In vitro shear stress measurements using particle image velocimetry in a family of carotid artery models: effect of stenosis severity, plaque eccentricity, and ulceration

Abstract

Atherosclerotic disease, and the subsequent complications of thrombosis and plaque rupture, has been associated with local shear stress. In the diseased carotid artery, local variations in shear stress are induced by various geometrical features of the stenotic plaque. Greater stenosis severity, plaque eccentricity (symmetry) and plaque ulceration have been associated with increased risk of cerebrovascular events based on clinical trial studies. Using particle image velocimetry, the levels and patterns of shear stress (derived from both laminar and turbulent phases) were studied for a family of eight matched-geometry models incorporating independently varied plaque features - i.e. stenosis severity up to 70%, one of two forms of plaque eccentricity, and the presence of plaque ulceration). The level of laminar (ensemble-averaged) shear stress increased with increasing stenosis severity resulting in 2-16 Pa for free shear stress (FSS) and approximately double (4-36 Pa) for wall shear stress (WSS). Independent of stenosis severity, marked differences were found in the distribution and extent of shear stress between the concentric and eccentric plaque formations. The maximum WSS, found at the apex of the stenosis, decayed significantly steeper along the outer wall of an eccentric model compared to the concentric counterpart, with a 70% eccentric stenosis having 249% steeper decay coinciding with the large outer-wall recirculation zone. The presence of ulceration (in a 50% eccentric plaque) resulted in both elevated FSS and WSS levels that were sustained longer (∼20 ms) through the systolic phase compared to the non-ulcerated counterpart model, among other notable differences. Reynolds (turbulent) shear stress, elevated around the point of distal jet detachment, became prominent during the systolic deceleration phase and was widely distributed over the large recirculation zone in the eccentric stenoses.

Figure 1. Example of one of the carotid-artery bifurcation phantoms incorporating a 50% eccentric stenosis (a), and a picture of the experimental set-up depicting the flow circuit and PIV components (b).

Figure 2. Volumetric flow-rate waveforms, measured using electromagnetic flow meters, at the inlet of the CCA and outlets of the ICA and ECA.

Figure 3. Color maps of ensemble-averaged velocity magnitudes shown for peak systole in a family of eight carotid bifurcation models.

Three cross-sectional slices are shown alongside the ICA lumen, for each stenosed model, at the locations indicated by the black horizontal lines at approximately 1, 2, and 3 CCA diameters (i.e. ∼8, 16, 24 mm) downstream of the bifurcation apex. For scale, note the downstream ICA diameter is 5.5 mm. Note the range-appropriate color bar for each row of models.

Figure 4. Color maps of the laminar (ensemble-averaged) shear stress shown for peak systole in the eight models.

Three cross-sectional slices are shown alongside the ICA lumen for the locations indicated (as described in Fig. 3). Note the bottom right color bar represents the seven stenosed models, and a separate color bar is used for the normal model as indicated in the enclosed box.

Figure 5. Spatial and temporal distribution of the maximum free (i.e. non wall) shear stress in the eight models shown for a 180-ms window, incorporating peak systole (PS), as indicated on the reference flow-rate waveform at the bottom right.

For each time point, maximum FSS values were extracted across the entire ICA lumen along 25(0 mm). Note the range-appropriate color bar associated with each row of models and the 1-Pa isocontour increments used for all maps.

Figure 6. Ensemble-averaged wall shear stress shown for peak systole in the eight carotid models.

For optimal display, the ICA is shown from two different perspectives as indicated by the orientation schematic in the bottom right corner. The color bar represents all the models including the normal geometry. For improved accommodation, the dynamic range of the color bar is reduced to a maximum of 30%-stenosed models.

Figure 7. Spatial and temporal distribution of the wall shear stress along (a) the inner wall and (b) the outer wall in the eight carotid models.

For each time point, wall-bounded values were extracted along the 25-mm analyzed length starting at the bifurcation apex. The analyzed 180-ms window (with peak systole denoted as PS) is highlighted on the reference flow waveform. Note the range-appropriate color bar associated with each row of models and the 4-Pa contour increments used for all maps.

Figure 8. Spatial distribution of inner WSS (upper row) and outer WSS (lower row) associated with an interval during peak systole.

Values are mean and standard deviation (whiskers) over five WSS values covering five time points straddling (±20 ms) peak systole.

Figure 9. In-plane RSS component () as a function of time for the three 50%-stenosed models.

Maps are shown at three time points: 20 ms before peak systole (top row), 20 ms after peak systole (middle), and 20 ms before the dicrotic notch (bottom), as indicated by the respective flow-rate waveforms on the right. Three cross-sectional slices are shown alongside the ICA lumen at the locations indicated by the black lines at approximately 2, 2.5, and 3 CCA diameters downstream (i.e. ∼16, 20, 24 mm). Note the separate color bar used for the bottom row with the same zero-value color as for the upper rows.

Figure 10. Color-encoded maps of orientation-dependent swirling strength (λ_ci) shown for the ICA central plane in each of the set of three 50%-stenosed models at time points identical to those applied to Fig. 9.

Swirling strength maps were obtained from x and y components of the ensemble-averaged (left panel in each column pair) and instantaneous (right panel in each column pair) velocity maps. Note the different limits of the color bar used for the bottom row. Positive (e.g. yellow to red) and negative values (e.g. green to violet) represent counter clock-wise and clock-wise swirling rotation, respectively.

Figure 11. Color-encoded maps of total shear stress for the time point of maximum TSS in each of the eight carotid models.

For each model, a map demonstrating maximum TSS is shown, where the time point corresponding to the maximum value varied only slightly (20±10 ms beyond peak systole) for the eight models. Note the bottom right color bar (set to the maximum of 150 Pa) represents the seven stenosed models; the time and color bar associated with the normal model are shown in the enclosed box.

Figure 12. Histogram of normalized distribution of TSS (≥2 Pa) for the ICA branch (0–35 mm distal to bifurcation apex) and over the systolic phase (same 180 ms window depicted in Fig. 5).

Plots represent the number of voxels accumulated over time and space for each TSS value (1-Pa bins) normalized by the total number of non-zero voxels accumulated for the same time frame in each model. Central plane (left column) includes ∼2000–2500 voxels and volumetric data (right column) includes ∼21000–32000 non-zero voxels, depending on geometry. Note, horizontal axes are presented in log-2 form, all values exceeding 200 Pa fall within the 200-Pa bin, and the normal model uses a different range for the vertical axis.