Journal of Engineering Mathematics

, Volume 66, Issue 1–3, pp 293–310 | Cite as

Ultrasound detection of externally induced microthrombi cloud formation: a theoretical study

Article

Abstract

A mathematical model for the formation of microaggregates (microthrombi) of fibrin polymers in blood flow is considered. It is assumed that the former are induced by an external source (which may be of inflammatory or tumor nature) located in a tissue near the vessel. In either case, specific agents (e.g. cytokines) are emitted from that pathological site. Such substances permeate through the vessel wall to act as primary activators of blood coagulation. A mathematical criterion to describe the formation of an intravascular microthrombi cloud, which is interpreted as an early indicator of subsequent macroscopic thrombi formation is discussed. Such criteria are compared with available experimental detection tests for microthrombi cloud formation by means of ultrasound techniques. Moreover, a similarity-type relation is proposed that links the location of the unfolding microthrombi cloud and the place at which such primary activator reaches the vessel wall.

Keywords

Coagulation equations Numerical simulation Similarity laws Thrombi formation 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.National Research Center for HaematologyMoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyRussia
  3. 3.IMI, Departamento de Matematica Aplicada, Facultad de MatematicasUniversidad ComplutenseMadridSpain

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