Dynamics of blood cells during a routine laboratory examination

Abstract

Centrifugation is a commonly performed laboratory procedure that helps to separate blood cells such as red blood cells \(RBCs\), white bood cells \(WBCs\), and platelets from plasma or serum. Although centrifugation is a routine procedure in most medical laboratories, factors that affect the efficacy of the centrifugation process have never been studied analytically. In this paper, we examine the effect of centrifugation time on the efficacy of the centrifugation process by studying the dynamics of blood cells via the well-known Langevin equation or equivalently, by solving the Fokker-Plank equation. Our result depicts that the speed of the centrifuge is one of the determinant factors concerning the efficacy of the centrifugation process. As angular speed increases, centrifugal force increases and as a result, the particles are forced to separate from plasma or serum. The room temperature also considerably affects the dynamics of the sample during centrifugation. Most importantly, the generation of heat during centrifugation increases the temperature within a centrifuge, and as a result, not only the stability of the sample but also the mobility of analyse is affected. We show that as the temperature within the centrifuge intensifies, the velocity of the cells as well as the displacement of the cells in the fluid increases. We then study the dynamics of the whole blood during capillary action where in this case the blood flows upward in a narrow space without the assistance of external forces. Previous investigations show that the height that the fluid rises increases as surface tension steps up. The viscosity of the fluid also affects the capillary action but to date, the dependence of the height on viscosity has never been explored due to the lack of a mathematical correlation between the viscosity of blood and surface tension [1]. In this work, we first examine the correlation between surface tension and viscous friction via data fitting. Our result exhibits that the viscosity of the blood increases linearly as surface tension increases. The mathematical relation between the height and viscous friction is derived. It is shown that the height of the blood that rises in the capillary increases as the viscous friction intensifies. As the temperature of the room steps up, the height also decreases. The dependence of erythrocytes sedimentation rate on surface tension is also studied. The results obtained in this work show that the erythrocyte sedimentation rate ESR increases as surface tension steps down.