CrossTalk opposing view: Forward and backward pressure waves in the arterial system do not represent reality

[ John Tyberg was born in Wisconsin. He completed his pre-medical studies at Bethel College, St. Paul, and his graduate (Ph.D., Physiology, 1967) and medical (M.D., 1972) degrees at the University of Minnesota in Minneapolis. As a post-doctoral research fellow, he studied with Dr. Edmund Sonnenblick at the Harvard Medical School. Before coming to the University of Calgary in 1981, he worked at the Cedars-Sinai Medical Center in Los Angeles and the Cardiovascular Research Institute, University of California, San Francisco. During his career he has supervised almost 50 graduate students or post-doctoral research fellows and has authored more than 180 peer-reviewed publications. Before focusing on the reservoir-wave approach to arterial hemodynamics, he developed the pressure-length loop to assess regional ischemic dysfunction, demonstrated how the pericardium mediates ventricular interaction, and showed how changes in venous capacitance modulate cardiac output.] For several decades, impedance analysis has been almost universally employed by physiologists to study arterial haemodynamics and by physicians to explain changes in the aortic pressure waveform that occur with ageing and disease (Laurent et al. 2006). This analysis has led to the concept of a wave being reflected from some distal reflecting site that accounts for systolic pressure augmentation and the 'augmentation index'. Evidence has arisen recently that leads us to question this conventional wisdom. The history of arterial haemodynamics goes back more than a century; notably, to the work of the German physiologist, Otto Frank, who applied the concept of the 'Windkessel' to the mechanics of the compliant aorta (Frank, 1899). The Windkessel was an air-filled reservoir that was used in primitive fire-fighting equipment to provide steady flow with a pulsatile pump; the concept effectively explained the decrease in aortic pressure during diastole but was found to be inadequate to explain the variation in pressure during systole. Westerhof solved this problem by introducing the three-element Windkessel, the third element being a resistor interposed between the flow source (i.e. the left ventricle) and the Windkessel (to engineers, a resistance–capacitance filter; Westerhof et al. 1969, 1971). The three-element Windkessel model is capable of fitting the aortic pressure waveform with admirable precision. The pioneering work of Womersley (1955), McDonald (1955) and Taylor (1957) was viewed with great interest 40 years ago. Essentially, these investigators applied electrical alternating current transmission-line theory to aortic pressure and flow. The regular heart beat created repetitive waveforms that were conveniently analysed; Westerhof and colleagues used Fourier analysis (which assumes sinusoidal wave trains) to describe the three-element Windkessel (Westerhof et al. 1969). The physical interpretation of this mathematical framework demanded that all the variations in flow and pressure were caused by forward- or backward-going waves. In this 'wave reflection model', forward waves generated by the heart travelled downstream from the aortic valve and backward waves reflected from distal sites travelled upstream towards the left ventricle. Physical interpretation required equal, self-cancelling forward and backward flow waves (Vermeersch et al. 2009) to explain the lack of diastolic flow while pressure declined. The accompanying forward (Pforward) and backward pressure waves (Pbackward) became the basis for explaining aortic systolic pressure augmentation (i.e. the mid-systolic 'bulge' in pressure) and of defining the augmentation index (i.e. that bulge expressed as a percentage of the pulse pressure; Davies et al. 2007, 2010). When ascending aortic pressure and flow waveforms were analysed to separate measured pressure into Pforward and Pbackward components, the results seemed plausible enough; Pbackward lagged Pforward by a fraction of a second, consistent with the possibility that Pbackward had been reflected from some distal arterial site. However, some serious inconsistencies in that analysis have come to light recently. We measured pressure and flow at four sites in the canine aorta and calculated Pforward and Pbackward from the data at each site (see Fig. 1; Wang et al. 2011). The results were unexpected and startling. At each site, the relation of Pforward and Pbackward was similar; Pbackward lagged Pforward by a fraction of a second. However, taken together and plotted as a function of distance, these results showed that Pbackward appeared first in the ascending aorta and only later in the distal aorta (Wang et al. 2011). If Pforward had travelled to the distal aorta and had been reflected, the interval between Pforward and Pbackward should have been shortest when calculated from the most distal data and should have become progressively longer when calculated from more proximal data. Thus, what has been interpreted as a backward-going wave appears to be propagated forward. This unexpected result forces us to question the fundamental presuppositions of the usual analysis. Separated pressure waveforms, Pforward (thin lines) and Pbackward (thick lines), calculated from pressure and flow measured at four aortic sites (root, black; arch, red; diaphragm, green; and bifurcation, purple) in an anaesthetized dog Waveforms are plotted relative to the diastolic minimal pressure to emphasize differences. Straight lines were positioned visually on the P = 0 mmHg plane corresponding to the feet (filled circles) of successive forward and backward waves. Note that Pbackward follows Pforward by approximately 70 ms at each site. Both Pforward and Pbackward travel forward down the aorta, arriving respectively later at more distal measurement sites. (From Wang et al. 2011 with permission from Elsevier.) We have proposed an alternative to the wave-reflection model, the 'reservoir-wave approach' (Wang et al. 2003; Tyberg et al. 2008, 2009). (Recently, we have substituted 'reservoir' for 'Windkessel', lest some readers find the classical term obscure.) Based on the assumption that the change in pressure of the compliant aortic reservoir should be proportional to its change in volume, we (Wang et al. 2003) calculated the change in volume and, thereby, reservoir pressure (Preservoir). The Preservoir calculated in this way is similar to the storage component of Westerhof's three-element Windkessel (Vermeersch et al. 2009). Using either of these estimations, an increase in Preservoir largely accounts for the increase in pulse pressure in the elderly (Davies et al. 2010). During most of systole Preservoir increases, because reservoir inflow exceeds reservoir outflow and the aorta expands. During the remainder of the cycle Preservoir decreases. Most importantly, when Preservoir is subtracted from measured aortic pressure, the difference (defined as Pexcess) is precisely proportional to aortic inflow in the anaesthetized dog. This proportionality implies that the shape of the aortic flow waveform is due only to the way in which the left ventricle contracts and relaxes. It contracts quickly and accelerates the stroke volume to a maximal flow rate and then immediately begins to relax, decelerating and finally stopping ejection of the stroke volume. Thus, we proposed that measured aortic pressure should be understood as the instantaneous sum of Preservoir (which is volume related) and Pexcess (which is wave related). This approach provides a mechanism to answer to an age-old physiological question: why should the aortic pressure and flow waveforms be so different in shape? When the effect of reservoir volume change (i.e. Preservoir) is accounted for, the remaining pressure (Pexcess) is, indeed, proportional to aortic inflow. The reservoir-wave approach, which involves wave-intensity analysis (Parker et al. 1988; Parker & Jones, 1990) of Pexcess and wave-related flow, yields a compelling, physically and physiologically plausible pattern of aortic wave reflection (Wang et al. 2011). As would be anticipated, waves are reflected positively from a remote site in the femoral circulation. Not widely anticipated is the conclusion that waves can be reflected negatively (Alexander, 1953) – pressure-increasing waves are reflected as pressure-decreasing waves and vice versa – from a subdiaphragmatic site. The pressure-increasing wave reflected from the femoral circulation might account for systolic pressure augmentation but, in our anaesthetized dogs, this wave arrives at the aortic valve after the valve has closed. These patterns of aortic wave reflection are modified plausibly by vasodilatation (e.g. sodium nitroprusside) and by vasoconstriction (e.g. methoxamine; Tyberg et al. 2010; Wang et al. 2012). We have proposed a new model of arterial haemodynamics, the reservoir-wave approach. This new model explains the differences in the pressure and flow waveforms in the ascending aorta and, importantly, overcomes the inconsistency of a backward (reflected) wave travelling forward that impairs the previous approach. Further clinical studies should be initiated to test the validity and the utility of this approach, which might provide new insights into the pressure changes associated with ageing and disease and a rationale for development of novel therapeutic interventions. Readers are invited to give their views on this and the accompanying CrossTalk articles in this issue by submitting a brief comment. Comments may be posted up to 6 weeks after publication of the article, at which point the discussion will close and authors will be invited to submit a 'final word'. To submit a comment, go to http://jp.physoc.org/letters/submit/jphysiol;591/5/1171 J.V.T. acknowledges grant support from the Canadian Institutes for Health Research. The authors appreciate the many constructive comments of Drs Justin Davies, Alun Hughes, Kim Parker and Brian Williams. Disclaimer: Supplementary materials have been peer-reviewed but not copyedited. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

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