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I am working on mathematical model for healing of dermal wounds. For anyone who's a bit familiar with Physics and Math, for the model I use the Cauchy Momentum Equation as a basis, and from there I use already established literature to expand to a so-called morphoelastic model.

From a physical perspective, if a force is exerted, you would expect a material to start moving, upon which stresses arise, until a new balance is found. This all usually happens on a timescale of second. Now when wound healing is regarded, the contraction force is exerted by fibroblasts. I have read that wound contraction happens at a speed of up to 0.75/mm per day. On the one hand this is impressive, yet on the other hand it is very slow when viewed from the mechanical perspective.

So my question is: Is there a biological effect or phenomenon that slows down? Could it be that the migration speed of fibroblasts is the bottle neck? Or maybe skin is in some way tethered to underlying tissue? I know very little about biology, so any help would be appreciated!

Thanks in advance

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  • $\begingroup$ Is it really that slow? What are you comparing it to? If you're comparing it to simple muscle contraction, you should note that muscle movement is transient and returns to its original shape when the stimulus/energy input ceases. When a wound is healing, it wants to change its shape permanently so it's more like tissue growth. (1/2) $\endgroup$
    – Jam
    Jul 3 '19 at 15:42
  • $\begingroup$ If you compare it with growth of maize root tips, which grow at only 2.4 mm/day or dendritic spine growth, which is only 0.13-0.17 mm/day it doesn't seem that bad. (2/2) $\endgroup$
    – Jam
    Jul 3 '19 at 15:42
  • $\begingroup$ As far as my biological knowledge goes (which is not very far), wound contraction happens due to stresses induced by ((proto-)myo-)fibroblasts. Before, during, and after wound contraction, collagen fibres are secreted in order to replace the injured skin. The new arrangement of the collagen is reflected by the mechanical properties of the tissue. If wound contraction was to be attributed to a tissue growth-like process, the rate at which it happened would completely make sense to me. But from what I have understood, wound contraction is a mechanical process. $\endgroup$
    – user161518
    Jul 3 '19 at 20:41
  • $\begingroup$ Your comment actually cuts right into the heart of morphoelasticity theory, where deformations are decomposed into an elastic (transient) and a plastic (growth) component $\endgroup$
    – user161518
    Jul 3 '19 at 20:43
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Short Answer : You can not pinpoint any single step for this delay. It is a combination of multiple processes.

Long Answer : I think there are multiple factors that can contribute to this. Dermal Wound healing is a multi-step and complex process typically includes inflammation, new tissue formation and remodeling (Gurtner et al 2008). Each of these stages involved very complex signaling pathways of various components. In addition, there are multiple types of fibroblast cells involved in this process. You are most likely talking about Myofibroblasts who bring the edges of a wound together. However, this itself is a very complex process involving interaction with the proliferation and migration of both mesenchymal and epithelial cells. This is further tightly controlled by Keratinocyte-fibroblast interactions (Werner et al 2007).

So what can you do? : The the physical analogy, which you are trying to implement here, has to apply within some assumptions. You can declare some fitting parameter(s) which can contribute to all the process and validate it according to good experimental data, probably with some kind of mutant data where the wound healing process is slowed down or accelerated. While deciding your assumptions, use as fewer assumptions as possible else you will end up creating Spherical Cow.

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