Download Comparison of the Force-Velocity Relation

Comparison of the Force-Velocity Relation
and the Ventricular Function Curve
as Measures of the Contractile State
of the Intact Heart
By James W. Covell, M.D., John Ross, Jr., M.D.,
Edmund H. Sonnenblick, M.D., and Eugene Braunwald, M.D.
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ABSTRACT
The contractile state of the intact canine left ventricle was investigated by
determining the instantaneous relations between tension and contractile element velocity (VCE) during the course of single, isovolumic beats produced
by balloon occlusion of the aorta. The relative sensitivity of this relation was
compared with that of the ventricular function curve (VFC) by exerting small
inotropic influences. In seven experiments, low doses of norepinephrine always
shifted the isovolumic force-velocity (FV) relation, increases occurring in
maximum VCB (32.7%) and maximum tension (P o ) (16.9%). The VFC was
unchanged in four of the seven dogs. Moderate hypothermia (average 30.8°C)
in four dogs increased P o (average 28%), with no change, or a fall, in maximum
VCE; the VFC during hypothermia was shifted upward and to the left in two
experiments and unchanged in two. Moderate increases in heart rate always
produced increases in maximum VCE (average 13.5%) but no change in the
VFC was observed. Thus, the isovolumic FV relation proved more sensitive
than the VFC in detecting changes in myocardial contractile state and allowed
more complete definition of these alterations by providing separation of
changes in shortening velocity from alterations in the strength of myocardial
contraction.
ADDITIONAL KEY WORDS
left ventricular performance
mechanics of cardiac muscle
end-diastolic volume
cardiac wall tension
cardiac output
heart rate
hypothermia
norepinephrine
cardiac contractility
anesthetized dogs
• The contractile state of isolated cardiac
muscle can be described in terms of the
instantaneous relations between the force of
contraction and the velocity of shortening.1' 2
Recently, it has been demonstrated that an
inverse relation between force and velocity
also applies to the intact canine left ventricle,3"5 and that when ventricular volume and
time are considered, the position of the curve
describing this relation reflects the contractile
state of the ventricle.5 Studies in this laboratory have shown that a single isovolumic
contraction can be induced in the intact heart
From the Cardiology Branch, National Heart Institute, Bethesda, Maryland.
Accepted for publication March 21, 1966.
364
by sudden elevation of the resistance to left
ventricular ejection during diastole; analysis
of the relation between the force of contraction and the velocity of the contractile elements (VCE) during the course of such an
isovolumic beat also provides an indication
of the level of contractile state.5'6
The present investigation was designed to
determine the usefulness of this type of
analysis in the detection of changes in the
contractile state of the intact left ventricle
and to compare its sensitivity with that of
the ventricular function curve. Relatively small
inotropic influences were exerted by low doses
of norepinephrine, mild hypothermia, or moderate increases in the rate of ventricular contraction. The relative sensitivity of the forceCirculation Reietrcb, Vol. XIX. August 1966
365
FORCE-VELOCITY AND LEFT VENTRICULAR FUNCTION
velocity (FV) relation during isovolumic
contractions was then compared with that of
two standard techniques for assessing ventricular performance: the relations between
the left ventricular end-diastolic pressure and
stroke work7'8 and stroke volume.9
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Methods
Fifteen mongrel dogs weighing between 14.5
and 23.6 kg were anesthetized with sodium
pentobarbital (average dose 40 mg/kg). The
trachea was intubated and ventilation with 1003!
oxygen was provided with a Harvard respiratory
pump. The experimental preparation, shown
schematically in figure 1, consisted of a right
heart bypass preparation, and a device for rapidly
occluding the aortic root during diastole. A bilateral thoracotomy was performed, the heart
was suspended in a pericardial cradle, and bypass of the right heart was carried out as described previously.10 Large-bore metal cannulae
were inserted into the femoral arteries pointing
toward the aorta and systemic arterial pressure
was regulated by means of a reservoir attached
to a compressed air circuit. The sinoatrial node
was crushed and heart rate was maintained constant or, in some experiments, was increased by
pacing the right atrium or right ventricle with
an electronic stimulator.* Left ventricular and
aortic pressures were measured through largebore (5 mm) metal cannulae inserted through
the left ventricular apex and the left subclavian
artery and connected directly to Statham P23Db
transducers. The first derivative of the left
ventricular pressure pulse (LV dp/dt) was obtained with an analog differentiating circuit.t
This circuit exhibited a phase shift of 90° ± 1°
to a sine wave input from 0 to 160 cps, and
amplitude was a linear function of frequency. A
flow transducer was placed around the ascending
aorta, and the flow was monitored with a gated
sine wave electromagnetic flowmetert to confirm
that ejection was absent during the isovolumic
contractions. The dynamic characteristics of this
instrument have been described previously.8 All
determinations were recorded together with the
electrocardiogram on a multichannel oscillograph! at a paper speed of 100 mm/sec.
•American Electronic Laboratories, Inc., Colmar,
Pa., Model No. 104A.
fAssembled by Electronic Gear Inc., Valley
Stream, N. Y., from a Philbrick #P65AU operational
amplifier.
tBiotronex Laboratories, Inc., Silver Spring, Maryland.
§Sanbom Model 350.
Circmlttion Rn$*rcb, Vol. XIX, August 1966
Rotary Pump
Hot
Exchanger
FIGURE 1
Schematic diagram of the preparation. Blood drains
from the inferior vena cava (I.V.C.), superior vena
cava (S.V.C.j, and right ventricle (RV) and is returned
via a heat exchanger and rotary pump to the main
pulmonary artery. Isovolumic beats are produced with
a balloon attached to a steel cannula positioned in
the aortic root at the level of the coronary ostia. The
balloon is rapidly filled with a power injector during
diastole. Left ventricular and aortic pressures are
monitored with Statham transducers (Pr.G.). A flow
probe is placed about the ascending aorta and flow
measured with an electromagnetic flowmeter (E.M.F.).
Mean aortic pressure is controlled by means of a
reservoir and compressed air circuit attached to cannulae inserted into both femoral arteries, or the abdominal aorta. Norepinephrine is administered by
means of the infusion pump.
Sudden occlusion of the aortic root was accomplished by rapid inflation of a rubber balloon
attached to the tip of a metal cannula. The cannula was inserted through the right subclavian
artery so that the balloon was positioned in the
ascending aorta just above the aortic valve (fig.
1). The tip of the cannula was placed in the left
366
COVELL, ROSS, SONNENBLICK,
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sinus of Valsalva, so that when the balloon was
inflated, it interfered with aortic valve opening;
systolic coronary blood flow was thereby minimized and the contraction was essentially isovolumic. A power syringefl was employed to inflate the balloon, and the syringe was triggered
by the electrocardiogram to fire at a selected
time during diastole.
Left ventricular function curves, i.e., the relations between left ventricular end-diastolic pressure (LVEDP) and stroke work7' 8 were determined by altering the output of the occlusive
pump and maintaining mean arterial pressure
constant. It should be emphasized that with the
right heart bypass preparation, in contrast to the
isolated supported heart,7' 8 relatively high flow
rates, in the neighborhood of 170 ml/min/kg,
are required to achieve LVEDP's of 20 cm H2O.
At higher flow rates, pulmonary hemorrhage frequently ensues, apparently as a result of the nonphysiologic pattern of pulmonary arterial perfusion. However, the flow rates employed were
sufficient to produce at least a threefold increase in the LVEDP; LVEDP averaged 5.4 cm.
H 2 O in the control state, and the physiologic
range was thus encompassed.
Stroke work (SW) in g-m was calculated as
the product of the mean left ventricular pressure
during ejection, determined by planimetric integration (mean LV), and stroke volume (SV),
using the following formula:
SW-
( m e a n L V - L V E D ) (1.36) (SV)
100
In some experiments, SW was also calculated using mean aortic pressure, and no differences in
the results were apparent. SV was determined
from the output of the calibrated occlusive pump
and the heart rate. Stroke power was calculated
by dividing stroke work by the ejection time.
Isovolumic contractions of the left ventricle, induced by sudden occlusion of the aorta by the
balloon in early diastole (fig. 1), were analyzed
only when no evidence of ventricular ejection
appeared in the aortic pressure or aortic flow
tracings. The diastolic pressure-volume curve of
the left ventricle was determined at the end of
each experiment using a method described in detail previously"; in brief, the heart was arrested
with 25? KC1, the mitral and aortic valves occluded, and the cavity filled with 2-ml increments of fluid. The left ventricular end-diastolic
volume of each beat was then determined directly from the pressure-volume curve.
Myocardial wall tension in isovolumic beats
flCordis Power Injector, Cordis Corp., Miami, Florida.
BRAUNWALD
was calculated at 10 msec intervals from the
Laplace relation, as described previously6; T =
P77T2, where T = wall tension in grams, P =
intraventricular pressure in g/cm 2 and r = internal left ventricular radius, r was calculated
from the end-diastolic volume by assuming a
spherical left ventricular model and solving the
equation V = 4/37rr8, for r.
Contractile element velocity (VCE) during the
isovolumic beats was considered equal to the rate
of lengthening (dl/dt) of the series elastic component, dl/dt being directly proportional to the
rate of tension development (dT/dt) and inversely proportional to the stiffness of the series elastic
component (dT/dl)»; thus, V C E =
In analyzing the instantaneous relations between force and velocity, a slow rise in VCE has
been found during the initial 20 to 30 msec of
contraction,5 which necessitates considerable estimation in constructing the extrapolation of the
force-velocity curve to zero tension ( V J ^ J ) .
Therefore, the maximum VCE reported herein
represents the greatest measured velocity on the
FV curve following this slow increase in VCE.
Comparisons between the maximum VCE before and after an intervention were always made
at the same tensions. The tension developed
during each beat when VCE was zero, i.e., the
maximum tension, is referred to as P o .
After determining the force-velocity relation
and the ventricular function curve during the
control state, the following interventions were
employed: (1) infusion of norepinephrine, in
doses ranging from 0.03 to 0.36 pig/kg/min, and
averaging 0.16 ju,g/kg/min (7 experiments); (2)
increases in heart rate of 17 to 42 beats per
minute and averaging 32 beats per minute (four
experiments); (3) hypothermia, induced by
blood cooling with the heat exchanger (fig.
1), to levels of 30.3° to 31.4°, and averaging
*The stiffness of the series elastic component has
been shown to be a linear function of tension in cardiac muscle: dT/dl = kT -f a12' 13 ; as described
previously,5 this factor corrected for 1 cm3 of muscle becomes: dT/dl = 28T. For the calculation of
dT/dt, tension is expressed per unit circumference,
assuming a constant wall thickness of 1 cm: T =
Pr/2. Differentiation of this equation yields: dT/dt
= %(T dP/dt — P dr/dt). Since dr/dt = zero in isovolumic beats, dT/dt = X r (dP/dt). VCE is expressed
for the entire circumference (2BT), and the final form
of the equation VCE =
v
CE
then becomes:
_(2.rr) (1/2 r dP/dt) _ n dP/dt
28 Pr/2
14P
CdrctfUtto* Rutrcb,
Vol. XIX, August 1966
367
FORCE-VELOCITY AND LEFT VENTRICULAR FUNCTION
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30.8°C (four experiments). During a steady
state following any of these interventions, the
isovolumic FV relation was again determined, the
LVEDP being maintained at a level identical to
that during the control period by altering the
output of the pump (fig. 1). The ventricular function curve was also determined again at the
same mean aortic pressure and heart rate (except
in experiments in which the effects of changing
this variable were studied); ordinarily, the FV
relation was determined before and after each
ventricular function curve. The mean aortic pressure in these studies ranged from 79 to 130 mm
Hg and averaged 98 mm Hg. In some experiments, sequential, paired measurements of the
isovolumic FV relation were made during a
steady state. The interval between these paired
analyses was 2 to 4 minutes, and the reproducibility of the technique was determined from a
comparison of these curves.
Results
1. Reprodudbility of FV curves. A curvilinear, inverse relation between force and
velocity was always obtained during isovolumic contractions plotted from maximum VCE
to peak tension (Po). Representative tracings
are shown in figure 2 and examples of this
relation obtained during the control state and
during various interventions are shown in
figures 3 to 5.
The reproducibility of these curves was
examined by determining the differences be-
00G *Kl
HYPOTHERMIA
CONTROL
Ao PRESS.
(nvnHg)
LV PRESS.
(rrmHg)
FIGURE 2
Recordings of auxotonic and isovolumic beats at
35.8°C (control) and 3O.8°C (hypothermia). Mean
aortic pressure (Ao. Press.) is 75 mm Hg during
both control and hypothermia. The arrows indicate
the onset of inflation of the balloon in the aortic
root, producing an isovolumic contraction in the following beat.
tween maximum VCE and Po in 14 pairs of
isovolumic beats. The differences between
paired determinations of maximum VCB
averaged 3.4* (range 0 to 10.8%, SD = ± 3.44$)
and of Po, 2.4% (range 0.4 to 5.9%, SD = ± 2.0%).
In absolute terms, the SD of the differences
2000
FIGURE 3
Isovolumic force-velocity curves and ventricular function curves obtained prior to (dots) and
during (triangles) the infusion of norepinephrine (0.03 ng/kg/min). The force-velocity relation
is shifted upward and to the right during norepinephrine infusion, while the relations between
left ventricular end-diastolic pressure (LVEDP) and stroke work and stroke volume show no
change.
CtrcuUiio* Rts—nb, Vol. XIX, August 1966
368
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of the values for maximum VCE and Po
during the control state was ± 0.38 cm/sec
and ± 34.8 g, respectively.
2. Effects of norepinephrine. In the seven
experiments in which norepinephrine was infused, Po always increased; these increases
ranged from 20.4* to 45.1%, and averaged
32.7?. In addition, maximum VCE was always augmented, the increases ranging from
14* to 29* and averaging 16.9*. In contrast,
in four of the seven experiments, the relations
between LVEDP and the SW or SV showed
no detectable alteration from the control
state during the infusion of norepinephrine;
curves representative of those showing no
discernible change are shown in figure 3. In
the remaining three experiments, the shift of
the FV relation was accompanied by a shift
in the relation between LVEDP and SW
upwards and to the left. In only one of the
seven experiments was there a clear-cut shift
of the relation between LVEDP and SV upwards and to the left. Stroke power at any
given LVEDP was increased in five of the
seven experiments, and LV dp/dt increased
in all experiments.
3. Effects of hypothermia. In the four experiments in which moderate hypothermia
was induced, Po was always increased, the
increases ranging from 22* to 40* and averaging 28*. In three experiments, maximum
VCE was unchanged (fig. 4, bottom), while
in one experiment it appeared to be slightly
decreased (fig. 4, top). The relations between
LVEDP and both SV and SW were slightly
shifted upward and to the left in two experiments (fig. 4, bottom) and were unchanged in
two (fig. 4, top). Stroke power and LV
dp/dt were slightly decreased in all experiments.
4. Effects of increases in heart rate. In
four experiments, moderate increases in heart
rate were induced. These increases averaged
32 beats per minute above control, and
maximum levels of 163/min (154 to 171)
were reached. In all four experiments maximum VCE increased by 10 to 18*, average
13.5* (fig. 5). Although Po was slightly
increased in all four experiments (1 to 8*,
COVELL, ROSS, SONNENBLICK, BRAUNWALD
500
O00
TENSION 5.
FIGURE 4
Isovolumic force-velocity curves and ventricular function curves from two experiments prior to (dots) and
following the induction of mild hypothermia (triangles). In both experiments there is an increase in
the maximum isovolumic tension (Po) during hypothermia. In dog no. 8 the maximum V0B appears to be
reduced with hypothermia and in dog no. 11, maximum V0B is unchanged. The ventricular function
curve is unchanged in dog no. 8 and is shifted slightly
upwards and to the left in dog no. 11.
average 3.5*), in three of them this change
was less than 2 SD of the differences between
Po in paired control beats. The increase in
heart rate did not alter the relations between
LVEDP and SV or SW. Stroke power and
LV dp/dt were slightly greater at the higher
heart rates.
Discussion
It has been shown previously that when the
LVEDP and the instantaneous relations between muscle length and time are controlled,
the force-velocity relation reflects the contractile state of the intact left ventricle.5 In the
present study, the usefulness and sensitivity
of the relation between wall tension and the
velocity of the contractile elements during
OrcuLlio*
Rn—rcb, Vol. XIX, August 1966
FORCE-VELOCITY AND LEFT VENTRICULAR FUNCTION
5
O
15
20
500
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LVEOPc H,0
1000
1500
2000
TENSION g
FIGURE 5
Isovolumic force-velocity curves and ventricular function curves at two heart rates: 112 (dots) and 154
(triangles). (See text.)
the course of single isovolumic left ventricular
contractions, which has also been shown to
reflect alterations in contractile state, 5 ' 8 was
examined using a less complicated preparation.
This experimental technique entails sudden
occlusion of the ascending aorta with a balloon,
and has the advantages of technical simplicity
and of being potentially applicable to the
closed-chest animal; moreover, since external
shortening does not occur, the calculations
are simplified.
The force-velocity (FV) relation calculated
during isovolumic beats consistently detected
relatively minor alterations in the contractile
state of the intact left ventricle. Thus, in
seven experiments in which small doses of
norepinephrine were infused, both maximum
VCE and Po always increased. These effects
on the FV relation were qualitatively similar
to those produced by norepinephrine in isolated cardiac muscle,1'2'V1 and by larger
doses of norepinephrine in the intact canine
left ventricle.6 In contrast, the effects of these
doses of norepinephrine on the ventricular
function curve were inconsistent, and in four
of the seven experiments these curves showed
no detectable change from control; the relation
between LVEDP and SV was shifted in only
one experiment. Thus, although it is clear
GrcUiw*
Rei—rcb, Vol. XIX, August 1966
369
that large doses of norepinephrine can shift
the relation between LVEDP and SW upwards
and to the left,7' 8 the isovolumic FV relation
proved to be more sensitive in describing
the alterations in the contractile state induced
by smaller doses of this agent. The increases
in Po and maximum VCE were sizeable and
averaged 20.1$ and 33.7$ of control, respectively, in the four experiments in which no
detectable shift in the ventricular function
curve occurred.
During hypothermia, the isovolumic FV
relation was also consistently altered, Po being
increased in all four experiments, and maximum VCE being unchanged in three and
slightly depressed in one. The ventricular
function curves were not shifted in two
experiments and were shifted upward and to
the left in two. It has been shown in isolated
cardiac muscle that hypothermia diminishes
Vmai.14-16 It is possible that the finding of a
diminution of maximum VCE in only one
of the present experiments is related to the
fact that they were performed at considerably
higher temperatures than those in the isolated
muscle. It has also been shown in isolated
cardiac muscle that hypothermia causes an
increase in Po,18'1T and that in the isovolumically18'19 or auxotonically20 contracting
left ventricle an increase in peak LV pressure,
or in LV contractile force measured with a
strain gauge arch, occurs during hypothermia. The consistent increases in Po in the
present studies, with a shift of the ventricular
function curve in only two of the experiments,
indicate that the isovolumic FV relation was
again more sensitive than the ventricular
function curve in detecting alterations in the
strength of left ventricular contraction. Moreover, the FV relation permitted more complete
definition of the effects of hypothermia on
left ventricular performance than the ventricular function curve, since, despite increases
in Po, the maximum velocity of contraction
was unchanged or reduced.
In the present study, moderate increases in
heart rate always resulted in an increase in
maximum VCE- The effect of heart rate on
Po was slight, this variable being significantly
370
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increased in only one experiment. In all four
experiments the ventricular function curves
showed no change from control at the increased contraction rates. In the isolated cat
papillary muscle, increasing the frequency of
contraction increases Vm0I, with a small increase in Po, the latter becoming negligible
at higher frequencies of stimulation.2 An increase in force has been observed in the
isovolumic dog left ventricle as heart rate
is elevated up to 148/min21 and in the isolated
right ventricle of the dog at rates up to
240/min.22 Mitchell and his co-workers have
also shown that the speed of contraction,
reflected in stroke power and LV dp/dt, is
increased by increasing heart rate, while stroke
work may remain unchanged.28 In the present
study, the increases in maximum VQE at
higher heart rates, in the absence of alteration
in the ventricular function curve, demonstrate
directly the inability of the latter to assess alterations in contractile state that are reflected
primarily in changes in the velocity of contraction, a conclusion suggested from previous observations in this laboratory.10
It is evident that determination of the FV
relation during the course of single isovolumic
contractions by the present method presents
certain theoretical problems. First, changes in
the level of active state with time may affect
the instantaneous relation between force and
velocity. However, in isolated cardiac muscle,
active state (defined as the time course of
contractile element velocity at constant load
and length) has been shown to be rather
slow in onset, to reach a plateau, and then
to decline at about the time peak tension
is reached.10'24 Thus it is likely that when
the FV relation is measured only between
maximum measured velocity and peak tension,
the effect of variations in the level of active
state is relatively minor. The effects of fiber
bundle slippage, and the compliance of the
short segment of aorta between the balloon and
the left ventricular outflow tract, while
probably small, would tend to make the calculated contractile element velocities too low.
Finally, in cardiac muscle, true Po as measured
in skeletal muscle cannot be determined be-
COVELL, ROSS, SONNENBLICK, BRAUNWALD
cause of inability to tetanize cardiac muscle.
In this connection it is of interest that the
higher Po during hypothermia may be related
solely to the increased duration of active state;
thus, it is possible that in the hypothermic
heart, the observed Po approaches true Po.
It is apparent, then, from the above considerations that in general the two extremes of
the FV curve during single isovolumic contractions, can provide only estimates of the
true Vmai and Po.
All of the comparisons between isovolumic
beats were made in contractions originating
from the same LVEDP, and any errors in
absolute volume would apply therefore during
both the control state and the intervention.
Moreover, although there are some suggestions to the contrary,25"27 the bulk of evidence suggests that norepinephrine, moderate
changes in heart rate, or mild hypothermia
do not affect diastolic compliance,1'2> 18'19' 28~85
and the assumption that a single diastolic
pressure-volume curve is applicable therefore
appears justified. Recent experiments in isolated papillary muscle in this laboratory have
further supported the concept that the interventions employed in the present studies have
no direct effect on diastolic compliance; thus
norepinephrine, mild hypothermia, and changes
in heart rate were found to have no influence
on resting length or tension under conditions
of isotonic contraction, although when large
increases in isometrically developed tension
were permitted to occur, stress relaxation of
a series viscous component resulted in small
reductions in resting tension.88 It should be
emphasized that in the present experiments,
the systolic tensions before and during the
interventions were maintained quite constant.
While it is recognized that apparent changes
in diastolic ventricular compliance can result
from incomplete relaxation of the myocardium
during tachycardia and hypothermia, the heart
rates employed were selected to avoid this
problem.28 Thus, the maximum heart rates
were below those which shift the diastolic
pressure-volume relations both at normal temperature and during mild hypothermia (154
to 177, and 92 to 106, respectively).
CircuUtio* Ru—rcb, VoL XIX, Aug*u
1966
371
FORCE-VELOCITY AND LEFT VENTRICULAR FUNCTION
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Several factors may play a role in the
greater sensitivity of the FV relation compared to the ventricular function curve in
detecting small increases in the velocity and
force of myocardial contraction under the
present experimental conditions. Most importantly, it is clear that the relation between
LVEDP and stroke work provides no direct
information concerning the speed of myocardial contraction, while the FV relation permits
comparison of instantaneous velocities at
comparable tensions, as well as estimation of
changes in V M I . Since positive inotropic
influences are generally accompanied by increased shortening of muscle fiber and elevation in the ratio of stroke volume to enddiastolic volume, these influences usually
augment the stroke work from the same
ventricular end-diastolic pressure and at a
constant mean aortic pressure; the ventricular
function curve is then shifted upwards, revealing the directional alteration in the extent
of muscle fiber shortening. However, the ventricular function curve appears to be less
sensitive than the FV relation in detecting
alterations in the force of contraction. An
explanation for the finding that in many experiments no increase in the stroke work
was apparent when positive inotropic influences were exerted, while the FV curve
was displaced, probably lies in the complexity
of the instantaneous relations between preload,
afterload, and length,1' -•37 as well as in the
varying level and duration of the active
state.10'24 All of these factors are reflected in
the isovolumic tension-velocity curve, while
the relation between mean systemic arterial
pressure, stroke volume, and the LVEDP appears to provide an indirect and less insensitive measure of actual tensions in the ventricular wall, and the extent of myocardial fiber
shortening.
3. FHY, D. L., GHIGCS, D. M., JR., AND GREENFIELD, J. C., JR.: Myocardial mechanics:
Tension-velocity-length relationships of heart
muscle. Circulation Res. 14: 73, 1964.
4.
velocity relations in the intact dog heart J.
Clin. Invest. 43: 1383, 1964.
5.
A study of inotropic mechanisms in the papillary muscle preparation. J. Gen. Physiol. 42:
533, 1959.
6. Ross, J., JR., COVELL, J. W., SONNENBLJCK,
E. H., AND BRAUNWALD, E.: Force velocity
relations during acute heart failure. (abstr.)
Physiologist 8: 263, 1965.
7. SARNOFF, S. J., AND BERGLUND, E.: Ventricular
function: I. Starling's law of the heart studied
by means of simultaneous right and left ventricular function curves in the dog. Circulation 9: 706, 1954.
8. SARNOFF, S. J., AND MITCHELL, J. H.: The con-
trol of the function of the heart. In Handbook of Physiology, Section 2: Circulation,
edited by W. F. Hamilton and Philip Dow.
Washington, D. C , Am. Physiol. Soc., vol. 1,
chap. 15, p. 489, 1962.
9. FRANK, O.: Zur Dynamic des Herzmuskels. Z.
Biol. 32: 370, 1895.
10.
Circulation Risurcb,
Vol. XIX, August 1966
Ross, J., JR., SONNENBLICK, E. H., KAISEH,
C. A., FROMMER, P. L., AND BRAUNWALD,
E.: Electroaugmentation of ventricular performance and oxygen consumption by repetitive application of paired electrical stimuli.
Circulation Res. 16: 332, 1965.
11. HILL, A. V.: The heat of shortening and the
dynamic constants of muscle. Proc. Roy. Soc.
(London), Ser. B., 126: 136, 1938.
12.
SONNENBLICK, E.
H.:
Implications
of
muscle
mechanics in the heart. Federation Proc. 21:
975, 1962.
13. SONNENBLJCK, E.
H.:
Series elastic and
con-
tractile elements in heart muscle: Changes in
muscle length. Am. J. Physiol. 207: 1330,
1964.
14.
ULLBICK, \V.
C:
Characteristic
force-velocity
equation of rat heart muscle. Am. J. Physiol.
206: 1285, 1964.
15.
MASHIMA, H., AND MATSUMURA, M.: The effect
of temperature on the mechanical properties
and action potential of isolated frog muscle.
Japan. J. Physiol. 14: 422, 1964.
16.
SONNENBLJCK, E.
H.:
Determinants
of
active
state in heart muscle: Force, velocity, instantaneous muscle length and time. Federation Proc. 24: 1396, 1985.
2. SONNENBUCT, E. H.: Force-velocity relations in
mammalian heart muscle. Am. J. Physiol.
202: 931, 1982.
Ross, J., JR., COVELL, J. W., SONNENBLJCX,
E. H., AND BRAUNWALD, E.: Contractile state
of the heart characterized by force-velocity
relations in variably afterloaded and isovolumic beats. Circulation Res. 18: 149, 1966.
References
1. ABBOTT, B. C , AND MOMMAERTS, W. F. H. M.:
LEVINE, H. J., AND BRIT-MAN, N. A.: Force-
17.
TRAUTWEIN, W., AND DUDEL, J.: Aktionspoten-
tdal und Mechanogramm des Katzenpapillar-
COVELL, ROSS, SONNENBLICK, BRAUNWALD
372
muskels als Funktion der Temperatur. Pfliigers Arch. Ges. Physiol. 260: 104, 1954.
18.
MONHOE, R. G., STRANC, R. H., LAFARGE, C. G.,
AND LEVY, J.: Ventricular performance, pressure-volume relationships, and O a consumption
during hypothermia. Am. J. Physiol. 206: 67,
1964.
19.
20.
21.
SALISBURY,
P. F., CROSS, C. E., AND RIEBEN,
P. A.: Integrarive study of the circulation in
moderate hypothermia. Am. J. Cardiol. 12:
184, 1963.
GOLDBERG, L. I.: Effects of hypothermia on
contractility of the intact dog heart. Am. J.
Physiol. 194: 92, 1958.
LENDRUM,
B., FEINBERC,
H.,
BOYD,
Downloaded from http://circres.ahajournals.org/ by guest on June 18, 2017
ROSENBLUETH,
A., ALANIS, J., RuBIO,
R., AND
LOPEZ, E.: The two staircase phenomena.
Arch. Intern. Physiol. Biochim. 67: 374,
1959.
23.
25.
BUCKLEY, N. M., AND ZEIG, N. J.: Acute uni-
lateral ventricular failure in the isolated dog
heart. Am. J. Physiol. 197: 247, 1959.
26.
HEFNER, L. L., COUGHLAN, H. C., JONES, W. B.,
AND REEVES, T. J.: Distensibility of the dog
left ventricle. Am. J. Physiol. 201: 97, 1961.
27.
30.
REMENSNYDER, J. P., AND AUSTEN, W. G.: Dias-
tolic pressure-volume relationships of the left
ventricle during hypothermia. J. Thoracic &
Cardiovas. Surg. 49: 339, 1965.
ULLRICH, K. J., RTECKER, G., AND KRAMER, K.:
Cardiac pressure-volume diagram of warmblooded animals; isometric balance curves.
Pfliigers Arch. Ges. Physiol. 259: 481, 1954.
31.
ROSENBLUETH,
A., A L A N I S ,
J., AND RuBIO, R.:
Some properties of the mammalian ventricular
muscle. Arch. Intern. Physiol. 67: 276, 1959.
32.
MONROE,
R.
G.,
AND FRENCH,
G.
N.:
Left
ventricular pressure-volume relationships and
myocardial oxygen consumption in the isolated
heart Circulation Res. 9: 362, 1961.
33.
MITCHELL, J. H., LINDEN, R. J., AND SARNOFF,
S. J.: Influence of cardiac sympathetic and
vagal nerve stimulation on the relation between left ventricular diastolic pressure and
myocardial segment length. Circulation Res.
8: 1100, 1960.
MITCHELL, J. H., WALLACE, A. G., AND SKIN-
NER, N. W., JR.: Intrinsic effects of heart
rate on left ventricular performance. Am. J.
Physiol. 205: 41, 1963.
24. BRADY, A.: Time characteristics of cardiac contractility. Federation Proc. 24: 1410, 1965.
BRAUNWALD, E., FRYE, R. L., AND ROSS, J., JR.:
Studies on Starling's law of the heart: II. Determinants of the relationship between left
ventricular end-diastolic pressure and circumference. Circulation Res. 8: 1254, 1960.
29. LUNDIN, G.: Mechanical properties of cardiac
muscle. Acra Physiol. Scand. 7: (suppl. 20): 1,
1944.
E., AND
KATZ, L. N.: Rhythm effects on contractility
of the bearing isovolumic left ventricle. Am. J.
Physiol. 199: 1115, 1960. 22.
28.
34.
SONNENBLICK, E . H., SnSCEL, J. H., AND S A R N -
OFF, S. J.: Ventricular distensibility and pressure-volume curve during sympathetic stimulation. Am. J. Physiol. 204: 1, 1963.
35.
LAFONTANT,
R. R., FEINBERG,
H., AND KATZ,
L. N.: Pressure-volume relationships in right
ventricle. Circulation Res. 9: 690, 1962.
36.
SONNENBLICK, E . H., COVELL, J. W., AND ROSS,
J., JR.: Force dependent hysteresis of a viscous series component in heart muscle,
(abstr.) Federation Proc. 25: 381, 1966.
37. SONNENBLICK, E. H.: Instantaneous force-velocity-length determinants in the contraction of
heart muscle. Circulation Res. 16: 441, 1965.
Circulation Rti—tcb, Vol. XIX, Angut 1966
Comparison of the Force-Velocity Relation and the Ventricular Function Curve as Measures
of the Contractile State of the Intact Heart
JAMES W. COVELL, JOHN ROSS, Jr., EDMUND H. SONNENBLICK and EUGENE
BRAUNWALD
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Circ Res. 1966;19:364-372
doi: 10.1161/01.RES.19.2.364
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