Biomedical Engineering Reference
In-Depth Information
risk factors. The disease results from the accumulation of lipid molecules within the
wall of the blood vessels, as well as from enhanced exposure to intramural penetra-
tion of nano-sized biological bodies [ 19 ]. The build up of the resultant soft tissue
and the eventual changes in its consistency leads to serious atherosclerotic
pathologies, including catastrophic events such as plaque rupture. Atherosclerotic
plaques appear in regions of disturbed blood flow where the local endothelial shear
stress (ESS) is low (
<
1. 0 Pa) or of alternating direction [ 9 ]. Hence, plaques tend
to form near arterial bifurcations where the flow is always altered compared to
unbranched regions [ 8 , 39 ].
Atherosclerosis primarily affects the coronary arteries, and the evidence that low
average ESS has a key role in the disease localization and progression is widely
accepted [ 8 , 23 , 43 , 9 ]. Predictions of where and how the illness is likely to develop
can be obtained by fluid-dynamics simulations as a routine methodology to study
blood flow patterns in human arteries. As a matter of fact, the shape and the structure
of endothelium play a number of important roles in the vascular system, and its
dysfunction may lead to several pathological states, including early development of
atherosclerosis [ 30 ]. The microscopic shape of the endothelium is defined by the
presence of endothelial cells (ECs henceforth), making the arterial wall undulated.
This effect becomes more pronounced in small-sized vessels, where the corrugation
degree increases. The study of blood flow over a regularly undulating wall made of
equally aligned and distributed ECs has been recently carried out in [ 34 ] where the
variation of wall shear stress over the ECs has been computed. Furthermore, the
endothelium is coated by long-chained macromolecules and proteins which form a
thin porous layer, called the glycocalyx [ 44 ]. The glycocalyx has a brushlike
structure and a thickness which varies with the vessel diameter, but its average is
100 nm for arterioles. It has several roles: it serves as a transport barrier, to prevent
ballistic red blood cell (RBC) interactions with the endothelium, and as a sensor and
transducer of mechanical forces, such as fluid shear stress, to the surface of ECs.
Actually, it has been recognized that the glycocalyx responds to the flow environ-
ment and, in particular, to the fluid stress, but the mechanism by which these proteins
sense the shearing forces and transduce mechanical into biochemical signals is still
not fully understood [ 30 ]. The glycocalyx itself is remodeled by the shearing flow
and by the compression exerted by the deformed erythrocytes in capillaries [ 38 ].
Flow-induced mechano transduction in ECs has been studied over the years with
emphasis on correlation between disturbed flow and atherosclerosis. Recently, some
mathematical modelling work has been carried out, using a porous medium to model
the endothelial surface layer (ESL henceforth) [ 1 , 42 ]. However, none of these
works includes the effect of the roughness, or wavy nature, of the wall, which should
be incorporated for a more realistic description. In the following sections we also
present a coarse-grained model that attempts to include some of the basic physical
microscale effects of the ESL attached to the EC surface and hence, examine to what
extent the wall shear stress may vary due to this layer in addition to the previously
examined EC shape and particulate transport.
Simulations of blood flows based on the Lattice Boltzmann (LB) method provide a
particularly efficient and flexible framework in handling complex arterial geometries.
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