Nonlinear modeling of venous leg ulcer healing rates

Abstract

Background: The purpose of this manuscript was to determine whether the change in wound surface area over time could be described through nonlinear mathematics.

Methods: We studied 3,588 serial wound tracings of 338 venous leg ulcers (VLUs) that had been followed during a controlled, prospective, randomized trial of two topical wound treatments.

Results: A majority (72%) of VLUs exhibited surface area reduction via an exponential decay model, particularly during the early stages of healing. These results were consistent with the mechanics of wound contraction and epithelial cell proliferation, supported by the higher frequency at which exponential surface area reduction associated with full wound closure (35% of wounds that fit the exponential model healed vs. 21% of wounds that did not fit the exponential model completely healed during the study period, p = 0.018). Goodness-of-fit statistics suggested that much of the individual variation in healing could be described as nonlinear variation from the exponential model.

Conclusion: We believe that parameter estimates from a mathematical model may provide a more accurate quantification of wound healing rates, and that similar models may someday reach routine use in comparing the efficacy of various treatments in routine practice and in product registration trials.

Figure 1

Flow chart of clinical and regression analysis results.

Figure 2

Boxplot (with medians) of goodness-of-fit statistics (r²) between VLU patients who healed and did not heal by Week 12.

Figure 3

Experimental and fitted regression data using a significantly correlated VLU data set. Residuals are distributed randomly about zero and are generally small in magnitude.

Figure 4

Experimental and fitted regression data using a nonsignificantly correlated VLU data set. Residuals are distributed less randomly about zero and are larger in magnitude, particularly at week #12 (2.27). Unusually large residuals are typically not attributable to regression variation, resulting in a poor model fit.