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- Andisheh, B., et al.
(författare)
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A Comparative Analysis of Radiobiological Models for Cell Surviving Fractions at High Doses
- 2013
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Ingår i: Technology in Cancer Research & Treatment. - : SAGE Publications. - 1533-0346 .- 1533-0338. ; 12:2, s. 183-192
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Tidskriftsartikel (refereegranskat)abstract
- For many years the linear-quadratic (LQ) model has been widely used to describe the effects of total dose and dose per fraction at low-to-intermediate doses in conventional fractionated radiotherapy. Recent advances in stereotactic radiosurgery (SRS) and stereotactic radiotherapy (SRT) have increased the interest in finding a reliable cell survival model, which will be accurate at high doses, as well. Different models have been proposed for improving descriptions of high dose survival responses, such as the Universal Survival Curve (USC), the Kavanagh-Newman (KN) and several generalizations of the LQ model, e.g. the Linear-Quadratic-Linear (LQL) model and the Pade Linear Quadratic (PLQ) model. The purpose of the present study is to compare a number of models in order to find the best option(s) which could successfully be used as a fractionation correction method in SRT. In this work, six independent experimental data sets were used: CHOAA8 (Chinese hamster fibroblast), H460 (non-small cell lung cancer, NSLC), NCI-H841 (small cell lung cancer, SCLC), CP3 and DU145 (human prostate carcinoma cell lines) and U1690 (SCLC). By detailed comparisons with these measurements, the performance of nine different radiobiological models was examined for the entire dose range, including high doses beyond the shoulder of the survival curves. Using the computed and measured cell surviving fractions, comparison of the goodness-of-fit for all the models was performed by means of the reduced e-test with a 95% confidence interval. The obtained results indicate that models with dose-independent final slopes and extrapolation numbers generally represent better choices for SRT. This is especially important at high doses where the final slope and extrapolation numbers are presently found to play a major role. The PLQ, USC and LQL models have the least number of shortcomings at all doses. The extrapolation numbers and final slopes of these models do not depend on dose. Their asymptotes for the cell surviving fractions are exponentials at low as well as high doses, and this is in agreement with the behaviour of the corresponding experimental data. This is an important improvement over the LQ model which predicts a Gaussian at high doses. Overall and for the highlighted reasons, it was concluded that the PLQ, USC and LQL models are theoretically well-founded. They could prove useful compared to the other proposed radiobiological models in clinical applications for obtaining uniformly accurate cell surviving fractions encountered in stereotactic high-dose radiotherapy as well as at medium and low doses.
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- Asadzadeh, Mohammad, 1952, et al.
(författare)
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Galerkin methods for primary ion transport in inhomogeneous media
- 2010
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Ingår i: Kinetic and Related Models. - : American Institute of Mathematical Sciences (AIMS). - 1937-5093 .- 1937-5077. ; 3:3, s. 373-394
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Tidskriftsartikel (refereegranskat)abstract
- This paper concerns the energy deposition of high-energy (e.g., approximate to 50 - 500 MeV) proton and carbon ions and high-energy electrons (of approximate to 50 MeV), in inhomogeneous media. Our goal is to develop a flexible model incorporated with the analytic theory for ions based on bipartition and Fokker-Planck developments. Both procedures are leading to convection dominated convection diffusion equations. We study convergence for semi-discrete and fully discrete approximations of a such obtained equation, for abroad beam model, using the standard Galerkin and streamline diffusion finite element methods. The analytic broad beam model of the light ion absorbed dose were compared with the results of the modified Monte Carlo (MC) code SHIELD-HIT+ and those of Galerkin streamline diffusion approach.
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| 6. |
- Asadzadeh, Mohammad, 1952, et al.
(författare)
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Ion transport in inhomogeneous media based on the bipartition model for primary ions
- 2010
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Ingår i: Computers & Mathematics with Applications. - : Elsevier BV. - 0898-1221. ; 60:8, s. 2445-2459
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Tidskriftsartikel (refereegranskat)abstract
- The present paper is focused on the mathematical modeling of the charged particle transport in nonuniform media. We study the energy deposition of high energy protons and electrons in an energy range of approximate to 50-500 MeV. This work is an extension of the bipartition model; for high energy electrons studied by Luo and Brahme in [Z. Luo, A. Brahme, High energy electron transport, Phys. Rev. B 46 (1992) 739-752] [42]; and for light ions studied by Luo and Wang in [Z. Luo, S. Wang, Bipartition model of ion transport: an outline of new range theory for light ions, Phys. Rev. B 36 (1987) 1885-1893]; to the field of high energy ions in inhomogeneous media with the retained energy-loss straggling term. In the bipartition model, the transport equation is split into a coupled system of convection diffusion equations controlled by a partition condition. A similar split is obtained in an asymptotic expansion approach applied to the linear transport equation yielding pencil beam and broad beam models, which are again convection diffusion type equations. We shall focus on the bipartition model applied for solving three types of problems: (i) normally incident ion transport in a slab; (ii) obliquely incident ion transport in a semi-infinite medium; (iii) energy deposition of ions in a multilayer medium. The broad beam model of the proton absorbed dose was illustrated with the results of a modified Monte Carlo code: SHIELD - HIT+.
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- Kempe, J., et al.
(författare)
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Solution of the Boltzmann equation for primary light ions and the transport of their fragments
- 2010
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Ingår i: Physical Review Special Topics - Accelerators and Beams. - 1098-4402. ; 13:10, s. 104702-
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Tidskriftsartikel (refereegranskat)abstract
- The Boltzmann equation for the transport of pencil beams of light ions in semi-infinite uniform media has been calculated. The equation is solved for the practically important generalized 3D case of Gaussian incident primary light ion beams of arbitrary mean square radius, mean square angular spread, and covariance. The transport of the associated fragments in three dimensions is derived based on the known transport of the primary particles, taking the mean square angular spread of their production processes, as well as their energy loss and multiple scattering, into account. The analytical pencil and broad beam depth fluence and absorbed dose distributions are accurately expressed using recently derived analytical energy and range formulas. The contributions from low and high linear energy transfer (LET) dose components were separately identified using analytical expressions. The analytical results are compared with SHIELD-HIT Monte Carlo (MC) calculations and found to be in very good agreement. The pencil beam fluence and absorbed dose distributions of the primary particles are mainly influenced by an exponential loss of the primary ions combined with an increasing lateral spread due to multiple scattering and energy loss with increasing penetration depth. The associated fluence of heavy fragments is concentrated at small radii and so is the LET and absorbed dose distribution. Their transport is also characterized by the buildup of a slowing down spectrum which is quite similar to that of the primaries but with a wider energy and angular spread at increasing penetration depths. The range of the fragments is shorter or longer depending on their nuclear mass to charge ratio relative to that of the primary ions. The absorbed dose of the heavier fragments is fairly similar to that of the primary ions and also influenced by a rapidly increasing energy loss towards the end of their ranges. The present analytical solution of the Boltzmann equation accurately accounts for the loss of primary particles as well as their energy losses and multiple scattering. At the same time these quantities for the fragments are also accurately derived as based on the generalized Gaussian solution of the primaries and compared both with Monte Carlo and experimental data. The results are useful for fast transport calculations and biologically optimized therapy planning with light ion beams.
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