Parameter Estimation in Population Balance Models

The aim of this manuscript is to elucidate some models focusing on the dynamics of cell populations in vitro and to bring them in line with methods established in the context of inverse problems. We concentrate on a population balance model that describes the cell number as a function of time and single cell mass, where the key variable fulfills a partial integro-differential equation (PIDE). According to this popular approach, three generally unknown physiological functions enter into the representation and the objective is to identify the corresponding parameters. In this article, the main concept of this equation type is outlined, some possibilities of data retrieval are explained and mathematical methods to solve the problem are expounded.