For citation:
Kuchumov A. G. Mathematical Modeling of Deposits Accumulation on the Plastic Biliary Stent Surface for Predicting Its Occlusion. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2020, vol. 20, iss. 2, pp. 220-231. DOI: 10.18500/1816-9791-2020-20-2-220-231, EDN: YQDFXT
Mathematical Modeling of Deposits Accumulation on the Plastic Biliary Stent Surface for Predicting Its Occlusion
Endoprosthetics with plastic stents has been used to restore bile drainage through the percutaneous or endoscopic method since the late 1970s. The long-term results cannot be considered satisfactory due to the high incidence of jaundice recurrence which is caused by the occlusion of plastic stents with a biliary sludge (accumulation of cholesterol crystals, pigment crystals, bacteria and calcium salts). Cholesterol is considered to be the main component of biliary sludge that stimulates the reduction of the stent lumen. The average lifetime of stents is 3–6 months. Despite numerous experimental studies of the occlusion process, the optimal timing for the replacement of the biliary plastic stent has not been established. Too frequent replacement of the stent can lead to additional complications, so an individualized forecast of the stent’s lifetime for a particular patient is needed. In this paper, a model of the flow of lithogenic bile as a non-Newtonian fluid is developed taking into account the transport of particles describing the behavior of cholesterol crystals that accumulate on the inner surface of the stent, stimulating a decrease in its lumen. A correlation was found between cholesterol concentration and occlusion time based on the use of a specially developed iterative procedure. The results of the numerical computations show that individual parameters (age, gender, bile viscosity, cholesterol concentration) have a significant impact on the rate of occlusion of the stent.
- Cilla M., Pena E., Martinez M. A. Mathematical modelling of atheroma plaque formation and development in coronary arteries. Journal of Royal Society Interface, 2014, vol. 11, no. 90, p. 20130866. DOI: https://doi.org/0.1098/rsif.2013.0866
- Yang C., Tang D., Yuan C., Kerwin W., Liu F., Canton G., Hatsukami T. S., Atluri S. Meshless generalized finite difference method and human carotid atherosclerotic plaque progression simulation using multi-year MRI patient-tracking data. CMES, 2008, vol. 28, no. 2, pp. 95–107.
- Wada S., Koujiya M., Karino T. Theoretical study of the effect of local flow disturbances on the concentration of low-density lipoproteins at the luminal surface of end-to-end anastomosed vessels. Medical and Biological Engineering and Computing, 2002, vol. 40, iss. 5, pp. 576–587. DOI: https://doi.org/10.1007/BF02345458
- Olgac U., Kurtcuoglu V., Poulikakos V. Computational modeling of coupled bloodwall mass transport of LDL: effects of local wall shear stress. American Journal of Physiology-Heart and Circulatory Physiology, 2008, vol. 294, no. 2, pp. 909–919. DOI: https://doi.org/10.1152/ajpheart.01082.2007
- Kwak B. R., Back M., Bochaton-Piallat M. L., Caligiuri G., Daemen M. J., Davies P. F., Hoefer I. E., Holvoet P., Jo H., Krams R., Lehoux S., Monaco C., Steffens S., Virmani R., Weber C., Wentzel J. J., Evans P. C. Biomechanical factors in atherosclerosis: mechanisms and clinical implications. European Heart Journal, 2014, vol. 35, no. 43, pp. 3013–3020. DOI: https://doi.org/10.1093/eurheartj/ehu353
- Thondapu V., Bourantas C. V., Foin N., Jang I. K., Serruys P. W., Barlis P. Biomechanical stress in coronary atherosclerosis: emerging insights from computational modelling. European Heart Journal, 2017, vol. 38, no. 2, pp. 81–92. DOI: https://doi.org/10.1093/eurheartj/ehv689
- Surwase S., Balakrishnan H., Acharya S., Makharia G., Kumaraswamy G., Prasad B. L. V. Accelerated in vitro model for occlusion of biliary stents: investigating the role played by dietary fibre. BMJ Innovations, 2018, vol. 4, no. 1, pp. 39–45. DOI: https://doi.org/10.1136/bmjinnov-2017-000209
- Kuchumov A. G., Gilev V., Popov V., Samartsev V., Gavrilov V. Non-Newtonian flow of pathological bile in the biliary system: experimental investigation and CFD simulations. Korea-Australia Rheology Journal, 2014, vol. 26, no. 1, pp. 81–90. DOI: https://doi.org/10.1007/s13367-014-0009-1
- Ooi R. C., Luo X. Y., Chin S. B., Johnson A. G., Bird N. C. The flow of bile in the human cystic duct. Journal of Biomechanics, 2004, vol. 37, iss. 12, pp. 1913–1922. DOI: https://doi.org/10.1016/j.jbiomech.2004.02.029
- Scheidt H. A., Huster D., Gawrisch K. Diffusion of cholesterol and its precursors in lipid membranes studied by 1H pulsed field gradient magic angle spinning NMR. Biophysical Journal, 2005, vol. 89, iss. 4, pp. 2504–2512. DOI: https://doi.org/10.1529/biophysj.105.062018
- Kuchumov A., Tuktamyshev V., Kamaltdinov M. Peristaltic flow of lithogenic bile in the Vateri’s papilla as non-Newtonian fluid in the finite-length tube: analytical and numerical results for reflux study and optimization. Lekar a technika – Clinician and Technology, 2017, vol. 47, no. 2, pp. 35–42.
- Speer A. G., Cotton P. B., MacRae K. D. Endoscopic management of malignant biliary obstruction: stents of 10 French gauge are preferable to stents of 8 French gauge. Gastrointestinal Endoscopy, 1988, vol. 34, iss. 5, pp. 412–417. DOI: https://doi.org/10.1016/S0016-5107(88)71407-8
- Kuchumov А. G., Gilev V. G., Popov V. A., Samartsev V. A., Gavrilov V. A. Experimental investigation of the pathologic bile rheology. Russian Journal of Biomechanics, 2011, vol. 15, no. 3 (53), pp. 43–50.
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