Wave Propagation in Coupled Left Ventricle–Arterial System
Implications for Aortic Pressure
Abstract The objective of this study was to examine the effects of wave propagation properties (global reflection coefficient, ΓG; pulse wave velocity, cph; and characteristic impedance, Zo) on the mechanical performance of the coupled left ventricle–arterial system. Specifically, we sought to quantify effects on aortic pressure (Pao) and flow (Qao) while keeping constant other determinants of Pao and Qao (left ventricular end-diastolic volume, Ved, and contractility, heart rate, and peripheral resistance, Rs). Isolated rabbit hearts were subjected to real-time, computer-controlled physiological loading. The arterial circulation was modeled with a lossless tube terminating in a complex load. The loading system allowed for precise and independent control of all arterial properties as evidenced by accurate reproduction of desired input impedances and computed left ventricular volume changes. While propagation phenomena affected Pao and Qao morphologies as expected, their effects on absolute Pao values were often contrary to the current understanding. Diastolic (Pd) and mean (Pm) Pao and stroke volume decreased monotonically with increases in ΓG, cph, or Zo over wide ranges. In contrast, these increases had variable effects on peak systolic Pao (Ps): decreasing with ΓG, biphasic with cph, and increasing with Zo. There was an interaction between ΓG and cph such that ΓG effects on Pm and Pd were augmented at higher cph and vice versa. Despite large changes in system parameters, effects on Pm and Ps were modest (<10% and <5%, respectively); effects on Pd were always two to four times greater. Similar results were obtained when the single-tube model of the arterial system was replaced by an asymmetrical T-tube configuration. Our data do not support the prevailing hypothesis that Ps (and therefore ventricular load) can be selectively and significantly altered by manipulating ΓG, cph, and/or Zo.
The arterial system Zin, the hydraulic load opposing ejection, consists of two components: a steady component composed of Rs and a pulsatile component consisting of distributed compliant and inertial properties (as well as, to a lesser extent, Rs). Together with the cyclic nature of ventricular ejection, these pulsatile load properties give rise to wave propagation phenomena; pressure and flow waves originate at the left ventricle and propagate along the arterial tree at finite wave propagation velocities, and the waves are partially reflected at sites of impedance mismatch (eg, bifurcations, arterioles).
That wave reflections and propagation affect Pao and Qao pulses has long been established, both theoretically and experimentally; of this there is little dispute.1 2 3 4 5 For example, the amplification of Pao as it propagates along the aorta is one manifestation of finite propagation velocities and peripheral reflections.4 6 Also, the morphological differences between Pao and Qao are due to reflections, as evidenced by their morphologies becoming more similar as reflections are reduced.3 6 7 8 The shape of Pao itself also contains some information regarding the magnitude of wave reflections and their timing.9 It has been suggested that in addition to the morphological changes in Pao, reflected waves reaching the ascending aorta in systole act to significantly augment measured systolic pressure, ie, ventricular load, and that this pressure elevation is greater with increased magnitude and/or earlier return of reflections.10 11 12 13 14 15 On the basis of these interpretations, it has been postulated that certain types of hypertension, particularly those with elevated systolic pressure, can be treated through reduction of reflections and wave velocity.15 16 17 Although these hypotheses seem reasonable, there exists no direct physical evidence that observed pressure reductions are due to reduced reflections and/or reduced wave velocity This is because of attendant experimental difficulties; studies designed to address these issues, in both humans and intact animals, leave uncontrolled one or more other factors that might contribute to changes in pressure and flow. Moreover, recent theoretical findings lead to the hypothesis that wave reflections themselves do not necessarily increase the load faced by the contracting left ventricle nor do they substantially affect mean ventricular outflow, especially when compared with the effects of Rs.8
In this study, we used an isolated heart preparation with real-time loading of the left ventricle18 19 to examine experimentally the effects of various wave propagation properties on the mechanical performance of the coupled left ventricle–arterial system (ie, Pao and Qao). This system allowed independent control of arterial system load, preload, and HR, thus permitting targeted changes in arterial properties. The results presented in this report will be compared with the previous model-based findings8 and discussed in light of experimental work in humans and intact animals. Finally, we will question the extent to which reduction of wave reflections and/or cph is beneficial to the left ventricle in terms of Pao and SV.
All protocols were reviewed and approved by the University of Chicago Institutional Animal Care and Use Committee and conform with the Guide for the Care and Use of Laboratory Animals (National Institutes of Health publication 85-23, revised 1985).
Experiments were performed on hearts isolated from normal, adult male rabbits (New Zealand White) weighing 2 to 3 kg. Rabbits were preanesthetized with 5.0 mg/kg xylazine (Vedco) and 0.2 mg/kg atropine (Elkins-Sinn) and after 10 minutes were anesthetized with 30 to 50 mg/kg ketamine (Kedalar, Parke-Davis) and 1.0 mg/kg acepromazine (Vedco). Tracheotomy was performed after anesthesia, and rabbits were artificially ventilated (model 683, Harvard Apparatus) with room air at a respiratory rate of 43 breaths/min and tidal volume of 25 to 30 mL. After median sternotomy and ligation of great vessels, a metal cannula connected to the perfusion system was inserted into the brachiocephalic artery and immediately flushed with heparinized saline (3.0 mL, 1000 U/mL). Retrograde perfusion of the coronary arteries was then begun at a constant perfusion pressure of 80 mm Hg and temperature of 37°C. The heart was perfused with oxygenated modified Krebs-Henseleit solution,19 which was not recirculated. Connective tissue was cut away and the heart removed from the chest while being constantly perfused. Therefore, coronary circulation was not interrupted at any time.
A thin latex balloon, secured at the end of a piston-cylinder device, was positioned in the left ventricle via the mitral orifice. A purse string tied around the mitral orifice secured the heart to the piston-cylinder device attached to a linear motor. A catheter-tip pressure transducer (model MPC-500, Millar Instruments, Inc) was advanced into the left ventricle via a side port in the piston-cylinder device. The piston position was sensed by a linear voltage displacement transformer (model 294, Transtek). More extensive details of the isolated heart setup can be found elsewhere.18 19 All hearts were paced with unipolar electrodes attached to the apex of the left ventricle.
Arterial System Model and Loading System
Fig 1A⇓ depicts schematically the features of the system that allow physiological loading of the isolated left ventricle. Instantaneous Pv is continuously monitored by the computer and acts as an input to the model of arterial circulation, in this case a single, uniform, elastic tube terminating in a complex load (Fig 1B⇓). The arterial system tube parameters are Zo, tube length (L), and cph. The ratio L/cph is τ, the one-way transmission time. Thus, propagation characteristics can be set by prescribing either τ or some combination of L and cph. The relative contribution of reflected waves at the left ventricle–arterial system interface is quantified by ΓG. It is important to note that the model formulation is such that Zo, τ, and ΓG can be varied independently. This allowed precisely controlled experiments on wave propagation that are, for all practical purposes, not possible in the real system because a change in a physical property (eg, vessel wall stiffness) produces simultaneous changes in Zo, cph, and ΓG. The terminal load, a variation on the three-element Windkessel,20 is given by C, high-frequency resistance (Ro), and Rs. The tube and load are matched at high frequencies, therefore,
Following Campbell et al,21 this coupled system can be described by the following delay-differential equation,
where Pc is the pressure in the terminal compliance chamber and constants α and β are given by
With measured Pv as input, Qao was calculated from numerical integration of the system (fourth-order explicit Adams predictor-corrector algorithm; step size=1.0 millisecond). The transitions from isovolumic contraction to ejection and from ejection to isovolumic relaxation occurred when Pv≥Pao and when Pv<Pao, respectively. Calculated Qao was in turn integrated to yield the desired reduction in instantaneous Vv. The piston was moved exactly by an amount equal to this desired volume change, and the whole process was continued in real time with Pv samples taken every 1.0 millisecond. After ejection, preset filling pressure (Pf) and filling resistance (Rf) were used for calculation of filling flow (Qf):
The onset of filling occurred when Pf≥Pv, and filling continued until the desired Ved was reached, at which time filling was stopped. Finally, HR was independently controlled and systemic nervous and humoral influences were not present. Thus, the experimental apparatus was able to reproduce the conditions of the computer experiments described in Berger et al8 with the same degree of precision and independent control of arterial load parameters.
Several protocols were performed in which a single property of the arterial system was altered, through adjustment of specific model parameters, while everything else was kept constant. These protocols were (1) protocol ΔΓ: adjusting ΓG(ω) while keeping Rs, Zo, and cph constant; (2) protocol Δcph: adjusting cph while keeping ￨ΓG￨, Rs, and Zo constant; and (3) protocol ΔZo: adjusting Zo while keeping cph and Rs constant. A total of 12 experiments were performed; six rabbits were used for protocols ΔΓ and Δcph combined and six for protocol ΔZo. Experimentally, ΓG(ω) was altered by adjusting only the value of C, thereby keeping the nonpulsatile hydraulic load constant.8 Changes in cph were accomplished by altering the wave transmission time, τ (Equations 2 through 4), in equispaced increments. These transmission times were converted to cph changes assuming a fixed tube length of 0.1 m. Altering cph in this manner results in a denser collection of points in the lower third of the cph range.
In all protocols, HR was fixed at 120 beats/min. Ved was first adjusted under isovolumic conditions to yield end-diastolic Pv of 5 to 10 mm Hg and thereafter was held constant throughout the experiment. A single experimental “run” consisted of eight different arterial loads in which only one wave propagation property or parameter was changed, eg, eight different ΓG(ω) values for protocol ΔΓ. The order of the eight predefined loads within a given run was randomly chosen and administered by the computer. Data were collected under numerical and physiological steady-state conditions only. For the first of eight loading conditions, the preparation was given 60 seconds to reach steady state; the seven subsequent load changes were given at least 30 seconds. Once steady state was reached, one ejection beat followed immediately by one isovolumic beat from the same Ved were sampled. This data collection scheme is illustrated in Fig 2⇓ with Pao and Pv (top), Qao (middle), and Vv (bottom) for the first two loading conditions in a run of protocol Δcph. Data from several runs were collected within each protocol, specifically, different cph for protocol ΔΓ, different ΓG(ω) for protocol Δcph, and different cph for protocol ΔZo. The Table⇓ contains Γ1, cph, and Zo values of all runs for protocols ΔΓ, Δcph, and ΔZo, respectively.
Occasionally, a premature ventricular contraction or other arrhythmia would occur during ejection, thereby disturbing the transition to steady state. Regardless of when this occurred, a full 30 seconds was given after the arrhythmia for steady state to be reached. The total time for a single run was 5 to 6 minutes, short enough so that natural degradation of the preparation was not a factor within a given run. The total time required for all runs reported here was approximately 1 hour, potentially long enough for degradation to affect ventricular function. To minimize any effects of degradation, we changed the order of protocols and runs within a protocol from heart to heart.
We subjected Pao and Qao data to traditional wave reflection analysis to obtain Zin(ω) and ΓG(ω), where Zin(ω)=Pao(ω)/Qao(ω), and ΓG(ω)=[Zin(ω)−Zo]/[Zin(ω)+Zo]. The magnitude of the first and most significant ΓG(ω) harmonic is denoted Γ1. Zin(ω)ω=0 was compared with the desired Rs. If the difference between the two values was greater than 2%, an indication that either the preparation was not in steady-state ejection or the closed-loop servocontrol was inadequate, that specific condition was excluded from further analysis. This was a rare occurrence. On the basis of Piso, Pdev was determined as the difference between peak and end-diastolic Piso. Pdev was used to evaluate changes in left ventricular contractility following each loading condition and over time.
The effects of changes in wave propagation properties on Pao and SV were analyzed. Specifically, we were interested in Ps, Pm, and Pd. Data from different hearts were analyzed together on the basis of percent changes from a common reference condition: smallest Γ1 (or equivalently largest C) for protocol ΔΓ, largest cph for protocol Δcph, and smallest Zo for protocol ΔZo.
First we evaluated the performance of the closed-loop servocontolled system. Fig 3A⇓ shows model-derived (analytic) magnitudes ‖Zin‖ and phases (θZin) of Zin(ω) superimposed on values calculated from experimental measurements of protocol ΔΓ. At all frequencies, an excellent agreement between model-derived and experimental Zin(ω) can be seen. Fig 3B⇓ shows a close correspondence between command Vv (integral of Qao) imposed on the left ventricle and actual Vv measured by the linear voltage displacement transformer during ejection.
Next we examined whether a variation in a specific wave propagation property of the model yielded the desired variation in the arterial system loading property. Zin spectra and ΓG(ω) magnitude (￨ΓG￨) from one experiment are shown in Figs 4⇓ and 5⇓, respectively. In protocol ΔΓ, diminished oscillations of both ￨Zin￨ and θZin (Fig 4⇓, left) as C increases indicate reduced wave reflections, an observation confirmed by the data in Fig 5⇓ (left). Furthermore, unchanged high-frequency ￨Zin￨ and little change in the zero-crossing of θZin (Fig 4⇓, left) confirm constant Zo and cph. In protocol Δcph, ￨Zin￨ exhibited diminished oscillations as cph increased and a more gradual convergence toward a common Zo, whereas the zero-crossing of θZin was shifted toward higher frequencies; ie, the system becomes more Windkessel-like (Fig 4⇓, middle). Despite these changes in Zin(ω), ￨ΓG￨ was completely unaffected by a change in cph (Fig 5⇓, middle). In protocol ΔZo, increasing Zo yielded the expected increase in ￨Zin￨ for all harmonics, with no change in the zero-crossing of θZin (Fig 4⇓, right). Increasing Zo also yielded a reduction in ￨ΓG￨ (Fig 5⇓, right), which is consistent with the definition of ΓG(ω).22 Also note that Rs was unchanged for all conditions; thus, Rs cannot be a factor in resultant Pao and Qao changes.
Within any given run, Pdev was fairly constant, never varying more than a few millimeters of mercury, and the time courses of Piso were practically superimposable. Over the course of the experiment (approximately 1 hour), a small but noticeable (approximately 5%) decrease in Pdev occurred. No other indications of diminished ventricular performance such as altered coronary flow or elevated end-diastolic Pv were observed in the hearts from which these data are reported.
Fig 6⇓ shows typical Pv, Pao, Qao, and Vv from a single heart for control (middle), increased reflections (left), and reduced reflections (right). Morphological changes in Pao were as expected: increased ΓG(ω) yielded increased pulse pressure and end-ejection Pao (Pee), with a systolic shoulder developing at high ΓG(ω). Furthermore, Pao morphology begins to approach that of Qao at low ΓG(ω). Both Ps and Pd increased with decreasing ΓG(ω), with relatively larger changes in Pd. Qao was also affected by ΓG(ω). Increased ΓG(ω) yielded a shorter ejection period, higher peak flow, and narrower flow profile. Specifically, ejection started and ended earlier with greater change in end-ejection time. Fig 7A⇓ shows Ps, Pm, and Pd with SV plotted against Γ1 over the full range tested. The trends for this heart are clear: decreased Ps and Pd with increasing Γ1 and changes in Pd becoming larger at high Γ1; relatively constant Pm, which eventually decreases at high Γ1; and changes in SV identical to those of Pm, which is mandatory because Rs and HR are unchanged.
The results from all six hearts in protocol ΔΓ are pooled in Fig 7B⇑, which shows percent changes (mean±SE) from the point of the minimum reflection coefficient. Despite the different absolute pressure levels between hearts, which were as great at 20 mm Hg, changes are quite consistent along the entire range of increasing Γ1: a steady and small decrease in Ps not exceeding 4%; a larger decrease in Pd approaching 14%; and an almost constant Pm until the highest values of Γ1, at which Pm decreased less than 2%. Since the Pd decrement was much greater than that of Ps, pulse pressure increased by 44% over the range of increasing Γ1. Note that although the choice of reference Γ1 is arbitrary, the directional changes observed are not dependent on the reference value of Γ1. This comment applies to all subsequent percent change results.
Fig 8⇓ depicts typical Pv, Pao, Qao, and Vv from a single experiment for cph=7.58 m/s (left), cph=3.79 m/s (middle), and cph=2.16 m/s (right). Altering cph, which affects the timing of the reflected wave, has clear, consistent effects on Pao morphology: distinct diastolic oscillations with reduced cph and a gradual elimination of these oscillations as the reflected wave arrives earlier with increasing cph. Both peak Qao and ejection period were affected little by cph, whereas the flow profile was more symmetrical at low cph. Fig 9A⇓ shows Ps, Pm, Pd, and SV over the full range of cph. Both Pm and Pd showed initial rapid decreases with increasing cph (SV followed Pm), leveling off at high velocities. Ps showed a biphasic response, with a minimum value occurring at approximately 5 m/s.
Percent changes (mean±SE) in Ps, Pm, and Pd for all six experiments in protocol Δcph are shown in Fig 9B⇑, with the highest velocity as the reference condition. These changes are remarkably consistent, with Pd being the most sensitive, showing a 12% change across the entire cph range. Changes in Ps and Pm were smaller: less than 4% for the former and 5% for the latter. Consequently, pulse pressure consistently increased with increasing cph. The biphasic Ps response was evident in all hearts.
Combined ΔΓ and Δcph
Percent changes in Ps, Pm, and Pd due to changes in Γ1 at three different cph and due to changes in cph at three different Γ1 are shown in Fig 10⇓. For each experiment, a single reference condition (lowest Γ1 and highest cph) was used for computation of these percent changes. Pd and Pm decrements after an increase in Γ1 were augmented as cph increased (Fig 10A⇓). Similarly Pm and Pd decrements in response to increasing cph were augmented by Γ1 increases (Fig 10B⇓). Regarding Ps, its biphasic response to changing cph also was augmented, and the point of minimum Ps was shifted to lower cph by increased Γ1 (Fig 10B⇓). In contrast, different cph had no effect on the slope of the Ps- Γ1 relationship until large values of Γ1 were reached. Also note that for any combination of Γ1 and cph changes, the percent change in Pd was by far the largest of the three pressures.
Fig 11⇓ shows typical Pv, Pao, Qao, and Vv for a single experiment for Zo=5.0 mm Hg·s/mL (left), Zo=7.0 mm Hg·s/mL (middle), and Zo=10.0 mm Hg·s/mL (right). Peak Qao decreased while ejection period increased (combined earlier start- and later end-ejection times) with increasing Zo. Increasing Zo over a wide range yielded increased pulse pressure through combined decreases in Pd and increases in Ps (Fig 12A⇓). The pooled data from six hearts in Fig 12B⇓ again show very consistent percent changes for all pressures. As in protocols ΔΓ and Δcph, Pd was the most sensitive variable, changing almost 16% over the Zo range. The percent change in Ps was also similar in magnitude to those from protocols ΔΓ and Δcph, increasing 4% as Zo increased over the range. The percent change in Pm (or equivalent in SV) was large compared with those from protocols ΔΓ and Δcph, decreasing 10% over the range.
Unlike in protocols ΔΓ and Δcph, in which rates of pressure changes varied over their respective ranges (ie, biphasic or eventually plateauing), the changes in pressures due to changes in Zo were linear over the entire range. Changes in cph shifted the Pd-Zo and Pm-Zo relationships in a parallel manner (Fig 13⇓); the effect on the Ps-Zo relationship was more subtle because of the biphasic response of Ps to changes in cph.
Our overall goal is to understand better the ways in which wave reflections and cph affect cardiovascular performance, from both mechanical and energetic perspectives. Here we report the effects of ΓG(ω), cph, and Zo on Pao and Qao generated in the coupled left ventricle–arterial system. This is the first experimental study that examines systematically the independent effects of the three aforementioned wave propagation properties under rigorously controlled conditions.
Adequacy of Experimental Control
For study of the direct effects of wave propagation phenomena on Pao and Qao, several experimental constraints must be met8 : (1) complete control of arterial system properties such that ΓG(ω) and cph can be altered independently of each other and Zo; (2) ability to alter propagation properties without affecting the steady component of the arterial load, ie, constant Rs; (3) control of preload, Ved, and HR; (4) elimination of neurohumoral feedback; and (5) a heart whose contractile properties do not change over time.
The isolated heart preparation readily fulfilled requirements 3 and 4. Data presented in Figs 3 through 5⇑⇑⇑ indicate that requirements 1 and 2 are also met. Regarding requirement 5, a genuine potential source of error was unavoidable degradation of the preparation, some of which was evident in the decreased Pdev as experiments progressed. Although the magnitude of this decrease was small (≤5%), it may have affected late in an experiment the sensitivities of Pao and Qao to load changes. To minimize the systematic effects of such degradation, we rearranged the order of protocols and runs within a protocol between hearts.
Are Results Specific to the Chosen Arterial Model?
The single-tube model treats all peripheral reflections as arising from one equivalent reflection site. To test the possibility that multiple reflection sights will yield different results, we loaded two hearts with the asymmetrical T-tube model21 23 consisting of two parallel circulations: head-end and body-end. Protocols ΔΓ, Δcph, and ΔZo were implemented by changing parameters of the two circulations simultaneously and in proportion. Results with T-tube loading (Fig 14⇓) were the same as those with single-tube loading. Thus, with uniform changes in the arterial system properties, as would occur in most cases, the number of reflection sites does not seem to matter. The issue of whether the same results will emerge with nonuniform changes (eg, localized alterations resulting in new, discrete reflection sites) needs further investigation.
Extending this argument further, we believe that results would be minimally affected if more complex models of the arterial system were used, eg, more branches, elastic and/or geometric taper, lossy tubes, etc. It is sufficient to use a minimal model that reproduces Zin accurately under a variety of vasoactive conditions and allows for independent changes in reflection coefficient and wave velocity. Single- and T-tube models with uniform, lossless tubes and complex terminal load satisfy these criteria.22 24 25 26
Reflection Coefficient and Pulse Wave Velocity: Comparison With Model-Based Study
Except for Pd, which was by far the most sensitive variable, changes in all pressures and SV were modest, especially considering the wide ranges of Γ1 and cph examined. These results, along with the morphological changes in Pao and Qao due to changes in ΓG(ω) and cph, are entirely consistent with those found in the model-based study.8 The physical reasons for these changes were discussed in detail elsewhere.8 Briefly, alterations in ΓG(ω) and cph result in a redistribution of pressure between diastole and systole such that Pm/SV is maintained (a consequence of constant HR and Rs). So, with a reduction in Γ1, for example, the simultaneous reduction of diastolic pressure decay and slight increase in SV yield a proportional increase in Pm and a redistribution of pressure from diastole to systole such that Ps increases slightly.
Unlike protocols ΔΓ and Δcph, changes in Zo simultaneously alter a second arterial system property, namely ΓG(ω). Thus, the effects of Zo on pressure and flow can be considered the result of changes in both Zo and ΓG(ω), and it is instructive to compare the results in Fig 12B⇑ with those in Fig 7B⇑. The increase in Zo from 3.0 to 10.0 mm Hg·s/mL yielded a decrease in Γ1 from 0.62 to 0.20 (Fig 5⇑). Over this range of decreasing Γ1, Ps increased by approximately 3%, Pm was unchanged, and Pd increased by approximately 6% (Fig 7B⇑). With protocol ΔZo, corresponding changes after an increase in Zo were (Fig 12B⇑) approximately 4% increase in Ps, approximately 9% decrease in Pm, and approximately 15% decrease in Pd. Thus, changes in Γ1 certainly contribute to Ps changes in protocol ΔZo. Since Pm was unaffected by Γ1 over this range, the Pm changes in protocol ΔZo are likely due to changes in Zo alone. Finally, note that the directional changes in Pd with decreasing Γ1 are opposite between protocols ΔΓ and ΔZo. Therefore, the effects of Zo alone (ie, with invariant ΓG) on Pd are expected to be greater than these observed in protocol ΔZo (↑ Zo and ↓ Γ1).
Interaction Among Γ1, cph, and Zo Effects
Results presented in Fig 10⇑ indicate that the sensitivities, and in some cases the directionality, of pressure responses due to changes in one parameter are greatly modified by changes in another. In general, effects of reflections are augmented at higher wave velocities and vice versa. On the other hand, percent changes in Ps, Pm, and Pd due to changes in Zo are unaffected by cph (ie, no slope change in Fig 13⇑). In contrast to the experiments described here, (patho)physiological events in the intact circulation (eg, exercise, disease processes, pharmacological treatment, aging) can simultaneously affect multiple arterial system properties. That is, certain arterial system properties tend to correlate, because of either shared underlying physical properties or dependence on common physiological responses. For example, aortic cph and Zo tend to follow one another because both are inversely related to vessel wall stiffness.1 By traversing along and between the families of curves (Figs 10⇑ and 13⇑), changes in pressures due to simultaneous changes in wave propagation properties can be predicted. In doing so, one would still observe that changes in Ps are much smaller than those in Pd.
Comparison With Previous Studies
Morphological changes in Pao and Qao observed in this study are consistent with those of previous reports. Specifically, development of a systolic shoulder in Pao is a classic morphological indicator of increased contribution of reflected waves,4 and the disappearance of diastolic oscillations and gradual similarity between Pao and Qao morphologies with reduced reflections has been observed in human and intact animal experiments.6 7
With respect to pressure and flow magnitudes, the general consensus is that wave reflections act to increase the pressure load on the ventricle. Consequently, reducing the magnitude of the reflections, delaying the return of reflections, or both have been associated with significantly reduced Ps with relatively little effect on Pd.11 12 13 Our results do not agree with these observations. We show small changes in Ps and Pm (or SV), and in some cases increases, with large reductions in ΓG(ω) and cph. Furthermore, changes in Pd are much larger than changes in both Ps and Pm.
The role of wave propagation has been investigated with one of two approaches: intact animal experiments or modeling experiments in which both the arterial system and left ventricle are represented by mathematical constructs. The present study represents a hybrid of the two: a real heart coupled to a physical/mathematical model of the arterial system. We will reconcile our observations with those in the literature on the basis of two issues: (1) the left ventricle is neither an ideal flow nor an ideal pressure source27 and (2) properties other than wave reflection and propagation are often left uncontrolled.
Regarding the first issue, making any change in the arterial system, however small, will change Zin(ω) in some way, thereby changing the hydraulic load into which the heart ejects. Therefore, the effects on Pao and Qao arising from changes in ΓG(ω), cph, and/or Zo are twofold: ejection and subsequent wave modification. In the dynamically coupled system, model or animal, the heart interacts with the load until steady-state solutions of Pao and Qao emerge. Therefore, all aspects of Pao and Qao are subject to change when the load changes, as seen in Figs 6⇑, 8⇑, and 11⇑. Changes in ΓG(ω) and cph provide information regarding only the nature of the backward wave relative to the forward wave; effects on the forward wave itself are not addressed. Thus, one cannot simply make predictions a priori about the effects of wave propagation properties on measured Pao and Qao based solely on the known effects of these properties on the relationship between forward and backward waves; the effects on ejection should not be overlooked.
Theoretical Model Studies
Although many studies have used wave transmission–type arterial models, only those in which a dynamic ventricular source is coupled to the arterial model are suitable for comparison with the results presented here. McIlroy and Targett28 showed both elevated Ps and Pd with increased ￨ΓG￨. Since ￨ΓG￨ was increased in their study by increasing Rs, both wave reflections and the steady component of load contributed to the observed changes in pressure.8 Using a multibranching arterial model, Fitchett29 decreased arterial compliance by increasing the elastic modulus for all segments (which corresponds to a simultaneous increase in cph and Zo and possibly a decrease in Γ1) and observed pressure changes that are consistent with our data (Figs 10⇑ and 13⇑). However, his observation that Ps changed more than Pd after increased wave reflections is contrary to our results. Although the difference cannot yet be fully explained, it may be due to the way in which wave reflections were manipulated: 80% occlusion and a fourfold increase in elastic modulus of a single segment. As mentioned before, such nonuniform, discrete changes in wave reflections will be the subject of future investigations. Finally, Latson et al30 and Burkhoff et al31 analyzed Pao generated by a left ventricle model connected to measured Zin and Pao generated by the same model left ventricle connected to an equivalent three-element Windkessel. Their Windkessel equivalent corresponded to not only an increase in cph to infinity but also a reduction in ￨ΓG￨, a consequence of maintaining the total arterial compliance (ie, redistribution from tube to load). Results from these studies are consistent with our data, keeping in mind that these changes in cph and ￨ΓG￨ have competing effects on Pd and Pm and variable effects on Ps (Fig 10⇑).
Isolated Heart Studies
Most isolated heart studies have used the three-element Windkessel model, in which cph is infinite.27 32 33 34 Nevertheless, changes in Windkessel compliance, Cw, are equivalent to changes in ΓG(ω); decreased Cw results in increased ￨ΓG￨. In all these studies, a reduction in Cw caused the following: a small decrease in Pm and SV, a decrease in Pd, and either an increase27 34 or a biphasic response32 33 in Ps. Changes in Ps relative to Pd were always smaller. These observations are entirely consistent with our results from protocol ΔΓ at the highest cph (15.15 m/s, Fig 10A⇑).
In contrast to the Windkessel loading, Kirkpatrick et al18 successfully loaded the isolated heart with wave transmission models; our loading system is identical to theirs. Although Kirkpatrick et al primarily focused on presenting a new methodology, one can observe effects of load compliance (Fig 7⇑ in Kirkpatrick et al) and wave velocity (Fig 6⇑ in Kirkpatrick et al) on Pao and SV that are similar to what we report here.
Intact Heart Studies
Several methods have been used to alter arterial wave propagation properties in the intact circulation: providing an alternative ejection path via either an artificial Windkessel35 or a stiff tube placed in the ascending aorta36 ; applying plaster or Lucite ferrules to various portions of the aorta and large arteries37 ; and replacing a section of native aorta with glass38 or Tygon39 tubing. These manipulations cause an increase in “aortic” wall stiffness, resulting in an increase in cph and in some cases an increase in Zo. All of these studies show that increasing aortic stiffness in these manners yields decreased Pd, increased pulse pressure, and a relatively smaller reduction in SV, observations consistent with the results of the present study. However, increments in Ps were significantly greater than those from the present study, their magnitudes being more comparable to the decrements in Pd. These magnitude discrepancies can be explained by changes in factors other than those associated with wave propagation. For example, Randall et al36 showed trends of increasing Rs and Ved (inferred from their left ventricular end-diastolic diameter and pressure) with increased aortic stiffness. Similarly, it can be inferred from the data of Kelly et al39 that Rs and Ved increased by approximately 20% and 13%, respectively. Since Pao is highly sensitive to Rs and Ved, even small increases in these quantities can significantly augment Ps, thus reconciling the discrepancies.
Another class of studies uses drug effects, aging, and disease processes to make inferences regarding the effects of wave propagation phenomena. In general, elevated systolic pressure (eg, isolated systolic hypertension in the elderly) is accompanied by increases in wave reflections and/or increased cph.40 41 42 Conversely, vasodilator drugs, such as nitroprusside and nitroglycerin, that lower systolic pressure also tend to reduce wave reflections.10 11 40 43 On the basis of these observations, it has been hypothesized that reducing wave reflections, especially with greatly elevated Ps, is beneficial in that Ps can be reduced significantly with little change in Pd. Our results are clearly inconsistent with these hypotheses. Once again, we propose that changes in factors other than wave reflections are responsible for this discrepancy. For example, Yaginuma et al11 report that in normotensive patients without cardiac disease, nitroglycerin reduces Ps, Pm, and SV significantly without any change in Pd. They attribute these changes to a reduction in peripheral reflections only; since Rs, Zo, cph, Cw, and HR did not change. We offer an alternative explanation. All pressure and SV changes observed by Yaginuma et al can be reproduced simply by a 20-mL reduction of Ved, consistent with vasodilator-induced venous pooling, without invoking any other cardiovascular changes. For a normal human left ventricle, this change in Ved would cause left ventricular end-diastolic pressure to decrease by less than 4 mm Hg,44 a pressure change that was actually observed by Yaginuma et al. Similar concerns are applicable to subsequent studies regarding effects of vasodilator-mediated changes in wave reflections and consequent alterations in Pao.12 13 14 16 That wave reflections are reduced with nitroglycerin and other vasodilators is not disputed; however, this reduction of reflections in itself cannot preferentially reduce Ps.
One must keep three things in mind when extrapolating to the intact circulation our results regarding the effects of wave propagation properties on Pao and Qao. First, we purposely examined very wide ranges of Γ1, cph, and Zo. Typical changes in these parameters under various (patho)physiological conditions are smaller, especially for cph (as much as threefold change) and Zo (as much as twofold change). Therefore, in the intact circulation, expected changes in Pao and Qao would be smaller than the extremes shown in this study. Second, effects are small for Pm (or SV) and Ps. Furthermore, since Γ1, cph, and Zo usually change in the same direction and their individual effects on Ps compete, the net response of Ps may be attenuated when two or more properties change simultaneously. Third, Pd is by far the most affected, especially with combined changes in which individual effects are in the same direction. Thus, our data do not support the hypothesis that Ps (hence, ventricular load) can be selectively and significantly reduced by reducing reflections.
In this study, we evaluated the relevance of wave propagation and reflection in normal hearts and solely in terms of the effects on Ps, Pm, Pd, and SV. It is worthwhile to also examine the effects of wave reflections on other variables, eg, left ventricular relaxation and filling, coronary flow, and myocardial oxygen consumption. Energetics and coronary flow are particularly interesting because of the greater sensitivity of Pd. Finally, the effects of wave reflections in diseased and hypertrophied hearts as well as the role of wave propagation phenomena, if any, in the remodeling process also remain to be elucidated.
Selected Abbreviations and Acronyms
|C||=||terminal load compliance of arterial system|
|c ph||=||pulse wave velocity|
|ΓG||=||global reflection coefficient|
|Γ1||=||magnitude of the first and most significant ΓG(ω) harmonic|
|P ao||=||aortic pressure|
|P d||=||minimum diastolic aortic pressure|
|P dev||=||peak developed left ventricular pressure in isovolumic beat|
|P iso||=||left ventricular pressure in isovolumic beat|
|P m||=||mean aortic pressure|
|P s||=||peak systolic aortic pressure|
|P v||=||left ventricular pressure in ejecting beat|
|Q ao||=||aortic flow (left ventricular outflow)|
|R s||=||peripheral resistance|
|V ed||=||left ventricular end-diastolic volume|
|V v||=||left ventricular volume|
|Z in||=||arterial system input impedance|
|Z o||=||characteristic impedance|
This study was supported in part by the National Institutes of Health, National Heart, Lung, and Blood Institute grant R01-HL-36185 (S.G. Shroff) and Cardiovascular Sciences Training grant HL-07381 (D.S. Berger).
- Received December 20, 1995.
- Revision received January 16, 1996.
- Accepted February 2, 1996.
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