A mechanistic model of high dose irradiation damage

The main goal of our study is to develop a realistic mechanistic model of the effect of ionizing radiation on DNA in mammalian cells. We consider a population of cells structured by the number of DNA double strand breaks due to radiation. Using the system of linear differential equation, the model describes the evolution of the irradiated population of cells in time. The work is in three parts. First, we consider the effect of a single dose of radiation, while in the second part we work on the model parameter estimation using Nelder–Mead simplex algorithm which allows us to relate the clinically useful parameters of the LQ relation to aspects of cellular activity that can be manipulated experimentally. In the third part, we deal with cell killing effects of fractioned doses of radiation. Using MATLAB, we observed the cell survival fractions can be well approximated by the Linear–Quadratic relation and also show fewer cell will die if the dose is fractionated in two or more fractions.

[1]  X Allen Li,et al.  Extending the linear-quadratic model for large fraction doses pertinent to stereotactic radiotherapy. , 2004, Physics in medicine and biology.

[2]  Joachim Widder,et al.  Recommendations for implementing stereotactic radiotherapy in peripheral stage IA non-small cell lung cancer: report from the Quality Assurance Working Party of the randomised phase III ROSEL study , 2009, Radiation oncology.

[3]  A. de Klein,et al.  Dose fractionation effects in primary and metastatic human uveal melanoma cell lines. , 2003, Investigative ophthalmology & visual science.

[4]  A. Kellerer,et al.  A generalized formulation of dual radiation action. , 2012, Radiation research.

[5]  Odo Diekmann,et al.  On the formulation and analysis of general deterministic structured population models I. Linear Theory , 1998, Journal of mathematical biology.

[6]  W. Sontag,et al.  Comparison of six different models describing survival of mammalian cells after irradiation , 1990, Radiation and environmental biophysics.

[7]  M. Löbrich,et al.  Repair of x-ray-induced DNA double-strand breaks in specific Not I restriction fragments in human fibroblasts: joining of correct and incorrect ends. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[8]  P. Hahnfeldt,et al.  DNA damage in non-proliferating cells subjected to ionizing irradiation at high or low dose rates , 1993, Journal of mathematical biology.

[9]  R. Stewart,et al.  Two-Lesion Kinetic Model of Double-Strand Break Rejoining and Cell Killing , 2001, Radiation research.

[10]  Robert V. Brill,et al.  Applied Statistics and Probability for Engineers , 2004, Technometrics.

[11]  Ollivier Hyrien,et al.  A comprehensive stochastic model of irradiated cell populations in culture. , 2006, Journal of theoretical biology.

[12]  E. Hall,et al.  Radiobiology for the radiologist , 1973 .

[13]  O. Diekmann,et al.  On the formulation and analysis of general deterministic structured population models II. Nonlinear theory , 2000 .

[14]  K H Chadwick,et al.  A molecular theory of cell survival. , 1973, Physics in medicine and biology.

[15]  M Zaider,et al.  Cell-survival probability at large doses: an alternative to the linear-quadratic model , 2010, Physics in medicine and biology.

[16]  S B Curtis,et al.  Lethal and potentially lethal lesions induced by radiation--a unified repair model. , 1986, Radiation research.

[17]  Carl Johan Lagerkvist.  Introductory Econometrics--Using Monte Carlo Simulation with Microsoft Excel , 2007 .

[18]  Francesca Ballarini,et al.  From DNA Radiation Damage to Cell Death: Theoretical Approaches , 2010, Journal of nucleic acids.

[19]  J. Cushing.  An introduction to structured population dynamics , 1987 .

[20]  Per Nilsson,et al.  The effect on the small bowel of 5-FU and oxaliplatin in combination with radiation using a microcolony survival assay , 2009, Radiation oncology.

[21]  Alan E. Nahum,et al.  The modified linear-quadratic model of Guerrero and Li can be derived from a mechanistic basis and exhibits linear-quadratic-linear behaviour , 2005 .

[22]  Kai Rothkamm,et al.  Evidence for a lack of DNA double-strand break repair in human cells exposed to very low x-ray doses , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[23]  C A Tobias,et al.  Neoplastic cell transformation by heavy charged particles. , 1985, Radiation research. Supplement.

[24]  M. Löbrich,et al.  DNA Double-Strand Break Repair of Blood Lymphocytes and Normal Tissues Analysed in a Preclinical Mouse Model: Implications for Radiosensitivity Testing , 2008, Clinical Cancer Research.

[25]  R K Sachs,et al.  The linear-quadratic model and most other common radiobiological models result in similar predictions of time-dose relationships. , 1998, Radiation research.

[26]  R. L. Constable,et al.  Basic Statistics: Tales of Distributions. , 1982 .

[27]  Kai Rothkamm,et al.  Pathways of DNA Double-Strand Break Repair during the Mammalian Cell Cycle , 2003, Molecular and Cellular Biology.

[28]  R K Sachs,et al.  The link between low-LET dose-response relations and the underlying kinetics of damage production/repair/misrepair. , 1997, International journal of radiation biology.

[29]  R K Sachs,et al.  Incorporating dose-rate effects in Markov radiation cell survival models. , 1990, Radiation research.

[30]  N Albright.  A Markov formulation of the repair-misrepair model of cell survival. , 1989, Radiation research.

[31]  P. Hahnfeldt,et al.  Evolution of DNA damage in irradiated cells , 1992, Journal of mathematical biology.

[32]  Xin Zhang,et al.  Development and Validation of a Nanodosimetry-Based Cell Survival Model for Mixed High- and Low-LET Radiations , 2006 .

[33]  S B Curtis,et al.  Mechanistic models. , 1991, Basic life sciences.

[34]  W Sontag,et al.  A cell survival model with saturable repair after irradiation , 1987, Radiation and environmental biophysics.

[35]  C A Tobias,et al.  The repair-misrepair model in radiobiology: comparison to other models. , 1985, Radiation research. Supplement.

[36]  D. M. Levine,et al.  Business Statistics: A First Course , 2000 .

[37]  Michael C. Joiner,et al.  Basic Clinical Radiobiology , 2009 .

[38]  M L Johnson,et al.  Parameter estimation by least-squares methods. , 1992, Methods in enzymology.