A New Conceptual Framework for the Therapy by Optimized Multidimensional Pulses of Therapeutic Activity. The case of Multiple Myeloma Model

Abstract

We developed simulation methodology to assess the eventual therapeutic efficiency of the exogenous multiparametric changes in a four-component cellular system described by the system of ordinary differential equations. The problem is conceived as an inverse optimization task where the alternative temporal changes of the selected parameters of the ordinary differential equations represent candidate solutions and the objective function quantifies the goals of the therapy. Then, on the basis of qualitative arguments, equilibrium approximations and short time perturbative expansion were analyzed. The results were interpreted from the viewpoint of the system consisting of two main cellular components, tumor cells and their cellular environment, respectively. Subsequently, the subset of model parameters closely related to the environment was substituted by exogenous time dependencies, combining the continuous functions and discrete parameters, subordinated thereafter to the optimization. The method is numerically implemented to simulate the temporal behavior of bone marrow cellular systems including multiple myeloma cells. The synergistic interaction between parametric impacts has been observed whereby two or more dynamic parameters give rise to the effects that absent if either parameter is stimulated alone. We expect that the theoretical insight obtained from the sensitivity studies derived for the unstable tumor growth could, eventually, help in designing novel therapies.