Vacuum Effects over the Closing of Enterocutaneous Fistulae: A Mathematical Modeling Approach |
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Authors: | D I Cattoni O Chara |
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Institution: | (1) Cátedra de Física, Departamento de Fisicomatemática, Facultad de Farmacia y Bioquímica, UBA, Buenos Aires, Argentina;(2) Instituto de Química y Fisicoquímica Biológica, Facultad de Farmacia y Bioquímica, UBA, Buenos Aires, Argentina;(3) Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), La Plata, Argentina;(4) Departamento de Fisiología y Biofísica, Facultad de Medicina, UBA, Buenos Aires, Argentina |
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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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Keywords: | Fistula Mathematical model Low pressure Elastic modulus Simulation Compressibility |
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