Mathematical Homogenization in the Modelling of Digestion in the Small Intestine
MathematicS In Action, Tome 6 (2013) no. 1, pp. 1-19.

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.

Publié le : 2013-07-09
DOI : https://doi.org/10.5802/msia.7
Classification : 92A09,  35B27,  34C29,  49L25
Mots clés: Digestion in the small intestine, peristalsis, intestinal villi, homogenization, viscosity solutions
@article{MSIA_2013__6_1_1_0,
     author = {Masoomeh Taghipoor and Guy Barles and Christine Georgelin and Jean-Ren\'e Licois and Philippe Lescoat},
     title = {Mathematical Homogenization in the Modelling of Digestion in the Small Intestine},
     journal = {MathematicS In Action},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
     volume = {6},
     number = {1},
     year = {2013},
     pages = {1-19},
     doi = {10.5802/msia.7},
     language = {en},
     url = {msia.centre-mersenne.org/item/MSIA_2013__6_1_1_0/}
}
Taghipoor, Masoomeh; Barles, Guy; Georgelin, Christine; Licois, Jean-René; Lescoat, Philippe. Mathematical Homogenization in the Modelling of Digestion in the Small Intestine. MathematicS In Action, Tome 6 (2013) no. 1, pp. 1-19. doi : 10.5802/msia.7. https://msia.centre-mersenne.org/item/MSIA_2013__6_1_1_0/

[1] G. Barles Solutions de viscosité des équations de Hamilton-Jacobi, Springer-Verlag, Paris, Mathématiques & Applications (Berlin) [Mathematics & Applications], Tome 17 (1994)

[2] G. Barles Nonlinear Neumann boundary conditions for quasilinear degenerate elliptic equations and applications, J. Differential Equations, Tome 154 (1999) no. 1, pp. 191-224 | Article

[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., Tome 57 (2008) no. 5, pp. 2355-2375 | Article

[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.), Tome 27 (1992) no. 1, pp. 1-67 | Article

[5] L. C. Evans The perturbed test function method for viscosity solutions of nonlinear PDE, Proc. Roy. Soc. Edinburgh Sect. A, Tome 111 (1989) no. 3-4, pp. 359-375 | Article

[6] L. C. Evans Periodic homogenisation of certain fully nonlinear partial differential equations, Proc. Roy. Soc. Edinburgh Sect. A, Tome 120 (1992) no. 3-4, pp. 245-265 | Article

[7] H. Ishii Perron’s method for Hamilton-Jacobi equations, Duke Math. J., Tome 55 (1987) no. 2, pp. 369-384 | Article

[8] J. Keener; J. Sneyd Mathematical physiology. Vol. II: Systems physiology, Springer, New York, Interdisciplinary Applied Mathematics, Tome 8/ (2009) | Article

[9] J. D. Logan; A. Joern; W. Wolesensky Location, time, and temperature dependence of digestion in simple animal tracts, J. Theoret. Biol., Tome 216 (2002) no. 1, pp. 5-18 | Article

[10] A. V. Mernone; J. N. Mazumdar; S. K. Lucas A mathematical study of peristaltic transport of a Casson fluid, Math. Comput. Modelling, Tome 35 (2002) no. 7-8, pp. 895-912 | Article

[11] R. Miftahof; N. Akhmadeev Dynamics of intestinal propulsion, J. Theoret. Biol., Tome 246 (2007) no. 2, pp. 377-393 | Article

[12] L. C. Piccinini Homogeneization problems for ordinary differential equations, Rend. Circ. Mat. Palermo (2), Tome 27 (1978) no. 1, pp. 95-112 | Article

[13] D. Randall; W. Burggren; K. French; R. Eckert Eckert Animal Physiology: Mechanisms and Adaptations, W.H. Freeman & Company (1997) http://amazon.com/o/ASIN/0716724146/

[14] J. Rivest; J. F. Bernier; C. Pomar A dynamic model of protein digestion in the small intestine of pigs, J Anim Sci, Tome 78 (2000) no. 2, pp. 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, Tome 294 (2012), pp. 114 -121 http://www.sciencedirect.com/science/article/pii/S002251931100539X | Article

[16] K.E. Yamauchi Review of a histological intestinal approach to assessing the intestinal function in chickens and pigs, Animal Science Journal, Tome 78 (2007), pp. 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, Tome 127 (1997) no. 12, pp. 2350-2356