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Hyperbolastic modeling of wound healing. (English) Zbl 1217.92058

Summary: A new mathematical model for wound healing is introduced and applied to three sets of experimental data. The model is easy to implement but can accommodate a wide range of factors affecting the wound healing process. The data sets represent the areas of trace elements, diabetic wounds, growth factors, and nutrition within the field of wound healing. The model produces an explicit function accurately representing the time course of healing wounds from a given data set. Such a function is used to study variations in the healing velocity among different types of wounds and at different stages in the healing process. A new multivariable model of wound healing capable of analyzing the effects of several variables on accelerating the wound healing process is also introduced. Such a model can help to formulate appropriate strategies to treat wounds. It also would enable us to evaluate the efficacy of different treatment modalities during the inflammatory, proliferative, and tissue remodeling phases.

MSC:

92C50 Medical applications (general)
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[1] Gillitzer, R.; Goebeler, M., Chemokines in cutaneous wound healing, J. leukoc. biol., 69, 513-521, (2001)
[2] Lauffenburger, D.A.; Wells, A., Quantitative parsing of cell multi-tasking in wound repair and tissue morphogenesis, Biophys. J., 84, 3499-3500, (2003)
[3] Park, H.Y.; Hwang, C.I.; Kang, M.J.; Seo, J.Y.; Chung, J.H.; Kim, Y.S.; Lee, J.H.; Kim, H.; Kim, K.A.; Yoo, H.J.; Seo, J.S., Gene profile of replicative senescence is different from progeria or elderly donor, Biochem. biophys. res. commun., 282, 934-939, (2001)
[4] Raffetto, J.D.; Mendez, M.V.; Phillips, T.J.; Park, H.Y.; Menzoian, J.O., The effect of passage number on fibroblast cellular senescence in patients with chronic venous insufficiency with and without ulcer, Am. J. surg., 178, 107-112, (1999)
[5] Chang, H.Y.; Nuyten, D.S.A.; Sneddon, J.B.; Hastie, T.; Tibshirani, R.; Sorlier, T.; Dai, H.; He, Y.D.; van’t Veer, L.J.; Bartelink, H.; van de Rijn, M.; Brown, P.O.; van de Vijver, M.J., Robustness, scalability, and integration of a wound response gene expression signature in predicting breast cancer survival, Proc. natl. acad. sci., 102, 3738-3743, (2005)
[6] Dvorak, H.F., Tumors: wounds that do not heal: similarities between tumor stroma generation and wound healing, N. engl. J. med., 315, 1650-1659, (1986)
[7] Mátrai, Z.; Péley, G.; Rényi Vámos, F.; Farkas, E.; Kovács, T.; Köves, I., The similarities between the mechanism of wound healing and tumor development—literature review on the occasion of a patient with colonic adenocarcinoma metastasis in a dog-bite wound, Orv. hetil., 146, 99-109, (2005)
[8] Yeo, T.-K.; Brown, L.; Dvorak, H.F., Alterations in proteoglycan synthesis common to healing wounds and tumors, Am. J. pathol., 138, 1437-1450, (1991)
[9] Harrington, C.; Zagari, M.J.; Corea, J.; Klitenic, J., A cost analysis of diabetic lower-extremity ulcers, Diabetes care, 23, 1333-1338, (2000)
[10] Diegelmann, R.F.; Evans, M.C., Wound healing: an overview of acute, fibrotic, and delayed healing, Front. biosci., 9, 283-289, (2004)
[11] Servold, S.A., Growth factor impact on wound healing, Clin. podiatr. med. surg., 8, 937-953, (1996)
[12] Cobbold, C.A.; Sherratt, J.A., Mathematical modelling of nitric oxide activity in wound healing can explain keloid and hypertrophic scarring, J. theoret. biol., 204, 257-288, (2000)
[13] Braiman-Wiksman, L.; Solomonik, I.; Spira, R.; Tennenbaum, T., Novel insights into wound healing sequence of events, Toxicol. pathol., 35, 767-779, (2007)
[14] Murray, J.D., Mathematical biology vol. II: spatial models and biomedical applications, (2003), Springer-Verlag New York · Zbl 1006.92002
[15] Fusi, L., Macroscopic models for fibroproliferative disorders: a review, Math. comput. modelling, 50, 1474-1494, (2009) · Zbl 1185.92061
[16] Bellomo, N.; Bellouquid, A.; Nieto, J.; Soler, J., Multiscale biological tissue models and flux-limited chemotaxis from binary mixtures of multicellular growing systems, Math. models methods appl. sci., 20, 1179-1207, (2010) · Zbl 1402.92065
[17] Cukjati, D.; Rebersek, S.; Karba, R.; Miklavcic, D., Modelling of chronic wound healing dynamics, Med. biol. eng. comput., 38, 339-347, (2000)
[18] Wallenstein, S.; Brem, H., Statistical analysis of wound-healing rates for pressure ulcers, Am. J. surg., 199, 73-78, (2004)
[19] Cardinal, M.; Phillips, T.; Eisenbud, D.E.; Harding, K.; Mansbridge, J.; Armstrong, D.G., Nonlinear modeling of venous leg ulcer healing rates, BMC dermatol., 9, (2009)
[20] Robson, M.C.; Hill, D.P.; Woodske, M.E.; Steed, D.L., Wound healing trajectories as predictors of effectiveness of therapeutic agents, Arch. surg., 135, 773-777, (2000)
[21] Tabatabai, M.; Williams, D.K.; Bursac, Z., Hyperbolastic growth models: theory and application, Theor. biol. med. model., 2, 1-13, (2005)
[22] Eby, W.M.; Tabatabai, M.A.; Bursac, Z., Hyperbolastic modeling of tumor growth with a combined treatment of iodoacetate and dimethylsulfoxide, BMC cancer, 10, 509, (2010)
[23] Z. Bursac, M. Tabatabai, D.K. Williams, Nonlinear hyperbolastic growth models and applications in craniofacial and stem cell growth, in: 2005 Proceedings of the American Statistical Association, Biometrics Section, Alexandria, VA, American Statistical Association, 2006 [CD-ROM].
[24] Tabatabai, M.A.; Bursac, Z.; Eby, W.M.; Singh, K.P., Mathematical modeling of stem cell proliferation, Med. biol. eng. comput., 1-10, (2010)
[25] Alimohammad, A.; Mohammadali, M.; Mahmod, K.; Khadijeh, S., A study of the effect of magnesium hydroxide on the wound healing process in rats, Med. J. islamic world acad. sci., 16, 165-170, (2008)
[26] Senni, K.; Foucault-Bertaud, A.; Godeau, G., Magnesium and connective tissue, Magnes. res., 16, 70-74, (2003)
[27] Geesin, J.C.; Gordon, J.S.; Berg, R.A., Regulation of collagen synthesis in human dermal fibroblasts by the sodium magnesium salts of ascorbyl-2-phosphate, Skin pharmacol., 6, 65-71, (1993)
[28] Lange, T.S.; Bielinsky, A.K.; Kirchberg, K.; Bank, I.; Herrmann, K.; Krieg, T.; Scharffetter-Kochanek, K., \(M g^{2 +}\) and \(C a^{2 +}\) differentially regulate \(\beta 1\) integrin-mediated adhesion of dermal fibroblasts and keratinocytes to various extracellular matrix proteins, Exp. cell res., 214, 381-388, (1994)
[29] Banai, S.; Haggroth, L.; Epstein, S.E.; Casscells, W., Influence of extracellular magnesium on capillary endothelial cell proliferation and migration, Circ. res., 67, 645-650, (1990)
[30] Grzesiak, J.J.; Pierschbacher, M.D., Shifts in concentrations of magnesium and calcium in early porcine and rat wound fluids activate the cell migratory response, J. clin. investig., 95, 227-233, (1995)
[31] Lange, T.S.; Kirchberg, K.; Bielinsky, A.K.; Leuker, A.; Bank, I.; Ruzicka, T.; Scharffetter-Kochanek, K., Divalent cations \((M g^{2 +}, C a^{2 +})\) differentially influence the \(\beta 1\) integrin-mediated migration of human fibroblasts and keratinocytes to different extracellular matrix proteins, Exp. dermatol., 4, 130-137, (1995)
[32] G.S. Schultz, G. Ladwig, A. Wysocki, Extracellular matrix: review of its roles in acute and chronic wounds, World Wide Wounds, 2005 (online).
[33] Schulze-Tanzil, G.; de Souza, P.; Merker, H.-J.; Shakibaei, M., Co-localization of integrins and matrix metalloproteinases in the extracellular matrix of chondrocyte cultures, Histol. histopathol., 16, 1081-1089, (2001)
[34] Cianfarani, F.; Zambruno, G.; Brogelli, L.; Sera, F.; Lacal, P.M.; Pesce, M.; Capogrossi, M.C.; Failla, C.M.; Napolitano, M.; Odorisio, T., Planceta growth factor in diabetic wound healing: altered expression and therapeutic potential, Am. J. pathol., 169, 1167-1182, (2006)
[35] Pierce, G.F., Inflammation in nonhealing diabetic wounds: the space – time continuum does matter, Am. J. pathol., 159, 399-403, (2001)
[36] Odorisio, T.; Cianfarani, F.; Failla, C.M.; Zambruno, G., The placenta growth factor in skin angiogenesis, J. dermatol. sci., 41, 11-19, (2006)
[37] Shyu, K.-G.; Hung, H.-F.; Want, B.-W.; Chang, H., Hyperbaric oxygen induces placental growth factor expression in bone marrow-derived mesenchymal stem cells, Life sci., 83, 65-73, (2008)
[38] Ågren, M.S.; Franzén, L., Influence of zinc deficiency on breaking strength of 3-week-old skin incisions in the rat, Acta chir. scand., 156, 667-670, (1990)
[39] Lansdown, A.B.G.; Mirastschijski, U.; Stubbs, N.; Scanlon, E.; Ågren, M.S., Zinc in wound healing: theoretical, experimental, and clinical aspects, Wound repair regen., 15, 2-16, (2007)
[40] Lim, Y.; Levy, M.; Bray, T.M., Dietary zinc alters early inflammatory responses during cutaneous wound healing in weanling CD-1 mice, J. nutr., 134, 811-816, (2004)
[41] Y. Lim, The role of nutrition during the early inflammatory stage of cutaneous wound healing, Ph.D. Dissertation, The Ohio State University, 2003.
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