A new conceptual framework for the therapy by optimized multidimensional pulses of therapeutic activity. The case of multiple myeloma model

We developed simulation methodology to assess eventual therapeutic efficiency of exogenous multiparametric changes in a four-component cellular system described by the system of ordinary differential equations. The method is numerically implemented to simulate the temporal behavior of a cellular system of multiple myeloma cells. The problem is conceived as an inverse optimization task where the alternative temporal changes of selected parameters of the ordinary differential equations represent candidate solutions and the objective function quantifies the goals of the therapy. The system under study consists of two main cellular components, tumor cells and their cellular environment, respectively. The subset of model parameters closely related to the environment is substituted by exogenous time dependencies - therapeutic pulses combining continuous functions and discrete parameters subordinated thereafter to the optimization. Synergistic interaction of temporal parametric changes has been observed and quantified whereby two or more dynamic parameters show effects that absent if either parameter is stimulated alone. We expect that the theoretical insight into unstable tumor growth provided by the sensitivity and optimization studies could, eventually, help in designing combination therapies.