Hybrid simulation algorithm for efficient numerical solution of population balance equations

Abstract

Cell-to-cell variability of multicellular systems affects many processes from bioprocess engineering, systems biology and systems medicine. Multiscale modeling of these cellular heterogeneities with population balance equations is a valuable tool to understand the interplay of individual cell dynamics (intracellular level), interactions of cells with each other (population level) and interactions of cells with other molecular species (extracellular level). The resulting mathematical models represent high dimensional partial integro-differential equations which are rarely solvable analytically. As alternative to classical numerical solution methods which are not well suited for efficient solution, we propose a hybrid simulation algorithm in this contribution. This technique is based on a combination of the method of partial characteristics and approximate moment methods using monomial cubatures. The technique’s efficiency and accuracy is shown for a multicellular system describing cell-to-cell signaling in osteochondro-switch models.