Combination of limited measurement information and multidimensional population balance models

Cell to cell variability with respect to intracellular composition as measured by flow cytometry is a core feature of many bioprocesses.Models of the underlying processes are often available from small scale or single cell observations but generally fail to account for heterogeneity within the cell culture. This heterogeneity can be incorporated using population balance equations that have to be adapted to the flow cytometric measurements.However, in general not the whole intracellular composition can be determined simultaneously for technical or economical reasons with flow cytometry. Furthermore, in many cases only integral quantities of certain compounds are measurable (e.g. overall amount of biomass in a cell culture).In this contribution we will present a procedure for combination of these limited measurement informations with complex models. Application will be shown for production of biopolymer poly(3-hydroxybutyrate) (PHB) in bacteria cultures. Starting from a single cell description a corresponding population balance model which describes the heterogeneity on a macroscopic scale will be derived. Afterwards an efficient approximate moment method and the Method of Characteristics will be used to combine population balance models and limited measurement data.