Sachs R K, Hlatky L, Hahnfeldt P, Chen P L
Department of Physics, University of California, Berkeley 94720.
Radiat Res. 1990 Nov;124(2):216-26.
Markov models for the survival of cells subjected to ionizing radiation take stochastic fluctuations into account more systematically than do non-Markov counterparts. Albright's Markov RMR (repair-misrepair) model (Radiat. Res. 118, 1-20, 1989) and Curtis's Markov LPL (lethal-potentially lethal) model [in Quantitative Mathematical Models in Radiation Biology (J. Kiefer, Ed.), pp. 127-146. Springer, New York, 1989], which assume acute irradiation, are here generalized to finite dose rates. Instead of treating irradiation as an instantaneous event we introduce an irradiation period T and analyze processes during the interval T as well as afterward. Albright's RMR transition matrix is used throughout for computing the time development of repair and misrepair. During irradiation an additional matrix is added to describe the evolving radiation damage. Albright's and Curtis's Markov models are recovered as limiting cases by taking T----0 with total dose fixed; the opposite limit, of low dose rates, is also analyzed. Deviations from Poisson behavior in the statistical distributions of lesions are calculated. Other continuous-time Markov chain models ("compartmental models") are discussed briefly, for example, models which incorporate cell proliferation and saturable repair models. It is found that for low dose rates the Markov RMR and LPL models give lower survivals compared to the original non-Markov versions. For acute irradiation and high doses, the Markov models predict higher survivals. In general, theoretical extrapolations which neglect some random fluctuations have a systematic bias toward overoptimism when damage to irradiated tumors is compared with damage to surrounding tissues.
与非马尔可夫模型相比，用于描述受电离辐射细胞存活情况的马尔可夫模型能更系统地考虑随机波动。阿尔布赖特的马尔可夫RMR（修复-误修复）模型（《辐射研究》118卷，第1 - 20页，1989年）和柯蒂斯的马尔可夫LPL（致死-潜在致死）模型[载于《辐射生物学中的定量数学模型》（J. 基弗编），第127 - 146页。施普林格出版社，纽约，1989年]，假设为急性辐射，在此被推广到有限剂量率情况。我们不再将辐射视为瞬时事件，而是引入一个辐照期T，并分析T期间以及之后的过程。在整个计算修复和误修复的时间发展过程中，都使用阿尔布赖特的RMR转移矩阵。在辐照期间，添加一个额外的矩阵来描述不断演变的辐射损伤。通过在总剂量固定的情况下取T→0，可将阿尔布赖特和柯蒂斯的马尔可夫模型作为极限情况恢复；同时也分析了低剂量率的相反极限情况。计算了损伤统计分布中与泊松行为的偏差。还简要讨论了其他连续时间马尔可夫链模型（“房室模型”），例如，包含细胞增殖和饱和修复模型的模型。结果发现，对于低剂量率，马尔可夫RMR和LPL模型与原始非马尔可夫版本相比存活率更低。对于急性辐射和高剂量，马尔可夫模型预测的存活率更高。一般来说，当将受辐照肿瘤的损伤与周围组织的损伤进行比较时，忽略一些随机波动的理论外推存在系统性的过度乐观偏差。
