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Radiation Protection Dosimetry Advance Access published online on January 11, 2008
Radiation Protection Dosimetry, doi:10.1093/rpd/ncm468
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Published by Oxford University Press 2007
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RESPONSE FUNCTIONS FOR COMPUTING ABSORBED DOSE TO SKELETAL TISSUES FROM PHOTON IRRADIATION

K. F. Eckerman1,*, W. E. Bolch2, M. Zankl3 and N. Petoussi-Henss3

1 Life Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6480, USA
2 Department of Nuclear and Radiological Engineering, University of Florida, Gainesville, FL 32611, USA
3 GSF-National Research Center for Environment and Health, Institute of Radiation Protection, Ingolstaedter Landstr, 1, 85764 Neuherberg, Germany

* Corresponding author: eckermankf{at}ornl.gov


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 RESPONSE FUNCTION FORMULATION
 RESULTS
 CONCLUSIONS
 FUNDING
 REFERENCES
 

The calculation of absorbed dose in skeletal tissues at radiogenic risk has been a difficult problem because the relevant structures cannot be represented in conventional geometric terms nor can they be visualised in the tomographic image data used to define the computational models of the human body. The active marrow, the tissue of concern in leukaemia induction, is present within the spongiosa regions of trabecular bone, whereas the osteoprogenitor cells at risk for bone cancer induction are considered to be within the soft tissues adjacent to the mineral surfaces. The International Commission on Radiological Protection (ICRP) recommends averaging the absorbed energy over the active marrow within the spongiosa and over the soft tissues within 10 µm of the mineral surface for leukaemia and bone cancer induction, respectively. In its forthcoming recommendation, it is expected that the latter guidance will be changed to include soft tissues within 50 µm of the mineral surfaces. To address the computational problems, the skeleton of the proposed ICRP reference computational phantom has been subdivided to identify those voxels associated with cortical shell, spongiosa and the medullary cavity of the long bones. It is further proposed that the Monte Carlo calculations with these phantoms compute the energy deposition in the skeletal target tissues as the product of the particle fluence in the skeletal subdivisions and applicable fluence-to-dose–response functions. This paper outlines the development of such response functions for photons.


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
RESPONSE FUNCTION FORMULATION
 RESULTS
 CONCLUSIONS
 FUNDING
 REFERENCES
 
Following the forthcoming revision of its radiation protection recommendations, the International Commission on Radiological Protection (ICRP) plans to formally adopt voxel-based computational phantoms derived from CT image data due to the improved anatomical realism compared with the mathematical ‘MIRD-like(1)’ phantoms that have been used in radiation protection for the past 30 y. The proposed phantoms(2) represent the adult male and female Reference Individuals set forth in ICRP Publication 89(3). The complex structure of the skeleton cannot be visualised in the CT images used to define these phantoms because the dimensions of these features are below the image resolution. The active marrow, the tissue of concern in leukaemia induction, is present within the spongiosa regions of trabecular bone, while the cells at risk for bone cancer induction are taken to be within the soft tissues adjacent to the mineral surfaces. The intermixture of bone mineral and soft tissue in the spongiosa cannot be represented in conventional geometric terms nor can it be assumed that charged particle equilibrium exists in these regions.

A variety of approaches have been used to derive estimates of the absorbed dose to the active marrow and endosteal tissues. The intractable geometry of the skeleton was noted in the publication of the mathematical phantom,(1) and thus the skeleton was represented as a homogenous mixture of bone mineral and marrow. The absorbed dose to the active marrow from photon irradiation was approximated by the absorbed dose to the mixture in the regions of skeleton containing active marrow. The absorbed dose to the endosteal tissues was taken as the dose to the homogenous skeleton. These procedures were noted to grossly overestimate the dose to the active marrow while underestimating the dose to endosteal tissues at photon energies below ~300 keV. Because of the overestimate at photon energies corresponding to diagnostic X-rays, Rosenstein(4) applied a correction factor to the computed dose in the active marrow, which represented the ratio of the mass energy absorption coefficient for active marrow to that for the homogeneous skeleton times the enhancement of the marrow dose suggested by Spiers(5). Similar correction factors for the active marrow dose were introduced into the Monte Carlo calculations by other investigators(6–8).

Eckerman and co-authors(9–11) undertook the development of response functions for use in Monte Carlo simulations in ‘MIRD-like’ phantoms, which relate the absorbed dose in the skeletal tissues to the photon and neutron fluence in skeletal regions. The response functions considered separately the interactions liberating secondary particles from the processes depositing energy in the target tissues. In these calculations, the geometry of the spongiosa was represented in a probabilistic manner based on chord-length distributions measured in planar sections of the spongiosa by Spiers and co-authors(12–14) at the University of Leeds. These response functions were used in the calculation of photon-specific absorbed fraction data(10) for internal photon emitters and in the photon and neutron dose estimates for the survivors of Hiroshima and Nagaski(15).

In recent work at the University of Florida, microCT 3-D images of bone specimens have been used to derive electron absorbed fraction data(16). An important aspect of these new data is the consideration of (1) electron escape from the spongiosa to the cortical shell surrounding the spongiosa, (2) the 50-µm depth from the mineral surface for the osteoprogenitor cells and (3) electrons originating in the cortical shell irradiating the spongiosa. A revision of the photon response functions is thus undertaken here as (1) the cells at risk for bone cancer induction are now considered to be localised out to 50 µm from the mineral surfaces of the spongiosa in trabecular bone and the medullary cavity of cortical bone, (2) the newer electron absorbed fraction data overcomes some of the weakness in the earlier data, and (3) the skeleton is defined in greater detail in the proposed ICRP computational phantoms. The latter development enables the composition of the individual bone regions to be considered in transport calculations and the fluence in the cortical shell and spongiosa derived in a manner that minimises concern regarding the depression of the flux in the spongiosa due to the cortical shell.


   RESPONSE FUNCTION FORMULATION
TOP
 ABSTRACT
 INTRODUCTION
 RESPONSE FUNCTION FORMULATION
RESULTS
 CONCLUSIONS
 FUNDING
 REFERENCES
 
Consider the spongiosa of a bone (Figure 1) experiencing a fluence {Phi}(E) of photon of energy E. Let m(r) denote the mass of r (r, the trabeculae TB and the marrow space MS) comprising the spongiosa. Denoting the type of photon interaction occurring in r by i then the absorbed dose in the target region T per photon fluence in the spongiosa, D(T)/{Phi}(E), can be expressed as:


Formula 468M1

(1)
where {phi}(T <- r; Eie) is the fraction in energy of a secondary electron liberated in r with energy Eie that is absorbed in target region T, µr,i (E) denotes the mass attenuation coefficient in medium r for photon interaction i (i, photoelectric, Compton and pair-production) and nr (Eie) dEie denotes the number of secondary electrons of energy between Eie and Eie + dEie liberated in region r by photon interaction i. A similar equation can be written for the photon fluence in the cortical shell surrounding the spongiosa. Photoelectrons are assumed to be of discrete energy equal to that of the photon because the binding energy of electrons in the low atomic number elements of the body is rather small. The energy distribution of Compton electrons and the positron–electron pair are continuous; the former is described by the Klein–Nishina relationship(17) and the latter is taken as uniform from zero up to a maximum given by the photon energy less 1.02 MeV. The contributions of secondary electrons liberated by photon interactions in the trabeculae and marrow space of the spongiosa of the cranium to the absorbed dose in the active marrow and trabecular bone endosteum is illustrated in Figures 2 and 3. The trabecular bone endosteum, denoted as TBE50, represents the soft tissues within 50 µm of the mineral surfaces of the spongiosa. Note the contribution of the secondary electrons liberated in the trabeculae to the absorbed dose in the targets and in particular, their substantial contribution to the absorbed dose in the TBE50 target.


Figure 1
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  		Figure 1. The upper end of the femur. The spongiosa is the mixture of bone mineral and marrow, lined by the cortical shell, containing active marrow. Modified from the work of ICRP(3).

 


Figure 2
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  		Figure 2. Absorbed dose in the active marrow, AM, of the cranium per photon fluence in the spongiosa. The dashed curves represent the contribution of electrons originating in the trabeculae and marrow space of the spongiosa to the dose in the active marrow (solid curve).

 


Figure 3
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  		Figure 3. Absorbed dose in the trabecular bone endosteum, TBE50, of the cranium per photon fluence in the spongiosa. The dashed curves represent the contribution of electrons originating in the trabeculae and marrow space of the spongiosa to the RBE50 dose (solid curve).

 

   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 RESPONSE FUNCTION FORMULATION
 RESULTS
CONCLUSIONS
 FUNDING
 REFERENCES
 
Fluence-to-dose–response functions have been calculated for photon energies between 10 keV and 10 MeV for 13 bone sites. The characteristics of these bone sites are listed in Table 1. The bone marrow cellularity, that is the mass fraction of the marrow that is active marrow, corresponds to the quotient of the mass of active marrow divided by the sum of the masses of active and inactive marrow given in the table. The last column of the table gives the mass of the soft tissue within 50 µm of the mineral surfaces of the spongiosa.


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  		Table 1. Characteristics of the 13 skeletal regions.

 
Active marrow response function
Figures 4 and 5 display the calculated absorbed dose in the active marrow D(AM) per photon fluence in the spongiosa {Phi}(Spongiosa) and cortical shell {Phi}(Cortical shell), respectively. The contribution of photon fluence in the spongiosa to the marrow dose exhibits little dependence of the bone region, particularly for photon energies <1 MeV. In contrast, the absorbed dose in the active marrow per photon fluence in the cortical shell strongly depends on the particular bone group as seen in Figure 5. The response functions for fluence in the cortical shell are one to two orders of magnitude lower than those for the spongiosa. At low-photon energy considerable noise is evident in response function of Figure 5. This arises from the statistical uncertainties in the absorbed fraction values for low-energy electrons liberated in the cortical shell. This can be addressed by smoothing the electron data at low energy.


Figure 4
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  		Figure 4. Absorbed dose in active marrow, AM, per photon fluence in spongiosa for various bones of the skeleton.

 


Figure 5
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  		Figure 5. Absorbed dose in active marrow, AM, per photon fluence in cortical shell for various bones of the skeleton.

 
Trabecular bone endosteum
Figures 6 and 7 display the calculated absorbed dose in the trabecular bone endosteum D(TBE50) per photon fluence in the spongiosa {Phi}(Spongiosa) and cortical shell {Phi}(Cortical shell), respectively, of the 13 skeletal regions. Both of these response functions exhibit strong dependence on the specific bone region. The origin of the noise in the response function of Figrue 7 is as discussed above with regard to Figure 5.


Figure 6
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  		Figure 6. Absorbed dose in trabecular bone endosteum, TBE50, per photon fluence in spongiosa for various bones of the skeleton.

 


Figure 7
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  		Figure 7. Absorbed dose in trabecular bone endosteum, TBE50, per photon fluence in the cortical shell for various bones of the skeleton.

 

   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 RESPONSE FUNCTION FORMULATION
 RESULTS
 CONCLUSIONS
FUNDING
 REFERENCES
 
The macro-level subdivision of the skeleton achieved in the proposed ICRP computational phantoms in conjunction with fluence-to-dose–response functions based on the micro-structure of the bones of the skeleton provides a state-of-the-art procedure for computation of the dose to skeletal tissues at risk. Further efforts are necessary to address the cortical bone endosteum region in the medullary cavities of the long bones and to compute the response functions for neutrons. A more comprehensive set of response functions is being prepared for subsequent use in Monte Carlo calculations with the new ICRP phantoms. It is anticipated that the set of function will be included in the publication of the ICRP phantoms.


   FUNDING
TOP
 ABSTRACT
 INTRODUCTION
 RESPONSE FUNCTION FORMULATION
 RESULTS
 CONCLUSIONS
 FUNDING
REFERENCES
 
This work was sponsored by the U.S. Environmental Protection Agency under Interagency Agreement 1824-C148-A1 with the U.S Department of Energy.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 RESPONSE FUNCTION FORMULATION
 RESULTS
 CONCLUSIONS
 FUNDING
 REFERENCES
 

  1. Snyder W. S., Ford M. R., Warner G. G. Estimates of absorbed fractions for monoenergetic photon sources uniformly distributed in various organs of a heterogeneous phantom. MIRD Pamphlet No. 5. J. Nucl. Med. (1969) 10(5):1–67.[Abstract/Free Full Text]
  2. Zankl M., Eckerman K. F., Bolch W. E. Adult male and female voxel-based models representing the ICRP Reference Man–the skeleton. Radiat Prot Dosim. (this issue).
  3. International Commission on Radiological Protection. Basic anatomical and physiological data for use in radiological protection: reference values. In: ICRP Publication 89 (2002) Oxford, UK: Pergamon Press.
  4. Rosenstein M. Organ doses in diagnostic radiology. In: HEW Publication FDA 76-8030 (1976) Rockville, MD: Food and Drug Administration.
  5. Spiers F. W. Transition-zone dosimetry. In: Radiation Dosimetry—Attix F. H., Tochilin E., eds. (1969) Vol. III. New York: Academic Press.
  6. Kramer R., Zankl M., Williams G., Drexler G. The calculation of dose from external photon exposure using reference human phantoms and Monte Carlo methods: Part 1. The male (Adam) and female (Eva) adult mathematical phantoms. (1982) Neuherberg: GSF-National Research Center for Environment and Health. GSF-Bericht S-885.
  7. Zankl M., Fill U., Petoussi-Henss N., Regulla D. Organ dose conversion coefficients for external photon irradiation of male and female voxel models. Phys. Med. Biol. (2002) 47:1–20.[Web of Science][Medline]
  8. Chao T. C., Bozkurt A., Xu X. G. Conversion coefficients based on the VIP-Man anatomical model and EGS4-VLSI code for external monoenergetic photons from 10 keV to 10 MeV. Health Phys. (2001) 81(2):163–193.[Web of Science][Medline]
  9. Eckerman K. F., Cristy M. Computational method for realistic estimates of the dose to active marrow. Radiation-Risk-Protection—Kaul A., Neider R., Pensko J., Stieve F. E., Brunner H., eds. (1985) Berlin: Fachverband fur Strahlenschutz.
  10. Cristy M., Eckerman K. F. Specific absorbed fractions of energy at various ages from internal photon sources, Part 1. (1987) Oak Ridge, TN: Oak Ridge National Laboratory. ORNL Report TM-8381/V1.
  11. Kerr G. D., Eckerman K. F. Neutron and photon fluence-to-dose conversion factors for active marrow of the skeleton. In: Radiation Protection, Proceeding Fifth Symposium on Neutron Dosimetry—Schraube H., Burger G., eds. (1985) Geneva: European Communities.
  12. Beddoe A. H., Darley P. J., Spiers F. W. Measurements of trabecular bone structure in man. Phys. Med. Biol. (1976) 21:589–607.[CrossRef][Web of Science][Medline]
  13. Whitwell J. R., Spiers F. W. Calculated beta-ray dose factors for trabecular bone. Phys. Med. Biol. (1976) 21:16–38.[CrossRef][Web of Science][Medline]
  14. Spiers F. W., Whitwell J. R., Beddoe A. H. Calculated dose factors for radiosensitive tissue in bone irradiated by surface-deposited radionuclides. Phys. Med. Biol. (1978) 23:481–494.[CrossRef][Web of Science][Medline]
  15. Kaul D. C., Egbert S. D., Otis M. D., Kuhn T., Kerr G. D., Eckerman K. F., Cristy M., Maruyama T., Ryman J. C., Tang J. S. Organ dosimetry. Reassessment of Atomic Bomb Radiation Dosimetry—Roesch W. C., ed. (1987) Hiroshima: Radiation Effects Research Foundation.
  16. Bolch W. E., Shah A. P., Watchman C. J., Jokisch D. W., Patton P. W., Rajon D. A., Zankl M., Petoussi-Henss N., Eckerman K. F. Skeletal absorbed fractions for electrons and alpha particles in the adult male–considerations of a revised 50 µm definition of the bone endosteum. Radiat. Prot. Dosim. (this issue).
  17. Evans R. D. X-ray and {gamma}-ray interactions. Radiation Dosimetry—Attix F. H., Roesch W. C., eds. (1968) Vol. I. New York: Academic Press.

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