Frank's Windkessel model described the hemodynamics of the arterial system in terms of resistance and compliance. It explained aortic pressure decay in diastole, but fell short in systole. Therefore characteristic impedance was introduced as a third element of the Windkessel model. Characteristic impedance links the lumped Windkessel to transmission phenomena (e.g., wave travel). Windkessels are used as hydraulic load for isolated hearts and in studies of the entire circulation. Furthermore, they are used to estimate total arterial compliance from pressure and flow; several of these methods are reviewed. Windkessels describe the general features of the input impedance, with physiologically interpretable parameters. Since it is a lumped model it is not suitable for the assessment of spatially distributed phenomena and aspects of wave travel, but it is a simple and fairly accurate approximation of ventricular afterload.

In pulmonary hypertension, the right ventricle adapts to the increasing vascular load by enhancing contractility ("coupling") to maintain flow. Ventriculoarterial coupling implies that stroke volume changes little while preserving ventricular efficiency. Ultimately, a phase develops where ventricular dilation occurs in an attempt to limit the reduction in stroke volume, with uncoupling and increased wall stress as a consequence. With pressure-volume analysis, we separately describe the changing properties of the pulmonary vascular system and the right ventricle, as well as their coupling, as important concepts for understanding the changes that occur in pulmonary hypertension. On the basis of the unique properties of the pulmonary circulation, we show how all relevant physiological parameters can be derived using an integrative approach. Because coupling is maintained by hypertrophy until the end stage of the disease, when progressive dilation begins, right ventricular volume is the essential parameter to measure in follow-up of patients with pulmonary hypertension.

In earlier studies we found that the three-element windkessel, although an almost perfect load for isolated heart studies, does not lead to accurate estimates of total arterial compliance. To overcome this problem, we introduce an inertial term in parallel with the characteristic impedance. In seven dogs we found that ascending aortic pressure could be predicted better from aortic flow by using the four-element windkessel than by using the three-element windkessel: the root-mean-square errors and the Akaike information criterion and Schwarz criterion were smaller for the four-element windkessel. The three-element windkessel overestimated total arterial compliance compared with the values derived from the area and the pulse pressure method ( P = 0.0047, paired t-test), whereas the four-element windkessel compliance estimates were not different ( P = 0.81). The characteristic impedance was underestimated using the three-element windkessel, whereas the four-element windkessel estimation differed marginally from the averaged impedance modulus at high frequencies ( P = 0.0017 and 0.031, respectively). When applied to the human, the four-element windkessel also was more accurate in these same aspects. Using a distributed model of the systemic arterial tree, we found that the inertial term results from the proper summation of all local inertial terms, and we call it total arterial inertance. We conclude that the fourelement windkessel, with all its elements having a hemodynamic meaning, is superior to the three-element windkessel as a lumped-parameter model of the entire systemic tree or as a model for parameter estimation of vascular properties.

Abstract-Wave reflections affect the proximal aortic pressure and flow waves and play a role in systolic hypertension. A measure of wave reflection, receiving much attention, is the augmentation index (AI), the ratio of the secondary rise in pressure and pulse pressure. AI can be limiting, because it depends not only on the magnitude of wave reflection but also on wave shapes and timing of incident and reflected waves. More accurate measures are obtainable after separation of pressure in its forward (P f ) and reflected (P b ) components. However, this calculation requires measurement of aortic flow. We explore the possibility of replacing the unknown flow by a triangular wave, with duration equal to ejection time, and peak flow at the inflection point of pressure (F tIP ) and, for a second analysis, at 30% of ejection time (F t30 ). Wave form analysis gave forward and backward pressure waves. Reflection magnitude (RM) and reflection index (RI) were defined as RMϭP b /P f and RIϭP b /(P f ϩP b ), respectively. Healthy subjects, including interventions such as exercise and Valsalva maneuvers, and patients with ischemic heart disease and failure were analyzed. RMs and RIs using F tIP and F t30 were compared with those using measured flow (F m Key Words: aorta Ⅲ blood flow Ⅲ blood flow velocity Ⅲ blood pressure Ⅲ pulse A ortic pressure, and especially pulse pressure (PP), is now recognized as an important indicator of cardiovascular risk 1-4 and can guide pharmaceutical treatment. 5,6 Wave reflections affect the pressure and flow wave in the proximal aorta, 7 and their contribution depends on their magnitude (determined by the periphery and the large arteries) and time of return (mainly determined by the large, conduit arteries). When the reflected wave arrives in systole, it augments pressure, leading to increased systolic and PP. This augmentation is greater when the heart is hypertrophied. 8 In heart failure, wave reflections affect the flow wave negatively, thereby reducing stroke volume and cardiac output. 8 -10 One way to estimate the amount of reflection is by waveform analysis in which aortic pressure is separated into its forward and backward components. 7,11,12 The ratio of the magnitudes of the backward (reflected) wave and the forward (incident) wave, the reflection magnitude (RM), allows for the estimation of the amount of reflection, but this waveform analysis requires measurement of both pressure and flow waves. A method that requires the measurement of pressure only is computation of the augmentation index (AI). 13,14 AI gives reproducible results 15,16 and is in use in clinical settings. [17][18][19][20] However, AI is determined by both the magnitude and timing of the reflected wave. This is evident from Figure 1A. In this figure, the original pressure wave is separated into its forward and backward components and then reassembled for different delays of the same backward wave. AI is clearly influenced by the time of return of the reflected wave. Figure 1B gives 2 examples in w...