Using wave intensity analysis to determine local reflection coefficient in flexible tubes

It has been shown that reflected waves affect the shape and magnitude of the arterial pressure waveform, and that reflected waves have physiological and clinical prognostic values. In general the reflection coefficient is defined as the ratio of the energy of the reflected to the incident wave. Since pressure has the units of energy per unit volume, arterial reflection coefficient are traditionally defined as the ratio of reflected to the incident pressure. We demonstrate that this approach maybe prone to inaccuracies when applied locally. One of the main objectives of this work is to examine the possibility of using wave intensity, which has units of energy flux per unit area, to determine the reflection coefficient. We used an in vitro experimental setting with a single inlet tube joined to a second tube with different properties to form a single reflection site. The second tube was long enough to ensure that reflections from its outlet did not obscure the interactions of the initial wave. We generated an approximately half sinusoidal wave at the inlet of the tube and took measurements of pressure and flow along the tube. We calculated the reflection coefficient using wave intensity (RdI and RdI0.5) and wave energy (RI and RI0.5) as well as the measured pressure (RdP) and compared these results with the reflection coefficient calculated theoretically based on the mechanical properties of the tubes. The experimental results show that the reflection coefficients determined by all the techniques we studied increased or decreased with distance from the reflection site, depending on the type of reflection. In our experiments, RdP, RdI0.5 and RI0.5 are the most reliable parameters to measure the mean reflection coefficient, whilst RdI and RI provide the best measure of the local reflection coefficient, closest to the reflection site. Additional work with bifurcations, tapered tubes and in vivo experiments are needed to further understand, validate the method and assess its potential clinical use.