What good is maths in studies of wound healing?

Cellular and molecular mechanisms of skin wound healing

Wound healing is a complex process that involves the coordinated actions of many different tissues and cell lineages. It requires tight orchestration of cell migration, proliferation, matrix deposition and remodelling, alongside inflammation and angiogenesis. Whereas small skin wounds heal in days, larger injuries resulting from trauma, acute illness or major surgery can take several weeks to heal, generally leaving behind a fibrotic scar that can impact tissue function. Development of therapeutics to prevent scarring and successfully repair chronic wounds requires a fuller knowledge of the cellular and molecular mechanisms driving wound healing. In this Review, we discuss the current understanding of the different phases of wound healing, from clot formation through re-epithelialization, angiogenesis and subsequent scar deposition. We highlight the contribution of different cell types to skin repair, with emphasis on how both innate and adaptive immune cells in the wound inflammatory response influence classically studied wound cell lineages, including keratinocytes, fibroblasts and endothelial cells, but also some of the less-studied cell lineages such as adipocytes, melanocytes and cutaneous nerves. Finally, we discuss newer approaches and research directions that have the potential to further our understanding of the mechanisms underpinning tissue repair.

An in silico modeling approach to understanding the dynamics of the post-burn immune response

Introduction

Burns are characterized by a massive and prolonged acute inflammation, which persists for up to months after the initial trauma. Due to the complexity of the inflammatory process, Predicting the dynamics of wound healing process can be challenging for burn injuries. The aim of this study was to develop simulation models for the post-burn immune response based on (pre)clinical data.

Methods

The simulation domain was separated into blood and tissue compartments. Each of these compartments contained solutes and cell agents. Solutes comprise pro-inflammatory cytokines, anti-inflammatory cytokines and inflammation triggering factors. The solutes diffuse around the domain based on their concentration profiles. The cells include mast cells, neutrophils, and macrophages, and were modeled as independent agents. The cells are motile and exhibit chemotaxis based on concentrations gradients of the solutes. In addition, the cells secrete various solutes that in turn alter the dynamics and responses of the burn wound system.

Results

We developed an Glazier-Graner-Hogeweg method-based model (GGH) to capture the complexities associated with the dynamics of inflammation after burn injuries, including changes in cell counts and cytokine levels. Through simulations from day 0 - 4 post-burn, we successfully identified key factors influencing the acute inflammatory response, i.e., the initial number of endothelial cells, the chemotaxis threshold, and the level of chemoattractants.

Conclusion

Our findings highlight the pivotal role of the initial endothelial cell count as a key parameter for intensity of inflammation and progression of acute inflammation, 0 - 4 days post-burn.

Fluctuations of cell geometry and their nonequilibrium thermodynamics in living epithelial tissue

We measure different contributions to entropy production in a living functional epithelial tissue. We do this by extracting the functional dynamics of development while at the same time quantifying fluctuations. Using the translucent Drosophila melanogaster pupal epithelium as an ideal tissue for high-resolution live imaging, we measure the entropy associated with the stochastic geometry of cells in the epithelium. This is done using a detailed analysis of the dynamics of the shape and orientation of individual cells which enables separation of local and global aspects of the tissue behavior. Intriguingly, we find that we can observe irreversible dynamics in the cell geometries but without a change in the entropy associated with those degrees of freedom, showing that there is a flow of energy into those degrees of freedom. Hence, the living system is controlling how the entropy is being produced and partitioned into its different parts.