A European randomised controlled trial for venous leg ulcers: a mathematical model analysis

Objective: Mathematical models have the potential to provide valuable insights into complex, biochemical and biomechanical processes. Previously, we developed a mathematical model with a non-linear growth function but could only confirm the feasibility of this model in clinical trials with a small number of patients. This limited the validity of our model. To increase validity, we applied the model to a larger number of patients. Method: The mathematical model was applied to patient data from a randomised controlled trial as part of the post-evaluation of the model. In this trial, patients with venous leg ulcers were randomised for treatment with either a two-layer bandage or a four-layer bandage. Results: Data for 186 patients were analysed (two-layer bandage group, n=93; four-layer bandage group, n=93). Using the non-linear growth function, it was confirmed that the two-layer bandage was not inferior to the four-layer bandage. In addition, the mathematical model calculated individual wound healing trajectories and mean wound healing trajectories for both bandage systems. By extrapolating to t-infinity, the two-layer bandage had a marginal benefit and resulted in a persistent wound area that was 7% of the initial wound area compared with 17% for the four-layer bandage. Conclusion: This analysis supported the previously performed statistical analysis, and allowed us to obtain details of the treated study population that may help in non-inferiority trials via extrapolation. It also provided new insights into the wound healing process by generating wound healing trajectories.