# Mathematical Homogenization in the Modelling of Digestion in the Small Intestine

• [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

top

## Abstract

top
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

top

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

top
1. G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi, 17 (1994), Springer-Verlag, Paris Zbl0819.35002MR1613876
2. G. Barles, Nonlinear Neumann boundary conditions for quasilinear degenerate elliptic equations and applications, J. Differential Equations 154 (1999), 191-224 Zbl0924.35051MR1685618
3. G. Barles, F. Da Lio, P.-L. Lions, P. E. Souganidis, Ergodic problems and periodic homogenization for fully nonlinear equations in half-space type domains with Neumann boundary conditions, Indiana Univ. Math. J. 57 (2008), 2355-2375 Zbl1173.35013MR2463972
4. M. G. Crandall, H. Ishii, P.-L. Lions, User’s guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.) 27 (1992), 1-67 Zbl0755.35015MR1118699
5. L. C. Evans, The perturbed test function method for viscosity solutions of nonlinear PDE, Proc. Roy. Soc. Edinburgh Sect. A 111 (1989), 359-375 Zbl0679.35001MR1007533
6. L. C. Evans, Periodic homogenisation of certain fully nonlinear partial differential equations, Proc. Roy. Soc. Edinburgh Sect. A 120 (1992), 245-265 Zbl0796.35011MR1159184
7. H. Ishii, Perron’s method for Hamilton-Jacobi equations, Duke Math. J. 55 (1987), 369-384 Zbl0697.35030MR894587
8. J. Keener, J. Sneyd, Mathematical physiology. Vol. II: Systems physiology, 8/ (2009), Springer, New York Zbl1273.92018MR2447179
9. J. D. Logan, A. Joern, W. Wolesensky, Location, time, and temperature dependence of digestion in simple animal tracts, J. Theoret. Biol. 216 (2002), 5-18 MR1942206
10. A. V. Mernone, J. N. Mazumdar, S. K. Lucas, A mathematical study of peristaltic transport of a Casson fluid, Math. Comput. Modelling 35 (2002), 895-912 Zbl1022.76058MR1901295
11. R. Miftahof, N. Akhmadeev, Dynamics of intestinal propulsion, J. Theoret. Biol. 246 (2007), 377-393 Zbl1120.92022MR2306905
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

## NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.