# The physics of Erythrocyte Sedimentation Rate

## TL;DR

This paper models erythrocyte sedimentation rate (ESR) using physics principles, showing how factors like cell aggregation and temperature influence sedimentation, aligning with experimental data and enhancing understanding of hematological tests.

## Contribution

It introduces a physics-based model of RBC sedimentation considering cell dynamics and temperature effects, providing insights into ESR behavior in clinical settings.

## Key findings

- ESR increases with the number of RBC rouleaux formations.
- Higher room temperature accelerates sedimentation rate.
- Model predictions align with experimental observations.

## Abstract

An erythrocytes sedimentation rate (ESR) measures how fast a blood sample sediments along a test tube in one hour in a clinical laboratory. Since elevated level of ESR is associated with inflammatory diseases, ESR is one of the routine hematology test in a clinical laboratory. In this paper, the physics of erythrocyte (RBC) sedimentation rate as well as the dynamics of the RBC is explored by modeling the dynamics of the cells as the motion of Brownian particle moving in a viscous medium. The viscous friction of blood $\gamma$ is considered to decrease as the temperature of the medium increases \cite{aa1}. The results obtained in this work show that the ESR increases as the number of red blood cells (that bind together in the sedimentation process) steps up. The room temperature also affects the sedimentation rate. As the room temperature rises up, the ESR steps up. Furthermore the dynamics of the RBC along a Westergren pipet that is held in an upright position is explored. The exact analytic result depicts that the velocity of cells increases as the number of cells that form rouleaux steps up. Since our study is performed by considering real physical parameters, the results obtained in this work non only agree with the experimental observations but also helps to understand most hematological experiments that are conducted in vitro.