Distributed Modeling and Parameter Estimation of Influenza Virus Replication During Vaccine Production

This contribution is concerned with population balance modeling of influenza virus replication in mammalian cell cultures. The cells are heterogeneous with respect to intracellular compounds like viral proteins. The amount of viral NP protein can be measured directly by means of flow cytometry. The corresponding degree of fluorescence is introduced as internal coordinate for a distributed deterministic modeling approach. The resulting model includes kinetic processes like infection, virus replication and release, apoptosis and cell death. It consists of three partial differential equations describing the distribution dynamics which are coupled to two differential equations that characterize the concentration of active and inactive virions in the medium. Kinetic parameters are determined from experimental data. The parameters are assumed to depend on the internal coordinate. The emerging infinite dimensional parameter estimation problem is translated to a finite dimension using a hermite spline representation of the distributed parameters. Hence the resulting inverse problem can be solved in a weighted nonlinear least squares framework. Spline approaches of different complexity are discussed and the estimation results are compared.