Arterial hemodynamics in general, and the determinants of the central arterial pressure pulse in particular, has intrigued scientists for decades. It has been well documented that the arterial pulse changes drastically with age or heart rate and in diseases affecting arterial stiffness. The pulse can be modulated using various classes of vasoactive drugs. A landmark study in this context was the work of Murgo et al. , who classified waveforms into categories. A-type waves, showing an early systolic inflection point and shoulder, are characteristic for older, aged individuals. The waveform in young people is rather characterized by an inflection point following peak systolic pressure, a so-called C-type profile. Also in diastole, the wave profile shows distinct differences, with a more convex profile in the young, becoming more concave in the old, wherein it is common to find a near exponential pressure decay over the complete diastolic period (Fig. 1).
The observed changes in waveform are commonly ascribed to arise from a change in timing (and to a lesser extent the magnitude) of wave reflections. The widely accepted (but therefore not necessarily accurate) view is that in the young, pulse wave velocity is low and the reflected pressure waves reach the ascending aorta in late systole to diastole. With ageing and increase in stiffness (and hence pulse wave velocity), the reflected waves return earlier, boosting systolic pressure and increasing the load on the heart. This paradigm has, however, been questioned based on the observation that even in young individuals, the reflected wave(s) seems to arrive well in systole . Although most studies in that meta-analysis assessed timing of reflections from waveform features – which is not always accurate  – it is indeed hard to find individuals in whom the reflected waves do arrive in diastole. This, however, does not preclude that they can still have their major effect in diastole. Wave travel and reflection in the arterial system is complex in nature [4–6], with the continuous branching and changes in diameter and elastic properties leading to a diffuse pattern of wave reflection, which is still poorly understood. Too often, wave reflection is overly simplified and cartoonized into the interaction of a single forward and backward wave .
Now, in addition to the ‘wave reflection’ view on arterial hemodynamics, one can also consider the arterial system as a lumped system, wherein the physics of wave travel and reflection is simply neglected [4–6]. The arterial tree is then seen as a reservoir (the windkessel) that cushions the pulsations from the heart and transforms them into a constant and a more steady outflow at the level of the small arteries. In such a system, the pressure in diastole would exhibit a pure exponential decay, with the time constant being the product of total peripheral resistance (R) and the total arterial compliance (C), the RC time constant. Paradoxically, it is mainly the arterial system of the elderly that can be described using these simplified models. This is evidenced by the fact that the input impedance of these systems progressively better resembles the input impedance of such windkessel models , or more simply by the observation that in older individuals, one finds the typical exponential pressure decay in diastole, which is nearly always absent in younger individuals. When using these simple lumped parameter models as a basis of interpreting and analyzing hemodynamic data, one can, for instance, explain the increase in pulse pressure or the faster decline of pressure in diastole with age by a decrease in total arterial compliance C .
The ‘wave system’ and ‘windkessel’ view of the arterial tree are two distinct paradigms to analyze the arterial tree, wherein the wave system view is clearly most general in nature and the more accurate description of the actual physics. It has repeatedly been shown in model studies that arterial network models incorporating effects of wave travel and reflection are capable of mimicking arterial hemodynamics and physiology [10–14]. Lumped models, by definition, do not account for any effect of wave travel and reflection, and intrinsically assume that pressure changes instantaneously throughout the system studied (i.e., an infinite wave speed). As such, again paradoxically, the higher the wave speed, the more an arterial system will adhere to the prerequisites of a windkessel system.
In recent works, Parker, Tyberg and colleagues introduced a hybrid conceptual model of the arterial system, wherein the pressure wave is considered as the superposition of a (slow) ‘reservoir component’ and an (fast) excess pressure, which is ascribed to wave travel and reflection [15–18]. Waves and wave reflections are then analyzed on the excess pressure component alone, first subtracting the reservoir (windkessel) component from the measured pressure wave. Wang et al.  applied this method in dogs and subsequently used wave intensity and wave separation analysis to assess the nature and direction of forward and backward waves in the aorta. When applying the conventional analysis, they found no logic in the timing of the backward wave, whereas wave separation analysis on the excess pressure waveforms seemed to provide a reflected wave that traveled from the distal to the proximal aorta. Intriguingly, the nature of the reflected waves was quite different from the conventional analysis: the reservoir–wave version of wave intensity displayed a backward expansion wave (i.e. decreasing pressure) suggestive of open-end (i.e. negative) wave reflection, in contrast to the conventional analysis, which predicted a pressure-increasing reflection wave. Overall, the reservoir–wave concept suggested a far less important role for wave reflections in the genesis of the pressure wave or in the actual waveform features such as the augmentation index .
The reservoir-excess pressure concept is, however, not without controversy. The observation that there is a clear and marked time delay when waves are measured along the aorta is difficult to match with the presence of a true reservoir (windkessel). This would imply that the reservoir component changes simultaneously throughout the arterial tree, which is not the case. In this issue of the Journal of Hypertension, Mynard et al.  question the reservoir-excess pressure concept, studying the effect of the reservoir pressure correction first in simple models with well defined reflections (both the site and nature of the reflection), gradually increasing model complexity and with final application in vivo. They demonstrate that when applying the reservoir–wave analysis, reflected compression waves are suppressed and expansion waves appear or get amplified. These observations confirm what was previously reported by Wang et al. and also by Borlotti and Khir  in a conference proceeding. Having a gold standard with the model predictions, however, Mynard et al. demonstrated that these findings are largely artefactual, as they demonstrated that the reservoir pressure correction artificially suppresses compression waves, artificially amplifies expansion waves and introduces spurious, nonexisting waves.
Imperfection is a characteristic shared by any known model of the arterial system, and it also seems to apply to the reservoir–wave model concept. Use of the reservoir–wave concept as such is not necessarily problematic, but problems might arise when a model is used beyond its limits. This might happen when using the excess pressure for subsequent (wave intensity) analysis. Even if the reservoir pressure as such would exist, any errors in its estimation are directly transferred to the excess pressure and get amplified in wave intensity analysis wherein they will introduce meaningless and spurious humps and wiggles in the wave intensity pattern. We previously attempted to apply the reservoir–wave concept on carotid pressure data measured in the framework of the Asklepios study . Using conventional curve-fitting techniques, we had difficulties to assess reliable reservoir pressure (and associated model parameters) in all individuals. Especially in young individuals, in whom an exponentially decaying pressure may be as good as absent (see also Fig. 1), it is challenging – if not impossible – to detect and determine a reservoir component in the pressure wave. Note that Wang et al. applied the method using data in dogs with prolonged diastolic periods to allow for a more reliable estimate of the reservoir component.
In conclusion, although the reservoir–wave concept remains an intriguing concept, its application appears to lead to flaws in the interpretation of hemodynamic data. Probably, the strict interpretation and implementation of the arterial tree as a reservoir is a too simple (mathematical) approximation of a reality that is more complex. The reservoir-like behavior is intricately linked and intertwined with the physics of wave travel and reflection in the aorta. As phrased by Mynard et al., the lumped parameter model is a reduced version of the one-dimensional model, implying that all phenomena accounted for by the windkessel model are also explicable using the more general one-dimensional models, including the exponentially decaying pressure in diastole . As such, one can probably not simply differentiate between a wave and reservoir component, as the latter is likely just a manifestation of (complex) wave behavior.
Conflicts of interest
There are no conflicts of interest.
1. Murgo JP, Westerhof N, Giolma JP, Altobelli SA. Aortic input impedance in normal man: relationship to pressure wave forms. Circulation
2. Baksi AJ, Treibel TA, Davies JE, Hadjiloizou N, Foale RA, Parker KH, et al. A meta-analysis of the mechanism of blood pressure change with aging. J Am Coll Cardiol
3. Segers P, Rietzschel ER, De Buyzere ML, De Bacquer D, Van Bortel LM, De Backer G, et al. Assessment of pressure wave reflection: getting the timing right!. Physiol Meas
4. Milnor WR. Hemodynamics. 2nd ed.Baltimore, Maryland:Williams & Wilkins; 1989.
5. Nichols WW, O’Rourke MF. McDonald's blood flow in arteries. 3rd ed.London:Edward Arnold; 1990.
6. Westerhof N, Stergiopulos N, Noble MIM. Snapshots of hemodynamics: an aid for clinical research and graduate education. 2nd ed.New York:Springer; 2010.
7. Pythoud F, Stergiopulos N, Westerhof N, Meister JJ. Method for determining distribution of reflection sites in the arterial system. Am J Physiol Heart Circul Physiol
8. Segers P, Rietzschel ER, De Buyzere ML, Vermeersch SJ, De Bacquer D, Van Bortel LM, et al. Noninvasive (input) impedance, pulse wave velocity, and wave reflection in healthy middle-aged men and women. Hypertension
9. Stergiopulos N, Segers P, Westerhof N. Use of pulse pressure method for estimating total arterial compliance in vivo. Am J Physiol Heart Circul Physiol
10. Avolio A. Multibranched model of the human arterial system. Med Biol Eng Comp
11. Karamanoglu M, Gallagher D, Avolio A, O’Rourke M. Functional origin of reflected pressure waves in a multibranched model of the human arterial system. Am J Physiol
12. Reymond P, Bohraus Y, Perren F, Lazeyras F, Stergiopulos N. Validation of a patient-specific one-dimensional model of the systemic arterial tree. Am J Physiol Heart Circul Physiol
13. Segers P, Stergiopulos N, Verdonck P, Verhoeven R. Assessment of distributed arterial network models. Med Biol Eng Comp
14. Stergiopulos N, Young DF, Rogge TR. Computer simulation of arterial flow with applications to arterial and aortic stenoses. J Biomech
15. Davies JE, Baksi J, Francis DP, Hadjiloizou N, Whinnett ZI, Manisty CH, et al. The arterial reservoir pressure increases with aging and is the major determinant of the aortic augmentation index. Am J Physiol Heart Circul Physiol
16. Tyberg JV, Davies JE, Wang ZB, Whitelaw WA, Flewitt JA, Shrive NG, et al. Wave intensity analysis and the development of the reservoir–wave approach. Med Biol Eng Comput
17. Wang J Jr, Shrive NG, Parker KH, Hughes AD, Tyberg JV. Wave propagation and reflection in the canine aorta: analysis using a reservoir–wave approach. Can J Cardiol
18. Wang JJ, O’Brien AB, Shrive NG, Parker KH, Tyberg JV. Time-domain representation of ventricular–arterial coupling as a windkessel and wave system. Am J Physiol Heart Circul Physiol
19. Mynard J, Penny DJ, Davidson MR, Smolich JJ. The reservoir–wave paradigm introduces error into arterial wave analysis: a computer modelling and in vivo study. J Hypertens
20. Borlotti A, Khir A. Wave speed and intensity in the canine aorta: analysis with and without the windkessel–wave system. 33rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC ’11); 2011; Boston.
21. Vermeersch SJ, Rietzschel ER, De Buyzere ML, Van Bortel LM, Gillebert TC, Verdonck PR, Segers P. The reservoir pressure concept: the 3-element windkessel model revisited? Application to the Asklepios population study. J Eng Math