Modelling and Identification of Immune Cell Migration during the Inflammatory Response

Neutrophils are the white blood cells that play a crucial role in the response of the innate immune system to tissue injuries or infectious threats. Their rapid arrival to the damaged area and timely removal from it define the success of the inflammatory process. Therefore, understanding neutrophil migratory behaviour is essential for the therapeutic regulation of multiple inflammation-mediated diseases. Recent years saw rapid development of various in vivo models of inflammation that provide a remarkable insight into the neutrophil function. The main drawback of the \textit{in vivo} microscopy is that it usually focuses on the moving cells and obscures the external environment that drives their migration. To evaluate the effect of a particular treatment strategy on neutrophil behaviour, it is necessary to recover the information about the cell responsiveness and the complex extracellular environment from the limited experimental data. This thesis addresses the presented inference problem by developing a dynamical modelling and estimation framework that quantifies the relationship between an individual migrating cell and the global environment. \par The first part of the thesis is concerned with the estimation of the hidden chemical environment that modulates the observed cell migration during the inflammatory response in the injured tail fin of zebrafish larvae. First, a dynamical model of the neutrophil responding to the chemoattractant concentration is developed based on the potential field paradigm of object-environment interaction. This representation serves as a foundation for a hybrid model that is proposed to account for heterogeneous behaviour of an individual cell throughout the migration process. An approximate maximum likelihood estimation framework is derived to estimate the hidden environment and the states of multiple hybrid systems simultaneously. The developed framework is then used to analyse the neutrophil tracking data observed in vivo under the assumption that each neutrophil at each time can be in one of three migratory modes: responding to the environment, randomly moving, and stationary. The second part of the thesis examines the process of neutrophil migration at the subcellular scale, focusing on the subcellular mechanism that translates the local environment sensing into the cell shape change. A state space model is formulated based on the hypothesis that links the local protrusions of the cell membrane and the concentration of the intracellular pro-inflammatory signalling protein. The developed model is tested against the local concentration data extracted from the in vivo time-lapse images via the classical expectation-maximisation algorithm

Estimation of potential field environments from heterogeneous behaviour of sensing agents

Abstract This paper proposes a novel modelling framework for estimating the global potential field from trajectories of multiple sensing agents whose perception of the unknown field is subject to abrupt changes. We derive a parametrised formulation of the estimation problem by combining the jump Markov non‐linear system (JMNLS) model of agent dynamics with a basis function decomposition of the environmental field. An approximate expectation‐maximisation algorithm is employed for joint estimation of the global field and of the agent behavioural modes from observed agent trajectories. To avoid prohibitive computational costs associated with the state estimation of JMNLS, we utilise two approximation steps. First, an interacting multiple model smoother is used to account for the hybrid structure that emerges in this problem. Second, we propose two approaches to approximating the non‐linear sufficient statistics during the expectation step. This results in the maximization step being exact. The performance of the developed framework is tested on simulation examples and demonstrated on an application study in which the observed movement patterns of immune cells are utilised in quantifying the underlying chemical concentration field that governs their migration. The results showcase that the proposed framework can be readily applied to problems where agents assume several behavioural modes