Fig 1.
Wound healing in embryonic epithelial tissues, displaying both the purse-string (red cable at wound border) and cell crawling (protrusions in leading edge cells).
Table 1.
Table summarizing the main models explored in the review. The listed features correspond to the minimal structural elements of each model class; additional couplings and fields commonly used in the literature are discussed in the main text.
Fig 2.
Schematic of a lattice model of wound healing, where is the wound region and the different colored pixel regions correspond to different cells.
Fig 3.
Schematic of a network model of wound healing, where is the wound region and the different colored polygons correspond to cells with different number of neighbours.
Fig 4.
(Left) Schematic of a phase field model of wound healing where is the wound region where
and the tissue region is where
.
(Right) Schematic of a multiphase field model of wound healing where is the phase field associated with cell i.
Fig 5.
Schematic of an active hydrodynamic model of wound healing.
corresponds to the wound region, and is the velocity field, driven by active stress (blue and red regions).
Fig 6.
2D deformation of a continuous body from an undeformed configuration B0 to a deformed configuration Bt.
X and x are the positions of an arbitrary point in the body in the undeformed and deformed configurations, respectively. In the example above the body has experienced a pure shear and a rotation.
Fig 7.
Schematic of a viscoelastic model of wound healing.
Where is the wound region and displacement is driven by the internal tissue stress σ.
Table 2.
Several models and the main references where core features of embryonic healing are addressed. Asterisks (*) denote hybrid models and indicate when a model serves as a basis for the hybridization. The table is split for interpretative clarity: the top block highlights features that explicitly emphasize wound-boundary dynamics, while the bottom block covers features from general epithelial mechanics and signaling relevant to wound healing.
Table 3.
Summary of the biological systems, species, wounding assays, and open-source implementations for the main physical models of epithelial wound healing reviewed. The table distinguishes between in vivo embryonic tissue and in vitro monolayer systems, highlighting where the reviewed models have been applied. Examples listed are not exhaustive. Hybrid and Data-driven systems are not included, as their application is not restricted to specific systems.