Download Effect of Heart Rate on Aortic Insufficiency as Measured by a Dye

Effect of Heart Rate on Aortic Insufficiency as
Measured by a Dye-Dilution Technique
By HOMER K. WARNER, M.D., P H . D . , AND ALAN F. TORONTO, M.D.
T
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areas under the two dye curves). Positioning of
the catheter tip at the point of origin of the
left subclavian artery from the aorta was accomplished in this way. An x-ray was then taken to
confirm this position. The catheter was then withdrawn through the femoral needle in 2-em. steps
and an injection made after each withdrawal.
These injections were made over the last 0.1 second
of systole and the first 0.1 second of diastole.
In this way, the point was located at which dye
injection first failed to result in the appearance of
any dye at the left radial sampling site on the
first circulation. The distance down the aorta to
this point from the point of origin of the left subclavian artery represents the distance over which
backflow travels during a single diastole. This
backflow distance (BFD) is the fundamental measurement obtained.
A number six Cournand catheter was advanced
from the left antecubital vein through the right
heart and into the pulmonary artery, and through
it dye was injected for measurement of cardiac
output. A second venous catheter was advanced
from the right antecubital vein into the right
atrium in such a way that its natural curvature
held its tip against the lateral wall of the atrium.
On the tip of this catheter was a smooth piece
of solder connected to a fine insulated wire which
traversed the lumen of the catheter. A 2 volt-1
millisecond square wave applied to this electrode
and to an indifferent electrode on the chest wall
(fig. 1) resulted in atrial contraction. This technique made it possible to increase the subject'."
heart rate. Measurements of backflow distance
were made in each of three patients at two heart
rates.
Results
Data obtained from the three subjects are
shown in table 1. Net cardiac output and
backflow distance per stroke were measured in
each of the subjects at two heart rates. The
slow heart rate in each instance is the subject's own sinus rate. In subjects (C.H.) and
(F.T.) cardiac output increased at the faster
rate. In all three subjects, backflow distance
per stroke decreased at the fast heart rate to
less than one-half the distance measured at
the slower rate.
The product of backflow distance and heart
HE PURPOSE of this paper is to present
data obtained on three young adults with
aortic insufficiency in whom aortic backflow
was estimated b}r a dye-dilution method at two
different heart rates, and to consider these
results in the light of calculations based on a
theoretical analysis of the hemodynamie factors involved.
Methods
The basic technique employed for the quantitation of aortic insufficiency was described in a
previous publication.1 Certain modifications of this
technique were used in the experiments here presented. A Peterson-type arterial catheter was
introduced into the right femoral artery through
a thin-walled, 18-gauge needle and advanced up
the aorta until its tip lay near the origin of the
left subclavian artery. This catheter was used for
delivering a small slug of dye (indoeyanine green)*
into the aorta. The distribution of the injected
dye between the left subelavian artery and the
descending aorta following each injection was
determined by recording dye concentration continuously in the left radial and the left femoral
artery blood. The dye was injected through the
arterial catheter using a pneumatic injection device
triggered from the R wave of the electrocardiogram
as described previously. This allowed injection of
dye over any interval of the cardiac cycle. Dye
was initially injected during the first 0.1 second
following the R wave. If the catheter had been
advanced too far, its tip would enter the left
subclavian artery and most of the dye would
appear in the first circulation at the left radial
sampling site. Then as the catheter tip was withdrawn and subsequent early systolic injections
made, a point could be found where dye was
distributed equally to both the left radial and left
femoral sampling sites (as indicated by equal
From the Departments of Physiology, University
of Utah and Latter-day Saints Hospital, Salt Lake
City, Utah.
Supported in part by grants-in-aid from the
American Heart Association.
Dr. Warner is an Established Investigator, American Heart Association.
Keceived for publication November 14, 1960.
*Indocyanine green was generously supplied by
Hynson, Westcott, and Dunning, Baltimore, Maryland.
Circulation Research. Volume IX, March 1961
413
WARNER, TORONTO
414
DATA FROM
r
-
NORMAL MEN
for HR55 to 130/min.
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*\
° 0.6
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z 0.3 —
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'
I 0.2
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d f in
*v
_
0.5
52
IE -0.18
r
cr.
^<.
•
/
.
0.1
1
°
40
1 1 1
1
1
1
1
1 1
50 60 70 80 90 100 HO 120 130 140 150
HEART RATE (mirC1)
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Figure 2
A plot of the duration of systole (Ts) and the
duration, of diastole (Td) as a function of heart
rate.
Figure 1
The white arrow points to the tip of the stimulating catheter in the right atrium. The black arrow
points to the tip of the arterial catheter in the
descending thoracic aorta. The other catheter
is curled in the pulmonary artery.
rate is the average backflow (BF) over the
whole heart cycle divided by the cross-sectional
area (A) of the aorta. Assuming that this area
does not change with heart rate, the ratio of
aortic backflow per unit time at the slow heart
rate to that at the faster heart rate may be
calculated. These ratios were 1.61, 1.75, and
1.71. If the descending aorta contributes a
constant fraction to the total baekflow across
the aortic valve, these measurements of backflow in the descending aorta are an accurate
index to the total baekflow across the aortic
valve.
Theoretical Analysis
The significance of these observations may
become evident through an analysis of the
heinodynamie factors involved. Since aortic
backflow occurs only during diastole, the baekflow per minute will depend upon the fraction
of each cycle occupied by diastole. As is well
known, increasing heart rate results in a much
greater decrease in the duration of diastole
than in the duration of systole (fig. 2). The
effect of heart rate on aortic insufficiency,
however, will depend not only on the duration
of diastole, but also upon the time-course of
backflow during diastole; that is, theflowcontour. Four cases will be considered.
Case l
Let us first consider the rather unrealistic
but easy-to-analyze case in which backflow (f)
is proportional to mean aortic pressure during
diastole (Pd)- This is expressed as
bf = P d ,
(1)
where (b) is a constant. The average backflow
over the whole cycle (BF) in this case will
he given by
" Td
(2)
BF=
b To
where (Td) and (Tc) are the duration of diastole and total cycle respectively. Under these
conditions, the average backflow over the
whole cycle is proportional to the ratio T<i/T0
(fig. 3). Backflow at a heart rate of 70 per
minute would be 1.32 times the backflow at a
heart rate of 120 per minute. Thus, this model
fails to account for our observed ratios which
were 1.6 or greater.
Case 2
Xext we consider the ease in which backflow during diastole is proportional to the inCirculation Research, Volume IX, March 1961
AORTIC INSUFFICIENCY
415
u, 08
1.4
" 07
o
,. 06
o
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1.2
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o I.I
' * / T e ' 0.87 -.003 HR
CM
0.4
uT 1.0
(0>50< HR<I3O
s
10J
•0.9
0.8
I 0.2
30
0.7
40
50
60
70
80
90
100
110
120
130
HEART RATE (mirC1)
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Figure 3
A plot of the fraction of the total heart cycle
occupied by diastole as a function of heart rate
based on the equations shown in figure 2.
stantaneous aortic pressure, P ( t ) - This is expressed as
bf = P( t ) ,
(3)
where (b) is a constant. From recording of
aortic pressure, it can be readily shoAvn that
to a good approximation
P ( t ) = P o e- kt
(4)
describes the time-course of pressure during
diastole. Here, (P o ) is the pressure in the
aorta at the onset of diastole and (k) is a
constant; (k) will depend upon the resistance
to backflow across the aortic valve, the systemic arterial resistance to forward flow, and
the distensibility of the aorta. By combining
equations (3) and (4), integrating over the
duration of diastole, and multiplying by the
heart rate (HR), the average rate of backflow
over the whole cycle (BF) is obtained. This
is given by
where (HR) is the heart rate and (Td) is the
duration of diastole at that heart rate. Examination of figure 4 shows that in the limit as
(k) becomes 0 the ratio of backflow at a heart
rate of 70 to backflow at heart rate 120 becomes 1.32 as in the case just discussed, and
that this ratio progressively decreases with
increasing values of (k). Since (k) was found
0.6
0.5
2
3
K (sec"1)
Figure 4
A plot based on calculations using equation (5)
of the effect of (k) on the ratio of backflow at
a heart rate of 70 to backflow at a heart rate of
120 beats per minute.
from examination of recordings of aortic pressure to vary from 0.7 to 2 per second, it can
be seen that this model fails by an even wider
margin to explain the observed effects of heart
rate on aortic backflow.
Case 3
In this case, the fact is recognized that the
column of blood in the aorta has inertia which
will limit the rate at which a new level of
backflow can be achieved. A term to account
for this is included in
a
ctf
—
kt
(6)
The coefficient (a) is a measure of the inertia
of the column of blood which must reverse its
flow at the onset of diastole and its units will
be mass divided by cross-sectional area
squared. The contour of the diastolic backflow curve predicted by solving this equation
on an analogue computer is shown in figure 5
for three values of (a) where (a) is expressed
in units of mm. Hg sec.2 cm."3. The analytical
expression for average backflow over the
whole cycle i a this case is given by
(7)
Circulation Research, Volume IX, March 1961
WARNER, TORONTO
416
CASE-4
TIME SFTER ONSET OF DIASTOLE
DISTRIBUTION OF DYE INFLOW STREAM
Q=0
0 1 Seconds
0 2 Seconds
a-0.02
0 3 Seconds
OA Seconds
0 5 Seconds
Figure 6
A diagrammatic representation of the effect of
development of laminar flow on the distribution of
dye in the aorta- at various times during diastole.
0=0.1
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Time marks = O.I Sec.
Figure 5
Analogue computer solutions of equation (6)
predicting the time-course of diastolic backfloiv
in the aorta for three values of the coefficient (a).
This expression is obtained by integrating
equation (6) twice and multiplying by heart
rate.
Solutions of this equation using data obtained from patient C.H. are shown in table 2.
Only when (a) is large (0.1 mm. Hg see.-'
cm."3) does this model predict a ratio which
approaches the value obtained experimentally.
Direct measurement of the time-course of
backflow in the ascending aorta in patients
with aortic insufficiency, through the use of
flowmeters at the time of surgery, would make
it possible to cheek on the validity of such a
value for (a) by comparing the predicted flow
curves shown in figure 5 with the flow curve
actually recorded. Unless the recorded back-
flow curves resemble the curve predicted by
equation (6), with (a) equal to 0.1, another
explanation for the results here presented
must be sought. In the three analyses so far
considered, the pressure on the left ventricular side of the aortic valve during diastole was
ignored, since left ventricular pressure was
not measured in these experiments. The fact
that left ventricular pressure certainly rises
during the course of diastole would make the
discrepancy between measured change in
backflow with change in heart rate and that
predicted by any of these models even more
pronounced.
Case 4
Finally, we consider the possibility that thp
proportionality constant which relates backflow distance traveled by the dye to backflow
volume may be dependent on heart rate. If
flow were turbulent throughout diastole, the
injected indicator would be distributed uniformly across the aorta at any given point
down its length. However, if laminar flow de-
Table 1
Measurements and Calculations Carried Out on Three Subjects (C. H., C. P., F. T.),
Each at Txco Different Heart Ttates
HR Heart Rate (min."1)
CO Cardiac output (liters/min.)
BFD Backflow distance per stroke (cm.)
BF/A = BFD X HR (cm./min.)
BF at slow HE
"BF~at fast HE
C.H.
79
4.5
22
1740
1.61
F.T.
C.P.
120
5.0
9
1080
84
6.2
10
750
120
6.0
4
360
60
5.3
19.5
1170
1.75
Circulation
105
6.5
6.5
685
1.71
Research,
Volume IX, March 1901
AORTIC INSUFFICIENCY
417
Table 2
Calculations from Patient C. H. Using Equation (7) to Show the Effect of the Parameter
(a) on the Expected Average Backflow at Two Heart Rate*
Measured
HE (min.-1)
T\i (sec.)
b (mm. Hg sec. cm. 4 )
k (sec."1)
Po (mm. Hg)
Assume
a (mm. Hg sec." cm.""")
Calculate
~BF" (litcr/min.-1)
HP"
79
120
0.49
0.265
1
0.9
122
1
0.9
113
0
0.02
0.1
0
0.02
0.1
3.80
1.19
3.85
1.19
3.13
1.47
3.2
3.23
2.13
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velops as the velocity of backflow diminishes
late in diastole, the distribution of dye in the
aorta 2 ' 3 will resemble that shown in figure 6.
Under these circumstances, the maximum distance any dye particle travels back up the
aorta during a single diastole may no longer
be multipled by aortic cross section to estimate volume. Such an effect, if present, would
be more prominent with the longer diastole,
and would result in an overestimate of backflow by this method at the slower heart rates.
The existence of such a phenomenon might be
detected by high-speed cineangiography. This
seems the most likely explanation of the results here presented.
Summary
Measurements of the distance a labeled particle of blood travels back up the descending
aorta during a single diastole have been car-
Circulation Retearch. Volume IX, March 1901
ried out at two different heart rates in each
of three patients with aortic insufficiency.
From these measurements, the ratios of backflow per unit time at the slow heart rate to
backflow at the faster heart rate were found
to be 1.61, 1.71, and 1.75. From an analysis
of the hemodynamic factors involved, it seems
likely that backflow is overestimated at the
slow heart rates by this technique due to the
development of laminar flow late in diastole.
References
1. WARNER, H. E., AND TORONTO, A. F . : Quantita-
tion of backflow in patients with aortic
insufficiency using an indicator technic. Circulation Besearch 6: 29, 1958.
2. MCDONALD, D. A.: Occurrence of turbulent flow
in the rabbit aorta. J. Physiol. 118: 340, 1952.
3. Rossi, H. H., POWERS, S. H., AND DWORK, B.:
Measurement of flow in straight tubes by
means of dilution technic. Am. J. Physiol.
173: 103, 1953.
Effect of Heart Rate on Aortic Insufficiency as Measured by a Dye-Dilution Technique
HOMER R. WARNER and ALAN F. TORONTO
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Circ Res. 1961;9:413-417
doi: 10.1161/01.RES.9.2.413
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