A mathematical model for the determination of mouse excisional wound healing parameters from photographic data

Abstract

We present a mathematical model to quantify parameters of mouse excisional wound healing from photographic data. The equation is a piecewise linear function in log scale that includes key parameters of initial wound radius (R ), an initial wound stasis phase (T ), and time to wound closure (T ); subsequently, these terms permit calculation of a latter active proliferative phase (T ), and the healing rate (HR) during this active phase. A daily photographic record of wound healing (utilizing 6 mm diameter splinted excisional wounds) permits the necessary sampling for robust parameter refinement. When implemented with an automated nonlinear fitting routine, the healing parameters are determined in an operator-independent (i.e., unbiased) manner. The model was evaluated using photographic data from a splinted excisional surgical procedure involving several different mouse cohorts. Model fitting demonstrates excellent coefficients of determination (R ) in each case. The model, thus, permits quantitation of key parameters of excisional wound healing, from initial wounding through to wound closure, from photographic data.

Fine-Sampled Photographic Quantitation of Dermal Wound Healing Senescence in Aged BALB/cByJ Mice and Therapeutic Intervention with Fibroblast Growth Factor-1

“…tified by photographic data and the inflammatory healing phase characterized by histology; furthermore, the active healing phase identified by photographic data corresponded to the proliferative healing phase characterized by histology. The mathematical analysis of fine-sampled photographic data reported by Blaber and colleagues 18 provides for a robust parameterization of healing phases (which is not possible with sparse-sampled histological data); furthermore, such analyses permit robust statistical analyses for cohort comparisons. Of significant additional benefit, photographic data are noninvasive, whereas histological sampling is a lethal event in mice (necessitating a correspondingly larger number of animals per cohort).…”

“…30 In the workflow, daily photographic data were analyzed to obtain wound area, and from this the wound radius. These data (i.e., wound radius as a function of time) were then fit to a mathematical model 18 (see Equation 1 below) by a nonlinear least squares routine-generating the fitted parameters. Macrophotography with a DSLR camera was utilized to achieve a full-frame composition of the wound onto the 6 MP CCD sensor (i.e., permitting the maximum countable pixels for the wound).…”

“…Wound radius as a function of time R(t) was fit to a piecewise linear function as described by Blaber and colleagues. 18 This model parameterizes the NOVEL PHOTOGRAPHIC QUANTITATION OF DERMAL HEALING initial wound radius R 0 , the initial period of wound stasis (covering the hemostasis and inflammatory phases) T i , and subsequent active proliferative phase of healing ending in the time to wound closure T c :…”

“…The initial period of wound stasis identified by photographic data is consistent with the hemostasis and inflammatory phases of healing; the subsequent proliferative phase identified by photographic data is consistent with the proliferative phase of healing. 18 Fitting of experimental photographic data (i.e., measured wound radius) to this function was accomplished by an independent analyst using the nonlinear least squares fitting software DataFit (Oakdale Engineering, Oakdale, PA). Coefficients of determination R 2 for the fit were also calculated using DataFit.…”

“…The surgical wound procedure utilized is the splinted excisional wound, which minimizes the skin contraction property of ''loose-skinned'' rodents, and more faithfully represents the primacy of re-epithelialization characteristic of human dermal healing. 16,17 The quantitation of wound healing utilizes a recently developed mathematical model of healing, 18 utilizing fine-sampled (i.e., daily) photographic wound healing data, and extracts substantially greater quantitative information compared with previous methodologies. This analysis permits quantitative determination and comparison of key wound healing parameters, including duration of the initial latent phase of healing (associated with hemostasis and inflammatory phases), wound radius during the stasis phase, duration of the subsequent active proliferative phase (T p ) of healing, rate of wound healing during the active phase, and overall time to wound closure (T c ).…”