title: Data-driven stochastic modelling of zebrafish locomotion.
abstract: In this work, we develop a data-driven modelling framework to reproduce the locomotion of fish in a confined environment. Specifically, we highlight the primary characteristics of the motion of individual zebrafish (Danio rerio), and study how these can be suitably encapsulated within a mathematical framework utilising a limited number of calibrated model parameters. Using data captured from individual zebrafish via automated visual tracking, we develop a model using stochastic differential equations and describe fish as a self propelled particle moving in a plane. Based on recent experimental evidence of the importance of speed regulation in social behaviour, we extend stochastic models of fish locomotion by introducing experimentally-derived processes describing dynamic speed regulation. Salient metrics are defined which are then used to calibrate key parameters of coupled stochastic differential equations, describing both speed and angular speed of swimming fish. The effects of external constraints are also included, based on experimentally observed responses. Understanding the spontaneous dynamics of zebrafish using a bottom-up, purely data-driven approach is expected to yield a modelling framework for quantitative investigation of individual behaviour in the presence of various external constraints or biological assays.
authors.affiliation: Department of Engineering Mathematics, University of Bristol, Bristol, UK.
authors.forename: Adam
authors.initials: A
authors.lastname: Zienkiewicz
authors.affiliation: Department of Engineering Mathematics, University of Bristol, Bristol, UK.
authors.forename: David A W
authors.initials: DA
authors.lastname: Barton
authors.affiliation: Department of Mechanical and Aerospace Engineering, New York University Polytechnic School of Engineering, New York, USA. mporfiri@nyu.edu.
authors.forename: Maurizio
authors.initials: M
authors.lastname: Porfiri
authors.affiliation: Department of Engineering Mathematics, University of Bristol, Bristol, UK. m.dibernardo@bristol.ac.uk.|Department of Electrical Engineering and ICT, University of Naples Federico II, Naples, Italy. m.dibernardo@bristol.ac.uk.
authors.forename: Mario
authors.initials: M
authors.lastname: di Bernardo
mesh_terms: D000818:Animals; D003198:Computer Simulation; D008124:Locomotion / Q000502:physiology; D055641:Mathematical Concepts; D008954:Models, Biological; D013269:Stochastic Processes; D013550:Swimming / Q000502:physiology; D015027:Zebrafish / Q000502:physiology*
keywords: Computational biology; Fish locomotion; Ornstein–Uhlenbeck; Stochastic models; Zebrafish