Mathematical modeling of thrombus growth in microvessels

A. G. Alenitsyn
Abdus Salam School of Mathematical Sciences GC University, Lahore, Pakistan.
A. S. Kondratyev
Herzen Pedagogical University of Russia, St-Petersburg, Russia.
I. Mikhailova
Pavlov Medical University, St-Petersburg, Russia.
I. Siddique
COMSATS Institute of Information Technology, Lahore, Pakistan.

\(^{1}\)Corresponding Author: kondrat6125@mail.ru

Copyright © 2008 A. G. Alenitsyn, A. S. Kondratyev, I. Mikhailova, I. Siddique. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: December, 2008.

Abstract

Richardson’s phenomenological mathematical model of the thrombi growth in microvessels is extended to describe more realistic features of the phenomenon. Main directions of the generalization of Richardson’s model are: 1) the dependence of platelet activation time on the distance from the injured vessel wall; 2) the nonhomogeneity of the platelet distribution in blood flow in the vicinity of the vessel wall. The generalization of the model corresponds to the main experimental results concerning thrombi formation obtained in recent years. The extended model permits to achieve a numerical agreement between model and experimental data.

Keywords:

Mathematical model, microvessels, thrombi growth, platelets.