Mathematical model for wound healing following autologous keratinocyte transplantation

Abstract

In times of increasing economical pressure on the health care systems, it is important to optimise the outpatient treatment of chronic wounds. Another aim of wound healing research is to discover agents to accelerate healing. Wound healing trajectories or healing velocities can provide information to demonstrate the endpoints for wound healing. A great problem in clinical trials is to specify these parameters. Therefore, we developed a mathematical model for more transparency. In this initial project, we observed 19 wounds to construct the wound healing trajectories after transplantation of autologous keratinocytes, and the results are so encouraging that investigation in this area will continue. The developed mathematical model describes the clinical observed healing process. It was possible to find parameters to distinguish between old and young patients, retrospectively or prospectively calculate the healing rates and to determine exactly the endpoint of healing. Therefore, our model might be very useful in practices or for studies.

Measuring progress to healing: A challenge and an opportunity

“…Indeed, it has previously shown a poor correlation to healing time. 25 The non‐linear nature of PAR has been variously modelled as approximating exponential 10 , 26 and as following other trajectories such as a Gompertz function 27 , 28 and other polynomial fits. 29 So, although shown to be useful as an early classifier of wounds into “healing” or “non‐healing” categories, PAR presents non‐trivial difficulties in extrapolating a healing trajectory to establish an ultimate time to complete healing.…”

Nonlinear modeling of venous leg ulcer healing rates

“…Prediction intervals, goodness-of-fit statistics, and residual error plots may lend more analytical information to the nature of the wound healing process than summary statistics of standard healing rates. Nonlinear curve fitting algorithms, primarily using a Gompertz function, have been applied to serial wound measurements with positive results [ 16 - 19 ]. Regression curve fitting may be a powerful method to mathematically describe contraction and epithelialization rates in a clinical context.…”

Transplantation of chronic wounds with epidermal sheets derived from autologous hair follicles—the Leipzig experience

“…This implies that the effect of autologous transplantation with Apligraf ® is most prominent in patients with an ulcer duration of >1 year. Our data and former clinical evaluations of EpiDex™ (14) suggest an increased benefit of EpiDex™ for patients with ulcer duration between 0.5-4 years, but yet the upper limit is not clear. We therefore hypothesise that the duration of ulceration might serve as a predictive marker for treatment success but this hypothesis has to be proven in future prospective studies.…”