Mathematical Homogenization in the Modelling of Digestion in the Small Intestine

Masoomeh Taghipoor[1]; Guy Barles[2]; Christine Georgelin[2]; Jean-René Licois[2]; Philippe Lescoat[3]

  • [1] Laboratoire de Mathématiques et Physique Théorique (UMR CNRS 7350). Fédération Denis Poisson (FR CNRS 2964) Université de Tours. Faculté des Sciences et Techniques, Parc de Grandmont, 37200 Tours, France INRA, UR83 Recherches Avicoles, 37380 Nouzilly, France.
  • [2] Laboratoire de Mathématiques et Physique Théorique (UMR CNRS 7350). Fédération Denis Poisson (FR CNRS 2964) Université de Tours. Faculté des Sciences et Techniques, Parc de Grandmont, 37200 Tours, France
  • [3] INRA, UR83 Recherches Avicoles, 37380 Nouzilly, France.

MathematicS In Action (2013)

  • Volume: 6, Issue: 1, page 1-19
  • ISSN: 2102-5754

Abstract

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Digestion in the small intestine is the result of complex mechanical and biological phenomena which can be modelled at different scales. In a previous article, we introduced a system of ordinary differential equations for describing the transport and degradation-absorption processes during the digestion. The present article sustains this simplified model by showing that it can be seen as a macroscopic version of more realistic models including biological phenomena at lower scales. In other words, our simplified model can be considered as a limit of more realistic ones by averaging-homogenization methods on biological processes representation.

How to cite

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Taghipoor, Masoomeh, et al. "Mathematical Homogenization in the Modelling of Digestion in the Small Intestine." MathematicS In Action 6.1 (2013): 1-19. <http://eudml.org/doc/275783>.

@article{Taghipoor2013,
abstract = {Digestion in the small intestine is the result of complex mechanical and biological phenomena which can be modelled at different scales. In a previous article, we introduced a system of ordinary differential equations for describing the transport and degradation-absorption processes during the digestion. The present article sustains this simplified model by showing that it can be seen as a macroscopic version of more realistic models including biological phenomena at lower scales. In other words, our simplified model can be considered as a limit of more realistic ones by averaging-homogenization methods on biological processes representation.},
affiliation = {Laboratoire de Mathématiques et Physique Théorique (UMR CNRS 7350). Fédération Denis Poisson (FR CNRS 2964) Université de Tours. Faculté des Sciences et Techniques, Parc de Grandmont, 37200 Tours, France INRA, UR83 Recherches Avicoles, 37380 Nouzilly, France.; Laboratoire de Mathématiques et Physique Théorique (UMR CNRS 7350). Fédération Denis Poisson (FR CNRS 2964) Université de Tours. Faculté des Sciences et Techniques, Parc de Grandmont, 37200 Tours, France; Laboratoire de Mathématiques et Physique Théorique (UMR CNRS 7350). Fédération Denis Poisson (FR CNRS 2964) Université de Tours. Faculté des Sciences et Techniques, Parc de Grandmont, 37200 Tours, France; Laboratoire de Mathématiques et Physique Théorique (UMR CNRS 7350). Fédération Denis Poisson (FR CNRS 2964) Université de Tours. Faculté des Sciences et Techniques, Parc de Grandmont, 37200 Tours, France; INRA, UR83 Recherches Avicoles, 37380 Nouzilly, France.},
author = {Taghipoor, Masoomeh, Barles, Guy, Georgelin, Christine, Licois, Jean-René, Lescoat, Philippe},
journal = {MathematicS In Action},
keywords = {Digestion in the small intestine; peristalsis; intestinal villi; homogenization; viscosity solutions; digestion in small intestine},
language = {eng},
number = {1},
pages = {1-19},
publisher = {Société de Mathématiques Appliquées et Industrielles},
title = {Mathematical Homogenization in the Modelling of Digestion in the Small Intestine},
url = {http://eudml.org/doc/275783},
volume = {6},
year = {2013},
}

TY - JOUR
AU - Taghipoor, Masoomeh
AU - Barles, Guy
AU - Georgelin, Christine
AU - Licois, Jean-René
AU - Lescoat, Philippe
TI - Mathematical Homogenization in the Modelling of Digestion in the Small Intestine
JO - MathematicS In Action
PY - 2013
PB - Société de Mathématiques Appliquées et Industrielles
VL - 6
IS - 1
SP - 1
EP - 19
AB - Digestion in the small intestine is the result of complex mechanical and biological phenomena which can be modelled at different scales. In a previous article, we introduced a system of ordinary differential equations for describing the transport and degradation-absorption processes during the digestion. The present article sustains this simplified model by showing that it can be seen as a macroscopic version of more realistic models including biological phenomena at lower scales. In other words, our simplified model can be considered as a limit of more realistic ones by averaging-homogenization methods on biological processes representation.
LA - eng
KW - Digestion in the small intestine; peristalsis; intestinal villi; homogenization; viscosity solutions; digestion in small intestine
UR - http://eudml.org/doc/275783
ER -

References

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  12. L. C. Piccinini, Homogeneization problems for ordinary differential equations, Rend. Circ. Mat. Palermo (2) 27 (1978), 95-112 Zbl0416.34019MR542236
  13. D. Randall, W. Burggren, K. French, R. Eckert, Eckert Animal Physiology: Mechanisms and Adaptations, (1997), W.H. Freeman & Company 
  14. J. Rivest, J. F. Bernier, C. Pomar, A dynamic model of protein digestion in the small intestine of pigs, J Anim Sci 78 (2000), 328-340 
  15. M. Taghipoor, P. Lescoat, J.-R. Licois, Ch. Georgelin, G. Barles, Mathematical modeling of transport and degradation of feedstuffs in the small intestine, Journal of Theoretical Biology 294 (2012), 114-121 
  16. K.E. Yamauchi, Review of a histological intestinal approach to assessing the intestinal function in chickens and pigs, Animal Science Journal 78 (2007), 356-370 
  17. X. T. Zhao, M. A. McCamish, R. H. Miller, L. Wang, H. C. Lin, Intestinal transit and absorption of soy protein in dogs depend on load and degree of protein hydrolysis., J Nutr 127 (1997), 2350-2356 

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