The impact of geometry, intramural friction, and pressure on the antegrade longitudinal motion of the arterial wall: A phantom and finite element study

Figures

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  FIGURE 1. (a) Ultrasound image of the common carotid artery during a measurement of arterial wall motion of a 42‐year‐old female. The yellow lines mark the demarcations between lumen and intima and the green lines the demarcation between media and adventitia. The lines are 5 mm long. The white arrow marks the direction of the blood flow. (b) Enlargement of the far wall. The orange displacement vector curve shows the two‐dimensional wall motion during a cardiac cycle. The longitudinal motion of this vector curve is also shown in Figure 2b. The black circle marks the starting and ending positions as shown in Figure 2b, and the white circle marks the onset of the antegrade motion in early systole. The white arrows mark the direction of the motion. The white line marks 1 mm.

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  FIGURE 2. Longitudinal motion (solid) of the intima‐media complex of the far wall and the corresponding diameter change (dashed) in the common carotid artery of (a) a 31‐year‐old female, (b) a 42‐year‐old female, (c) a 53‐year‐old male, and (d) a 64‐year‐old female, after 10 min of rest. The subjects were healthy, non‐obese, non‐smoking and free from current medication. For longitudinal motion, a positive deflection denotes motion in the direction of blood flow. ECG is shown as reference (when available) at the bottom. The small circles mark the onset of an antegrade motion in early systole (also denoted by the origin of coordinates). The distinct antegrade motion is followed by a distinct retrograde motion in systole and a second distinct motion in early diastole. In the older subjects in (c) and (d), the first antegrade motion is preceded by a distinct retrograde motion. The longitudinal motion and diameter change were measured using the methods of Nilsson et al. (2013 and 2014), respectively. The curves shown are an average of curves from four to six cardiac cycles. Figures adapted from data collected from Cinthio et al. (Cinthio et al., 2018) and Ahlgren et al. (Ahlgren et al., 2023).

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  FIGURE 3. Schematic, cross‐sectional view along the centre axis of the four phantoms produced. L = 130 mm, h = 70 mm, t = 2 mm, D = 16 mm, d = 6 mm. These dimensions were from the unloaded phantoms; L refers to the length of the surrounding block; the inner part was 10 mm longer to make assembly possible. The figure is not to scale. (a) A phantom containing a tapered region with an inclination angle of 30°, (b) with a taper angle of 60°, (c) a straight phantom, and (d) a continuously tapered phantom with a taper angle of 2°. The flow was as indicated from left to right in the figures, and the distance from inlet to the beginning of the tapered region in (a) and (b) was 70 mm. In the enlarged section of sub section (b), pressure is indicated as vectors perpendicular to the surface. Upon assembly, the inner part inflated and filled the one‐millimeter gap shown between the parts in the figure. The measurement positions in the experiment are marked by white rectangles.

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  FIGURE 4. Photograph of the working phantom submerged in water. The direction of flow is from left to right in the image. The acoustic dampening material (black) can be seen beneath the phantom and above it the transducer and clamp.

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  FIGURE 5. Diagram of the experimental setup. The phantom was placed on a sound‐absorbing material and connected to the pump and reservoir via elastic tubes. The pump and pressure sensor were computer‐controlled. The ultrasound equipment stored cine loops of B‐mode images, and post processing to extract motion data was performed offline.

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  FIGURE 6. Finite element meshes of (a) the 30°, (b) 60°, (c) straight (d) continuously 2°narrowing models. The inner part consists of approximately 20,000 elements, the surrounding cylinder contains approximately 30,000, making a total of 50,000 elements for the complete model. The inner part was comprised of three layers of elements. Displacements were extracted from the nodes indicated by thicker black lines and arrows.

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  FIGURE 7. Results from phantom measurements of longitudinal wall displacements in relation to pulse pressure for the phantom with (a) 30° tapered region, (b) 60° tapered region, (c) straight lumen, and (d) continuously 2° narrowing lumen. Results extracted from the proximal position is marked with +, in‐between with •, and the distal position with o; see Figure 3 for measurement locations. Correlation coefficients R and p values, as well as the slope k (um/mmHg) are given. In the 2° continuously tapered phantom (d), the size of the distinct ultrasound echoes altered, especially in the proximal location, indicating out‐of‐plane motion and, thus, suboptimal measurements conditions.

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  FIGURE 8. Contour plots of longitudinal displacement in 60° digital simulation model at 24 mmHg. (a) Represents the frictionless case and in (b) the coefficient of friction was 0.06. The scale is indicated to the right.

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  FIGURE 9. Longitudinal displacement as a function of distance from the inlet of the 60° digital simulation model with different coefficients of friction at the interface between the two parts. The arrows indicate the position of two local extrema proximal to the tapered region and the vertical lines show the tapered region.

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  FIGURE 10. Longitudinal displacements of the digital simulation models with a (a) 30° tapered region, (b) 60° tapered region, (c) straight lumen, and (d) 2° continuously tapered lumen as a function of distance from inlet. The vertical lines show the beginning and end of the tapered regions. Each model was subjected to three different pressures, indicated in the legend in subfigure (b).