New mathematical model reveals how surrounding tissue forces heal wounds

Understanding how wounds heal after injury could be a step closer thanks to a new mathematical model developed by researchers at the University of Bristol.

The study published in Physical Review Letters builds on previous work in fruit flies, where the researchers observed how skin‑like epithelial cells move to cover a wound.

A crucial part of wound repair is re‑epithelialisation, the process where skin cells spread across a wound to rebuild the body's outer protective barrier. When this process breaks down, wounds can remain open and vulnerable to infection and so it's important to understand what physical mechanisms and forces contribute to effective closure.

To explore how this healing step works at the level of individual cells, the research team studied wound repair in fruit flies. Using advanced deep‑learning tools to analyse thousands of cells, they discovered that the cells in the fly's wing are arranged in a highly organised pattern; each cell has head‑to‑tail symmetry and tends to align along the long axis of the wing.

The new mathematical model developed aimed to understand how these cell alignment patterns influence the way a wound closes. The model treated the tissue like a fluid composed of many elongated, aligned cell‑shaped particles. This approach allowed the researchers to estimate how previously overlooked forces, acting within the tissue around the wound, affect closure.

The model predicted that these surrounding, or "bulk", forces can cause a wound that starts out round to become stretched or squashed as it closes, aligning with the natural direction of the surrounding tissue. When the researchers checked their predictions against experimental data, they found exactly this pattern, the shape of the wound changed in line with the tissue's own orientation.

This research highlights the importance of forces generated in the tissue surrounding a wound, which have thus far been neglected by previous mechanical models of re-epithelialization. It also highlights the importance of interdisciplinary collaboration, as without our experimental observations of cellular alignments, we wouldn't be able to deduce a model for these bulk tissue forces."

Henry Andralojc, PhD student from the School of Mathematics and co-author

Tanniemola Liverpool, Professor of Theoretical Physics in the School of Mathematics, and a co-author, added: "Our research has found that the forces generated by the surrounding tissue play a major role in how quickly a wound heals. When the tissue pulls inward, the wound closes faster. When the tissue pushes outward, wound closure slows down.

"The model we've developed suggests that the alignment of cells around the wound can create temporary disruptions in this orderly pattern, but these small irregularities disappear as the wound finally closes."