Cukjati D, Rebersek S, Karba R, Miklavcic D
Faculty of Electrical Engineering, University of Ljubljana, Slovenia.
Med Biol Eng Comput. 2000 May;38(3):339-47. doi: 10.1007/BF02347056.
Following chronic wound area over time can give a general overview of wound healing dynamics. Decrease or increase in wound area over time has been modelled using either exponential or linear models, which are two-parameter mathematical models. In many cases of chronic wound healing, a delay of healing process was noticed. Such dynamics cannot be described solely with two parameters. The reported study deals with two-, three-, and four-parameter models. Assessment of the models was based on weekly measurements of 226 chronic wounds of various aetiologies. Several quantitative fitting criteria, i.e. goodness of fit, handling missing data and prediction capability, and qualitative criteria, i.e. number of parameters and their biophysical meaning were considered. The median of goodness of fit of three- and four-parameter models was between 0.937 and 0.958, and the median of two-parameter models was 0.821 to 0.883. Two-parameter models fitted wound area over time significantly (p = 0.01) worse than three- and four-parameter models. The criterion handling missing data provided similar results, with no significant difference between three- and four-parameter models. Median prediction error of two-parameter models was between 111 and 746; three-parameter models resulted in an error of 64 to 128, and finally four-parameter models resulted in the highest prediction error of 407 and 238. Based on the values of quantitative fitting criteria obtained, three parameters were chosen as the most appropriate. Based on qualitative criteria, the delayed exponential model was selected as the most general three-parameter model. It was found to have good prediction capability and in this capacity it could be used to help physicians choose the most appropriate treatment for patients with chronic wounds after an initial three-week observation period, when the median error increase of fitting is 74%.
随着时间推移跟踪慢性伤口面积，可以对伤口愈合动态有一个总体了解。伤口面积随时间的减少或增加已使用指数模型或线性模型进行建模，这两种都是双参数数学模型。在许多慢性伤口愈合的案例中，都注意到愈合过程存在延迟。这种动态不能仅用两个参数来描述。所报道的研究涉及双参数、三参数和四参数模型。模型评估基于对226例不同病因的慢性伤口的每周测量。考虑了几个定量拟合标准，即拟合优度、处理缺失数据和预测能力，以及定性标准，即参数数量及其生物物理意义。三参数和四参数模型的拟合优度中位数在0.937至0.958之间，双参数模型的中位数在0.821至0.883之间。双参数模型随时间拟合伤口面积的效果明显（p = 0.01）比三参数和四参数模型差。处理缺失数据的标准提供了类似的结果，三参数和四参数模型之间没有显著差异。双参数模型的预测误差中位数在111至746之间；三参数模型的误差为64至128，最后四参数模型的预测误差最高，为407和238。根据获得的定量拟合标准值，选择三个参数作为最合适的。基于定性标准，延迟指数模型被选为最通用的三参数模型。发现它具有良好的预测能力，并且在此能力下，它可用于帮助医生在初始三周观察期后为慢性伤口患者选择最合适的治疗方法，此时拟合的中位数误差增加74%。
