Analytical Study of Non-Newtonian Blood Flow through Arterial Stenosis under Hepatic Disorder Conditions
DOI:
https://doi.org/10.69996/fmep.2026036Keywords:
Arterial stenosis, Hematocrit, Hepatic artery, Herschel–Bulkley model, Non-Newtonian blood flowAbstract
Blood flow through stenosed arteries has attracted considerable attention in biomedical engineering, physiology, and bio-fluid mechanics because arterial narrowing significantly alters hemodynamic behavior and pressure distribution. Hepatic disorders such as Hepatitis A influence blood viscosity, hematocrit concentration, and vascular resistance, thereby affecting arterial circulation. The present study develops a mathematical model for non-Newtonian blood flow through stenosed hepatic arteries using two-phase fluid assumptions and Herschel–Bulkley rheological behavior. The governing equations of continuity and momentum conservation are formulated in cylindrical coordinates and solved under physiological boundary conditions. Expressions for velocity distribution, wall shear stress, volumetric flow rate, and pressure drop are derived analytically. Clinical hematocrit data are incorporated to examine the variation of pressure drop with blood viscosity. The results indicate that stenosis severity and hematocrit significantly increase pressure resistance and reduce volumetric blood flow. Graphical analysis further reveals that blood pressure drop rises sharply with increasing hematocrit concentration. The study concludes that mathematical modeling of stenosed arterial flow provides important biomedical insight into hepatic circulatory disorders and may assist in clinical diagnosis and therapeutic planning.
References
[1] Y. C. Fung, “Biomechanics: Circulation,” Springer, 1997.
[2] A. C. Guyton and J. E. Hall, “Textbook of Medical Physiology,” Elsevier, 2006.
[3] G. B. Thurston, “Viscoelasticity of Human Blood.” Biophysical Journal, vol. 69, pp. 72-90, 1972.
[4] R. B. Bird, W. E. Stewart and E. N. Lightfoot, “Transport Phenomena,” Wiley, 2002.
[5] W. H. Herschel and R. Bulkley, “Measurement of Consistency as Applied to Rubber-Benzene Solutions,” American Society Testing Materials, vol. 39, pp. 291-300, 1926.
[6] S. Whitaker, “Introduction to Fluid Mechanics,”Krieger Publishing, 1981.
[7] P. Chaturani and R. P. Samy, “Pulsatile Flow of Casson’s Fluid through Arteries,” Biorheology, vol. 23, no. 5, pp. 499-511, 1985.
[8] R. Vinoth, “Computational Fluid Dynamics Simulation of Blood Flow.”
[9] E. W. Merrill, “Rheology of Blood,” Physiological Reviews, 1969.
[10] R. Cassidy, N. S. Singh, P. R. Schiratti, A. Semwanga, P. Binyaruka, N. Sachingongu, C. M. Chama-Chiliba, Z. Chalabi, J. Borghi, and K. Blanchet, “Mathematical modelling for health systems research: A systematic review of system dynamics and agent-based models,” BMC Health Services Research, vol. 19, 2019
[11] A. Saleem, S. Akhtar, and S. Nadeem, “Bio-mathematical analysis of electro-osmotically modulated hemodynamic blood flow inside a symmetric and nonsymmetric stenosed artery with Joule heating,” International Journal of Biomathematics, vol. 15, no. 2, 2021.
[12] B. Divya and K. Kavitha, “A review on mathematical modelling in biology and medicine,” Adv. Math. Sci. J., vol. 9, no. 8, pp. 5869–5879, 2020.
[13] R. Ahmed, N. Ali, K. Al-Khaled, S. U. Khan, and I. Tlili, “Finite difference simulations for nonisothermal hydromagnetic peristaltic flow of a bio-fluid in a curved channel: Applications to physiological systems,” Comput. Methods Programs Biomed., vol. 195, Art. no. 105672, 2020.
[14] L. Formaggia, D. Lamponi, and A. Quarteroni, “One-dimensional models for blood flow in arteries,” J. Eng. Math., vol. 47, nos. 3–4, pp. 251–276, 2003.
[15] X. Jiang, G. A. Siamas, K. Jagus, and T. G. Karayiannis, “Physical modelling and advanced simulations of gas–liquid two-phase jet flows in atomization and sprays,” Prog. Energy Combust. Sci., vol. 36, no. 2, pp. 131–167, 2010.
