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Monte Carlo simulation of age-dependent radiation dose from alpha- and beta-emitting

radionuclides to critical trabecular bone and bone marrow targets

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IOP PUBLISHING PHYSICS INMEDICINE ANDBIOLOGY

Phys. Med. Biol.58 (2013) 33013319 doi:10.1088/0031-9155/58/10/3301

Monte Carlo simulation of age-dependent radiationdose from alpha- and beta-emitting radionuclides tocritical trabecular bone and bone marrow targets

James T Dant1, Richard B Richardson2 and Linda H Nie1,3

1 School of Health Sciences, Purdue University, West Lafayette, IN, USA2 Atomic Energy of Canada Limited (AECL), Chalk River, Ontario, Canada

E-mail:[email protected]

Received 29 October 2012, in final form 22 March 2013

Published 25 April 2013

Online atstacks.iop.org/PMB/58/3301

Abstract

Alpha () particles and low-energy beta () particles present minimal risk for

external exposure. While these particles can induce leukemia and bone cancer

due to internal exposure, they can also be beneficial for targeted radiation

therapies. In this paper, a trabecular bone model is presented to investigate the

radiation dose from bone- and marrow-seeking and emitters to different

critical compartments (targets) of trabecular bone for different age groups.

Two main issues are addressed with Monte Carlo simulations. The first is the

absorption fractions (AFs) from bone and marrow to critical targets within

the bone for different age groups. The other issue is the application of 223

Rafor the radiotherapy treatment of bone metastases. Both a static model and a

simulated bone remodeling process are established for trabecular bone. The

results show significantly lower AFs from radionuclide sources in the bone

volume to the peripheral marrow and the haematopoietic marrow for adults

than for newborns and children. The AFs from sources on the bone surface

and in the bone marrow to peripheral marrow and haematopoietic marrow

also varies for adults and children depending on the energy of the particles.

Regarding the use of 223Ra as a radionuclide for the radiotherapy of bone

metastases, the simulations show a significantly higher dose from223Ra and its

progeny in forming bone to the target compartment of bone metastases than

that from two other more commonly used -emitting radiopharmaceuticals,153Sm and 89Sr. There is also a slightly lower dose from 223Ra in forming

bone to haematopoietic marrow than that from 153Sm and 89Sr. These results

indicate a higher therapy efficiency and lower marrow toxicity from 223Ra

and its progeny. In conclusion, age-related changes in bone dimension and

cellularity seem to significantly affect the internal dose from and emitters

in the bone and marrow to critical targets, and 223Ra may be a more efficient

3 Author to whom any correspondence should be addressed.

0031-9155/13/103301+19$33.00 2013 Institute of Physics and Engineering in Medicine Printed in the UK & the USA 3301
http://dx.doi.org/10.1088/0031-9155/58/10/3301mailto:[email protected]://stacks.iop.org/PMB/58/3301http://stacks.iop.org/PMB/58/3301mailto:[email protected]://-/?-http://dx.doi.org/10.1088/0031-9155/58/10/3301

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3302 J T Dantet al

radiopharmaceutical for the treatment of bone metastases than 15 3Sm and 89Sr,

if the diffusion of219Rn to the bone marrow is insignificant.

(Some figures may appear in colour only in the online journal)

1. Introduction

Alpha () particles andlow-energybeta () particlespresent minimal risk for external radiation

exposure because of their short range (i.e., no farther than 150 m) in soft tissue. While these

particlescan be hazardous in cases of inadvertent or inappropriate internal exposure, when used

properly they can be beneficial in targeted radiation therapies. The radiation dose assessment

for internal exposure from and particles remains a challenge to the scientific community,

largely due to the difficulty in quantifying the spatial distribution of radioisotopes. In this

paper, a trabebecular bone model is presented to investigate the radiation dose from bone- and

marrow-seeking- and -emitting radionuclides to critical target compartments in trabecular

bone across different age groups. In the paper, trabecular bone includes all components in the

trabecular bone cavity such as fat and haemotopoietic marrow.Two scenarios are simulated using Monte Carlo analysis. The first is a more general

scenario, where the results are derived for a wide range of and particle energies, and

can be used for different situations including accidental ingestion of the radionuclides from

the environment or the deliberate administration of radionuclides to disease treatment. In this

general scenario, the absorbed fractions, or AFs (i.e., the fraction of the total radiation energy

emitted from a source compartment and deposited in a target compartment) of trabecular bone

models are first calculated for different age groups. Then, using these AF calculations, the

absorbed dose to newborn, 1-year old, 5-year old, 10-year old, and adult groups are compared.

The second scenario is a specific and detailed example of the first scenario, where the

treatment of bone metastases in adults is investigated using the 223RaCL2 and its progeny,

where 95% of the dose is from four emitters, namely 223Ra (with particle energy of

5.8 MeV) and its progeny, 21 9Rn (6.9 MeV), 2 15Po, (7.5 MeV) and 211Bi (6.7 MeV) (Bruland

et al 2006). In the model, we used the same value of 6.8 MeV as the alpha energy for both219Rn and 211Bi. In addition to the static bone models used in the first scenario, the second

scenario uses a bone remodeling simulation. The bone remodeling simulation allows for the

calculation of the radiation dose being delivered to the bone metastasis site based on the

presence of223Ra and its progeny in the forming bone. Similar simulations are also conducted

for two other commercially available-emitting radiopharmaceuticals. The targeted treatment

of bone metastases with these radionuclides is then analyzed for therapy efficiency (i.e., the

ratio of the biological radiation dose to the targeted area) and marrow toxicity (i.e., the ratio

of the biological radiation dose to the haematopoietic marrow).

The following sections provide background information concerning radiation exposure,

especially in childhood, and targeted radiotherapy for the treatment of bone metastasis.

1.1. Radiation exposure in adults and children

Ionizing radiation is one of the most significant risk factors associated with leukemia and

bone cancer. Children could be exposed to radiation through the environment, radiotherapy, or

radiation terrorism attack. While the incidence of internal exposure of children to radionuclides

is likely to be quite small, it is still desirable to develop methods to accurately estimate the

internal exposure dose for children because of the significance of the potential consequence

(development of cancer) and the enhanced sensitivity of children to radiation. Marrow and

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Monte Carlo simulation of age-dependent radiation dose from alpha- and beta-emitting radionuclides 3303

bone seeking and emitters are a potential risk factor for leukemia and bone cancer

for both children and adults (Richardson 2011). Currently, the International Commission

on Radiological Protection (ICRP) defines haematopoietic marrow (red marrow) as the main

ionizing radiation target for leukemia, and the 50m marrow layer adjacent to the bone surface

as the target for bone cancer (ICRP2013). As trabecular bone has much more haematopoieticmarrow and a much faster bone remodeling rate than cortical bone, it presents a greater

potential for radiation risk.

Children are more susceptible than adults to radiation exposure because childrens skeletal

systems have a much higher cellularity (i.e. a greater proportion of haematopoietic marrow)

and a much faster bone remodeling rate (ICRP1995, Rozmanet al1989). Nearly 100% of a

newborns bone marrow is haematopoietic marrow; as the child grows, fatty yellow marrow

gradually replaces the haematopoietic marrow, until an average of 41% fat is present in adult

bone marrow (Rozman et al 1989). These differences in skeletal systems lead to a higher

radiation risk of haematopoietic malignancies in children than in adults.

In this project, age-dependent changes in the dimensions of the trabecular cavities and in

cellularity are studied to see how they affect the radiation dose and health risk associated with

and particles in children as compared to adults.

1.2. Targeted radiotherapy for the treatment of bone metastases

The highest prevalence of metastases in bone occurs in conjunction with primary breast and

prostate cancers (Coleman2001). Approximately half of all patients with systemic cancers

develop bone metastases (Shawet al1989), and while the exact incidence of metastatic bone

disease is unknown, it is estimated that about 350 000 people die from it each year in the

United States (Mundy2002).

Bone metastases generally form within the bone marrow adjacent to the bone surface,

which is rich with stem cells. Two forms of stem cells are found within the bone marrow:

haematopoietic stem cells (HSC) and mesenchymal stem cells (MSC). Cancerous stem cells

originating from HSC and MSC can develop within the bone marrow. Metastasis stem cells

from primary cancers, such as breast and prostate cancers, can also parasitize the endogenousstem cell niches within the marrow especially in areas of active bone remodeling (Baccelli

and Trumpp2012). As bone metastases normally have multiple tumor locations within the

skeleton, traditional cancer treatments (e.g., external radiotherapy and chemotherapy) are

usually inefficient; consequently, radionuclide targeted therapy has become one of the more

efficient treatments for bone metastasis (Vaidyanathan and Zalutsky 2011). This treatment

uses bone-seeking radiopharmaceuticals that selectively deliver ionizing radiation to bone

metastasis sites while binding to these sites to kill the cancer cells.

Currently, two radionuclide-based pharmaceuticals that useemitters are approved by the

US Food and Drug Administration (FDA) and are commercially available for the treatment

of bone metastases. One of these is Metastron ( 89SrCl2), which utilizes the emitter 89Sr

as the radionuclide; the other is Quadramet (153Sm-EDTMP), which employs the emitter153

Sm (Bruland et al 2006). Recently, an emitter-based pharmaceutical called Alpharadin(223RaCl2) has become available and it is being reviewed by the FDA for approval of use.

Alpharadin uses the bone-seeking radionuclide 223Ra, which has a half-life of 11.4 days. To

date, only one study has used a skeletal model to investigate the bone marrow toxicity for223Ra-emitter radiopharmaceutical therapy (Hobbset al2012); no studies have investigated

its treatment efficiency.

In our study, an adult trabecular bone model is developed to simulate the bone remodeling

process and to perform dose assessment for 153Sm, 89Sr, and 223Ra and its progeny. The

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3304 J T Dantet al

Table 1.Radionuclide energy and ranges in water.

emittersEnergy (MeV) Radionuclide Range (m)

0.5 N/A 3

1.8 144Nd 92.5 146Sm 133.2 148Gd 184.0 232Th 264.8 226Ra 335.8 223Ra 446.9 219Rn 517.5 215Po 708.8 212Po 80

10.0 N/A 109

emitters

Average energy (keV) Radionuclide Range (m)

6 3H 6

49 14C 290233 153Sm 550580 89Sr 2400

therapy efficiency and marrow toxicity for targeted treatment for bone metastasis with these

radionuclides are compared.

2. Materials and methods

2.1. Monte Carlo simulations and radiation sources

The Monte Carlo N-Particle Transport Code (MCNP5/MCNPX, Los Alamos National

Laboratory) is used to simulate the transportation and energy deposition of and particles.

Different and emitters are selected as sources to cover a distribution of energies and

ranges, as listed in table1. As particles from a particular radionuclide are mono-energetic,

a single value is specified in the Monte Carlo simulation for each radionuclides. However,

as particles from a particular radionuclide have continuous energies, an energy spectrum is

defined for each radionuclide. The -particle energy spectra for 3H and 14C are obtained

from the work of Cross et al (1983), while the spectra for 153Sm and 89Sr are from ICRP

(2008).

In the simulations, a uniform distribution of radionuclides within the specified source

compartments is assumed. In each run of the simulation, 106 particle histories are followed

for every source location to ensure a dose calculation uncertainty of no more than 2%.

2.2. Static trabecular bone models

The details of the trabecular bone cavity model for an adult have been described in previous

papers (Richardson et al 2007, Nie and Richardson 2009). In brief, the model consists of

a lattice of repeated 3 3 3 cubes to represent the trabecular cavities within the bone

structure, with one of these cubes shown in figure1. Bone plates and rods are represented by

the gray area of the figure, while bone marrow and other skeletal soft tissue fill the rest of the

volume. As described in Richardsonet al(2007), bone remodeling units (BMUs) are inserted

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Figure 1. Trabecular bone cavity model for adults based on the Cartesian coordinate system(Reproduced with permission from Richardson et al 2007 Radiat. Prot. Dosim. 12715862.Copyright Oxford University Press.)

Table 2.Age-dependent parameters of the trabecular bone cavity model.

Age (years) Cavity diameter (m) Bone annulus diameter (m)

0 (Newborn) 672 8271 891 9745 1206 1294

10 1364 145435 (Adult) 1694 1786

into some of the bone rods to enable the bone forming process. The proportion of the bone

rods with a BMU is determined by the bone remodeling rate. In this study, one BMU is present

in one cavity based on the bone remodeling rate for an adult.

A more detailed cross-sectional review of the trabecular cavity model and a description

of various tissue and cell compartments (some not shown in figure1)are presented in Nie and

Richardson (2009); for example, in the model, bone marrow is simulated by fat cells located

in the haematopoietic marrow.

For this study, models of the trabecular cavities for newborns and for children ages 1, 5,

and 10 are scaled from the dimensions shown in table2(Richardson and Dubeau2003).

The diameters of the trabecular cavity and the annulus across all ages are used to calculatethe average age-dependent change in trabecular bone diameter by applying this fractional

change to the dimension of every tissue and cell compartment in the static model. The change

in volume of the trabecular bone cavity is the cubic value of the change in cavity length in one

dimension.

Age-dependent changes in bone volume are listed in table 3, which shows that a newborns

trabecular bone volume is about 8% of that of an adult. Accordingto ICRP 70, theentire skeletal

volume of a newborn is about 34% of that of an adult (ICRP1995). However, the percentage
http://dx.doi.org/10.1093/rpd/ncm364http://dx.doi.org/10.1093/rpd/ncm364http://dx.doi.org/10.1093/rpd/ncm364http://dx.doi.org/10.1093/rpd/ncm364

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3306 J T Dantet al

Table 3.Age-related fractional change of trabecular bone volume across different ages.

Age (years) Fractional change in bone volume

0 (Newborn) 0.0811 0.154

5 0.37110 0.53135 (Adult) 1

Table 4.The composition and density of haematopoietic marrow and bone (based on Richardsonand Dubeau(2003)).

Elemental composition (% by mass) Density

H C N O Na Mg P S Cl K Ca (kg m3)

Marrow and FatFat/yellow marrow 12 77 11 920(all ages)Haematopoietic 10.2 14.3 3.4 70.8 0.2 0.3 0.3 0.2 0.3 1060

marrow (all ages)

Trabecular Bone

0 Years (Newborn) 4.8 15.8 4.3 49.8 0.1 0.2 8.1 0.2 0.1 16.5 1650

1 Year 4.7 16.4 4.5 48.3 0.1 0.2 8.4 0.3 0.1 17 16605 Years 4.4 16.1 4.5 46.5 0.1 0.2 8.9 0.3 0.1 19 1700

10 Years 4.0 16.1 4.4 45.4 0.1 0.2 9.3 0.3 0.1 20 175035 Years (Adult) 3.5 15.9 4.3 44.7 0.1 0.2 9.5 0.3 21.5 1900

of trabecular bone in newborns is more than two times greater than that in adults (though this

varies somewhat between the different bones of the body), making 8% a good estimation for

the percentage of trabecular bone in newborn skeletal systems.

The thicknesses of the ICRP target for bone cancer, the peripheral marrow adjacent to

the bone, are assumed to change linearly according to fractional changes in cavity dimension.The thickness of the peripheral marrow for an adult is 50 m, while it is calculated to be

21m for newborns and 27, 36, and 40m for children ages 1, 5, and 10 years, respectively.

Furthermore, as mentioned above, children have a much higher cellularity (i.e., a greater

proportion of haematopoietic marrow) than adults. The approximate average cellularity at

birth, at 1, 5, and 10 years, and during adulthood are assumed to be 99.5%, 91%, 76%, 67%,

and 59%, respectively (Rozmanet al1989). The composition and density of marrow and bone

across the age groups is obtained from Woodard and White (1986) and shown in table4.

2.3. Trabecular bone remodeling simulation

The basic idea of the bone remodeling simulation was also described in Nie and Richardson

(2009), where it was referred to as the dynamic model. As mentioned in section 2.2, BMUsare inserted into bone rods to represent the bone forming process. The BMU includes a

bone remodeling compartment (BRC) and several other compartments related to the bone

remodeling process. The BRC stem cell niche is located just outside the BRC canopy, where

active stem cells self-renew and form osteoprogenitors that are the precursors to osteoblasts

and osteoclasts.

The bone remodeling process consists of five phases. The first three phases occur

over approximately 50 days, during which the resorption by osteoclasts is followed by the

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Figure 2.The BMU structure at sub-stage 1 of the Monte Carlo simulation.

Table 5. The 7 sub-stages of the bone remodeling process, as simulated by the Monte Carlosimulation.

Sub-stage BRC sinus (m) Osteoblast (m) Osteoid (m) New bone (m)

1 24 7a 16 82 16 7 16 163 8 7 16 244 7 16 325 16 406 8 487 56

a There is 1m of bone outside the BRC sinus.

appearance of preosteoblasts in the excavated cavity (Salmon et al 1999). The actual bone

forming takes place during the fourth and fifth phases. The fourth phase is the formation of

the osteoid layer, which takes about 15 days. The fifth and final phase is the formation of

the new bone, which takes about 135 days. During the fourth and fifth phases, preosteoblasts

migrate to the BMU and maturate into osteoblasts. These osteoblasts synthesize and produce

the osteoid layer with unmineralized bone matrix. While the resulting osteoid seam initially

measures 1520m, it progressivelymineralizesand thins as new bone is formed. Extracellular

mineralization occurs at the junction of the osteoid and the newly formed bone, resulting in

lamellae that are about 810m thick (Jee2001).

The fifth phase is the only phase modeled in this paper, and it is broken down into 7

sub-stages. The BMU cavity is approximately 56 m thick, therefore lamellae layers of 8mwere simulated for the new bone. The Monte Carlo simulation discussed in this paper follows

the 7 sub-stages, as shown in table5. Figure2shows the structure of the BMU at sub-stage 1,

with the BMU cavity surrounded by bone marrow and fat cells.

The bone forming process draws calcium or its analogues into the bone, thereby attracting

bone-seeking emitters such as 223Ra.Skeletalmetastases occur mainly at thebone remodeling

sites. BRC stem cell niches, where active bone stem cells are located, are the most critical sites

for bone metastases. Hence the bone remodeling site plays a critical role for radiotherapy of

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3308 J T Dantet al

bone metastases when using bone-seekingandemitters (Coleman2001, Guise etal 2006).

Alpha energies of 5.8 Mev (from223Ra), 6.8 Mev (from223Ras progeny:211Bi and219Rn), and

7.5 Mev (from 22 3Ras progeny: 215Po) are used in the simulation to calculate the doses from

the forming bone (including osteoid and new bone) to the target compartment of the cavity.

The efficiency of the radiotherapy can be estimated based on the dose from the forming boneto the BRC stem cell niche. Marrow toxicity can be estimated via the dose from the forming

bone to the haematopoietic marrow.

2.4. Absorption fraction, dose, and dose ratio

As mentioned above, the AF determines the fraction of the total radiation energy (hence dose)

emitted from a certain source compartment and deposited within a certain target compartment.

The average absorption fractionAF(TS;t) in targetTper particle emission in source S at

time tis calculated as the average energy absorbed by the target region per radiation emission

from sourceS, divided by the average energy of the radiation:

AF(T S; t) =E(T S; t)

Eavg. (1)

The compartments of interest here are the radiation targets for the consequential induction of

leukemia and bone cancer; these targets are the total haematopoietic marrow (which includes

haematopoietic marrow in the peripheral marrow layer and the rest of the marrow in the central

part of the trabecular cavity) and the peripheral marrow layer, respectively.

For a specific source S and target T, and for a committed dose over a particular period,

the age-dependent dose ratio at agesxandy is calculated as:

Dose ratio=E(T S)x/mx

E(T S)y/my. (2)

For example, the dose ratios for a newborn and for an adult are calculated for source S and

target Tas:

Dose ratio=E(T S)newborn/mT,newbornE(T S)adult/mT,adult

, (3)

whereE(TS)newbornis the energyE deposited to a certain target for a newborn; mT,newbronis

the massmof the target for a newborn;E(TS)adultis the energy deposited to the same target

for an adult; andmT,adultis the mass of the same target for an adult. Since the energy deposited

to a specific target organ equals the product of the AF and the total energy emitted from the

source organ (i.e.,E(TS)newborn =AFnewbornESource, newborn), equation(3) can be written as:

Dose ratio=E(T S)newborn/mT,newborn

E(T S)adult/mT,adult=

AFnewborn Esource,newborn/mT,newborn

AFadult Esource,adult/mT,adult, (4)

where ESource,newborn is the total energy emitted from the source organ for a newborn, and

Esource, adultis the total energy emitted from the source organ for an adult. Because the ratio of

total energy emitted from the source between the newborn and the adult is approximately the

same as the ratio of the target mass between the newborn and the adultthat is,

Esource,newborn

Esource,adult=

mT,newborn

mT,adult, (5)

the dose ratio is thus the same as the ratio of the AFs for different ages:

Dose ratio=AFnewborn

AFadult. (6)

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2.5. Therapy efficiency and marrow toxicity

As mentioned in section2.3,the radiotherapy efficiency of the radionuclides used for targeted

radiotherapy can be estimated via the dose from the forming bone (including osteoid and new

bone) to the BRC stem cell niche. Likewise, the marrow toxicity can be estimated via the dosefrom the forming bone to the haematopoietic marrow.

Assuming uniform distribution of the radionuclide source in the osteoid and new forming

bone with equal energyE in joules distributed in one 8m layer of forming bone (which can

be converted to Bq g1 bone with a conversion factor), the dose from the forming bone to the

bone metastasis site/BRC stem cell niche and haematopoietic marrow for emitters 153Sm

and89Sr, and for emitter 223Ra, can be calculated by the following equation:

Dose =E 7

n=1AF(T osteoid)n Nn,osteoid

mT

+E 7

n=1AF(T newborn)n Nn,newborn

mT, (7)

whereE is the energy distributed in 8 m of forming bone (osteoid or new bone); AF(T

osteoid)n is the AF from the osteoid to the targeteither the bone metastasis site or thehaematopoietic marrowat stage n;Nn,osteoidis the number of 8m osteoid layers at stagen;

AF (T osteoid)nis the AF from new bone to the target at stage n;Nn,newbone is the number

of 8 m new bone layers at stagen; andmTis the mass of the target.

3. Results

3.1. Static model: AFs from bone and marrow to the targets across all ages

The AFs for the uniform distribution of radionuclide sources in the bone surface, bone volume,

and haematopoietic marrow are calculated using a Monte Carlo simulation that employs the

static model. The results for four -emitter and three selected -emitter energies are shown

in tables68.Also shown in these tables are the best fit curves for the AFs of all emitters

shown in table1,with energy ranging from 0.5 to 10 MeV. The coefficients A, B, C, and Dgiven in the tables correspond to the equation below, fitted as a polynomial function:

AF = A E3 +BE2 +C E +D, (8)

where AF is the absorption fraction andE (MeV) is the energy of the emitter. The correlation

coefficients of determination (R2) for these fitted lines are also tabulated. Table6lists the AFs

for various radionuclide sources in the bone surface that irradiate either the peripheral marrow

or the total haematopoietic marrow.

Table7 lists the AFs for various radionuclide sources in the bone volume that irradiate

either peripheral marrow or the total haematopoietic marrow.

Table 8 lists the AFs for various radionuclide sources in the haematopoietic marrow

(which includes the haematopoietic marrow in the peripheral marrow) that irradiate either the

peripheral marrow or the haematopoietic marrow.

Figure3 plots the AFs for radionuclides in the bone surface to 50 m thick peripheralmarrow against the particle energy for different age groups; this figure corresponds to the

data listed in the first part of table6.

3.2. Using the static model to calculate dose ratios for newborns and adults

The dose ratios between newborns and adults (i.e. dose to the newborns divided by the dose

to the adults), as calculated for the amount of radioactivity from bone and marrow passing to

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3310 J T Dantet al

Figure 3. AFsfor emitters in thebonesurface to 50m thickperipheral marrow versusparticle

energy with curves for different age groups.

the critical targets, are shown in table9.These ratios assume a uniform source distribution in

the source compartments. When comparing newborns to adults, the greatest increase in dose

from radiation sources in the bone surface to the peripheral marrow is for the lower energy

and emitters. When the particles energy increases, the ranges of the particles become vast

enough to traverse and exit the thinner peripheral marrow layer of a newborn; hence, the doses

for a newborn are lower than those for adults, with dose ratios lower than 1.

The same trend is observed for dose ratios from the bone volume to the peripheral marrow.

However the dose ratios from bone volume to peripheral marrow are much higher, indicating a

significantly higher risk for newborns and younger children in this case. (The assumption here

is that risk increases when the radiation dose from the same type of radionuclide increases.)

In terms of low- and high-energy emitters, dose ratios from radiation sources in the bonesurface to the haematopoietic marrow show a higher dose in newborns relative to adults.

However, for the mid-range emitters, the ratio is close to 1. The increase in dose from the

higher-energyemitters in newborns is due to the higher cellularity in the newborns marrow.

When the source is located in the bone volume, the dose ratios decrease as energy

increases. This is partially due to the larger bone volume in adults, which absorbs a relatively

higher dose from the higher energy particles. The overall ratios are significantly higher in

newborns because of the increased cellularity of younger children.

The dose ratios between children of other age groups and adults can be calculated from

the tables shown in section3.1. The data is not shown here. Overall, the trend of the ratios is

the same, while the results show less effect due to cellularity as children age.

3.3. Bone remodeling simulation: Comparing adult radiotherapy efficiency and marrowtoxicity among 153Sm, 89Sr and223Ra

The radiation doses from the forming bone to the bone metastasis site and the haematopoietic

marrow are calculated using equation (7), described in section2.4.The results are presented

in table10. The doses to the BRC niche from 223Ra and its progeny are much higher than

those from 153Sm and 89Sr, indicating the higher efficiency of 223Ra targeted radiotherapy.

Furthermore, the doses to the haematpoietic marrow from 223Ra and its progeny are much

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Table 6. AFs from radionuclide sources in the bone surface that irradiate the peripheral or thehaematopoietic marrow. The coefficients A, B, C, and D given in the tables correspond to theequation fitted as a polynomial function AF =A E3 + B E2 + C E +D.

AFs to peripheral marrow

radionuclide or 0 years 35 yearsparticle energy (Newborn) 1 year 5 years 10 years (Adult)

3H 0.27 0.24 0.20 0.19 0.1614C 0.34 0.37 0.40 0.41 0.43153Sm 0.15 0.16 0.18 0.18 0.2089Sr 0.06 0.08 0.10 0.11 0.12

4.0 MeV 0.47 0.47 0.46 0.46 0.45

5.8 MeV 0.39 0.43 0.47 0.47 0.477.5 MeV 0.31 0.35 0.40 0.43 0.46

Fitted curve

parametersA 1.80 103 1.40 103 9.00 104 8.00 104 7.00 104

B 3.40 102

2.90 102

2.32 102

2.14 102

1.96 102

C 1.65 101 1.61 101 1.52 101 1.48 101 1.46 101

D 2.29 101 2.05 101 1.76 101 1.67 101 1.44 101

R2 0.997 0.995 0.986 0.980 0.971

AFs to haematopoietic

marrow radionuclide or 0 years 1 year 5 years 10 years 35 yearsparticle energy (Newborn) (Adult)3H 0.27 0.24 0.20 0.19 0.1614C 0.52 0.50 0.47 0.47 0.47153Sm 0.62 0.62 0.56 0.53 0.4989Sr 0.30 0.34 0.38 0.38 0.40

4.0 MeV 0.47 0.47 0.46 0.46 0.45

5.8 MeV 0.48 0.48 0.47 0.47 0.477.5 MeV 0.49 0.48 0.46 0.46 0.47

Fitted curve

parametersA 1.10 103 1.00 103 1.10 103 1.00 103 1.00 103

B 1.99 102 1.97 102 2.32 102 2.20 102 2.23 102

C 1.18 101 1.25 101 1.47 101 1.47 101 1.53 101

D 2.59 101 2.31 101 1.81 101 1.70 101 1.42 101

R2 0.982 0.973 0.979 0.977 0.976

lower than those from 153Sm and 89Sr, indicating a lower marrow toxicity for 223Ra targeted

radiotherapy than for emitter targeted radiotherapy.

4. Discussion

4.1. An overview of bone models used for internal dosimetry study in the literature

In this work, both static and remodeling trabecular bone models have been developed to

estimate the internal radiation doses from bone seeking and emitters to critical targets in

the skeleton. Kvinnslandet al(2001) use a 3 3 3 cubical trabecular cavity model, with

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Table 7. AFs from radionuclide sources in the bone volume that irradiate the peripheral or thehaematopoietic marrow.


Radionuclide or 0 years 35 years

particle energy (Newborn) 1 year 5 years 10 years (Adult)

3H 0.003 0.002 0.001 0.001 0.00114C 0.16 0.15 0.13 0.12 0.11153Sm 0.13 0.14 0.15 0.15 0.1689Sr 0.06 0.07 0.09 0.10 0.11

4.0 MeV 0.10 0.08 0.06 0.05 0.04

5.8 MeV 0.16 0.14 0.11 0.010 0.08

7.5 MeV 0.20 0.18 0.15 0.14 0.12Fitted curve

parametersA 4.00 104 4.00 104 3.00 104 3.00 104 2.00 104

B 5.60 103 5.70 103 5.30 103 4.80 103 3.70 103

C 9.80 103

3.20 103

2.00 103

2.70 103

2.10 103

D 4.10 103 1.10 103 2.00 103 2.30 103 1.80 103

R2 0.999 0.999 1.000 1.000 1.000


marrow

radionuclide or 0 years 1 year 5 years 10 years 35 years

particle energy (Newborn) (Adult)3H 0.003 0.002 0.001 0.001 0.00114C 0.28 0.23 0.16 0.15 0.12153Sm 0.59 0.58 0.52 0.48 0.4489Sr 0.30 0.33 0.36 0.36 0.384.0 MeV 0.10 0.08 0.06 0.05 0.04

5.8 MeV 0.18 0.14 0.11 0.10 0.08

7.5 MeV 0.27 0.22 0.16 0.15 0.12Fitted curve

parametersA 2.00 104 1.00 104 1.00 104 1.00 104 7.00e-05

B 5.20 103 3.90 103 3.20 103 3.20 103 2.40 103

C 6.20 103 5.50 103 3.50 103 1.60 103 1.60 103

D 2.00 104 1.10 103 1.10 103 2.00 104 5.00 104

R2 1.000 1.000 1.000 1.000 1.000

some similarities to our geometrical model, to investigate haematopoietic stem cell survival

after radionuclide therapy. Their model is unique in that it assumes an exponential spatialdistribution of target cells in the bone marrow adjacent to the bone surface, which is suggested

by Watchman etal (2007). Another type of geometrical modelnamely, a simplified spherical

model representinga trabecular bone andmarrow cavity, similar to that presentedin Richardson

and Dubeau (2003)is used by Hobbs etal (2012) to investigate the marrow toxicity for 223Ra

targeted radiotherapy for bone metastasis. Conversely, a model that is more closely related to

the anatomical skeletal structure is an image-based voxellated model acquired from CT and

micro-CT scans (Houghet al2011).

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Table 8.AFs from radionuclide sources in the haematopoietic marrow that irradiate the peripheralor the haematopoietic marrow.


radionuclide or 0 years 35 years

particle energy (Newborn) 1 year 5 years 10 years (Adult)

3H 0.18 0.19 0.22 0.24 0.2714C 0.13 0.14 0.16 0.18 0.21153Sm 0.12 0.12 0.13 0.14 0.1489Sr 0.05 0.07 0.08 0.09 0.11

4.0 MeV 0.15 0.17 0.19 0.22 0.24

5.8 MeV 0.14 0.15 0.17 0.20 0.23

7.5 MeV 0.13 0.14 0.16 0.17 0.21Fitted curve

parametersA 1.00 104 1.00 104 1.00 104 1.00 104 2.00 104

B 1.40 103 1.60 103 1.80 103 2.20 103 3.20 103

C 2.80 103 1.00 103 1.40 103 9.00 104 1.03 102D 1.77 101 1.89 101 2.16 101 2.40 101 2.48 101

R2 0.999 1.000 1.000 1.000 0.997


marrow radionuclide or 0 years 1 year 5 years 10 years 35 years

particle energy (Newborn) (Adult)3H 1.00 0.99 0.99 0.99 0.9814C 0.92 0.88 0.80 0.76 0.72153Sm 0.68 0.69 0.64 0.59 0.5689Sr 0.32 0.36 0.40 0.40 0.42

4.0 MeV 0.97 0.94 0.88 0.85 0.83

5.8 MeV 0.95 0.91 0.81 0.77 0.74

7.5 MeV 0.93 0.88 0.78 0.73 0.69

Fitted curve

parameters

A 3.00e-05 1.00 104 3.00 104 4.00 104 5.00 104

B 1.10 103 1.30 103 3.40 103 4.80 103 5.10 103

C 3.30 103 1.22 102 2.29 102 2.67 102 2.97 102

D 9.99 101 1.00e+00 1.01e+00 1.01e+00 9.99 101

R2 1.000 0.999 0.996 0.996 0.997

Nevertheless, the geometrical model presented in this work has two unique features that

the other models do not have:(1) it covers all postnatal development and can be used to assessinternal dose from and particles in children; and (2) it takes into account bone formation

in the bone remodeling simulation. However, there are also some limitations to this model.

Firstly, the structure of the bone cavities is an approximation of the real bone structure. To

some degree this will affect dose estimations for all radionuclides, since the particles need

to travel across different-sized compartments to deposit energy to their target compartments.

The effect is particularly noteworthy for 89Sr, because the 2.4 mm range of the average 89Sr

beta is greater than the dimensions of the cavities, which means the particles will need to

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Table 11.AFs for particles in adults. Comparison between Hobbs et al (2012) and the presentwork.

Hobbset al This work Hobbset al This workSource to target (6 MeV) (5.8 MeV) (7 MeV) (7.5 MeV)

HM to HM 0.95 0.74 0.94 0.69HM to EL or PM 0.03 (EL) 0.23 (PM) 0.03 (EL) 0.21 (PM)BS to HM 0.24 0.47 0.28 0.47BS to EL or PM 0.24 (EL) 0.47 (PM) 0.20 (EL) 0.46 (PM)

Note 1: HM, haemotopoietic marrow; EL, endosteal layer; BS, bone surface; PM, peripheralmarrow.Note 2: Hobbset alassume bone cancer targets of a different thickness (i.e., 10m, as comparedto this works 50m), and their HM excludes EL, while our HM includes the PM.

Table 12.AFs for particles in adults. Comparison between Hough et al (2011) and the presentwork.

Source Hough This Hough This Hough This Hough Thisto et al work et al work et al work et al worktarget (6 keV) (3H) (50 keV) (14C) (200 keV) (153Sm) (600 keV) (89Sr)

BM to BM 0.99 0.98 0.79 0.72 0.50 0.56 0.42 0.42BS to BM 0.17 0.16 0.17 0.47 0.19 0.49 0.21 0.40BV to BM 0.00 0.00 0.02 0.12 0.12 0.44 0.17 0.38BM to PM 0.12 0.27 0.11 0.21 0.08 0.14 0.08 0.11BS to PM 0.53 0.16 0.48 0.43 0.19 0.20 0.12 0.12BV to PM 0.00 0.00 0.06 0.11 0.13 0.16 0.10 0.11

Note 1: HM, haemotopoietic marrow; EL, endosteal layer; BM, bone volume; BS, bone surface.Note 2: Houghet aland our work both assume bone cancer targets of 50 m thickness (which they call shallowmarrow) and their HM (which they call marrow) excludes PM or shallow marrow, while our HM includes the PM.Shaded rows indicate close results.

These AFs forparticles can also be compared to the values for similar energies presented

in Hobbset al(2012) as shown in table11.They present significantly higher AFs from active

bone marrow (i.e. haematopoietic marrow) to haemotopoietic marrow, and significantly lower

AFs from haemotopoietic marrow to the endosteal layer (in our case peripheral marrow layer),from the bone surface to the haematopoietic marrow, and from the bone surface to the endosteal

layer. This discrepancy is partly due to the exclusion of the 10 m endosteal layer in their

haematopoietic marrow target. Different definitions of the bone cancer target also contribute

to the discrepancy; we define it as the peripheral layer comprising of a 50 m layer of marrow

adjacent to the bone, and they define it as a 10 m endosteal layer of marrow adjacent to

the bone. In addition, the different values may be partly due to the differences in model

construction. The distribution of the fat component in bone marrow in their model is different

from ours, and we also model a more realistic trabecular bone cavity than they do.

A comparison for the results obtained for the particles can be made with the data from

Hough et al (2011), as shown in table 12. They calculated AFs for electrons with monoenergies

(table 5 in Hough etals paper), with no results forparticles. Comparison was made of the our

particle AFs modeled for the full particle spectra for radionuclides such as3

H, to Houghet als AFs for monoenergetic electrons, in the case of3H having an average energy of 6 keV.

The AFs from active bone marrow (i.e. haematopoietic marrow) to haematopoietic marrow,

from bone surface to 50 m peripheral marrow layer (which they term shallow marrow),

and from bone volume to endosteal layer are found to be very close in value to our results,

while significant discrepancies are observed for AFs from bone surface and bone volume to

haematopoietic marrow, and from haematopoietic marrow to peripheral marrow. The main

reason for this discrepancy is: in Hough et als model, they did not include 50 m peripheral

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3316 J T Dantet al

marrow layer in the haematopoietic marrow compartment. The inclusion of this layer in our

case results in much higher AFs from bone surface or bone volume to haematopoietic marrow.

Another factor that contributes to a discrepancy between the models at lower energies and, to

a lesser degree, at higher energies is that we use full energy spectra for particles, whereas

Houghet aluse mono-energy electrons.Similar observations apply when comparing our results with those published by Kramer

et al (2011). The models published by Hough et al (2011) and Kramer et al (2011) both

utilize voxellated phantom models. While this approach does add realism to the extraction

of exact bone structure, to date there are some unresolved issues with this method. First, the

resolution of the imaging needs improvement, especially if the bone remodeling is simulated.

Second, it only represents the dimensions for a single individual, and many voxellated images

are needed to obtain average values. Third, it is a long and complex task to construct a

voxellated phantom, especially at the necessary 1-micron resolution. Nevertheless, with rapid

improvements in imaging technology and the employment of hybrid geometrical-voxellated

phantoms, this is a good approach for accurate dose estimation. Indeed, in the future, we plan

to improve our model with voxellated images taken from human bodies of all ages.

4.3. Absorption fractions and radiation dose

In this work, the AFs and radiation dose changes between newborns, children, and adults are

consistent with what are expected. With the bone surface as the source (see tables 6 and 9),

lower energy particles deposit more energy in the 50m target layer at younger ages (with the

exception of 3H); as energy increases, however, the particles begin to escape the target area

and deposit deeper in the bone marrow. With bone surface as the source and haematopoietic

marrow as the target, lower energy particles deposit most of the energy to the peripheral

marrow layer portion of the hematopoietic marrow. The AFs for targets in peripheral marrow

and hematopoietic marrow are virtually the same, as very little radiation reaches the central

marrow. With bone volume as the source (see tables7and9), at low energies the dose to the

50m layer of peripheral marrow increases significantly in newborns as compared to adults

and approaches 1 as the energy increases; this trend is the same for each age group. Thedose from bone volume to the hematopoietic marrow relies on the fat content in the marrow,

with newborns receiving a higher dose at low energies relative to adults. As energy increases,

however, more absorption is seen in the fat cells of older individuals, resulting in newborn

dose levels in haemotopoietic marrow around 2.22.8 times higher than those of adults at

median to high energies. With hematopoietic marrow as the source (see tables 8and9), lower

energy particles deposit the majority of their energy in the hematopoietic marrow; as energy

increases, however, the proportion of fat begins to absorb some of the dose, as can be seen by

comparing newborns to adults, where the maximum dose ratio is 1.35.

4.4. 223Ra therapy efficiency, bone marrow toxicity, and future research

Hobbset al(2012) discuss bone marrow toxicity for223

Ra radiopharmaceutical therapy. Theydemonstrate that the absorbed dose from 223Ra is predominantly deposited near the trabecular

bone surface. This is consistent with what we find with our modelthat the AFs of 223Ra

and its progeny from the bone surface to the peripheral marrow are about the same as those

from the bone surface to the haemotopoietic marrow (see table 6). With bone volume as the

source, and without considering bone remodeling, 223Ra and its progeny have much lower

absorption in haemotopoietic marrow than the two emitters, 153Sm and 89Sr, commonly

used to treat bone metastasis (see table7). These results indicate that 223Ra has much lower

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Table 13.Trabecular bone remodeling rate (% per year).

Age (years) 0 (Newborn) 1 5 10 35 (Adult)

Proportion 300 105 66 48 18

marrow toxicity than the widely used emitters, provided that it is deposited in the bone

volume. However, as illustrated in section2.3, the dose to the critical target compartments is

better evaluated through the use of a bone remodeling simulation, rather than by using these

static model AFs. Table 10 shows a significantly higher dose from the forming bone to the

bone metastasis site for 223Ra and its progeny, as compared with that for emitters 153Sm and89Sr, indicating a much higher therapy efficiency with emitter 223Ra. A significantly lower

dose from the forming bone to the haemotopoietic marrow is also observed for 22 3Ra and its

progeny, indicating the much lower marrow toxicity of22 3Ra.

Two assumptions are made in this paper for the assessment of therapy efficiency and

marrow toxicity for 223Ra targeted treatment for bone metastasis. One is that 223Ra will be

drawn to the bone remodeling site and deposited in the forming bones. We consider this a valid

assumption, because 223Ra is a bone-seeking element. The other assumption is that 223Ra and

its progeny have a point decay (i.e., that there is no diffusion involved for these radionuclides).

This second assumption needs to be further investigated, because one of 223Ras progeny,219Rn, diffuses rapidly in fat. If the proportion of haemotopoietic marrow is much higher

in the peripheral marrow region, as assumed in our paper and in some other models (i.e.,

Kvinnslandet al2001, Watchmanet al2007), then the diffusion will not make a significant

difference because of219Rns short half-life of 4 s. If fat cells are randomly distributed within

the marrow cavity(Allenet al 1995) and therefore a significant proportion of the peripheral

marrow, however, the diffusion of219Rn may result in a significantly higher dose and toxicity to

the bone marrow. There is limited radon data available, yet reasonable values for the diffusion

coefficient in lean tissue and fat are (5.0 0.9) 104 mm2 s1 and (0.068 0.01) mm2 s1,

respectively, are reported by Richardson(2008). Although the half-life for 219Rn is only 4 s

(for mean lifetime, divide by ln 2), the diffusion length is estimated at 53 and 630 m for

pure hematopoietic marrow and pure fat, respectively, calculated as the square root of theproduct of the mean lifetime and diffusion coefficient. If these are reasonable estimates for

these critical 223Ra parameters, this means that a significant proportion of total 22 3Ra progeny

energy (progeny 21.1 MeV of total 26.9 MeV) may migrate away from the bone surface,

crossing the 50m peripheral marrow or BRC niche, and irradiate the central marrow within

the trabecular cavity, causing marrow toxicity.

At present, bone remodeling is only modeled in the adult group. Future research could

incorporate the change in the bone remodeling rate (see table 13) into the all-age model to

examine how the risk of bone cancer can change. As mentioned previously, to account for the

change in the bone remodeling rate, the number of BMUs incorporated in the bone plates can

be adjusted relative to the adult remodeling rate for each age group. Other future work could

incorporate the bio-kinetic models of different radionuclides to calculate the doses delivered

to critical skeletal compartments in different scenarios.

5. Conclusion

With bone and haemotopoietic marrow as the target sites, the change in dose ratios with

age show that the changing dimensions of the trabecular bone cavity and its critical targets

significantly affect the internal dose from bone- and marrow-seeking - and -emitting

radioisotopes to the target sites for leukemia and bone cancer. Secondly, both the static

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3318 J T Dantet al

and bone remodeling simulations indicate that 22 3Ra may be a more efficient radioisotope for

radionuclide targeted treatments of bone metastasis than the more commonly used emitters.

Acknowledgments

This research has been supported in part by the Start-up Fund and Faculty Summer Research

Grant provided by Purdue University for LHN. JTD was supported by the Nuclear Engineering

and Health Physics Fellowship Program provided by Nuclear Regulatory Commission (NRC).

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