Biomechanics and Modeling in Mechanobiology

, Volume 15, Issue 3, pp 713–722

A reduced-dimensional model for near-wall transport in cardiovascular flows

Original Paper

DOI: 10.1007/s10237-015-0719-4

Cite this article as:
Hansen, K.B. & Shadden, S.C. Biomech Model Mechanobiol (2016) 15: 713. doi:10.1007/s10237-015-0719-4

Abstract

Near-wall mass transport plays an important role in many cardiovascular processes, including the initiation of atherosclerosis, endothelial cell vasoregulation, and thrombogenesis. These problems are characterized by large Péclet and Schmidt numbers as well as a wide range of spatial and temporal scales, all of which impose computational difficulties. In this work, we develop an analytical relationship between the flow field and near-wall mass transport for high-Schmidt-number flows. This allows for the development of a wall-shear-stress-driven transport equation that lies on a codimension-one vessel-wall surface, significantly reducing computational cost in solving the transport problem. Separate versions of this equation are developed for the reaction-rate-limited and transport-limited cases, and numerical results in an idealized abdominal aortic aneurysm are compared to those obtained by solving the full transport equations over the entire domain. The reaction-rate-limited model matches the expected results well. The transport-limited model is accurate in the developed flow regions, but overpredicts wall flux at entry regions and reattachment points in the flow.

Keywords

Mass transport Boundary layer High Schmidt number  Thrombosis Atherosclerosis Wall shear stress Multiscale modeling Advection–diffusion 

Funding information

Funder NameGrant NumberFunding Note
National Heart, Lung, and Blood Institute
  • HL108272
National Science Foundation
  • 1354541

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of CaliforniaBerkeleyUSA

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