Kinetic Modelling of the Input/Output Dynamics of a Perfused 3D Multi-Compartment Capillary Membrane Bioreactor for Extracorporeal Liver Support

The provision of standardised bioreactor technology for liver cell research and liver support therapy requires along the devices’ design a quantitative characterisation of their dynamic input/output behaviour under operation. Characterisation of abiotic prior to biotic behaviour is here an essential step served by studies on the distribution of model substances in the systems. We report here on the kinetic modelling of the input/output dynamics of a clinical scale perfused 3D multi-compartment capillary membrane bioreactor based on NaCl tracer experiments. The experimental set-up consisted of the bioreactor and a perfusion circuit with two pumps for medium feeding and recirculation. NaCl sensors monitored the medium inflow and recirculation loop. The system was ‘charged’/‘discharged’ by switching the feeding solution between 0.05% and 0.45%. Various combinations of feeding rates (50/100/150ml/h) and recirculation rates (125/250/500ml/min) were analysed. Based on the measurements, mass balancing and general process knowledge, an initial model was developed and its parameters fitted to the data using a nonlinear differential equation system. The modelling considered the general experimental results: i) the feeding rate has a dominating effect on the NaCl distribution in the system compared to the recirculation rate, ii) there is a marked difference in the bioreactor dynamics between ‘charging’ and ‘discharging’, the latter taking considerably longer, e.g. about 6 times at a recirculation rate of 250ml/min. The 2-compartment model developed takes into account the perfusion and the liver cell compartment (approx. volumes: 900/600ml). The two coupled differential equations describe the NaCl concentration in either compartment. The model includes the feeding rate and concentration, two unknown (i.e. to be fitted) parameters correcting for the approximate compartment volumes and an unknown parameter for the specific mass transfer coefficient quantifying membrane characteristics and diffusion with the NaCl concentration difference between the two compartments as driving force. To account for the markedly different dynamics of the ‘charging’/‘discharging’ process, the mass transfer coefficient was modelled dependent on the direction of the concentration difference. This model and its parameters fit the experimental data well. Although still phenomenological, the model can already serve to plan further experiments to arrive at more complex mechanistic models.

Fig. 1: 3D Multi-Compartment Capillary Membrane Bioreactor with Schematic Representation and Equations of the 2-Compartment Model

Key words

Extracorporeal Liver Support - Kinetic Modelling - Multi-Compartment Bioreactor