The differences in shape between central aortic pressure (P(Ao)) and flow waveforms have never been explained satisfactorily in that the assumed explanation (substantial reflected waves during diastole) remains controversial. As an alternative to the widely accepted frequency-domain model of arterial hemodynamics, we propose a functional, time-domain, arterial model that combines a blood conducting system and a reservoir (i.e., Frank's hydraulic integrator, the windkessel). In 15 anesthetized dogs, we measured P(Ao), flows, and dimensions and calculated windkessel pressure (P(Wk)) and volume (V(Wk)). We found that P(Wk) is proportional to thoracic aortic volume and that the volume of the thoracic aorta comprises 45.1 +/- 2.0% (mean +/- SE) of the total V(Wk). When we subtracted P(Wk) from P(Ao), we found that the difference (excess pressure) was proportional to aortic flow, thus resolving the differences between P(Ao) and flow waveforms and implying that reflected waves were minimal. We suggest that P(Ao) is the instantaneous summation of a time-varying reservoir pressure (i.e., P(Wk)) and the effects of (primarily) forward-traveling waves in this animal model.
The pulmonary arterial branching pattern suggests that the early systolic forward-going compression wave (FCW) might be reflected as a backward-going expansion wave (BEW). Accordingly, in 11 open-chest anesthetized dogs we measured proximal pulmonary arterial pressure and flow (velocity) and evaluated wave reflection using wave-intensity analysis under low-volume, high-volume, high-volume + 20 cmH2O positive end-expiratory pressure (PEEP), and hypoxic conditions. We defined the reflection coefficient R as the ratio of the energy of the reflected wave (BEW [-]; backward-going compression wave, BCW [+]) to that of the incident wave (FCW [+]). We found that R = -0.07 +/- 0.02 under low-volume conditions, which increased in absolute magnitude to -0.20 +/- 0.04 (P < 0.01) under high-volume conditions. The addition of PEEP increased R further to -0.26 +/- 0.02 (P < 0.01). All of these BEWs were reflected from a site ~3 cm downstream. During hypoxia, the BEW was maintained and a BCW appeared (R = +0.09 +/- 0.03) from a closed-end site ~9 cm downstream. The normal pulmonary arterial circulation in the open-chest dog is characterized by negative wave reflection tending to facilitate right ventricular ejection; this reflection increases with increasing blood volume and PEEP.
The parameters of wave intensity analysis are calculated from incremental changes in pressure and velocity. While it is clear that forward- and backward-traveling waves induce incremental changes in pressure, not all incremental changes in pressure are due to waves; changes in pressure may also be due to changes in the volume of a compliant structure. When the left ventricular ejects blood rapidly into the aorta, aortic pressure increases, in part, because of the increase in aortic volume: aortic inflow is momentarily greater than aortic outflow. Therefore, to properly quantify the effects of forward or backward waves on arterial pressure and velocity (flow), the component of the incremental change in arterial pressure that is due only to this increase in arterial volume--and not, fundamentally, due to waves--first must be excluded. This component is the pressure generated by the filling and emptying of the reservoir, Otto Frank's Windkessel.
. Systemic venous circulation. Waves propagating on a windkessel: relation of arterial and venous windkessels to systemic vascular resistance. Am J Physiol Heart Circ Physiol 290: H154 -H162, 2006. First published August 19, 2005 doi:10.1152/ajpheart.00494.2005.-Compared with arterial hemodynamics, there has been relatively little study of venous hemodynamics. We propose that the venous system behaves just like the arterial system: waves propagate on a time-varying reservoir, the windkessel, which functions as the reverse of the arterial windkessel. During later diastole, pressure increases exponentially to approach an asymptotic value as inflow continues in the absence of outflow. Our study in eight open-chest dogs showed that windkessel-related arterial resistance was ϳ62% of total systemic vascular resistance, whereas windkesselrelated venous resistance was only ϳ7%. Total venous compliance was found to be 21 times larger than arterial compliance (n ϭ 3). Inferior vena caval compliance (0.32 Ϯ 0.015 ml ⅐ mmHg Ϫ1 ⅐ kg Ϫ1 ; mean Ϯ SE) was ϳ14 times the aortic compliance (0.023 Ϯ 0.002 ml ⅐ mmHg Ϫ1 ⅐ kg Ϫ1 ; n ϭ 8). Despite greater venous compliance, the variation in venous windkessel volume (i.e., compliance ϫ windkessel pulse pressure; 7.8 Ϯ 1.1 ml) was only ϳ32% of the variation in aortic windkessel volume (24.3 Ϯ 2.9 ml) because of the larger arterial pressure variation. In addition, and contrary to previous understanding, waves generated by the right heart propagated upstream as far as the femoral vein, but excellent proportionality between the excess pressure and venous outflow suggests that no reflected waves returned to the right atrium. Thus the venous windkessel model not only successfully accounts for variations in the venous pressure and flow waveforms but also, in combination with the arterial windkessel, provides a coherent view of the systemic circulation. systemic circulation SIGNIFICANT EFFORTS have been devoted to the understanding of arterial hemodynamics, but much less attention has been paid to the venous systems (3, 24). The application of frequencydomain impedance analysis to venous pressure and flow seemed less successful than to arterial pressure and flow because the apparent reflection site was difficult to explain physiologically (27,32). Brecher studied venous hemodynamics, and Sjostrand suggested that the cavae constituted a "surge chamber," which Rushmer termed a "preventricular sump." Noordergraaf (24) concluded that "no analytical treatment of the pressure-flow relationship in relation to. . .cardiac activity has been proposed. As a consequence, Brecher's suggestion that the central veins constitute the functional counterpart of the arterial reservoir, transforming steady flow into pulsatile flow, has not received the scientific scrutiny that such an intuitively appealing idea deserves." Thus we have endeavored to develop a new model in an attempt to follow Brecher's suggestion and to understand venous hemodynamics better.In 1992, Tyberg (33) proposed a steady-state hydraulic mod...
. Assessment of left ventricular diastolic suction in dogs using wave-intensity analysis. Am J Physiol Heart Circ Physiol 288: H1641-H1651, 2005. First published November 24, 2004 doi:10.1152/ajpheart.00181.2004.-Two apparently different types of mechanisms have emerged to explain diastolic suction (DS), that property of the left ventricle (LV) that tends to cause it to refill itself during early diastole independent of any force from the left atrium (LA). By means of the first mechanism, DS depends on decreased elastance [e.g., the relaxation time constant ()] and, by the second, end-systolic volume (VLVES). We used waveintensity analysis (WIA) to measure the total energy transported by the backward expansion wave (IWϪ) during LV relaxation in an attempt to reconcile these mechanisms. In six anesthetized, open-chest dogs, we measured aortic, LV (PLV), LA (PLA), and pericardial pressures and LV volume by orthogonal ultrasonic crystals. Mitral velocity was measured by Doppler echocardiography, and aortic velocity was measured by an ultrasonic flow probe. Heart rate was controlled by pacing, VLVES by volume loading, and by isoproterenol or esmolol administration. IWϪ was found to be inversely related to and VLVES. Our measure of DS, the energy remaining after mitral valve opening, IWϪDS, was also found to be inversely related to and VLVES and was ϳ10% of the total "aspirating" energy generated by LV relaxation (i.e., I WϪ). The size of the Doppler (early filling) E wave depended on IWϪDS in addition to IWϩ, the energy associated with LA decompression. We conclude that the energy of the backward-going wave generated by the LV during relaxation depends on both the rate at which elastance decreases (i.e., ) and V LVES. WIA provides a new approach for assessing DS and reconciles those two previously proposed mechanisms. The E wave depends on DS in addition to LA decompression. diastole; hemodynamics; mitral valve; ventricles DIASTOLIC SUCTION (DS) is defined as that property of the left ventricle (LV) that tends to cause it to refill itself during early diastole independent of any force from the left atrium (LA). Two apparently different types of mechanistic explanations have emerged. The first type is represented by Katz (30) and Wiggers (52), who related DS to the decrease in ventricular elastance, and by several contemporary investigators (11,12,38,47) who emphasized the importance of the rate of LV relaxation in subsequent diastolic filling. In 1957, Wiggers wrote that "During early moments of ventricular relaxation, elastic stresses created during contraction are released. . . If blood could enter the ventricular chamber during this phase of diastole, such a rapid drop in pressure would unquestionably constitute a potent aspirating force" (52).Wiggers implied that the relaxing LV generates an "aspirating force" from the moment LV pressure begins to decrease. Accordingly, as elaborated upon below, the first effect of a relaxation-generated aspirating force must be to decelerate the mass represented by the stroke v...
. Direct and series transmission of left atrial pressure perturbations to the pulmonary artery: a study using wave-intensity analysis. Am J Physiol Heart Circ Physiol 286: H267-H275, 2004. First published September 25, 2003 10.1152/ ajpheart.00505.2002-Pressure waves are thought to travel from the left atrium (LA) to the pulmonary artery (PA) only retrogradely, via the vasculature. In seven anesthetized open-chest dogs, a balloon was placed in the LA, which was rapidly inflated and deflated during diastole, early systole, and late systole. High-fidelity pressures were measured within and around the heart. Measurements were made at low volume [LoV; left ventricular end-diastolic pressure (LVEDP) ϭ 5-9 mmHg], high volume (HiV; LVEDP ϭ 16-19 mmHg), and HiV with the pericardium removed. Wave-intensity analysis demonstrated that, except during late systole, balloon inflation created forwardgoing PA compression waves that were transmitted directly through the heart without measurable delay; backward PA compression waves were transmitted in-series through the pulmonary vasculature and arrived after delays of 90 Ϯ 3 ms (HiV) and 103 Ϯ 5 ms (LoV; P Ͻ 0.05). Direct transmission was greater during diastole, and both direct and series transmission increased with volume loading. Pressure waves from the LA arrive in the PA by two distinct routes: rapidly and directly through the heart and delayed and in-series through the pulmonary vasculature. lung; arteries; hemodynamics; wave transmission WAVE TRANSMISSION through the heart is poorly understood. Among the clinical syndromes in which wave transmission could be an important, unappreciated factor are the stiff left atrium (LA) syndrome (6, 15) and the Bernheim syndrome (1,5,24). To study the transmission of waves generated in the LA, we created a system where a backward-going wave, originating from the LA, could be detected in the proximal pulmonary artery (PA; backward and forward are defined with respect to PA flow.) To create such a wave in a controlled fashion, we used an LA counterpulsation balloon. Pressure and velocity waveforms in the proximal PA were analyzed to evaluate the effects of LA pressure (P LA ) perturbations.Most commonly, pulsatile arterial phenomena have been characterized using Fourier analysis where the observed waveforms are decomposed into sinusoidal wave trains, and the results are expressed as amplitude and phase as a function of frequency (16,17). This frequency-domain analysis has provided much information. However, wave-intensity analysis where the observed waveforms are decomposed into a succession of infinitesimal wave fronts that are described by their amplitude and time (13,19) allows the interaction of forwardand backward-going waves and their relation to primary hemodynamic parameters (pressure, flow, etc.) to be studied directly. This method utilizes changes in pressure and velocity to evaluate the direction, intensity, and type of waves and has been used recently to study the systemic (18), pulmonary (8,11,22), and coronary circulations...
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