Estimation of hidden chemoattractant field from observed cell migration patterns

Neutrophilic chemotaxis is essential to immune system response to external threats. During this process cells alternate between directed motion towards the higher concentration of external stimuli and correlated random walk. An individual neutrophil migration can thus be characterised as a stochastic dynamical process driven by an external chemotactic environment that is typically not measured. This introduces the problem of estimating spatially-varying chemoattractant concentration field from the observed migration patterns of cell populations. We propose a solution to this estimation problem in a statistical inference framework. The framework has measured cell positions in the field as inputs and employs the expectation-maximisation algorithm for joint estimation of full cell states and parameters of the chemoattractant field decomposed with cubic B-splines. The performance of the developed algorithm is accessed via process in vivo measurements of cell positions in the injured tail fin of zebrafish. Estimation results for different injury types evidence that the proposed estimation algorithm provides a rigorous connection between mathematical modelling and experimental data.