Wave potential and the one - dimensional windkessel as a wave - based 2 paradigm of diastolic arterial hemodynamics 3

30 Controversy exists about whether one-dimensional (1D) wave theory can explain the ‘self31 cancelling’ waves that accompany the diastolic pressure decay and discharge of the arterial 32 reservoir. Although it has been proposed that reservoir and wave effects be treated as separate 33 phenomena, thus avoiding the issue of self-cancelling waves, we have argued that reservoir 34 effects are a phenomenological and mathematical subset of wave effects. However, a complete 35 wave-based explanation of self-cancelling diastolic expansion (pressure-decreasing) waves has 36 not yet been advanced. These waves are present in the forward and backward components of 37 arterial pressure and flow ( P± and Q± ), which are calculated by integrating incremental 38 pressure/flow changes ( dP± and dQ± ). While the integration constants for this calculation have 39 previously been considered arbitrary, we show that physiologically meaningful constants can be 40 obtained by identifying ‘undisturbed pressure’ as mean circulatory pressure. Using a series of 41 numerical experiments, absolute P± and Q± values are shown to represent ‘wave potential’, 42 gradients of which produce propagating wavefronts. With the aid of a ‘1D windkessel’, we show 43 how wave theory predicts discharge of the arterial reservoir. Simulated data, along with 44 hemodynamic recordings in seven sheep, suggest that self-cancelling diastolic waves arise from 45 repeated and diffuse reflection of the late systolic forward expansion wave throughout the 46 arterial system and at the closed aortic valve, along with progressive leakage of wave potential 47 from the conduit arteries. The combination of wave and wave potential concepts leads to a 48 comprehensive one-dimensional (i.e. wave-based) explanation of arterial hemodynamics, 49 including the diastolic pressure decay. 50 51