During the lifetime of all living multicellular organisms, wounds in their tissues are frequently observed. Thecapability of closing those gaps is fundamental for a healthy development. If done deficiently, many diseasesmay occur from simple inflammation to tumor formation. The wound healing process in epithelial tissueoccurs in three different stages. The first one is the assembly of a supra-cellular actomyosin cable and itsmigration towards the wound edge, triggered by biochemical processes in which calcium plays a distinctiverole. How this process is orchestrated following damage remains unclear. Later, after its positioning, thecable contracts driving the tissue towards the gap and reducing the wound area. Finally, cell migrationtowards the interior of the wound ends up sealing the tissue. In this work, we make use of a mechanicalcontinuum model for the first two stages in order to developed and 2D finite element simulations within amonolithically fully implicit implementation. The model for the actomyosin cable formation involves thecoupling of transient calcium ions transport, with actin fibers and myosin motors recruitment and non-linearmechanical response of the tissue. The contraction stage, the active deformation of the previously formedactomyosin cable is taken into account. The relative motion of the myosin motors over the actin filaments ismodeled so there exists an active tissue contraction in the direction of those fibers. Upon implementation,the model is capable of performing a wide range of biophysical situations reported experimentally, as wedemonstrate in our numerical results. We have been able to rationalize through computational mechanicsthe firing of calcium in the wound right after damage infliction as well as the consequent formation of actinring, reproducing nicely what has been reported in biological literature. Thereafter, the numerical modelof acto-myosin contraction, fully integrated with the non-linear mechanics of the problem, correlates withthe mechanics of wound closure at the actin-ring contraction stage. More importantly, the approach is thefirst of its kind in the modeling of epithelial and embryonic cell layers, where a wide number of complexmechanics has been integrated and solved though computational methods in engineering. We believe thatthe simulations will help to unravel new insights in open questions of developmental biology.

Peer Reviewed