Modeling and inverse simulation of somersaults on the trampoline

Considering waves in the arteries as infinitesimal wave fronts rather than sinusoidal wavetrains, the change in pressure across the wave front, dP, is related to the change in velocity, dU, that it induces by the ʹwater hammerʹ equation, dP=±c dU, where is the density of blood and c is the local wave speed. When only unidirectional waves are present, this relationship corresponds to a straight line when P is plotted against U with slope c. When both forward and backward waves are present, the PU-loop is no longer linear. Measurements in latex tubes and systemic and pulmonary arteries exhibit a linear range during early systole and this provides a way of determining the local wave speed from the slope of the linear portion of the loop. Once the wave speed is known, it is also possible to separate the measured P and U into their forward and backward components. In cases where reflected waves are prominent, this separation of waves can help clarify the pattern of waves in the arteries throughout the cardiac cycle.