Wave reflection leads to over- and underestimation of local wave speed by the PU- and QA-loop methods: theoretical basis and solution to the problem

Single-point methods such as the PU- and QA-loop methods are used to estimate local pulse wave velocity (PWVPU and PWVQA) in arteries from a combination of pressure (P), flow (Q), velocity (U) or cross-sectional area (A) waveforms. Available data indicate that the PU-loop method tends to overestimate PWV, while the QA-loop method tends to underestimate. Wave reflection has been suggested as a factor playing a role in the agreement between different methods. In this work, we first provide a theoretical basis to (i) demonstrate the interference of wave reflection with the PU-loop method for both solitary sinusoidal waves as well as physiological waveforms; (ii) develop an operator-independent method to correct for the presence of reflections. Fluid-structure interaction simulations in a tube and carotid artery model with known mechanical properties confirm the theory. For the carotid artery model, PWVPU severely overestimates PWV, while PWVQA underestimates PWV. Correction (leading to an estimate termed PWV1-5) seems to eliminate the impact of reflections. Finally, methods are applied in vivo. Compared to PWVPU and PWVQA, PWV1-5 leads to significantly better correlations of carotid PWV with PWV derived from carotid distensibility based on the Bramwell-Hill equation (with r(2) improving from about 0.25 to 0.91). We conclude that neither the PU-loop nor the QA-loop method provides reliable estimates of local PWV in settings where wave reflections are present-even when the PU-or QA-loops show a linear segment. They offer no alternative for the Bramwell-Hill based approach and their application should therefore be discouraged, especially for the carotid artery, although caution is probably warranted in general