Equivalence of the linear-quadratic and two-lesion kinetic models.

Double strand breaks (DSBs) are widely accepted as the main type of DNA damage responsible for cell killing in the range of doses and dose rates relevant to radiation therapy. Although the standard linear-quadratic (LQ) model with one first-order repair term often suffices to explain the results of some radiobiological experiments, converging lines of evidence suggest that DSBs are rejoined at two or more distinct rates. A two-lesion kinetic (TLK) model has been proposed to provide a direct link between biochemical processing of the DSBs and cell killing. A defining feature of the TLK model is that the family of all possible DSBs is subdivided into simple and complex DSBs, and each kind may have its own unique repair characteristics. Break-ends associated with both kinds of DSB are allowed to interact in pairwise fashion to form irreversible lethal and non-lethal chromosome aberrations. This paper examines the theoretical and practical linkages between the TLK and LQ models. The TLK formalism is used to derive an LQ formula with two first-order repair terms (dose protraction factors) and to relate the intrinsic radiosensitivity parameters used in one model to the parameters used in the other. Two extensive radiobiological datasets, one for CHO 10B2 cells and one for C3H 10T1/2 cells, are analysed using the TLK and LQ models. The LQ with two repair terms and the TLK are equally capable of explaining the CHO 10B2 and C3H 10T1/2 cell survival data. For the doses and dose rates most relevant to radiation therapy, tests of model equivalence indicate that an LQ formula with two first-order repair terms is an excellent approximation to the TLK model. We find the LQ and TLK models useful complementary tools for the analysis and prediction of radiobiological effects.

[1]  A. Nahum,et al.  Incorporating biologic measurements (SF(2), CFE) into a tumor control probability model increases their prognostic significance: a study in cervical carcinoma treated with radiation therapy. , 2001, International journal of radiation oncology, biology, physics.

[2]  J. Hopewell,et al.  Repair kinetics in pig epidermis: an analysis based on two separate rates of repair. , 1996, International journal of radiation biology.

[3]  P. Deschavanne,et al.  The relationship between radiosensitivity and repair of potentially lethal damage in human tumor cell lines with implications for radioresponsiveness. , 1990, Radiation research.

[4]  A Brahme,et al.  Individualizing cancer treatment: biological optimization models in treatment planning and delivery. , 2001, International journal of radiation oncology, biology, physics.

[5]  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.

[6]  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.

[7]  J. Hendry,et al.  Two components of repair in irradiated kidney colony forming cells. , 1994, International journal of radiation biology.

[8]  C. W. Gear,et al.  Numerical initial value problem~ in ordinary differential eqttations , 1971 .

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

[10]  D. Brenner.  Correlations between α/β and T½: implications for clinical biological modelling , 1992 .

[11]  J. M. Watt.  Numerical Initial Value Problems in Ordinary Differential Equations , 1972 .

[12]  Lawrence F. Shampine,et al.  A User’s View of Solving Stiff Ordinary Differential Equations , 1979 .

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

[14]  J. Bedford,et al.  An ionizing radiation-sensitive mutant of CHO cells: irs-20. II. Dose-rate effects and cellular recovery processes. , 1993, Radiation research.

[15]  H D Thames,et al.  Impact of spinal cord repair kinetics on the practice of altered fractionation schedules. , 1992, Radiotherapy and oncology : journal of the European Society for Therapeutic Radiology and Oncology.

[16]  P. Canney,et al.  Derivation and application of equations describing the effects of fractionated protracted irradiation, based on multiple and incomplete repair processes. Part 2. Analysis of mouse lung data. , 1993, International journal of radiation biology.

[17]  R Mohan,et al.  Radiobiological considerations in the design of fractionation strategies for intensity-modulated radiation therapy of head and neck cancers. , 2000, International journal of radiation oncology, biology, physics.

[18]  H. Thames,et al.  Recovery from radiation damage in mouse lung: interpretation in terms of two rates of repair. , 1993, Radiation research.

[19]  J. Fowler,et al.  A new incomplete-repair model based on a 'reciprocal-time' pattern of sublethal damage repair. , 1999, Acta oncologica.

[20]  J. Bedford,et al.  Dose-rate effects in mammalian cells. IV. Repairable and nonrepairable damage in noncycling C3H 10T 1/2 cells. , 1983, Radiation research.

[21]  J F Fowler,et al.  Is repair of DNA strand break damage from ionizing radiation second-order rather than first-order? A simpler explanation of apparently multiexponential repair. , 1999, Radiation research.

[22]  C C Ling,et al.  Towards multidimensional radiotherapy (MD-CRT): biological imaging and biological conformality. , 2000, International journal of radiation oncology, biology, physics.

[23]  T. McMillan,et al.  The intrinsic alpha/beta ratio for human tumour cells: is it a constant? , 1992, International journal of radiation biology.

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

[25]  T. McMillan,et al.  The Intrinsic α/β Ratio for Human Tumour Cells: Is It a Constant? , 1992 .