A voxel-based multiscale model to simulate the radiation response of hypoxic tumors I. Espinoza, P. Peschke, and C. P. Karger Citation: Medical Physics 42, 90 (2015); doi: 10.1118/1.4903298 View online: http://dx.doi.org/10.1118/1.4903298 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/42/1?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in Dose prescription complexity versus tumor control probability in biologically conformal radiotherapy Med. Phys. 36, 4379 (2009); 10.1118/1.3213519 Self-consistent tumor control probability and normal tissue complication probability models based on generalized EUDa) Med. Phys. 34, 2807 (2007); 10.1118/1.2740010 Investigating the effect of cell repopulation on the tumor response to fractionated external radiotherapy Med. Phys. 30, 735 (2003); 10.1118/1.1567735 An analysis of the relationship between radiosensitivity and volume effects in tumor control probability modeling Med. Phys. 27, 1258 (2000); 10.1118/1.599003 Volume and Kinetics in Tumor Control and Normal Tissue Complications Med. Phys. 26, 1407 (1999); 10.1118/1.598815
A voxel-based multiscale model to simulate the radiation response of hypoxic tumors I. Espinozaa) Institute of Physics, Pontificia Universidad Católica de Chile, Santiago 7820436, Chile and Department of Medical Physics in Radiation Oncology, German Cancer Research Center (DKFZ), Heidelberg 69120, Germany
P. Peschke Clinical Cooperation Unit Molecular Radiooncology, German Cancer Research Center (DKFZ), Heidelberg 69120, Germany
C. P. Karger Department of Medical Physics in Radiation Oncology, German Cancer Research Center (DKFZ), Heidelberg 69120, Germany
(Received 13 May 2014; revised 11 November 2014; accepted for publication 15 November 2014; published 16 December 2014) Purpose: In radiotherapy, it is important to predict the response of tumors to irradiation prior to the treatment. This is especially important for hypoxic tumors, which are known to be highly radioresistant. Mathematical modeling based on the dose distribution, biological parameters, and medical images may help to improve this prediction and to optimize the treatment plan. Methods: A voxel-based multiscale tumor response model for simulating the radiation response of hypoxic tumors was developed. It considers viable and dead tumor cells, capillary and normal cells, as well as the most relevant biological processes such as (i) proliferation of tumor cells, (ii) hypoxiainduced angiogenesis, (iii) spatial exchange of cells leading to tumor growth, (iv) oxygen-dependent cell survival after irradiation, (v) resorption of dead cells, and (vi) spatial exchange of cells leading to tumor shrinkage. Oxygenation is described on a microscopic scale using a previously published tumor oxygenation model, which calculates the oxygen distribution for each voxel using the vascular fraction as the most important input parameter. To demonstrate the capabilities of the model, the dependence of the oxygen distribution on tumor growth and radiation-induced shrinkage is investigated. In addition, the impact of three different reoxygenation processes is compared and tumor control probability (TCP) curves for a squamous cells carcinoma of the head and neck (HNSSC) are simulated under normoxic and hypoxic conditions. Results: The model describes the spatiotemporal behavior of the tumor on three different scales: (i) on the macroscopic scale, it describes tumor growth and shrinkage during radiation treatment, (ii) on a mesoscopic scale, it provides the cell density and vascular fraction for each voxel, and (iii) on the microscopic scale, the oxygen distribution may be obtained in terms of oxygen histograms. With increasing tumor size, the simulated tumors develop a hypoxic core. Within the model, tumor shrinkage was found to be significantly more important for reoxygenation than angiogenesis or decreased oxygen consumption due to an increased fraction of dead cells. In the studied HNSSC-case, the TCD50 values (dose at 50% TCP) decreased from 71.0 Gy under hypoxic to 53.6 Gy under the oxic condition. Conclusions: The results obtained with the developed multiscale model are in accordance with expectations based on radiobiological principles and clinical experience. As the model is voxel-based, radiological imaging methods may help to provide the required 3D-characterization of the tumor prior to irradiation. For clinical application, the model has to be further validated with experimental and clinical data. If this is achieved, the model may be used to optimize fractionation schedules and dose distributions for the treatment of hypoxic tumors. C 2015 American Association of Physicists in Medicine. [http://dx.doi.org/10.1118/1.4903298] Key words: radiotherapy, tumor hypoxia, reoxygenation, response simulation 1. INTRODUCTION Cancer is the leading cause of death in many developed countries and will become a major cause of morbidity and mortality in the coming decades in all regions of the world.1 It is estimated that today approximately 50% of all cancer patients receive radiotherapy during their treatment,2 but 90
Med. Phys. 42 (1), January 2015
optimal treatment is still compromised by the limited knowledge of the tumor response to irradiation. With this respect, mathematical models may help to reduce this uncertainty and optimize the radiation treatment. Many analytical mathematical models of tumor growth, radiation response and treatment optimization were developed in the past and have been of great relevance for the understanding
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© 2015 Am. Assoc. Phys. Med.
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Espinoza, Peschke, and Karger: Simulation of the response of hypoxic tumors
of the radiation response. However, they become prohibitively complex, when a large number of biological processes and interactions are considered. Thus, computer simulation models became increasingly important as they could handle more complex algorithms and were able to consider the heterogeneous nature of tumors as well as the stochastic properties of the radiation response by Monte Carlo methods. Titz and Jeraj3 classified the existing radiobiological computer models in three categories according to the spatial scale on which they focus. (i) Microscopic models consider individual interacting cells and are usually computationally limited to small tumor sizes (
A voxel-based multiscale model to simulate the radiation response of hypoxic tumors I. Espinozaa) Institute of Physics, Pontificia Universidad Católica de Chile, Santiago 7820436, Chile and Department of Medical Physics in Radiation Oncology, German Cancer Research Center (DKFZ), Heidelberg 69120, Germany
P. Peschke Clinical Cooperation Unit Molecular Radiooncology, German Cancer Research Center (DKFZ), Heidelberg 69120, Germany
C. P. Karger Department of Medical Physics in Radiation Oncology, German Cancer Research Center (DKFZ), Heidelberg 69120, Germany
(Received 13 May 2014; revised 11 November 2014; accepted for publication 15 November 2014; published 16 December 2014) Purpose: In radiotherapy, it is important to predict the response of tumors to irradiation prior to the treatment. This is especially important for hypoxic tumors, which are known to be highly radioresistant. Mathematical modeling based on the dose distribution, biological parameters, and medical images may help to improve this prediction and to optimize the treatment plan. Methods: A voxel-based multiscale tumor response model for simulating the radiation response of hypoxic tumors was developed. It considers viable and dead tumor cells, capillary and normal cells, as well as the most relevant biological processes such as (i) proliferation of tumor cells, (ii) hypoxiainduced angiogenesis, (iii) spatial exchange of cells leading to tumor growth, (iv) oxygen-dependent cell survival after irradiation, (v) resorption of dead cells, and (vi) spatial exchange of cells leading to tumor shrinkage. Oxygenation is described on a microscopic scale using a previously published tumor oxygenation model, which calculates the oxygen distribution for each voxel using the vascular fraction as the most important input parameter. To demonstrate the capabilities of the model, the dependence of the oxygen distribution on tumor growth and radiation-induced shrinkage is investigated. In addition, the impact of three different reoxygenation processes is compared and tumor control probability (TCP) curves for a squamous cells carcinoma of the head and neck (HNSSC) are simulated under normoxic and hypoxic conditions. Results: The model describes the spatiotemporal behavior of the tumor on three different scales: (i) on the macroscopic scale, it describes tumor growth and shrinkage during radiation treatment, (ii) on a mesoscopic scale, it provides the cell density and vascular fraction for each voxel, and (iii) on the microscopic scale, the oxygen distribution may be obtained in terms of oxygen histograms. With increasing tumor size, the simulated tumors develop a hypoxic core. Within the model, tumor shrinkage was found to be significantly more important for reoxygenation than angiogenesis or decreased oxygen consumption due to an increased fraction of dead cells. In the studied HNSSC-case, the TCD50 values (dose at 50% TCP) decreased from 71.0 Gy under hypoxic to 53.6 Gy under the oxic condition. Conclusions: The results obtained with the developed multiscale model are in accordance with expectations based on radiobiological principles and clinical experience. As the model is voxel-based, radiological imaging methods may help to provide the required 3D-characterization of the tumor prior to irradiation. For clinical application, the model has to be further validated with experimental and clinical data. If this is achieved, the model may be used to optimize fractionation schedules and dose distributions for the treatment of hypoxic tumors. C 2015 American Association of Physicists in Medicine. [http://dx.doi.org/10.1118/1.4903298] Key words: radiotherapy, tumor hypoxia, reoxygenation, response simulation 1. INTRODUCTION Cancer is the leading cause of death in many developed countries and will become a major cause of morbidity and mortality in the coming decades in all regions of the world.1 It is estimated that today approximately 50% of all cancer patients receive radiotherapy during their treatment,2 but 90
Med. Phys. 42 (1), January 2015
optimal treatment is still compromised by the limited knowledge of the tumor response to irradiation. With this respect, mathematical models may help to reduce this uncertainty and optimize the radiation treatment. Many analytical mathematical models of tumor growth, radiation response and treatment optimization were developed in the past and have been of great relevance for the understanding
0094-2405/2015/42(1)/90/13/$30.00
© 2015 Am. Assoc. Phys. Med.
90
91
Espinoza, Peschke, and Karger: Simulation of the response of hypoxic tumors
of the radiation response. However, they become prohibitively complex, when a large number of biological processes and interactions are considered. Thus, computer simulation models became increasingly important as they could handle more complex algorithms and were able to consider the heterogeneous nature of tumors as well as the stochastic properties of the radiation response by Monte Carlo methods. Titz and Jeraj3 classified the existing radiobiological computer models in three categories according to the spatial scale on which they focus. (i) Microscopic models consider individual interacting cells and are usually computationally limited to small tumor sizes (
