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A study on mathematical modeling on human blood in reference to the variation of hematocrit

Mathematical model to compute the velocity, flux and resistance of flow of blood in relation to iron deficiency anemia (IDA) has been studied in this paper. Viscosity of the blood for iron deficiency is computed and compared with that of physiological value i.e. 100 ml of blood containing 15 gm of hemoglobin contain 50 mg of iron. Percentage of iron is calculated by processing the green leaves collected from the different locations. Ten individuals aged from 5-20 years have been adapted for hemoglobin monitoring. Total protein minus albumin (TPMA 40-30g/l) a chemical variable composed of fibrinogen and globulin for estimating the iron percentage is used in the mathematical model. Analytically computed values of iron percentage gave the insight to record the decrease of viscosity by 0.001poise. Corresponding decrease of hematocrit 42.7% to 34.0% is observed and the decrease of hematocrit is not negotiable with heme biosynthesis. This change of hematocrit lowers the binding between hemoglobin and enzymes ultimately causes the unstable hemoglobin and further causes the lowering of normal proteins in the blood. Although the body has a number of compensatory mechanisms, which delay the on set of iron deficiency but when the iron deficient state is prolonged so that the iron stores become depleted. As a result hemoglobin synthesis is impaired and the prevalence of iron deficiency anemia develops. This causes the smaller erythrocytes (microcytes) than normal in the blood. Then the hematocrit (volume of packed cells) is lower and each red cell has decreased hemoglobin content. Results show the biological variability among human activities. The fluid (blood) with iron deficiency is considered as non-Newtonian. Walburn - Schneck (W-S model) equation is used as initial parameter to the power exponent of the power law equation. Taylor’s series method is employed to compute the velocity, flux, and resistance of flow. Numerical results show good agreement with that of experimental values Fredrick J et. al. [1976], C M Rodkiewch et. al. [1990] and X Y. Luo et al. [1992].