# American Institute of Mathematical Sciences

October  2015, 8(5): 953-967. doi: 10.3934/dcdss.2015.8.953

## Numerical algorithm for tracking cell dynamics in 4D biomedical images

 1 Department of Mathematics, Slovak University of Technology, Radlinskeho 11, 813 68 Bratislava, Slovak Republic 2 Institut de Neurobiologie Alfred Fessard, CNRS UPR 3294, Av. de la Terrasse, 91198 Gif-sur-Yvette, France

Received  January 2014 Revised  July 2014 Published  July 2015

The paper presents new numerical algorithm for an automated cell tracking from large-scale 3D+time two-photon laser scanning microscopy images of early stages of zebrafish (Danio rerio) embryo development. The cell trajectories are extracted as centered paths inside segmented spatio-temporal tree structures representing cell movements and divisions. Such paths are found by using a suitably designed and computed constrained distance functions and by a backtracking in steepest descent direction of a potential field based on these distance functions combination. The naturally parallelizable discretization of the eikonal equation which is used for computing distance functions is given and results of the tracking method for real 4D image data are presented and discussed.
Citation: Karol Mikula, Róbert Špir, Nadine Peyriéras. Numerical algorithm for tracking cell dynamics in 4D biomedical images. Discrete & Continuous Dynamical Systems - S, 2015, 8 (5) : 953-967. doi: 10.3934/dcdss.2015.8.953
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