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Original Article
Three-Phase Computational Modeling of Hemodynamics in Renal Capillary Blood Flow during Dengue Infection
Dr.Bhaskar Pandey1
V.Upadhyay2
1 Department of Mathematics, M.G.C.G.V Chirakoot, Satna, Madhya Pradesh, India. 2 Professor of Mathematics, HOD Physical Sciences Department, M.G.C.G.V Chitrakoot, Satna, Madhya Pradesh, India.
Published Online: May-June 2026
Pages: 258-273
Cite this article
↗ https://www.doi.org/10.59256/ijrtmr.20260603030References
1. Elvira Barvera,A three-phase model for blood flow,May 2023,Ricerche di Matematica 74(8)
2. Secomb,T.W., Mechanics of Blood Flow in Capillaries,2nd Micro and Nano Flows Conference West London, UK, 1-2 September 2009.
3. Gidaspow, D. Multiphase Flow and Fluidization Continuum and Kinetic Theory Descriptions; Academic Press: Cambridge, MA,
USA, 1994; ISBN 0-12-282470-9.
4. Wu, W.; Yang, F.; Antaki, J.; Aubry, N.; Massoudi, M. Study of blood flow in several benchmark micro-channels using a two-fluid
approach. Int. J. Eng. Sci. 2015, 95, 49–59.
5. Savage, S.B. Granular flow at high shear rates. In Theory of Dispersed Multiphase Flow; Meyer, R.E., Ed.; Academic Press: New York,
NY, USA, 1983; pp. 339–358.
6. Barnard, A.C.L., Lopez, L., Hellums, J.D., 1968. Basic theory of blood flow in capillaries. Microvasc. Res. 1:23-34.
7. Secomb, T.W., Hsu, R., Pries, A.R., 2001. Effect of the endothelial surface layer on transmission of fluid shear stress to endothelial cells.Biorheology 38:143-150.
8. Secomb, T.W., Hsu, R., Pries, A.R., 2002. Blood flow and red blood cell deformation in nonuniform capillaries: effects of
the endothelial surface layer. Microcirculation 9:189-196.
9. Secomb, T.W., Skalak, R., Ozkaya, N., Gross, J.F., 1986. Flow of axisymmetric red blood cells in narrow capillaries. Journal of Fluid
Mechanics 163:405-423.
10. Secomb, T.W., Styp-Rekowska, B., Pries, A.R., 2007. Two-dimensional simulation of red blood cell deformation and lateral migration in
microvessels. Ann. Biomed. Eng 35:755-765.
11. Lombardi R, Yu L, Younes-Ibrahim M, et al. Epidemiology of acute kidney injury in Latin America. Semin Nephrol 2008; 28: 320–329.
12. Glassock RJ et al, Immune complex-induced glomerular injury in viral diseases: an overview. Kidney Int Suppl 1991; 35: S5–S7.
13. ISMAIL A et al,Renal arterial doppler velocimetric indices among healthy subjects in north west nigeria:j west afr coll surg. 2018 jan-
mar;8(1):40-49.
14. Lukas M. Trunz,Rashmi Balasubramanya et al,Doppler Renal Assessment, Protocols, and Interpretation: National Library of
Medicine ,2023.
15. Tokunori Yamamoto, Yasuo Ogasawara et al,Blood Velocity Profiles in the Human Renal Artery by Doppler Ultrasound and Their
Relationship to Atherosclerosis, Arteriosclerosis, Thrombosis, and Vascular Biology,1996;Vol 16, No 1.
16. Alžbeta Bohiniková et al ,Modeling Red Blood Cell Viscosity Contrast Using Inner Soft Particle Suspension; Micromachines 2021, 12,
974.
17. B.Pandey et al,Non Newtonian Model for Two Phase Blood Flow in Hepatic Arterioles in Case of Dengue using Herschel –Bulkley Law,
SAMRIDDHI,2022; Volume 14, Issue 4 .
18. B.Pandey et al,Mathematical Modelling on Two Phase Blood Flow in Human Hepatic artery for Dengue Disease Using Power Law Model;
neuroquantology | november 2022 | volume 20 | issue 11 | page 7881-7887.
19. B.Pandey,Extention of two phase power law model in three phase blood flow in human renal artery in case of dengue,International Journal
of Physics and Mathematics 2025; 7(2): 141-154
20. Haynes, R.H and Burton,A.C. et al,Role of non Newtonian Behaviour of blood in Hemodynamics;Am.J.Physiol.,1959;Vol.197,p.943.
21. Shrivastava ,V.P. and Saxena.M,A et al,Two –Fluid Model of Non Newtonian blood flow Induced by Peristaltic Waves;Rheol.Act
a,1995;Vol.34,No.4pp.406-414.
22. Haynes ,R.H et al,Physical Basis of the Dependence of Blood Viscosity on Tube Radius;Am.J.Physiol.1960;Vol.198,pp.1193-1200.
23. Bugliarello,G. and Sevilla, J et al, Velocity Distribution and other Characteristics of steady and Pulsatile Blood Flow in Fine Glass Tubes
;Biorheology , Vol.7,pp.85-107,1970.
24. B.Pandey,Initial step for developing software for two phase blood flow power law model in human renal artery for dengue disease with
help of python coding,International Journal of Statistics and Applied Mathematics 10(8):160-170,2025.
25. B.Pandey,Two phase modelling for hepatic capillary blood flow in dengue disease by power law model,Journal of Mathematical Problems
Equations and Statistics 6(2):484-493,2025.
26. Figure,https://www.nursinghero.com/study-guides/cuny-kbcc-ap2/regulation-of-renal-blood-flow.
27. World Health Organization. Dengue: Guidelines for Diagnosis, Treatment, Prevention and Control, New edition Geneva: World
Health Organization, 2009.
28. A.Bohle,Human glomerular structure under normal conditions and in isolated glomerular diseaseKidney Int Suppl 1998
Sep:67:S186-8.
2. Secomb,T.W., Mechanics of Blood Flow in Capillaries,2nd Micro and Nano Flows Conference West London, UK, 1-2 September 2009.
3. Gidaspow, D. Multiphase Flow and Fluidization Continuum and Kinetic Theory Descriptions; Academic Press: Cambridge, MA,
USA, 1994; ISBN 0-12-282470-9.
4. Wu, W.; Yang, F.; Antaki, J.; Aubry, N.; Massoudi, M. Study of blood flow in several benchmark micro-channels using a two-fluid
approach. Int. J. Eng. Sci. 2015, 95, 49–59.
5. Savage, S.B. Granular flow at high shear rates. In Theory of Dispersed Multiphase Flow; Meyer, R.E., Ed.; Academic Press: New York,
NY, USA, 1983; pp. 339–358.
6. Barnard, A.C.L., Lopez, L., Hellums, J.D., 1968. Basic theory of blood flow in capillaries. Microvasc. Res. 1:23-34.
7. Secomb, T.W., Hsu, R., Pries, A.R., 2001. Effect of the endothelial surface layer on transmission of fluid shear stress to endothelial cells.Biorheology 38:143-150.
8. Secomb, T.W., Hsu, R., Pries, A.R., 2002. Blood flow and red blood cell deformation in nonuniform capillaries: effects of
the endothelial surface layer. Microcirculation 9:189-196.
9. Secomb, T.W., Skalak, R., Ozkaya, N., Gross, J.F., 1986. Flow of axisymmetric red blood cells in narrow capillaries. Journal of Fluid
Mechanics 163:405-423.
10. Secomb, T.W., Styp-Rekowska, B., Pries, A.R., 2007. Two-dimensional simulation of red blood cell deformation and lateral migration in
microvessels. Ann. Biomed. Eng 35:755-765.
11. Lombardi R, Yu L, Younes-Ibrahim M, et al. Epidemiology of acute kidney injury in Latin America. Semin Nephrol 2008; 28: 320–329.
12. Glassock RJ et al, Immune complex-induced glomerular injury in viral diseases: an overview. Kidney Int Suppl 1991; 35: S5–S7.
13. ISMAIL A et al,Renal arterial doppler velocimetric indices among healthy subjects in north west nigeria:j west afr coll surg. 2018 jan-
mar;8(1):40-49.
14. Lukas M. Trunz,Rashmi Balasubramanya et al,Doppler Renal Assessment, Protocols, and Interpretation: National Library of
Medicine ,2023.
15. Tokunori Yamamoto, Yasuo Ogasawara et al,Blood Velocity Profiles in the Human Renal Artery by Doppler Ultrasound and Their
Relationship to Atherosclerosis, Arteriosclerosis, Thrombosis, and Vascular Biology,1996;Vol 16, No 1.
16. Alžbeta Bohiniková et al ,Modeling Red Blood Cell Viscosity Contrast Using Inner Soft Particle Suspension; Micromachines 2021, 12,
974.
17. B.Pandey et al,Non Newtonian Model for Two Phase Blood Flow in Hepatic Arterioles in Case of Dengue using Herschel –Bulkley Law,
SAMRIDDHI,2022; Volume 14, Issue 4 .
18. B.Pandey et al,Mathematical Modelling on Two Phase Blood Flow in Human Hepatic artery for Dengue Disease Using Power Law Model;
neuroquantology | november 2022 | volume 20 | issue 11 | page 7881-7887.
19. B.Pandey,Extention of two phase power law model in three phase blood flow in human renal artery in case of dengue,International Journal
of Physics and Mathematics 2025; 7(2): 141-154
20. Haynes, R.H and Burton,A.C. et al,Role of non Newtonian Behaviour of blood in Hemodynamics;Am.J.Physiol.,1959;Vol.197,p.943.
21. Shrivastava ,V.P. and Saxena.M,A et al,Two –Fluid Model of Non Newtonian blood flow Induced by Peristaltic Waves;Rheol.Act
a,1995;Vol.34,No.4pp.406-414.
22. Haynes ,R.H et al,Physical Basis of the Dependence of Blood Viscosity on Tube Radius;Am.J.Physiol.1960;Vol.198,pp.1193-1200.
23. Bugliarello,G. and Sevilla, J et al, Velocity Distribution and other Characteristics of steady and Pulsatile Blood Flow in Fine Glass Tubes
;Biorheology , Vol.7,pp.85-107,1970.
24. B.Pandey,Initial step for developing software for two phase blood flow power law model in human renal artery for dengue disease with
help of python coding,International Journal of Statistics and Applied Mathematics 10(8):160-170,2025.
25. B.Pandey,Two phase modelling for hepatic capillary blood flow in dengue disease by power law model,Journal of Mathematical Problems
Equations and Statistics 6(2):484-493,2025.
26. Figure,https://www.nursinghero.com/study-guides/cuny-kbcc-ap2/regulation-of-renal-blood-flow.
27. World Health Organization. Dengue: Guidelines for Diagnosis, Treatment, Prevention and Control, New edition Geneva: World
Health Organization, 2009.
28. A.Bohle,Human glomerular structure under normal conditions and in isolated glomerular diseaseKidney Int Suppl 1998
Sep:67:S186-8.
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