Rebuttal from Nico Westerhof and Berend E. Westerhof

Abstract

Tyberg et al. (2013) present new information of which few people are aware, namely that the time differences between the forward and backward wave are comparable at different aortic locations and therefore the backward wave appears to be travelling forward, i.e. to the periphery. This apparent inconsistency with generally accepted thinking needs attention. Tyberg et al. (2013) and we (Westerhof & Westerhof, 2013) appear to agree that forward and backward waves exist. However, we disagree with the suggestion that forward and backward wave waves do not represent reality. Waves do represent reality, but the interpretation of waves requires reconsideration. Interpretation (including Tyberg et al. 2013) is most often based on a uniform tube, an incorrect representation of the real arterial system. In this model, forward and backward waves maintain their shape and differ only in timing while traveling to the end of the tube and back. In the arterial system, with its many reflection sites, the waves are reflected and re-reflected; thus, forward and backward waves are compound waves. Compare an echo in a single hallway with the compound echo arising from a system of corridors. Echos from many sites and directions, including reverberation, result in a compound wave, in which the return time does not provide a measure of the length of the corridor. Thus, the backward wave is a compound wave arising from many reflections and not a single wave travelling backwards as in the tube model. At any location, the reflection depends on characteristic impedance and distal input impedance. The input impedance phase angle determines the time difference between forward and backward waves, and these phases are similar at different aortic locations. The reservoir-wave model (Wang et al. 2003) predicts the (reservoir) pressure of Frank's Windkessel plus an ‘excess pressure’ coined by Lighthill (1978), who was not aware of the three-element Windkessel with characteristic impedance (Westerhof et al. 1971). Indeed, Wang et al. (2003) and others (Vermeersch et al. 2009) have shown that the ‘excess pressure’ almost exactly equals characteristic impedance multiplied by flow. The reservoir pressure is twice the backward pressure; both run simultaneously to arrive later in the periphery (Wang et al. 2011). The ‘self-cancelling forward and backward flow waves’ model is correct if reflection is complete, i.e. when measured flow is negligible, such as at the distal end of a closed-ended tube (not in the arterial tree) and at closed aortic valves (in diastole). Implications The data of Tyberg et al. (2013) imply that backward wave return time, the inflection point of measured pressure, and augmentation index should be reconsidered (Baksi et al. 2009; Westerhof & Westerhof, 2012).