Bifurcation reflection of an arterial pressure wave ($r=(Y_1-Y_d)/(Y_1+Y_d)$)

At a lossless vascular junction, pressure continuity and volumetric flow rate balance give $1+r=t$ and $Y_1(1-r)=Y_{d}t$, where $Y_d$ is the sum of daughter characteristic admittances of an arterial wave. Eliminating transmission amplitude $t$ gives the displayed reflection coefficient. A decrease in total area yields positive reflection if parent and daughter wave speeds are equal; differing stiffnesses require comparison of the admittances rather than areas alone.

For incident and reflected harmonic arterial pressure waves with real $0<r<1$, the local pressure and flow phasors are proportional to $1+r{e}^{-i\vartheta }$ and $1-r{e}^{-i\vartheta }$. Their maximum-time difference is the displayed phase lag, on the branch $0<\vartheta <\pi$. Here $\vartheta =2\omega d/c$ is the round-trip phase to the reflector. Its derivative has the sign of $\cos \vartheta$. Raising the wave speed reduces the lag when $0<\vartheta <\pi /2$, but increases it when $\pi /2<\vartheta <\pi$. This conditional harmonic model does not establish an age trend for arbitrary vascular geometry or measurement stations beyond the sole reflector.