Dynamic Density Estimation in Heterogeneous Cell Populations

Abstract

Multicellular systems play a key role in bioprocess and biomedical engineering. Cell ensembles encountered in these setups show phenotypic variability like size and biochemical composition. As this variability may result in undesired effects in bioreactors, close monitoring of the cell population heterogeneity is important for maximum production output, and accurate control. However, direct measurements are mostly restricted to a few cellular properties. This motivates the application of modelbased online estimation techniques for the reconstruction of non-measurable cellular properties. Population balance modeling allows for a natural description of cell-to-cell variability. In this contribution, we present an estimation approach that, in contrast to existing ones, does not rely on a finite-dimensional approximation through grid based discretization of the underlying population balance model. Instead, our so-called characteristics based density estimator employs sample approximations. With two and three-dimensional benchmark examples we demonstrate that our approach is superior to the grid based designs in terms of accuracy and computational demand.

Identification of cell‐to‐cell heterogeneity through systems engineering approaches

“…Unfortunately, this minimization problem (Equation 5) is nontrivial to solve. First of all, the problem is infinite‐dimensional since its decision variable is a function instead of a finite‐dimensional vector . Usually, one has to rely on an approximation method to solve such an optimization problem.…”

“…First of all, the problem is infinite-dimensional since its decision variable is a function instead of a finite-dimensional vector. 2,38 Usually, one has to rely on an approximation method to solve such an optimization problem. Second, it is expected that the PDFs of the entire parameter set are difficult to be estimated accurately from the measurements due to the unidentifiability of the PDFs of the model parameters.…”

Estimation methods for heterogeneous cell population models in systems biology

“…In past studies, the L 2 norm has been used for this optimization [53,68], though using other norms is also possible. Another measure to compare density functions from the model and the data is the Kullback-Leibler divergence, which has been used in a recently proposed particle filter for the estimation of cell populations [101]. The PBE in (4.2) needs to be solved k times before running the optimization, but not within the optimization itself.…”