Nonlinear Order Reduction of Discretized Cell Population Models

Dynamic cell population balance models consist of nonlinear partial differential-integro equations. An accurate discretized approximation typically yields a large number of nonlinear ordinary differential equations which are not well suited for dynamic analysis and model-based controller design. In this paper, proper orthogonal decomposition is used to construct nonlinear reduced-order models from spatiotemporal data sets obtained via simulation of an accurate discretized cell population model. Dynamic simulation and bifurcation analysis results demonstrate that reduced-order models with a comparatively small number of differential equations yield accurate predictions over a wide range of operating conditions. We study the spectrum of the linearized model as a function of the level of discretization probing the existence of spectral gaps which typically lead to good model reduction.