Calculus of Variations and Geometric Measure Theory

G. Bevilacqua - P. Ciarletta - A. Quarteroni

Morphomechanical model of the torsional c-looping in the embryonic heart

created by bevilacqua on 16 Dec 2021
modified on 24 Apr 2024


Published Paper

Inserted: 16 dec 2021
Last Updated: 24 apr 2024

Journal: SIAM Journal on Applied Mathematics
Volume: 81
Number: 3
Pages: 897–918
Year: 2021
Doi: 10.1137/20M1370720

ArXiv: 2010.01006 PDF


Before septation processes shape its four chambers, the embryonic heart is a straight tube that spontaneously bends and twists breaking the left-right symmetry. In particular, the heart tube is subjected to a cell remodelling inducing ventral bending and dextral torsion during the c-looping phase. In this work we propose a morphomechanical model for the torsion of the heart tube, that behaves as a nonlinear elastic body. We hypothesize that this spontaneous looping can be modeled as a mechanical instability due to accumulation of residual stresses induced by the geometrical frustration of tissue remodelling, which mimics the cellular rearrangement within the heart tube. Thus, we perform a linear stability analysis of the resulting nonlinear elastic boundary value problem to determine the onset of c-looping as a function of the aspect ratios of the tube and of the internal remodelling rate. We perform numerical simulations to study the fully nonlinear morphological transition, showing that the soft tube develops a realistic self-contacting looped shape in the physiological range of geometrical parameters.

Keywords: nonlinear elasticity, embryogenesis, elastic stability, heart tube, c-looping, remodeling