Characterization of blood velocity in arteries using a combined analytical and Doppler imaging approach

We report an experimental and analytical approach to characterize the pulsatile blood flow field based on Doppler ultrasound imaging of the carotid and brachial arteries. The diameter-averaged velocity, obtained from the instantaneous velocity histograms extracted from the Doppler waveform, was adapted to the solution of a pulsatile flow in a pipe, from which the instantaneous velocity profiles were predicted and compared to local velocity measurements in the carotid and brachial arteries of four healthy human subjects. Very good agreement as demonstrated by the regression slope of 0.97 and the near-zero intercept was observed between the spatiotemporal flow field predictions and local velocity measurements at specific distances from the vessel wall. Near-real-time in vivo measurements statistically demonstrate that the analytical and experimental approach presented herein precisely captures the pulsatile blood flow behavior in large blood vessels.

Figure 1

(a) A cross-sectional view of the artery. (b) A longitudinal view of the carotid artery with the measurement window spanning the entire diameter (5.8 mm). The sample line can be seen halfway across from either side of the measurement window. (c) Waveform of the velocity resulting from the measurement shown in (b). $x$-axis: the interval between two consecutive bold markers represents 1 s. $y$-axis: velocity (cm/s).

Figure 2

(a) A longitudinal view of the carotid artery (diameter: 5.8 mm) with the measurement window narrowed down (1 mm) around the location of interest. (b) Using pixel coordinates to compute the radial locations of the measurement window's center. The figure is obtained by reading the ultrasound image in matlab. (c) Waveform of the velocity resulting from the measurement shown in (a).

Figure 3

Comparison of the analytical solution for different values of viscosity, with experimental data for the time-dependent velocity in the brachial artery at $r/R=0.047$, where $R=1.4\mathrm{mm}$.

Figure 4

Comparison of the analytical solution with experimental data at the peak systole of the cardiac cycle for three radial locations in the brachial artery: $r/R=0.047$, 0.64, and 0.69, where $R=1.4\mathrm{mm}$.

Figure 5

A scatter plot showing a statistical version of the comparison in Fig. 3 with an added regression line: $\mathrm{slope}=0.98$, $\mathrm{intercept}=1.68\mathrm{cm}/\mathrm{s}$ ($4.2\%$ of the maximum measured velocity), $R\text{−}\mathrm{squared}=0.96$.

Figure 6

Predicted local velocity vs the one measured experimentally, in the brachial artery at $r/R=0.64$ where $R=1.4\mathrm{mm}$. (a) Using the DA velocity, $\mathrm{rms}\mathrm{error}=9.87\%$; (b) using VC, $\mathrm{rms}\mathrm{error}=17.4\%$; (c) wall shear rate, where the systolic difference between the two methods is $49.8\%$.

Figure 7

The WSS in the brachial artery referred to in Fig. 3, throughout a cardiac cycle, for two limiting values of the normal range of human blood viscosity.

Figure 8

A scatter plot showing a more comprehensive version of the comparison in Fig. 5 with an added regression line: $\mathrm{slope}=0.97$, $\mathrm{intercept}=1.71\mathrm{cm}/\mathrm{s}$ ($1.89\%$ of maximum measured velocity), $R\text{−}\mathrm{squared}=0.79$.

Figure 9

Comparison of the analytical solution with experimental data at the peak systole of the cardiac cycle for six radial locations in the carotid artery: $r/R=0.06$, 0.22, 0.23, 0.4, 0.51, and 0.75, where $R=2.9\mathrm{mm}$.

Figure 10

Comparison of the analytical solution with experimental data for the time-dependent velocity in the carotid artery at $r/R=0.4$, where $R=2.9\mathrm{mm}$.

Figure 11

A scatter plot showing a statistical version of the comparison in Fig. 10 with an added regression line: $\mathrm{slope}=0.95$, $\mathrm{intercept}=-1.69\mathrm{cm}/\mathrm{s}$ ($2.01\%$ of the maximum measured velocity), $R\text{−}\mathrm{squared}=0.92$.

Figure 12

The WSS in the carotid artery referred to in Fig. 10, throughout a cardiac cycle, for two limiting values of the normal range of human blood viscosity.

Figure 13

Standard deviation from the average measured systolic velocities as a function of dimensionless radial position.