Wave intensity amplification and attenuation in non-linear flow: Implications for the calculation of local reflection coefficients

Local reflection coefficients (R) provide important insights into the influence of wave reflection on vascular haemodynamics. Using the relatively new time-domain method of wave intensity analysis, R has been calculated as the ratio of the peak intensities (RPI) or areas (RCI) of incident and reflected waves, or as the ratio of the changes in pressure caused by these waves (RΔP). While these methods have not yet been compared, it is likely that elastic non-linearities present in large arteries will lead to changes in the size of waves as they propagate and thus errors in the calculation of RPI and RCI. To test this proposition, RPI, RCI and RΔP were calculated in a non-linear computer model of a single vessel with various degrees of elastic non-linearity, determined by wave speed and pulse amplitude (ΔP+), and a terminal admittance to produce reflections. Results obtained from this model demonstrated that under linear flow conditions (i.e. as ΔP+→0), RΔP is equivalent to the square-root of RPI and RCI (denoted by RPIp and RCIp). However for non-linear flow, pressure-increasing (compression) waves undergo amplification while pressure-reducing (expansion) waves undergo attenuation as they propagate. Consequently, significant errors related to the degree of elastic non-linearity arise in RPI and RCI, and also RPIp and RCIp, with greater errors associated with larger reflections. Conversely, RΔP is unaffected by the degree of non-linearity and is thus more accurate than RPI and RCI.