Parameter identifiability and model selection for partial differential equation models of cell invasion

Abstract

When employing mechanistic models to study biological phenomena, practical parameter identifiability is important for making accurate predictions across wide ranges of unseen scenarios, as well as for understanding the underlying mechanisms. In this work, we use a profile-likelihood approach to investigate parameter identifiability for four extensions of the Fisher–Kolmogorov–Petrovsky–Piskunov (Fisher–KPP) model, given experimental data from a cell invasion assay. We show that more complicated models tend to be less identifiable, with parameter estimates being more sensitive to subtle differences in experimental procedures, and that they require more data to be practically identifiable. As a result, we suggest that parameter identifiability should be considered alongside goodness-of-fit and model complexity as criteria for model selection.

Structural and practical identifiability of contrast transport models for DCE-MRI

“…In contrast, the optimal value estimated for v p does not significantly changes with respect to K trans variation. This is in line with the results in (13), where we can notice how v p does not have any relation with K trans . In the (RR) case, K trans is not practically identifiable, evident from the flat likelihood profile, which makes it not possible to identify a lower or upper bound of a confidence region with respect to the optimal value K trans .…”

“…Here we consider the structural and practical identifiability of four nested contrast transport compartmental models frequently used to analyze DCE-MRI data. Identifiability is a fundamental property to create models able to capture the dynamics shown in the data with well-determined parameters [ 13 , 14 ]. The issue of model identifiability revolves around the question of whether it is possible to use data to accurately and uniquely estimate parameters in the model.…”

Structural identifiability analysis of linear reaction–advection–diffusion processes in mathematical biology

“…However, many forms of biological data are inherently spatial, and therefore not well described by ODE models [20]: data relating to cell migration [21,22] or diffusive processes [23,24], for example. Yet, tools for assessing the structural identifiability of the partial differential equation (PDE) models that capture spatial heterogeneity remain almost entirely undeveloped.…”