451
Input Impedance of the Systemic Circulation in Man
WILMER W.
NICHOLS, C. RICHARD CONTI, WILLIAM E. WALKER, AND
WILLIAM R.
MILNOR
SUMMARY To determine the systemic input impedance, pulsatile pressure and flow were measured in the ascending aorta in
16 human subjects who were undergoing diagnostic cardiac catheterization. Blood flow was measured with a catheter-tip electromagnetic velocity meter, and pressure with an external transducer
connected with the fluid-filled lumen of the catheter. Five subjects were found to have no evidence of cardiovascular disease
(group A, mean age 32 ± 2 years, mean aortic pressure 97 ± 4
mm Hg). Seven had clinical and angiographic signs of coronary
arterial disease, and mean pressures less than 100 mm Hg (group
B, mean age 48 ± 2 years). Four subjects had signs of coronary
disease and mean pressures greater than 100 mm Hg (group C,
mean age 48 ± 3 years). The frequency spectra of impedance
were qualitatively similar in all three groups and resembled those
previously observed in the canine aorta. Characteristic impedance
was lower in the normal subjects (group A, average 53 dyn sec
cm"5) than in the subjects with coronary artery disease (groups B
and C, average 129 dyn sec cm 5 ) . Among the subjects with
coronary disease, characteristic impedance was higher in the hypertensive subjects (group C, average 202 dyn sec cm"5) than in
those with lower mean pressures (group B, average 95 dyn sec
cm"5). External left ventricular work per unit time (hydraulic
power) averaged 1715 milliwatts (niYV) in group A, 1120 mVV in
group B, and 2372 mVV in group C. Cardiac outputs were within
normal limits in all subjects, but tended to be lower in group B
than in group C. These results suggest that the subjects of group C
were better able to meet the increased energy demands imposed
by an abnormally high aortic input impedance. Further investigation is needed to learn whether the high impedances in subjects
with coronary disease represent an increase with age and transmural pressure alone, or whether some additional factor is involved. The data on relatively normal subjects permit a tentative
definition of the normal limits for aortic input impedance in man:
26-80 dyn sec cm"5.
CLINICAL investigations of cardiovascular function have
until recently been based on what might be called "steady
flow hemodynamics." in that mean blood flow (cardiac
output) has been measured, rather than pulsatile flow.
The time-varying contours of pressure pulsations have
been studied intensively, but the lack of methods for
measuring instantaneous blood flow in human subjects
prevented similar studies of flow waves. The first direct
measurements of pulsatile flow in the ascending aorta of
man were obtained with a perivascular electromagnetic
probe placed around the vessel at the time of surgery.U2
Advances in design have now made it possible to place the
probe at the tip of a cardiac catheter that can be inserted
into a peripheral vessel and then advanced to the site
where the flow is to be measured.3"5 As a result, pulsatile
pressure and flow can be measured simultaneously during
clinical aortic catheterization. and from these data the
input impedance of the arterial tree and the total hydraulic
energy required to move blood into the system can be
calculated. The input impedance of an arterial system,
defined as the ratio of pressure harmonics to flow harmonics at the entrance to the system, depends on the dimensions and viscoelasticity of the artery involved, on the
physical properties of the blood, and on waves reflected
from more distal parts of the arterial tree. Measurements
of aortic input impedance provide information about the
physical state of the arteries, an assessment of the external
"afterload" faced by the left ventricle.6"8 and complete
data for calculating the external work of the ventricle.9""
The present investigation was undertaken to determine
the aortic input impedance spectra, and the hydraulic
power associated with aortic blood flow, in human subjects who had no cardiovascular disease, to the extent such
individuals could be found among patients referred to a
diagnostic catheterization laboratory, and in patients with
coronary arterial disease. Studies of this kind have been
reported previously on only a few subjects.1'2- 12> 13 Our
results provide a tentative definition of the normal impedance spectrum, based on five relatively normal subjects,
and show higher values of impedance moduli in 11 patients with coronary arterial disease. The linearity of pulsatile pressure-flow relationships was tested in some of
these patients by measuring aortic impedance at different
heart rates.
From the Department of Medicine, University of Florida. College of
Medicine, Gainesville, Florida, and the Departments of Medicine and
Physiology, The Johns Hopkins University School of Medicine, Baltimore,
Maryland.
Supported in part by Grants 5 R01 HL 17717-02 and HL 12607 from
the National Institutes of Health.
Dr. Walker's present address is: Department of Surgery, Vanderbilt
University School of Medicine, Nashville, Tennessee.
Received July 14, 1976; accepted for publication October 23, 1976.
Methods
The observations reported here were made on adults
who were undergoing diagnostic cardiac catheterization.
Patients with evidence of congenital or valvular heart
disease were excluded, but the subjects were otherwise
unselected. The study was approved by the appropriate
institutional committees for clinical investigation, and informed consent was obtained from each patient. Sodium
pentobarbital (100 mg p.o.) was given prior to catheterization. Clinical and angiographic signs of coronary arterial
disease were found in 11 of the 16 patients studied. The
remaining five gave a history of nonspecific chest pain, but
had normal coronary angiograms. normal hemodynamics.
and no objective indications of cardiovascular disease.
Velocity of blood flow was measured with electromagnetic catheter-tip velocity transducers. A Mills catheter-tip
probe3'13"16, and flowmeter (model 275. S.E. Laborato-
452
CIRCULATION RESEARCH
ries. Feltham. Middlesex. England) were used in nine
cases. The frequency response of this system at the filter
settings used in this study, measured by applying an appropriate electrical input signal to the system," was constant in
amplitude (±5%) from 0 to 32 Hz. Phase shift was approximately linear and equivalent to a time delay of 17
msec. This response is adequate for accurate measurement
of pulsatile velocities in the human aorta because more
than 98% of the variance of the pulsations is included in
the first seven harmonics (unpublished observations). In
the seven other subjects, a Carolina probe flowmeter4' 17~19
was used (model 601D, Carolina Medical Electronics).
The dynamic response of this system was constant (±5%)
in amplitude from 0 to 14.5 Hz. with a time delay of 35
msec. The catheter containing the Carolina probe included
a flexible radiopaque tail19 extending 5 cm beyond the
velocity sensor. The tail was advanced through the aortic
valve and into the left ventricle, so that the sensing electrodes were at approximately the upper border of the
sinuses of Valsalva. This arrangement tends to stabilize
the probe in the central axis of the ascending aorta, eliminates the spurious signal that appears if the probe comes
to lie against the wall of the vessel, and minimizes artifacts
in the recorded velocity waveform caused by motion of the
catheter.
Measurements of blood flow were calibrated by one of
two different methods. In the first method, the velocity
calibration of the probe was determined in vitro in a
hydraulic model, and the internal cross-sectional area of
the vessel was measured by radiography at the time of
catheterization. Since the velocity profile of the ascending
aorta is relatively flat."- 2°-23 the product of measured velocity and cross section is volume of blood flow per unit
time. In the second method, the output signal of the
velocity meter was calibrated in cm3/sec by reference to a
simultaneous determination of cardiac output by the dyedilution method. A comparison of the two calibration
techniques in eight subjects showed excellent correlation
(r = 0.97. y = l.O&t - 0.33 liters/min. P < 0.001). The
velocity signal averaged over the last third of diastole was
taken to represent zero flow. Both kinds of velocity probe
have been shown to be thermally and electrically safe for
use in man.24 Under local anesthesia with 1 % lidocaine. a
sterilized velocity catheter was inserted percutaneously
into a femoral artery, or else through a brachial arteriotomy. With the aid of fluoroscopy. the velocity probe was
then positioned in the ascending aorta.
Aortic pressure was measured through the fluid-filled
lumen of the velocity catheter with a Millar strain gauge
transducer attached externally. The frequency response of
this sytem was determined by the free vibration technique.6 and the damped natural frequency in these studies
ranged from 27 to 36 Hz. with a damping ratio of 0.120.17.
The pressure and velocity signals were recorded on
analog magnetic tape (Hewlett-Packard, model 3960) and
later digitized at a sampling interval of 10 msec by an
analog-to-digital converter (Technical Instruments, model
400B). Data analysis was carried out on a programmable
calculator (Hewlett-Packard, model 9820A) which converted pressure and velocity data to Fourier series, applied
VOL.
40, No. 5,
MAY
1977
corrections for the measured dynamic responses of the
transducers, and computed aortic impedance and hydraulic power as functions of frequency. Input impedance
modulus at each harmonic frequency was computed by
dividing flow modulus into pressure modulus, and impedance phase by subtracting the phase angle of flow from
that of pressure." The impedance of 0 Hz. or "input
resistance," was calculated by dividing mean flow into
mean pressure. Impedances were not calculated for harmonics in which the pressure modulus was less than 0.6
mm Hg. or flow modulus less than 1 cm3/sec; these are
values that probably represent the noise levels of our
measurement systems. In effect, this procedure eliminated
all data above about 1 2 Hz. Characteristic impedance was
estimated by averaging impedance moduli between 2
and 12 Hz." Theoretically, characteristic impedance depends on the physical properties of the vessel under study,
while input impedances oscillate around the characteristic
value because of waves reflected from more distal
points."'7> 25'2(i The hydraulic energies associated with aortic blood flow were computed by methods previously reported.10
Results
The data obtained from each subject are summarized in
Tables 1-3. Clinical and angiographic signs of coronary
arterial disease were found in 11 of the 16 subjects studied, including two who had previously been treated surgically for coronary disease. No cardiovascular abnormality
was found in the other five individuals. For purposes of
comparison, the subjects were divided into three groups:
Group A ("normals"): Five subjects who had given a
history of nonspecific chest pain, but who were found to
have normal hemodynamics. normal coronary angiograms, and no objective indications of cardiovascular disease. Their ages ranged from 28 to 37 years and averaged
32 years. Mean aortic pressure averaged 97 ± 4 (SEM) mm
Hg.
Group B: Seven subjects with evidence of coronary
disease and mean aortic pressures <100 mm Hg. Their
average age was 48 years, and average aortic pressure 85
± 1 (SEM) mm Hg.
Group C: Four subjects with coronary disease, and
mean aortic pressures >100 mm Hg. Average age was 48
years, and average pressure 120 ± 5 (SEM) mm Hg.
Peripheral vascular resistance in these subjects was not
significantly different from that in group B. but cardiac
outputs were higher in group C than in group B.
The waveforms of the measured flow curves were similar to those previously recorded by electromagnetic flowmeters in the ascending aorta of the dog8 and
m a n i.2. i3. is. i6. is, 19 A n e x a m p l e from each group is
shown in Figures 1-3. Peak flows were much lower in
subjects with coronary artery disease (average in groups B
and C = 433 ± 27 ml/sec) than in the normal subjects
(average = 712 ± 53 ml/sec). The low peak flows in group
C were associated with prolonged ejection times (0.367 ±
0.022 seconds as compared to 0.313 ± 0.019 seconds for
the normals).
The average aortic input impedance spectrum for each
group is shown in Figures 4-6. Because of the large differ-
AORTIC INPUT IMPEDANCE/Mdiofr et al.
TABLE
453
1 Hemodynamic Data
Subject
1
2
3
4
5
Mean ± SEM
6
7
8
9
10
11
12
Mean ± SEM
13
14
15
16
Mean ± SEM
Age, sex
Diagnosis
Ejection fraction
37 M
32 M
28 M
35 M
30 M
32 ± 2
52 M
45 F
52 F
57 M
43 F
44 F
40 M
48 ± 2
48 F
42 M
57 F
46 M
48 ± 3
Normal
Normal
Normal
Normal
Normal
0.71
0.65
0.61
0.66
0.57
0.64 ± 0.02
0.60
0.74
0.53
0.65
0.30
0.23
0.34
0.48 ± 0.07
0.82
0.67
0.72
0.82
0.76 ± 0.04
CAD
CAD
CAD
CAD*
CAD
CAD
CAD
CAD
CAD
CAD
CAD*
Cardiac index (liters/min/m!)
Aortic radius (cm)
1.42
1.43
1.54
1.91
1.71
1.60 ± 0.10
1.42
1.45
2.6
5.3
2.5
3.0
2.9
3.3 ± 0.52
3.0
2.68
3.4
2.6
3.2
2.8
2.2
Heart rate
(beats/min)
2.8 ± 0.20
4.3
3.7
3.5
4.0
3.9 ± 0.20
2.28
2.06
2.23
2.10
1.90
2.11 ± 0.07
64
64
90
83
77
76 ± 5
79
81
98
69
80
97
102
3.4
1.15
1.34
1.60
1.43
1.39 ± 0.05
1.52
1.34
1.42
1.33
1.40 ± 0.06
Surface area (m2)
1.7
1.39
1.94
2.19
1.03
1.97
1.96
1.74 ± 0.15
1.86
1.86
1.99
1.70
1.85 ± 0.06
87 ± 5
79
75
59
80
73 ± 5
CAD = coronary artery disease.
' Post-saphenous vein bypass.
ences in heart rate, the aortic input impedance data were
grouped for averaging by frequency rather than harmonic
number. In all cases, the moduli of the input impedance
fell steeply from a high value at zero frequency (the input
resistance) to a minimum between 2.3 and 5.3 Hz. and
then rose to a less well defined peak at 6-9 Hz. In the
subjects of group A the minimum occurred at frequencies
between 2.5 and 4.2 Hz (average. 3.1); in group B,
between 2.3 and 5.3 Hz (average. 4.1); and in group C,
between 3.7 and 5.0 Hz (average. 4.5). The impedance
phase was negative (i.e., flow led pressure) for the first
three harmonics in 14 of the 16 cases. The phase angle was
positive for the higher harmonics, crossing zero at approximately the frequency of the modulus minimum.
The average characteristic impedances of the three
groups differed to a striking degree. The value in the
normal group was 53 ± 4 dyn sec cm*5, while the average
in group B was almost twice that value, and the average in
group C was 4 times the normal level (Table 2). Input
resistances were approximately the same in all groups.
Total hydraulic power associated with aortic blood flow
(including kinetic energy) averaged 1715 ± 240 milliwatts
(mW) in group A (Table 3). Average total power was
significantly lower in group B than in the normals (group
TABLE 2 Hemodynamic Data — continued
Aortic pressure (mm Hg)
Aortic flow
Mean (ml/
sec)
Mean
Systolic
Diastolic
Pulse
SV (ml)
Peak (ml/
sec)
86
92
97
102
106
103
111
116
114
126
67
73
80
84
86
36
38
36
30
40
94
172
62
77
72
632
917
628
684
698
97 ± 4
114 ± 4
78 ± 4
36 ± 2
95 + 20
712 ± 53
6
7
8
9
10
11
12
81
88
83
84
88
83
89
101
119
111
109
117
105
101
67
65
72
65
67
65
74
34
54
39
44
50
40
27
66
47
67
83
41
58
42
434
274
560
410
442
420
295
87
62
110
95
55
92
72
Mean
85+1.3
109 ± 3
68 ± 1.4
41 ± 3
58 + 6
405 ± 36
82 + 7
15
16
131
115
109
125
187
150
161
147
90
84
74
95
97
66
87
52
101
93
117
85
533
439
437
524
133
115
116
113
Mean
120 ± 5
161 + 9
86 ± 5
76 ± 10
99 ± 7
483 ± 26
119 ± 5
Subject
1
2
3
4
5
Mean
Ejection time
(sec)
R
0.267
0.380
0.320
0.297
0.300
114 ± 17 0.313 ± 0.019
1395
1298
1530
1218 ± 147
0.306
0.295
0.257
0.346
0.226
0.243
0.232
0.272 ± 0.017
1242
1860
1000
1180
2132
1204
1653
1390 ± 163
0.372
0.378
0.387
0.330
0.367 ± 0.022
133
115
96
182
93
105
92
1200
671
Zo
51
50
67
43
53
53 ± 4
± SEM
115
118
60
124
81
95
85
95 + 12
± SEM
13
14
1254
1484
1344 ± 49
273
160
214
95
202 ± 32
± SEM
R = input resistance in dyn sec cm
SV = stroke volume.
5
(mean aortic pressure divided by mean flow); Z,, = characteristic input impedance modulus (see text) in dyn sec cm 5 ;
CIRCULATION RESEARCH
454
TABLE
1
2
3
4
5
Mean
40, No. 5, MAY 1977
3 External Hydraulic Power of the Left Ventricle (Milliwatts)
Kinetic power
Potential power
Subject
VOL.
Steady flow
Pulsatile
1256
2233
1203
1436
1304
1486 ± 190
94
371
162
216
169
Combined
192 ± 37
Steady flow Pulsatile
1350
2550
1365
1652
1473
1678 ± 224 2.6
Total power
Combined
Steady flow
Pulsatile
power
2
37
39
1258
131
414
8
107
115
2241
176
15
1
14
1204
232
17
1
16
1437
11
179
1
10
1305
± 1 . 4 37 ± 18 39 ± 19 1489 ± 192 226 ± 50
Pulsatile/
Combined
total power
total power
1389
2655
1380
1699
1484
1715 ± 240
10
16
13
14
12
(%)
13 ± 1
± SEM
6
7
8
9
10
11
12
Mean
± SEM
13
14
15
16
Mean
947
762
1121
860
174
178
259
213
139
165
95
928 ± 75
175 ± 20
1220
1065
628
1021
940
1479
1278
767
1177
955
2330
474
381
1747
535
1697
283
1891
1916 ± 144 418 ± 55
1103 ± 90
1
13
1
5
2
36
3
31
1
14
1
7
1
5
1.4 ± 0 . 3 16 ± 5
2804
2128
2232
2174
2335 ± 158 4.0
3
21
4
28
6
53
3
33
± 0.7 34 ± 7
14
6
38
34
15
8
6
34 ± 8
929 ± 75
190 ± 24
1120 ± 94
17 ± 1.3
2828
2160
2291
2210
2372 ± 154
18
19
26
14
1222
1068
629
1013
17 ± 5
24
32
59
36
1135
861
187
183
294
244
153
172
100
948
763
495
2333
409
1751
588
1703
316
1894
1920 ± 143 452 ± 58
946
1516
1312
782
1185
961
17
19
19
18
20
15
10
19 ± 2.5
± SEM
A), and there was little overlap in the individual values.
Six of the seven subjects in group B had levels of hydraulic
power lower than any observed in the normal subjects.
Average total power in group C, however, was significantly higher than in group A. The group A average
probably overestimates the total power to be expected in
normal subjects, because of the relatively high cardiac
output (11.0 liters/min) in one individual (subject 2). If
this subject were excluded, the average would be 1,488
mW. Adopting this value for the normal average would
not alter the significance of the differences discussed
above. The "pulsatile component" of hydraulic power.10
which expresses the energy entailed in pulsations and
depends predominantly on the physical properties of the
aorta, constituted a larger part of total power in the subjects with coronary disease than in the normal subjects
(Table 3). Kinetic energy accounted for approximately
2% of the total power in all three groups.
LINEARITY
The valid representation of a continuous function such
as a pressure or flow wave by Fourier series requires that
these waves be periodic, and that the system be in a steady
state. These conditions are satisfied in the dog27 and there
is no reason to believe that they are not satisfied in man.
The use of Fourier analysis to define impedance also
assumes linearity of the system in which the pressure and
flow pulses are measured. Several techniques have been
employed to test this assumption in the arterial system of
the dog,28"32 and all of them have shown approximately
linear relationships. To test the linearity of the pressureflow relationships in the human aorta, we measured
impedance as the input waveforms were altered by electrically pacing the heart at different rates28- 31>32 in five subjects. Changes in the fundamental frequency, or heart
rate, in the range 1.4-2.6 Hz produced no consistent
changes in the impedance spectrum, demonstrating that
the system behaves in an almost linear fashion in this
FLOW MODULI
( Normal)
FLOW MODULI
(P<IOO)
0
(Normal)
2
4
6
8
Harmonics
FIGURE 1 Pressure and flow curves obtained with a Mills velocity
catheter in the ascending aorta of a young adult subject with normal
cardiovascular hemodynamics (group A). The bar graph shows the
harmonic content of the flow curve. The mean value of the curve is
represented by the dark-shaded bar at the 0 harmonic. Heart rate
was 1.07/sec and ejection time, 0.267 second.
2
4
Harmonics
FIGURE 2 Pressure and flow curves obtained with a Carolina
velocity catheter in the ascending aorta of a subject with coronary
artery disease (CAD) and normal blood pressure (group B). Heart
rate was 1.62/sec and ejection time, 0.243 second.
AORTIC INPUT IMPEDANCE/Mc/io/5 et al.
FLOW MODULI
(P>IOO)
1400
455
CAO,
P<IOO
(N = 7)
1200
300"
2
4
200-
Harmonics
FIGURE 3 Pressure and flow curves obtained with a Carolina
velocity catheter in the ascending aorta of a subject with coronary
artery disease (CA D) and elevated mean aortic pressure (group C).
Heart rate was 1.25/sec and ejection time, 0.378 second.
range. Pacing was carried out in at least one subject from
each group and an example from group A is shown in
Figure 7. The relatively small shifting of points on the
impedance spectrum with pacing appeared to be a random
variation associated with errors of measurement rather
than a systematic change related to the fundamental rates.
Another conceivable source of error lies in the respiratory swings of intrathoracic pressure, which might alter
aortic compliance and hence impedance. In all subjects
studied there were small variations in the pressure and
flow during the respiratory cycle. In four subjects pulses
were analyzed throughout the respiratory cycle, including
NORMAL
(N=5)
-1200-
m
E
> \
100-
4
6
Freq (Hz)
-
o
-2
FIGURE 5 Average aortic input impedance of seven subjects with
coronary artery disease (CA D) and mean aortic pressure less than
100 mm Hg (group B). The resistance was 1,390 ± 163 dyn sec
cm~b, and the characteristic impedance, 95 ± 12 dyn sec cm'5.
samples at maximum inspiration and expiration. The results of each test were similar to the example shown in
Figure 8. demonstrating that respiration per se does not
influence aortic input impedance.
300 \
1400
»
CAD, P>IOO
200-
4
6
Freq (Hz)
FIGURE 4 Average aortic input impedance of five normal adult
subjects (group A). The standard errors of the means of modulus,
phase, and frequency are represented by vertical and horizontal
bars. Z o is the estimated characteristic impedance (53 ± 4 dyn sec
cm~s) obtained by averaging the moduli above 2 Hz. The input
impedance modulus (lop panel) falls from a high value at zero
frequency (mean aortic pressure divided by mean flow, 1,218 ±
147 dyn sec cm~h) to a minimum and then rises to a maximum. The
impedance phase (lower panel), which is initially negative (flow
leads pressure), crosses zero in the neighborhood of the first modulus minimum and becomes positive (pressure leads flow).
-2J
FIGURE 6 Average aortic input impedance of four subjects with
coronary artery disease (CA D) and elevated mean aortic pressure
(group C). The resistance was 1,344 ± 49 dyn sec cm~b and the
characteristic impedance, 202 ± 32 dyn sec cm~b.
CIRCULATION RESEARCH
456
I4OO
PACING
• E 1200-
i 3003
200
100-
4
6
8
Freq (Hz)
2i
-2
(Normal)
FIGURE 7 Input impedance of the systemic circulation in a normal young adult at five different heart rates, showing no significant
change of impedance pattern. Resting heart rate was 84 beats /min,
and faster rates were produced by electrical pacing. The relative
constancy of the impedance patterns with changes of heart rate is
evidence that the arterial system is approximately linear. There is a
well defined minimum in the modulus at 2.5 Hz.
Discussion
NORMAL IMPEDANCES
The aortic input impedance spectra in our subjects
closely resemble the examples published previously by
other investigators.1-2- l2f 13 In spite of the variety of methods and subjects, certain distinctive features of the aortic
impedance spectrum have been noted consistently.
Impedance moduli are usually less than '/io the amplitude
of the input resistance, and there is a steep decline in
modulus at low frequencies to a minimum between 2 and 6
Hz. followed by a maximum at about twice the frequency
of the minimum, and only small oscillations of amplitude
at higher frequencies. The impedance phase angle is negative (denoting that flow leads pressure) at low frequencies,
becomes zero at approximately the frequency of the minimum modulus, and is usually positive at higher frequencies. A similar impedance pattern has been found in the
canine aorta. 6 ''• 9 although the impedance moduli are
greater in magnitude in that species. The difference in
magnitude is related to the general constancy of pulse
pressures in mammals of different size, combined with the
direct correlation between flow amplitudes and body size.
The spectrum of impedance vs. frequency is thus qualitatively the same for the human as for the canine aorta,
and conclusions that have been drawn from such spectra
on the basis of experiments in the dog presumably apply
also to man. Two examples may be cited. First, the fundamental harmonic for heart rates in the physiological range
falls on the steep, low frequency portion of the impedance
modulus curve. Consequently, at rates below about 120
beats/min. the slower the rate, the greater the external
VOL.
40, No. 5,
MAY
1977
cardiac work needed to eject a given pulsatile flow.10
Second, because the steepness of this curve depends on
reflections from the peripheral vascular tree, the vasomotor state of the peripheral vessels can influence significantly the impedance in the ascending aorta.6- 9-25
The characteristic impedance in our normal subjects (53
± 4 dyn sec cm"5) is lower than that in previously published human aortic impedance spectra.1- 2- 12> 13 but the
spectra previously reported were from subjects with cardiovascular disease. Patel and his colleagues2 measured
impedance in the ascending aorta in three subjects with
atrial septal defects, and the average characteristic impedance was approximately 82 dyn sec cm"5 (our estimate
from their figures). The ages of their subjects were 24-35
years; mean aortic blood pressures were 74-94 mm Hg.
Their data were obtained with a rigid velocity probe
around the aorta, and under conditions of open thoracotomy. Gabe and his associates12 catheterized the aorta with
a double-lumen catheter in three subjects with rheumatic
mitral valvular disease, measured flow by a pressure-gradient method, and computed impedance. Their figures
indicate an average characteristic impedance of about 100
dyn sec cm"5. Age ranged from 37 to 39 years, and mean
pressure from 83 to 98 mm Hg. Mills and his group.13 who
used methods similar to those in the present investigation,
presented impedance spectra for the ascending aorta in
two subjects. 40 and 51 years of age. both diagnosed as
cases of ischemic heart disease. (Data from 21 other subjects were reported in Mills' paper, but ascending aortic
impedance measurements were presented for only two.)
The characteristic impedance in these subjects was apparently much higher than in our normal subjects. Their
impedances were expressed as pressure-velocity ratios.
RESPIRATORY CYCLE
400
\
\
1200
\
• Inspirotion
\
o Expiration
\
300
200
\
O
o
°*\
\\
«• o
•
-""'^
\
100
•bo~"~ o
4
6
Freq ( H z )
J—i
(CAD)
FIGURE 8 Input impedance of the systemic circulation in a subject
with coronary artery disease (CA D). Pressure and flow for analysis
were selected at intervals throughout one complete respiratory
cycle. The impedance data points at each frequency did not change
with respiration, even though there were changes in pressure and
flow during the cycle.
AORTIC INPUT IMPEDANCE/Mc/io/s et al.
and we estimate the characteristic impedance at approximately 600 dyn sec cm"3. Converted to the same units, our
group A average is 416 dyn sec cm"3. Blood pressures and
cardiac outputs were normal in their subjects.
We conclude from these reports and our own observations that many different pathological conditions can elevate the characteristic impedance in the ascending aorta.
The number of normal subjects studied is as yet too small
to permit firm conclusions about normal limits, but we
suggest as a tentative guide that in the absence of cardiovascular disease or elevated blood pressure, under basal
conditions, characteristic impedance in the ascending
aorta in man is usually between 26 and 80 dyn sec cm"5
(group A mean ± 3 SD).
457
_ 300
0 70 80
20
IOO
PA 0 (MM HG)
80
AGE (YEARS)
sion. In any case, the response to vasoactive agents is not
an appropriate test, because they alter not only the distending pressure but also the active tension of smooth
muscle in the vessel being examined. The evidence is
inconclusive, and it may be that transmural pressure plays
only a small part in determining characteristic impedance
in vivo. Conceivably, our results may depend less on
transmural pressure than on a correlation between disease
of the coronary arteries and some pathological process in
the aortic wall, perhaps an exaggeration of the intramural
effects of aging on the whole arterial tree.
TOTAL EXTERNAL POWER
t
V
r
00
oscillatory terms
O
milliwatt
on
OD
Transmural pressure and age are known to have an
important influence on the stiffness of the vascular
wall.33-34 and for that reason it has been widely assumed
that these variables affect the characteristic impedance of
arteries. Consideration of the characteristic impedance
(Zo) in relation to mean aortic blood pressure and age in
our subjects suggests that these two factors may account
for the relatively high characteristic impedances in the
individuals with coronary disease (Fig. 9). The graph on
the left side of Figure 9 shows that the difference in Z,,
between groups A and C appears to be related to the
higher pressures in the latter group. The right side of the
figure indicates that the difference between groups A and
B is associated with the older age of the subjects in the
latter group. In addition, groups B and C have about the
same age distribution, and the subjects with higher pressures tend to have the highest characteristic impedance.
Whether age and distending pressure completely account
for the observed differences, however, is a question that
cannot be answered until data are available on older normal subjects, and on subjects with coronary disease who
are under the age of 40.
A direct relation between age and arterial impedance is
to be expected. Arteries unquestionably become less compliant with age.6'33 and experimental stiffening of the
aortic wall by external constraints has been shown to
increase characteristic aortic impedance.9 The effect of
increased transmural pressure on vascular impedance is far
from certain, however. Arteries become stiffer as they are
distended, presumably because more and more of the wall
stress is borne by collagen as the diameter increases.34
Vascular impedance is directly proportional to the stiffness
(elastic modulus) of the vascular wall, but it is also inversely proportional to the cross-sectional area of the
vessel.s-25 The net effect of increased transmural pressure
on impedance is therefore difficult to predict, and the
literature on the subject gives no definitive answer. The
elevation of arterial pressure that follows intravenous infusion of norepinephrine. for example, is not accompanied
by an increase in characteristic aortic impedance in the
dog.7-35 though the impedance minimum is shifted to
higher frequencies. Nevertheless, in two of the three subjects studied by Gabe and his associates12 there was a slight
increase in aortic impedance during norepinephrine infu-
60
FIGURE 9 Variations in characteristic impedance (Zo) with age
and mean arterial pressure. Values for the subjects with normal
cardiovascular hemodynamics (group A) are indicated by the open
circles (O). Values for the subjects with coronary artery disease and
mean arterial pressures less than 100 mm Hg (group B) are
indicated by the closed circles (%). Values for the subjects with
coronary artery disease and mean arterial pressures greater than
100 mm Hg (group C) are indicated by the crosses (x). See text for
discussion.
LIC POWER (
EFFECTS OF AGE AND PRESSURE
40
16
24
GROUP
A
PATIENTS 1-5
6-9
10-16
FIGURE 10 Total external hydraulic power of the left ventricle in
the three groups of subjects. The upper portion of the figure
indicates the amount of power required to move blood through the
systemic circulation in a pulsatile manner (oscillatory terms) and
the lower portion indicates the amount of power associated with
mean blood flow (mean terms).
CIRCULATION RESEARCH
458
HYDRAULIC POWER
The hydraulic power, or work per unit time, associated
with blood flow at the root cf the aorta depends not only
on the ability of the left ventricle to do external work, but
also on the properties of the arterial tree into which blood
is ejected. Aortic input impedance is an expression of
these properties. On the one hand, the stiffer the aorta,
the higher the impedance moduli and the greater the
amount of work required to produce a given blood flow.
On the other hand, given a constant impedance spectrum,
the smaller the pressure and flow generated by the ventricle, the lower the external work and power. Consequently,
the performance of the heart and the state of the aorta
must both be taken into account in interpreting measurements of hydraulic power. A useful "rule of thumb" for
this purpose, derived from the equations for computing
hydraulic power,10 states that power equals flow squared
multiplied by resistance (or impedance). The "steady
flow" component of power is calculated by using mean
flow and input resistance as the elements in this expression. The pulsatile component for any one harmonic is
calculated by inserting the appropriate flow modulus and
real impedance.
The relatively low total hydraulic power in the subjects
of group B (average, 1,120 mW, as compared to 1,715
mW in group A) (Table 3 and Fig. 10) thus indicates that
the increased characteristic impedance in Group B was
outweighed by a relatively low blood flow in that group.
The subjects in group C, in contrast, had mean flows that
were not significantly different from those in the normal
subjects, in spite of a high impedance. They maintained
normal cardiac outputs in spite of an increased afterload.
in other words, though at the cost of a marked increase in
work per unit time (2,372 mW). This ability to generate
more power in the face of a high impedance suggests that
ventricular performance in group C was in some sense
better than in group B. The possibility that this relationship might be used to evaluate ventricular behavior is
worth exploring.
The distinction between "oscillatory" and "mean" or
"steady flow" components of hydraulic power10 is useful
because the steady flow terms represent energy that is
dissipated primarily in the arterioles and capillaries, while
the pulsatile terms depend mainly on the elasticity of the
aorta. One manifestation of diminished aortic compliance
is an increase in pulsatile power, as is evident in group C.
In the oldest subject of that group the pulsatile component
was 588 mW, or 26% of total power. Whatever the cause
of the elevated aortic impedance in these subjects, the
physical state of the aorta has clearly increased the energy
that must be supplied by the left ventricle to move blood
into the systemic circulation.
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