICRP 26.

Table 5.5 A comparison of the renormalized ICRP 26 tissue weighting factors and the uncertainty analysis

Organ ICRP 26 wT

Renormalized GM




Lung 0.12 0.242 2.86 TRUE Bone 0.03 0.012 2.83 TRUE Breast 0.15 0.214 2.83 TRUE Thyroid 0.03 0.027 3.89 TRUE Bone Marrow 0.12 0.161 4.25 TRUE Remainder 0.30 0.251 3.35 TRUE Gonads* 0.25 0.093 2.80 TRUE Total: 1.00 1.000

*Gonads reflects gonads and ovaries

Page: 68 Once the renormalization is performed (Table 5.5), all statistically significant

differences between ICRP 103 and 26 weighting factors disappear.

5.6 Tissue Weighting Factor Comparison Summary

As concluded from the previous sections, the tissue weighting factors have not

changed beyond two geometric standard deviations of the ICRP 103 uncertainties. There is,

however, noticeable change between the publications (Figure 5.4), as discussed below.

Figure 5.4 Box‐plot of the ICRP 103 uncertainty analysis data, with the deterministic tissue weighting factors from the various documents highlighted. The box represents the middle

two quartiles of the uncertainty analysis data.

Due to the publication of BEIR IV (National Research Council, 1988) the ICRP 26

weighting factor for bone (0.03) is a factor of three different than the ICRP 60 and 103

weighting factors, and appears outside of the inner two quartiles. Because of the different

method of calculation, the ICRP 26 and 60 gonads weighting factor also appears outside of

the inner two quartiles. The remainder category is the least consistent of any site. This is

Page: 69 not surprising due to the different number of organs represented in the remainder category

from each document.

Page: 70 6 Chapter 6 – Conclusion

In the health physics community, it is commonly thought that tissue weighting factors

are intended to be exact measures of radiation risk. This is not the case, as can be

concluded from the results of the previous chapters. The proper way to interpret tissue

weighting factors is that they are an indication of organ risk, relative to other organs. For

example, if organ A had a tissue weighting factor of 0.20 and organ B had a weighting factor

of 0.05, organ A is not four times as radiosensitive as organ B. The proper interpretation

would be to say that organ A is significantly more radiosensitive than organ B, but by an

uncertain amount.

Quantification of radiation risk has come a long way since the first report published

by the IXRPC in 1928, proposing dose limitations to medical workers exposed to radiation.

Since then, the ICRP has published several incredibly influential documents, including ICRP 2

(1960), 26 (1977), 60 (1991), and 103 (2007), which have guided, and continue to guide

radiation protection methodology. It is, however, important that the recommendations be

fully understood before implementing, to avoid using a quantity in a way which was not

intended. The intent of this work, therefore was:

• to understand the meaning of the tissue weighting factor; and

• given their inherent uncertainties, determine how the weighting factors have

changed over the past 30 years.

The history of the tissue weighting factors was explored through the years, tracking

changes to the weighting factors based on the discovery of new information about radiation

risk. The ICRP 103 report is certainly not the last publication by the ICRP to recommend

Page: 71 adjustments to the weighting factors. When new data is obtained suggesting a need to

update the weighting factors, the ICRP will release an update to ICRP 103. Judging by the

relative frequency of the previous documents, this update won’t be at least until 2020. Until

then, the ICRP 103 weighting factors are the most up to date calculation of organ risk

available to the international community.

The ICRP 26 tissue weighting factors were based only on the risk of fatal cancer to six

organs plus a remainder category (five organs). The ICRP 60 Committee used risk of fatal

cancer in its calculation, but also incorporated the lethality (to determine risk from non‐fatal

cancers), genetic risk (only to gonads), and years of life lost from a particular cancer for

twelve organs plus a remainder (ten organs). The ICRP 103 report uses a similar calculation,

but uses cancer incidence instead of mortality, and a factor to account for the pain and

suffering from the development and treatment of a particular cancer for fourteen organs

plus a remainder (fourteen organs).

The ICRP 103 tissue weighting factors are a complex set of numbers that say a lot more

than one might think at first glance. They not only attempt to measure the likelihood of

cancer in a particular organ, but also the lethality, pain and suffering, and the years of life

lost. Each weighting factor also is not necessarily representative of relative detriment. Four

fairly arbitrary factors are selected and organs are assigned weighting factors based the

necessity to sum to unity, which implies that the weighting factors are not independent of

one another. Because the weighting factors measure risk relative to other organs, one

organ’s radiosensitivy influences all other organ’s weighting factors. For example, if organ A

Page: 72 is particularly radiosensitive, it will make organ B appear less radiosensitive relative to organ

A, even though organ B’s absolute radiosensitivity is not dependant on other organs.

In light of the results from the uncertainty analysis above, it is suggested that 10.CFR.20

be updated to reflect a mixture of the ICRP 26 and 103 methodologies. Specifically, the

tissue weighting factors could be calculated using only cancer mortality data (as in ICRP 26)

for the fourteen organs (plus remainder) defined in ICRP 103. This method would

significantly simplify the definition of the tissue weighting factors without changing them

beyond the bounds of uncertainties introduced by the additional complexities of ICRP 103.

It is not surprising that there is dialog regarding the usefulness of updating the radiation

weighting factors. According to this work, other than including more organs, there has been

no appreciable change of the tissue weighting factors in the last 30 years; however, given

the right conditions, there could be a significant difference in the recorded effective dose.

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Page: 77

APPENDICIES

Page: 78 Appendix A – Steps in the development of the tissue weighting system, taken from (ICRP,

2007)

ICRP 103 listed a very detailed procedure that was heavily utilized in this work. It is

presented in ICRP 103 (2007) as Box A.1, page 191.

The development of the tissue weighting system was based upon relative radiation

detriment primarily for cancer. The sequential steps used were as follows:

• Determine lifetime cancer incidence risk estimates for radiation‐associated cancers:

for 14 organs or tissues, male and female lifetime excess cancer risk were estimated

using both the excess relative risk (ERR) and excess absolute risk (EAR) models and

were then averaged across sexes.

• Apply a dose and dose‐rate effectiveness factor (DDREF): the lifetime risk estimates

were adjusted downward by a factor of two to account for a DDREF (except for

leukemia, where the linear‐quadratic model for risk already accounts for the

DDREF).

• Transfer risk estimates across populations: To estimate radiation risk for each

cancer site, a weighting of ERR and EAR lifetime risk estimates was established that

provided a reasonable basis for generalizing across populations with different

baseline risks (ERR:EAR weights of 0:100% were assigned for breast and bone

marrow, 100:0% for thyroid and skin, 30:70% for lunch and 50:50% for all others).

• Nominal risk coefficients: these weighted risk estimates, when applied to and

averaged across seven western and Asian populations, provided the nominal risk

coefficients given in tables A.4.1 and A.4.2 [in ICRP 103].

Page: 79

• Adjustment for lethality: The lifetime risks for respective cancer sites, which were

based on excess incident cancers, were converted to fatal cancer risks by

multiplying by their lethality fractions, as derived from representative national

cancer survival data.

• Adjustment for quality of life: A further adjustment was applied to account for the

morbidity and suffering associated with non‐fatal cancers.

• Adjustment for years of life lost: since the age distributions of types of cancers

differ, the average ages of several types of cancer were estimated from national

cancer data and converted to average years of life lost when a cancer occurs. An

adjustment for years of life lost was then applied to the result of the previous steps.

• Radiation detriment: The results of the calculations above yielded and estimate of

radiation detriment associated with each type of cancer. These, when normalized

to sum to unity, constitute the relative radiation detriments in table A.4.1 [in ICRP

103]

• Tissue weight factors: since the detailed relative radiation determents in Table A.4.1

[in ICRP 103] are imprecise because of uncertainties associated with their

estimation, they were grouped into four categories broadly reflecting the relative

detriments. A group of residual ‘remainder tissues’ was also added to account for

radiation risks to organs or tissues for which detailed radiation risk calculations were

uninformative.

Page: 80 Appendix B – A summary of all input parameters in the uncertainty analysis

Table B.1 Nominal risk input parameters used in the uncertainty analysis

Parameter Distribution Type Mean* Standard Deviation**

Nominal Risk

Esophagus Log‐Normal 15.1 3

Stomach Log‐Normal 79.1 2.4

Colon Log‐Normal 65.4 1.50

Liver Log‐Normal 30.3 2.20

Lung Log‐Normal 114.2 1.40

Bone Normal 7 1.8

Skin Log‐Normal 1000 3

Breast Log‐Normal 112.1 1.41

Ovary Log‐Normal 10.6 1.41

Bladder Log‐Normal 43.4 2.35

Thyroid Log‐Normal 32.5 2.89

Bone Marrow Log‐Normal 41.9 2.35

Gonads Beta 21.4 1.86

Remainder Log‐Normal 143.8 1.85

* For log‐normal distributions, GM is displayed; for normal distributions, regular mean; for triangular distributions, most likely value

** For log‐normal distributions, GSD is displayed, for normal distributions, regular SD, for triangular and uniform distributions, bounds

Page: 81

Table B.2 Lethality fraction input parameters used in the uncertainty analysis


Lethality Fraction

Esophagus Uniform ‐‐ 0.92, 0.95

Stomach Uniform ‐‐ 0.82, 0.86

Colon Uniform ‐‐ 0.47, 0.49

Liver Uniform ‐‐ 0.94, 0.96

Lung Uniform ‐‐ 0.88, 0.89

Bone Uniform ‐‐ 0.44, 0.47

Skin Triangular 0.002 0, 1

Breast Uniform ‐‐ 0.28, 0.30

Ovary Uniform ‐‐ 0.56, 0.58

Bladder Uniform ‐‐ 0.28, 0.30

Thyroid Uniform ‐‐ 0.06, 0.08

Bone Marrow Uniform ‐‐ 0.66, 0.68

Gonads Uniform ‐‐ 0.56, 0.81

Remainder Triangular 0.49 0, 1 * For log‐normal distributions, GM is displayed; for normal distributions, regular mean; for triangular distributions, most likely value


Page: 82

Table B.3 Minimum lethality weight input parameters used in the uncertainty analysis

Parameter Distribution Type Mean* Standard Deviation** Minimum Lethality Weight (qmin)

Esophagus Triangular 0.1 0, 0.3

Stomach Triangular 0.1 0, 0.3

Colon Triangular 0.1 0, 0.3

Liver Triangular 0.1 0, 0.3

Lung Triangular 0.1 0, 0.3

Bone Triangular 0.1 0, 0.3

Skin Triangular 0.0 0, 0.3

Breast Triangular 0.1 0, 0.3

Ovary Triangular 0.1 0, 0.3

Bladder Triangular 0.1 0, 0.3

Thyroid Triangular 0.2 0, 0.3

Bone Marrow Triangular 0.1 0, 0.3

Gonads Triangular 0.1 0, 0.3

Remainder Triangular 0.1 0, 0.3



Page: 83

Table B.4 Relative length of life lost input parameters used in the uncertainty analysis


Relative length of life lost

Esophagus Log‐Normal 13.05 1.71

Stomach Log‐Normal 13.20 1.82

Colon Log‐Normal 14.55 1.77

Liver Log‐Normal 13.20 1.81

Lung Log‐Normal 12.00 1.69

Bone Uniform ‐‐ 0, 30

Skin Uniform ‐‐ 0, 30

Breast Log‐Normal 19.35 1.66

Ovary Log‐Normal 16.80 1.72

Bladder Log‐Normal 10.65 1.76

Thyroid Log‐Normal 19.35 1.76

Bone Marrow Log‐Normal 24.45 2.31

Gonads Log‐Normal 19.80 1.72

Remainder Triangular 15.45 0, 30



Page: 84 Appendix C – Relative detriment plots generated by Crystal Ball

Figure C.1 Crystal Ball graphical output for the results of the uncertainty analysis on the esophagus relative detriment

Figure C. 2 Crystal Ball graphical output for the results of the uncertainty analysis on the stomach relative detriment

Page: 85

Figure C.3 Crystal Ball graphical output for the results of the uncertainty analysis on the colon relative detriment

Figure C.4 Crystal Ball graphical output for the results of the uncertainty analysis on the liver relative detriment

Page: 86

Figure C.5 Crystal Ball graphical output for the results of the uncertainty analysis on the lung relative detriment

Figure C.6 Crystal Ball graphical output for the results of the uncertainty analysis on the bone relative detriment

Page: 87

Figure C.7 Crystal Ball graphical output for the results of the uncertainty analysis on the skin relative detriment

Figure C.8 Crystal Ball graphical output for the results of the uncertainty analysis on the breast relative detriment

Page: 88

Figure C.9 Crystal Ball graphical output for the results of the uncertainty analysis on the ovary relative detriment

Figure C.10 Crystal Ball graphical output for the results of the uncertainty analysis on the bladder relative detriment

Page: 89

Figure C.11 Crystal Ball graphical output for the results of the uncertainty analysis on the thyroid relative detriment

Figure C.12 Crystal Ball graphical output for the results of the uncertainty analysis on the bone marrow relative detriment

Page: 90

Figure C.13 Crystal Ball graphical output for the results of the uncertainty analysis on the gonads relative detriment

Figure C.14 Crystal Ball graphical output for the results of the uncertainty analysis on the remainder relative detriment

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