Abstract
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 moels was 0.821 to 0.883. Two-parameter models fitted wound area over time significantly (p=0.001) 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%.
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References
Baker, L. L., DeMuth, S. K. Chambers, R., andVillar, F. (1997): ‘Effects of electrical stimulation on wound healing in patients with diabetic ulcers’,Diabetes Care,20, pp. 405–412
Barosley, W. G., Sattar, A., Armstrong, J. R., Shah, M., Brosnan, P., andFerguson, M. W. J. (1995): ‘Quantitative analysis of wound healing’.Wound Repair Regeneration,3, pp. 426–441
Baigolucci, A. A. andThomas, D. R. (1992): ‘Using principal component analysis to describe wound status’,Adv. Wound Care,10, pp. 93–95.
Birke, J. A., Novick, A., Patout, C. A., andColeman, W. C. (1992): ‘Healing rates of plantar ulcers in leprosy and diabetes’,Leprosy Rev.,63, pp. 365–374.
Cuddigan, J. (1977): ‘Pressure ulcer classfication: what do we have? what do we need?’,Adv. Wound Care,10, pp. 13–15.
Dagher, J. F. (1985): ‘Cutaneous wounds’ (Futura Publishing Company, Mount Kisco, NY), pp. 99–220
Devore, J. L. (1995): ‘Probability and statistics for engineering and the sciences’ (Duxbury Press), 4th edn
Feedar, J. A., Kloth, L. C., andGentzkow, D. (1991): ‘Chronic dermal ulcer healing enhanced with monophasic pulsed electrical stimulation’,Physical Therapy,71, pp. 639–649
Gentzkow, G. D., andMiller, K. H. (1991): ‘Electrical stimulation for dermal wound healing’,Wound Healing,8, pp. 827–841
Gorin, D. R., Cordts, P. R., LaMorte, W. W., andMenzoian, J. O. (1996): ‘The influence of wound geometry on the measurement of wound healing rates in clinical trials’,J. Vasc. Surg.,23, pp. 524–528
Jerĉinović, A., Karba, R., Vodovnik, L., Stefanovska, A., Kroŝelj, P., Turk, R., Didić, I., Benko, H., andŜavrin, R. (1994): ‘Low frequency pulsed current and pressure ulcer healing’,IEEE Trans. Rehab. Eng.,2, pp. 225–233
Johnson, M. (1977): ‘Using cluster analysis to develop a healing typology in vascular ulcers’,J. Vasc. Nursing,15, pp. 45–49
Karba, R., Ŝemrov, D., Vodovnik, L., Benko, H., andŜavrin, R. (1997): ‘DC electrical stimulation for chronic wound healing enhancement. Part 1. Clinical study and determination of electrical field distribution in the numerical wound model’,Bioelectrochem. Blaenergetics,43, pp. 265–270.
Lindeberg, T. C. M., Eriksson, S. V., andMalm, M. (1992): ‘Electrical nerve stimulation improves healing of diabetic ulcers’,Ann. Plastic Surg.,29, pp. 328–331
Miklavĉiĉ, D., Jarm, T., Karba, R. andSerŝa, G. (1995): ‘Mathematical modelling of tumor growth in mice following electrotherapy and bleomycin treatment,”,Math. Comput. Simulation,39, pp. 597–602
Press, W. H., Teukolsky, S. A., Vetterling, W. T., andFlannery, B. P. (1992): ‘Modeling of Data, in Numerical recipes in C, The art of scientific computing’ (Cambridge University Press), 2nd edn
SPSS Inc. (1997): ‘SYSTAT’ 7.0: Statistic’. SPSS Inc.
Stefanovska, A., Vodovnik, L., Benko, H., andTurk, R. (1993): ‘Treatment of chronic wounds by means of electric and electromagnetic fields. Part 2. Value of FES parameters for pressure sore treatment,’,Med. Biol. Eng. Comput.,31, pp. 213–220
Vaidya, V. G. andAlexandro, F. G. Jr. (1982): ‘Evaluation of some mathematical models for tumor growth,’Int. J. Biomed. Comput.,13, pp. 19–35
Vodovnik, L., andKarba, R. (1992): ‘Treatment of chronic wounds by means of electric and electromagnetic fields. Part 1. Literature review’.,Med. Biol. Eng. Comput. 30, pp. 256–266.
Yarkony, G. M. (1994): ‘Pressure ulcers: a review,’,Arch. Phys. Med. Rehab.,75, pp. 908–917.
Waldore, H. andFewkes, J. (1995): ‘Wound healing’,Adv. Dermatol.,10, pp. 77–97
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Cukjati, D., Reberŝek, S., Karba, R. et al. Modelling of chronic wound healing dynamics. Med. Biol. Eng. Comput. 38, 339–347 (2000). https://doi.org/10.1007/BF02347056
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DOI: https://doi.org/10.1007/BF02347056