Statistical Hemodynamics and In Vivo Genomics

In vivo experimentation is the most realistic approach for exploring the vascular biological response to the hemodynamic stresses that are present in life. We wish to carry out molecular measurements on freshly harvested tissue whose in vivo hemodynamic environment is known. The best way to estimate the distribution of hemodynamic variables in a vascular segment of interest is to recover the geometry of the segment via in situ casting or imaging, and to use this geometry as input to a computational fluid dynamic (CFD) simulation. However, vascular casting, which provides the greater geometric resolution, destroys the critically important endothelium of the tissue. Imaging allows subject-specific hemodynamics to be determined, without damaging the endothelium, but the flow simulations would ordinarily be carried out after tissue harvest, introducing delays that would compromise tissue viability and the reliability of subsequent assays.

Two statistical approaches, regional (RSH) and linear (LSH) statistical hemodynamics, have been developed in our laboratory and are currently being used to characterize the shear distribution in defined arterial regions. In these techniques, the in vivo shear field is calculated at the outset in several realistic instances of the region of interest based on vascular casts. These calculations are used to define the shear stress distribution in the region in a statistical fashion. Subsequent in vivo experiments can be conducted without necessitating additional flow simulation.

An application of the regional (RSH) approach is summarized below.

The time-varying shear stress was calculated in six porcine iliac arteries whose geometry was based on casts obtained from three swine. The mathematical representation of each artery was cut along its dorsal aspect and opened, and the shear distribution at the endothelial surface was presented as an en face 2-D shear map

For each shear map, pixels were divided into low, medium, and high shear bins

Low, medium, and high shear likelihood maps were constructed based on data from all six arteries (see figure, left). Each pixel is color coded according to the number of arteries in which that pixel fell into the low, medium or high shear bins

Based on these maps, three regions (boxed areas in figure) were selected that were most likely to have been exposed to high, medium or low shear stresses.

The shear stress probability distribution in each of the chosen regions was constructed (see figure, right) to demonstrate the most likely distribution of shear levels in each region.

Subsequently, RNA was extracted from the endothelium of the RSH-defined regions of eight uncasted iliac arteries

The mRNA expression of genes in these regions was compared using microarray assays and quantitative real time PCR.

Endothelial cells from the high shear stress region exhibit downregulation of some inflammatory genes and upregulation of others, and upregulation of some structural genes, relative to cells from the medium shear region

Many of the responses of cells from the low shear region are similar to those from the high shear region

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