MODELLING RADIATION TRANSPORT IN VOXEL GEOMETRIES WITH THE MONTE CARLO CODE MCNPX

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1 MODELLING RADIATION TRANSPORT IN VOXEL GEOMETRIES WITH THE MONTE CARLO CODE MCNPX G. Gualdrini 1, C. Daffara 2, K.W. Burn 3, M. Pierantoni 4, P. Ferrari 1 1 ENEA - ION-IRP, V. dei Colli 16, Bologna guald@bologna.enea.it 2 Dipartimento di Fisica, V.le C.B. Pichat 6/2, Bologna 3 ENEA - FIS-NUC, V. M.M. Sole 4, Bologna 4 Istituti Ortopedici Rizzoli, Servizio Informatico, Sal. S.Benedetto 1, Bologna Abstract. Numerical methods for the simulation of radiation transport, in particular Monte Carlo techniques, are playing a fundamental role in the field of dosimetry for radiation protection. For the last 30 years or so, reference quantities have been since about 30 years calculated relying on mathematical analytical human phantoms representative of the standard man. These calculations, in large part based on Monte Carlo techniques, allowed large sets of conversion coefficients between physical quantities (such as radiation fluence) and dose related quantities (such as organ equivalent dose or effective dose) to be produced and transfer coefficients to be used for internal dosimetry purposes. For some years more detailed mathematical human phantoms based on Computer Tomography or Magnetic Resonance (voxel phantoms) have been implemented and are nowadays increasingly used both in the medical physics field and in the radiation protection fields thanks to the large computer power currently available. The present paper summarizes the research activities carried out at ENEA Bologna to develop a voxel option within the Monte Carlo code MCNPX. Examples of application in the field of external and internal dosimetry are given. 1. Introduction Numerical methods for the simulation of radiation transport, in particular Monte Carlo techniques, are playing a fundamental role in the field of dosimetry for radiation protection[1,2]. Very often they provide the only system to determine quantities that are not directly measurable, such as the distribution of the deposited energy within the human body during an exposure to an external radiation source or for internal dosimetry applications. The evolution of computer power in recent years and the development of versatile Monte Carlo radiation transport codes such as EGS [3], MCNP TM [4] and MCNPX TM [5], widely used in internal dosimetry, have allowed problems of increasing complexity to be modelled. Dose calculations within the human body require the computational model of the body with the description of the internal structures, organs and tissues from the point of view of both the geometry and radiation interaction properties (cross sections of the elements). In an anthropomorphic phantom the geometry of the organs can be described in terms of mathematical equations providing a simplified representation [6,7,8]; these equations are expressed relying on the conventional geometry formalism of the employed Monte Carlo code. In the case of MCNPX the geometry is represented by means of Boolean operators on surfaces up-to the 4 th order (tori) defining cells or lattice repeated structures. The digital medical image acquisition techniques based on CT or MR have allow more accurate anatomical models based on the voxel ( volume element ) description, taken directly from the data of an individual patient [9,10,11], to be built. In recent years an integrated methodology has been implemented at ENEA (Radiation Protection Institute and Applied Physics Department) in collaboration with Istituti Ortopedici of the Rizzoli Hospital. The methodology is based on the MCNPX code modelling radiation transport in voxel anthropomorphic phantoms for dosimetry applications [12,13,14,15,16]. In the developed approach the set of voxel data is directly transferred to the MC model without any geometry pre-processing interface. The work implied: (i) the development of a MCNPX transport algorithm suitable for voxel geometries; (ii) the conversion of voxel phantom information from medical images to a suitable format for MCNPX; (iii) the implementation of some new code options to evaluate quantities of interest for internal and external dosimetry studies based on a voxel modelling of the organs of the phantom. The present paper summarizes the main features of the methodology and presents some examples of application in the field of internal and external dosimetry.

2 2. MCNPX-VOXEL Methodology 2.1.The MCNPX-VOXEL code The developed MCNPX-VOXEL code is an extension of the MCNPX Monte Carlo code (version 2.4.k) recently converted to 2.5.d3 for radiation transport in voxel geometries [12]. The main feature of the algorithm, from the user point of view, is that the voxel geometry is superimposed on the standard MCNP geometry allowing the co-existence of the two treatments. The x-y-z voxel grid is independent of the MCNP geometry and the intersections of the particle tracks are calculated both for the voxel and standard MCNP surfaces. If the distance to the voxel surface is less than that to the MCNP surface (and less than the distance to the next collision) the voxel surface is crossed and the particle is transported according to the new transport algorithm. The physical parameters governing the transport within a predefined region are those of the voxel and not of the standard MCNP cell. As well as being useful for modelling geometry outside the phantom, the standard MCNP geometry may be employed for the tallying of physical quantities of interest, e.g. fluence, deposited energy, etc. within the phantom. This allows the simulation of problems of interest in dosimetry, e.g. sensors placed within the human body, in which the transport is followed in the voxel human phantom and the radiation fluence, or energy deposition, is estimated in superimposed MCNP cells. The code is also equipped with the features of tallying a required result or of uniformly sampling a radionuclide source throughout regions (or union of regions) identified by a material indicator. This option is well suited for organ dose calculations both in internal and external dosimetry studies. Furthermore the mesh-tally option of MCNPX allows energy deposition mapping in a further superimposed grid independent of the problem geometry. This option, among other applications, allows evaluations in the medical field, e.g. treatment planning. The voxel phantom is transferred to the MCNPX-VOXEL code directly from the CT Dicom file, but it is also possible to externally pre-process the data (e.g. voxel rescaling, segmentation). The material assignment is specified through a card in the MCNPX-VOXEL.inp file. In the case of a segmented model a direct correspondence between the material and tissue index is established. In the case of a set of non-segmented data (i.e. a file with the original Hounsfield numbers that define a correspondence between pixel and the attenuation coefficient of a medium), a minimum is performed by the code on the basis of a partition throughout the whole volume, assigning a correspondence between a stated Hounsfield number range and the material identification number, according to the calibration curve of the employed tomography equipment Voxel Model from CT images The voxel model of the human body can be represented as a 3-D matrix, whose elements are identified by the corresponding material number and the spatial indices of the voxel coordinates according to the spatial resolution (voxel dimension). A first model was developed based on a plastic dosimetric skull (Alderson TM ) [17]. It was taken from CT images with a resolution of mm 3. The data, exported in DICOM format, were processed to build the final voxel model (comprising roughly 70 million voxels) to be transferred to MCNPX via the following steps: DICOM interpretation, image segmentation, transfer of the voxel matrices to the code [13]. The image segmentation, i.e. the collection of the regions including all voxels of the same assigned tissue, is carried out through semi-authomated techniques including manual corrections, mainly graylevel thresholding and region growing. The segmentation process operates in the 2-D domain and is sequentially applied to the CT slices of the whole system. Each segmented image is thereafter included in a multilayer fashion into the final segmented volume, where the internal structures of the phantom (organs and tissues) are identified. For each voxel composition the density of the constituent material is defined. Fig. 1 shows the dosimetric phantom and its voxel model for MCNPX.

3 FIG.1. Anthropomorphic Alderson TM phantom and its voxel model Radiation transport in human voxel phantoms The MCNPX-VOXEL methodology can simulate radiation transport in human voxel phantoms to determine the organ absorbed dose for external and internal irradiation [14]. The Voxelman phantom developed by Zubal et al. [11] from NMR images of a real patient was implemented in MCNPX- VOXEL. The phantom, representing a standard male anatomy, is described by a cubic voxel matrix (~ 4 mm size) and about 50 anatomical segmented regions (Fig. 2). Material densities and compositions were taken from ICRP 23 [18] and ICRU 46 [19]. The usual approaches reported in the literature vary: the anthropomorphic phantoms are often described by a restricted number of tissues, usually soft tissue, bone, lungs (e.g. mathematical MIRD phantom[7]), eventually with the addition of skin and bone marrow (e.g GSF calculations with the analytical ADAM phantom[20]). Instead the adopted model is characterized by 35 materials (detailed segmentation). The photon transport within Voxelman is simulated employing the detailed physics treatment of MCNP [4] including photoelectric absorption with fluorescence, pair production and coherent and incoherent scattering with form factors to take into account binding effects. The secondary electron transport is not simulated: i.e. the so-called kerma approximation is employed, assuming that the secondary charged particle equilibrium (c.p.e.) conditions are fulfilled and therefore the energy is deposited locally. The bremsstrahlung radiation produced by the secondaries (although not transported) is treated in the TTB (Thick Target Bremsstrahlung) approximation. The energy cut-off for photons is 1 kev. The organ doses are estimated using the modified MCNP F6 estimator, that calculates the energy deposition in all the voxels labeled with the organ tissue of interest. FIG.2. Voxelman Phantom: sagittal and coronal sections and skull rendering

4 3. MCNPX-VOXEL usage in radiation protection dosimetry 3.1. External Dosimetry: conversion coefficients for monoenergetic photons Organ doses (D T ) were calculated for monoenergetic photons in the range 10 kev - 10 MeV and for four standard irradiation geometries with the phantom placed in vacuum and irradiated by plane parallel beams impinging on the phantom with directions: anterior-posterior AP, posterior-anterior PA, and lateral RLAT, LLAT. Fig. 3 reports, as an example, the air kerma to organ dose conversion coefficients for the four investigated irradiation conditions (target organ stomach). The comparison with the coefficients calculated on the ADAM analytical phantom [8] demonstrates significant discrepancies between the two models. The reasons for such discrepancies are widely discussed in the literature[21,22]. Fig. 4 provides a comparison with the GSF (Germany) results [22] and shows a satisfactory agreement. 2.0 Air Kerma to Organ Absorbed Dose photon conversion coefficient organ: stomach AP Voxel (Voxelman) Mathematical (Adam) D/Ka PA RLAT LLAT E (MeV ) 1 10 FIG.3. Voxelman and Adam conversion coefficients comparison 1.4 Air Kerma to Organ Absorbed Dose photon conversion coefficient organ: stomach D/Ka GSF MCNP - VOXEL MCNP - VOXEL (segmentazione dettagliata) (detailed segmentation) 0.0 FIG.4. Comparison with GSF results (A-P irradiation) [22]

5 3.2. Internal Dosimetry: SAF calculations for monoenergetic photons A series of absorbed energy specific fractions (SAFs) for photons has been calculated in the energy range 10 kev 4 MeV for various source and target organs (an example is reported in Fig. 5). The source is uniformly sampled among the voxels constituting the source organ. The comparison between the results obtained for the Voxelman phantom and for the MIRD phantom [23] show a systematic discrepancy over the whole energy range for a large number of target organs, that confirms the oversimplified representation of the organs in the analytical phantom (Fig. 6). To guarantee a consistent comparison, the same tissues (densities and compositions) were used both in the MIRD and Voxelman phantoms. The factor mainly influencing the energy deposition is the different geometry of the two phantoms: the shapes and relative positions (similar conclusions were also reached in [24]). A comparison was carried out with the results obtained by Yoriyaz et al. [25] based on the same voxel phantom and the MCNP code in the standard version (lattice option). The agreement is again satisfactory (see Fig. 7) SAFs for photons (source organ: liver) SAF (g-1) 1.E-03 1.E-04 1.E-05 1.E-06 1.E-07 1.E-08 1.E-09 1.E-10 1.E-11 FIG.5. Absorbed energy specific fractions for monoenergetic photons with source organ liver and various target organs. lungs liver oesophagus stomach colon thyroid testes bladder heart adrenals kidneys pancreas small bowel spleen brain cerebellum gallbladder prostate bone marrow rectum spinal cord SAF: SAF: liver fegato > > stomaco stomach SAF: liver SAF: fegato kidneys > reni 1.0 E E E E-05 SAF (g-1) 1.0 E-0 6 Voxelman MIRD SAF (g-1) 1.0E-06 Voxelman MIRD 1.0 E E-07 FIG.6. Absorbed energy specific fractions for monoenergetic photons: Comparison between Voxelman and MIRD.

6 SAF Liver > stomach 3.5E E E-05 SAF (g-1) 2.0E E-05 MCNP (Yoriyaz et al.) 1.0E-05 MCNP - VOXEL 5.0E-06 MCNP - VOXEL (detailed segmentation) (segmentazione dettagliata) 0.0E+00 FIG.7. Results comparison with data from Yoriyaz et al. [25] 3.3. Design of a calibration head phantom for in vivo measurements of actinides A Whole Body Counter (WBC) is routinely used to estimate the contamination derived from occupational and accidental incorporation of gamma emitters. At the ENEA Radiation Protection Institute a WBC equipped with Germanium detectors is employed. In this context, the Alderson TM plastic anthropomorphic phantom and its voxel model have been used for the characterization of a suitable calibration phantom[16]. The plastic phantom was activated with a known quantity of the investigated radionuclide in order to reproduce the contamination of a real subject. The adopted criterion is based on the optimized positioning of a series (24) of calibrated sources within the skull and on the calculation of suitable correction factors to be applied to the detectors efficiency for the calibration condition (heterogeneous distribution of the sources) with respect to the in vivo measurement on the contaminated subject (contamination assumed as homogeneous). The procedure is strongly dependent on the accuracy of the Monte Carlo modelling of the entire experiment, including Ge detectors, dosimetric phantom and positioning of the sources and detectors in the measurement situation (Fig. 8). In previous works [26,27], the experimental set-up was simulated relying on a multilayer analytical phantom described with the standard MCNP geometry manually developed from CT images. The MCNPX-VOXEL methodology allows the accuracy of the model to be substantially improved. voxel multilayer analytical model FIG.8. Set-up of the WBC measurement, MCNP multilayer model and MCNPX-VOXEL model

7 4. Conclusions An integrated methodology (MCNPX-VOXEL) has been presented that solves the radiation transport problem in voxel geometries and is based on an extension of the Monte Carlo Code MCNPX. A preprocessing interface for the MCNP standard input is not required. A set of medical data (e.g. CT or NMR), representing the geometry of a real patient (or of an anthropomorphic dosimetric phantom) is transferred to the MCNPX-VOXEL code directly from the original DICOM format. The extended version of the code allows the co-existence of the voxel and analytical geometry, maintaining the capabilities of the standard code. Some specific options were implemented to solve typical dosimetric problems with the voxel approach. The code is open to further improvements that are underway. 5. References 1. Gualdrini G., Monte Carlo studies in the field of area monitoring and personal dosimetry for photons between 10 kev and 10 MeV and neutrons below 20 MeV, Workshop Computing Radiation Dosimetry, Lisbon, June 2002 (proceedings to be published) 2. Gualdrini G., Monte Carlo studies in the field of internal dosimetry of incorporated radionuclides, Workshop Computing Radiation Dosimetry, Lisbon, June 2002 (proceedings to be published) 3. Nelson W.R., Hirayama H. and Rogers W.O., The EGS Code System, Stanford Linear Accelerator Centre report SLAC-265 (1985) 4. Briesmeister J.F., Ed., MCNP TM - A General Monte Carlo N-Particle Transport Code, Version 4C, LA M (April 2000) 5. Waters L. S., Ed., MCNPX TM User s Manual, Version 2.4.0, Los Alamos National Laboratory report LA-CP (September 2002) 6. Snyder W.S., Ford M.R., Warner G.G. and Fisher H.R., Estimates of absorbed fraction for monoenergetic photon sources uniformly distributed in various organs of a heterogeneous phantom, J. Nucl. Med. 10, Suppl. 3, Pamphlet No. 5 (1969) 7. Cristy M., Mathematical Phantoms representing children of various ages for use in estimates of internal dose, ORNL/NUREG/TM-367 Oak Ridge National Laboratory (TN-USA) (1980) 8. Kramer R., Zankl M., Williams G. and Drexler G., The Calculation of Dose from External Photon Exposures using Reference Human Phantoms and Monte Carlo Methods. Part 1. The Male (ADAM) and Female (EVA) Adult Mathematical Phantom. GSF-Bericht S-885 (1982) 9. Zankl M., Petoussi N. and Wittmann A., The GSF Voxel Phantom and their Application in Radiology and Radiation Protection, Proc. Workshop on Voxel Phantoms, NRPB Chilton, UK 6-7 July Ed. P.J. Dimbylow (1996) 10. Dimbylow P.J., The development of realistic voxel phantoms for electromagnetic field dosimetry, ibid. 11. Zubal I.G., Harrel C.R., Smith E.O., Rattner Z., Gindi G. and Hoffer P.B., Computerized threedimensional segmented human anatomy, Med. Phys. 21(2), (1994) 12. Burn k.w., Daffara C., Gualdrini G. and Pierantoni M., Radiation transport in voxel geometries: an integrated approach based on an extended version of MCNPX, ENEA Technical Report RT/2002/50/FISS 13. Daffara C., Pierantoni M., Gualdrini G. and Burn K.W., Developing voxel anthropomorphic models based on CT images for dosimetric applications, ENEA Technical Report RT/2002/53/ION 14. Daffara C., Gualdrini G., Burn K.W. and Pierantoni M., Monte Carlo modelling of a voxel human anatomy for external and internal dosimetry, ENEA Technical Report RT/2003/36/ION 15. Daffara C., Monte Carlo Modelling of Radiation Transport in Voxel Geometries with Applications to Dosimetry and Medical Physics, PhD Thesis, Faculty of Mathematical, Physical and Natural Sciences, Dept. of Physics, University of Bologna, (2003) 16. Daffara C., Gualdrini G., Monteventi F., Battisti P., Ferrari P., Burn K.W. and Pierotti L., Development and characterization of a voxel head phantom for in vivo measurements of actinides, ENEA Technical Report (submitted 2003) 17. Radiology Support Devices Inc., CA, USA

8 18. ICRP Publication 23, Report of the Task Group on the Reference Man, Pergamon Press, Oxford (1975) 19. ICRU Report 46, International Commission on Radiation Units and Measurements, Photon, electron, proton and neutron interaction data for body tissue, Bethesda, Maryland (1992) 20. Zankl M., Drexler G., Petoussi-Henss N. and Saito K., The calculation of dose from external photon exposures using reference human phantoms and Monte Carlo methods, Part VII, GSF- Bericht 8/97 (1997) 21. Jones D.G. A Realistic Anthropomorphic Phantom for Calculating Organ Doses Arising from External Photon Irradiation Radiat. Prot. Dosim. 72(1), (1997) 22. Zankl M., Fill U., Petoussi-Henss N. and Regulla D., Organ dose conversion coefficients for external photon irradiation of male and female voxel models, Phys. Med. Biol. 47(14), (2002) 23. Cristy M. and Eckerman K.F., Specific Absorbed Fractions of Energy at various ages from internal photon sources. PART I: Methods, ORNL/TM-8381/VI Oak Ridge National Laboratory (TN-USA) (1987) 24. Jones D.G. A Realistic Anthropomorphic Phantom for Calculating Specific Absorbed Fractions of Energy Deposited from Internal Gamma Emitters, Radiat. Prot. Dosim. 79(1-4), (1998) 25. Yoriyaz, H., dos Santos A., Stabin M.G. and Cabezas R., Absorbed fractions in a voxel-based phantom calculated with the MCNP-4B code, Med. Phys 27(7), (2000) 26. Gualdrini G., Battisti P., Biagini R., De Felice P., Fazio A. and Ferrari P., Development and characterisation of a head calibration phantom for in vivo measurements of actinides, Appl. Rad. Isot. 53, 387 (2000) 27. Gualdrini G., Ferrari P., Battisti P., De Felice P. and Pierotti L., MCNP Analytical Models of a Calibration Head Phantom for Bone-Seeker Nuclide in Vivo Measurements Proc. of the Monte Carlo 2000 Conf., 489, Lisbon (2000)

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