Efficient DQMOM for Multivariate Population Balance Equations and Application to Virus Replication in Cell Cultures

Population balances play an important role in process and bioprocess engineering. They represent PDEs which are often multidimensional. The numerical solution of these is quite challenging in particular for high dimensional problems. For this reason the distribution dynamics are usually represented by the respective moments. As the corresponding dynamic moment equations can only be computed in a closed form under strict assumptions, approximate moment methods have to be applied. However, existing techniques can not be implemented efficiently for high dimensional problems. In this manuscript an efficient implementation of the Direct Quadrature Method of Moments (DQMOM) is derived using monomial cubature rules. Furthermore, application is demonstrated for a five dimensional PBE which is based on a single cell model for viral replication in cell cultures. The algorithm is used to analyze the effects of different model assumptions on the overall dynamics.