Measurement, Analysis and Interpretation of Pressure/Flow Waves in Blood Vessels

Figures

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  FIGURE 1. (Left) Illustration of a forward-propagating wave that increases pressure and flow. (Right) A forward-propagating wave encounters an impedance mismatch (increased vessel stiffness indicated by thicker wall) and is partially transmitted and partially reflected. The reflected wave propagates backward and causes a further increase in pressure but a decreased flow. Red arrows indicate blood flow or average blood velocity over a cross-section (larger arrow means higher flow/velocity), while black arrows indicate wave speed and direction of wave propagation. Increased pressure is indicated by increased vessel diameter. Time plots (bottom) indicate the evolution of pressure and flow at three locations along the vessel indicated with color-coded circles.

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  FIGURE 2. Imaging methods for obtaining cross-sectional area or diameter waveforms and flow or mean velocity waveforms. See text for explanation. Note that echo-tracking is similar to standard M-mode but uses raw radio-frequency signals. For Doppler ultrasound, Vmax and Vmean are the maximum and mean velocities in the sample volume, respectively.

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  FIGURE 3. Calculation of Augmentation Index (AIx) with examples of (A) positive augmentation and (B) negative augmentation. AP, augmentation pressure; P1, initial pressure rise; PP, pulse pressure; Ti, inflection time.

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  FIGURE 4. Wave separation analysis for pressure (P) and flow (Q) signals. Forward components (P+ and Q+) and backward components (P– and Q–) are calculated using the equations in Table 1, with an assumed undisturbed pressure (Pud) of 10 mmHg. Arrows indicate wave potential at that time.

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  FIGURE 5. (A) With the pressure-velocity (PU) loop method, wave speed (c) is calculated from the slope of the early-systolic PU relation (red line), where ρ is blood density. (B) Misalignment of pressure and velocity signals introduces curvature in the early systolic relation. This example shows the effect of velocity leading or lagging pressure by 10 ms (solid and dashed gray lines, respectively).

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  FIGURE 6. Wave intensity analysis in the carotid artery, based on pressure (P, derived from measured diameter), mean velocity (U), forward and backward components of pressure (P+ and P–), net wave intensity (dI) and forward and backward wave intensity components (dI+ and dI–). There are four possible wave types, forward compression waves (FCW), forward decompression wave (FDW), backward compression wave (BCW), and backward decompression wave (BDW). Wave size is quantified via peak or cumulative intensity. Whether a wave is a compression or decompression wave can be judged by its effect on the respective pressure components (green and red arrows in the middle panel; note that waves shown in the zoomed inset in the bottom panel are not labeled in the middle panel). The asterisk (*) indicates a time where a BCW and FDW arrive at the measurement site around the same time and therefore wave separation is essential for revealing the presence/magnitude of these waves.

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  FIGURE 7. Mechanisms that produce pressure/flow waves in blood vessels. See text for detailed explanation. Red arrows indicate blood flow or velocity (larger arrow means higher flow/velocity). Solid black arrows indicate compression (pressure-increasing) waves, while outlined black arrows indicate decompression (pressure-decreasing) waves. Panels (A,B) illustrate wave generation via active pump contraction and relaxation respectively. In panel (C), a barrier is placed in a vessel that contains flowing blood. In panel (D), a barrier is removed between two vessels containing blood at different pressures. In panel (E), increases or decreases in characteristic impedance (Zc; or combined Zc in the case of the bifurcation) are plotted versus horizontal position. Viscous resistance per unit length (R/L, given by Poiseuille’s law, where μ is blood viscosity and A is cross-sectional area) is small in large vessels but becomes dominant in small vessels.

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  FIGURE 8. Mechanisms that affect wave intensity magnitude as a wave propagates (A–C) or when two waves propagating in the same direction, but generated from separate mechanisms, combine constructively or destructively (D). Waves shown in (B,C) could be any wave type (FCW, FDW, BCW, or BDW). In the examples of wave superposition shown in (D), the shaded and unshaded waves indicate an FDW and FCW, respectively.

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  FIGURE 9. Decomposition of pressure (P) into a reservoir pressure (Pres) and an excess pressure (Pex).