Geodesic
Modeling of blood glucose dynamics with account of systemic loop topology
Matematičeskoe modelirovanie, Tome 27 (2015) no. 2, pp. 3-24.

Voir la notice de l'article provenant de la source Math-Net.Ru

Paper describes a model of human glucose regulation with account of cardiovascular system topology. It is based on convectional and diffusive transport of insulin and glucose through a closed loop of blood vessels. Main types of interaction between substances and organs/tissues are taken into account. Presented approach shows possibility to simulate basic glucose regulation mechanisms with respect to cardiovascular topology.
Keywords: mathematical modeling, diabetes, insulin, glucose
Mots-clés : substance transport. 
@article{MM_2015_27_2_a0,
     author = {A. G. Borzov and A. V. Dreval and S. I. Mukhin},
     title = {Modeling of blood glucose dynamics with account of systemic loop topology},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--24},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2015_27_2_a0/}
}
TY  - JOUR
AU  - A. G. Borzov
AU  - A. V. Dreval
AU  - S. I. Mukhin
TI  - Modeling of blood glucose dynamics with account of systemic loop topology
JO  - Matematičeskoe modelirovanie
PY  - 2015
SP  - 3
EP  - 24
VL  - 27
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2015_27_2_a0/
LA  - ru
ID  - MM_2015_27_2_a0
ER  - 
%0 Journal Article
%A A. G. Borzov
%A A. V. Dreval
%A S. I. Mukhin
%T Modeling of blood glucose dynamics with account of systemic loop topology
%J Matematičeskoe modelirovanie
%D 2015
%P 3-24
%V 27
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2015_27_2_a0/
%G ru
%F MM_2015_27_2_a0
A. G. Borzov; A. V. Dreval; S. I. Mukhin. Modeling of blood glucose dynamics with account of systemic loop topology. Matematičeskoe modelirovanie, Tome 27 (2015) no. 2, pp. 3-24. http://geodesic.mathdoc.fr/item/MM_2015_27_2_a0/

[1] IDF official website, http://www.idf.org/fact-sheets

[2] A. Makroglou, J. Li, Y. Kuang, “Mathematical models and software tools for the glucose-insulin regulatory system and diabetes: an overview”, Applied Numerical Mathematics, 56 (2006), 559–573 | DOI

[3] A. Boutayeb, A. Chetouani, “A critical review of mathematical models and data used in diabetology”, BioMedical Engineering OnLine, 5:43 (2006), 9 pp.

[4] C. Landersdorfer, W. Jusko, “Pharmacokinetic/pharmacodynamic modelling in diabetes mellitus”, Clinical Pharmacokinetics, 47:7 (2008), 417–448 | DOI

[5] S. M. Gomeniuk, A. O. Emelianov, A. P. Karpenko, S. A. Chernechov, “Metody prognozirovaniia optimalnykh doz insulina dlia bolnykh sakharnym diabetom I tipa. Obzor”, Nauka I obrazovanie, 2009, no. 4

[6] A. V. Dreval, Lechenie sakharnogo diabeta I tipa i soputstvuiushikh zabolevanii, Eksmo, M., 2010

[7] V. Bolie, “Coefficients of normal blood glucose regulation”, J. of Appl. Physiology, 1961, Sep. 16, 783–788

[8] R. Bergman, C. Cobelli, G. Toffolo, “Minimal models of glucose/insulin dynamics in the intact organism: A novel approach for evaluation of factors controlling glucose tolerance”, Transactions of the Institute of Measurement and Control, 3:4 (1981), 207–216 | DOI

[9] R. Bergman, L. Phillips, C. Cobelli, “Physiologic evaluation of factors controlling glucose tolerance in man: measurement of insulin sensitivity and $\beta$-cell glucose sensitivity from the response to intravenous glucose”, J. of Clinical Investigations, 68:6 (1981), 1456–1467 | DOI

[10] A. De Gaetano, O. Arino, “Mathematical modeling of the intravenous glucose tolerance test”, Journal of Mathematical Biology, 40:2 (2000), 136–168 | DOI

[11] J. Li, Y. Kuang, B. Li, “Analysis of IVGTT glucose-insulin interaction models with time delay”, Discrete and continuous dynamical systems. Series B, 1:1 (2001), 103–124 | DOI

[12] A. Mukhopadhyay, A. De Gaetano, O. Arino, “Modeling the intra-venous glucose tolerance test: A global study for a single-distributed-delay model”, Discrete and continuous dynamical systems. Series B, 4:2 (2004), 407–417 | DOI

[13] B. Bequette, “A critical assessment of algorithms and challenges in the development of a closed-loop artificial pancreas”, Diabetes Technology and Therapeutics, 7:1 (2005), 28–46 | DOI

[14] B. Kovatchev, M. Breton, C. Dalla Man, C. Cobelli, “In silico preclinical trials: a proof of concept in closed-loop control of type 1 diabetes”, J. of Diabetes Science and Technology, 3:1 (2009), 44–55 | DOI

[15] R. Hovorka, F. Shojaee-Moradie, P. Carroll, L. Chassin, I. Gowrie, N. Jackson, R. Tudor, A. Umpleby, R. Jones, “Partitioning glucose distribution/transport, disposal, and endogenous production during IVGTT”, American J. of Physiology-Endocrinology and Metabolism, 282 (2002), 992–1007 | DOI

[16] M. V. Abakumov, N. B. Esikova, S. I. Mukhin, N. V. Sosnin, V. F. Tishkin, A. P. Favorskii, Raznostnaia skhema resheniia zadach gemodinamiki na grafe, Preprint, Dialog-MGU, M., 1998

[17] I. V. Ashmetkov, A. Ia. Bunicheva, V. A. Lukshin, V. B. Koshelev, S. I. Mukhin, N. V. Sosnin, A. P. Favorskii, A. B. Khrulenko, “Matematicheskoe modelirovanie krovoobrasheniia na osnove programmnogo kompleksa SVCC”, Komputernye modeli i progress meditsyny, Nauka, M., 2001, 194–218

[18] V. B. Koshelev, S. I. Mukhin, N. V. Sosnin, A. P. Favorskii, Matematicheskie modeli kvaziodnomernoi gemodinamiki, Metodicheskoe posobie, MAKS Press, M., 2010

[19] A. G. Borzov, S. I. Mukhin, N. V. Sosnin, “Konservativnye skhemy perenosa veschestva po sisteme sosudov, zamknutykh cherez serdtse”, Differents. uravneniya, 48:7 (2012), 935–944

[20] A. A. Samarskii, Iu. P. Popov, Raznostnye metody resheniia zadach gazovoi dinamiki, Nauka, M., 1992

[21] A. N. Tikhonov, A. A. Samarskii, Uravnenia matematicheskoi fiziki, 6-e izd., Izd-vo MGU, M., 1999

[22] R. F. Schmidt, G. Tews, Human Physiology, Second, Complety Revised Edition, Springer-Verlag, Berlin–Heilderberg, 1983, 1989 pp.

[23] V. M. Udrintsov, I. M. Udrintsov, L. D. Serova, “Sarkopenia — novaia meditsinskaia nozologiia”, Fizkultura v profilaktike, lechenii b reabilitatsii, 31:4 (2009), 7–16

[24] O. Tschritter, A. Fritsche, F. Shirkavand, F. Machikao, H. Häring, M. Stumvoll, “Assessing the shape of the glucose curve during an oral glucose tolerance test”, Diabetes Care, 26:4 (2003), 1026–1033 | DOI

[25] A. Tura, U. Morbiducci, S. Sbrignadello, Y. Winhofer, G. Pacini, A. Kautzky-Willer, Shape of glucose, insulin, C-peptide curves during a 3-h oral glucose tolerance test: any relationship with the degree of glucose tolerance?, American J. of Physiology — Regulatory, Integrative and Comparative Physiology, 300 (2011), 941–948 | DOI

[26] W. Zhou, Y. Gu, H. Li, M. Luo, “Assessing 1-h plasma glucose and shape of the glucose curve during oral glucose tolerance test”, European J. of Endocrinology, 155 (2006), 191–197 | DOI