ORAU TEAM

Dose Reconstruction

Project for NIOSH

Oak Ridge Associated Universities I Dade Moeller I MJW Technical Services

Page 1 of 73

DOE Review Release 07/23/2014

Guiding Reconstruction of Intakes of 

Thorium Resulting from Nuclear Weapons 

Programs

ORAUT-OTIB-0076 Rev. 00

Effective Date: 07/10/2014

Supersedes: None

Subject Expert(s): Thomas R. LaBone

Document Owner 

Approval: Signature on File Approval Date: 06/24/2014

Thomas R. LaBone, Document Owner

Concurrence: Signature on File Concurrence Date: 06/25/2014

John M. Byrne, Objective 1 Manager

Concurrence: Signature on File Concurrence Date: 06/24/2014

Edward F. Maher, Objective 3 Manager

Concurrence: Dianne Poncio Signature on File for Concurrence Date: 06/24/2014

Kate Kimpan, Project Director

Approval: Signature on File Approval Date: 07/10/2014

James W. Neton, Associate Director for Science

New Total Rewrite Revision Page Change

FOR DOCUMENTS MARKED AS A TOTAL REWRITE, REVISION, OR PAGE CHANGE, REPLACE THE PRIOR 

REVISION AND DISCARD / DESTROY ALL COPIES OF THE PRIOR REVISION.
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 2 of 73

PUBLICATION RECORD

EFFECTIVE 

DATE

REVISION 

NUMBER DESCRIPTION

07/10/2014 00 New technical information bulletin to detail how to evaluate chest 

counts, whole-body counts, and various types of urine samples after 

intakes of 232Th. Incorporates formal internal and NIOSH review 

comments. Training required: As determined by the Objective 

Manager. Initiated by Thomas R. LaBone.
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 3 of 73

TABLE OF CONTENTS

SECTION TITLE PAGE

Acronyms and Abbreviations ............................................................................................................... 7

1.0 Introduction .............................................................................................................................. 8

1.1 Purpose........................................................................................................................ 8

1.2 Background .................................................................................................................. 8

2.0 Equilibrium and Shared Kinetics............................................................................................... 9

2.1 Chest and Whole-body Counts..................................................................................... 9

2.2 Urine........................................................................................................................... 10

3.0 Disequilibrium and Shared Kinetics........................................................................................ 11

3.1 Chest and Whole-body Counts................................................................................... 11

3.2 Urine Bioassay ........................................................................................................... 14

4.0 Exact Calculations Assuming Independent Kinetics ............................................................... 15

4.1 Urine Bioassay ........................................................................................................... 19

5.0 Chronic Intakes ...................................................................................................................... 22

5.1 Urine Bioassay ........................................................................................................... 24

6.0 Using IMBA for Efficiency Calculations................................................................................... 25

7.0 Using IMBA for Chest Counts ................................................................................................ 25

7.1 Acute Intakes.............................................................................................................. 25

7.1.1 Triple-Separated Thorium Mixture................................................................ 27

7.1.2 Adjustment of Thorium Intakes..................................................................... 29

7.1.3 Guidance for Acute Intakes .......................................................................... 30

7.2 Chronic Intakes .......................................................................................................... 30

7.2.1 Adjustment of Chronic Thorium Intakes........................................................ 32

7.2.2 Guidance for Chronic Intakes....................................................................... 35

8.0 Using IMBA for Whole-Body Counts ...................................................................................... 36

8.1 Acute Intakes.............................................................................................................. 36

8.1.1 Triple-Separated Thorium Mixture................................................................ 37

8.1.2 Adjustment of Thorium Intakes..................................................................... 39

8.1.3 Guidance for Acute Intakes .......................................................................... 40

8.2 Chronic Intakes .......................................................................................................... 40

8.2.1 Adjustment of Chronic Thorium Intakes........................................................ 42

8.2.2 Guidance for Chronic Intakes....................................................................... 43

9.0 Using IMBA for Total Thorium in Urine................................................................................... 45

9.1 Acute Intakes.............................................................................................................. 45

9.1.1 Triple-Separated Thorium Mixture................................................................ 47

9.1.2 An Additional Approximation ........................................................................ 48

9.1.3 Guidance for Acute Intakes .......................................................................... 49

9.2 Chronic Intakes .......................................................................................................... 50

9.2.1 Guidance for Chronic Intakes....................................................................... 53

10.0 Using IMBA for Thorium-228 in Urine..................................................................................... 54
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 4 of 73

10.1 Acute Intakes.............................................................................................................. 54

10.1.1 Triple-Separated Thorium Mixture................................................................ 56

10.1.2 Guidance for Acute Intakes .......................................................................... 57

10.2 Chronic Intakes .......................................................................................................... 57

10.2.1 Guidance for Chronic Intakes....................................................................... 59

11.0 Attributions and Annotations .................................................................................................. 59

References ........................................................................................................................................ 60

ATTACHMENT A, STANDARD THORIUM MIXTURES .................................................................... 61

ATTACHMENT B, OBTAINING CHRONIC INTAKE IRFs FROM ACUTE INTAKE IRFs................... 67

ATTACHMENT C, SUMMARY OF GUIDANCE FOR ASSESSING THORIUM INTAKES FROM 

BIOASSAY .......................................................................................................... 72

LIST OF TABLES

TABLE TITLE PAGE

A-1 Ratios of 228Th to 232Th activities for secular equilibrium and after one, two, and three 

chemical separations ............................................................................................................. 65

A-2 Relative amounts of 232Th, 228Ra, and 228Th in single separated thorium as a function of 

time since separation ............................................................................................................. 66

LIST OF FIGURES

FIGURE TITLE PAGE

1-1 First eight members of the 232Th decay chain........................................................................... 8

3-1 Activity of 228Th present as a function of time after chemical purification of 1 Bq of 232Th 

in equilibrium with its progeny ................................................................................................ 11

3-2 Radium-228 and 224Ra present as a function of time after chemical purification of 1 Bq 

of 232Th in equilibrium with its progeny.................................................................................... 12

4-1 Chest burdens of 232Th, 228Ac, and 212Pb after a unit acute inhalation intake of pure 

Type S 232Th...........................................................................................................................16

4-2 Chest burdens of 228Ra, 228Ac, and 212Pb after a unit acute inhalation intake of pure 

Type S 228Ra ..........................................................................................................................16

4-3 Chest burdens of 228Th and 212Pb after a unit acute inhalation intake of pure Type S 

228Th.......................................................................................................................................16

4-4 Chest burdens of 224Ra and 212Pb after a unit acute inhalation intake of pure Type S 

224Ra ......................................................................................................................................17

4-5 Thorium-232 and 228Th in a 24-hour incremental urine sample after a unit acute 

inhalation intake of pure Type S 232Th .................................................................................... 20

4-6 Radium-228 and 228Th in a 24-hour incremental urine sample after a unit acute 

inhalation intake of pure Type S 228Ra.................................................................................... 20

4-7 Thorium-228 in a 24-hour incremental urine sample after a unit acute inhalation intake 

of pure Type S 228Th............................................................................................................... 21
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 5 of 73

7-1 Lead-212 chest burden after an acute inhalation intake of Type S thorium having a 

228Th to 232Th ratio of 1:1 ........................................................................................................ 26

7-2 Lead-212 chest burden after an acute inhalation intake of Type S thorium having a 

228Th to 232Th ratio of 0.19:1 ................................................................................................... 28

7-3 Lead-212 chest burden after an acute inhalation intake of Type M thorium having a 

228Th to 232Th ratio of 0.19:1 ................................................................................................... 29

7-4 Lead-212 chest burden after an acute inhalation intake of Type S thorium having a 

228Th to 232Th ratio of 0.19:1 with vertical dashed line at t = 30 days after intake .................... 29

7-5 Lead-212 chest burden after an acute inhalation intake of Type M thorium having a 

228Th to 232Th ratio of 0.19:1 with vertical dashed line at t = 30 days after intake .................... 30

7-6 Lead-212 chest burden after a chronic inhalation intake of Type S thorium having a 

228Th to 232Th ratio of 0.19:1 ................................................................................................... 31

7-7 Lead-212 chest burden after a chronic inhalation intake of Type M thorium having a 

228Th to 232Th ratio of 0.19:1 ................................................................................................... 32

7-8 Lead-212 chest burden during and after a 365-day chronic inhalation intake of Type S 

thorium having a 228Th to 232Th ratio of 0.19:1 ........................................................................ 33

7-9 Lead-212 chest burden during and after a 1,000-day chronic inhalation intake of Type 

S thorium having a 228Th to 232Th ratio of 0.19:1..................................................................... 33

7-10 Lead-212 chest burden during and after a 5,000-day chronic inhalation intake of Type 

S thorium having a 228Th to 232Th ratio of 0.19:1..................................................................... 34

7-11 Lead-212 chest burden during and after a 365-day chronic inhalation intake of Type M 

thorium having a 228Th to 232Th ratio of 0.19:1 ........................................................................ 34

7-12 Lead-212 chest burden during and after a 1,000-day chronic inhalation intake of Type 

M thorium having a 228Th to 232Th ratio of 0.19:1 .................................................................... 35

7-13 Lead-212 chest burden during and after a 5,000-day chronic inhalation intake of Type 

M thorium having a 228Th to 232Th ratio of 0.19:1 .................................................................... 35

8-1 Lead-212 whole-body burden after an acute inhalation intake of Type S thorium having 

a 228Th to 232Th ratio of 1:1 ..................................................................................................... 36

8-2 Lead-212 whole-body burden after an acute inhalation intake of Type S thorium having 

a 228Th to 232Th ratio of 0.19:1 ................................................................................................ 37

8-3 Lead-212 whole-body burden after an acute inhalation intake of Type M thorium having 

a 228Th to 232Th ratio of 0.19:1 ................................................................................................ 39

8-4 Lead-212 whole-body burden after an acute inhalation intake of Type S thorium having 

a 228Th to 232Th ratio of 0.19:1 with vertical dashed line at t = 30 days after intake ................. 39

8-5 Lead-212 whole-body burden after an acute inhalation intake of Type M thorium having 

a 228Th to 232Th ratio of 0.19:1 with vertical dashed line at t = 30 days after intake ................. 40

8-6 Lead-212 whole-body burden after a chronic inhalation intake of Type S thorium having 

a 228Th to 232Th ratio of 0.19:1 ................................................................................................ 41

8-7 Lead-212 whole-body burden after a chronic inhalation intake of Type M thorium 

having a 228Th to 232Th ratio of 0.19:1 ..................................................................................... 42

8-8 Lead-212 whole-body burden during and after a 365-day chronic inhalation intake of 

Type S thorium having a 228Th to 232Th ratio of 0.19:1 ............................................................ 42

8-9 Lead-212 whole-body burden during and after a 1,000-day chronic inhalation intake of 

Type S thorium having a 228Th to 232Th ratio of 0.19:1 ............................................................ 43

8-10 Lead-212 whole-body burden during and after a 5,000-day chronic inhalation intake of 

Type S thorium having a 228Th to 232Th ratio of 0.19:1 ............................................................ 43

8-11 Lead-212 whole-body burden during and after a 365-day chronic inhalation intake of 

Type M thorium having a 228Th to 232Th ratio of 0.19:1............................................................ 44

8-12 Lead-212 whole-body burden during and after a 1,000-day chronic inhalation intake of 

Type M thorium having a 228Th to 232Th ratio of 0.19:1............................................................ 44

8-13 Lead-212 whole-body burden during and after a 5,000-day chronic inhalation intake of 

Type M thorium having a 228Th to 232Th ratio of 0.19:1............................................................ 45
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 6 of 73

9-1 Thorium in 24-hour incremental urine samples after an acute inhalation intake of Type 

S thorium having a 228Th to 232Th ratio of 1:1.......................................................................... 45

9-2 Thorium urine content after an acute inhalation intake of Type S thorium having a 228Th 

to 232Th ratio of 0.19:1 ............................................................................................................ 47

9-3 Thorium urine content after an acute inhalation intake of Type S thorium having a 228Th 

to 232Th ratio of 0.19:1 showing excretion with Approximation A and with 

Approximations A and B......................................................................................................... 50

9-4 Thorium urine content after an acute inhalation intake of Type M thorium having a 228Th 

to 232Th ratio of 0.19:1 showing excretion with Approximation A and with 

Approximations A and B......................................................................................................... 50

9-5 Thorium urine content after a chronic inhalation intake of Type S thorium having a 228Th 

to 232Th ratio of 0.19:1 ............................................................................................................ 51

9-6 Thorium urine content after a 365-day chronic inhalation intake of Type S thorium 

having a 228Th to 232Th ratio of 0.19:1 ..................................................................................... 52

9-7 Thorium urine content after a 1,000-day chronic inhalation intake of Type S thorium 

having a 228Th to 232Th ratio of 0.19:1 ..................................................................................... 53

9-8 Thorium urine content after a 365-day chronic inhalation intake of Type M thorium 

having a 228Th to 232Th ratio of 0.19:1 ..................................................................................... 53

9-9 Thorium urine content after a 1,000-day chronic inhalation intake of Type M thorium 

having a 228Th to 232Th ratio of 0.19:1 ..................................................................................... 54

10-1 Thorium-228 in 24-hour incremental urine samples after an acute inhalation intake of 

Type S thorium having a 228Th to 232Th ratio of 1:1 ................................................................. 54

10-2 Thorium-228 urine content after an acute inhalation intake of Type S thorium having a 

228Th to 232Th ratio of 0.19:1 ................................................................................................... 56

10-3 Thorium-228 urine content after a chronic inhalation intake of Type S thorium having a 

228Th to 232Th ratio of 0.19:1 ................................................................................................... 58

A-1 Thorium-232 and 228Th present as a function of time after separation of thorium from 

other elements in the decay chain.......................................................................................... 62

A-2 Thorium-232, 228Ra, and 224Ra present after separation of thorium from other elements 

in the decay chain ..................................................................................................................63

A-3 Thorium-232 and 228Th present as a function of time after a second separation of 

thorium from other elements in the decay chain ..................................................................... 63

A-4 Thorium-232, 228Ra, and 224Ra present as a function of time after a second separation 

of thorium from other elements in the decay chain ................................................................. 64

A-5 Thorium-232 and 228Th present as a function of time after a third separation of thorium 

from other elements in the decay chain.................................................................................. 64

A-6 Thorium-232, 228Ra, and 224Ra present as a function of time after a third separation of 

thorium from other elements in the decay chain ..................................................................... 65

B-1 Plot of whole-body retention versus time after an acute uptake of the hypothetical 

radioactive material................................................................................................................ 68

B-2 Plot of whole-body retention versus time for a constant chronic uptake.................................. 70
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 7 of 73

ACRONYMS AND ABBREVIATIONS

AMAD activity median aerodynamic activity

Bq becquerel

d day

DOE Department of Energy

hr hour

ICRP International Commission on Radiological Protection

IMBA Integrated Modules for Bioassay Analysis

IRF intake retention factor

M moderate absorption type

nCi nanocurie

NIOSH National Institute for Occupational Safety and Health

ORAU Oak Ridge Associated Universities

pCi picocurie

s second

S slow absorption type

SRDB Ref ID Site Research Database Reference Identification (number)

TIB technical information bulletin

yr year

U.S.C. United States Code

μm micrometer

§ section or sections
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 8 of 73

1.0 INTRODUCTION

Technical information bulletins (TIBs) are not official determinations made by the National Institute for 

Occupational Safety and Health (NIOSH) but are rather general working documents that provide 

historical background information and guidance to assist in the preparation of dose reconstructions at 

particular sites or categories of sites. They will be revised in the event additional relevant information 

is obtained about the affected site(s). TIBs may be used to assist NIOSH staff in the completion of 

individual dose reconstructions.

In this document, the word “facility” is used as a general term for an area, building, or group of 

buildings that served a specific purpose at a site. It does not necessarily connote an “atomic weapons 

employer facility” or a “Department of Energy (DOE) facility” as defined in the Energy Employees 

Occupational Illness Compensation Program Act of 2000 [42 U.S.C. § 7384l(5) and (12)].

1.1 PURPOSE

The purpose of this report is to detail how to evaluate chest counts, whole-body counts, and various 

types of urine samples after intakes of 232Th. The computational methods for this TIB used the DCAL 

software and properly accounted for disequilibrium and independent kinetics. In addition, methods 

are offered that allow conservative approximations to the exact solutions to be made with existing 

Project software [i.e., Integrated Modules for Bioassay Analysis (IMBA)].

1.2 BACKGROUND

Thorium-232 is a long-lived radionuclide that has a decay chain with 10 progeny that are themselves 

radioactive. Figure 1-1 shows the first eight members of the chain. Evaluating bioassay data to 

calculate intakes of 232Th and its progeny can be one of the most challenging tasks in internal 

dosimetry. The primary challenges are caused by disequilibrium of the 232Th decay chain and 

independent biokinetics of the members of the decay chain.

→ → →

→ → → → →

10 232 1.405×10 yr 228 5.75 yr 228 6.13hr 228

228 1.91yr 224 3.62d 220 55.6s 216 0.146s 212 10.6hr

Th Ra Ac Th

Th Ra Rn Po Pb

Figure 1-1. First eight members of the 232Th decay chain.

Equilibrium versus Disequilibrium

Thorium-232 confined in one place with its progeny will eventually come into “secular equilibrium” 

(i.e., the activity of all members of the decay chain will be equal to that of the parent 232Th). As this 

document shows, equilibrium makes it relatively easy to estimate intakes from bioassay data. 

Chemical processing separates the members of the decay chain based on what element they are, 

disrupt this equilibrium, and cause the progeny to be present in varying amounts that change over 

time. This “disequilibrium” complicates evaluation of bioassay data because dose reconstructors 

usually have to specify the nature of the disequilibrium to evaluate bioassay data.

Shared versus Independent Kinetics

“Shared kinetics” refers to the assumption that all members of the decay chain have the same 

biokinetics as 232Th (i.e., all progeny are transported, deposited, and retained in the body just like the 

parent). Shared kinetics are used in the International Commission on Radiological Protection (ICRP) 

Publication 30 biokinetic models for thorium (ICRP 1979–1988). 

“Independent kinetics” refers to the assumption that all members of the decay chain have biokinetics 

based on the element. For example, 232Th has the biokinetics of thorium until it decays to 228Ra, at 
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 9 of 73

which point is has the biokinetics of radium (thorium and radium have very different biokinetics). 

Independent kinetics are used in the newer ICRP Publication 68 biokinetic models (ICRP 1995), 

which are the models the NIOSH Project uses to evaluate bioassay data. Independent kinetics 

complicates the evaluation of bioassay data because IMBA does not support independent kinetics for 

the 232Th chain. However, the DCAL1 software does properly account for independent kinetics and 

was used for this analysis to obtain exact solutions.

2.0 EQUILIBRIUM AND SHARED KINETICS

2.1 CHEST AND WHOLE-BODY COUNTS

Thorium-232 and 228Th do not emit photon radiation that is useful for quantifying the thorium in the 

body with in vivo bioassay (chest or whole-body counting). For this reason, in vivo bioassay for 232Th 

is often performed by quantifying the activity of the 228Ac or 212Pb progeny in the body and then 

calculating the amount of 232Th (and relatively long-lived progeny 228Ra and 228Th) present by 

assuming the material is in secular equilibrium. This is considered to be a reasonable approach 

when:

• The inhaled thorium has been locked in an insoluble physical matrix for a long period (e.g., for 

natural thorium mined from the ground), and

• The inhaled thorium particulate does not dissolve in the lungs to any great extent.

Example 2-1

For example, assume that a person inhaled 1 nCi of 5-μm activity median aerodynamic activity 

(AMAD) Type S 232Th in equilibrium with its progeny. IMBA and DCAL can be used to calculate2 the 

232Th chest burden, denoted here as qth232(t), where t is time in days. At 100 days after the intake it 

would be:

qth232 (100 3.670E-02nCi ) = (per nCi intake of 232Th) (2-1)

Note that the intake retention fraction (IRF), denoted here as mth232(t), is:

( ) th232 ( )

th232

100

100

1nCi

q

m = (2-2)

at t = 100 days after the intake. The discussion in this report uses both IRFs and burdens to develop 

the concepts.

Under the stated conditions, equilibrium implies that the chest burdens of all the progeny of 232Th, 

including that of 212Pb (qpb212), are the same as the parent 232Th chest burden:

qpb212 (100 3.670E-02nCi ) = (per nCi intake of 232Th) (2-3)

 1 http://www.epa.gov/radiation/assessment/dcal.html. 2 DCAL was used for all calculations for this report. DCAL and IMBA produce similar results in situations where both are 

applicable. For example, the burden per unit intake IMBA calculated in this case is 3.666E-2 nCi per nCi intake of 232Th.
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 10 of 73

If a chest burden of 10 nCi of 212Pb was measured at 100 days after an acute inhalation intake, the 

intake of 232Th (Ith232) is:

( ) ( ) th232

pb212 th232

10nCi 10nCi 10nCi 272 5nCi

100 100 3.67E-2

I .

m m

      =   =   = =        

(2-4)

The intake of each progeny of 232Th is equal to the intake of 232Th. For a measured a chest burden of 

10 nCi of 228Ac instead of 10 nCi of 212Pb, the resulting 232Th intake estimate would be the same as 

above. The evaluation of whole-body count data is completely analogous to the evaluation of chest 

count data, the only difference being that whole-body burdens are substituted for the chest burdens.

2.2 URINE

Thorium in urine is typically quantified using one of the following three analyses:

• Isotopic thorium (232Th and 228Th activities reported separately),

• Total thorium (sum of 232Th and 228Th activity reported), and

• 228Th (only 228Th activity reported).

Assuming equilibrium and shared kinetics makes the evaluation of thorium urine bioassay results 

relatively straightforward because the 232Th and/or 228Th are measured directly. 

Example 2-2

Assume that a person inhaled 10 pCi of 5-μm AMAD Type S 232Th in equilibrium with its progeny. We 

can calculate that at 100 days after this intake the person would have a 24-hour urine sample 

containing:

qth232 (100 3.650E-06pCi ) = (per 10 pCi intake of 232Th) (2-5)

Note that this is an incremental 24-hour urine sample and by convention it was completed at 100 days 

after the intake. If 10 pCi of 232Th is measured in the urine, the intake of 232Th is:

( ) th232

th232

10pCi 10pCi 2.740E+07pCi 100 3 650E-07

I

m .

    =   = =      

(2-6)

where mth232 is the IRF for 232Th in a 24-hour urine sample.

Example 2-3

If 10 pCi of 228Th is measured in the urine, the intake of 232Th is:

( ) ( ) th232

th228 th232

10pCi 10pCi 10pCi 2.740E+07pCi 100 100 3 650E-7

I

mm .

     =    = = =       

(2-7)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 11 of 73

Example 2-4

If 10 pCi of total thorium is measured in the urine, the intake of total thorium is:

( ) ( ) ( ) th

th232 th228 th232

5pCi 5pCi 10pCi 2.740E+07pCi 100 100 100

I

mm m

    

=+=      = =

    

(2-8)

This calculation assumes that half of the total thorium activity in the urine is 232Th and half is 228Th. 

The intakes of 232Th and 228Th are therefore:

I I .I th232 th228 th = = = 0 5 1.370E+07pCi (2-9)

where Ith is the total thorium intake activity.

3.0 DISEQUILIBRIUM AND SHARED KINETICS

3.1 CHEST AND WHOLE-BODY COUNTS

Thorium that has been chemically purified consists primarily of 232Th and 228Th. Progeny that are not 

isotopes of thorium are absent immediately after purification and begin to grow in. The progeny can 

exist in various degrees of disequilibrium with the parent 232Th depending on the timing and number of 

separations. For example, the plot in Figure 3-1 shows the activity of 228Th present as a function of 

time after a chemical separation that removes all of the nonthorium isotopes. Immediately after the 

separation the ratio of 228Th to 232Th is 1:1, but it decreases to a minimum of 1:0.422 at 4.55 years 

after separation. This behavior is the result of the 228Ra being removed from the material and its 

subsequent in growth.

Figure 3-1. Activity (Bq) of 228Th (red line) present as a function of time after 

chemical purification of 1 Bq of 232Th in equilibrium with its progeny.

The ingrowth curves for 228Ra and 224Ra are shown in Figure 3-2. These two progeny are important 

because 212Pb (which can be measured in vivo) is in equilibrium with the 224Ra, and 228Ac (also in vivo 
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 12 of 73

measurable) is in equilibrium with the 228Ra. Therefore, we can use 212Pb to quantify the 228Th present 

and 228Ac to quantify the 228Ra present. In addition, note that the minimum in the 228Th:232Th curve in 

Figure 3-1 is always greater than zero, whereas the minimum of the 228Ra:232Th curve in Figure 3-2 is 

zero. The practical consequences of all this are:

• If there is 212Pb present, there is always 228Th and 232Th present. Even though the exact 

activity of 232Th is unknown, it is feasible to come up with a conservative estimate based on the 

212Pb.

• If there is 228Ac present, there might or might not be 232Th present because the 228Ra parent of 

228Ac has a half-life long enough to exist independently of the 232Th. It is difficult to come up 

with a conservative estimate of the 232Th based on the 228Ac because there is no nonzero 

minimum in the ingrowth curve.

Figure 3-2. Radium-228 (blue line) and 224Ra (red line) present as a 

function of time after chemical purification of 1 Bq of 232Th in equilibrium 

with its progeny. Note that the 224Ra curve is basically the same as the 

228Th curve in Figure 3-1.

In summary, to properly interpret a 212Pb or 228Ac chest count in terms of the 232Th intake, the dose 

reconstructor needs to know something about the relative amounts of the 232Th progeny in the 

material. This information is usually derived from a knowledge of the separation history of the 

material and a liberal application of the Bateman equations. To facilitate dose reconstructions based 

on 212Pb, four standard thorium mixtures are used (see Appendix A):

• Unseparated (equilibrium) thorium, which has a 1:1 228Th to 232Th ratio;

• Single-separated thorium, which has a 0.42:1 228Th to 232Th ratio;

• Double-separated thorium, which has a 0.26:1 228Th to 232Th ratio; and

• Triple-separated thorium, which has a 0.19:1 228Th to 232Th ratio.

There are two important points to make about these standard mixtures. First, once a mixture is 

selected for a particular application, it is assumed to be a constant and does not change as a function 

of time. For example, if a worker is assumed to be chronically exposed to triple-separated thorium in 
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 13 of 73

a facility from 1980 to 1995, then the same mixture applies for the entire exposure period; that is, 

there is no ingrowth of 228Th during the 15 years. Second, the mixtures define the relative amounts of 

232Th and 228Th but not any of the other members of the decay chain. More specifically, these thorium 

mixtures do not contain any 228Ra.

Analogous standard thorium mixtures for evaluating 228Ac chest counts are discussed in Attachment 

A. In practice, the age of the thorium (i.e., the years since separation) must be specified to interpret 

an 228Ac chest count.

Example 3-1

Assume that after a chemical separation the thorium is fabricated into an insoluble material, which is 

inhaled by a worker. Assuming the worker inhaled 5-μm AMAD Type S single-separation thorium, the 

exact expression for the 212Pb chest burden of 10 nCi is given by:

q ( ) Im Im pb212 100 10nCi = = th232 pbth232 (100) + th228 pbth228 (100) (3-1)

where mpbth228(t) is the IRF for 212Pb that grows in from the 228Th intake and mpbth232(t) is the IRF for the 

212Pb that grows in from the 232Th. Based on the discussion above and that in Attachment A, the 

following assumptions are used:

m tm t pbth228 ( ) = th228 ( ) (3-2)

m t pbth232 ( ) = 0 3 (3-3)

th228

th232

0 42 I . I = (3-4)

Therefore, the intake of 228Th simplifies to:

( ) ( ) th228

th228

10nCi 10nCi 3.012E+02nCi

100 3 320E-02

I

m .

  

=    = =

  

(3-5)

The 232Th intake is equal to 301.2 ÷ 0.42 = 717.2 nCi, but the intakes of all other 232Th progeny are 

0 nCi. This intake estimate is relatively insensitive to the time that has elapsed since separation (i.e., 

the age of the thorium) and is a conservative intake estimate as long as the thorium has only been 

processed once.

Example 3-2

If we had measured 10 nCi of 228Ac 100 days after an acute inhalation of thorium (thorium in general), 

the exact expression for the 228Ac chest burden would be:

10nCi = Im Im th232 acth232 (100) + ra228 acra228 (100) (3-6)

where macth232(t) is the IRF for 228Ac that grows in from the 232Th intake, and macra228(t) is the IRF for

228Ac that grows in from the 228Ra intake.

 3 Because of the long physical half life of 232Th there is negligible ingrowth of 212Pb.
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 14 of 73

Single-separation thorium is assumed to contain no 228Ra, so the second term is equal to zero:

10nCi = I m th232 acth232 (100) (3-7)

The intake is therefore:

( ) th232

acth232

10nCi 10nCi 8 403E+03nCi

100 1190E-03

I .

m .

    =   = =      

(3-8)

This is a rather large intake of 232Th given a modest 10-nCi 228Ac chest burden. The IRF for 

228Ra/228Ac that grows in from 232Th is very sensitive the time that has elapsed since separation, and 

there is no conservative time that can be specified that is applicable for all situations. This means that 

the time since separation has to be specified in the evaluation of 228Ac chest count data. This is in 

contrast to the evaluation of 212Pb chest counts, where conservative mixtures and times can be 

specified that are applicable to all situations.

3.2 URINE BIOASSAY

The standard disequilibrium mixtures are easily incorporated into the urine bioassay calculations. 

Example 3-3

Continuing the previous example with Type S single-separation thorium, if 10 pCi of 232Th is measured 

in the urine, the intakes of 232Th and 228Th are:

( ) th232

th232

10pCi 2.740E+07pCi 100

I

m

 

=   =

 

(3-9)

th228 0 42 1.151E+07pCi th232 I .I = = (3-10)

Example 3-4

If 10 pCi of 228Th is measured in the urine, the intakes of 228Th and 232Th are:

( ) th228

th228

10pCi 10pCi 3 021E+07pCi 100 3 310E-07

I .

m .

    =   = =      

(3-11)

and:

th228

th232 7 193E+07pCi 0 42

I I . . = = (3-12)

Example 3-5

There are 10 pCi of total thorium measured in the urine. Given that:

Im Im th232 th232 (100) + = th228 th228 (100 10pCi ) (3-13)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 15 of 73

and:

th228

th232

0 42 I . I = (3-14)

then the 232Th intake is :

( ) ( )

( ) ( )

= +

= +

=

th232

th232 th228

10pCi

100 0 42 100

10pCi

3 650E-07 0 42 3 310E-07

1984E+07 Ci

I

m .m

. ..

. p

(3-15)

The intake of 228Th is:

th228 0 42 8 333E+06pCi th232 I .I . = = (3-16)

4.0 EXACT CALCULATIONS ASSUMING INDEPENDENT KINETICS

Implicit in the calculations above is the assumption that the 232Th and its progeny remain together in 

the body. This assumption of shared kinetics is reasonable for insoluble thorium particulates in the 

lung, but once the thorium matrix dissolves and the members of the decay chain become subject to 

the metabolic processes of the body this assumption is not sufficient over time4

. The current ICRP 

biokinetic models for the 232Th decay chain account for this by assuming that each element (especially 

thorium, radium, and radon) follows its own biokinetic model once it is released from or born outside 

of an insoluble matrix. The progeny of the 232Th decay chain are said to have independent kinetics.

All of the calculations up to this point can be performed with burdens from IMBA. From a practical 

point of view, independent kinetics significantly complicates the calculation of IRFs and evaluation of 

bioassay data because IMBA employs shared kinetics rather than independent kinetics and can no 

longer be used in all cases.

The DCAL software is capable of using independent kinetics to calculate burdens of 212Pb, 228Ac, and 

228Th that are the decay products of radionuclides ahead of them in the decay chain. For example, 

chest burdens that were calculated with DCAL for unit acute inhalation intakes of 5-μm AMAD Type S 

materials (

232Th, 228Ra, 228Th, 224Ra) are shown in Figures 4-1 through 4-4. 

 4 All of the ICRP Publication 30 biokinetic models except for tellurium assumed shared kinetics (ICRP 1979–1988).
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 16 of 73

Figure 4-1. Chest burdens of 232Th, 228Ac, and 212Pb after a unit acute 

inhalation intake of pure Type S 232Th.

To further refine the calculations, assume that 232Th in secular equilibrium with its progeny was 

inhaled. Of primary concern here are the biokinetics of 232Th through 212Pb, 228Ra through 212Pb, and 

228Th through 212Pb. All other unsupported progeny in the initial intake have half-lives that are short 

enough to limit their contribution to the observed 212Pb whole-body burden except in the first couple of 

days after the inhalation. To confirm this, the analysis also examined the 224Ra through 212Pb decay 

chain, which should be the most significant of the short-lived chains because of the half-life of 224Ra. 

The following discussion provides examples. 

Figure 4-2. Chest burdens of 228Ra, 228Ac, and 212Pb after a unit acute 

inhalation intake of pure Type S 228Ra. The 228Ac activity is equal to the 

228Ra activity.

Figure 4-3. Chest burdens of 228Th and 212Pb after a unit acute inhalation 

intake of pure Type S 228Th.

Example 4-1

1 10 100 1000 10000

1e-10 1e-07 1e-04 1e-01

Time After Intake (days)

Chest Burdens

Th-232

Pb-212

Ac-228

1 10 100 1000 10000

1e-07 1e-05 1e-03 1e-01

Time After Intake (days)

Chest Burdens

Ra-228

Pb-212
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 17 of 73

If the measured chest burden of 212Pb at 100 days after an acute inhalation intake of 5-μm AMAD 

Type S material is 10 nCi, what would be the intakes assuming they consisted of four different pure

materials? 

The quantity of 212Pb present in the chest at time t after a unit intake of pure 232Th is denoted by

m t pbth232 ( ) .

Therefore:

mpbth232 (100 4.640E-05 ) = (4-1)

Figure 4-4. Chest burdens of 224Ra and 212Pb after a unit acute inhalation 

intake of pure Type S 224Ra.

and:

( ) th232

pbth232

10nCi 10nCi 2.155E+05nCi

100 4.640E-05

I

m

 

=   = =

 

(4-2)

For comparison, what would the intake be if the 212Pb and 232Th were in secular equilibrium, exhibited 

shared kinetics, and no 220Rn was lost from the body?:

th232 ( )

10nCi 10nCi 2.725E+02nCi

100 3.670E-02

I

m= = = (4-3)

Note that the IRF in this equation is for the 232Th because the 212Pb is assumed to be present in a 

quantity equal to that of the 232Th. It is of interest to note that this simplistic assumption results in an 

intake estimate that is lower than the exact estimate by a factor of:

3.670E-02 790

4.640E-05 ≈ (4-4)

1 2 5 10 20 50 100

1e-07 1e-05 1e-03 1e-01

Time After Intake (days)

Chest Burdens

Ra-224

Pb-212
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 18 of 73

Here are the exact calculations for the other intakes:

( ) ra228

pbra228

10nCi 10nCi 3.413E+03nCi

100 2.930E-03

I

m= = = (4-5)

( ) th228

pbth228

10nCi 10nCi 3.268E+02nCi

100 3.060E-02

I

m= = = (4-6)

( ) ra224

pbra224

10nCi 10nCi 4 386E+10nCi

100 2 280E-10

I .

m . = = = (4-7)

The calculations for whole-body counts are the same as above except whole-body burdens per unit 

intake are substituted for the chest-burdens per unit intake.

Example 4-2

For the same 10 nCi 212Pb chest burden, what would the intake be if the source material was 232Th in 

equilibrium with its progeny?:

Im Im Im th232 pbth232 (100) ++= ra228 pbra228 (100) th228 pbth228 (100 10nCi ) (4-8)

The intake of 228Ra and 228Th are assumed to equal the intake of 232Th because the material is in 

equilibrium, so this can be simplified to:

Im m m th232 pbth232   (100) ++ = pbra228 (100 100 10nCi ) pbth228 ( )   (4-9)

which can be rearranged to give the intake:

( ) ( ) ( ) th232

pbth232 pbra228 pbth228

10nCi 2.978E+02nCi

100 100 100

I

mmm = = + +

(4-10)

This means that 297.8 nCi of 232Th and 297.8 nCi of each of its progeny was inhaled. The inclusion of 

224Ra does not change the intake estimate because it contributes practically no 212Pb at t = 100 days 

after intake:

pbth232 ( ) pbra228 ( ) pbth228 ( ) pbra224 ( )

10nCi 2.978E+02nCi

100 100 100 100

I

mmmm = = +++

(4-11)

For the purpose of evaluating 212Pb in vivo counts, only the long-lived radionuclides 232Th, 228Ra, and 

228Th in the source term need to be specified. Attributing any 212Pb contributed by short-lived progeny 

like 224Ra would result in an overestimate of the intakes of the dosimetrically significant 232Th, 228Ra, 

and 228Th.

Example 4-3
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What would the intake be if the source material was 232Th with the activity of the 228Ra in the source 

material being one-half of the 232Th activity and the activity of the 228Th in the source material being 

one-quarter of the 232Th activity?

I m th232 pbth232   (100 0 5 100 0 25 100 10nCi ) ++ = . mpbra228 ( ) . mpbth228 ( )   (4-12)

( ) ( ) ( ) = = + + th232

pbth232 pbra228 pbth228

10nCi 1.092E+03nCi

100 0 5 100 0 25 100

I

m . m . m

(4-13)

This means the inhalation intake consisted of 1,092 nCi of 232Th, 1,092 ÷ 2 = 546 nCi of 228Ra, and 

1,032 ÷ 4 = 273 nCi of 228Th. This result is unchanged with the inclusion of 224Ra.

Example 4-4

What would the intake be if the source material was 232Th in equilibrium with its progeny and the 

measured chest burden was 10 nCi of 228Ac? Analogous to the way we looked at the 212Pb burdens, 

we have:

Im I m th232 acth232 (100) + = acra228 pbra228 10nCi (4-14)

The intake of 228Ra is assumed to equal the intake of 232Th, so this can be simplified to:

Im m th232 acth232   (100 100 10nCi ) + = acra228 ( )   (4-15)

which can be rearranged to give the intake:

( ) ( ) = = = + + th232

acth232 acra228

10nCi 10nCi 2.726E+02nCi

100 100 1 19 -3 3 55 -2

I

m m .E .E (4-16)

This means that 272.6 nCi of 232Th and 272.6 nCi of each of its progeny was inhaled.

4.1 URINE BIOASSAY

Plots of 232Th, 228Ra, and 228Th urinary excretion curves calculated with DCAL for unit acute inhalation 

intakes of 5-μm AMAD Type S materials are shown in Figures 4-5 through 4-7.
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 20 of 73

Figure 4-5. Thorium-232 and 228Th in a 24-hour incremental urine sample 

after a unit acute inhalation intake of pure Type S 232Th. Note that IRFs 

from IMBA can be used to model 232Th in urine after a 232Th intake.

Figure 4-6. Radium-228 and 228Th in a 24-hour incremental urine sample 

after a unit acute inhalation intake of pure Type S 228Ra.

1 10 100 1000 10000

1e-13 1e-09 1e-05

Time After Intake (days)

Urine Content

Th-232

Th-228

1 10 100 1000 10000

1e-10 1e-08 1e-06 1e-04

Time After Intake (days)

Urine Content

Ra-228

Th-228
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 21 of 73

Figure 4-7. Thorium-228 in a 24-hour incremental urine sample after a 

unit acute inhalation intake of pure Type S 228Th. Note that IRFs from 

IMBA can be used to model 228

Th in urine after a 228Th intake.

Example 4-5

If 10 pCi of 232Th is measured in the urine at 100 days after an acute inhalation intake of 5-μm AMAD 

Type S material, the intake of 232Th is:

( ) th232

th232

10pCi 2.740E+07pCi 100

I

m

 

=   =

 

(4-17)

To get the intakes of the other members of the decay chain like 232Th we have to assume a particular 

mixture. For single-separation thorium the 228Th intake is:

th228 0 42 1.151E+07pCi th232 I .I = = (4-18)

Note that IRFs from IMBA can be used to evaluate 232Th in urine.

Example 4-6

Assume that 10 pCi of 228Th is measured in the urine after an intake of single-separation thorium. It is 

instructive to look at the excretion function like this:

  Im Im th232 thth232 (100) + = th228 th228 (100 10pCi )   (4-19)

Note that 228Ra does not contribute to the 228Th in the urine because it was all removed in the 

separation process. Given that mthth232(100) is the amount of 228Th in the urine at 100 days after an 

acute inhalation intake of pure 232Th, the intake of 228Th is:

th228 0 42 th232 I .I = (4-20)

which gives:

I m th232 thth232   (100 0 42 100 10pCi ) + = . mth228 ( )   (4-21)

1 10 100 1000 10000

1e-10 1e-08 1e-06

Time After Intake (days)

Urine Content

Th-228
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 22 of 73

Rearranging and solving this equation gives the 232Th intake:

( ) ( )

( ) ( )

 

=  

+  

 

=  

+  

= +

th232

thth232 th228

10pCi

100 0 42 100

10pCi

4 640E-10 0 42 3 310E-07

7 169E 07pCi

I

m . m

. ..

.

(4-22)

The 228Th intake is:

th228 = = 0 42 3 011E+07pCi th232 I .I . (4-23)

Example 4-7

Finally, what are the 232Th and 228Th intakes if there is a measured 10 pCi of total thorium in the urine? 

As before, the excretion function is:

  Im Im Im th232 th232 (100) ++= th232 thth232 (100) th228 th228 (100 10pCi )   (4-24)

Assuming single-separation thorium, this simplifies to:

I m m th232 th232   (100 100 0 42 100 10pCi ) ++ = thth232 ( ) . mth228 ( )   (4-25)

Rearranging and solving this equation gives the 232Th intake:

( ) ( ) ( )

( ) ( ) ( )

th232

th232 thth232 th228

10pCi

100 100 0 42 100

10pCi

3 650E-07 4 640E-10 0 42 3 310E-07

1982E+07pCi

I

m m . m

. . ..

.

= + +

= + +

=

(4-26)

The 228Th intake is:

th228 0 42 8 325E+06pCi th232 I .I . = = (4-27)

5.0 CHRONIC INTAKES

DCAL does not generate burdens that result from constant chronic intakes. Methods for calculating 

chronic intake burdens from acute intake burdens are discussed in Appendix B. The results of these 

calculations are chronic intake IRFs (denoted by m ) such as the one shown below for 212Pb in the 

chest after an intake of pure 232Th:

m t,T t T  pbth232 ( ) ≥

where
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 23 of 73

T = length of chronic intake period

t = time that the 212Pb chest burden is measured relative to start of chronic intake

This IRF is interpreted as being the ratio of the amount of 212Pb present in the chest at t days after the 

start of the chronic intake to the total amount of 232Th inhaled over the T-day chronic intake period. 

This in contrast to IMBA, where the IRF is interpreted as being the ratio of the amount of 212Pb present 

in the chest at t days after the start of the chronic intake to the intake rate of 232Th over the T-day 

chronic intake period.

Example 5-1

As an example, assume a 10-nCi chest burden of 212Pb at 365 days after the start of a 100-day 

chronic inhalation intake of 5-μm AMAD Type S material. What would be the total intakes if they 

consisted of the four different pure materials?

( ) th232

pbth232

10nCi 10nCi 2 878E+04nCi

365 100 3 475E-04

I .

m ,. = = =  (5-1)

( ) ra228

pbra228

10nCi 10nCi 1578E+03nCi

365 100 6 339E-03

I .

m ,. = = =  (5-2)

( ) th228

th228

10nCi 10nCi 5 327E+02nCi

365 100 1877E-02

I .

m ,. = = =  (5-3)

( ) ra224

ra224

10nCi 10nCi 2 309E+30nCi

365 100 4 331E-30

I .

m,. = = =  (5-4)

The intake rates are given by dividing the respective intakes by 100 days. What would the intake be if 

the source material was 232Th in equilibrium with its progeny? As with the acute intake:

  Im , Im , Im , th232 pbth232 (365 100) ++ = ra228 pbra228 (365 100) th228 pbth228 (365 100 10nCi )    (5-5)

Setting the intakes of 228Ra and 228Th equal to the intake of 232Th and rearranging gives:

( ) ( ) ( ) th232

pbth232 pbra228 pbth228

10nCi 3 928E+02nCi

365 100 365 100 365 100

I .

m ,m ,m , = =  + +

(5-6)

The intakes of all the members of the 232Th decay chain are equal to the intake of 232Th.

Example 5-2

What would the intake be if the source material was 232Th with the activity of the 228Ra in the source 

material being one-half of the 232Th activity and the activity of the 228Th in the source material being 

one-quarter of the 232Th activity?

( ) ( ) ( ) th232

pbth232 pbra228 pbth228

10nCi 1218E+03nCi

365 100 0 5 365 100 0 25 365 100

I .

m , .m , . m , = =   + +

(5-7)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 24 of 73

This means the inhalation intake consisted of 1,218 nCi of 232Th, 1,218 ÷ 2 = 609 nCi of 228Ra, and 

1218 ÷ 4 = 305 nCi of 228Th.

Example 5-3

What would the intake be if the 212Pb and 232Th were in secular equilibrium, exhibited shared kinetics, 

and no 220Rn was lost from the body?

( ) th232

th232

10nCi 10nCi 3 595E+02nCi

365 100 2 782E-02

I .

m,. = = =  (5-8)

Note that the IRF in this equation is for the 232Th because the 212Pb is assumed to be present in a 

quantity equal to that of the 232Th.

Example 5-4

What would the intake be if the source material was 232Th with the activity of the 228Ra in the source 

material being one-half of the 232Th and there was a measured 10 nCi of 228Ac in the chest 365 days 

after the start of a 100-day chronic intake?

( ) ( )

( ) ( )

= +

= +

=

  th232

acth232 acra228

10nCi

365 100 0 5 365 100

10nCi

2 732E-03 0 5 2 507E-02

6 549E+02nCi

I

m , .m ,

. ..

.

(5-9)

This means the intake consisted of 655 nCi of 232Th and 655 ÷ 2 = 328 nCi of 228Ra.

5.1 URINE BIOASSAY

Example 5-5

What are the 232Th and 228Th intakes implied by 10 pCi of total thorium measured in the urine at 365 

days after the start of a 100-day chronic intake? As with the acute intake version of this problem, the 

excretion function is:

  Im , Im , Im , th232 th232 (365 100) ++= th232 thth232 (365 100) th228 th228 (365 100 10pCi )     (5-10)

Assuming single-separation thorium, this simplifies to:

I m , m , .m , th232 th232   (365 100 365 100 0 42 365 100 10pCi ) ++ = thth232 ( ) th228 ( )     (5-11)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 25 of 73

Rearranging and solving this equation gives the 232Th intake:

( ) ( ) ( )

( ) ( ) ( )

th232

th232 thth232 th228

10pCi

365 100 365 100 0 42 365 100

10pCi

2 896E-07 3 503E-09 0 42 2 129E-07

2 614E+07pCi

I

m , m , .m ,

. . ..

.

= + +

= + +

=

 

(5-12)

The 228Th intake is:

th228 0 42 1098E+07pCi th232 I .I . = = (5-13)

6.0 USING IMBA FOR EFFICIENCY CALCULATIONS

DCAL can be used to perform best-estimate dose reconstructions of thorium intakes based on 

bioassay data and the resulting organ doses. However, DCAL is not ideal for routine dose 

reconstructions because it is designed to be used in a batch mode and its output requires further 

processing with a custom code to obtain chronic intake burdens.

To facilitate efficiency calculations, ways are suggested here to adjust intakes and intake rates that 

are calculated with IMBA so that they will not underestimate those that are calculated with exact 

methods based on DCAL. A summary of the efficiency calculations is given in Attachment C. These 

adjustments can be used to perform efficiency calculations when an overestimate of dose is 

appropriate and a single measurement is being evaluated (which is typical for missed dose 

calculations). Efficiency methods using IMBA are not provided for 228Ac chest counts5

, which should 

be evaluated with DCAL. IMBA cannot be used for best estimates of intake and dose, which require 

the use of DCAL. 

7.0 USING IMBA FOR CHEST COUNTS

7.1 ACUTE INTAKES

Assume a mixture of 1 nCi of 232Th and 1 nCi of 228Th (both being 5-μm AMAD Type S material) was 

inhaled. The 212Pb chest burden as a function of time after the acute intake is shown in Figure 7-1.

 5 The approximations given in Equations 7-3 and 7-4 that make efficiency calculations feasible for 212Pb do not have valid 

counterparts for 228Ac. 
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 26 of 73

Figure 7-1. Lead-212 chest burden after an acute inhalation intake of 

Type S thorium having a 228Th to 232Th ratio of 1:1.

The exact chest burden q of 212Pb at t days after an acute inhalation intake is given by:

qt q t q t ( ) = + pbth232 pbth228 ( ) ( ) (7-1)

where qpbth232 is the chest burden of 212Pb that grows in from the inhaled 232Th and qpbth228 is the chest 

burden of 212Pb that grows in from the inhaled 228Th. 

These exact burdens are calculated with DCAL, which accounts for independent kinetics of the 

thorium decay chain and the loss of 220Rn. This relationship can be restated in terms of intakes and 

IRFs:

qt I m t I m t ( ) = th232 pbth232 th228 pbth228 ( ) + ( ) (7-2)

Two approximations can be made:

1. The amount of 212Pb present equals the amount of 228Th present at all times after the intake:

m tm t pbth228 ( ) = th228 ( ) (7-3)

2. There is negligible ingrowth of 212Pb from the 232Th component of the intake:

m t pbth232 ( ) = 0 (7-4)

This gives the following approximation to q:

qt I m t ′( ) = th228 th228 ( ) (7-5)

where mth228 is the 228Th chest IRF at time t (which can be calculated with IMBA). As seen in the plot 

above, these approximations provide reasonably accurate estimates of the 212Pb burden between 

approximately 10 and 1,000 days after the intake.

1 5 10 50 100 500 5000

1e-04 1e-03 1e-02 1e-0

1 nCi Th-232 & 1 nCi Th-228

Time of Chest Count (days)

Pb-212 Chest Bu 

Exact (red)

Approx (blue)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 27 of 73

Example 7-1

For example, assume that a 212Pb chest burden of 1.5 nCi is observed at 100 days after an acute 

inhalation intake of this thorium. Given a 228Th:232Th ratio of 1: 1, the intake of 232Th is:

( ) ( )

( ) ( )

th232

pbth232 pbth228

1 5nCi

100 100

1 5nCi

4 640E-05 3 060E-02

4 895E+01nCi

. I

m m

.

. .

.

= +

= +

=

(7-6)

which translates into 48.95 nCi of 228Th. These exact intakes (calculated with DCAL) can be checked 

by calculating the expected 212Pb chest burden to determine if it equals the burden from which the 

intakes were calculated:

1 5nCi 48 95nCi 4 64E-05 48 95nCi 0 0306 . .. .. = ( )( ) + ( )( ) (7-7)

With the approximate method we have a 228Th intake of:

th228 ( )

1 5nCi 1 5nCi 45 18nCi

100 0 0332

. . I . , m . = = = (7-8)

which translates into a 45.18 nCi intake of 232Th. Note that in this example:

• For a given intake the exact method gives a lower chest burden than does the approximate 

method at t = 100 days (see Figure 7-1).

• However, for a given chest burden the exact method gives a larger intake than does the 

approximate method.

In practice dose reconstructors typically calculate intakes from chest burdens. Therefore, the plot in 

Figure 7-1 can be interpreted to mean that the approximate method will underestimate intakes at 

times before ~300 days after the intake (where the curves cross) and overestimate intakes after that 

day.

7.1.1 Triple-Separated Thorium Mixture

As noted in Section 3.0, triple-separated thorium has a 228Th:232Th ratio of 0.19:1. Assume a mixture 

of 1 nCi of 232Th and 0.19 nCi of 228Th (both being 5-μm AMAD Type S material) was inhaled. The 

212Pb chest burden as a function of time after the acute intake is shown in Figure 7-2. 
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 28 of 73

Figure 7-2. Lead-212 chest burden after an acute inhalation intake of 

Type S thorium having a 228Th to 232Th ratio of 0.19:1.

Once again, the exact chest burden q of 212Pb at t days after an acute inhalation intake is given by:

qt I m t I m t ( ) = th232 pbth232 th228 pbth228 ( ) + ( ) (7-9)

and the approximation is:

qt I m t ′( ) = th228 th228 ( ) (7-10)

Example 7-2

For example, assume that a 212Pb chest burden of 1.5 nCi is observed at 100 days after an acute 

inhalation intake of this triple-separated Type S thorium. Given a 228Th:232Th ratio of 0.19, the exact 

intake (calculated with DCAL) of 232Th is:

( ) ( )

( )( )

th232

pbth232 pbth228

1 5nCi

100 0 19 100

1 5nCi

4 64E-05 0 19 0 0306

255 96nCi

. I

m . m

.

. ..

.

= +

= +

=

(7-11)

which translates into 0.19 × 255.96 nCi = 48.63 nCi of 228Th. As a check, it is useful to show that:

1 5nCi 255 96nCi 4 64E-05 48 63nCi 0 0306 . .. .. = ( )( ) + ( )( ) (7-12)

With the approximate method the intake of 228Th is:

( ) th228

th228

1 5nCi 1 5nCi 45 18nCi

100 0 0332

. . I .

m . = = = (7-13)

which gives 45.18 nCi ÷ 0.19 = 237.79 nCi of 232Th.

1 5 10 50 100 500 5000

1e-05 1e-03 1e-0

1 nCi Th-232 & 0.19 nCi Th-228

Time of Chest Count (days)

Pb-212 Chest Bu 

Exact (red)

Approx (blue)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 29 of 73

The plot for Type M triple-separated thorium is shown in Figure 7-3. Other than the fact that there is 

faster clearance of the thorium from the chest, all of the discussion above is directly applicable to 

Type M material.

Figure 7-3. Lead-212 chest burden after an acute inhalation intake of 

Type M thorium having a 228Th to 232Th ratio of 0.19:1.

7.1.2 Adjustment of Thorium Intakes

As shown in the plots above, for a given thorium intake, the approximate method will overestimate the

212Pb chest burden for a length of time after the intake (~1 year for Type S material). Therefore, for a 

given 212Pb chest burden, the approximate method will underestimate the thorium intake for the same 

length of time. In Figures 7-4 and 7-5, an adjustment factor of 1/1.1 is applied to the approximate 

212Pb chest burdens to ensure that they do not overestimate the exact 212Pb chest burdens at times 

greater than 30 days after intake.

Figure 7-4. Lead-212 chest burden after an acute inhalation intake of 

Type S thorium having a 228Th to 232Th ratio of 0.19:1 with vertical dashed 

line at t = 30 days after intake.

1 5 10 50 100 500 5000

1e-05 1e-03 1e-0

1 nCi Th-232 & 0.19 nCi Th-228

Time of Chest Count (days)

Pb-212 Chest Bu 

Exact (red)

Approx (blue)

1 5 10 50 100 500 5000

0.004 0.006 0.008

1 nCi Th-232 & 0.19 nCi Th-228

Time of Chest Count (days)

Pb-212 Chest Bu 

Exact (red)

Approx (blue)

Approx/1.1 (gold)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 30 of 73

Figure 7-5. Lead-212 chest burden after an acute inhalation intake of 

Type M thorium having a 228Th to 232Th ratio of 0.19:1 with vertical dashed 

line at t = 30 days after intake.

When using the approximate method to calculate thorium intakes from 212Pb chest burdens, the intake 

calculated with IMBA is multiplied by an adjustment factor of 1.1 to achieve the desired end of not 

underestimating the intake that would have been calculated using the exact method.

7.1.3 Guidance for Acute Intakes

Based on the discussion above, the following guidance is offered on how to use the approximate 

method to evaluate 212Pb chest count data after acute inhalation intakes of Type M or S tripleseparated thorium:

Assume a single measured 212Pb chest burden. Evaluate the chest burden with a 228Th biokinetic 

model in IMBA. Multiply the calculated 228Th intake by a factor of 1.1 and assign it as the intake of 

228Th. Divide this estimated 228Th intake by the 228Th:232Th ratio of 0.19:1 to obtain the 232Th intake. 

For 212Pb chest burdens that are measured more than 30 days after an acute intake, these 

approximate intakes will not underestimate the intakes that would be calculated with exact methods.

7.2 CHRONIC INTAKES

The plot in Figure 7-6 shows the 212Pb chest burden as a function of time after a chronic intake of 

1 nCi/d of 232Th and 0.19 nCi/d of 228Th (both being 5-μm AMAD Type S material). In other words, the 

time on the abscissa is the length of the time after the start of the chronic intake and the time that the 

chest burden is determined. The two curves cross at ~700 days.

1 5 10 50 100 500 5000

0.004 0.006 0.008

1 nCi Th-232 & 0.19 nCi Th-228

Time of Chest Count (days)

Pb-212 Chest Bu 

Exact (red)

Approx (blue)

Approx/1.1 (gold)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 31 of 73

Figure 7-6. Lead-212 chest burden after a chronic inhalation intake of 

Type S thorium having a 228Th to 232Th ratio of 0.19:1.

The equations for chronic intakes are essentially the same as in the case of acute intakes except that 

the functions have an argument for the length of the constant chronic intake period. The exact chest 

burden q of 212Pb at t days after the start of a chronic inhalation intake lasting tc days is given by:

q t,t q t,t q t,t t t ( c c cc ) =+ ≥ pbth232 ( ) pbth228 ( ) (7-14)

The relationship expressed in terms of intakes and IRFs is:

( ) =+ ≥ ( ) ( )   q t,t I m t,t I m t,t t t c c cc th232 pbth232 th228 pbth228 (7-15)

Applying the two approximations from Section 7.1 gives the following approximation to q:

′ ( ) = ( )  q t,t I m t,t c c th228 th228 (7-16)

Example 7-3

For example, assume that a 212Pb chest burden of 1.5 nCi is observed at the end of a 365-day chronic 

inhalation intake of Type S triple-separated thorium. Given a 228Th:232Th ratio of 0.19:1, the total 

intake of 232Th is:

( ) ( )

( )( )

= +

= +

=

  th232

pbth232 pbth228

1 5nCi

365 365 0 19 365 365

1 5nCi

1641E-04 0 19 0 02654

288 1nCi

. I

m , .m ,

.

. ..

.

(7-17)

which translates into 0.19 × 288.1 nCi = 54.74 nCi of 228Th. This can be seen by rearranging the 

above equation:

1 5nCi 288 1nCi 1 641E-04 54 74nCi 0 02654 . .. . . = ( )( ) + ( )( ) (7-18)

5 10 20 50 100 200 500 1000 5000

0.01 0.05 0.50 5.00

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time of Chest Count (days)

Pb-212 Chest Bu 

Exact (red)

Approx (blue)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 32 of 73

The intake rates are obtained by dividing the intakes by tc = 365 days. With the approximate method 

the intake of 228Th is:

( ) ( ) = = =  th228

th228

1 5nCi 1 5nCi 50 34nCi

365 365 0 02980

. . I .

m, .

(7-19)

which translates into 50.34 nCi ÷ 0.19 = 264.9 nCi of 232Th.

The plot for Type M triple-separated thorium is shown in Figure 7-7. After a few hundred days the 

212Pb chest burden achieves a steady state condition with the approximate method giving a chest 

burden ~10% higher than the exact method.

Figure 7-7. Lead-212 chest burden after a chronic inhalation intake of 

Type M thorium having a 228Th to 232Th ratio of 0.19:1.

7.2.1 Adjustment of Chronic Thorium Intakes

In Figures 7-8 to 7-13, the 212Pb chest burdens at various times during and after 365 day, 1,000 day, 

and 5,000-day constant chronic intakes are presented. As with the acute intakes, the approximate 

212Pb chest burdens are adjusted by a factor of 1/1.1. This illustrates that intake rates that are 

calculated from 212Pb chest counts with the approximate method can be adjusted by a factor of 1.1 to 

ensure that the intake rates do not underestimate the intake rates that are calculated with the exact 

method.

5 10 20 50 100 200 500 1000 5000

0.01 0.05 0.50 5.00

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time of Chest Count (days)

Pb-212 Chest Bu 

Exact (red)

Approx (blue)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 33 of 73

Figure 7-8. Lead-212 chest burden during and after a 365-day chronic 

inhalation intake of Type S thorium having a 228Th to 232Th ratio of 0.19:1. 

The vertical dashed line is at t = 365 days.

Figure 7-9. Lead-212 chest burden during and after a 1,000-day chronic 

inhalation intake of Type S thorium having a 228Th to 232Th ratio of 0.19:1. 

The vertical dashed line is at t = 1,000 days.

200 400 600 800 1000

1.0 1.5 2.0 2.5

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time of Chest Count (days)

Pb-212 Chest Bu 

Exact (red)

Approx (blue)

Approx/1.1 (gold)

800 1000 1200 1400 1600 1800 2000

0.5 1.0 2.0 5.0

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time of Chest Count (days)

Pb-212 Chest Bur 

Exact (red)

Approx (blue)

Approx/1.1 (gold)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 34 of 73

Figure 7-10. Lead-212 chest burden during and after a 5,000-day chronic 

inhalation intake of Type S thorium having a 228Th to 232Th ratio of 0.19:1. 

The vertical dashed line is at t = 5,000 days.

Figure 7-11. Lead-212 chest burden during and after a 365-day chronic 

inhalation intake of Type M thorium having a 228Th to 232Th ratio of 0.19:1. 

The vertical dashed line is at t = 365 days.

4000 4500 5000 5500 6000 6500 7000

0.5 1.0 2.0 5.0

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time of Chest Count (days)

Pb-212 Chest Bu 

Exact (red)

Approx (blue)

Approx/1.1 (gold)

300 350 400 450 500

0.5 1.0 1.5

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time of Chest Count (days)

Pb-212 Chest Bur 

Exact (red)

Approx (blue)

Approx/1.1 (gold)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 35 of 73

Figure 7-12. Lead-212 chest burden during and after a 1,000-day chronic 

inhalation intake of Type M thorium having a 228Th to 232Th ratio of 0.19:1. 

The vertical dashed line is at t = 1,000 days.

Figure 7-13. Lead-212 chest burden during and after a 5,000-day chronic 

inhalation intake of Type M thorium having a 228Th to 232Th ratio of 0.19:1. 

The vertical dashed line is at t = 5,000 days.

7.2.2 Guidance for Chronic Intakes

Based on the discussion above, the following guidance is offered on how to use the approximate 

method to evaluate 212Pb chest count data after constant chronic inhalation intakes of triple-separated 

thorium:

Assume a single measured 212Pb chest burden. Evaluate the chest burden with a 228Th biokinetic 

model in IMBA. Multiply the calculated 228Th intake rate by a factor of 1.1 and assign it as the intake 

rate of 228Th. Divide this estimated 228Th intake rate by the 228Th:232Th ratio of 0.19:1 to obtain the 

232Th intake rate. For chronic intakes longer than 1 year these approximate intakes will not 

underestimate the intakes that would be calculated with exact methods.

900 950 1000 1050 1100

0.6 0.8 1.0 1.4

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time of Chest Count (days)

Pb-212 Chest Bu 

Exact (red)

Approx (blue)

Approx/1.1 (gold)

4600 4800 5000 5200 5400

0.1 0.2 0.5 1.0

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time of Chest Count (days)

Pb-212 Chest Bu 

Exact (red)

Approx (blue)

Approx/1.1 (gold)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 36 of 73

8.0 USING IMBA FOR WHOLE-BODY COUNTS

8.1 ACUTE INTAKES

Assume a mixture of 1 nCi of 232Th and 1 nCi of 228Th (both being 5-μm AMAD Type S material) was 

inhaled. The 212Pb whole-body burden as a function of time after the acute intake is shown in 

Figure 8-1.

Figure 8-1. Lead-212 whole-body burden after an acute inhalation intake 

of Type S thorium having a 228Th to 232Th ratio of 1:1.

Analogous to the chest counts, the exact body burden q of 212Pb at t days after an acute inhalation 

intake is given by:

qt q t q t ( ) = + pbth232 pbth228 ( ) ( ) (8-1)

where qpbth232 is the whole-body burden of 212Pb that grows in from the inhaled 232Th and qpbth228 is the 

whole-body burden of 212Pb that grows in from the inhaled 228Th. The relationship expressed in terms 

of intakes and IRFs is:

qt I m t I m t ( ) = th232 pbth232 th228 pbth228 ( ) + ( ) (8-2)

Applying the two approximations from Section 7.1 gives the following approximation to q:

qt I m t ′ ( ) = th228 th228 ( ) (8-3)

As seen in the plot above, these approximations provide reasonably accurate estimates of the 212Pb 

burden between approximately 10 and 1,000 days after the intake.

1 5 10 50 100 500 5000

1e-04 5e-03 1e-01

1 nCi Th-232 & 1 nCi Th-228

Time of Count (days)

Pb-212 Whole-Bod 

Exact (red)

Approx (blue)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 37 of 73

Example 8-1

For example, assume that a 212Pb whole-body burden of 1.5 nCi is observed at 100 days after an 

acute inhalation intake of this Type S thorium. Given a 228Th:232Th ratio of 1:1, the intake of 232Th is:

( ) ( )

( ) ( )

= +

= +

=

th232

pbth232 pbth228

1 5nCi

100 100

1 5nCi

4 750E-05 3 130E-02

4 785E+01nCi

. I

m m

.

. .

.

(8-4)

which translates into 47.85 nCi of 228Th. These intakes can be checked by calculating the expected 

212Pb whole-body burden and seeing if it equals the burden from which the intakes were calculated:

= ( )  ( ) + ( )   1 5nCi 4.785E+01nCi 4 750E-05 3 130E-02 . . . (8-5)

With the approximate method we have a 228Th intake of:

( ) th228 = = =

th228

1 5nCi 1 5nCi 4 386E+1nCi

100 3.420E-02

. . I .

m

(8-6)

which translates into a 43.86 nCi intake of 232Th.

The plot in Figure 8-1 can be interpreted to mean that the approximate method will underestimate 

intakes at times before ~500 days after the intake (where the curves cross) and overestimate intakes 

after that day.

8.1.1 Triple-Separated Thorium Mixture

As noted in Section 3.0, triple-separated thorium has a 228Th:232Th ratio of 0.19:1. Assume a mixture 

of 1 nCi of 232Th and 0.19 nCi of 228Th (both being 5-μm AMAD Type S material) was inhaled. The 

212Pb whole-body burden as a function of time after the acute intake is shown in Figure 8-2.

Figure 8-2. Lead-212 whole-body burden after an acute inhalation intake 

of Type S thorium having a 228Th to 232Th ratio of 0.19:1.

1 5 10 50 100 500 5000

1e-05 1e-03 1e-0

1 nCi Th-232 & 0.19 nCi Th-228

Time of Count (days)

Pb-212 Whole-Bo 

Exact (red)

Approx (blue)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 38 of 73

As shown above, the 212Pb body burden expressed in terms of intakes and IRFs is:

qt I m t I m t ( ) = th232 pbth232 th228 pbth228 ( ) + ( ) (8-7)

Applying the two approximations from Section 7.1 gives the following approximation to q:

qt I m t ′ ( ) = th228 th228 ( ) (8-8)

Example 8-2

For example, assume that a 212Pb whole-body burden of 1.5 nCi is observed at 100 days after an 

acute inhalation intake of this Type S thorium. Given a 228Th:232Th ratio of 0.19:1, the intake of 232Th 

is:

( ) ( )

( ) ( )( )

th232

pbth232 pbth228

1 5nCi

100 0 19 100

1 5nCi

4 130E-05 0 19 3 900E-02

2 013E+02nCi

. I

m . m

.

. ..

.

= +

= +

=

(8-9)

which translates into 0.19 × 201.3 nCi = 38.25 nCi of 228Th. As a conceptual check, it is useful to 

show that:

1 5nCi 201.3nCi 4 130E-05 38 25 3 900E-02 . = ( )( . .. ) + ( )( ) (8-10)

With the approximate method the intake of 228Th is:

( ) th228 = = =

th228

1 5nCi 1 5nCi 4 386E+01nCi

100 3.420E-02

. . I .

m

(8-11)

which translates into 43.86 nCi ÷ 0.19 = 230.8 nCi of 232Th.

The plot for Type M triple-separated thorium is shown in Figure 8-3. Other than the fact that there is 

faster clearance of the thorium from the chest, all of the discussion above is directly applicable to 

Type M material.
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 39 of 73

Figure 8-3. Lead-212 whole-body burden after an acute inhalation intake 

of Type M thorium having a 228Th to 232Th ratio of 0.19:1.

8.1.2 Adjustment of Thorium Intakes

As shown in Figures 8-1 to 8-3, for a given thorium intake, the approximate method will overestimate

the 212Pb whole-body burden for a length of time after the intake (~2 years for Type S material). 

Therefore, for a given 212Pb whole-body burden, the approximate method will underestimate the 

thorium intake for the same length of time. In Figures 8-4 and 8-5, an adjustment factors of 1/1.2 

(Type S) and 1/1.5 (Type M) are applied to the approximate 212Pb whole-body burdens to ensure that 

they do not overestimate the exact 212Pb whole-body burdens at times greater than 30 days after 

intake.

Figure 8-4. Lead-212 whole-body burden after an acute inhalation intake 

of Type S thorium having a 228Th to 232Th ratio of 0.19:1 with vertical 

dashed line at t = 30 days after intake.

1 5 10 50 100 500 5000

1e-04 1e-03 1e-02 1e-0

1 nCi Th-232 & 0.19 nCi Th-228

Time of Count (days)

Pb-212 Whole-Bo 

Exact (red)

Approx (blue)

1 5 10 50 100 500 5000

0.001 0.005 0.020 0.10

1 nCi Th-232 & 0.19 nCi Th-228

Time of Count (days)

Pb-212 Whole-Bo 

Exact (red)

Approx (blue)

Approx/1.2 (gold)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 40 of 73

Figure 8-5. Lead-212 whole-body burden after an acute inhalation intake 

of Type M thorium having a 228Th to 232Th ratio of 0.19:1 with vertical 

dashed line at t = 30 days after intake.

When using the approximate method to calculate thorium intakes from 212Pb whole-body burdens, the 

intake is multiplied by the appropriate adjustment factor to achieve the desired end of not 

underestimating the intake that would have been calculated using the exact method.

8.1.3 Guidance for Acute Intakes

Based on the discussion above, the following guidance is offered on how to use the approximate 

method to evaluate 212Pb whole-body count data after acute inhalation intakes of Type M or S thorium:

Assume a single measured 212Pb whole-body burden. Evaluate the whole-body burden with a Type M 

228Th biokinetic model in IMBA. Multiply the calculated 228Th intake by a factor of 1.5 and assign it as 

the intake of 228Th. Divide this estimated 228Th intake by the 228Th:

232Th ratio of 0.19:1 to obtain the 

232Th intake. For 212Pb whole-body burdens that were measured more than 30 days after an acute 

intake, these approximate intakes will not underestimate the Type M intakes that would be calculated 

with exact methods. For Type S thorium use a factor of 1.2 instead of 1.5.

8.2 CHRONIC INTAKES

The plot in Figure 8-6 shows the 212Pb whole-body burden as a function of time after a chronic intake 

of 1 nCi/d of 232Th and 0.19 nCi/d of 228Th (both being 5-μm AMAD Type S material). In other words, 

the time on the abscissa is the length of the time after the start of the chronic intake and the time that 

the whole-body burden is determined.

1 5 10 50 100 500 5000

0.001 0.005 0.020 0.100

1 nCi Th-232 & 0.19 nCi Th-228

Time of Count (days)

Pb-212 Whole-Bod 

Exact (red)

Approx (blue)

Approx/1.5 (gold)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 41 of 73

Figure 8-6. Lead-212 whole-body burden after a chronic inhalation intake 

of Type S thorium having a 228Th to 232Th ratio of 0.19:1.

The equations for chronic intakes are essentially the same as in the case of acute intakes except that 

the functions have an argument for the length of the constant chronic intake period. The exact wholebody burden q of 212Pb at t days after the start of a chronic inhalation intake over tc days is given by:

q t,t q t,t . q t,t t t ( c c cc ) = pbth232 ( ) + ≥ 0 19 pbth228 ( ) (8-12)

Applying the two approximations from Section 7.1 gives the following approximation to q:

q t,t q t,t ′ ( c c ) = th228 ( ) (8-13)

Example 8-3

For example, assume that a 212Pb whole-body burden of 1.5 nCi is observed at the end of a 365-day 

chronic inhalation intake of Type S triple-separated thorium. The exact total intake of 232Th is:

( ) ( )

( ) ( )( )

= +

= +

=

  th232

pbth232 pbth228

1 5nCi

365 365 0 19 365 365

1 5nCi

1681E-04 0 19 2.767E-02

2 765E+02nCi

. I

m , .m ,

.

. .

.

(8-14)

which translates into 0.19 × 276.7 nCi = 52.53 nCi of 228Th. This can be seen by rearranging the 

above equation:

1 5nCi 276 7nCi 1681E-04 52 53nCi 2.767E-02 . .. . = ( )( ) + ( )( ) (8-15)

The intake rates are obtained by dividing the intakes by tc = 365 days. With the approximate method 

the intake of 228Th is:

( ) ( ) = = =  th228

th228

1 5nCi 1 5nCi 4 440E+01nCi

365 365 3 378E-02

. . I .

m, .

(8-16)

5 10 20 50 100 200 500 1000 5000

0.01 0.05 0.50 5.00

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time of Count (days)

Pb-212 Whole-Bod 

Exact (red)

Approx (blue)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 42 of 73

which gives 44.40 nCi ÷ 0.19 = 233.7 nCi of 232Th. The plot for Type M triple-separated thorium is 

shown in Figure 8-7.

Figure 8-7. Lead-212 whole-body burden after a chronic inhalation intake 

of Type M thorium having a 228Th to 232Th ratio of 0.19:1.

8.2.1 Adjustment of Chronic Thorium Intakes

In Figures 8-8 to 8-13, the 212Pb whole-body burdens at various times during and after 365-, 1,000-, 

and 5,000-day constant chronic intakes are presented. As with the acute intakes, the approximate 

212Pb whole-body burdens are adjusted by a factor of 1/1.2 for Type S and 1/1.5 for Type M. This 

illustrates that intake rates that are calculated from 212Pb whole-body counts with the approximate 

method can be adjusted by the appropriate factor to ensure that the intake rates do not underestimate 

the intake rates that would be calculated with the exact method.

Figure 8-8. Lead-212 whole-body burden during and after a 365-day 

chronic inhalation intake of Type S thorium having a 228Th to 232Th ratio of 

0.19:1. The vertical dashed line is at t = 365 days.

5 10 20 50 100 200 500 1000 5000

0.01 0.05 0.50 5.00

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time of Count (days)

Pb-212 Whole-Bo 

Exact (red)

Approx (blue)

200 400 600 800 1000

0.5 1.0 1.5 2.5

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time of Count (days)

Pb-212 Whole-Bo 

Exact (red)

Approx (blue)

Approx/1.2 (gold)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 43 of 73

Figure 8-9. Lead-212 whole-body burden during and after a 1,000-day 

chronic inhalation intake of Type S thorium having a 228Th to 232Th ratio of 

0.19:1. The vertical dashed line is at t = 1,000 days.

Figure 8-10. Lead-212 whole-body burden during and after a 5,000-day 

chronic inhalation intake of Type S thorium having a 228Th to 232Th ratio of 

0.19:1. The vertical dashed line is at t = 5,000 days.

8.2.2 Guidance for Chronic Intakes

Based on the discussion above, the following guidance is offered on how to use the approximate 

method to evaluate 212Pb whole-body count data after constant chronic inhalation intakes of tripleseparated thorium:

Assume a single measured 212Pb whole-body burden. Evaluate the whole-body burden with a Type M 

228Th biokinetic model in IMBA. Multiply the calculated 228Th intake rate by a factor of 1.5 and assign 

it as the intake rate of 228Th. Divide this estimated 228Th intake rate by the 228Th:232Th ratio of 0.19:1 to 

obtain the 232Th intake rate. For chronic intakes longer than 1 year these approximate intakes will not 

underestimate the Type M intakes that would be calculated with exact methods. For Type S thorium 

use a factor of 1.2 instead of 1.5.

800 1000 1200 1400 1600 1800 2000

0.5 1.0 2.0 5.0

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time of Count (days)

Pb-212 Whole-Bo 

Exact (red)

Approx (blue)

Approx/1.2 (gold)

4000 4500 5000 5500 6000 6500 7000

0.5 1.0 2.0 5.0

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time of Count (days)

Pb-212 Whole-Bo 

Exact (red)

Approx (blue)

Approx/1.2 (gold)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 44 of 73

Figure 8-11. Lead-212 whole-body burden during and after a 365-day 

chronic inhalation intake of Type M thorium having a 228Th to 232Th ratio of 

0.19:1. The vertical dashed line is at t = 365 days.

Figure 8-12. Lead-212 whole-body burden during and after a 1,000-day 

chronic inhalation intake of Type M thorium having a 228Th to 232Th ratio of 

0.19:1. The vertical dashed line is at t = 1,000 days.

300 400 500 600 700 800 900

1 2

3

4

5

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time of Count (days)

Pb-212 Whole-Bod 

Exact (red)

Approx (blue)

Approx/1.5 (gold)

1000 1200 1400 1600 1800 2000

1 2

5 10

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time of Count (days)

Pb-212 Whole-Bod 

Exact (red)

Approx (blue)

Approx/1.5 (gold)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 45 of 73

Figure 8-13. Lead-212 whole-body burden during and after a 5,000-day 

chronic inhalation intake of Type M thorium having a 228Th to 232Th ratio of 

0.19:1. The vertical dashed line is at t = 5,000 days.

9.0 USING IMBA FOR TOTAL THORIUM IN URINE

This section discusses methods for adjustment of intakes and intake rates of 232Th and 228Th that are 

calculated with IMBA from total thorium (232Th + 228Th) measurements of urine samples so that the 

intakes and intake rates will not underestimate those that would be calculated with exact methods 

(i.e., using DCAL). These adjustments can be used when an overestimate of dose is appropriate. 

Best estimates of dose require the use of DCAL.

9.1 ACUTE INTAKES

Assume a mixture of 1 nCi of 232Th and 1 nCi of 228Th (both being 5-μm AMAD Type S material) was 

inhaled. The total thorium (henceforth referred to simply as “thorium”) in 24-hour incremental urine 

samples as a function of time after the acute intake is shown in Figure 9-1.

Figure 9-1. Thorium in 24-hour incremental urine samples after an acute 

inhalation intake of Type S thorium having a 228Th to 232Th ratio of 1:1.

4800 4900 5000 5100 5200 5300 5400 5500

2

5 10 20

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time of Count (days)

Pb-212 Whole-Bod 

Exact (red)

Approx (blue)

Approx/1.5 (gold)

1 5 10 50 100 500 5000

1e-07 5e-07 5e-06

1 nCi Th-232 & 1 nCi Th-228

Time After Intake (days)

Total Thorium in U 

Exact (red)

Approx (blue)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 46 of 73

The exact content q of thorium in the urine at t days after an acute inhalation intake is given by:

qt q t q t q t ( ) =+ + th232 thth232 th228 ( ) ( ) ( ) (9-1)

where qth232 is the amount of 232Th in the sample, qthth232 is the amount of 228Th in the sample that 

grows in from the inhaled 232Th, and qth228 is the amount of 228Th in the sample from the inhaled 228Th. 

These exact contents are calculated with DCAL, which accounts for independent kinetics of the 

thorium decay chain. The red excretion curve in Figure 9-1 was calculated using the exact method. 

An approximation that can be made here is that there is negligible ingrowth of 228Th from the 232Th 

component of the intake. That is:

q t thth232 ( ) = 0 {Approximation A} (9-2)

This gives the following approximation to q:

qt q t q t ′( ) = + th232 th228 ( ) ( ) (9-3)

where qth232 is the 232Th urine content and qth228 is the 228Th urine contents at time t, both of which can 

be calculated with IMBA. The blue excretion curve in Figure 9-1 was calculated using the 

approximate method. As seen in Figure 9-1, this approximation provides reasonably accurate 

estimates of the thorium urine content for a couple of years after the intake. At later times the 

approximate method underestimates the urinary excretion rate.

Example 9-1

For example, assume that 0.0015 nCi of thorium is observed in a 24-hour urine sample completed at 

100 days after an acute inhalation intake of this Type S thorium. Given a 228Th:232Th ratio of 1:1, the 

intake of 232Th is:

( ) ( ) ( ) th232

th232 thth232 th228

0 0015nCi

100 100 100

0 0015nCi

3 65E-07 4 64E-10 3 31E-07

2 154nCi

. I

mm m

.

...

,

= + +

= + +

=

(9-4)

which translates into 2,154 nCi of 228Th. These intakes can be checked by calculating the expected 

thorium urine content and determining if it equals the content from which the intakes were calculated:

0 0015nCi . Im Im Im =+ + th232 th232 (100) th232 thth232 (100) th228 th228 (100) (9-5)

0 0015nCi 2 154nCi 3 65E-07 2 154nCi 4 64E-10 2 154 . ,. ,. ,. =++ ( )( ) ( )( ) ( nCi 3 31E-07 )( ) (9-6)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 47 of 73

With the approximate method we have a 232Th intake of:

( ) ( ) th232

th232 th228

0 0015nCi

100 100

0 0015nCi

3 65E-07 3 31E-07

2 155nCi

. I

m m

.

. .

,

= +

= +

=

(9-7)

which translates into a 2,155 nCi intake of 228Th. From the equations above it should be evident that, 

for a given quantity of thorium in the urine, the approximate method will always give an intake that is 

greater than or equal to the intake from the exact method (this is reflected in Figure 9-1). Further, this 

is true regardless of the 228Th:232Th ratio, dissolution type (M or S), or exposure pattern (acute or 

chronic).

9.1.1 Triple-Separated Thorium Mixture

As noted in Section 3.0, triple-separated thorium has a 228Th:232Th ratio of 0.19:1. Assume a mixture 

of 1 nCi of 232Th and 0.19 nCi of 228Th (both being 5-μm AMAD Type S material) was inhaled. The 

thorium urine content as a function of time after the acute intake is shown in Figure 9-2.

Figure 9-2. Thorium urine content after an acute inhalation intake of Type 

S thorium having a 228Th to 232Th ratio of 0.19:1.

1 5 10 50 100 500 5000

1e-07 5e-07 2e-06 1e-05

1 nCi Th-232 & 0.19 nCi Th-228

Time After Intake (days)

Total Thorium in 

Exact (red)

Approx A (blue)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 48 of 73

Example 9-2

For example, assume that 0.0015 nCi of thorium is observed in a 24-hour urine sample completed at 

100 days after an acute inhalation intake of this Type S thorium. Given a 228Th:232Th ratio of 0.19:1, 

the intake of 232Th is:

( ) ( ) ( )

( )( )

th232

th232 thth232 th228

0 0015nCi

100 100 0 19 100

0 0015nCi

3 65E-07 4 64E-10 0 19 3 31E-07

3 502nCi

. I

m m . m

.

. . ..

,

= + +

= + +

=

(9-8)

which translates into 665 nCi of 228Th. These intakes can be checked by calculating the expected 

thorium urine content and seeing if it equals the content from which the intakes were calculated:

( )( ) ( )( )

( )( )( )

0 0015nCi 3 502nCi 3 65E-07 3 502nCi 4 64E-10

0 19 3 502nCi 3 31E-07

. ,. ,.

., .

= +

+

(9-9)

With the approximate method we have a 232Th intake of:

( ) ( )

( )( )

th232

th232 th228

0 0015nCi

100 0 19 100

0 0015nCi

3 65E-07 0 19 3 31E-07

3 506nCi

. I

m .m

.

. ..

,

= +

= +

=

(9-10)

which translates into a 666 nCi intake of 228Th.

9.1.2 An Additional Approximation

The approximation above will provide an estimate of the intake that will not be less than the intake 

that would be calculated with the exact method regardless of the dissolution type or exposure pattern. 

However, in practice this approximation is cumbersome to use in IMBA because it requires calculation 

of intakes of two different radionuclides (232Th and 228Th), a task that requires two computational runs. 

An additional simplifying approximation that can be used with triple-separated thorium is to use the 

232Th urinary excretion function in place of the 228Th function:

q tq t th228 th232 ( ) = ( ) {Approximation B} (9-11)

which gives:

qt q t . q t ′′( ) = + th232 ( ) 0 19 th232 ( ) (9-12)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 49 of 73

This approximation is shown in Figure 9-3 as the gold curve, which partially obscures the exact (red) 

curve. Applying Approximations A and B gives a 232Th intake of:

( ) ( ) ( ) th232

th232 th232 th232

0 0015nCi 0 0015nCi

100 0 19 100 1 19 100

. . I

m .m .m = = +

(9-13)

( )( ) ( )( ) = = = + 232

0 0015nCi 0 0015nCi 3 453nCi

3 65E-07 0 19 3 65E-07 1 19 3 65E-07 th

. . I , . .. .. (9-14)

which translates into a 656-nCi intake of 228Th. These approximations provide intake estimates for 

Type S material that are within ±5% of the exact intake for the periods studied here (i.e., less than 

4,000 days).

As shown in Figure 9-4, there is a maximum nonconservative discrepancy on the order of 12% when 

Approximations A and B are applied to Type M thorium. To adjust for these underestimates, 232Th 

intakes that are calculated with Approximations A and B are multiplied by a factor of 1.15. However, 

the ratio of 1.15:1.19 can be rounded up to 1, a conservative approximation that allows us to simplify 

the guidance even further:

th232 th232

1 15

1 19

. I I .

  =     {Approximation C} (9-15)

9.1.3 Guidance for Acute Intakes

Based on the discussion above, the following guidance could be offered on how to use the 

approximate method to evaluate thorium urine bioassay measurements after acute inhalation intakes 

of Type M or S thorium:

Assume a single measured thorium urine bioassay result. Evaluate the result with a 232Th biokinetic 

model in IMBA to obtain an estimate of the 232Th intake. Multiply this estimate of the 232Th intake by 

the 228Th:232Th ratio of 0.19:1 to obtain the estimate of the 228Th intake. These approximate intakes will 

not underestimate the intakes that would be calculated with exact methods.
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 50 of 73

Figure 9-3. Thorium urine content after an acute inhalation intake of Type 

S thorium having a 228Th to 232Th ratio of 0.19:1 showing excretion with 

Approximation A (blue line) and with Approximations A and B (gold line).

Figure 9-4. Thorium urine content after an acute inhalation intake of Type 

M thorium having a 228Th to 232Th ratio of 0.19:1 showing excretion with 

Approximation A (blue line) and with Approximations A and B (gold line).

9.2 CHRONIC INTAKES

The plot in Figure 9-5 shows the thorium content of a 24-hour incremental urine sample as a function 

of time after a chronic intake of 1 nCi/d of 232Th and 0.19 nCi/d of 228Th (both being 5-μm AMAD 

Type S material). The time on the abscissa is the length of time after the start of the chronic intake 

that the urine sample was completed. The actual length of the chronic intake is 1 day less than the 

day the urine sample was completed (i.e., urine samples are not collected while the individual is being 

exposed).

1 5 10 50 100 500 5000

1e-07 5e-07 2e-06 1e-05

1 nCi Th-232 & 0.19 nCi Th-228

Time After Intake (days)

Total Thorium in U 

Exact (red)

Approx A (blue)

Approx A&B (gold)

1 5 10 50 100 500 5000

1e-06 1e-05 1e-04 1e-03

1 nCi Th-232 & 0.19 nCi Th-228

Time After Intake (days)

Total Thorium in U 

Exact (red)

Approx A (blue)

Approx A&B (gold)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 51 of 73

Figure 9-5. Thorium urine content after a chronic inhalation intake of Type 

S thorium having a 228Th to 232Th ratio of 0.19:1.

The equations for chronic intakes are essentially the same as in the case of acute intakes except that 

the functions have an argument for the length of the constant chronic intake period. The exact 

thorium content q of a 24-hour urine sample completed at t days after the start of a chronic inhalation 

intake over tc days is given by:

q t,t q t,t q t,t q t,t t t ( c c ccc ) = + + th232 ( ) thth232 ( ) th228 ( ) { ≥ + 1} (9-16)

Applying Approximation A gives the following:

q t,t q t,t q t,t t t ( c ccc ) = + th232 ( ) th228 ( ) { ≥ + 1} (9-17)

In terms of intakes and IRFs:

q t,t I m t,t I m t,t I m t,t t t ( c c c cc ) = th232 th232   ( ) + th232 thth232 ( ) + th228 th228 ( ) { ≥ + 1} (9-18)

and:

q t,t I m t,t I m t,t t t ( c c cc ) = th232 th232   ( ) + th228 th228 ( ) { ≥ + 1} (9-19)

Example 9-3

For example, assume that 0.0015 nCi of thorium is observed in a 24-hour urine sample completed on 

day 366 after a 365-day chronic inhalation intake of Type S triple-separated thorium. Given a 228Th: 

232Th intake ratio of 0.19:1, the total intake of 232Th is:

( ) ( ) ( )

( )( )

th232

th232 thth232 th228

0 0015nCi

366 365 366 365 0 19 366 365

0 0015nCi

4 006E-07 1657E-09 0 19 3 500E-07

3 200nCi

. I

m , m , .m ,

.

. . ..

,

= + +

= + +

=

 

(9-20)

5 10 20 50 100 200 500 1000 5000

5e-05 2e-04 1e-0

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time Urine Sample Completed (days)

Total Thorium in U 

Exact (red)

Approx (blue)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 52 of 73

which translates into 0.19 × 3,200 nCi = 608 nCi of 228Th. This can be verified as accomplished 

before by using the intakes to calculate the 228Th content of the urine sample:

0 0015nCi 3 200nCi 4 006E-07 3200nCi 1 657E-09 60 . ,. = ++ ( )( ) ( )( . ) ( 8nCi 3 500E-07 )( . ) (9-21)

The intake rates are obtained by dividing the intakes by tc = 365 days. With the application of 

Approximation A the intake of 232Th is:

( ) ( )

( )( )

= +

= +

=

  th232

th232 th228

0 0015nCi

366 365 0 19 366 365

0 0015nCi

4 006E-07 0 19 3 500E-07

3 212nCi

. I

m , .m ,

.

. ..

,

(9-22)

which translates into a 610 nCi intake of 228Th.

Figures 9-6 to 9-9 show the thorium urinary excretion curves for chronic intakes of Type M and S 

triple-separated thorium. The 15% intake adjustment applied in the acute intake case above is 

adequate to make chronic intake rates that are estimated with Approximations A and B not 

underestimate the intake rates that would be calculated with the exact method. For example, the 

232Th intake that was calculated with Approximations A, B, and C is:

( ) th232

th232

0 0015nCi 0 0015nCi 3 745nCi

365 365 4 006E-07

. . I ,

m,. = = =  (9-23)

The 228Th intake is 712 nCi.

Figure 9-6. Thorium urine content after a 365-day chronic inhalation 

intake of Type S thorium having a 228Th to 232Th ratio of 0.19:1. The blue 

line is the excretion with Approximation A and the gold line is the excretion 

with Approximations A and B.

5 10 20 50 100 200 500 1000 5000

2e-05 5e-05 1e-04

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time Urine Sample Completed (days)

Total Thorium in 

Exact (red)

Approx A (blue)

Approx A&B (gold)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 53 of 73

Figure 9-7. Thorium urine content after a 1,000-day chronic inhalation 

intake of Type S thorium having a 228Th to 232Th ratio of 0.19:1. The blue 

line is the excretion with Approximation A and the gold line is the excretion 

with Approximations A and B.

9.2.1 Guidance for Chronic Intakes

Based on the discussion above, the following guidance is offered on how to use the approximate 

method to evaluate thorium urine bioassay measurements after constant chronic inhalation intakes of 

Type M or S thorium:

Assume a single measured thorium urine bioassay result. Evaluate the result with a 232Th biokinetic 

model in IMBA to obtain an estimate of the 232Th intake rate. Multiply this estimate of the 232Th intake 

rate by the 228Th:

232Th ratio of 0.19:1 to obtain the estimate of the 228Th intake rate. These 

approximate intake rates will not underestimate the intake rates that would be calculated with exact 

methods.

Figure 9-8. Thorium urine content after a 365-day chronic inhalation 

intake of Type M thorium having a 228Th to 232Th ratio of 0.19:1. The blue 

line is the excretion with Approximation A and the gold line is the excretion 

with Approximations A and B.

5 10 20 50 100 200 500 1000 5000

2e-05 5e-05 2e-04

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time Urine Sample Completed (days)

Total Thorium in U 

Exact (red)

Approx A (blue)

Approx A&B (gold)

5 10 20 50 100 200 500 1000 5000

5e-04 2e-03 5e-0

 

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time Urine Sample Completed (days)

Total Thorium i 

Exact (red)

Approx A (blue)

Approx A&B (gold)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 54 of 73

Figure 9-9. Thorium urine content after a 1,000-day chronic inhalation 

intake of Type M thorium having a 228Th to 232Th ratio of 0.19:1. The blue 

line is the excretion with Approximation A and the gold line is the excretion 

with Approximations A and B.

10.0 USING IMBA FOR THORIUM-228 IN URINE

This section discusses adjustments to intakes and intake rates of 232Th and 228Th that are calculated 

with IMBA from 228Th that is measured in urine samples so that the intakes and intake rates will not 

underestimate those that would be calculated with exact methods (DCAL). These adjustments may 

be used when an overestimate of dose is appropriate. Best estimates of dose require the use of 

DCAL.

10.1 ACUTE INTAKES

Assume a mixture of 1 nCi of 232Th and 1 nCi of 228Th (both being 5-μm AMAD Type S material) was 

inhaled. The 228Th in 24-hour incremental urine samples as a function of time after the acute intake is 

shown in Figure 10-1.

Figure 10-1. Thorium-228 in 24-hour incremental urine samples after an 

acute inhalation intake of Type S thorium having a 228Th to 232Th ratio of 

1:1.

5 10 20 50 100 200 500 1000 5000

0.001 0.002 0.004

yp p p 

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time Urine Sample Completed (days)

Total Thorium in 

Exact (red)

Approx A (blue)

Approx A&B (gold)

1 5 10 50 100 500 5000

5e-09 1e-07 5e-06

1 nCi Th-232 & 1 nCi Th-228

Time After Intake (days)

Th-228 in Urine (

Exact (red)

Approx (blue)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 55 of 73

The exact content q of 228Th in the urine at t days after an acute inhalation intake is given by:

( ) ( ) ( )

( ) ( )

thth232 th228

th232 thth232 th228 th228

qt q t q t

I m tI m t

= +

= +

(10-1)

where qthth232 is the amount of 228Th in the sample that grows in from the inhaled 232Th and qth228 is the 

amount of 228Th in the sample from the inhaled 228Th. These exact contents are calculated with 

DCAL, which accounts for independent kinetics of the thorium decay chain and the loss of 220Rn. The 

red excretion curve in Figure 10-1 was calculated using the exact method. An approximation that can 

be made here is that there is negligible ingrowth of 228Th from the 232Th component of the intake. That 

is:

q t thth232 ( ) = 0 (10-2)

This gives the following approximation to q:

qt q t ′( ) = th228 ( ) (10-3)

where qth228 is the 228Th urine content at time t (which can be calculated with IMBA). The blue 

excretion curve in Figure 10-1 was calculated using the approximate method. As seen in the plot 

above, this approximation provides reasonably accurate estimates of the 228Th urine content for a 

couple of years after the intake. At later times the approximate method underestimates the urinary 

excretion rate.

Example 10-1

For example, assume that 0.0015 nCi of 228Th is observed in a 24-hour urine sample completed at 

100 days after an acute inhalation intake of this Type S thorium. Given a 228Th:232Th ratio of 1: 1, the 

intake of 232Th is:

( ) ( ) th232

thth232 th228

0 0015nCi

100 100

0 0015nCi

4.64E-10 3.31E-07

4 525nCi

. I

m m

.

,

= +

= +

=

(10-4)

which translates into 4,525 nCi of 228Th. These intakes can be checked by calculating the expected 

228Th urine content and determining if it equals the content from which the intakes were calculated:

0 0015nCi 4 525nCi 4.64E-10 4,525nCi 3.31E-07 . , = ( )( ) + ( )( ) (10-5)

With the approximate method we have a 228Th intake of:

( ) th228

th228

0 0015nCi 0 0015nCi 4,532nCi 100 3.31E-07. . I

m= = = (10-6)

which translates into a 4,532-nCi intake of 232Th. From the equations given above it should be evident 

that, for a given quantity of 228Th in the urine, the approximate method will always give an intake that 
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 56 of 73

is greater than or equal to the intake from the exact method (this is reflected in Figure 10-1). Further, 

this is true regardless of the 228Th:232Th ratio, dissolution type (M or S), or exposure pattern (acute or 

chronic).

10.1.1 Triple-Separated Thorium Mixture

Assume a mixture of 1 nCi of 232Th and 0.19 nCi of 228Th (both being 5-μm AMAD Type S material) 

was inhaled. The 228Th urine content as a function of time after the acute intake is shown in 

Figure 10-2.

Figure 10-2. Thorium-228 urine content after an acute inhalation intake of 

Type S thorium having a 228Th to 232Th ratio of 0.19:1.

The exact content q of 228Th in the urine at t days after an acute inhalation intake is given by:

qt q t q t ( ) = + thth232 th228 ( ) ( ) (10-7)

The approximation to q is:

qt q t ′( ) = th228 ( ) (10-8)

In terms of intakes and IRFs:

qt I m t I m t ( ) = th232 thth232 th228 th228 ( ) + ( ) (10-9)

qt I m t ′( ) = th228 th228 ( ) (10-10)

1 5 10 50 100 500 5000

5e-10 1e-08 5e-07

1 nCi Th-232 & 0.19 nCi Th-228

Time After Intake (days)

Th-228 in Urine (n

Exact (red)

Approx (blue)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 57 of 73

Example 10-2

For example, assume that 0.0015 nCi of 228Th is observed in a 24-hour urine sample completed at 

100 days after an acute inhalation intake of this Type S thorium. Given a 228Th:232Th ratio of 0.19:1, 

the intake of 232Th is:

( ) ( )

( )( )

th232

thth232 th228

0 0015nCi

100 0 19 100

0 0015nCi

4 64E-10 0 19 3.31E-07

23,676nCi

. I

m . m

.

. .

= +

= +

=

(10-11)

which translates into 4,499 nCi of 228Th. These intakes can be checked by calculating the expected 

228Th urine content and determining if it equals the content from which the intakes were calculated:

0 0015nCi 23 676nCi 4 64E-10 4 499nCi 3 31E-07 . ,. ,. = ( )( ) + ( )( ) (10-12)

With the approximate method we have a 228Th intake of:

( ) th228

th228

0 0015nCi 0 0015nCi 4 532nCi

100 3.31E-07

. . I ,

m= = = (10-13)

which translates into 4,532 nCi ÷ 0.19 = 23,851 nCi of 232Th intake.

10.1.2 Guidance for Acute Intakes

Based on discussion given above, the following guidance is offered on how to use the approximate 

method to evaluate 228Th urine bioassay measurements after acute inhalation intakes of Type M or S 

thorium:

Assume a single measured 228Th urine bioassay result. Evaluate the result with a 228Th biokinetic 

model in IMBA and assign it as the intake of 228Th. Divide this estimated 228Th intake by the 

228Th:232Th ratio of 0.19:1 to obtain the 232Th intake. These approximate intakes will not underestimate 

the intakes that would be calculated with exact methods.

10.2 CHRONIC INTAKES

The plot in Figure 10-3 shows the 228Th content of a 24-hour incremental urine sample as a function of 

time after a chronic intake of 1 nCi/d of 232Th and 0.19 nCi/d of 228Th (both being 5-μm AMAD Type S 

material). The time on the abscissa is the length of time after the start of the chronic intake that the 

urine sample was completed. The actual length of the chronic intake is 1 day less than the day the 

urine sample was completed (i.e., urine samples are not collected while the individual is being 

exposed).
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 58 of 73

Figure 10-3. Thorium-228 urine content after a chronic inhalation intake 

of Type S thorium having a 228Th to 232Th ratio of 0.19:1.

The equations for chronic intakes are essentially the same as in the case of acute intakes except that 

the functions have an argument for the length of the constant chronic intake period. The exact 228Th 

content q of a 24-hour urine sample completed at t days after the start of a chronic inhalation intake 

over tc days is given by:

q t,t q t,t q t,t t t ( c ccc ) = + thth232 ( ) th228 ( ) { ≥ + 1} (10-14)

Applying the approximation gives the following:

q t,t q t,t ′ ( c c ) = th228 ( ) (10-15)

In terms of intakes and IRFs:

q t,t I m t,t I m t,t ( c cc ) = th232 thth232 ( ) + th228 th228 ( )   (10-16)

qt I m t ′( ) = th228 th228 ( ) (10-17)

Example 10-3

For example, assume that 0.0015 nCi of 228Th is observed in a 24-hour urine sample completed on 

day 366 after a 365-day chronic inhalation intake of Type S triple-separated thorium. Given a 

228Th:232Th ratio of 0.19:1, the total intake of 232Th is:

( ) ( )

( )( )

th232

thth232 th228

0 0015nCi

366 365 0 19 366 365

0 0015nCi

1657E-09 0 19 3 500E-07

22 007 nCi

. I

m , .m ,

.

. ..

,

= +

= +

=

 

(10-18)

5 10 20 50 100 200 500 1000 5000

5e-06 2e-05 1e-04

1 nCi/day Th-232 & 0.19 nCi/day Th-22

Time Urine Sample Completed (days)

Th-228 in Urine 

Exact (red)

Approx (blue)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 59 of 73

which translates into 0.19 × 22,007 nCi = 4,181 nCi of 228Th. This can be verified as accomplished 

before by using the intakes to calculate the 228Th content of the urine sample:

0 0015nCi 22 007nCi 1 657E-09 4 181nCi 3 500E-07 . ,. ,. = ( )( ) + ( )( ) (10-19)

The intake rates are obtained by dividing the intakes by tc = 365 days. With the approximate method 

the intake of 228Th is:

( )

( )

=

=

=

 th228

th228

0 0015nCi

365 365

0 0015nCi

3 500E-07

4 286nCi

. I

m ,

.

.

,

(10-20)

which gives 4,286 nCi ÷ 0.19 = 22,556 nCi of 232Th.

10.2.1 Guidance for Chronic Intakes

Based on discussion above, the following guidance is offered on how to use the approximate method 

to evaluate 228Th urine bioassay measurements after constant chronic inhalation intakes of Type M or 

S thorium:

Assume a single measured 228Th urine bioassay result. Evaluate the result with a 228Th biokinetic 

model in IMBA and assign it as the intake rate of 228Th. Divide this estimated 228Th intake rate by the 

228Th:232Th ratio of 0.19:1 to obtain the 232Th intake rate. These approximate intake rates will not 

underestimate the intake rates that would be calculated with exact methods.

11.0 ATTRIBUTIONS AND ANNOTATIONS

All information requiring identification was addressed via references integrated into the reference 

section of this document.
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 60 of 73

REFERENCES

ICRP (International Commission on Radiological Protection, 1979–1988, Limits for Intakes of 

Radionuclides by Workers, Publication 30, Parts 1–4 and Supplements, Pergamon Press, 

Oxford England. [SRDB Ref ID: 22733]

ICRP (International Commission on Radiological Protection, 1995, Dose Coefficients for Intakes of 

Radionuclides by Workers, Publication 68, Pergamon Press, Oxford England. [SRDB Ref ID: 

22731]
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 61 of 73

ATTACHMENT A

STANDARD THORIUM MIXTURES

LIST OF TABLES

TABLE TITLE PAGE

A-1 Ratios of 228Th to 232Th activities for secular equilibrium and after one, two, and three 

chemical separations .............................................................................................................65

A-2 Relative amounts of 232Th, 228Ra, and 228Th in single separated thorium as a function of 

time since separation .............................................................................................................66

LIST OF FIGURES

FIGURES TITLE PAGE

A-1 Thorium232 and 228Th present as a function of time after separation of thorium from 

other elements in the decay chain.......................................................................................... 62

A-2 Thorium-232, 228Ra, and 224Ra present after separation of thorium from other elements 

in the decay chain ..................................................................................................................63

A-3 Thorium-232 and 228Th present as a function of time after a second separation of 

thorium from other elements in the decay chain ..................................................................... 63

A-4 Thorium-232, 228Ra, and 224Ra present as a function of time after a second separation 

of thorium from other elements in the decay chain ................................................................. 64

A-5 Thorium232 and 228Th present as a function of time after a third separation of thorium 

from other elements in the decay chain.................................................................................. 64

A-6 Thorium-232, 228Ra, and 224Ra present as a function of time after a third separation of 

thorium from other elements in the decay chain ..................................................................... 65
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 62 of 73

ATTACHMENT A

STANDARD THORIUM MIXTURES (continued)

To accurately evaluate a 212Pb or 228Ac chest count in terms of an intake of thorium, the relative 

amounts of 232Th, 228Ra, and 228Th in the inhaled material have to be known. In certain cases a 

mixture of radionuclides can be specified that will provide a conservative estimate of the intake. 

These standard thorium mixtures are defined in this attachment.

Assume 1 Bq of 232Th in equilibrium with all of its progeny chemically stripped of everything except for 

the 232Th and 228Th. The time at which this occurs is referred to as t = 0 years. The activity of 228Th 

that is present in the source at various times after t = 0 years is shown in Figure A-1 (the activity of 

232Th is constant at 1 Bq). The 228Th activity hits a minimum of 0.42 Bq at 4.55 years.

Figure A-1. Thorium-232 and 228Th present as a function of time after 

separation of thorium from other elements in the decay chain. At the time 

of separation all members of the decay chain were in equilibrium with the 

232Th.

For all practical applications 224Ra, with a half-life of 3.66 days, is always in secular equilibrium with 

228Th. However, 228Ra, with its half-life of 5.75 years is depleted and takes years to grow back to any 

significant degree. These progeny are important because 212Pb (which can be measured in vivo) is in 

secular equilibrium with the 224Ra (which cannot be measured in vivo) and 228Ac (which can be 

measured in vivo) is in secular equilibrium with the 228Ra (which cannot be measured in vivo). The 

ingrowth curves for 224Ra and 228Ra are shown in Figure A-2. The minimum in the 224Ra curve 

coincides with the minimum in the 228Th curve.

If there is a second separation at 4.55 years after the first, the thorium will have the 228Th ingrowth 

curve shown in Figure A-3, which has a minimum of 0.26 Bq at 2.54 years after the second separation 

(or 2.54 + 4.55 = 7.09 years after the first separation).

The corresponding 224Ra and 228Ra curves after the second separation are shown in Figure A-4.

If there is a third separation at 7.09 years after the first, the thorium will have the 228Th ingrowth curve 

shown in Figure A-5, which has a minimum of 0.19 Bq at 1.75 years after the third separation (or 1.75 

+ 2.54 + 4.55 = 8.84 years after the first separation).

0 5 10 15 20

0.1

1

Th228

Th-228 Present After Separation

Time (years)

Th-228 (Bq)
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ATTACHMENT A

STANDARD THORIUM MIXTURES (continued)

The corresponding 224Ra and 228Ra curves after the third separation are shown in Figure A-6.

Figure A-2. Thorium-232, 228Ra, and 224Ra present after separation of 

thorium from other elements in the decay chain. At the time of separation 

all members of the decay chain were in equilibrium with the 232Th.

Figure A-3. Thorium-232 and 228Th present as a function of time after a 

second separation of thorium from other elements in the decay chain. At 

the time of separation 4.55 years had elapsed since the first separation.

0 5 10 15 20

0.1

1

Ra224

Ra228

Ra-228 & 224 Present After Separation

Time (years)

Activity (Bq)

0 5 10 15 20

0.1

1

Th228

Th-228 Present After Separation

Time (years)

Th-228 (Bq)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 64 of 73

ATTACHMENT A

STANDARD THORIUM MIXTURES (continued)

Figure A-4. Thorium-232, 228Ra, and 224Ra present as a function of time

after a second separation of thorium from other elements in the decay 

chain. At the time of separation 4.55 years had elapsed since the first 

separation.

Figure A-5. Thorium-232 and 228Th present as a function of time after a 

third separation of thorium from other elements in the decay chain. At the 

time of separation 7.086 years had elapsed since the first separation.

0 5 10 15 20

0.1

1

Ra224

Ra228

Ra-228 & 224 Present After Separation

Time (years)

Activity (Bq)

0 5 10 15 20

0.1

1

Th228

Th-228 Present After Separation

Time (years)

Th-228 (Bq)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 65 of 73

ATTACHMENT A

STANDARD THORIUM MIXTURES (continued)

Figure A-6. Thorium-232, 228Ra, and 224Ra present as a function of time

after a third separation of thorium from other elements in the decay 

chain. At the time of separation 7.086 years had elapsed since the first 

separation.

These data are summarized in Table A-1. The ratio of 228Th activity to 232Th activity is shown for the 

cases of secular equilibrium (no chemical separation), a single chemical separation at t = 0 years, a 

second chemical separation at t = 4.550 years, and a third chemical separation at t = 7.086 years. 

Note that these chemical separations are timed to produce the greatest possible reduction of the 

228Th/232Th ratio.

Table A-1. Ratios of 228Th to 232Th activities for secular equilibrium 

and after one, two, and three chemical separations.

Time

(yr)

No separations

Th-228

(nCi/nCi 232Th)

One 

separation

Th-228

(nCi/nCi 232Th)

Two 

separations

Th-228

(nCi/nCi 232Th)

Three 

separations

Th-228

(nCi/nCi 232Th)

0.000 1.000 1.0000 1.0000 1.0000

4.550 1.000 0.4221 0.4221 0.4221

7.086 1.000 0.4771 0.2633 0.2633

8.840 1.000 0.5446 0.3010 0.1905

Therefore, the standard thorium mixtures are:

• Unseparated (equilibrium) thorium, which has a 1:1 228Th to 232Th ratio;

• Single-separated thorium, which has a 0.42:1 228Th to 232Th ratio;

• Double-separated thorium, which has a 0.26:1 228Th to 232Th ratio; and

• Triple-separated thorium, which has a 0.19:1 228Th to 232Th ratio.

0 5 10 15 20

0.1

1

Ra224

Ra228

Ra-228 & 224 Present After Separation

Time (years)

Activity (Bq)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 66 of 73

ATTACHMENT A

STANDARD THORIUM MIXTURES (continued)

Note that there is no 228Ra in these standard mixtures and that once a mixture is selected for a 

particular application it is assumed to be a constant and does not change as a function of time. For 

example, if triple-separated thorium is chosen for a facility during 1980 then the same mixture applies 

in 1995; that is, there is no ingrowth of 228Th during the 15 years.

The standard thorium mixtures give conservative 228Th to 232Th ratios that are independent of the age 

of the thorium. This means that to evaluate a 212Pb chest count we have to specify the number of 

separations the material has gone through but not the time since separation (i.e., the age of the 

thorium). To evaluate an 228Ac chest count the age of the standard thorium mixture has to be 

specified because the quantity of parent 228Ra present is a strong function of the age of the thorium 

and an age that results in useful, conservative intake estimates cannot be specified. Relative 

quantities of 232Th, 228Ra, and 228Th present in single separated thorium (which is the most 

conservative mixture for evaluating 228Ac chest counts) as a function of time since separation are 

presented in Table A-2. In practice, one would specify the date that thorium separation activities 

ended at a given site and the minimum elapsed time between this date and the dates of the chest 

counts. The activity ratios for that elapsed time would be used to evaluate all 228Ac chest counts.

 Table A-2. Relative amounts of 232Th, 228

 Ra, and 228Th in single separated thorium 

 as a function of time since separation.

Years Th-232 Ra228 Th228

0.5 1.000 0.058 0.839

1.0 1.000 0.114 0.715

2.0 1.000 0.214 0.548

3.0 1.000 0.303 0.461

4.0 1.000 0.383 0.426

5.0 1.000 0.453 0.425

6.0 1.000 0.515 0.443

7.0 1.000 0.570 0.474

8.0 1.000 0.619 0.511

9.0 1.000 0.662 0.551

10.0 1.000 0.700 0.591

11.0 1.000 0.734 0.630

12.0 1.000 0.765 0.667

13.0 1.000 0.791 0.701

14.0 1.000 0.815 0.732

15.0 1.000 0.836 0.761

16.0 1.000 0.855 0.787

17.0 1.000 0.871 0.810

18.0 1.000 0.886 0.831

19.0 1.000 0.899 0.850

20.0 1.000 0.910 0.867

 
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 67 of 73

ATTACHMENT B

OBTAINING CHRONIC INTAKE IRFs FROM ACUTE INTAKE IRFs

LIST OF FIGURES

FIGURES TITLE PAGE

B-1 Plot of whole-body retention versus time after an acute uptake of the hypothetical 

radioactive material................................................................................................................68

B-2 Plot of whole-body retention versus time for a constant chronic uptake.................................. 70
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 68 of 73

ATTACHMENT B

OBTAINING CHRONIC INTAKE IRFs FROM ACUTE INTAKE IRFs (continued)

DCAL can provide acute intake IRFs but not chronic intake IRFs. However, this is not a major 

problem because a convolution integral can be used to calculate chronic intake IRFs from values of 

the acute intake IRFs.

To illustrate the technique, assume that the fractional retention of the hypothetical radioactive 

material6 in the whole body (the intake retention function or IRF) after an acute instantaneous uptake 

to the bloodstream is described by the following equation:

( ) ln(2) exp 10d

m t t   = −   

(B-1)

A plot of the whole-body retention after a unit uptake is shown in Figure B-1, where q(t) is the content 

of the whole body at t days after the uptake.

Figure B-1. Plot of whole-body retention versus time after an acute 

uptake of the hypothetical radioactive material.

 6 A biological half-life of 11.25 days is combined with a radiological half-life of 90 days to produce the effective half-life of 

10 days used here.

0 5 10 15 20 25 30

0.0 0.2 0.4 0.6 0.8 1.0

Time

Whole Body Content q(t)
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 69 of 73

ATTACHMENT B

OBTAINING CHRONIC INTAKE IRFs FROM ACUTE INTAKE IRFs (continued)

The IRF is typically used to calculate an acute intake I from the measured whole-body content (i.e., 

the bioassay result). For example, if the whole-body content is measured to be 100 Bq at 25 days 

after the acute intake, the intake is estimated to be:

( )

( )

25d 100Bq 566Bq 25d ln(2) exp 25d 10d

q I

m= = =  

−   

(B-2)

To do the same sort of calculation for a constant chronic intake, given only the acute intake IRFs and 

the measured whole-body content, assume the following variables and constants, which are used to 

construct the plot of the predicted whole-body retention versus time:

T = length of chronic intake period = 15 days

t = time that q(t) is measured relative to start of chronic intake = 25 days

τ = variable time in days

dτ = infinitesimally short time increment in days

İ = the unit intake rate = 1 Bq/d

I = İT = the total intake = 15 Bq

The convolution integral7 for the curve in Figure B-2 is:

( ) ( )

0

τ T

τ

τ

q t Id m t τ

=

=

=    − ∫     (B-3)

Note that İdτ is an infinitesimally small intake at time τ and that m(t – τ) is the acute retention function 

for that intake. Summing up all the infinitesimally small intakes from time 0 days to time T days gives 

the content of the whole body at t days resulting from the chronic intake.

To solve the integral, first change variables:

τ

x t τ

t x τ

dx d

= −

= +

= −

(B-4)

Then express the lower and upper limits in terms of the new variables:

τ tx 0

x t

= = −

= lower limit (B-5)

τTtx

xtT

= = −

= − upper limit (B-6)

 7 Note that the IRF must include radiological removal (i.e., the stable element IRF cannot be used here).
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 70 of 73

ATTACHMENT B

OBTAINING CHRONIC INTAKE IRFs FROM ACUTE INTAKE IRFs (continued)

Figure B-2. Plot of whole-body retention versus time for a constant 

chronic uptake.

This gives the following integral:

( ) ( )

xtT

x t

q t Idx m x

= −

=

= −   ∫     (B-7)

Pulling the constant intake rate outside of the integral and reversing the limits puts the integral in a 

form more suitable for solving:

( ) ( )

x t

xtT

q t I m x dx

=

= −

= ∫  (B-8)

This can in turn be rearranged to give:

( )

( ) 1 x t

xtT

q t I

m x dx

T

=

= −

=

∫

(B-9)

0 5 10 15 20 25 30

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Time

Whole Body Content q(t)

 T t

d
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 71 of 73

ATTACHMENT B

OBTAINING CHRONIC INTAKE IRFs FROM ACUTE INTAKE IRFs (continued)

or:

( )

( )

q t I

m t,T =  (B-10)

where:

( ) ( ) 1 x t

xtT

m t,T m x dx T

=

= −

= ∫  (B-11)

is the chronic intake retention function. For the simple example given here the integral can be solved 

analytically:

( )

25d

10 d

1 ln(2) 10d 25d exp 0.3108667

15d 10d m , x dx    = −=       ∫  (B-12)

Once again assuming q(25 d) = 100 Bq:

( )

( )

100Bq 322Bq 0.3108667

q t I

m t,T = = =  (B-13)

DCAL generates tables of acute IRFs for a range of times. These tabulated values are used to create 

an interpolation function that gives the value of the IRF for any given time. The interpolation function 

is then numerically integrated to yield a chronic intake IRF as described above. These calculations 

were performed with a script written in the R programming language.
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 72 of 73

ATTACHMENT C

SUMMARY OF GUIDANCE FOR ASSESSING THORIUM INTAKES FROM BIOASSAY

Triple-separated thorium is assumed in the guidance given below. This is applied as a favorable to 

claimant assumption in the absence of more specific information. If the details of processing are 

known at a site, these should be used. These methods are approximations and result in intakes that 

will not underestimate the intakes that would be calculated with exact methods. Approximate 

methods are not available for 228Ac chest counts, so such cases must be evaluated with exact 

methods. Contact the Principal Internal Dosimetrist when a best estimate or evaluation of an 228Ac 

chest count is needed.

Chronic Intakes

Given a single 212Pb chest count result for a chronic intake longer than 1 year:

1. Evaluate the chest burden using the 228Th biokinetic model in IMBA. 

2. Multiply the intake rate obtained in step 1 by a factor of 1.1 and assign it as the intake rate 

of 228Th. 

3. Divide the 228Th intake rate by 0.19 to obtain the 232Th intake rate. 

Given a single 212Pb whole body count result for a chronic intake longer than 1 year:

1. Evaluate the whole-body burden using the 228Th biokinetic model in IMBA. 

2. Multiply the intake rate obtained in step 1 by a factor of 

a. 1.5 for an intake of Type M material

b. 1.2 for an intake of Type S material 

3. Assign the result from step 2 as the intake rate of 228Th. 

4. Divide the 228Th intake rate by 0.19 to obtain the 232Th intake rate. 

Given a single total thorium urine bioassay result:

1. Evaluate the urine result using the 232Th biokinetic model in IMBA to obtain the 232Th intake 

rate. 

2. Multiply the 232Th intake rate by 0.19 to obtain the 228Th intake rate.

Given a single 228Th urine bioassay result:

1. Evaluate the urine result using the 228Th biokinetic model in IMBA to obtain the 228Th intake 

rate. 

2. Divide the 228Th intake rate by 0.19 to obtain the 232Th intake rate. 

Acute Intakes

Given a single 212Pb chest count result more than 30 days after an acute intake:

1. Evaluate the chest count using the 228Th biokinetic model in IMBA. 

2. Multiply the intake obtained in step 1 by a factor of 1.1 and assign it as the intake of 228Th. 

3. Divide the 228Th intake by 0.19 to obtain the 232Th intake. 
Document No. ORAUT-OTIB-0076 Revision No. 00 Effective Date: 07/10/2014 Page 73 of 73

ATTACHMENT C

SUMMARY OF GUIDANCE FOR ASSESSING THORIUM INTAKES FROM BIOASSAY (continued) 

Given a single 212Pb whole body count result more than 30 days after an acute intake:

1. Evaluate the whole-body burden using the 228Th biokinetic model in IMBA. 

2. Multiply the intake in step 1 by a factor of 

a. 1.5 for an intake of Type M material

b. 1.2 for an intake of Type S material 

3. Assign the result from step 2 as the intake of 228Th. 

4. Divide the 228Th intake by 0.19 to obtain the 232

Th intake rate. 

Given a single total thorium urine bioassay result:

1. Evaluate the urine result using the 232Th biokinetic model in IMBA to obtain the 232Th 

intake. 

2. Multiply the 232Th intake by 0.19 to obtain the 228Th intake.

Given a single 228Th urine bioassay result:

1. Evaluate the urine result using the 228Th biokinetic model in IMBA to obtain the 228Th 

intake. 

2. Divide the 228Th intake by 0.19 to obtain the 232Th intake.