Mathematical Model of Wound Healing Predicts Tissue Alignment Effects on Closure

New Model Reveals How Cell Alignment Shapes Wound Healing

Researchers at the University of Bristol have developed a mathematical model describing how the alignment of epithelial cells influences wound closure.

The study, published in Physical Review Letters, builds on observations of wound repair in fruit flies. It introduces a novel focus on "bulk" forces within the surrounding tissue—a factor previously overlooked by mechanical models of re-epithelialisation.

The model treats tissue as a fluid composed of elongated, aligned cell-shaped particles. It predicts that forces within the tissue surrounding a wound can alter the wound's shape, causing round wounds to become stretched or squashed along the tissue's natural direction.

This focus on "bulk" forces in the surrounding tissue marks a key departure from previous mechanical models of re-epithelialisation.

Predictions from the model were validated against experimental data from wounds in fruit fly wings. Researchers studied the repair process using deep-learning tools to analyze thousands of cells.

"The research highlights the importance of forces generated in the tissue surrounding a wound, which have been neglected by previous mechanical models." — Henry Andralojc, PhD student and co-author

They found that cells in the fly's wing are arranged in a highly organized pattern with head-to-tail symmetry aligned along the long axis of the wing. Experimental observations confirmed that wound shape changes according to this tissue orientation.

The forces generated by the surrounding tissue play a major role in wound healing speed. When the tissue pulls inward, the wound closes faster; when the tissue pushes outward, wound closure slows down.

"When the tissue pulls inward, the wound closes faster; when the tissue pushes outward, wound closure slows down." — Tanniemola Liverpool, Professor of Theoretical Physics and co-author

Liverpool added that the model suggests the alignment of cells around a wound can create temporary disruptions in the orderly pattern, but these irregularities disappear as the wound closes.

Re-epithelialisation is the process by which skin cells spread across a wound to rebuild the outer protective barrier.