Predicting tumor cell repopulation after response: Mathematical modeling of cancer cell growth

The kinetics of regrowth of tumor cells after treatment may offer a new end-point for clinical trials. Based on our testing, it is best described in this manner: y(t) = a*exp(-b*t) + c*exp(d*t). Human malignant glioma cells U87 MG were treated with etoposide and allowed to regrow after treatment. The cell number versus time data were fitted mathematically to the two-term exponential model. Parameters b and d were independent of the drug concentration, while a increased c decreased as the drug dose increased. The concentration independence of b and d indicated that both cell proliferation and cell death kinetics were independent of the drug treatment, which suggests constant times for cell cycle and apoptosis. The concentration dependence of c suggests that the time until the cells started regrowing depended on the treatment, repair mechanisms taking longer after heavy damage. The two-term exponential model predicted tumor repopulation in this in vitro system. These results indicated that the velocities of the logarithm of cell growth and cell death were independent of drug treatment, while the recovery time of the tumor repopulation was dependent on the drug dose. The two-term exponential model can be used to predict tumor repopulation in an in vitro system and this model will be further tested using clinical data.