Dresden 2020 – wissenschaftliches Programm
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BP 10.4: Poster
Montag, 16. März 2020, 17:30–19:30, P2/3OG
Spherical harmonics analysis of in-vivo force probes for tissue stress quantification — •Alejandro Jurado, Bernhard Wallmeyer, Christoph Engwer, and Timo Betz — Institute of Cell Biology, ZMBE, University of Münster
The mechanical analysis of tissue motion offers a new insight in key biological processes such as embryogenesis, cancer cell invasion and wound healing. Force quantification at this scale has been drastically improved with the emergence of in-vivo sensors such as oil droplets or hydrogel beads which open up the possibility of non-invasive studies. Many approaches in recent literature rely on numerical processes to iteratively reconstruct the surface of measured beads, which can be computationally expensive and rendering results that are difficult to interpret. In this work we present the analysis of arbitrarily deformed beads based on the expansion in Spherical Harmonics in a Python custom software. We exploit the fast converging algorithms offered by SHTools  to reduce the great complexity of three-dimensional radial deformations to an affordable harmonic coefficient table which is directly fed into an analytical solution of the Navier-Cauchy equation. As a first proof-of-concept we show the performance of the software with polyacrylamide beads injected into zebrafish embryo at early developmental stages, in which the stress field could help understanding the processes of epiboly and shield formation.
 Wieczorek M.A., Meschede M., 2018. SHTools: Tools for working with spherical harmonics, Geochem. Geophys. Geosyst. 19(8), 2574-2592