On the mathematical modeling of monocytes transmigration

Numerical Mathematics and Advanced Applications - ENUMATH 2015, Lecture Notes in Computational Science and Engineering, 112 (2016), 107-115
https://link.springer.com/chapter/10.1007%2F978-3-319-39929-4_49

Monocytes play a significant role in the atherosclerosis development. During the inflammation process, monocytes that circulate in the blood stream are activated. Upon activation, they adhere to the endothelium and extravasate through the latter to migrate into the intima. In this work we are concerned with the transmigration stage. Micropipette aspiration experiments show that monocytes behave as polymeric drops during suction. In our study, the constitutive equations for Oldroyd-B fluids are used to capture the viscoelastic behavior of monocytes. We first establish and analyze a simplified mathematical model describing the coupled deformation-flow of an individual monocyte in a microchannel. Then we describe the numerical implementation of the mathematical model using the level set method and show the numerical results. Further extensions of this model are also discussed.