Extraction of Physiological State Functions in Heterogeneous Cell Population Models*

A simple yet generic approach is presented to extract the growth and breakage kinetics from the temporal data of heterogeneous cell population. The moment form of the one-dimensional population balance equation is directly solved by a MATLAB solver for linear systems to extract the kinetics. The corresponding systems of linear equations are, however, highly underdetermined and ill-conditioned. To address this, the problem is regularized by assuming a suitable upper bound of the solution. The range between minimum and maximum possible values of the solution is discretized into several sub-intervals. The system is then solved against each sub-interval, whose values are used as lower and upper bounds in a suitable MATLAB solver and a local solution is obtained in all these ranges. The final solution is then computed by taking average of all solutions having residual norms less than a particular threshold. To validate the method, the results of the inverse technique are compared and discussed against two theoretical experiments.