Vol. 274, Issue 4, H1141-H1151, April 1998
Myocardial contractile depression from high-frequency
vibration is not due to increased cross-bridge breakage
Kenneth B.
Campbell1,2,
Yiming
Wu1,
Robert D.
Kirkpatrick1, and
Bryan K.
Slinker1
1 Department of Veterinary and
Comparative Anatomy, Pharmacology, and Physiology, and
2 Department of Biological Systems
Engineering, Washington State University, Pullman, Washington 99164
 |
ABSTRACT |
Experiments were conducted in 10 isolated
rabbit hearts at 25°C to test the hypothesis that vibration-induced
depression of myocardial contractile function was the result of
increased cross-bridge breakage. Small-amplitude sinusoidal changes in
left ventricular volume were administered at frequencies of 25, 50, and
76.9 Hz. The resulting pressure response consisted of a depressive
response [
Pd(t),
a sustained decrease in pressure that was not at the perturbation
frequency] and an in-frequency response
[Pf(t), that part at the perturbation frequency].
Pd(t)
represented the effects of contractile depression. A cross-bridge model
was applied to
Pf(t)
to estimate cross-bridge cycling parameters. Responses were obtained
during Ca2+ activation and during
Sr2+ activation when the time
course of pressure development was slowed by a factor of 3. Pd(t)
was strongly affected by whether the responses were activated by
Ca2+ or by
Sr2+. In the
Sr2+-activated state,
Pd(t)
declined while pressure was rising and relaxation rate decreased.
During Ca2+ and
Sr2+ activation, velocity of
myofilament sliding was insignificant as a predictor of
Pd(t)
or, when it was significant, participated by reducing
Pd(t)
rather than contributing to its magnitude. Furthermore, there was no
difference in cross-bridge cycling rate constants when the
Ca2+-activated state was compared
with the Sr2+-activated state. An
increase in cross-bridge detachment rate constant with volume-induced
change in cross-bridge distortion could not be detected. Finally,
processes responsible for
Pd(t) occurred at slower frequencies than those of cross-bridge detachment. Collectively, these results argue against a cross-bridge detachment basis for vibration-induced myocardial depression.
contractility; muscle cross bridge; cross-bridge model; strontium; activation
| |
INTRODUCTION |
DEPRESSION OF MYOCARDIAL contractile function in
response to high-frequency vibration is a well-known phenomenon. This
depression is characterized not only by a loss of force-generating
capacity (16, 17, 20, 26), but also by an increased efficiency of force
production (20) and a shortening of the relaxation period (11, 12, 24).
A commonly held hypothesis, put forth originally by Vukas et al. (27)
and accepted by most workers since then, is that vibration induces an
increased rate of cross-bridge breakage, such that fewer cross bridges
remain in the attached force-bearing state at any one time. A decrease
in force-bearing cross bridges results in a loss of force-generating
capacity. This is a logical hypothesis, because vibration was thought
to cause cross-bridge strain to deviate from the strain found in
isometric conditions, and such deviation has long been taken as a
primary means of increasing cross-bridge detachment rates (9).
We tested this hypothesis in a series of experiments in which left
ventricular (LV) volume was perturbed sinusoidally using frequencies
from 25 to 76.9 Hz. We saw a characteristic depressive response that
was similar to those reported by other workers using various
high-frequency vibrations. We asked three questions:
1) Is the depressive response during
Ca2+ activation different from
that during Sr2+ activation in a
manner that is consistent with sinusoid-induced cross-bridge breakage,
or is the difference in depressive response related to the activation
process? 2) Is the dependence of the depressive response on frequency, amplitude, and velocity of
perturbation consistent with what would be expected from increased
cross-bridge breakage? 3) Can
increased cross-bridge breakage with volume sinusoids be detected? The
answers to these three questions lead us to conclude that contractile
depression during high-frequency vibration is not due to increased
cross-bridge breakage. Instead, we propose that some feature of the
activation process is likely affected by vibrational perturbations such
that a depressive response ensues.
| |
METHODS AND PROCEDURES |
Many aspects of these experimental methods have been reported
previously (4, 5, 13). They are briefly repeated here for the sake of
completeness.
Experimental preparation.
Hearts were isolated from 10 adult male rabbits (avg wt = 3.26 ± 0.20 kg). Procedures for isolating the heart and attaching it to a
volume-servo device have been described in detail elsewhere (4, 13).
Briefly, the brachiocephalic artery was cannulated, and perfusion was
begun with oxygenated relaxing solution (in mM: 121.4 Na+, 35.0 K+, 137.4 Cl
, 0.1 Ca2+, 1.1 Mg2+, 21.0 
, 0.36 
, and 11.1 glucose and 2.5 U/l
insulin) to arrest the heart before it was isolated from the rabbit.
The perfusate was oxygenated by vigorous bubbling with 95%
O2-5%
CO2.
The heart was transferred to a perfusion support system consisting of a
gas-exchange chamber, a roller pump, a constant-pressure chamber, and
an environmental chamber. The heart was placed within an environmental
chamber, where the coronary arteries were perfused at 90 mmHg.
Temperature was kept constant at 25°C. The heart was submerged in
perfusate at all times by allowing the coronary effluent to accumulate
in the environmental chamber until it reached the chamber overflow at
the level of the base of the heart. The perfusate was not recirculated.
A thin latex balloon, secured to the piston cylinder of a volume-servo
system, was drawn into the LV chamber, such that its tip was anchored
through a puncture in the apex. The puncture in the apex served as a
vent for any fluids between the balloon and chamber wall. A draw-string
suture in the mitral annulus was tightened around the obturator of a
piston-cylinder device and secured the balloon in the LV chamber. The
balloon was filled with degassed distilled water until passive chamber
pressures reached 5 mmHg. Balloons were sized to fill the ventricle
with neither excessive folding nor contribution to pressure at the volumes encountered in these ventricles. Thus balloons did not contribute to measured pressure.
The perfusing solution was changed from the relaxing solution to one
that allowed spontaneous beating (in mM: 148.4 Na+, 7.4 K+, 139.1 Cl, 1.24 Ca2+, 1.1 Mg2+, 21.0 , 0.36 , and 11.1 glucose and 2.5 U/l
insulin). Spontaneous beating always occurred with a period >1 s,
such that the heart, suspended in the spent perfusate, was paced at 1 Hz with field stimulation using 5-ms pulses of 15 mV and 250 mA from
5-cm2 copper plates placed 4.5 cm
apart on either side of the heart.
The volume-servo system consisted of a linear motor, a piston-cylinder
device, and a linear variable differential transformer (LVDT). The
piston-cylinder device was a modified 5-ml glass syringe (East
Rutherford Syringes) with two side ports. One side port allowed
calibrated infusion of volume into the LV balloon to establish a
baseline volume (VBL). The
second port was used to introduce a 5-Fr catheter-tipped pressure
transducer (Millar, Houston, TX) into the center of the balloon. The
pressure measurement system had a frequency response of 1 kHz. The
piston was driven by the armature shaft of the linear motor. Motions of
the piston produced LV volume changes around
VBL at a resolution of 0.001 ml.
The LVDT (model 0294-0000, Trans-Tek) had a frequency response of 1 kHz. This allowed precise measurement of the piston position and,
therefore, with proper calibration, the instantaneous LV volume.
Motion of the motor armature, and consequently piston motion, was
controlled to achieve specified changes in chamber volume. Volume was
controlled by feeding back the position signal from the LVDT, comparing
it with a reference position signal from a supervisory-control
computer, and passing the difference through an analog
proportional-integral-derivative compensator. Output from the
compensator was used to drive a high-current amplifier, which delivered
electrical current to the motor. Resulting forces on the motor armature
caused a change in the piston position to match the volume command.
The supervisory-control computer controlled experimental protocols
according to programmed instructions and also acquired data for later
analysis. Pressure and volume signals were acquired using 12-bit
analog-to-digital conversion at 2-kHz sampling rate. These signals were
amplified to make maximal use of the 12-bit range of the
analog-to-digital converter.
Experimental use of animals was approved by the Animal Care and Use
Committee at Washington State University. The investigation conforms
with the Guide for the Care and Use of Laboratory
Animals [DHHS Publ. No. (NIH) 85-23, revised
1985].
Protocols.
A single-beat Frank-Starling protocol (4) was conducted to establish
the VBL at which experiments were
to be performed. VBL was chosen as
the volume equal to 80% of volume at which maximum developed pressure
occurred. The average LV free wall-plus-septum weight and
VBL among these 10 hearts were
5.25 ± 0.39 g and 1.76 ± 0.15 ml, respectively. This protocol
was also used to establish the passive pressure-volume relationship. A
monoexponential equation was fit to points over the range of
end-diastolic pressure and volume values generated in this protocol.
Thus the contribution to pressure by parallel passive structures at any
volume was estimated and removed from all ensuing data records so that
we could focus only on active contractile properties.
After VBL was established, a
high-frequency volume perturbation protocol was conducted as follows.
Nine records, consisting of pressure and volume signals, were taken.
Each record consisted of an unperturbed beat that took place
isovolumically at VBL, as had the
steady-state train of beats that preceded it, and a single
volume-perturbed beat. During the volume-perturbed beat, the linear
motor was commanded to deliver a sinusoidal volume change
[Vc(t) = Vc · sin(2
ft)]
at one of three frequencies (f = 76.9, 50, or 25 Hz corresponding to periods of 13, 20, or 40 ms) and one of
three commanded amplitudes (Vc = 0.75, 1.0, or 1.25% of VBL).
As a result of the dynamic responsiveness of the volume-servo system
(damping ratio = 0.5, damped natural frequency = 80 Hz), volume change
measured using the LVDT signal from the linear motor was slightly
different from the commanded volume change. Therefore, the measured
signal was fit with the function V(t) = V · sin(2ft + 
), and the fitted V(t) and
estimated V, rather than the commanded values, were used in all
analyses (5). Repeated records were taken until all nine combinations of frequencies and amplitudes were recorded. Pressure responses to the
volume perturbation are the subject of analysis.
Following the high-frequency volume perturbation protocol, a second
single-beat Frank-Starling protocol was conducted to generate a
Frank-Starling curve that could be compared with that collected at the
onset of the experiment. This allowed detection of any deterioration in
the preparation during the course of the high-frequency protocol. No
detectable deterioration occurred.
The protocol was run during an initial period, in which beating took
place with Ca2+ as the activator
substance, and it was run once again after the perfusate had been
changed to one in which beating took place with
Sr2+ as the activator substance
(in mM: 148.4 Na+, 7.4 K+, 140.8 Cl, 0.10 Ca2+, 2.0 Sr2+, 1.1 Mg2+, 21.0 , 0.36 , and 11.1 glucose and 2.5 U/l
insulin). Approximately 20 min elapsed before steady-state beating was
obtained after switching to the Sr2+ perfusate. Data were taken
only after steady state had been reached. Differences in responses
between the Ca2+- and
Sr2+-activated states were
fundamental to testing the hypothesis that sinusoid-induced depression
of contraction was due to increased cross-bridge breakage.
Data analysis.
The pressure response
[P(t)] to sinusoidal
volume perturbation
[V(t)] was defined as
the difference between the pressure of the reference isovolumic beat
[Piso(t),
i.e., the pressure that would have developed had no volume perturbation
been administered] and the pressure of the perturbed beat
[P(t)]
|
(1)
|
Representative
Piso(t),
P(t), and
P(t) are shown in Fig.
1 [frequency of vibration
(f) = 50 Hz,
Vc = 1%
VBL]. All responses clearly
contained two components: a depressive response
[Pd(t), called "depressive" because it represented a sustained decrease in pressure below
Piso(t)
that was not at the perturbation frequency] and an in-frequency
response
[Pf(t),
i.e., that part of the response at the perturbation frequency].
Thus
|
(2)
|
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Fig. 1.
Pressure (P) and volume (V) of isovolumic (iso) beat just before
vibrational perturbation and pressure and volume of beat to which
vibration was applied. Pressure response to sinusoidal perturbation
[P(t)] is difference
between pressure of unperturbed beat
[Piso(t)]
and pressure of perturbed beat
[P(t)].
|
|
Pd(t)
and
Pf(t)
were individually identified as follows.
P(t) was considered to be composed
of
Pf(t) and a pressure around which
Pf(t)
occurred
[Pr(t)]. Pr(t)
was extracted from P(t) by filtering
P(t) to remove
Pf(t) and leave a signal
[Pr(t)]
without frequency content at the perturbation frequency. Filtering to
obtain
Pr(t)
was done by assumimg a Fourier series representation of
P(t) and then truncating that series after the 15th harmonic. Then the truncated series that did not contain
the harmonic of vibration was fit to
P(t) using a heuristic minimization
procedure (Levenberg-Marquardt algorithm) to adjust the parameters of
the Fourier series so as to minimize the sum of square errors between
the Fourier series and P(t). The
result was a time series,
Pr(t),
that contained virtually all the signal content of
P(t) minus the component at the
frequency of vibration. This is given as
|
(3)
|
where
n is the harmonic number,
Bn and
n are harmonic amplitude and
phase, respectively, and T is the beat
period. Because the shortest beat period used in these studies was 1 s, the 15th harmonic (15 Hz) was well below the lowest frequency used in
the perturbation signal, i.e., 25 Hz. The amplitude and phase
parameters (Bi
and i) had no particular
significance other than to give a wave shape to
Pr(t)
that did not include components of the in-frequency response. Once
Pr(t)
was identified by fitting with Eq. 3,
it was subtracted from P(t) to yield
Pf(t)
|
(4)
|
Subtraction
of
Piso(t)
from
Pr(t)
generated
Pd(t)
|
(5)
|
The entire process by which signals for analysis were extracted from
measured P(t) and
Piso(t)
is illustrated in Fig. 2.
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Fig. 2.
In-frequency and depressive components
[Pf (t)
and
Pd(t),
respectively] of pressure response were extracted from measured
signals by first filtering P(t) to
obtain pressure around which
Pf (t)
occurred
[Pr(t)].
Then
Pr(t)
was subtracted from P(t) to obtain
Pf (t).
Finally,
Pr(t)
was subtracted from
Piso(t)
to obtain
Pd(t).
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|
The topic of this report is
Pd(t).
We sought to determine whether
Pd(t)
was due to increased cross-bridge breakage. To that end,
Pf(t)
was analyzed to obtain cross-bridge detachment information to establish
whether cross-bridge mechanisms are responsible for
Pd(t).
Detailed description and interpretation of
Pd(t) analysis have been published elsewhere (5).
Pd(t)
was quantified by its value at the time of peak
Pr(t)
(PdT),
by its maximum value
(Pd max), and by its
average value over the entire heart period
(Pd avg). The
dependence of these quantities on f
and amplitude of the volume perturbation was established by regression
procedures described below. In addition, differences in these
quantities between the Ca2+- and
Sr2+-activated state were also
established. Finally, qualitative features of
Pd(t)
were noted and compared between
Ca2+ and
Sr2+ activation, including
time in the contraction cycle when
Pd max was reached
(TPd max).
Mean values of the various quantities between
Ca2+ and
Sr2+ activation were
compared by paired t-test.
Dependence of depressive response on amplitude, frequency, and
velocity of perturbation.
If, during sinusoidal perturbation, cross bridges are caused to detach
more rapidly, then cross-bridge-generated force and, consequently, LV
pressure will be depressed. Current cross-bridge theory dictates that
cross bridges detach more rapidly when the velocity with which
myofilaments slide past one another increases and/or when
cross-bridge strain is caused to deviate from the strain achieved
during isometric contraction (6, 9, 10, 21, 22, 25). Because
myofilament sliding velocity and cross-bridge strain are causally
linked (see Eqs. 10, 11, and
17), these are not independent
factors causing enhanced cross-bridge detachment. In this analysis, we
dealt with each factor using separate approaches: myofilament sliding
velocity was treated empirically using regression analysis, whereas
cross-bridge strain was evaluated theoretically using a cross-bridge
model. In the presence of small-amplitude sinusoidal volume
perturbation, the root-mean-square velocity of lineal motion within the
muscular LV wall is proportional to f · V (see
APPENDIX in Ref. 5). For this reason,
f · V may also be
taken as a measure of myofilament sliding velocity. Thus it is expected
that increased cross-bridge detachment due to sinusoid-induced velocity
of myofilament sliding would yield a significant dependence of measures
of the depressive response on the
f · V term in the regression analysis. Failure of that term to be included as a significant predictor variable would mean that velocity (and, consequently, increased cross-bridge breakage due to velocity) makes no
significant contribution to
Pd(t).
To determine the dependence of the depressive response on
f, V, and
f · V,
quantitative measures of that response
(PdT and Pd max) were
regressed against each variable. Stepwise multiple regression
techniques (Minitab, release 9 for Windows) were used to facilitate
predictor variable selection. The regression equations were of the form
|
(6a)
|
|
(6b)
|
where
ai and
bi are
regression coefficients and
f · V,
f 2, and
V2 allow for nonlinear
dependencies. The stepwise regression procedure incorporated a test of
whether the individual
ai and
bi were
significantly different from zero. If not different from zero, the
coefficient and its associated candidate predictor variable were not
included in the final regression equation. Dummy variables and effects coding were used to account for between-subjects differences, and the
subject dummy variables were forced into the stepwise regression (7). A
candidate predictor variable was considered significant when
P for its inclusion was <0.05.
Assessment of cross-bridge detachment dynamics.
To evaluate differences in
Pd(t)
between Sr2+ and
Ca2+ activation, it was desirable
to determine whether there was any difference in the rate constants of
cross-bridge detachment during these two activation conditions. To do
this, the component of the response that was in-frequency with the
vibration,
Pf(t),
was analyzed using a cross-bridge model. Rationale for the analysis and
the model are given elsewhere (5). Briefly, cross bridges were viewed
as force generators that, as a result of their actions, also generated
pressure. Small perturbations and an assumption of homogenous
myocardium allowed a linear transformation between force-length
relationships of the myocardium and pressure-volume relationships of
the LV chamber (5). A linear transformation allows myocardial force and
LV pressure to be treated as analogous variables and myocardial fiber
length and LV chamber volume to also be treated as analogous variables.
Therefore, inasmuch as cross-bridge dynamics can be observed in
myocardial force-length behavior, these dynamics can also be observed
in LV pressure-volume behavior.
Cross bridges, as parallel elastic force generators, generate
myocardial force equal to the stiffness of the entire parallel population times the average distortion among these cross bridges. By
analogy, LV pressure equals chamber elastance times average volumetric
distortion. Cross bridges exist in two stiffness-possessing (attached)
states: a prepower stroke attached state
(e0) and a postpower stroke attached
state (ep). These states differ, in that the prepower stroke state does not contribute to force generation during isometric contraction, whereas the postpower stroke state, having been mechanically distorted by the mechanochemical energy transduction event of the power stroke, is solely responsible for
isometric force. However, during changes in length, as in a vibration,
because pre- and postpower stroke states are attached, cross bridges in
both states are subject to induced distortion and contribute to the
pressure. If our analogy for small perturbations is pursued further,
cross-bridge stiffness is analogous to chamber elastance and
cross-bridge distortion is analogous to volumetric distortion of
elastance elements. Thus pressure is given by
|
(7)
|
where
Ee0(t)
and
Xe0(t)
are the respective elastance and volumetric distortion associated with
the prepower stroke state and
Eep(t)
and
Xep(t)
are the respective elastance and volumetric distortion associated with
the postpower stroke state.
During volume vibration around an otherwise isovolumic condition
|
(8)
|
|
(9)
|
|
(10)
|
|
(11)
|
where
iso indicates a value during the isovolumic condition and indicates
vibration-induced changes in the respective variable. By the manner in
which we defined pre- and postpower stroke isometric distortion,
Xisoe0 = 0, whereas
Xisoep(t) and is a constant. Therefore
|
(12)
|
By use of an important assumption that is discussed below, the
various components on the right-hand side of Eq. 12 can be assigned as follows
|
(13)
|
|
(14)
|
|
(15)
|
which, when substituted
back into Eq. 12, relate definitions
of the various parts of the pressure response given in
Eqs. 1, 2, 4, and
5 to their elastance and distortion
origins.
The assumption allowing Eqs. 14 and 15 was based on the notion that the
time scale of vibration-induced changes in
Eep(t)
was slow relative to the time scales of vibration-induced changes in
Xe0 and
Xep. The
slowness of
Eep(t)
was such that very little change in this variable occurred during the
period of a single vibrational cycle of 25-77 Hz. In contrast, the
speed of change in
Xe0(t)
and
Xep(t)
was such that changes in these variables were clearly expressed in
those same cycle periods. Thus
Pf (t)
was made up entirely of vibration-induced distortion changes,
Pd(t)
was made up entirely of vibration-induced elastance changes, and the
time variation in elastance due to background activation changes served
to amplitude modulate these responses. Defense of this assumption rests
on the notion that variation in elastance is the result of recruitment
and derecruitment of actively cycling cross bridges and that the
process responsible for recruitment/derecruitment, i.e., activation, is
slow relative to the process governing the distortion of force-bearing
cross bridges. These issues are discussed at length elsewhere (5).
A model of transitions between pre- and postpower stroke cross-bridge
states is given in Fig. 3. Transitions
between and away from these states invoke the following rate constants:
g (the constant governing the
detachment of the postpower stroke state), h (the constant governing the power
stroke), and d (the constant governing
the backreaction of the prepower stroke state to detached states). By
use of this model, it has been shown (5) that elastances may be
calculated from
Pr(t)
and the relevant model parameters according to
|
(16)
|
|
(17)
|
Equation 17 is derived in Ref. 5 by relating
Eep(t)
and
Ee0(t)
to the cross-bridge states
Nep and
Ne0 in Fig. 3
and then substituting Eq. 16 into the
differential equation describing the kinetics of
Ne0. Further
considerations in Ref. 5 allow differential equations describing the
time rate of change of distortion to be written as
|
(18)
|
|
(19)
|
where
a dot over a variable indicates its first time derivative. These
equations demonstrate that distortions are dynamically driven by the
derivative of V(t), and these
distortions recover from a volume disturbance at a rate that depends on
the respective elastances and the rate constants governing
disappearance of the state. Equations
16-19 constitute the cross-bridge model.
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Fig. 3.
Schematic of attached states in cross-bridge cycle.
Ni is number of
generators in ith state. Transitions
between states are governed by rate constants: b, d,
h, and g. Attached
generators in states e0 and
ep are the only cross-bridge states to
possess elastance. Attached generators may be distorted during a volume
perturbation, such that both contribute to pressure response. Under
isovolumic conditions, generators enter state
e0 without distortion and do not
generate pressure. Transition between state
e0 and state
ep is power stroke and induces a
baseline distortion in postpower stroke
(ep) generators, which, as a result
of their elastance, causes development of isovolumic pressure.
Isovolumic pressure is modified during a volume perturbation by induced
distortion in post- and prepower stroke states
(ep and
e0, respectively) and by whatever
influence volume perturbation has on recruitment of generators into or
out of cross-bridge cycle.
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|
By use of measured values of
(t),
estimated values of g, h, and
d, and calculated values of
Ee0(t)
and
Eep(t)
per Eqs. 16 and 17, the differential
Eqs. 18 and 19 were integrated numerically by
fourth-order Runge-Kutta methods (integration step size = 0.5 ms) to
obtain predicted values of
Xe0(t)
and
Xep(t).
These values, together with the calculated elastances, were then
inserted into Eq. 15 to predict
Pf(t).
By use of this procedure, the model was fit to the collective set of
nine records (3 amplitudes and 3 frequencies) of in-frequency responses
obtained during each of the separate
Ca2+ and
Sr2+ activation episodes. Fit was
obtained by using the heuristic search procedure of a modified
Levenberg-Marquardt algorithm to adjust the values of
g, h, d, and
Xisoep to
minimize the sum of square errors between model prediction and
observation (5). The outcome of the fitting procedure was a close
approximation of
Pf(t)
and the estimation of model cross-bridge cycling parameters
h, d, and
g and the isovolumic-distortion parameter
Xisoep. To
test whether cross-bridge detachment activated by
Ca2+ was different from that
activated by Sr2+, the averages of
estimates of h, d,
g, and
Xisoep in
the Ca2+-activated state were
compared, by paired t-test, with
averages in the Sr2+-activated
state.
A second use of the model was to determine whether sinusoidal volume
perturbation increased cross-bridge detachment. The cross-bridge detachment rate constant g was
examined for evidence of distortion dependence. A functional form of
distortion-dependent g in accord with
cross-bridge theory may be given by
|
(20)
|
where
g0 is the value
of g during isovolumic beating and
g1 is a
coefficient representing the strength of induced-distortion influences
on g. In Eq. 20, g > g0 for positive
and negative values of
Xep(t);
i.e., reduction, as occurs during shortening, and enhancement, as
occurs during stretch, of baseline distortion increase
g and the rate of detachment. This
distortion-dependent g was then
incorporated into the model. Equations describing the model with
distortion-dependent g are given in
Ref. 5.
Two tests were used to determine whether there was degradation or
improvement in the representation of the
Pf(t) signal when fitting with the model with constant
g rather than the model with
distortion-dependent g. The first of
these tests used the Aikake information criterion (AIC) and the
Schwartz criterion (SC) (19). These were calculated, from model fits
with and without the distortion-dependent term in Eq. 20 included, according to
|
(21)
|
where N is the number of sampled
data points (2,000 points/record × 9 records fit simultaneously = 18,000 points), RSS is the residual sum of squares, and
K is the number of parameters (K = 4 with constant
g; K = 5 with distortion-dependent g). In considering two competing model formulations, the better formulation is
the one with the smaller AIC and SC. The second test to determine whether significant reduction in the RSS occurred with incorporation of
distortion-dependent detachment was an incremental
F test (7).
| |
RESULTS |
The time course of isovolumic pressure was very different, depending on
whether the response was activated by
Ca2+ or
Sr2+ (Fig.
4), with a much slower pressure time course
during Sr2+ than during
Ca2+ activation. For instance,
time to peak isovolumic pressure was three times greater in the
Sr2+-activated state (0.85 ± 0.081 s) than in the
Ca2+-activated state (0.29 ± 0.013 s, P < 0.0001). Despite
differences in time course, magnitudes of peak isovolumic pressure
(Piso max) during
Sr2+ and
Ca2+ activations were not
different: 144.1 ± 18.9 mmHg during
Ca2+ activation and 150.3 ± 14.4 mmHg during Sr2+ activation
(P = 0.14). The extended time of
contraction during Sr2+
activation, especially the extended time during which pressure rose to
its peak value, presented more opportunity for sinusoidal volume
perturbations to induce cross-bridge breakage while pressure was rising
and maintained than was the case during
Ca2+ activation.
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|
Fig. 4.
Contrasting time course of isovolumic pressure in
Ca2+- and
Sr2+-activated states. Duration of
contraction is much prolonged during
Sr2+ activation while peak
isovolumic pressure is maintained.
|
|
Depressive response during
Sr2+ activation
is qualitatively and quantitatively different from that during
Ca2+ activation.
Qualitative differences in
Pd(t)
between the Ca2+- and the
Sr2+-activated state are shown in
Fig. 5 (f = 50 Hz, Vc = 1%
VBL). Quantitative measures of
these differences were as follows:
1) in the
Ca2+-activated state,
TPd max
occurred during late contraction, always on the descending limb of
isovolumic pressure; in the
Sr2+-activated state, it occurred
during early contraction, mostly on the ascending limb and never after
time of peak pressure (Table 1). It is
particularly relevant that the depressive response is declining as
pressure is rising during Sr2+
activation, which is inconsistent with continued vibration-induced breakage of cross bridges as more cross bridges form during increasing activation. 2)
Pd(t)
during late relaxation was strongly negative in the
Ca2+-activated state, indicating
that relaxation is speeded in the perturbed beat relative to the
nonperturbed beat; this in contrast to
Sr2+ activation, where
Pd(t)
was often positive, indicating that relaxation was slowed in the
perturbed beat relative to the nonperturbed beat. This effect of volume
perturbation on relaxation is confirmed by evaluation of the time
required for pressure to fall from 75 to 25% of
Piso max
(T75-25).
The T75-25
of perturbed beats was smaller than that of nonperturbed beats in the
Ca2+-activated state, indicating
that relaxation was speeded by the volume sinusoid. However, in the
Sr2+-activated state,
T75-25 of
perturbed beats was longer than that of nonperturbed beats, indicating
that relaxation had been slowed by the volume sinusoid (Table
2). 3)
Pd(t)
was greater in the Ca2+- than in
the Sr2+-activated state;
Pd max and
Pd avg are compared in
Table 3. These differences establish that the nature of
the depressive response depends on the manner in which the myofilament
system is activated.
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Fig. 5.
Depressive response
[Pd(t)]
in Ca2+- and
Sr2+-activated states:
f = 50 Hz, V = 1% of baseline
volume.  , Time when peak isovolumic pressure was reached and at
which 1 measure of depressive response,
PdT, was
assessed. A second measure,
Pd max, was obtained when
depressive response reached its maximum. During
Ca2+ activation, magnitude of
depressive response increased progressively while pressure was rising
through time of peak isovolumic pressure and then continued to increase
as relaxation progressed; maximum amplitude of depressive response
(Pd max) occurred late
in relaxation. This contrasts with
Sr2+ activation, in which
Pd max occurred early
during ascending limb of isovolumic pressure, and depressive response
did not increase as pressure continued to rise on its way to peak
isovolumic pressure. During relaxation, depressive response declined in
magnitude and actually became positive as relaxation entered its final
phase.
|
|
Depressive response depends mostly on sinusoidal amplitude with
little dependence on frequency or velocity.
An example of a family of nine
Pd(t)
responses obtained in one heart at the three
f and three
Vc used in this study is shown in Fig. 6. Clearly,
Pd(t)
increased with increasing Vc.
Apparently, Pd(t)
also increased with increasing f.
However, because of the underdamped character of the volume-servo
system, the actual V increased with increasing
f, such that the apparent increase in Pd(t)
with f may have been secondary to the
concordant increase in V, despite the constant
Vc. This effect is accounted
for in the regression analysis, where measured V is used rather than Vc.
These apparent trends in Fig. 6 were quantitatively evaluated using
data from all 10 hearts, with stepwise multiple regression analysis of
PdT and
Pd max and
Eq. 6, a and
b. According to our criteria for
acceptance of predictor variables (and not reporting coefficients for
between-subjects variability), the simplest best regression equations
for predicting
PdT and
Pd max
were
|
(22a)
|
|
(22b)
|
for Ca2+ activation
and
|
(23a)
|
|
(23b)
|
for
Sr2+ activation. V appeared in
all equations, whereas f appeared only
during Ca2+ activation and
f · V appeared
only in Eq. 22a. In all cases, V was the first variable entered in the stepwise regression. This was
because V alone accounted for >90% of all the variation in Pd in every case. Neither
f nor
f · V appeared as
significant variables in determining either measure of the depressive
response (PdT and
Pd max) in the
Sr2+-activated state. To determine
the relative importance of V, f,
and f · V in
Eq. 22, a and
b, we considered how a change in each
around some reference values
(V|0 and
f |0)
contributed to a change in Pd.
Thus we write
|
(24)
|
where d represents the differential change in the variable,
and the partial derivatives were the values of the corresponding coefficients in the regression equation. Around a reference
V|0 of 1%
VBL (~0.02 ml) and a reference
f|0
of 50 Hz, Eq. 22a predicts a
PdT of
4.53 mmHg. A 50% increase in V causes a further increment in
the depressive response of 3.74 mmHg for a total PdT of
8.27 mmHg, i.e., an 82% increase in
PdT magnitude. This compares with a 50% increase in
f, which takes away 1.11 mmHg from the
depressive response for a total
PdT of
3.42 mmHg, a 24% decrease in
PdT
magnitude. Furthermore, a 50% increase in
f · V takes away
0.51 mmHg from the depressive response for a total
PdT of
4.02 mmHg. These calculations show that, rather than
contributing to the depressive response, f and
f · V actually
reduce that response. Continuing these calculations with
Eq. 22b for
Pd max, a
V|0 of 1%
VBL (~0.02 ml) and an
fq|0 of 50 Hz predict a Pd max
of 7.02 mmHg. A 50% increase in V brings about a 100%
increase in the magnitude of
Pd max, whereas a 50%
increase in f takes away 90% of
Pd max.
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Fig. 6.
Families of depressive responses
[Pd(t)]
obtained during sinusoidal perturbations at 3 frequencies (25, 50, and
76.9 Hz) and 3 amplitudes (0.75, 1.0, and 1.25% of baseline volume).
Top:
Ca2+-activated state;
bottom:
Sr2+-activated state. , Time of
peak isovolumic pressure. Increasing magnitude of depressive response
in any 1 panel is associated with increasing amplitude of
perturbation.
|
|
To summarize these results, V was always a significant predictor of
the depressive response during
Ca2+ and
Sr2+ activation and, by itself,
accounted for >90% of the variation in
PdT and
Pd max. Of less
importance, and of significance only during
Ca2+ activation and not during
Sr2+ activation, was the effect of
f. Instead of increasing the
depressive response, f decreased it;
larger f resulted in less magnitude of
PdT and
Pd max. This decrease in
the depressive response with f has
consequence with regard to the character of underlying dynamic
processes and is discussed relative to the dynamics of
f-induced changes in cross-bridge
strain in the DISCUSSION. Importantly,
f · V (analogous
to the velocity of filament sliding) was not a significant predictor of
Pd max during
Ca2+ activation, nor was it a
significant predictor of
PdT or
Pd max during
Sr2+ activation. During
Ca2+ activation,
f · V was found
to be a significant predictor of the depressive response only for
PdT. In
that one case, it was the last variable entered in the stepwise
regression, indicating that its incremental contribution in accounting
for variation in
PdT was
least among all the candidate variables. Furthermore, rather than
contributing to the depressive response, f · V actually
reduced that response, an effect that is contrary to the hypothesis
that increased cross-bridge breakage due to increased velocity of
filament sliding is contributing to the depressive response.
Cross-bridge cycling in the
Sr2+-activated
state was not different from that in the
Ca2+-activated
state.
As we found in our earlier study (5),
Pf(t)
was well fit with the cross-bridge-based model, i.e.,
Eqs. 16-19. Fit was to all nine
responses simultaneously. The median
R2 of fit in
Ca2+- and
Sr2+-activated states were 0.974 and 0.981, respectively. Very little of the total variation in
Pf(t),
which was due not only to the sinusoidal changes in V but also to the
changes in f and V among the nine
separate responses that were fit, remained unaccounted for by the
model. Importantly, cross-bridge cycling parameters g,
h, and d were
estimated to be the same during
Ca2+ and
Sr2+ activation (Table
4; some caution should be used in the
interpretation of the value of d, as
discussed in Ref. 5). Despite in the depressive response between the
Ca2+- and the
Sr2+-activated states, there were
no differences in the underlying dynamics of cross-bridge cycling
between Ca2+ and
Sr2+ activation.
Cross-bridge detachment rate does not increase with sinusoidal
volume perturbation.
We could find no evidence for increased cross-bridge detachment during
sinusoidal volume perturbation due to perturbation-induced changes in
cross-bridge distortion. There was no improvement in accounting for
variation in the data when distortion-dependent attachment was
incorporated into the cross-bridge model: median R2 was the same
for the models with and without distortion-dependent detachment in the
Ca2+- (0.9768 with and without
distortion-dependent detachment) and the
Sr2+-activated state (0.9810 with
and without distortion-dependent detachment). Furthermore, during
Ca2+ activation,
incorporating distortion-dependent detachment into the model resulted
in a lower AIC in only 3 of 10 hearts and resulted in a lower SC in
only 1 of 10 hearts. Furthermore, a significant reduction in RSS as
determined by the incremental F test
was achieved in only 1 of 10 hearts. This compares with
Sr2+ activation, during which
there was a reduction in AIC and SC in only 1 of 10 hearts and a
significant incremental F test also in
only 1 of 10 hearts. Finally, the values of g, h,
d, and
X0 were virtually
unaffected by whether or not distortion-dependent detachment was part
of the model. These results, showing no detectable improvement in the
model with the addition of distortion-dependent detachment [i.e.,
g1 in
Eq. 20), are completely in accord
with earlier results from an identical test conducted on
Pf(t) data from 14 other Ca2+-activated
hearts at 30°C and reported in Ref. 5]. Thus, accounting for
distortion-dependent detachment did not improve the model representation of the data. These results are consistent with no
increased cross-bridge breakage in the perturbed beat over and above
that during the isovolumic beat as a consequence of the sinusoidal
perturbation that produced the depressive response.
| |
DISCUSSION |
We present six lines of evidence to indicate that small-amplitude
volume sinusoids do not depress cardiac contraction through increased
breakage of cross bridges. 1) The
depressive response was strongly affected by whether the myocardium was
activated by Ca2+ or by
Sr2+ (Fig. 4), indicating that the
depressive response was dependent on activation as opposed to
cross-bridge cycling. 2) During
prolonged contraction, as in the
Sr2+-activated state, rather than
increased depression as pressure rose on the ascending limb of the
pressure waveform, the depressive response actually declined (Fig. 5,
Table 3), despite the extended opportunity for volume sinusoids to
cumulatively break more cross bridges and cause greater depression.
3) Although relaxation rate was
increased with volume sinusoids during
Ca2+ activation, as is consistent
with volume-induced increase in cross-bridge detachment, the relaxation
rate actually decreased with volume sinusoids during
Sr2+ activation (Table 2), which
is counter to an increase in cross-bridge detachment rate.
4)
f · V, as an
analog of velocity of myofilament sliding, which is assumed to enhance
cross-bridge breaking, was insignificant as a predictor of the
depressive response or, when significant, participated by diminishing
the depressive response rather than contributing to its
magnitude (Eqs. 22 and 23).
5) Despite the differences in the
depressive response between the Ca2+- and the
Sr2+-activated state, we found no
difference in cross-bridge detachment rate constant or in any other
cross-bridge cycling parameters (Table 4).
6) We were unable to detect any
increase in the cross-bridge detachment rate constant due to
volume-induced change in cross-bridge strain, as would be predicted
from current cross-bridge theory and as one must assume in a
rationale to support a hypothesis for vibration-induced increase in
cross-bridge breakage. Collectively, these results argue against a
cross-bridge detachment-based cause for a sinusoidally induced
myocardial depressive response.
Depressive response during
Ca2+ activation
in these experiments is identical to vibration-induced contractile
depression reported by others.
One difference between our method and the methods of most other workers
for mechanically inducing contractile depression is that we used a
sinusoidal LV volume perturbation, whereas others have used external
vibrators on the LV wall (15-17, 20, 24, 26). These other workers
have found that vibrations imposed on the LV anterior wall travel to
the posterior wall and throughout the myocardium (14, 20) to induce a
global myocardial effect. Although none of these previously reported LV
depressions were analyzed in the same quantitative manner as we have
done here, certain similarities can be seen in the contractile
depression obtained in our experiments and that obtained by others. In
the only other studies in which vibrations were applied over the full cycle duration of an isovolumically beating heart (16, 20), the
qualitative features of the depression in those blood-perfused dog
hearts at 37°C appeared to be the same as those in our
Ca2+-activated rabbit heart at
25°C. In studies where vibration was imposed on ejecting hearts
(16, 17, 26), the depressive response involved decrements in
pressure and in ejection, which makes comparison with the current
results in isovolumic hearts difficult.
Of particular interest is the comparison to data obtained when
vibration was confined to the relaxation and diastolic phases of the
cycle (12, 24). These authors found, as we did in the Ca2+-activated heart (Table 2),
that mechanical perturbations during this phase of the cycle caused a
speeding of relaxation. That this effect originated from the
contractile apparatus rather than from some other feature of the intact
heart was confirmed by studies in isolated rat papillary muscle where
length vibration speeded relaxation (11). Of particular note in these
papillary muscle studies was that the vibrational effect that speeded
relaxation did not depend on frequency of vibration for frequencies
>30 Hz, whereas this effect was strongly dependent on vibrational
amplitude at these frequencies. This is consistent with our findings in these isolated heart studies that the depressive response was not
dependent on frequency of 25-76.9 Hz but strongly dependent on
amplitude at all frequencies.
Therefore, despite the differences in method of mechanical
perturbation, whether it is given as a sinusoidal change in LV volume,
a myocardial vibration by an external oscillator on the LV anterior
wall, or a sinusoidal change in papillary muscle length, the net result
to depress contractile function is the same.
Dynamics underlying depressive response are different from those
associated with cross-bridge detachment.
Features of dynamic processes are revealed by the manner in which the
response variable changes with f. For
instance, in simple first-order systems, the response variable will
change strongly with f if the
characteristic frequency of the process is in the vicinity of
f but will change only weakly with
f if
f is far greater than the
characteristic frequency. Furthermore, the response will decrease with
f if the process is driven directly by
the input but will increase with f if
it is driven by the derivative of the input (e.g., the
f dependence of a 1st-order low-pass
filter vs. that of a 1st-order high-pass filter). We found that the
depressive response did not change significantly with
f or, in the one instance in which
f was significant, changed by
decreasing magnitude with increasing
f. Furthermore, decreasing magnitude
of the response variable with increasing
f was sufficient to prove that
(t), analogous to
f · V, was not
the effective driving function for the depressive response as it is for
the in-frequency response (5). As argued in the following paragraph,
our findings that the depressive response does not depend on
f or decreased with f argue against accepting
perturbation-induced cross-bridge breakage as being responsible for the
depressive response.
We reasoned that if contractile depression depends on increased
cross-bridge breakage due to changes in cross-bridge distortion, as
currently hypothesized (5), then the depressive response will change
with f and V in the same manner as
cross-bridge distortion. Previously (5), we showed that, to an
approximation, frequency-dependent changes in distortion of the
force-bearing state,
X(f),
with sinusoidal volume changes,
V(f), are given
by
|
(25)
|
where j = 
and
(f) is the phase
difference between the distortional response and input volume sinusoid.
From Eq. 25, a root-mean-square
distortion
(Xrms) at any f and V may be calculated as
|
(26)
|
Equation 26 defines the manner in which an average distortion
varies with f and V during
sinusoidal perturbations: for all 2f within some range around
g,
Xrms increases
with f and V. For
2f far above
g,
Xrms retains a
strong dependence on V and continues to increase with
f but only weakly. For instance, a g of 50 s1, as we estimated with
these data, yields a characteristic frequency of ~8 Hz. This means
that increasing f from 25 to 75 Hz
would cause a 5% increase in distortion. Such an increase in
distortion would be expected to cause an increase in the depressive
response if this response was due to increased cross-bridge breakage
secondary to increased distortion. However, this is opposite to what
was observed when increased f was
associated with no change or a decrease in the depressive response.
Thus the depressive response and cross-bridge distortion do not change
similarly with f, and different
dynamic processes must be responsible for each. Furthermore, these data support the hypothesis that the characteristic frequency of the process
underlying the depressive response is much lower (a slower process)
than that responsible for cross-bridge detachment.
Possible mechanism involves activation, perhaps the cooperative
feedback between force-bearing cross bridges and activation.
Previous studies have attempted to discriminate between
Ca2+ handling associated with
excitation-contraction coupling and cross-bridge kinetics
as competing alternative mechanisms for vibrational depression of
contraction. Considerable evidence has now accumulated to eliminate Ca2+ handling associated with
excitation-contraction coupling as a possible mechanism (11, 20). By
default then, explanations were sought for the effects of vibration on
cross-bridge kinetics. This was reasonable, because vibration-induced
myofilament sliding or vibration-induced variation in cross-bridge
strain would, according to current cross-bridge theory, enhance
cross-bridge breakage and reduce force (6, 9, 10, 21, 22, 25). In fact, mathematical models incorporating vibrational effects in cross-bridge kinetics do reproduce, at least qualitatively, some aspects of contractile depression (8). However, the two above alternatives do not
constitute a complete list of possible mechanisms, for it is now known
that other factors can modulate force development in the presence of
fixed Ca2+ without changing
cross-bridge kinetics (18, 23). Among these other factors are
1) changes in the force developed by
individual cross bridges, 2) changes
in the binding affinity of Ca2+
for troponin C, and 3) changes in
the cooperative mechanisms by which force-bearing cross bridges feed
back to enhance their own activation.
The results reported here demonstrate that vibration does not change
cross-bridge kinetics. Thus we must reject changes in cross-bridge
kinetics as the basis for vibration-induced depression of contraction.
Furthermore, changes in force by an individual cross bridge are
associated with changes in the isometric strain of these cross bridges
(18). It has been shown that the
Xisoep parameter in
our cross-bridge model is related to cross-bridge isometric strain (2).
Because Xisoep did
not change, even when the depressive response was markedly different,
as it was during Ca2+ vs.
Sr2+ activation (Table 4), we
reject the possibility that vibrational depression of contraction is
due to a decrease in force developed by individual cross bridges. Thus
we are left with choosing between a vibration-induced decrease in the
binding affinity of Ca2+ for
troponin C and a vibration-induced decrease in the cooperative feedback
between force-bearing cross bridges and cross-bridge activation. We
favor the latter of these two possibilities, because we found that the
dynamics of the processes underlying contractile depression were slower
than the dynamics of cross-bridge cycling. We recently demonstrated (1)
that cooperativity in activation will cause force transients to become
much slower than would be predicted on the basis of the speed of
cross-bridge cycling. The consequence is that the characteristic
frequency of the activation process is much lower than that of the
cross-bridge cycle. This suggests that our finding of an apparently
slow process underlying the depressive response is consistent with
activation being that underlying process. That we observed such
different depressive responses relative to pressure development with
Ca2+ and
Sr2+ activation argues further
that the underlying mechanism is based on activation.
In summary, we conclude that contractile depression due to
small-amplitude perturbation at frequencies in the 25- to 76.9-Hz range
is not due to increased cross-bridge breakage but, more likely,
involves a change in the manner in which thin filaments are activated,
perhaps in the cooperative feedback between force-bearing cross bridges
and activation.
| |
ACKNOWLEDGEMENTS |
This work was supported by National Heart, Lung, and Blood
Institute Grant HL-21462.
| |
FOOTNOTES |
Address for reprint requests: K. B. Campbell, Depts. of VCAPP and
Biological Systems Engineering, Washington State University, Pullman,
WA 99164.
Received 29 May 1997; accepted in final form 4 December 1997.
| |
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AJP Heart Circ Physiol 274(4):H1141-H1151
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Abstract
Introduction
