John V. Tyberg

The case for the reservoir-wave approach

The Reservoir-Wave Approach is an alternative, time-domain approach to arterial hemodynamics that is based on the assertion that measured pressure and flow can be resolved into their volume-related (i.e., reservoir) and wave-related (i.e., excess) components. The change in reservoir pressure is assumed to be proportional to the difference between measured inflow and calculated outflow. Wave intensity analysis of the excess components yields a pattern of aortic wave propagation and reflection in the dog that is novel and physiologically plausible: waves are reflected positively from a site in the femoral circulation and negatively from a site below the diaphragm, where the total daughter-vessel cross-sectional area exceeds the mother-vessel area. With vasodilatation, the negative reflection is augmented and with vasoconstriction, it is virtually eliminated. On the other hand, conventional hemodynamic analysis has been shown to yield a paradoxical forward-going backward wave and the impedance minimum, previously assumed to be an indicator of the source of wave reflection according to quarter-wave-length theory, has been shown to be due to the reservoir component. Clinical studies employing the Reservoir-Wave Approach should be undertaken to verify experimental observations and, perhaps, to gain new diagnostic and therapeutic insights.

The Reservoir-Wave Paradigm: Potential Implications for Hypertension

Consistent with a straightforward, time-domain interpretation of Westerhofs classic circuit diagram of the 3- element Windkessel, we have concluded that measured aortic pressure is the instantaneous sum of a constant (P∞), a Windkessel/reservoir pressure, and a wave-related pressure. According to our interpretation, the resistive element interposed between the left ventricle and the resistance-capacitance (RC) filter is, in fact, a hydraulic resistance in the proximal aorta that defines the wave-related pressure. The RC filter subserves the Windkessel/reservoir function and is distributed anatomically within the large arteries. The lower potential (pressure) of the RC filter (P∞) is not zero or even venous or mean circulatory pressure, but rather a higher pressure (∼30 – 40 mmHg) toward which aortic pressure declines asymptotically during diastole. As previously recognized, the Windkessel/reservoir pressure describes aortic diastolic pressure very precisely; in the new paradigm, the addition of the wave-related pressure provides the complement that describes systolic pressure equally precisely. This new interpretation has several potential implications for our understanding of hypertension. Diastolic hypertension would seem to be related most directly to alterations in reservoir pressure, particularly P∞ and reservoir resistance. Systolic hypertension may be a function of several factors: wave reflection, increased proximal aortic resistance, and decreased aortic compliance.

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

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

Alterations in aortic wave reflection with vasodilation and vasoconstriction in anaesthetized dogs.

BACKGROUNDnUsing the reservoir-wave approach, we studied wave propagation, reflection, and re-reflection in the canine aorta with administrations of sodium nitroprusside (NP) and methoxamine (Mtx).nnnMETHODSnIn 8 anaesthetized dogs, excess pressures were calculated from pressure and flow measurements at 4 locations along the aorta; wave intensity analysis was employed to identify wavefronts and the type of waves.nnnRESULTSnNP (intravenous; 14 μg/min) decreased mean aortic pressure from 80 ± 3 mm Hg to 48 ± 1 mm Hg; Mtx (intravenous; 10 μg/min) increased mean pressure from 80 ± 3 mm Hg to 104 ± 4 mm Hg. NP increased negative reflection near the kidneys (reflection coefficient: -0.33 vs -0.18; P < 0.01) and produced new negatively reflecting sites just beyond the arch and in the proximal femoral arteries, consistent with a vasodilating effects of nitrates on conducting arteries. Mtx negated negative reflection from near the kidneys (-0.02 vs -0.17; P < 0.01) and increased positive femoral reflection (0.38 vs 0.26; P < 0.01). The large reflected compression wave was re-reflected from the closed aortic valve to produce a prominent increase in middiastolic pressure in the distal aorta.nnnCONCLUSIONSnThe reservoir-wave approach explains decreasing diastolic pressure without positing waves that travel at near-infinite velocities and reveals the pressure changes that are uniquely due to wave motion.

Arterial hemodynamics and wave analysis in the frequency and time domains: an evaluation of the paradigms

‘‘These laws [of hydraulics] accurately inform us how water will conduct itself under all different circumstances, on account of its gravity, the unconditioned mobility of its parts, and its want of elasticity. Hydrostatics teaches how it is brought to rest through gravity; hydrodynamics, how it is set in motion; and the latter has also to take account of hindrances which adhesion opposes to the will of water: the two together constitute hydraulics.’’ Arthur Schopenhauer ‘‘On the objectification of the will in unconscious nature’’ The World as Will and Representation (1819)

A review of the current status of pericardial closure following cardiac surgery

Some cardiac surgeons prefer to close the pericardium whenever possible following surgery, others specifically avoid this practice, and still others believe that neither alternative has any meaningful influence on clinical outcomes. Unfortunately, scientific evidence supporting either approach is scarce, making a consensus regarding best practice impossible. In this article, the known functions of the native intact pericardium are summarized, and the arguments for and against pericardial closure after surgery are examined. In addition, the techniques and materials that have been utilized for pericardial closure previously, as well as those that are currently being developed, are assessed.

Wave reflections in the pulmonary arteries analysed with the reservoir–wave model

In the pulmonary artery, we use the reservoir–wave model to separate the effects of a charging and discharging, elastic arterial reservoir from the effects of waves created by the contracting and relaxing heart. Wave intensity analysis quantifies the effects of waves that cause changes in pressure and flow and precisely identifies when waves created by the heart and reflections of these waves start and end. We show that negative wave reflections arise from the junction of lobar arteries stemming from the left and right pulmonary arteries. When blood volume is increased and pulmonary arteries become distended, the strength of negative wave reflections increases when 100% O2 is used for ventilation. Negative reflections suck blood downstream and, as they arrive when the heart is developing maximal pressure, negative reflections help to lower the back pressure the heart must pump against and, thus, they tend to increase the forward flow of blood.

Partitioning pulmonary vascular resistance using the reservoir-wave model

The conventional determination of pulmonary vascular resistance does not indicate which vascular segments contribute to the total resistance of the pulmonary circulation. Using measurements of pressure and flow, the reservoir-wave model can be used to partition total pulmonary vascular resistance into arterial, microcirculation, and venous components. Changes to these resistance components are investigated during hypoxia and inhaled nitric oxide, volume loading, and positive end-expiratory pressure. The reservoir-wave model defines the pressure of a volume-related reservoir and the asymptotic pressure. The mean values of arterial and venous reservoir pressures and arterial and venous asymptotic pressures define a series of resistances between the main pulmonary artery and the pulmonary veins: the resistance of large and small arteries, the microcirculation, and veins. In 11 anaesthetized, open-chest dogs, pressure and flow were measured in the main pulmonary artery and a single pulmonary vein. Volume loading reduced each vascular resistance component, whereas positive end-expiratory pressure only increased microcirculation resistance. Hypoxia increased the resistance of small arteries and veins, whereas nitric oxide only decreased small-artery resistance significantly. The reservoir-wave model provides a novel method to deconstruct total pulmonary vascular resistance. The results are consistent with the expected physiological responses of the pulmonary circulation and provide additional information regarding which segments of the pulmonary circulation react to hypoxia and nitric oxide.

Genesis of the characteristic pulmonary venous pressure waveform as described by the reservoir‐wave model

In pressure flow data from a pulmonary vein, we use the reservoir wave model to separate the effects of an elastic venous reservoir from the effects of waves created by the heart. Wave intensity analysis was used to separate the effects of waves generated upstream by the right ventricle from the effects of waves generated downstream by the left atrium and left ventricle. Most waves are created by the left atrium and left ventricle and can be linked to events that occur during the cardiac cycle. Waves transmitted through the pulmonary circulation are attenuated less when blood volume is increased but are attenuated more and delayed when the lungs are expanded. The drainage of pulmonary arterial and venous reservoirs are responsible for substantial changes in measured pulmonary venous pressure and flow but waves are associated with the conventional landmarks of these characteristic waveforms.

Response to the letter of Mynard and Smolich.

a Departments of Cardiac Sciences and Physiology/Pharmacology and Libin Cardiovascular Institute of Alberta, University of Calgary, Canada b Post-Doctoral Fellow, Department of Surgery, Yale University, New Haven, Connecticut, USA c Department of Bioengineering, Imperial College, London, United Kingdom d Department of Civil Engineering, Schulich School of Engineering, University of Calgary, Canada e Department of Medicine, Fu Jen Catholic University, New Taipei City, Taiwan