Asian Journal of Pure and Applied Mathematics

Sickle cell disease (SCD) is a hereditary haematological disorder characterised by the synthesis of an abnormal form of haemoglobin, haemoglobin S (HbS). This study derives and analyzes a mathematical modeling of voltage generation, cell displacement, and acceleration using the piezoelectric properties of sickle cells. Blood is an electrically active biological fluid whose mechanical and electrical properties depend strongly on the behavior of its cellular components. In sickle cell disease (SCD), red blood cells undergo structural deformation and reduced deformability, which significantly alter blood flow dynamics, ion transport, and electrical characteristics. Understanding these effects is essential for the development of low-cost and non-invasive diagnostic approaches, especially in regions with limited access to advanced medical facilities. The main objective of this study is to formulate and examine a mathematical model describing the coupled mechanical and electrical responses of packed sickle red blood cells under physiological flow conditions. The model incorporates piezoelectric constitutive relations, mechanical stress, and electrical charge generation arising from cell motion and deformation. The governing equations were derived using Newton’s laws of motion and Kirchhoff’s voltage law, transformed into a state-space form, and solved analytically. Numerical simulations were performed using Wolfram Mathematica version 12 to evaluate the effects of stiffness, noninvasive constant, applied force, and number of sensors. The results showed that cell displacement and acceleration increase with Reynolds number and applied force but decrease with increasing stiffness. Voltage generation rises with increasing turbulence, stiffness, and external force, confirming strong electromechanical coupling. These findings highlight the potential of voltage-based bioelectrical techniques for noninvasive diagnosis and monitoring of sickle cell disease.