Abstract
Enterocutaneous fistulae are pathological communications between the intestinal lumen and the abdominal skin. Under surgery the mortality of this pathology is very high, therefore a vacuum applying system has been carried previously on attempting to close these fistulae. The objective of this article is the understanding of how these treatments might work through deterministic mathematical modelling. Four models are here proposed based on several assumptions involving: the conservation of the flow in the fistula, a low enough Reynolds number justifying a laminar flow, the use of Poiseuille law to model the movement of the fistulous liquid, as well as phenomenological equations including the fistula tissue and intermediate chamber compressibility. Interestingly, the four models show fistulae closing behaviour during experimental time (t<60 sec). To compare the models, both, simulations and pressure measurements, carried out on the vacuum connected to the patients, are performed. Time course of pressure are then simulated (from each model) and fitted to the experimental data. The model which best describes actual measurements shows exponential pumping flux kinetics. Applying this model, numerical relationship between the fistula compressibility and closure time is presented. The models here developed would contribute to clarify the treatment mechanism and, eventually, improve the fistulae treatment.
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Adimja, M., Craustea, F., Ruanb, S., 2006. Modelling Haematopoiesis mediated by growth factors with applications to periodic hematological diseases. Bull. Math. Biol. 68, 2321–2351.
Altomare, D.F., Serio, G., Pannarale, O.C., Lupo, L., Palasciano, N., Memeo, V., Rubino, M., 1990. Prediction of mortality by logistic regression analysis in patients with postoperative enterocutaneous fistulae. Br. J. Surg. 77, 450–453.
Alvarez, A.A., Maxwell, G.L., Rodriguez, G.C., 2001. Vacuum-assisted closure for cutaneous gastrointestinal fistula management. Gynecol. Oncol. 80, 413–416.
Araujo, R., McElwain, D., 2004. A history of the study of solid tumor growth: the contribution of mathematical modelling. Bull. Math. Biol. 66, 1039–1091.
Argenta, L.C., Morykwas, M.J., 1997. Vacuum-assisted closure: a new method for wound control and treatment: clinical experience. Ann. Plast. Surg. 38, 563–577.
Ballard, K., Baxter, H., 2001. Vacuum-assisted closure. Nurs. Times 97, 51–52.
Bishop, J.J., Nance, P.R., Popel, A.S., Intaglietta, M., Johnson, P.C., 2000. Diameter changes in skeletal muscle venules during arterial pressure reduction. Am. J. Physiol. Heart Circ. Physiol. 279, 47–57.
Campos, A.C.L., Andrade, D.F., Campos, G.M.R., Matias, J.E.F., Coelho, J.C.U., 1999. A multivariate model to determine prognostic in gastrointestinal fistulae. J. Am. Coll. Surg. 188, 483–490.
Erdmann, D., Drye, C., Heller, L., Wong, M.S., Levin, S.L., 2001. Abdominal wall defect and enterocutaneous fistula treatment with the Vacuum-Assisted Closure (V.A.C.) system. Plast. Reconstr. Surg. 108, 2066–2068.
Fernández, E.R., Cornalo, A.O., González, D., Villilla, V., 1992. Nuevo enfoque en el tratamiento de las fístulas enterocutáneas postquirúrgicas. Rev. Argent. Cirug. 62, 117–127.
Fung, Y.C., 1981. Biomechanics: Mechanical Properties of Living Tissues, vol. 433. Springer, New York.
Hernández, J.A., 2002. Stability properties of elementary dynamic models of membrane transport. Bull. Math. Biol. 65, 175–197.
Levy, E., Frileux, P., Cugnenc, P.H., Honiger, J., Olliver, J.M., Parc, R., 1989. High-output external fistulae of the small bowel: management with continuous enteral nutrition. Br. J. Surg. 76, 676–679.
Lynch, A., Delaney, C., Senagore, A., Connor, J., Remzi, F., Fazio, V., 2004. Clinical outcome and factors predictive of recurrence after enterocutaneous fistula surgery. Ann. Surg. 240, 825–831.
Miller, P.R., Thompson, J.T., Faler, B.J., Meredith, J.W., Chang, M.C., 2002. Late fascial closure in lieu of ventral hernia: the next step in open abdomen management. J. Trauma 53, 843–849.
Rothe, C.F., 1984. Venous system: physiology of the capacitance vessels. In: The Cardiovascular System. Pheripheral Circulation and Organ Blood Flow. Handbook of Physiology. Am. Physiol. Soc., Bethesda, Sect. 2 vol. III, part 1, chap. 13. pp. 397–452.
Saxena, V., Hwang, C.W., Huang, S., Eichbaum, Q., Ingber, D., Orgill, D.P., 2004. Vacuum-assisted closure: microdeformations of wounds and cell proliferation. Plast. Reconstr. Surg. 114, 1086–1096.
Smye, S.W., Bloor, M.I.G., 1990. A single-tube mode of reactive hyperaemia. Phys. Med. Biol. 35, 103–113.
Smye, S.W., Clayton, R.H., 2002. Mathematical modelling for the new millennium: medicine by numbers. Med. Eng. Phys. 24, 565–574.
Wainstein, D.E., Gild, A.I., Rainone, P.E., Delgado, D., Marino, A., Rainone, J.E., 2005. Fístulas enterocutáneas postoperatorias de alto débito. Manejo y tratamiento mediante compactación por vacío. Rev. Argent. Cirug. 87, 227–238.
Webb, L.X., 2002. New techniques in wound management: vacuum-assisted wound closure. J. Am. Acad. Orthop. Surg. 10, 303–311.
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Cattoni, D.I., Chara, O. Vacuum Effects over the Closing of Enterocutaneous Fistulae: A Mathematical Modeling Approach. Bull. Math. Biol. 70, 281–296 (2008). https://doi.org/10.1007/s11538-007-9258-1
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DOI: https://doi.org/10.1007/s11538-007-9258-1