Developing a computational model of blood platelets with fluid dynamics applications

TL;DR

This paper develops a computational model of blood platelets incorporating fluid dynamics, providing analytical expressions for their structure and a method to compute drag coefficients, with applications in biophysics and scientific modeling.

Contribution

The paper introduces a novel analytical and computational framework for modeling blood platelet structures and their fluid dynamic properties, including a C++ program for drag coefficient calculation.

Findings

Analytical models for platelet structure in various states

Explicit equations approximating platelet shape in 3D

A method to compute drag coefficients from images

Abstract

This paper worked towards modeling blood platelets. Blood platelets, also known as thrombocytes, play a key role in blood clotting which is a vital human function. Furthermore, the role of these entities in strokes, myocardial infarctions, and coronary artery disease add to the importance of blood platelets. Analytical expressions for the structure of blood platelets in both their inactivated and activated states were developed, beginning with randomized two-dimensional models in polar coordinates. Weak frameworks in spherical and cylindrical systems were then created. Next, using rotational matrices to change the position and direction of a simple projection, useful, explicit, parametric system of equations were attained in three-dimensional Cartesian space which roughly approximate the structure of a blood platelet. Finally, a methodology to return the drag coefficient ($c_d$) for any inputted set of blood platelet images was designed. This method was incorporated into a C++ program returning the functional representation and drag coefficient of any given platelet. This work has primary applications in computational biophysics and fluid dynamics. Additionally, if the parameters of the model are extended, there could be ramifications in other areas of scientific modelling by connecting analytical expressions with instrinsic characteristics.