TO THE EDITOR: As some of our commenters appreciate (see Ref. 2), our Viewpoint (4) is that classical "impedance analysis" inevitably produces two important, conspicuously unexplained results: 1) equal and opposite, self-cancelling, diastolic "flow waves" and 2) "apparently paradoxical" forward-going backward waves. (How much more paradoxical could they be?) Our reservoir-wave approach (3) obviates the first problem. It explains decreasing diastolic arterial pressure by the depletion of the

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... rial reservoir. Therefore, there is no need to divide the diastolic pressure decrease into two equal parts, arbitrarily assigned to forward and backward waves. Furthermore, after reservoir pressure is subtracted from measured pressure, the difference is essentially zero (in the ascending aorta). With respect to the second, the thrust of this paper is to demonstrate that, throughout the arterial system, the classical backward wave (P b ) is merely the result of the fact that flow peaks before pressure. Only a backward compression wave can cause flow to decrease while pressure continues to increase. These two unfortunate unexplained results occur because investigators have chosen a model in which all changes in pressure and flow must be explained only by forward and backward waves. Adding a reservoir (i.e., the Windkessel), eliminates both problems. Rather than provide new evidence or a clear, cogent, mechanistic explanation, Westerhof and Westerhof (see Ref. 2) restate their beliefs, albeit with evident exasperation. Perhaps it should not be surprising that others have found a constant P f -P b lag of~70 ms; most likely, this equaled the interval between the pressure upstroke and the flow peak. Mynard and Smolich (see Ref. 2) state that this paradoxical forward-going backward wave does not arise from the conventional wave model but from a simplistic notion that the aorta is a uniform tube. Conceivably, such a paradoxical wave might be explained by the assumption of a uniform tube. However, our conclusions do not relate to or depend upon a uniform-tube model; our conclusions are based upon experimental physiologic measurements. We were incorrect to state that Alexander (1) found the area of the daughter vessels was 70% greater than that of the mother vessel. Not counting the area of the abdominal aorta, he found a daughter-mother ratio of~140%. Our average measured reflection coefficient was Ϫ0.18 Ϯ 0.02, which implied a daughter-mother ratio of~160% (6). We are more impressed with the changes with vasoactive drugs that we demonstrated (5) than are Mynard and Smolich. Classical impedance analysis has features that elude convincing explanation; as we have suggested before, the reservoir-wave approach deserves continuing serious consideration. AUTHOR CONTRIBUTIONS J.V.T., L.M.B., J.-J.W., and N.G.S. drafted manuscript; J.V.T., L.M.B., J.-J.W., and N.G.S. edited and revised manuscript; J.V.T., L.M.B., J.C.B., J.-J.W., N.G.S., and K.H.P. approved final version of manuscript. DISCLOSURES No conflicts of interest, financial or otherwise, are declared by the authors. REFERENCES 1. Alexander RS. The genesis of the aortic standing wave.