ORIGINAL PAPER

Pulse Pressure, Arterial Compliance and Wave Reflection UnderDifferential Vasoactive and Mechanical Loading

John K-J. Li • Ying Zhu • Pamela S. Geipel

Published online: 10 December 2010

� 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 pres-

sure 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 con-

currently 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

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 dif-

ferences in the geometric and elastic properties of arteries at

differing anatomic sites and the varied extent of vasoactiv-

ities of the vascular beds. These become clear from mea-

surements 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 three-

element 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 ven-

tricular 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)

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: johnkjli@rci.ruters.edu

123

Cardiovasc Eng (2010) 10:170–175

DOI 10.1007/s10558-010-9107-y

and peripheral resistance (Rs), contribute to this load

during acute pressure loading induced mechanically with

descending thoracic aorta (DTA) occlusion and vasoac-

tively 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 monoexpo-

nential fit to the sampled points of the aortic pressure decay

from end-systole (Pes) to end-diastole (Pd) during the dia-

stolic period (td), such that

Pd ¼ Pese�td=s ð1Þ

and since

s ¼ RSC 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 P� Pdð Þ=Q 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,

C ¼ Pr

Pf¼ �Qr

Qfð6Þ

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 Pþ QZoð Þ=2 ð7Þ

Pr ¼ P� QZoð Þ=2 ð8Þ

These expressions permit the subsequent resolution of the

forward and reflected waveforms (Li 1986, 2000; Geipel

and Li 1987).

Animal Experiment

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 iso-

lated 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 simulta-

neous measurement of aortic pressure. A standard lead

electrocardiogram (ECG) was also recorded. The fre-

quency 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 subse-

quently sampled at 10 ms intervals for computer analysis.

Protocol

The steady state signals prior to interventions were used to

serve as control signals. Mechanical loading was accom-

plished 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 repe-

ated after 5 min. When the control level was again estab-

lished, 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 com-

parative 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 por-

tion 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

Cardiovasc Eng (2010) 10:170–175 171

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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 per-

formed 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 com-

pared 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

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 sec-

ondary 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 22.4 ± 2.8

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

Fig. 1 Simultaneously measured tracings of ascending aortic pres-

sure 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)

Control 0.199 ± 0.016 4.14 ± 0.837 0.453 ± 0.189

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

172 Cardiovasc Eng (2010) 10:170–175

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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 pharmaco-

logical 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 unfavor-

able hemodynamic effects by altering impedance match-

ing, 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.

Significantly increased pulse pressure is indicative of

reduced compliance, particularly an increase in systolic

blood pressure, as observed in systolic hypertension (Ber-

ger 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 investiga-

tors (e.g. Ferguson and Randall 1986; Stergiopoulos et al.

1999). Drastically elevated mean blood pressures, as

observed here during loading, would alter such relation-

ship. 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 pre-

dominantly 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

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

Cardiovasc Eng (2010) 10:170–175 173

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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 sug-

gests 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 perfu-

sion 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, espe-

cially 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 mis-

matching 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 resis-

tance, 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 differenti-

ated 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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