A mathematical model that describes the replication of influenza A virus in animal cells in large-scale microcarrier culture is presented. The virus is produced in a two-step process, which begins with the growth of adherent Madin-Darby canine kidney (MDCK) cells. After several washing steps serum-free virus maintenance medium is added, and the cells are infected with equine influenza virus (A/Equi 2 (H3N8), Newmarket 1/93). A time-delayed model is considered that has three state variables: the number of uninfected cells, infected cells, and free virus particles. It is assumed that uninfected cells adsorb the virus added at the time of infection. The infection rate is proportional to the number of uninfected cells and free virions. Depending on multiplicity of infection (MOI), not necessarily all cells are infected by this first step leading to the production of free virions. Newly produced viruses can infect the remaining uninfected cells in a chain reaction. To follow the time course of virus replication, infected cells were stained with fluorescent antibodies. Quantitation of influenza viruses by a hemagglutination assay (HA) enabled the estimation of the total number of new virions produced, which is relevant for the production of inactivated influenza vaccines. It takes about 4-6 h before visibly infected cells can be identified on the microcarriers followed by a strong increase in HA titers after 15-16 h in the medium. Maximum virus yield Vmax was about 1x10(10) virions/mL (2.4 log HA units/100 microL), which corresponds to a burst size ratio of about 18,755 virus particles produced per cell. The model tracks the time course of uninfected and infected cells as well as virus production. It suggests that small variations (<10%) in initial values and specific rates do not have a significant influence on Vmax. The main parameters relevant for the optimization of virus antigen yields are specific virus replication rate and specific cell death rate due to infection. Simulation studies indicate that a mathematical model that neglects the delay between virus infection and the release of new virions gives similar results with respect to overall virus dynamics compared with a time delayed model.

An assay for measuring the number of adherent cells on microcarriers that is independent from dilution errors in sample preparation was used to investigate attachment dynamics and cell growth. It could be shown that the recovery of seeded cells is a function of the specific rates of cell attachment and cell death, and finally a function of the initial cell-to-bead ratio. An unstructured, segregated population balance model was developed that considers individual classes of microcarriers covered by 1-220 cells/bead. The model describes the distribution of initially attached cells and their growth in a microcarrier system. The model distinguishes between subpopulations of dividing and nondividing cells and describes in a detailed way cell attachment, cell growth, density-dependent growth inhibition, and basic metabolism of Madin-Darby canine kidney cells used in influenza vaccine manufacturing. To obtain a model approach that is suitable for process control applications, a reduced growth model without cell subpopulations, but with a formulation of the specific cell growth rate as a function of the initial cell distribution on microcarriers after seeding was developed. With both model approaches, the fraction of growth-inhibited cells could be predicted. Simulation results of two cultivations with a different number of initially seeded cells showed that the growth kinetics of adherent cells at the given cultivation conditions is mainly determined by the range of disparity in the initial distribution of cells on microcarriers after attachment.

To describe the growth behavior of anchorage-dependent mammalian cells in microcarrier systems, various approaches comprising deterministic and stochastic single cell models as well as automaton-based models have been presented in the past. The growth restriction of these often contact-inhibited cells by spatial effects is described at levels with different complexity but for the most part not taking into account their metabolic background. Compared to suspension cell lines these cells have a comparatively long lag phase required for attachment and start of proliferation on the microcarrier. After an initial phase of exponential growth only a moderate specific growth rate is achieved due to restrictions in space available for cell growth, limiting medium components, and accumulation of growth inhibitors. Here, a basic deterministic unstructured segregated cell model for growth of Madin Darby Canine Kidney (MDCK) cells used in influenza vaccine production is described. Four classes of cells are considered: cells on microcarriers, cells in suspension, dead cells, and lysed cells. Based on experimental data, cell attachment and detachment is taken explicitly into account. The model allows simulation of the overall growth behavior in microcarrier culture, including the lag phase. In addition, it describes the time course of uptake and release of key metabolites and the identification of parameters relevant for the design and optimization of vaccine manufacturing processes.

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