放疗中肿瘤生长数学模型及放射敏感性分析

Mathematical Model of Tumor Growth in Radiotherapy and Radiosensitivity Analysis

目的建立放射治疗下肿瘤生长及浸润的数学模型,数值模拟放射治疗对肿瘤生长的影响,并进行敏感性分析。方法建立放射治疗前后肿瘤生长和浸润随时间演变的数学模型,模型包括肿瘤浸润过程中4个关键变量:肿瘤细胞、细胞外基质、基质降解酶和氧,利用线性二次(LQ)模型模拟放疗后的肿瘤细胞存活概率,探讨肿瘤放射治疗下不同放疗方案和系数对治疗效果的影响,并将传统放疗和术中靶向放射治疗进行对比分析。结果在总剂量不变的前提下,放疗结果与放疗系数成正比,与放疗频率无关联;术中靶向放疗与标准治疗相比,治疗成效更好。结论模拟结果和临床实验结果基本相符,术中靶向放疗作为一种更加有效的治疗手段,能够为临床肿瘤治疗提供一种新思路。

Objective To establish a mathematical model of tumor growth and invasion under radiotherapy,so as to numerically simulate the effect of radiotherapy on tumor growth and make sensitivity analysis.Methods The mathematical model of tumor growth and invasion with time evolution before and after radiotherapy was established.The model included four key variables in the process of tumor invasion:tumor cells,extracellular matrix(ECM),matrix-degradative enzymes(MDEs)and oxygen.The linear quadratic(LQ)model was used to simulate the survival probability of tumor cells after radiotherapy,and the effects of different radiotherapy schemes and radiotherapy coefficients on the treatment effect were discussed.Traditional radiotherapy and intraoperative targeted radiotherapy were compared.Results Under the premise of constant total dose,the results of radiotherapy were directly proportional to the radiotherapy coefficient,but not related to the radiotherapy frequency;the therapeutic effect of intraoperative targeted radiotherapy was better than that of standard treatment.Conclusions Simulation results are basically consistent with clinical experimental results.As a more efficient treatment method,intraoperative targeted radiotherapy can provide new ideas for clinical tumor treatment.