Non-Newtonian flow of pathological bile in the biliary system: experimental investigation and CFD simulations

Alex G. Kuchumov; Valeriy Gilev; Vitaliy Popov; Vladimir Samartsev; Vasiliy Gavrilov

Korea-Australia Rheology Journal, Vol.26, No.1, 81-90, February, 2014

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Non-Newtonian flow of pathological bile in the biliary system: experimental investigation and CFD simulations

Alex G. Kuchumov^†, Valeriy Gilev¹, Vitaliy Popov¹, Vladimir Samartsev², and Vasiliy Gavrilov²

Department of Theoretical Mechanics, Perm National Research State Polytechnical University, 29 Komsomolskii Prospect, 614990, Perm, Russia, Russian Federation
¹Department of Phase Transition Physics, Perm State National Research University, 15 Bukirev Street, 614990, Perm, Russia, Russian Federation
²Department of General Surgery, Academician E.A. Wagner Perm State Medical Academy, 39 Kuybishev Street, 614990, Perm, Russia, Russian Federation

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The paper presents an experimental study of pathological human bile taken from the gallbladder and bile ducts. The flow dependences were obtained for different types of bile from patients with the same pathology, but of different age and sex. The parameters of the Casson’s and Carreau’s equations were found for bile samples. Results on the hysteretic bile behavior at loading-unloading tests are also presented, which proved that the pathologic bile is a non-Newtonian thixotropic liquid. The viscosity of the gallbladder bile was shown to be higher compared to the duct bile. It was found that at higher shear stress the pathological bile behaves like Newtonian fluid, which is explained by reorientation of structural components. Moreover, some pathological bile flow in the biliary system CFD simulations were performed. The velocity and pressure distributions as well as flow rates in the biliary segments during the gallbladder refilling and emptying phases are obtained. The results of CFD simulations can be used for surgeons to assess the patient’s condition and choose an adequate treatment.

Keywords:bile;thixotropy;CFD;bio-fluid;hysteresis

[References]

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Azikri de Deus HP, Dupim GSP, Physics Letters A., 377, 478 (2013)
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[1] Adrian T, Motility and other disorders of the biliary tract, xPharm: The Comprehensive Pharmacology Reference, 1, 1 (2007)

[2] Agarwal S, Sinha AK, Singh SF, Int. J. Appl. Math., 8, 92 (2012)

[3] Al-Atabi MT, Chin SB, Luo XY, Journal of Flow Visualization and Image Processing., 12, 301 (2005)

[4] Al-Atabi MT, Chin SB, Luo XY, Journal of Mechanics in Medicine and Biology., 6, 249 (2006)

[5] Al-Atabi MT, Chin SB, Luo XY, Journal of Engineering Science and Technology., 1, 1 (2006)

[6] Al-Atabi MT, Chin SB, Luo XY, Beck SBM, Journal of Biomechanical Science and Engineering., 3, 411 (2008)

[7] Al-Atabi MT, Chin SB, Luo XY, ASME Journal of Biomechanical Engineering., 132, 247 (2010)

[8] Al-Atabi MT, Ooi RC, Luo XY, Chin SB, Bird NC, Medical Eng. Phys., 34, 1177 (2012)

[9] Azikri de Deus HP, Dupim GSP, Physics Letters A., 377, 478 (2013)

[10] Bouchier IAD, Cooperband SR, Kodsi BM, Gastroenterology., 49, 343 (1965)

[11] Cho SW, Kim SW, Sung MH, Ro KC, Ryou HC, Korea-Aust. Rheol. J., 23, 7 (2011)

[12] Coene PPLO, Groen AK, Davids PHP, Hardeman M, Tytgat GNG, Huibregtse K, Scand J.Gastroenterol., 29, 757 (1994)

[13] Cowie AGA, Sutor JD, Digestion., 13, 312 (1975)

[14] Doty JE, Pitt HA, Kuchenbecker SL, Porter-Fink V, DenBesten L, Am. J. Surg., 145, 54 (1983)

[15] Everhartet JE, Khare M, Hill M, Maurer KR, Gastroenterology., 117, 632 (1999)

[16] Gavrilenko SL, Vasin RA, Shilko SV, Russian Journal of Biomechanics., 6, 90 (2002)

[17] Gottschalk M, Lochner A, Gastroenterol. J., 50, 65 (1990)

[18] Guelrud M, Gastroenterology., 104, A361 (1993)

[19] Harada H, Ueda O, Kochi F, Kobayashi T, Komazawa M, Gastroenterologia Japonica., 16, 623 (1981)

[20] Jian C, Wang G, Bio-Medical Materials and Engineering., 1, 105 (1991)

[21] Jungst D, Niemeyer A, Muller I, Zundt B, Meyer G, Wilhelmi M, del Pozo R, World J. Gastroenterology., 7, 203 (2001)

[22] Khuroo MS, Mahajan R, Zargar SA, Javid G, Sapru S, Gut., 30, 201 (1989)

[23] Kocevar-Nared J, Kristl J, Smid-Korbar J, Biomaterials., 18, 677 (1997)

[24] Krøen J, Hyncik L, Mathematics and Computers in Simulation., 76, 116 (2007)

[25] Kuchumov AG, Nyashin YJ, Samarcev VA, Gavrilov VA, Mesnard M, Russian Journal of Biomechanics., 15, 28 (2011)

[26] Kuchumov AG, Nyashin YI, Samarcev VA, Gavrilov VA, Acta of Bioengineering and Biomechanics., Modelling of the pathological bile flow in the duct with a calculus, DOI: 10.5277/abb130402. (2013)

[27] Li WG, Luo XY, Johnson AG, Hill NA, Bird N, Chin SB, ASME J. Biomech. Eng., 129, 164 (2007)

[28] Li WG, Luo XY, Chin SB, Hill NA, Johnson AG, Bird NC, Annals of Biomedical Engineering., 36, 1893 (2008)

[29] Luo XY, Li WG, Bird N, Chin SB, Hill NA, Johnson AG, World J. Gastroenterol., 13, 1384 (2007)

[30] Luo XY, Chin SB, Ooi RC, Clubb M, Johnson AG, Bird N, The rheological properties of human bile, Fourth International Conference on Fluid Mechanics, Dalian, China (2004)

[31] Maiti S, Misra JC, International Journal of Engineering Science., 49, 950 (2011)

[32] Mongkolwongrojn M, Wongseedakaew K, Kennedy FE, Tribology International., 43, 1017 (2010)

[33] Nagarani P, Lewis A, Korea-Aust. Rheol. J., 24(1), 1 (2012)

[34] Ooi RC, Luo XY, Chin SB, Johnson AG, Bird NC, J. Biomech., 37, 1913 (2004)

[35] Portincasa P, Di Ciaula A, Baldassarre G, Palmieri V, Gentile A, Cimmino A, Palasciano G, J. Hepatol., 21, 430 (1994)

[36] Rodkiewicz CM, Otto WJ, J. Biomech., 12, 411 (1979)

[37] Ryan J, Cohen S, Am. J. Physiol., 230, 1461 (1976)

[38] Samartsev VA, Paths of the improvement of the cholelithiasis treatment at the high operative risk groups: optimization of the diagnostics methods, landmark endoscopic and less-invasive tratment, predicting and prophylactics of the complications, Doctor of Medical Sciences Thesis, Academician EA Wagner Perm State Medical Academy, Russia. (2005)

[39] Szwajczak E, Russian Journal of Biomechanics., 8, 89 (2004)

[40] Tera H, Ann. Surg., 157, 468 (1963)

[41] Vitetta L, Sali A, HPB Surgery., 6, 23 (1992)