Mathematical modeling of liver metastases tumour growth and control with radiotherapy

被引:11
作者
Campbell, Adrienne [1 ]
Sivakumaran, Thiru [1 ]
Davidson, Melanie [4 ]
Lock, Michael [2 ]
Wong, Eugene [1 ,2 ,3 ,5 ]
机构
[1] Univ Western Ontario, Dept Phys & Astron, London, ON, Canada
[2] Univ Western Ontario, Dept Oncol, London, ON, Canada
[3] Univ Western Ontario, Dept Med Biophys, London, ON, Canada
[4] Sunnybrook Hlth Sci Ctr, Odette Canc Ctr, Toronto, ON M4N 3M5, Canada
[5] London Hlth Sci Ctr, London Reg Canc Program, London, ON, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
D O I
10.1088/0031-9155/53/24/015
中图分类号
R318 [生物医学工程];
学科分类号
0831 ;
摘要
Generating an optimized radiation treatment plan requires understanding the factors affecting tumour control. Mathematical models of tumour dynamics may help in future studies of factors predicting tumour sensitivity to radiotherapy. In this study, a time-dependent differential model, incorporating biological cancer markers, is presented to describe pre-treatment tumour growth, response to radiation, and recurrence. The model uses Gompertzian-Exponential growth to model pre-treatment tumour growth. The effect of radiotherapy is handled by a realistic cell-kill term that includes a volume-dependent change in tumour sensitivity. Post-treatment, a Gompertzian, accelerated, delayed repopulation is employed. As proof of concept, we examined the fit of the model's prediction using various liver enzyme levels as markers of metastatic liver tumour growth in a liver cancer patient. A tumour clonogen population model was formulated. Each enzyme was coupled to the same tumour population, and served as surrogates of the tumour. This dynamical model was solved numerically and compared to the measured enzyme levels. By minimizing the mean-squared error of the model enzyme predictions, we determined the following tumour model parameters: growth rate prior to treatment was 0.52% per day; the fractional radiation cell kill for the prescribed dose (60 Gy in 15 fractions) was 42% per day, and the tumour repopulation rate was 2.9% per day. These preliminary results provided the basis to test the model in a larger series of patients, to apply biological markers for improving the efficacy of radiotherapy by determining the underlying tumour dynamics.
引用
收藏
页码:7225 / 7239
页数:15
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