Math. Model. Nat. Phenom.
Volume 13, Number 5, 2018
Mathematical Modelling of Physiological Flows
|Number of page(s)||16|
|Published online||06 September 2018|
Mathematical study of a single leukocyte in microchannel flow
Hassan II University of Casablanca,
FSAC. B.P 5366,
2 Instituto Superior Técnico, Univ. Lisboa, Department of Mathematics and CEMAT, Lisbon, Portugal.
* Corresponding author: firstname.lastname@example.org
Accepted: 30 May 2018
The recruitment of leukocytes and subsequent rolling, activation, adhesion and transmigration are essential stages of an inflammatory response. Chronic inflammation may entail atherosclerosis, one of the most devastating cardiovascular diseases. Understanding this mechanism is of crucial importance in immunology and in the development of anti-inflammatory drugs. Micropipette aspiration experiments show that leukocytes behave as viscoelastic drops during suction. The flow of non-Newtonian viscoelastic fluids can be described by differential, integral and rate-type constitutive equations. In this study, the rate-type Oldroyd-B model is used to capture the viscoelasticity of the leukocyte which is considered as a drop. Our main goal is to analyze a mathematical model describing the deformation and flow of an individual leukocyte in a microchannel flow. In this model we consider a coupled problem between a simplified Oldroyd-B system and a transport equation which describes the density considered as non constant in the Navier–Stokes equations. First we present the mathematical model and we prove the existence of solution, then we describe its numerical approximation using the level set method. Through the numerical simulations we analyze the hemodynamic effects of three inlet velocity values. We note that the hydrodynamic forces pushing the cell become higher with increasing inlet velocities.
Mathematics Subject Classification: 35Q53 / 34B20 / 35G31
Key words: Individual leukocyte / inflammation / adhesion / deformation / microchannel flow / Oldroyd–B model / level set method.
© EDP Sciences, 2018
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