New Perspectives on Sensitivity and Identifiability Analysis using the Unscented Kalman Filter

Detailed dynamical systems' models used in the life sciences may include hundreds of state variables and many input parameters, often with physical meaning. Therefore, efficient and unique input parameter identification, from experimental data, is an essential but challenging task for this class of model. To clarify our understating of the process (which within a clinical context amounts to a personalisation), we utilise the computational methods of Unscented Kalman filtration (UKF), sensitivity and orthogonality analysis. We have applied these three techniques to a test-bench model of a single ventricle, coupled, via Ohmic valves, to a Compliance-Resistor-Compliance (CRC) Windkessel electrical analogue model of the systemic circulation, chosen in view of its relative simplicity, interpretability and prior art. Utilising an efficient, novel and real-time implementation of the UKF (Code available at https://github.com/H-Sax/CMSB-2023), we show how, counter-intuitively, input parameters are efficiently recovered from experimental data \emph{even if they are not sensitive parameters in the currently accepted sense}. This result (i) exposes potential limitations in the standard interpretation of what it means for an input parameter to be designated identifiable and (ii) suggests that the concepts of sensitivity and identifiability may have a weaker relationship than commonly thought - at least in the presence of an appropriate data set. We rationalise these observations. Practically, we present results which show the UKF to be an efficient method for assigning personalised input parameters from experimental data in real-time, which enhances the clinical significance of our approach.