Population-based estimation for PDE system – Applications in electroporation of tumor spheroids

Abstract

The estimation of partial differential systems (PDE) – in particular, the identification of their parameters – is fundamental in many applications to combine modeling and available measurements. However, it is well known that parameter prior values must be chosen appropriately to balance our distrust of measurements, especially when data are sparse or corrupted by noise. A classic strategy to compensate for this weakness is to use repeated measurements collected in configurations with common priors, such as multiple subjects in a clinical trial. In the mixed-effects approach, all subjects are pooled and a global distribution of model parameters in the population is estimated. However, due to the high computational cost, this strategy is often not applicable in practice for PDE. In this paper, we propose an estimation strategy to overcome this challenge. This sophisticated method is based on two important existing methodological strategies: (1) a population-based Kalman filter and, (2) a joint state-parameter estimation. More precisely, the errors coming from the initial conditions are controlled by a Luenberger observer and the parameters are estimated using a population-based reduced-order Kalman filter restricted to the parameter space. The performance of the algorithm is evaluated using synthetic and real data for tumor spheroid electroporation.