Download Importance of Atrial Compliance in Cardiac Performance

Importance of Atrial Compliance in Cardiac Performance
HIROYUKI SUGA
Circ. Res. 1974;35;39-43
Circulation Research is published by the American Heart Association. 7272 Greenville Avenue, Dallas,
TX 72514
Copyright © 1974 American Heart Association. All rights reserved. Print ISSN: 0009-7330. Online ISSN:
1524-4571
The online version of this article, along with updated information and services, is
located on the World Wide Web at:
http://circres.ahajournals.org
Subscriptions: Information about subscribing to Circulation Research is online at
http://circres.ahajournals.org/subscriptions/
Permissions: Permissions & Rights Desk, Lippincott Williams & Wilkins, a division of Wolters
Kluwer Health, 351 West Camden Street, Baltimore, MD 21202-2436. Phone: 410-528-4050. Fax:
410-528-8550. E-mail:
[email protected]
Reprints: Information about reprints can be found online at
http://www.lww.com/reprints
Downloaded from circres.ahajournals.org by on May 8, 2007
Importance of Atrial Compliance in Cardiac Performance
By Hiroyuki Suga
ABSTRACT
Effects of changes in atrial compliance on cardiac performance were analyzed using a
circulatory analog model. The atrium was assumed to be a noncontracting chamber with
a constant compliance. It connected the venous return system, which was represented by
mean circulatory filling pressure and a venous return resistance in accordance with
Guyton's concept, with the ventricle, which was characterized by a time-varying elasticity.
Atrial compliance was increased from near zero to a value at which atrial volume was
twice ventricular stroke volume, while the parameters of ventricular contractility were
kept unchanged. Cardiac output increased from 2,400 to 3,240 ml/min with increases in
atrial compliance from 0.1 to 20 ml/mm Hg (venous return resistance 0.1 mm Hg sec/ml),
whereas mean atrial pressure simultaneously decreased from 3.0 to 2.2 mm Hg. This result
indicates that cardiac performance in terms of the cardiac output-mean atrial pressure
relationship was markedly improved by increases in atrial compliance in spite of constant
ventricular contractility. The analysis of the model strongly suggests that natural atrial
compliance in situ, by pooling venous return flow during systole and supplying it to the
ventricle during diastole, facilitates the transformation of the continuous venous return
flow into the intermittent ventricular filling flow.
KEY WORDS
ventricular filling
cardiac output
Starling's law of the heart
circulatory analog model
venous return
• The physiological significance of atrial compliance is not well understood, but some indirect evidence does suggest that it is important in hemodynamics. Brighton et al. (1) and Peters et al. (4th
Annual Meeting of the Biomedical Engineering
Society, 1973) have observed that the addition of
a flexible atrium to the inlet of an artificial heart
substantially improves the heart's output. However, performance of an artificial heart is not equal
to that of the natural ventricle, and doubt still
exists about the physiological significance of atrial
compliance.
The purpose of the present analysis was to
evaluate quantitatively the importance of atrial
compliance in natural cardiac performance. In
animal experiments, it is difficult to change atrial
compliance alone without affecting venous return
resistance, and slight changes in venous return
resistance sensitively affect cardiac output (2).
Therefore, a reasonable analog model of the cardiovascular system based on physiological findings
in the literature was used in the present study.
Atrial compliance was varied in the model while
the other parameters of the venous return system—
ventricular contractile state, valve characterisFrom the Department of Physiology, Faculty of Medicine,
University of Tokyo, Japan.
Received January 2, 1974. Accepted for publication March
19, 1974.
atrial function
atrial size
tics, and arterial pressure—were kept constant.
The results of this analysis suggest that an atrium
with an appropriate compliance can increase cardiac output 35-80%.
Methods
Figure 1 shows the electric analog model of the circulatory system used in the present study; the right heart
and the pulmonary circulation were purposely eliminated from the model to simplify the analysis. Arterial
pressure (Pa) was modeled as if it were held constant
and therefore represented by a constant-voltage battery.
The venous return system was modeled in accordance
with Guyton's concept (2) as a venous return source
pressure (Pv), which represents mean circulatory filling
pressure, and a venous return resistance (Rv).
The ventricle was represented by a time-varying elasticity (E[t] ) (the instantaneous pressure-volume ratio)
in accordance with previous experimental findings on
the ventricular pressure-volume relationship (3-5); a
ventricular model of this type has conventionally been
used by others (6-9). The time-varying elasticity of the
ventricle increases during systole and reaches its peak
value (Emax) at the end of systole (3-5). My previous
mathematical analysis (3) has shown that the peak value
of elasticity determines end-systolic intraventricular
volume and hence stroke volume when the end-diastolic
volume is given and that the time course per se of timevarying elasticity is not a primary determinant of either
end-systolic or stroke volume. Therefore, in the present
analysis, a simple time course was assigned to timevarying elasticity as a reasonable approximation of the
physiologically observed time course. Elasticity was
39
Circulation Ra earth. Vol. 35, July 1974
Downloaded from circres.ahajournals.org by on May 8, 2007
40
SUGA
SF-Illab-2
VEIN
ATRIUM
VENTRICLE
ARTERY
FIGURE 1
Analog model of the circulatory system. Pa = arterial pressure, Pv = venous return source pressure
(mean circulatory filling pressure), Pat = atrial pressure. Vat - atrial volume, Vvt = ventricular
volume, Fv =• venous return flow, Rv = venous return resistance, Rat, = atrioventricular valvular
resistance, Rvt = aortic valvular resistance, Cat = atrial compliance, and E(t) •= ventricular timevarying elasticity (instantaneous ventricular pressure-volume ratio). See text for further discussion.
considered to be zero during diastole, implying that
diastolic ventricular compliance was infinite. Peak elasticity was considered to be constant during systole; this
condition is similar to Warner's (6) assumption. Furthermore, in the model, the ventricle was connected to the
artery via an aortic valve with a small resistance (Rvt).
The atrium, which was represented by a linear compliance (Cat), was connected to the ventricle via a valve
with a small resistance (Rat). It was also connected directly to the venous return resistance.
The parameters of the model elements were:
Pa = 80 mm Hg, Pv = 5 mm Hg, Emax = 4.5 mm Hg/
ml, Rvt = 0.01 mm Hg sec/ml, Rat = 0.01 mm Hg sec/
ml, Rv = 0.1 or 0.2 mm Hg sec/ml, and Cat = 0.1-20
ml/mm Hg. These values seem reasonable for a 20-kg
dog at rest.
The performance of the model was analyzed with an
analog computer (Pace, TR-10). As indicated in Figure
1, venous return flow (Fv) through the venous return resistance, atrial pressure (Pat), atrial volume (Vat), and
ventricular volume (Vvt) were measured while the linear
compliance of the atrium was changed in steps. Mean
atrial pressure was calculated by averaging the instantaneous atrial pressure tracing. The same variables were
again measured after venous return resistance had been
changed to a second value. Heart rate was modeled as if
it were constant at 120 beats/min.
Results
Peak systolic and diastolic values (full excursion)
of the measured variables and the calculated cardiac output are listed in Table 1. Some sample
tracings showing both a large and a small atrial
compliance are illustrated in Figure 2. As atrial
compliance increased from a value close to zero,
the magnitude of the changes in venous return flow
and atrial pressure became smaller, the mean level
of venous return flow increased, the atrial volume
increased, the mean atrial pressure decreased, the
ventricular stroke volume increased, and the enddiastolic volume increased; end-systolic volume,
however, remained unchanged. Hence, cardiac
output (stroke volume x heart rate) increased. Figure 3 shows the marked increases in stroke volume
that occurred in response to the increases in atrial
compliance.
The increases in atrial compliance from 0.1 ml/
mm Hg to 20 ml/mm Hg increased cardiac output
logarithmically up to 35% when venous return resistance was 0.1 mm Hg sec/ml and up to 80% when
venous return resistance was 0.2 mm Hg sec/ml. At
an atrial compliance of 5 ml/mm Hg, cardiac output had already increased significantly; any additional increase in atrial compliance above 5 ml/mm
Hg did not affect cardiac output much. Therefore,
it seems that a significant improvement in cardiac
performance is attained when the atrial compliance is such that atrial volume is more than half of
the concomitant stroke volume of the ventricle.
Figure 4 shows the relationship between cardiac
output and mean atrial pressure. Increases in atrial
compliance caused a considerable improvement in
cardiac performance in terms of the cardiac output-mean atrial pressure relationship, since a
larger cardiac output was pumped from a lower
mean atrial pressure at a higher atrial compliance.
Circulation Rttmrth, VoL 35, July 1974
Downloaded from circres.ahajournals.org by on May 8, 2007
41
ATRIAL COMPLIANCE
TABLE 1
Effects of Various Levels of Atrial Compliance on Cardiac Performance
Atrial compliance
(ml/mm Hg)
Venous return
• oci
of
Qnpo
rcololallLc
(mmHgsec/ml)
0.2
Phase
0.1
0.2
0.5
1
2
Diastole
Systole
Systole
Diastole
Systole
Diastole
Diastole
Systole
45
l
0.5
0.1
5.0
0.1
29.0
18.0
1320
44
1
0.5
0.1
4.9
0.5
29.5
18.0
1380
44
2
2.5
0.3
4.9
0.6
31.0
18.0
1560
44
5
4.6
0.6
4.6
0.6
33.0
18.0
1800
44
15
8.5
2.0
4.2
1.0
34.7
18.0
2000
Diastole
Systole
Systole
Diastole
Systole
Diastole
Diastole
Systole
82
2
0.5
0.1
5.0
0.7
38.0
18.0
2400
81
2
1.0
0.1
4.8
0.7
38.5
18.0
2460
80
2
2.4
0.4
4.8
0.7
39.0
18.0
2520
80
2
4.8
0.7
4.8
0.7
40.0
18.0
2640
80
9
8.8
1.4
4.4
0.7
41.5
18.0
2820
Variables
Fv (ml/sec)
Vat (ml)
Pat (mm Hg)
Vvt (ml)
C O . (ml/min)
0.1
Fv (ml/sec)
Vat (ml)
Pat (mm Hg)
Vvt (ml)
C O . (ml/min)
10
20
43
28
13.0
5.0
2.6
1.0
36.5
18.0
2220
43
34
18.0
9.0
1.8
1.0
37.5
18.0
2340
43
38
31.0
21.0
1.5
1.0
38.0
18.0
2400
79
30
16.5
4.0
3.3
0.8
44.0
18.0
3120
75
48
30.0
14.0
3.0
1.4
45.0
18.0
3240
62
56
48.0
31.0
2.4
1.5
45.0
18.0
3240
5
Fv = venous return flow, Vat - atrial volume, Pat - atrial pressure, Vvt - ventricula • volume, and C O . = cardiac output.
SF-Illab-2
mmHg
ml
CD
VENOUS RETURN FLOW Fv
1 5 0
ml/sec
|"
...
oL
ATRIAL VOLUME VAT
3 0 r
ml
0
AA/W
L
^
5r
OL
W r
HEART RATE - 120
/
A A A A
Jl/l/l/l lf\AAAAi
LARGE
-—
MM
A A A A AA
JU
QL
ATRIAL COMPLIANCE
^
CNI
A A A AA
A/X/VV J
BI
sec
_^
ATRIAL PRESSURE P A T
nnEg
VENTRICULAR VOLUME VVT
Rv = 0.1
^—•-
VJ V V V W J
Rv = 0.2
9-
CD
OH
)-_
CO
p'
SMALL
boats/min
FIGURE 2
Effects of atrial compliance on cardiodynamics.
0
1
2
3
i*
ATRIAL COMPLIANCE
5 20
ml/mmHg
FIGURE 3
The two rectilinear lines in Figure 4 are the theoretically calculated venous return curves for the
two venous return resistances used in the model.
The pressure-axis intercept of both lines is the
specified venous return source pressure (Pv = 5
mm Hg), and their slopes are the reciprocals of
the specified venous return resistances. The data
point under a given venous return resistance moves
Effects of atrial compliance on stroke volume. Rv - venous return resistance.
along the corresponding venous return curve as
atrial compliance is varied. The effect of increases
in atrial compliance on cardiac output is greater
with the larger venous return resistance.
Interestingly, the peak and the mean level of
atrial pressure during diastole increased with in-
Circulation Rtstanh. Vol. 35, July 1974
Downloaded from circres.ahajournals.org by on May 8, 2007
42
SUGA
SF-Illab-2
Rv = 0 . 1 mmHg s e c / m l
\ CAT = 20ml/nm
Rv = 0.2 \
\
\
\
c
•H
CAT ==
= 2o\
CAT
csi
\
-
0.1
\
\
CAT
=
O.A \\ \\
\ \^
\\
i
i
1
1
0
1
2
3
i
\\
MEAN ATRIAL PRESSURE
FIGURE 4
Effects of atrial compliance on cardiac performance in terms
of the cardiac output-mean atrial pressure relationship. The
two rectilinear lines are the theoretically calculated venous return curves. Rv - venous return resistance and Cat = atrial
compliance. See text for further discussion.
creases in atrial compliance, although the mean
level of atrial pressure during the entire cardiac
cycle decreased.
Discussion
The results of this analysis suggest that atrial
compliance is an important determinant of the performance of the heart as a whole. The natural
atrium contracts and, therefore, is not fully consistent with the present assumption of linearity
and constancy of atrial compliance. However, more
than half of the ventricular filling process occurs
during the diastolic period before the atrial contraction (10, 11). Therefore, the present assumption is
still a practically reasonable approximation, and
the resultant suggestion should hold in the natural
situation.
The apparent improvement in cardiac performance with larger atrial compliances can be explained as follows. The smaller the atrial compliance is in the model, the greater are the amplitude
and the mean level of atrial pressure. However,
simultaneously, the mean level of atrial pressure
during the period of ventricular filling, which serves
as the effective source pressure of ventricular filling, is smaller. The smaller source pressure causes
less filling and a smaller end-diastolic ventricular
volume. Moreover, venous return to the atrium
decreases because of the higher mean atrial pressure. In contrast, when the atrial compliance is
large, the atrial pressure variation is small and
the mean level of atrial pressure during ventricular
filling is maintained at a relatively high level. Thus,
atrial compliance serves to buffer the pressure
changes in the atrium during a cardiac cycle and
to smooth the transformation of the steady venous
return flow into the intermittent ventricular filling
flow.
The finding that a larger atrial compliance improves cardiac performance more when the venous
return resistance is larger suggests that the natural
atrial compliance is more advantageous when the
caval veins are partially collapsed. This finding corroborates the importance of a compliant atrium at
the inlet of the artificial heart ventricle, because
the artificial heart actively sucks blood and collapse of the caval veins would occur without such
an atrium.
The observed dissociation of the mean atrial
pressure averaged over the entire cardiac cycle and
the end-diastolic ventricular volume is physiologically significant. It suggests that mean atrial pressure does not always serve as the source pressure of
ventricular filling. Rather, the mean value of atrial
pressure averaged only over the period of ventricular filling seems to be the effective, direct source
pressure of ventricular filling. The situation is similar for ventricular pressure. Nobody thinks that
the mean ventricular pressure averaged over the
entire cardiac cycle is the source pressure of aortic
flow during ejection. Instead, the ventricular pressure during the ejection period serves as the effective source pressure of ventricular ejection.
References
1. BRIGHTON
JA,
WADE ZA,
PIERCE WS,
PHILLIPS
WM,
O'BANNON W: Effect of atrial volume on the performance
of a sac-type artificial heart. Trans Am Soc Artif Intern
Organs 19:567-572, 1973
2. GUYTON AC: Cardiac Output and Its Regulation. Philadelphia, W. B. Saunders Company, 1963, pp 163-220
3. SUGA H: Theoretical analysis of a left ventricular pumping
model based on the systolic time-varying pressure-volume
ratio. IEEE Trans Biomed Eng 18:47-55, 1971
4. SUGA H, SAGAWA K: Mathematical interrelationship be-
tween instantaneous ventricular pressure-volume ratio
and myocardial force-velocity relation. Ann Biomed Eng
1:160-181, 1972
Circulation Ratarth. Vol 35. July 1B74
Downloaded from circres.ahajournals.org by on May 8, 2007
43
ATRIAL COMPLIANCE
5. SUCA H, SACAWA K, SHOUKAS AA: Load independence of
the instantaneous pressure-volume ratio of the canine
left ventricle and effects of epinephrine and heart rate
on the ratio. Circ Res 32:314-322, 1973
6. WARNER HR: Control of the circulation as studied with analog computer techniques. In Handbook of Physiology, sec
2, vol 3, Circulation, edited by WF Hamilton and P Dow.
Washington, D. C, American Physiological Society,
1965, pp 1825-1841
7. BENEKEN JEW, DEWIT B: Physical approach to hemodynamic aspects of the human cardiovascular system. In
Physical Basis of Circulatory Transport: Regulation and
Exchange, edited by EB Reeve and AC Guyton. Philadelphia, W. B. Saunders Company, 1967, pp 1-45
8. RIDEOUT VC: Cardiovascular system simulation in biomedical engineering education. IEEE Trans Biomed Eng 19:
101-107, 1972
9. COOK AM, SIMES JG: Simple heart model designed to demonstrate biological system simulation. IEEE Trans Biomed Eng 19:97-100, 1972
10. BRECHEK GA, GALLETTI PM: Functional anatomy of cardiac
pumping. In Handbook of Physiology, sec 2, vol 2, Circulation, edited by WF Hamilton and P Dow. Washington,
D. C, American Physiological Society, 1963, pp 759-798
11. NOLAN SP, DIXON SH JR, FISHER RD, MORROW AG: Influ-
ence of atrial contraction and mitral valve mechanics on
ventricular filling: Study of instantaneous mitral valve
flow in vivo. Am Heart J 77:784-791, 1969
Circulation Raearch. Vol. 3S, July 1974
Downloaded from circres.ahajournals.org by on May 8, 2007