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Effects of vasoconstriction and vasodilatation on LV and segmental circulatory energetics

¹Libin Cardiovascular Institute of Alberta, Departments of Cardiac Sciences, Physiology and Biophysics, and Civil Engineering, University of Calgary, Calgary, Canada; and ²Department of Bioengineering, Imperial College of Science, Technology and Medicine, London, England

Submitted 24 August 2007 ; accepted in final form 12 December 2007

	ABSTRACT

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Although the hydraulic work generated by the left ventricle (LV) is not disputed, how the work was dissipated through the systemic circulation is still subject to interpretation. Recently, we proposed that the systemic circulation should be considered as waves and a reservoir system (Wk). By combining the arterial and venous reservoirs, the systemic vascular resistance can be viewed as a series of resistors, which in sequence are the large-artery resistance, arterial reservoir resistance, the microcirculatory resistance, venous reservoir resistance, and large-vein resistance, and propelling blood through these resistance elements represents resistive losses. We then studied the changes in the fraction of the work consumed by each element when infusing methoxamine (MTX), a vasoconstrictor, and sodium nitroprusside (NP), a vasodilator. Results show that, under control condition, 50% of the LV stroke work was dissipated through arterial reservoir resistance (NP, 36%; MTX, 27%), another 25% was dissipated by the microcirculation (NP, 20%; MTX, 66%), and 20% of work by the large-artery resistances (NP, 37%; MTX, 6%). The energy dissipated by the venous resistances was small and had limited variation with NP and MTX, where the large-vein and venous reservoir resistances shared 1 and 3% of LV stroke work, respectively. Approximately 60% of LV stroke work is stored as the potential energy during systole under control, and the ratio decreases to 45% with NP and 80% with MTX.

left ventricle circulatory coupling; systemic vascular resistance; arterial and venous reservoirs

We recently proposed a new approach to the systemic circulation, using the principle of Otto Frank's windkessel (8, 9), in which arterial reservoir pressure (P_A-Res) is proportional to the instantaneous blood volume. Viewed in the time domain, the arterial reservoir is a hydraulic integrator; the reservoir is charged when inflow exceeds outflow (during systole) and vice versa during diastole (22). The measured central aortic pressure (P_Ao) is equal to the sum of the P_A-Res and the pressure due to arterial wave motion (wave pressure; P_A-Wave). Our best analogy for this mechanism is that of a canal lock. The water level, which corresponds to P_A-Res, can increase or decrease depending on the balance of inflow and outflow, and, at any level, any perturbation such as throwing a stone into the lock will produce a propagating wave. Recently, we also showed that the venous system behaves simply as an inverse of the arterial system (21): in diastole, the arterial reservoir discharges, and the venous reservoir charges. To view the systemic circulation as a whole, we observed that, during diastole, P_Ao and P_A-Res decrease exponentially and asymptotically approach a nonzero level (P_A-), and inferior vena caval pressure (P_IVC) and venous reservoir pressure (P_V-Res) rise exponentially to approach P_V-. Generally, P_V- is different from P_A-.

By considering the arterial and venous wave-reservoir models together, systemic vascular resistance (SVR) can be viewed as a network of resistances arranged in series (21). In the absence of reflections, P_A-Wave is precisely proportional to the measured aortic flow (Q_Ao), and the ratio, P_A-Wave to Q_Ao, is numerically equal to characteristic impedance. We interpret P_A-Wave-to-Q_Ao ratio to be a measure of large-artery resistance (R_Lrg-A), the resistance separating the LV from the arterial reservoir. The arterial reservoir resistance (R_A-Res) is the resistance regulating the flow out of the reservoir and is equal to _A/C_A, where _A is the exponential time constant of the decline of diastolic P_Ao, and C_A is the arterial compliance. The large-vein resistance (R_Lrg-V) is the resistance separating the right atrium from the venous reservoir and is equal to the ratio of P_V-Wave to Q_IVC, where P_V-Wave is the venous wave pressure and Q_IVC is the inferior venal caval flow. The venous reservoir resistance (R_V-Res) is the resistance regulating the flow into the venous reservoir and is equal to _V/C_V, where _V is the exponential time constant of the rise of diastolic P_IVC and C_V is the venous compliance. Finally, we consider that the resistance defined by the difference between P_A- and P_V- divided by the mean flow [i.e., cardiac output (CO)] is the microcirculation resistance (R_µcirc). R_µcirc is also equal to SVR – R_i, where R_i is the summation of the above identified resistances. These incremental resistances correspond very well (21) to measurements of pressure drop across the vascular elements in the hamster cheek pouch (5). From that comparison, we suggested that R_A-Res involves arterial vessels as small as 60 µm and that R_V-Res also involves venous vessels as small as 60 µm.

Propelling blood through these resistance elements represents resistive losses, which can be quantified through the integration of the flow across a resistive element over time. In the steady state, LV stroke work equals the sum of the energy dissipated by all the resistive elements. Not all the LV stroke work, which is generated during systole, is dissipated during that interval; part of it is dissipated to produce systolic flow, but the remainder is stored as potential energy by the compliant arterial reservoir to be dissipated during diastole in pushing blood through the resistive components.

Differently from the impedance point of view in which LV stroke work is separated into mean and oscillatory components, we here demonstrate how LV stroke work can be separated into energy-dissipation components corresponding to each serial resistive element. Furthermore, we demonstrate how the distribution of this energy dissipation varies with the administration of a vasodilator, sodium nitroprusside (NP), and a vasoconstrictor, methoxamine (MTX).

	MATERIALS AND METHODS

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Theory

Determination of arterial and venous properties. The experimental protocol was approved by the Institutional Animal Care Committee of the University of Calgary Faculty of Medicine and met the standards of the American Physiological Society. The values of resistive components were by-products of the calculations of the P_A-Res and P_V-Res. The methods of calculation were detailed elsewhere (21, 22). In brief, the arterial asymptotic pressure, P_A-, is initially determined by fitting P_Ao during the later part of diastole by using a three-parameter exponential-decay equation. P_A-, R_A-Res, and arterial reservoir compliance (C_A-Res) were determined by using a nonlinear search algorithm with appropriate initial guesses to minimize the mean-squared error between the calculated P_A-Res and the measured P_Ao during late diastole, during which wave action was assumed to be negligible. The logic of the venous reservoir is the inverse of the arterial reservoir. In late diastole, both P_IVC and P_V-Res rise exponentially, approaching P_V-, which had been determined by fitting a three-parameter exponential-rise equation to P_IVC in late diastole. P_V-, R_V-Res, and venous reservoir compliance (C_V-Res) were similarly determined by minimizing the mean-squared error between the calculated P_V-Res and the measured P_IVC.

Separation of SVR into serial resistive components. The separation of SVR into its serial resistive components is shown in Fig. 1 (t = 0 corresponded to the onset of the atrial contraction for all figures). SVR was calculated as the pressure gradient between and divided by , where the overbar signifies the mean value. On the basis of P_A- and P_V-, SVR was separated into the arterial resistance (between and P_A-, red hatching), the venous resistance (between P_V- and blue hatching), and the R_µcirc (between P_A- and P_V-, purple crosshatching). The arterial resistance was further separated into the R_Lrg-A (i.e., the gradient between and , , divided by ) and the R_A-Res (i.e., the gradient between and P_A- divided by ). The venous resistance can also be further separated into the R_Lrg-V (i.e., the gradient between and , , divided by ) and the R_V-Res (i.e., the gradient between P_V- and divided by ).

View larger version (56K): [in this window] [in a new window]   Fig. 1. An example demonstrates the separation of systemic vascular resistance (SVR) into serial components of resistance: large-artery (RLrg-A), arterial reservoir (RA-Res), microcirculatory (Rµcirc), venous reservoir (RV-Res), and large-vein (RLrg-V) resistance. Arterial resistances are indicated by red hatching, microcirculatory resistance by purple cross-hatching, and venous resistances by blue hatching. Measured aortic and IVC pressures are shown in black, and calculated aortic and venous reservoir pressures are in green. Mean values are indicated by dashed lines. The value of each resistance was calculated by using the mean pressure gradient across it divided by the mean flow. See MATERIALS AND METHODS for details of each calculation. , arterial wave pressure; , measured aortic flow; , arterial reservoir pressure; PA-, arterial asymptotic pressure; PV-, venous asymptotic pressure; , venous reservoir pressure; ; venous wave pressure.

The energy dissipated by the proximal R_Lrg-A is

(1)

and by the R_A-Res is

(2)

where Q_A-Res is the outflow from the arterial reservoir, calculated by dividing the gradient between the P_A-Res and P_A- by the arterial reservoir resistance, R_A-Res. t₁ and t₂ are the instants at which the aortic valve opens and closes, respectively.

Since the flow in microcirculation is generally steady, the energy dissipated during systole can be calculated as

(3)

The energy dissipation by the R_V-Res and the R_Lrg-V is calculated as

(4)

and

(5)

, respectively. Q_V-Res is the inflow of the venous reservoir, which is driven by the pressure gradient between P_V- and P_V-Res across R_V-Res. t₃ and t₄ are instants at which the right atrium begins to contract during sequential beats. Because we did not measure flow in the superior vena cava, Q_IVC was scaled so that its integrated volume over a cycle equaled that of the stroke volume.

All the LV stroke work is injected into the systemic circulation during systole, but only part of it is dissipated by resistive components during that interval; the remaining energy is stored as potential energy via the compliance of the arterial reservoir. The energy dissipated during systole can be calculated as the sum of Eq. 1 to Eq. 5 during systole (each equation integrated between t₁ and the time of the minimum of the subsequent incisura). The energy stored as the potential energy at end systole is the difference between LV stroke work and the systolic energy dissipation. In the steady state, the potential energy remaining at end systole equals the energy dissipated during diastole.

Experimental preparation and protocol. Studies were performed on eight healthy mongrel dogs weighing between 18 and 29 kg. They were anesthetized with thiopental sodium (20 mg/kg), followed by fentanyl citrate (30 µg·kg^–1·h^–1), and ventilated with a 1:1 nitrous oxide-oxygen mixture. The rate of a constant-volume respirator (model no. 607; Harvard Apparatus, Natick, MA) (tidal volume = 15 ml/kg) was adjusted to maintain normal blood gas tensions and pH. Body temperature was maintained at 37°C with a circulating-water warming blanket and a heating lamp. A lactated Ringer solution was infused through the jugular vein to manipulate LV end-diastolic pressure (P_LVED).

We measured pressure in the LV and right ventricle, and simultaneous pressure and flow were measured at the aortic root and IVC (within 2 cm of the right atrium). Pressures were measured with high-fidelity catheter-tip manometers (Millar Instruments, Houston, TX) and flows with ultrasonic flow probes (Transonic Systems, Ithaca, NY). The LV pressure catheter was introduced through the apex. Aortic root pressure was measured by introducing the catheter through the femoral artery and advancing it, retrogradely, into the root of the aorta, 1.5 cm from the valve. The IVC pressure catheter was inserted through the right jugular vein and was positioned in the IVC, 1 cm beyond the right atrium. The flow probes were located within 1 cm of the pressure transducers. After control recordings, NP (0.3 mg/min iv) was administered. After a 20-min period of recovery, MTX (5 mg iv bolus) was administered.

	RESULTS

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Table 1 shows mean values of heart rate, CO, mean arterial and IVC pressures, and parameters (R, C, and P_-) for the arterial and venous reservoirs for the three conditions: NP administration, the control state, and MTX administration.

In Fig. 2, top, the magnitude of SVR and all resistive components are presented for the control state and the administration of NP and MTX; the resistive components (bottom) are presented as fractions of SVR for each condition. These data are summarized in Table 2. Under control conditions, SVR was 60 mmHg·min·l^–1, which decreased to half (30 mmHg·min·l^–1) with NP and increased fivefold (300 mmHg·min·l^–1) with MTX. With respect to the response of each resistive component to the administration of NP and MTX, the arterial reservoir and the R_µcirc accounted for most of the changes in SVR; the R_V-Res and R_Lrg-V were relatively insensitive to these manipulations. Although small in absolute magnitude, R_Lrg-A increased with NP and decreased with MTX, expressed as a percentage of SVR.

View larger version (16K): [in this window] [in a new window]   Fig. 2. Top: the absolute values of total SVR and each resistive component under control conditions are compared with those under the administration of sodium nitroprusside (NP) and methoxamine (MTX). Bottom: the same comparisons are presented with the component resistances expressed as percentages of SVR. (Data from 7 dogs; *P < 0.05 compared with control values.)

View larger version (17K): [in this window] [in a new window]   Fig. 3. An example (data from the same beat as shown in Fig. 1) of power (top) and energy (bottom), generated by the left ventricle (LV) and dissipated by each resistive component, presented as a function of time. LV stroke power and stroke work are in black. The power and work (W) dissipated by the RLrg-A, RA-Res, Rµcirc, RV-Res, and RLrg-V are in solid red, dashed red, purple, dashed blue, and solid blue lines, respectively; the total dissipation, i.e., the summation of the energy dissipated by all resistances, is in pink. The vertical dashed line indicates the end of systole, at which time stroke work reached its maximum. Potential energy was calculated as the difference between LV stroke work (black) and total energy dissipation (pink) at the end of systole.

View larger version (17K): [in this window] [in a new window]   Fig. 4. A typical example of recorded and calculated pressures (top; see Fig. 1 for details) and power (middle) and work (bottom) generated by the LV and dissipated by each resistive component varied through the administration of NP and MTX. The color code is the same as in Fig. 3.

View larger version (19K): [in this window] [in a new window]   Fig. 5. Top: absolute values of LV stroke work and segmental energy dissipation under control are compared with those under the administration of NP and MTX. Bottom: the same comparisons are presented with the segmental energy dissipation expressed as a percentage of LV stroke work. (Data from 7 dogs; *P < 0.05 compared with control values.)

View larger version (16K): [in this window] [in a new window]   Fig. 6. Potential energy, expressed as a percentage of LV stroke work, varied with the administration of NP and MTX. (Data from 7 dogs; *P < 0.05 compared with control values.)

	DISCUSSION

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In this study, we have proposed an operational method to break up SVR into its serial resistive components, on the basis of our understanding that the systemic circulation functions as waves propagating on time-varying arterial and venous reservoirs (21, 22). The measured arterial and venous pressures are respectively separated into a wave-related pressure and a reservoir pressure, both of which vary with respect to time during the cardiac cycle; each resistance is proportional to the pressure gradient across it. As shown elsewhere (21), by determining the two asymptotic pressures, P_A- and P_V-, SVR is divided into arterial, microcirculatory, and venous resistances (see Fig. 1). Furthermore, the arterial component can be divided into R_Lrg-A and R_A-Res, and, similarly, the venous component can be divided into R_Lrg-V and R_V-Res. The R_µcirc is equal to the difference between the two asymptotic pressures, divided by the mean flow. Therefore, SVR is considered as the serial summation of the R_Lrg-A, the R_A-Res, the R_µcirc, the R_V-Res, and the R_Lrg-V.

Although calculation of LV stroke work is straightforward, how this energy was dissipated by the systemic circulation was poorly understood. For decades, the interpretation of the systemic circulation has been dominated by Fourier-based methods, where the measured aortic pressures and flows were separated into a mean value and oscillatory components about it. The aortic pressure-flow relationship was presented via harmonics, where the modulus at 0 Hz was designated as the SVR and the average of the moduli of the high-frequency harmonics was defined as the characteristic impedance. Thus the energy dissipated by the systemic circulation was separated dichotomously into mean (which was a function of SVR) and oscillatory (which was a function of the summation of each harmonic term) components (12). So far, no attempt has been made to separate the energy dissipation with respect to the corresponding serial vascular structures.

Among the five different serial components of SVR identified in this study, the combination of the R_A-Res and the R_µcirc dominated the SVR under all conditions (control state, 90%; NP, 85%; and MTX, 95%; see Fig. 2, bottom, and Table 2). With the infusion of NP, CO increased 10% (from 1.3 to 1.4 l/min), and SVR decreased by 45% (from 62 to 34 mmHg·min·l^–1), relative to the control values. Most of the decrease in SVR was due to decreases in R_A-Res (by 50%, from 35 to 17 mmHg·min·l^–1) and the R_µcirc (by 45%, from 22 to 12 mmHg·min·l^–1). With a bolus of MTX, CO decreased by 80% (from 1.3 to 0.3 l/min) and SVR increased fivefold (from 62 to 307 mmHg·min·l^–1). Most of the increase in SVR was due to the increase in the R_A-Res (by 3.5-fold, from 35 to 123 mmHg·min·l^–1) and especially R_µcirc (by approximately eightfold, from 22 to 173 mmHg·min·l^–1). As mentioned in the introduction, by comparing our normal data to those of Davis et al. (5), who measured the distribution of the pressure drop in the vasculature of the hamster cheek pouch, the arterial reservoir would seem to involve vessels as small as 60 µm. We speculate that MTX constricts arterioles, increasing R_µcirc by making that component longer [i.e., as terminal arterioles become less than 60 µm in diameter, they functionally become part of the microcirculation, according to our comparison (21) with the data of Davis et al. (5)] and increasing R_A-Res by reducing arteriolar caliber (i.e., larger arterioles also constrict but remain >60 µm in diameter).

As shown in Table 1, the relative compliance ratios (i.e., C_V-Res to C_A-Res) were 22 for control conditions and for MTX administration. These values are consistent with previous estimates (11, 16, 17) and support the validity of our reservoir analysis (20). The value of the ratio for NP administration (i.e., 12) was less, perhaps because of an increase in C_A-Res due to the reduction in mean P_Ao.

As illustrated in Fig. 4 and Fig. 5, top, both the administration of NP and MTX decreased LV stroke work, relative to the control value. With NP infusion, this implies that LV systolic pressure decreased even more than stroke volume increased. With a bolus of MTX, this implies that stroke volume decreased even more than LV systolic pressure increased. The energy dissipated as blood flows through each serial resistance can be calculated by integrating the dissipation of power (see Fig. 3), which is the pressure difference across the resistance multiplied by flow or, equivalently, the square of flow multiplied by the resistance (Q² x R). As shown in Table 3, under control conditions, the energy dissipated by the R_Lrg-A (60 mJ) is comparable with that of the R_µcirc (76 mJ) and is half the energy dissipated by the R_A-Res (144 mJ), although the magnitude of the R_Lrg-A is only 10% of the R_µcirc and 5% of the R_A-Res (see Table 2). With NP, the LV stroke work decreased 25% relative to the control value (from 298 to 221 mJ). Dissipation by the R_Lrg-A increased by 50% (from 60 to 88 mJ) and became comparable with the dissipation by the R_A-Res (82 mJ, down from 144 mJ, a 43% decrease) and approximately twice the dissipation by the R_µcirc (38 mJ, down from 76 mJ, a 50% decrease). Thus, with vasodilation by NP, the absolute and relative energy losses due to dissipation by the R_Lrg-A became substantial and perhaps physiologically important.

Although the concept of an arterial reservoir is not new, no one had previously demonstrated quantitatively how the energy produced by LV systolic ejection is stored as potential energy and subsequently dissipated during diastole. Our rationale to determine the potential energy is simple. In the steady state, the energy dissipated by all the resistive components (pink solid line, Figs. 3 and 4) must equal the LV stroke work (black line) at the end of the cycle. We define potential energy as the undissipated energy remaining at the end of systolic ejection, the vertical difference between the black line and the pink line, and define the arterial reservoir function as the percentage fraction of total stroke work that remains as potential energy at end systole. As shown in Fig. 6, arterial reservoir function decreases with the infusion of NP (40%, down from 60%) and increases with MTX (80%).

Based on Frank's concept of the windkessel (reservoir), we calculated the pressure (P_A-Res) that would prevail in the reservoir, assuming that the change in pressure was equal to the change in volume, divided by the compliance (21). Having thus calculated P_A-Res, we subtracted it from measured P_Ao and found that the difference (previously called excess pressure; now called wave-related pressure, P_A-Wave) was proportional to aortic inflow (Q_Ao). In the anesthetized dog, P_A-Wave was shown to be entirely due to forward-traveling waves generated by the LV (21) and due to the combination of forward- and backward-traveling waves, when such were generated by a counterpulsation balloon (21). Therefore, from these and other observations (unpublished data), we have concluded that P_Ao = P_A-Res + P_A-Wave, where P_A-Wave equals the pressure drop across R_Lrg-A, which is numerically equal to characteristic impedance (22).

Of course, this interpretation of characteristic impedance differs from the conventional one. Westerhof et al. (24) supplied the classical electrical circuit diagram of the three-element windkessel (a.k.a. the "westkessel"). Although they and others represent characteristic impedance as a resistance and acknowledge that impedance has units of resistance, they do not consider it to be truly a hydrodynamic resistance, i.e., that it dissipates energy. [In contrast, also see Fogliardi et al. (7), where they do equate characteristic impedance with a true resistance.] Earlier our laboratory (22) showed that characteristic impedance was numerically identical to the linear slope of the relation between wave-related (excess) pressure and flow, thus demonstrating fundamentally resistive behavior. In the present article, we demonstrate that R_Lrg-A (i.e., characteristic impedance) and its resultant energy dissipation are measurable and can increase substantially with NP administration.

Some people have argued that the "line loss" of the aorta is negligible. To be sure, careful measurements of the decrease in mean aortic pressure along its length show a decrease of only a few millimeters of mercury. However, we suggest that this number is more a function of mean flow than of peak ejection rate. Preliminary efforts to measure the pressure drop associated with water flowing at peak ejection rates through aorta-sized plastic tubes have indicated pressure differences of the same order of magnitude as predicted [i.e., 25 mmHg at 15 l/min; see Fig. 2 in Wang et al. (22)].

Ohmic or "waterfall" behavior? We have analyzed the systemic circulation, assuming that it can be considered to be a series network of resistors, and we have defined that network by determining arterial and venous asymptotic pressures, which imply waterfall phenomena. Ohmic behavior is not obviously consistent with waterfall behavior. Although the resolution of this question is not clear, the systemic circulation does behave as if it is ohmic, and it also behaves as if there is a waterfall phenomenon. Our best evidence for ohmic behavior is how well our model predicts the pressure drops across serial elements in the systemic circulation. As shown in Fig. 7 in Wang et al. (21), the pressure drops across the serial elements in our model agree very well with the direct observations of Davis et al. (5), who made micropuncture measurements of pressure in the hamster cheek pouch. With respect to waterfall behavior, we are not the first to make this claim. Magder and his associates (18, 19) have described Starling-resistor behavior in skeletal muscle, and investigators (6, 16, 17) who tried to estimate mean circulatory filling pressure (MCFP) arrested the heart briefly (15 s) and observed an asymptotic decrease of arterial pressure and an asymptotic increase in venous pressure.

View larger version (19K): [in this window] [in a new window]   Fig. 7. A comparison of the arterial reservoir effects with administration of a profoundly vasodilating dose of NP (left) and a vasoconstricting dose of MTX (right). See DISCUSSION.

A-

Effects of the arterial reservoir on the impedance spectra. The relative importance of the arterial reservoir (i.e., windkessel) is greatest with MTX and least with NP (see Fig. 7; also note _A in Table 1). The top two rows show the pressure and flow rate in the ascending aorta. In the first row, P_Ao is shown in black, calculated P_A-Res in green, and calculated P_A- as a dashed horizontal line. Note that P_A-Res is minimal with NP but is almost identical to P_Ao with MTX. In the second row, Q_Ao is shown in black and calculated P_A-Wave in red. Note that P_A-Wave is scaled so that its peak value corresponds to the peak value of Q_Ao, thus emphasizing the similarity in their waveforms.

The next two rows show the impedance spectra, modulus and phase, calculated for the different pressures and flows. Impedance is calculated from measured values, P_Ao/Q_Ao (black), reservoir pressure, P_A-Res/Q_Ao (green), and wave-related pressure, P_A-Wave/Q_Ao (red). With NP, P_A-Res is very small, and so the impedance based on P_A-Wave is very similar to the impedance based on P_Ao. Also note that the modulus of the impedance is effectively constant at all frequencies and equal to the characteristic impedance. This follows from the relatively very small value of P_A-Res and from the close correspondence between P_Ao and P_A-Wave with NP. With MTX, the modulus of impedance on the basis of P_Ao shows the more common behavior of increasing substantially as the frequency decreases toward the fundamental frequency. Note, however, that the modulus based on P_A-Res is very similar to the measured modulus, and the modulus based on P_A-Wave, which is the difference since P_Ao = P_A-Res + P_A-Wave, is relatively constant for all frequencies and again equal to the characteristic impedance.

The fifth (Fig. 7, bottom) row shows measured Q_Ao plotted against measured P_Ao. With NP there is a very high correlation between P_Ao and Q_Ao (r² = 0.97), indicating that almost all the variance in Q_Ao is explained by P_Ao. Since P_Ao = P_A-Res + P_A-Wave and we have seen that P_A-Wave Q_Ao, we conclude for NP that P_Ao is approximately equal to P_A-Wave and the effect of P_A-Res is negligible. In contrast, with MTX, the correlation is very poor (r² = 0.05), indicating that virtually none of the variance in Q_Ao is explained by P_Ao. Thus we conclude that P_Ao is approximately equal to P_A-Res and that the effect of P_A-Wave is very small.

These observations suggest that the commonly seen increase in the modulus of measured impedance as the frequency decreases to the fundamental frequency (the input impedance) is, in fact, a result of treating the reservoir pressure as part of the aortic wave instead of a separate time-varying component of pressure induced by the windkessel mechanism. This observation is consistent in all of the analyses that we have performed but needs to be tested and explored more fully because of its implications in the interpretation of impedance spectra.

With the administration of NP, the nearly linear relationship between P_Ao and Q_Ao has been interpreted as evidence of improvement in ventriculo-arterial coupling (i.e., that reflected waves had become negligible) (3). However, our analysis suggests, instead, that the nearly linear relationship between P_Ao and Q_Ao is due to the reservoir effect having become negligible.

Possible clinical implications. With respect to the treatment of hypertension, an important clinical implication of our approach pertains to characteristic impedance (i.e., R_Lrg-A). There is broad agreement that characteristic impedance is elevated in the presence of systolic hypertension (13, 14). If characteristic impedance is elevated, more wave-related pressure must be generated to accelerate the stroke volume, thus increasing the load on the LV and leading to systolic hypertension. This understanding might possibly lead to the development of novel and more useful therapeutic approaches.

	GRANTS

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The study was supported in part by the Canadian Institutes for Health Research (Ottawa) sequential-operating Grants MOP-57801 and MOP-67223 (to J. V. Tyberg, N. G. Shrive, and I. Belenkie).

	ACKNOWLEDGMENTS

 
We acknowledge with gratitude the incisive hemodynamic insights provided by Dr. I. Belenkie and the outstanding technical skill of Cheryl Meek.

	FOOTNOTES

 

Address for reprint requests and other correspondence: J. V. Tyberg, Cardiac Sciences and Physiology & Biophysics, Univ. of Calgary, Health Sciences Ctr., 3330 Hospital Dr. NW, Calgary, AL, Canada T2N 4N1 (e-mail: jtyberg{at}ucalgary.ca)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

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