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We developed simulation methodology to assess eventual therapeutic efficiencyof exogenous multiparametric changes in a four-component cellular systemdescribed by the system of ordinary differential equations. The method isnumerically implemented to simulate the temporal behavior of a cellular systemof multiple myeloma cells. The problem is conceived as an inverse optimizationtask where the alternative temporal changes of selected parameters of theordinary differential equations represent candidate solutions and the objectivefunction quantifies the goals of the therapy. The system under study consistsof two main cellular components, tumor cells and their cellular environment,respectively. The subset of model parameters closely related to the environmentis substituted by exogenous time dependencies - therapeutic pulses combiningcontinuous functions and discrete parameters subordinated thereafter to theoptimization. Synergistic interaction of temporal parametric changes has beenobserved and quantified whereby two or more dynamic parameters show effectsthat absent if either parameter is stimulated alone. We expect that thetheoretical insight into unstable tumor growth provided by the sensitivity andoptimization studies could, eventually, help in designing combinationtherapies.

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