Adaptive Short Term Ahead Tumor Growth Inhibition Prediction Subjected in Anticancer Agents Given in Combination

Combination chemotherapy, i.e. multiple anticancer drugs given in combination, is a very common strategy combating cancer. Despite the high complexity of the disease, the tumor and drug dynamics and kinetics can be mathematically described and modeled and numerically simulated accurately enough. In this article, the development and parameter identification of a dynamic input-output state-space mathematical model capable of simulating with accuracy the tumor growth in xenografted mice under the effects of antineoplastic drug agents in combination is first carried out. Through a nonlinear optimization algorithm and Monte Carlo simulations the pharmacodynamic-pharmacokinetic (PK-PD) parameters values of the dynamic input-output mathematical model were estimated for specific cases of drugs administered in combination, with the objective the mathematical model to best fit in the experimental data. Then, the ability of the identified nonlinear tumor growth inhibition (TGIadd) state-space model to forecast with precision in the short-term i.e. one, two or three steps ahead in the near future the tumor growth under the effects of anticancer agents administered in combination was explored and through the same two numerical experiments was evaluated and confirmed. It is shown that such a high prediction power of the specific tumor growth inhibition mathematical model is of great importance at a clinical context, since it could provide oncologists an important help in the appropriate modification of a combination chemotherapy strategy to optimize it and make it more personalized and consequently more effective, thus prolonging patient's life.