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Aim
We are using computational fluid dynamics (CFD) to characterize the flow fields in coronary and systemic arteries, with the goal of relating fluid dynamic stresses at the vessel wall to various biological and morphological parameters of the tissue. A particularly challenging aspect of this research is our need to obtain highly realistic flow field simulations using geometries derived from real vessels.
Past Work
One region which we have studied in the past is the porcine aortic trifurcation, where the aorta divides into the left external, right external and common internal iliac branches. The computational region was created from a point cloud obtained by laser scanning post-mortem vascular casts of the region of interest. The point cloud data were read into a proprietary mesh generator, and a hexahedral finite element volume mesh was constructed. The flow wave at the inlet to the region was based on ultrasonic flowmeter measurements made earlier on the living animal. The porosities of porous plugs placed at the vessel termini were adjusted to obtain the desired partition of flows among the branches. Pulsatile flow calculations were performed using the finite-element code FIDAP (Fluent Inc., Lebanon, NH). The wall shear stress distributions were then extracted from FIDAP and related indices were calculated. These data were separated into left and right iliac regions, unrolled, and converted into gray levels. The following pictures show an example of an unrolled color-coded image of time-averaged shear stress and a gray level image of oscillatory shear index (OSI). These data could then be compared on a point-by-point basis with the local albumin permeability of the same tissue.
Present Work
We are currently exploring the relationship between the fluid dynamic environment of the porcine right coronary artery and the permeability, cell morphology, and protein expression patterns of the corresponding tissue. In a modification of the previous protocol, we obtain 3-D ACIS body information from a laser scan of the arterial cast. The scanned volume is meshed with tetrahedral elements using GAMBIT software (Fluent Inc., Lebanon, NH). The inlet flow wave is based on flow measurements by Hendry and colleagues (1996), corrected for the weight and measured heart rate of each animal. Initial pulsatile flow simulations performed using the finite-element code FIDAP (Fluent Inc., Lebanon, NH) enable wall shear stress distributions to be calculated as shown below.
Time-averaged wall shear stress (Pa) calculated for the xy- and
yz-planes of a porcine right coronary artery.
To directly compare wall shear stress and the corresponding tissue measures, the CFD results are unwrapped and registered using custom written software. This allows the wall shear stress calculated in the 3-D geometry to be compared to the 2-D distribution of the properties of the cut and mounted tissue. As shown below, wall shear stress can be compared to the local albumin permeability of the same tissue.
The fluid dynamic environment calculated from actual vessel geometry can be directly compared with corresponding tissue patterns of properties such as macromolecular permeability.
A) Calculated time-averaged wall shear stress distribution (Pa) displayed as a function of axial and circumferential location. B) Measured distribution of Evans blue dye optical density (OD) in the corresponding tissue region; OD is directly proportional to local macromolecular permeability.
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