We develop a theoretical framework to study the dynamics of a fluid inclusion (modeling the cellular tissue) embedded in an elastic matrix (the ECM), which undergoes surface degradation/deposition.
In this work, we make use of a mechanical continuum model for the first two stages in order to developed and 2D finite element simulations within a monolithically fully implicit implementation. The model for the actomyosin cable formation involves the coupling of transient calcium ions transport, with actin fibers and myosin motors recruitment and non-linear mechanical response of the tissue. The contraction stage, the active deformation of the previously formed actomyosin cable is taken into account. The relative motion of the myosin motors over the actin filaments is modeled so there exists an active tissue contraction in the direction of those fibers.