Modeling of Pulsating Flow in Blood Capillaries

T. A. Khmel ; A. V. Fedorov

Matematičeskaâ biologiâ i bioinformatika, Tome 8 (2013) no. 1, pp. 1-11.

Résumé

A physical-mathematical model of unsteady flow in capillaries with the wall motion and flow into the interstitial space is proposed. In the frame of the semi-empirical model based on the data of intra-capillary pressure changes in time and space, the theoretical analysis of internal capillary blood flow is performed. The solutions obtained are consistent with experimental data on the measurement of the velocity fluctuations in the blood capillaries. The presence of a phase shift in the oscillations of the pressure and the radius is revealed that indicates the possible involvement of wall motion in the implementation of the filtration mechanism of transcapillary exchange.

Bibliographie

[1] Caro C. G., Pedley T. G., Schroter R. G., Seed W. A., The mechanics of the circulation, Oxford University Press, New York, 1978 | Zbl | Zbl

[2] Jeong J. H., Sugii Ya., Minamiyama M., Okamoto K., “Measurement of RBC deformation and velocity in capillaries in vivo”, Microvascular Research, 71 (2006), 212–217 | DOI

[3] Lee J. J., Tyml K., Menkis A. N., Novick R. J., Mckenzie F. N., “Evaluation of pulsatile and nonpulsatile flow in capillaries of goat skeletal muscle using intravital microscopy”, Microvascular Research, 48:3 (1994), 316–327 | DOI

[4] Khmel T. A., Fedorov A. V., Zakharov V. N., Orlov V. A., Panov S. V., “Pulsovye kolebaniya prosveta kapillyarov i modelirovanie mikrogemotsirulyatsii”, Mezhd. konf., posvyaschennaya 90-letiyu akad. N. N. Yanenko, Sovremennye problemy prikladnoi matematiki i mekhaniki: teoriya, eksperiment i praktika (30 maya–4 iyunya 2011 g.), IVT SO RAN, Novosibirsk, 2011 (data obrascheniya: 11.10.2012) http://conf.nsc.ru/niknik90

[5] Bagayev S. N., Zakharov V. N., Orlov V. A., Panov S. V., Fomin Yu. N., “Investigation of physical mechanisms of blood microcirculation and transcapillary exchange by using the phase sensitive laser method”, Russian Journal of Biomechanics, 10:3 (2006), 21–38

[6] Bagayev S. N., Zakharov V. N., Orlov V. A., Panov S. V., Ratushnyak A. S., Zapara T. A., “Regulation of the transcapillary exchange by pulse pressure blood”, Russian Journal of Biomechanics, 12:3 (2008), 7–14

[7] Egorov V. A., Regirer S. A., Shadrina N. Kh., “Techenie krovi v mikrososudistoi seti myshtsy pri regulyarnykh reaktsiyakh: kvazistatsionarnye zadachi”, Mekhanika zhidkosti i gaza, 1993, no. 1, 137–1145

[8] Regirer S. A., Shadrina N. Kh., “Matematicheskoe opisanie dvizheniya krovi v mikrososudistom module skeletnoi myshtsy”, Biofizika, 39:1 (1994), 107–115 | MR

[9] Regirer S. A., Shadrina N. Kh., “Elementarnaya model sosuda so stenkoi, chuvstvitelnoi k mekhanicheskim stimulam”, Biofizika, 47:5 (2002), 908–913

[10] Shadrina N. Kh., Buchin V. A., “O modelirovanii reaktsii rezistivnogo sosuda na davlenie”, Biofizika, 54:2 (2009), 267–273

[11] Buchin V. A., Shadrina N. Kh., “O regulyatsii prosveta rezistivnogo krovenosnogo sosuda mekhanicheskimi stimulami”, Mekhanika zhidkosti i gaza, 2010, no. 2, 51–63

[12] Shabrykina N. S., “Matematicheskoe modelirovanie mikrotsirkulyatornykh protsessov: nestatsionarnaya model”, Rossiiskii zhurnal biomekhaniki, 10:4 (2006), 70–83

[13] Shabrykina N. S., “Modelirovanie mikrotsirkulyatornykh protsessov: nestatsionarnoe techenie zhidkosti v tkani”, Izvestiya Saratovskogo universiteta. Ser. Matematika. Mekhanika. Informatika, 7:1 (2007), 69–73 | MR

[14] Khmel T. A., Fedorov A. V., Fomin V. M., Orlov V. A., “Modelirovanie protsessov mikrogemotsirkulyatsii s uchetom pulsovykh kolebanii davleniya”, Prikladnaya mekhanika i tekhnicheskaya fizika, 2011, no. 2, 92–102

[15] Pozrikidis C., “Axisymmetric motion of a file of red blood cells through capillaries”, Physics of Fluids, 17:3 (2005), 031503–031514 | DOI | MR

[16] Secomb T. W., “Mechanics and computational simulation of blood flow in microvessels”, Medical Engineering Physics, 33:7 (2011), 800–804 | DOI

[17] Medvedev A. E., Samsonov V. I., Fomin V. M., “Matematicheskoe modelirovanie techeniya krovi v sosudakh”, Sistema krovoobrascheniya i arterialnaya gipertoniya: biofizicheskie i genetiko-fiziologicheskie mekhanizmy, matematicheskoe i kompyuternoe modelirovanie, eds. Ivanov L. N. i dr., Izd-vo SO RAN, Novosibirsk, 2008, 80–105

[18] Ovsyannikov L. V., Lektsii po osnovam gazovoi dinamiki, Izd-vo NGU, Novosibirsk, 1967

[19] Fedorov A. V., Fomin V. M., Matematicheskoe modelirovanie raboty magistralnykh truboprovodov, Preprint No 35-83 Instituta teoreticheskoi i prikladnoi mekhaniki Sibirskogo otdeleniya AN SSSR, ITPM SO RAN, Novosibirsk, 1983 | MR

[20] Zweifach B. W., “Quantitative Studies of Microcirculatory Structure and Function. II: Direct Measurement of Capillary Pressure in Splanchnic Mesenteric Vessels”, Circulation Research, 34 (1974), 858–866 | DOI