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Bulletin of Mathematical Biology

, Volume 70, Issue 1, pp 281–296 | Cite as

Vacuum Effects over the Closing of Enterocutaneous Fistulae: A Mathematical Modeling Approach

  • D. I. Cattoni
  • O. CharaEmail author
Original Article

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.

Keywords

Fistula Mathematical model Low pressure Elastic modulus Simulation Compressibility 

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References

  1. 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. CrossRefMathSciNetGoogle Scholar
  2. 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. CrossRefGoogle Scholar
  3. Alvarez, A.A., Maxwell, G.L., Rodriguez, G.C., 2001. Vacuum-assisted closure for cutaneous gastrointestinal fistula management. Gynecol. Oncol. 80, 413–416. CrossRefGoogle Scholar
  4. 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. CrossRefMathSciNetGoogle Scholar
  5. 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. CrossRefGoogle Scholar
  6. Ballard, K., Baxter, H., 2001. Vacuum-assisted closure. Nurs. Times 97, 51–52. Google Scholar
  7. 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. Google Scholar
  8. 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. CrossRefGoogle Scholar
  9. 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. CrossRefGoogle Scholar
  10. 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. Google Scholar
  11. Fung, Y.C., 1981. Biomechanics: Mechanical Properties of Living Tissues, vol. 433. Springer, New York. Google Scholar
  12. Hernández, J.A., 2002. Stability properties of elementary dynamic models of membrane transport. Bull. Math. Biol. 65, 175–197. CrossRefGoogle Scholar
  13. 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. CrossRefGoogle Scholar
  14. 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. CrossRefGoogle Scholar
  15. 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. CrossRefGoogle Scholar
  16. 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. Google Scholar
  17. 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. CrossRefGoogle Scholar
  18. Smye, S.W., Bloor, M.I.G., 1990. A single-tube mode of reactive hyperaemia. Phys. Med. Biol. 35, 103–113. CrossRefGoogle Scholar
  19. Smye, S.W., Clayton, R.H., 2002. Mathematical modelling for the new millennium: medicine by numbers. Med. Eng. Phys. 24, 565–574. CrossRefGoogle Scholar
  20. 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. Google Scholar
  21. Webb, L.X., 2002. New techniques in wound management: vacuum-assisted wound closure. J. Am. Acad. Orthop. Surg. 10, 303–311. MathSciNetGoogle Scholar

Copyright information

© Society for Mathematical Biology 2007

Authors and Affiliations

  1. 1.Cátedra de Física, Departamento de Fisicomatemática, Facultad de Farmacia y BioquímicaUBABuenos AiresArgentina
  2. 2.Instituto de Química y Fisicoquímica Biológica, Facultad de Farmacia y BioquímicaUBABuenos AiresArgentina
  3. 3.Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB)La PlataArgentina
  4. 4.Departamento de Fisiología y Biofísica, Facultad de MedicinaUBABuenos AiresArgentina

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