Pulse Pressure, Arterial Compliance and Wave Reflection Under Differential Vasoactive and Mechanical Loading
Cardiovascular Engineering An International Journal ISSN 1567-8822 Volume 10 Number 4 Cardiovasc Eng (2010) 10:170-175 DOI 10.1007/s10558-010-9107y
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Author's personal copy Cardiovasc Eng (2010) 10:170–175 DOI 10.1007/s10558-010-9107-y
ORIGINAL PAPER
Pulse Pressure, Arterial Compliance and Wave Reflection Under Differential Vasoactive and Mechanical Loading John K-J. Li • Ying Zhu • Pamela S. Geipel
Published online: 10 December 2010 Ó Springer Science+Business Media, LLC 2010
Abstract Similar pulse pressure increases and flow reductions have been reported by many investigators, despite dissimilar forms of arterial loading applied. Increased vascular load is most commonly observed due to mechanical and vasoactive interventions. The present study intended to differentiate the hemodynamic contributions of these two forms of arterial loading at closely matched blood pressure levels. To accomplish this, proximal aortic characteristic impedance (Zo), total arterial compliance (C), peripheral vascular resistance (Rs) and time-domain resolved forward (Pf) and reflected (Pr) waves were obtained in six anesthetized, thoracotomized and ventilated dogs. Acute loading was accomplished by brief descending thoracic aorta (DTA) occlusion or by intravenous bolus infusion of methoxamine (MTX:5 mg/ml) Systolic pressure increases were matched to a similar extent. Results showed that pulse pressures were drastically increased, reflecting large increases in wave reflections and decreases in arterial compliances. Changes in Zo, Rs and C were quantitatively different between the two forms of loading. DTA occlusion primarily increased Zo and Rs with a concurrently large reduction in C. MTX infusion significantly increased small vessel Rs to the same extent as DTA occlusion, but with a slight decrease in C secondary to an increase in pressure, with Zo unchanged. Examination of dynamic loading showed similar increases in reflection coefficients, but Pf and Pr were qualitatively different. We conclude that vasoactive methoxamine infusion provides primarily an increased resistive load, while mechanical
J. K-J.Li (&) Y. Zhu P. S. Geipel Cardiovascular Engineering Lab, Department of Biomedical Engineering, Rutgers University, 599 Taylor Rd, Piscataway, NJ 08854, USA e-mail:
[email protected]
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DTA occlusion provides an increased complex load to the left ventricle. These loads also occur earlier and variably during ventricular ejection. Keywords Ventricular afterload Arterial compliance Pulse pressure Wave reflection Methoxamine infusion Aortic occlusion
Introduction The afterload which opposes ventricular ejection is an important hemodynamic quantity. Changing afterload affects the ventricle’s function as a pump and alters pulse transmission characteristics in the arterial system (Li 2000). Thus, it is important to be able to quantify this load and differentiate its various contributors. The complexity of this afterload is attributed to the differences in the geometric and elastic properties of arteries at differing anatomic sites and the varied extent of vasoactivities of the vascular beds. These become clear from measurements of hemodynamic parameters such as pressure, flow, and diameter. To understand the behavior of the entire arterial tree from these measurements, however, requires considerable effort. Thus, models of the arterial system have been proposed to identify features of the tree. The threeelement windkessel model has been widely used, because of its simplicity and its reasonable approximation to the input impedance of the arterial system (Noordergraaf 1978). Input impedance is an important determinant of ventricular afterload (e.g. Li 2004). Changes in this impedance alter the matching characteristics between the ventricle and the arterial system. The present investigation examines how the different components of input impedance, namely, the characteristic impedance (Zo), arterial compliance (C)
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and peripheral resistance (Rs), contribute to this load during acute pressure loading induced mechanically with descending thoracic aorta (DTA) occlusion and vasoactively with methoxamine infusion, and to see how these changes modify the pressure and flow waveforms in terms of their forward and reflected components.
Methods Theoretical Analysis For the time domain identification of the three-element windkessel model parameters, the peripheral resistance can be obtained as mean aortic pressure (P) to mean aortic flow (Q) to a good approximation. The diastolic aortic pressure decay constant, s, can be calculated from a monoexponential fit to the sampled points of the aortic pressure decay from end-systole (Pes) to end-diastole (Pd) during the diastolic period (td), such that Pd ¼ Pes etd=s
ð1Þ
and since s ¼ RS C
ð3Þ
where Pd is the aortic diastolic pressure. Measured pressure and flow waveforms in the arterial tree can be considered as the sum of their forward (f), and their reflected (r) pressure (P) and flow (Q) waves, i.e. P ¼ Pf þ Pr
ð4Þ
Q ¼ Qf þ Qr
ð5Þ
The ratio of reflected wave to the forward wave defines the reflection coefficient, C¼
Pr Qr ¼ Pf Qf
Experiments were performed on six mongrel dogs. The dogs were of either sex and of body weights between 20 to 25 kg. Each animal was anaesthetized with 30 mg/kg Nembutal and placed on a respirator. A left thoracotomy was performed at the fifth intercostal space to expose the heart and the great vessels. The ascending aorta was isolated for placement of a cuff-type electromagnetic flow probe for measurement of aortic flow. A catheter-tip pressure transducer was advanced from the femoral artery to the immediate vicinity of the flow probe for simultaneous measurement of aortic pressure. A standard lead electrocardiogram (ECG) was also recorded. The frequency response of the pressure transducer was flat to well beyond 100 Hz. The flowmeter output low-pass filter was 3 dB down at 100 Hz. At this setting the amplitude response was flat to within ± 5% to 30 Hz with a linear phase shift. The flow probes were statistically calibrated against known volume flow rates in excised vessels. Simultaneous recordings of aortic pressure, flow and ECG were made on a four channel recorder and subsequently sampled at 10 ms intervals for computer analysis.
ð2Þ
the compliance can be easily calculated. Finally the characteristic impedance Zo can be estimated from the early ejection phase of systole, as before (Li 1986; Lucas et al. 1988), Zo ¼ ðP Pd Þ=Q
Animal Experiment
ð6Þ
The negative sign indicates that reflected pressure and flow are 180° out of phase or that an increase in reflected pressure wave decreases flow. The forward and reflected components of pressure can be resolved according to the relations, Pf ¼ ðP þ QZo Þ=2
ð7Þ
Pr ¼ ðP QZo Þ=2
ð8Þ
These expressions permit the subsequent resolution of the forward and reflected waveforms (Li 1986, 2000; Geipel and Li 1987).
Protocol The steady state signals prior to interventions were used to serve as control signals. Mechanical loading was accomplished by a brief total occlusion (10 s) of the descending thoracic aorta (DTA) at approximately 3–5 cm distal to the aortic arch by a hemostat. The signals normally returned to control within 30 s after release. The occlusion was repeated after 5 min. When the control level was again established, vasoactve loading began via intravenous bolus infusion of methoxamine (5 mg/ml). The dose was chosen such that systolic pressure increases were about the same as during DTA occlusion. This was necessary for later comparative analysis of mechanical and vasoactive loadings at matched blood pressure levels. The peak steady state response was recorded. Data Analysis Recorded pressure and flow waveforms were sampled at 10 ms intervals. In the time domain, Zo was obtained from the average of the instantaneous ratios of aortic pressure to flow during the first 60 ms of ejection. The diastolic portion of the aortic pressure was fitted to a mono-exponential (correlation coefficient r [ 0.93) to obtain the pressure decay time constant, s, so that arterial compliance, C, could be computed. Once the forward and reflected waves were resolved from Eqs. (7) and (8) above, they were input to a discrete
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Fourier program to obtain harmonic moduli and phases for the calculation of the reflection coefficient for the first five harmonics. All data were pooled and statistical analysis was performed to determine the level of significance (t-test).
Results Hemodynamic results were tabulated as seen in Table 1, listing the mean values and the standard deviations of the measured variables, including heart rates, systolic, diastolic, and mean aortic blood pressures and mean aortic blood flows at control, during mechanical loading via descending aortic occlusion and vasoactive loading via methoxamine infusion. No significant difference was found among the heart rates, but pressures increased significantly during both forms of pressure loading, as expected. The extent of the systolic pressure increases as designed was about the same level for the occlusion and methoxamine cases. Typical waveforms of the analyzed signals are presented in Fig. 1. DTA occlusion shows an elevated pulse pressure and a distinctive dicrotic notch in the pressure wave and a reduced flow compared to its control (Table 1). MTX exhibits a slow rise to a high peak pressure, which occurs late in systole, and a large pulse pressure. Flow is slightly decreased in MTX than in control (Table 1). There is however, distinctive differences in the waveforms and the resolved components between DTA occlusion and MTX infusion, despite their similar responses. This is seen from Table 2. The time domain identified model parameters, i.e. Zo, C and Rs are summarized in Table 2. Both mechanically and vasoactively induced pressure loading increased Rs, and decreased C. C was significantly decreased as compared to control during DTA occlusion, but much less so during the methoxamine infusion. The extent of decrease in C was different between the two forms of ventricular loading. Zo was increased during DTA occlusion, but unchanged during MTX infusion. The forward and reflected pressure waves are also shown in Fig. 1. The forward pressure peaks in mid systole and is larger in magnitude during DTA occlusion. The
Fig. 1 Simultaneously measured tracings of ascending aortic pressure and flow from one experiment for control (left panel), aortic occlusion (middle panel), and methoxamine infusion (right panel). Corresponding time-domain resolved forward (dotted line) and reflected (dashed line) waves are also shown
Table 2 Computed lumped parameters of the arterial system for the mechanical loading (DTA occlusion) and vasoactive loading (MTX infusion) conditions as compared to control Zo (mmHg/ml/s)
Rs (mmHg/ml/s)
C(ml/mmHg) 0.453 ± 0.189
Control
0.199 ± 0.016
4.14 ± 0.837
DTA
0.259 ± 0.037**
8.24 ± 2.12**
0.176 ± 0.042**
MTX
0.187 ± 0.070#
7.90 ± 3.02*
0.353 ± 0.143#
* Indicate p \ .05, ** p \ .01 compared to control #
Indicate p \ .05, DTA compared to MTX
Zo = characteristic impedance of the proximal aorta, Rs = total peripheral resistance and C = total arterial compliane
reflected pressure also peaks in mid systole, but slightly later, and is also larger than control. Time to peak reflected pressure is shorter than in control. The forward pressure during MTX also increased in magnitude. The reflected pressure is considerably larger and oscillates with a secondary peak in late systole. In contrast, control Pf peaks earlier in systole and falls off more gradually, while Pr peaks at late systole and does not dip. The reflection coefficients for the first five harmonics are shown in Fig. 2. Pressure loading increased the magnitudes of the reflection coefficient for all harmonics. The increase is most pronounced at the fundamental frequency where
Table 1 Summary of measured hemodynamic variables for control, mechanical loading via descending thoracic aortic occlusion (DTA) and vasoactive loading via intravenous bolus infusion of methoxamine (MTX) HR
Ps
Pd
P
Q
Control
117.0 ± 13.8
103.6 ± 11.4
78.0 ± 11.2
91.2 ± 12.4
DTA
121.1 ± 19.1
153.0 ± 20.8**
112.6 ± 19.5**
131.8 ± 20.1**
16.5 ± 2.9**
MIX
108.5 ± 15.9
158.0 ± 27.1**
128.2 ± 20.8**
143.8 ± 22.5**
20.0 ± 6.6
Pressures are in mmHg and flow in ml/s ** p \ .01 as compared to control
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22.4 ± 2.8
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Fig. 2 Reflection coefficients as a function of frequency. Both descending aortic occlusion (DTA; circle) and methoxamine infusion (MTX; triangle) increased the coefficients for all harmonics. Notice the much more pronounced oscillations during loading
the mean reflection coefficients of 0.77, 0.68 and 0.39 were found for MTX, DTA and control respectively. At higher frequencies, the reflection coefficients remain large and are more oscillatory as compared to control. These frequency domain findings correspond to the time domain changes.
Discussion Cardiac muscle shortening is dependent on its preload and afterload (Braunwald 1977; Du et al. 2001; Li 2004). These loads have opposite effects: increased preload alone increases shortening, as dictated by the Starling’s law of the heart; increased afterload alone however, decreases muscle shortening, as suggested by the Hill’s equation. Thus, just what kind of afterload the ventricle ejects against has been of considerable interest. Input impedance of the systemic arterial tree is an important determinant of afterload (Pepine et al. 1979; Gundel et al. 1981; Murgo et al. 1981). We have investigated the contributions of its components to the load facing the ventricular ejection, during mechanical loading and during vasoactive loading. There are several means for altering the load to cardiac ejection. These can be from mechanical, neural or pharmacological interventions. The present investigation differentiates the mechanical and pharmacological means of pressure loading the left ventricle. Methoxamine, a vasopressor, can raise blood pressure to a great extent (Imai et al. 1961). It acts primarily on small vessels in a distributed manner. It is a preferential alpha one agonist, constricting the arterioles and capacitance vessels (Zandberg et al. 1984). Its action causes unfavorable hemodynamic effects by altering impedance matching, primarily through increased peripheral resistance. Although the compliance is decreased, it is not statistically significantly different from control. The decrease in arterial compliance is secondary to an increase in pressure.
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Significantly increased pulse pressure is indicative of reduced compliance, particularly an increase in systolic blood pressure, as observed in systolic hypertension (Berger and Li 1990; Li et al. 1994; Li 2000; Safar and Laurent 2003). The inverse relationship between pulse pressure and arterial compliance has been studied by several investigators (e.g. Ferguson and Randall 1986; Stergiopoulos et al. 1999). Drastically elevated mean blood pressures, as observed here during loading, would alter such relationship. The determinants of pulse pressure are many, not all attributed to the arterial system through the interplay of arterial compliance and peripheral resistance. As pressure and flow are generated by the heart, cardiac contraction is also a main contributing factor. Compliance, as we have noted previously, is a function of arterial pressure (e.g. Randall 1982; Li and Zhu 1994). Such pressure-dependent compliance changes can be more accurately quantified with a nonlinear arterial system model (Li et al. 1990; Matonick and Li 2001) and should be further explored. The main effects of mechanical loading of the ventricle through descending aortic occlusion are regional, residing primarily in the aorta (Stokland et al. 1980). Aortic characteristic impedance increased considerably, with a large concurrent decrease in arterial compliance. Since a large portion of the systemic arterial compliance is in the aorta, the site of occlusion will determine the level of ventricular loading, as found by other investigators (Van den Bos et al. 1976). These two methods of raising aortic blood pressure have been used as experimental models of acute hypertension. Our findings could clarify the hemodynamic mechanisms promoting this diseased state. Both form of loading have consistently produced increased systolic and diastolic blood pressures, or the so called combined hypertension. The increases in peripheral resistance are about the same in the two forms of loading (99% for DTA occlusion and 91% for MTX infusion). But only in DTA occlusion cases, the compliance is decreased significantly, by about 61%. This may be due to the fact that arterial compliances normally contributed by the aorta and systemic arteries distal to the DTA occlusion site were effectively removed. In isolated systolic hypertension (Li et al. 2007) which occurs predominantly in the elderly, a systolic pressure greater than 165 mmHg and a diastolic pressure of about normal, a large decrease in compliance (greater than 75%) and a smaller but significant increase in peripheral resistance (about than 25%) are found (Berger and Li 1990). It is clear from the present study that the left ventricle faces an increased steady state load, mainly from the periphery, i.e. small resistance and capacitance vessels during ejection in the methoxamine induced hypertension cases. Whereas, the ventricle faces a changing complex load, i.e. increased aortic characteristic impedance, decreased large vessel compliance and increased peripheral
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resistance during mechanical loading through descending aortic occlusion. The increased wave reflections during the ejection period in general decrease ventricular outflow. This is particularly true in the case of DTA occlusion; flow is significantly decreased by about 26%. This decrease was only about 11%, and statistically insignificant during methoxamine infusion, despite similar increases in peripheral resistance. This suggests that pressure loading that alters both components of the complex load is perhaps more detrimental to ventricular function. Since aortic pressure serves as the coronary perfusion pressure, particularly during diastole (Li 2000), whether increased aortic pressure due to the two types of loading may lead to differential coronary flow (Ohtsuka et al. 1987) or its resistance-compliance behavior (Liao and Li 2005) is unclear. The magnitude of the reflected pulse waves increased by about 2fold during the interventions. Since wave reflections are energetically wasteful (Li 1989), such increases, especially during the ejection phase, have the effects of retarding flow. The reflection coefficients remain high at high frequencies, indicating that the local reflections at aortic branching junctions are large, due to large mismatching of characteristic impedances of branching vessels (Li et al. 1984). The forward components are also increased during loading, reflecting the changing cardiac state. Ventricular performance under such circumstances can be evaluated from its load sensitivity, as we have shown previously (Geipel et al. 1989). Afterload reduction with vasodilator therapy is still a popular means of treating cardiovascular diseases (Cohn and Franciosa 1977; Pepine et al. 1979; Gundel et al. 1981; Yin et al. 1983; Brin and Yin 1984; Vogt et al. 1988; Li 2000), particularly the hypertensive. It is thus important to be able to differentiate this load and reduce its magnitude by either decreasing wave reflections, or selectively improving large vessel compliance and decreasing peripheral resistance, or both.
Conclusion Arterial load reduction with drug therapy and by surgical means are still popular means of treating vascular diseases. The present investigation provided a means and differentiated the hemodynamic mechanism of the increased load due to mechanical or vasoactive alterations. Unloading should then be accompanied by either appropriately decreasing wave reflections, or selectively improving large vessel compliance and decreasing peripheral resistance or both. Acknowledgments This work was supported in part by a grant from the American Heart Association and New Jersey Commission on Spinal Cord Research.
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