Healing of venous ulcers using compression therapy: Predictions of a mathematical model

• Healing of venous ulcers under treatment investigated with a mathematical model.
• Clinical data was used to calibrate the model.
• Three layered bandages predicted to heal wounds faster than standard bandages.
• The model can be used as a predictive tool to estimate the time needed for a wound to heal.

Venous Leg Ulceration (VLU) is a chronic condition for which healthcare systems worldwide face rising treatment costs. VLU can be due to sustained venous hypertension which causes the veins to become cuffed with fibrin, inhibiting the supply of nutrients to the wound site. For patients that cannot tolerate compression therapy with an inelastic short stretch (SS) bandage, the mainstay treatment, an elastic three layered (3L) bandage is an alternative. In this paper, a mathematical model is developed to investigate whether the healing of venous ulcers under SS and 3L bandages occurs at different rates and to postulate the reason for any difference. The two treatments were applied to a simplified wound geometry, under the assumption that the rate limiting step of healing is the supply of oxygen to the wounded tissue. Clinical data of wound size over time under the two treatments from Weller et al. (2012) was used to fit key, unknown, model parameters using a least squares approach. Numerical results are presented for the oxygen distribution within the wound space, using the fitted parameter values. The 3L bandage allows more oxygen flow into the wound than the SS bandage and, hence, the 3L bandage results in faster healing, however the difference is more significant for wounds of larger initial size. The model can be used as a predictive tool in a clinical setting to estimate the time to heal for a wound of a given initial size, treated with either a SS or 3L bandage.