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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

Abstract

Localized cellular transport and micro-vessel friction are difficult to map using conventional single-phase and two-phase blood flow models, particularly in pathological situations like dengue virus infection. In order to study cellular interactions and pressure decreases, this research proposes a comprehensive three-phase computational framework to model hemodynamics in micro-vessels, especially renal capillaries. Three interacting layers make up the model of whole blood: a pure Newtonian plasma wall layer (a≤r≤R), a Newtonian leukocyte/platelet intermediate phase (a≤r≤b), and a central non-Newtonian power-law Red Blood Cell (RBC) core (0≤r≤a). Under steady-state, axisymmetric laminar flow assumptions, cylindrical coordinates are used to translate and solve the governing equations of continuity and motion. Due to the no-slip situation, the velocity shows a blunt shape in the central core, a steeper decrease in the WBC-rich layer, and a quick drop to zero at the capillary wall. The highest Wall Shear Stress 𝜏𝑤=107.94 Pascal is driven by a strain rate that is almost negligible at the centerline and rises dramatically in the plasma layer close to the wall.An increase in hematocrit H raises the effective viscosity, causing a proportional decrease in axial velocity at all radial locations. An 8-day patient timeline shows that Hematocrit H, Mean Blood Pressure Drop (MBPD), and Capillary Drop (RCBPD) move in perfect synchronization, all peaking on Day 5 (H=43.59%), (MBPD = 2923.91 Pascal), (RCBPD= 2392.53 Pascal).

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