Poster - Thurs Eve-04: Mathematical modeling of liver metastases tumour growth and control with radiotherapy.

Abstract

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 tumor 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 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. Enzyme data were derived from repeated serum blood tests, and radiation treatment-related data were retrieved from the patient's chart. 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 0.7% per day; the fractional radiation cell kill for the prescribed dose was 60% per day; and tumour repopulation rate was 3.5% 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.