(Circulation. 1997;96:2368-2375.)
© 1997 American Heart Association, Inc.
Articles |
Relation Between Muscle Contraction Speed and Hydraulic Performance in Skeletal Muscle Ventricles
From the Department of Human Anatomy and Cell Biology (J.C.J., M.M.N.K., S.J.G., S.S.) and the Department of Clinical Engineering (A.S., R.A.B.), the University of Liverpool (UK), and the Royal Brompton Hospital (R.M.E.), London, UK.
Correspondence to Dr J.C. Jarvis, Department of Human Anatomy and Cell Biology, University of Liverpool, Liverpool L69 3BX, UK. E-mail jcj{at}liverpool.ac.uk
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Abstract |
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Background The fatigue resistance and power-to-weight ratio of skeletal muscle that has been conditioned by electrical stimulation makes cardiac assistance from a graft of such muscle a realistic prospect. A skeletal muscle must be surgically reconfigured to act on the circulating blood, but little is known about the power losses that accompany such interventions. We investigated in acute experiments the hydraulic performance of approximately cylindrical pumps made from sheep latissimus dorsi (LD) muscles, having first characterized the performance of each muscle in situ.
Methods and Results Force-length and force-velocity relations were measured in situ for LD that had received either 8 weeks of stimulation at 2 Hz or no chronic stimulation. Two sizes of skeletal muscle ventricle (SMV) were formed from the same muscles, and their hydraulic performance was measured. The hydraulic performance was also calculated from the linear data, models of the force-length and force-velocity curves, and a description of the stress distribution within the SMV wall. The model predicted well the isovolumetric function of the ventricles and the optimum afterload but overestimated the flow and therefore the power. In conditioned ventricles the performance was particularly poor because of the slow contractile properties of the muscles.
Conclusions If SMVs are to pump effectively against the arterial impedance, the pressure drop caused by flow (or the internal resistance) should be lower than that of the ventricles we constructed. Progress can be made through refinement of surgical technique and stimulation protocols that generate faster fatigue-resistant muscles.
Key Words: muscles • heart-assist device • ventricles
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Introduction |
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For more than 10 years the challenge of forming an auxiliary blood-pumping chamber from the latissimus dorsi (LD) muscle has been the focus of considerable research effort. In humans, as in the sheep used in this study, the fibers of the LD muscle run directly from their origin on the inferior angle of the scapula and the thoracolumbar fascia to a tendinous insertion on the humerus. Their normal mode of action is therefore to produce a force that is aligned approximately with the long axis of the muscle. However, when such a muscle is formed into a conical pumping chamber with the fibers running circumferentially, the stresses on the fibers are more complex: contraction of the muscle produces both a tangential and a radial component of force. It has been demonstrated that some of the characteristics of such skeletal muscle ventricles (SMVs) are directly analogous to the properties of the linear muscles from which they are formed.1 2 3 For example, Spotnitz et al1 were able to predict the maximum isometric pressure of SMVs by means of the Laplace relation between wall stress and pressure and an experimental measurement of the maximum isometric force produced by the rectus abdominis muscle in situ.
There is no doubt that SMVs can produce pumping work,4 5 6 but it is still not clear how the power output of the muscle in the ventricular configuration compares with its power output in the normal anatomic position. The active performance of an SMV will be determined by (a) the relation between the pressure inside the ventricle and the stress within its muscular wall and (b) the relation between the wall stress and the movement of the wall, with regard to the force-velocity characteristics of the muscle used to make the ventricle. This second relation is important for the following reason. Most mammalian skeletal muscles can maintain only a very low level of continuous work; their properties are suited to intermittent activity rather than the continuous activity needed to assist the heart. Such muscles will, however, respond to regimens of electrical stimulation that deliver continuous neural activity to the muscle,7 8 undergoing changes that confer higher sustainable power output than untrained muscles. These conditioned muscles have the potential to provide continuous assistance to the heart, but they have a reduced speed of shortening against a given load.9 10 In practice, therefore, the muscle used to make SMVs will be slower to contract than control muscle. The consequences of reconfiguration and conditioning for SMV performance are not well understood.
Here we present mechanical measurements made on sheep LD muscle both in its anatomic (linear) configuration and after wrapping the muscle into single-layered, approximately cylindrical SMVs of two different sizes. The measurements were carried out on both control (fast-contracting) muscles and muscles that had been stimulated chronically for 6 to 8 weeks and were therefore fatigue resistant but slow contracting. The results have been interpreted through a novel description of SMVs on the basis of the force-velocity properties of linear muscle and the distribution of wall stress within a thick-walled chamber described by Lamé's equation.11 This has been used to predict the performance that might be expected from an SMV if the muscle performance were unaffected by reconfiguration into a conical pumping chamber and if it pumped against a noninertial load. Discrepancies between this idealized model and recordings from real SMVs have enabled us to highlight areas that require further investigation.
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Methods |
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Chronic stimulation of the left LD muscle was performed in a group of 8 sheep with body weight between 61 and 71 kg. Anesthesia was induced with intravenous thiopentone (10 mg/kg). After intubation, anesthesia was maintained with halothane (2%) in 50% nitrous oxide/50% oxygen. Mechanical ventilation was available but rarely necessary. Under aseptic conditions, electrodes were woven into the proximal part of the LD muscle near the motor nerve branches and secured with titanium clips. The electrodes were connected to an implantable neuromuscular stimulator (Itrel, Medtronic Inc) placed under the rectus abdominis muscle. One week later, the stimulators were switched on and delivered 210-µs pulses at a constant frequency of 2 Hz.
After 6 to 8 weeks of stimulation, the sheep were anesthetized as before and subjected to the terminal procedure to be described. The same procedure was carried out on 4 control sheep in which the LD muscle had not been stimulated.
The sheep were placed on their right side, and the LD muscle was exposed. Electrodes, where present, were disconnected from the implantable stimulator; in the unstimulated control group, electrodes were placed as described above. In both cases, the electrodes were then connected to an external stimulator. The resting length of the muscle was measured with the forelimb in its normal (upright standing) position, and marker sutures were placed at 5-cm intervals in the midline of the muscle.
The distal attachments of the muscle were divided and sutured around an aluminum tube. Velcro strips were used as pledgets to maintain adequate mechanical integrity. The aluminum tube was connected by a steel cable to the lever arm of a servomotor muscle testing system (Cambridge model 310B) that measured the position of the muscle attachment and the tension. The humerus (and therefore the proximal attachment of the muscle) was immobilized by strapping it to a steel frame, to which the servomotor was also attached.
The position of the servomotor arm, the stimulation delivered to the muscle, and the collection of data from the servomotor were controlled by a suite of software written in-house. The length corresponding to maximum twitch force was determined and used as the starting point for subsequent contractions. A series of afterloaded isotonic contractions was then elicited from the muscle at constant loads up to 50N. From the displacement records, the initial velocity of shortening achieved against each load was measured to generate the force-velocity and the derived power-velocity relations.
The muscle was then disconnected from the servomotor. Velcro strips
were placed at the level of, and 94 mm proximal to, the distal
myotendinous junction, with the muscle at resting length. The two
Velcro strips were then apposed and sutured together to make an
approximately cylindrical ventricle of 15-mm radius. The neck of the
ventricle was formed from the anterior border of the muscle by sewing
it to a fabric conical ring that connected the ventricle to the
hydraulic testing apparatus. A latex condom provided a
watertight lining. The hydraulic testing system is illustrated in Fig 1
. An in-line flow probe
(Transonic Inc) was connected to a T-piece that incorporated a port for
a ventricular pressure transducer (Gaeltech). The side arm
of the T-piece led to the volume control system, and the distal arm led
through a one-way valve to a pressurized afterload chamber (10-cm
diameter) that contained a small volume of water. The air space above
the water was connected to a 40-L air chamber that could be pressurized
to any desired afterload by a cylinder pump. Since the volume ejected
from the ventricle was very small compared with the air chamber volume,
the afterload was effectively constant during ejection. An acrylic
block was placed at the bottom of the afterload chamber so that the
cross-sectional area available to the fluid was very small. A
calibration mark on the side of the chamber thus made it possible to
return to the ventricle the precise volume of fluid expelled from it
during a single ejection.
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The pressure produced both passively and actively by the muscle was measured at a series of ventricular volumes. The muscle was stimulated at 100 Hz for the active measurements. The length of the burst was 300 ms for the control muscles and 500 ms for the stimulated (slower) muscles, allowing both types of muscle to reach maximum force. The muscles were rested for 30 seconds between contractions.
The ventricles then contracted against constant afterloads at a series of preloads. For those contractions that led to an ejection of fluid from the ventricle, the fluid was transferred back into the ventricle before the next contraction.
When the ventricle of 15-mm radius had been characterized, the
muscle was reformed into a ventricle of 20-mm radius. Since the length
of the ventricle was 
100 mm in each case, the nominal volumes
of the two sizes of ventricle were 70 and 125 mL.
The sheep were given an overdose of sodium pentobarbital. Samples were taken from the LD muscles and quick-frozen for subsequent biochemical and morphological examination.
Myosin Heavy Chain Isoform Composition
Crude myosin was prepared by the method of Aigner et
al12 with the addition of a protease inhibitor
cocktail (Complete, Boehringer Mannheim) in the
homogenization buffer at the manufacturer's
recommended dilution. The myosin heavy chains were separated by sodium
dodecyl sulfate (SDS)-polyacrylamide gel
electrophoresis by a modification of the method of Talmadge and
Roy.13 The separating gel contained 8%
N,N'-methylene-bis-acrylamide (43.25:
1), 37.5% glycerol, 0.2 mol/L Tris (pH 8.8). 0.1 mol/L
glycine, 0.4% SDS, and 0.05% ammonium persulfate. The stacking gel
contained 4%
N,N'-methylene-bis-acrylamide (50:
1), 30% glycerol, 70 mmol/L Tris (pH 6.7), 4 mmol/L
EDTA, 0.4% SDS, and 0.1% ammonium persulfate. Polymerization of both
parts of the gel was initiated by the addition of 0.05%
N,N,N',N'-tetramethylethylenediamine (TEMED). Approximately
2.5 µg of protein was loaded onto each lane of the gel.
Electrophoresis ran for 40 hours at 70 V, with the temperature of the
apparatus maintained at 4°C. The bands were then stained
with Coomassie blue.
Predictive Model
Lamé's equation was used to predict the hoop-stress
distribution within the ventricular wall from the pressure
and dimensions of the chamber.
According to this equation, the hoop stress at radius r is given by
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Results |
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Linear Muscle: Passive Properties
The force-length curves were typical of skeletal muscle. Fig 2a
shows the passive tension over a range of ±10% of resting
length. The zero position of
the servomotor lever arm corresponds to the resting length of the
muscle, judged from the marker sutures. Examination of the force-length
curves shows that the steeper portion of the curves started at
different positions of the lever for different muscles, so that some of
the muscles must have been more stretched than others. The difficulty
of setting up the muscles consistently, illustrated by Fig 2, is relevant also to the construction of ventricles of a given resting
volume (see below). We were, however, able to fit the force-length data
with single exponential curves. The fitted curves were used to predict
the passive pressure-volume curves of the ventricles formed later from
the same muscles.
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Linear Muscle: Dynamic Characteristics
The general form of the relation between force and velocity (Fig 2b
) was also typical of skeletal muscle. The data from the faster
control muscles did not lie on a smooth curve, because the force
records contained oscillations arising from lateral
movement of the muscle and of the linkage between the muscle and the
servomotor caused by the abrupt increase in tension upon activation.
For this reason it was difficult to make accurate measurements of the
initial velocity at small loads. Nonetheless, the records were good
enough to determine the parameters needed for a comparison
of the mechanical behavior of the muscles with previously published
data from smaller mammals. The untreated force-velocity data were
fitted to the Hill equation:
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The control muscles had a maximum velocity at zero load of 950±139 mm s-1, or 3.8 muscle lengths s-1. Extrapolation of the fitted curve to zero velocity gave a maximum force of 68±14N. This force may be expressed relative to the "physiological cross-sectional area": mass/(lengthxdensity). The maximum specific force was then 116 kN m-2, less than one third of the value in rabbit tibialis anterior muscle.10
The force-velocity curves obtained from the chronically stimulated muscles were smoother and had a greater curvature than those from the control muscles. The force records were less affected by oscillations because the contractions were neither as forceful nor as fast. The maximum velocity was 557±74 mm s-1, or 58% of the control value. The maximum force, obtained by extrapolation of the fitted curves, was 36±3N, or 53% of the control value.
The power-velocity relations are shown in Fig 2c. The peak of the power
curve represents the maximum instantaneous power output (not to
be confused with the sustainable power output). Stimulated muscles
produced a maximum power output of 2 W and control muscles 10 W.
The average weight of the control muscles was 196±91 g and of the
stimulated muscles 151±28 g. The large variation in mass was due in
part to adherent fatty tissue. We made a more precise estimate from the
average thickness of muscle tissue measured from histology blocks and
the area of the chest wall covered by the muscle. On this basis, the
maximum power output per unit mass of the muscles in situ was 90 W
kg-1 in the control muscles and 15 W
kg-1 in the stimulated muscles.
Myosin Isoform Composition
Fig 3 shows the distribution of myosin heavy chain isoforms in the
stimulated and contralateral control LD muscles of three sheep and in
control LD muscles from dog and
rabbit. Lanes 1 and 2 are from
the proximal and distal parts, respectively, of a sheep LD. There was
no difference in the isoform distribution. The conditions for
electrophoretic separation were optimized for the sheep myosin
preparation and do not give as good a separation of the fast heavy
chains of dog (lane 9) or rabbit (lane 10). The type-2A fast heavy
chain is the most abundant isoform in sheep LD, and it is associated
with a smaller proportion of the type 2D/X and type-1 isoforms. Lanes
3, 4, and 8 demonstrate the complete transformation of sheep LD that
resulted from 2-Hz stimulation for 8 weeks: only the slow type-1
isoform was expressed in these muscles. A small amount of the fast
isoform continued to be expressed in one stimulated muscle (lane 6). It
may be that a small proportion of the motor units making up this muscle
escaped activation by the intramuscular electrodes and therefore
remained fast.
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Isovolumetric Performance
The passive pressure-volume curves from the various ventricles
varied considerably and the sets of curves from the ventricles of
nominal radius 15 mm overlapped with those from ventricles of
nominal radius 20 mm. Despite this variation, the mean data
presented in Fig 4a show that the ventricles formed two readily
distinguishable sets. The mean
curves for control and stimulated muscle are similar—the stimulation
therefore had little effect on the passive properties of a single
thickness of muscle tissue. The arrows in Fig 4 indicate that the mean
passive intraventricular pressure at the nominal
volumes of 70 and 125 mL was similar for the two sets of ventricles:
close to 20 mm Hg. To minimize the effect of variability in the
construction of the ventricles, data on pumping performance are
presented from two groups of four ventricles whose passive
pressure-volume characteristics, reflecting their construction, were
very similar (Fig 4b). Each group comprises ventricles of 15-mm radius
and 20-mm radius made from one control and one conditioned muscle.
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Prediction of Passive Pressure-Volume Curves From Force-Length
Data
The exponential curves fitted to the passive force-length data
were used to predict the passive pressure-volume relation of the
ventricles by equating the linear stress at a particular fractional
extension to the hoop stress of the hypothetical ventricle according to
Lamé's equation. The mean compliance of the ventricles was
slightly greater than that predicted by this model (Fig 4c), so the
wrapping procedure did not appear to make the muscle more
resistant to passive stretch. Fig 4d shows an example of the
predicted and actual pressure-volume curves.
Active Isovolumetric Performance
Fig 5 shows the mean developed isovolumetric pressure (the excess
of maximum pressure over the preload pressure) at preloads between 0
and 80 mm Hg for ventricles made from six different
muscles.
Representative error bars (SD) are included at the
highest preload but are excluded elsewhere for clarity. Each of the
three control and three stimulated muscles was made into a ventricle of
15-mm nominal radius (broken lines) and then one of 20 mm nominal
radius (solid lines). There was no significant difference at any
preload between the pressure developed by the two sizes of ventricle.
The pressure developed by the control ventricles was significantly
greater than that developed by the stimulated ventricles at 80–mm Hg
preload (P=.02 and P=.05 for the small and large
ventricles, respectively). The pressure developed by the conditioned
ventricles was not as dependent on preload as that developed by the
control ventricles. The mean data are illustrated by original pressure
recordings obtained from one control SMV (Fig 6a) and one
chronically stimulated SMV (Fig 6b). Fig 6 also shows the
slower rate of rise of pressure within the conditioned SMVs, and in Fig 7 the maximum rate of rise of pressure is plotted for the control and
conditioned ventricles.
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Dynamic Hydraulic Performance
The pressure and flow records for each ejection were
analyzed to determine the stroke volume, peak power, and work
done in each contraction at each preload and against each afterload.
Results are shown for the two pairs of ventricles that we chose for
their similarity of construction (see above; Figs 8 and 9, a through f)
together with results taken from the literature (g through i) for
ventricles made acutely in dogs14 replotted for comparison
with our
data.
The dynamic measurements revealed a greater difference between the
control and conditioned ventricles than the isovolumetric
measurements.
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Stroke Volume
Fig 8 shows that the stroke volume of the ventricles was highly
dependent on preload when the afterload was small and that the
performance of the SMVs made from stimulated muscle (open
symbols) was inferior to that of the SMVs made from control
muscle (filled symbols). The stroke volume of the larger ventricles
(solid lines) was usually greater than that of the smaller ventricles
(dotted lines), but an exception is seen in d, e, and f, in which the
large control ventricle performed poorly compared with the other
ventricles at low preloads but relatively well at high preloads. The
stroke volume of the ventricles made from conditioned muscle was lower
than that of the control ventricles, and the conditioned ventricles did
not eject at all against an afterload of 120 mm Hg.
Maximum Instantaneous Power Output
The calculated data in Fig 9 illustrate an important procedural
problem in making measurements of hydraulic performance.
Measurement of the linear power of the muscle (forcexvelocity) was
made by subjecting the muscle to a servo-controlled constant force that
had no inertial component. In the hydraulic situation there was a
significant inertial component to the ventricular load.
Consequently, the pressure and flow traces were out of phase (Fig 10a)
and the maximum power of the ventricle was not, therefore, determined
by the maximum value of ventricular
pressurexflow. Phase
differences of this type have not been explicitly dealt with in
previous work. We calculated the maximum power as maximum pressure
measured during ejectionxmaximum flow measured during ejection.
Maximum power was highly sensitive to preload but not to afterload (Fig 9, a, b, and c). The value obtained from the large control ventricle
was just over 1 W at 40–mm Hg preload and 80–mm Hg afterload
compared with 10 W from the muscle measured with a noninertial load
in its normal anatomic configuration (Fig 2c). The maximum power of the
small control ventricle was much less than that of the large ventricle
and smaller still in both ventricles made from conditioned muscle. The
maximum power output of the conditioned ventricle was 0.3 W, which
may be compared with 2 W measured with a noninertial load in the normal
anatomic configuration.
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Work
The work done in a single contraction was calculated from the
difference in pressure between the preload and afterload multiplied by
the stroke volume. This estimate was chosen rather than the integral of
pressurexflow because of the phase shift problem referred to above.
The curves for work (Fig 9, d through f) are similar to those for
maximum power, and there is good correspondence between our data from
the 20-mm-radius control ventricle and data from Oda et
al14 (Fig 9, g through i).
Predictions of Pump Function on the Basis of Lamé's
Theorem
The peak flow during ejection was inversely proportional to the
afterload pressure (Figs 10b and 11a). The slope of the
relation is an approximation to the internal resistance of the
ventricle (the pressure drop resulting from a particular flow rate). A
full analysis of the ventricular resistance is
outside the scope of this study, but we made some preliminary
comparisons of the actual pressure-flow curves with predictions made
from the model described above and with published data from a dog left
ventricle15 (Fig 12).
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Discussion |
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In this article we have attempted as complete a description as possible of the mechanical behavior of sheep LD muscles in situ, the effect on these properties of chronic stimulation, and the mechanical performance of the muscle when configured as an SMV. We have also used a simple model of cylindrical pumping chambers to highlight the areas of performance that are most affected by reconfiguration.
The mechanical properties of the LD muscles were typical of skeletal muscle, although measurement was more difficult in this preparation than in the more familiar fusiform skeletal muscles of the rat or rabbit hindlimb. Our estimates of tension per unit of cross-sectional area were lower than published values. This is due in part to the anatomy of the LD muscle: Because the fibers of the anterior border are considerably longer than the fibers of the posterior border, and the posterior border is thicker than the anterior border, some of the force was dissipated in a twisting motion of the distal aponeurosis. The estimates of force, speed, and power are therefore low but still provide a valid comparison with the measured pressures and flows of the SMVs that were formed subsequently from the same muscles.
After 6 weeks or more of stimulation at 2 Hz, the muscles exclusively synthesized the slow, type 1 myosin heavy chain isoform. In the rabbit, this degree of transformation calls for stimulation at a frequency >5 Hz, and stimulation at 2.5 Hz has been shown to produce a stable intermediate state characterized by expression of type 2A but not type 1 heavy chains of myosin.9 We conclude that myosin transitions are induced with a lower absolute activity threshold16 in the larger mammal. During normal behavior, motor neurons fire at higher frequencies in smaller mammals, and the fusion frequency of their muscles is correspondingly higher. Thus, an increase from the endogenous activity in sheep muscle to continuous 2-Hz stimulation may be homologous to the elevation in activity produced by continuous 10-Hz stimulation in rabbits.
The dynamic measurements revealed a greater difference between the
control and conditioned ventricles than the isovolumetric measurements.
This was to be expected, since conditioning affects not only the force
(which determines the ability to develop pressure) but also the
contractile speed of the muscle tissue. Hydraulic power is proportional
to the product of the two. We have argued previously that fully
transformed muscle is not optimal for use in cardiac
assistance.17 18 19 The present study confirms and
extends this argument to muscles configured as SMVs. The maximum stroke
work of the conditioned ventricles was 50 mJ when the afterload was
<80 mm Hg. This is only 10% of the stroke work of the
natural left ventricle in sheep. SMVs made from control muscle produced
up to 40% of the stroke work of the left ventricle. Dr L.W.
Stephenson's laboratory in Detroit has the largest experience of
creating SMVs in dogs; the stroke work of SMVs formed there ranges from
20 mJ20 to 92 mJ,21 compared with a left
ventricular stroke work of 100 mJ.21
Procedural differences could explain the smaller values of stroke work
obtained in the present study. We used only part of the muscle to
make ventricles of a particular size with a single layer of muscle,
whereas the practice in Stephenson's laboratory is to involve most of
the muscle in a multilayered wrap. Moreover, we made the SMVs
immediately after mobilization; in Stephenson's group the SMVs were
tested at least 3 weeks after their formation to allow for
revascularization of the distal part of the
muscle.
The maximum instantaneous power developed by the SMVs was between
10% and 20% of that measured when the muscle contracted linearly.
Some of the loss can be attributed to unavoidable differences in the
conditions of measurement. First, linear properties were recorded
with noninertial servo-controlled loads, whereas measurement of
hydraulic performance involved accelerating the volume of water
inside the SMV, even though the pressure was maintained at the set
level by the large air chamber. We reduced the volume of the measuring
system as much as possible to minimize this effect. Second, the SMVs
were formed from a part of the muscle, whereas the linear power output
was measured from the whole of the muscle. Nevertheless, in this acute
series, the wrapping procedure was associated with a reduction in peak
power output per unit weight of 
70%.
Oda and his colleagues14 constructed SMVs from the whole
LD muscle of mongrel dogs. They showed a passive pressure-volume
relation (Fig 2 of Reference 1414 ) similar to that shown in Fig 4b in
this article. Fig 8 also shows that the performance of
ventricles made at a nominal radius of 20 mm from sheep LD muscle
(upper curves; a, b, and c) are in good agreement with the results from
SMVs made from dog LD muscle (g, h, and i; Oda et al,14
1993; ventricles referred to in that article as large, single-layered
[LSLV]). This is to our knowledge the first time that comprehensive
performance data from isolated SMVs made in different
laboratories has been shown to be comparable.
A simple numerical model, based on the assumption that power losses
caused by wrapping and the effects of an inertial load were negligible,
showed striking correspondences with the experimental findings. First,
the predicted isovolumetric pressure (zero flow) was quite close to
that determined experimentally. Second, the model predicted little
difference between the performance of the two sizes of
ventricle. Third, the model predicted the afterload range for which the
power output of the ventricles was highest. On the other hand, Fig 11a
shows that the pressure-flow curves of the real SMVs had a much greater
rate of reduction in pressure with increasing flow than the predictions
for ventricles of the same shape derived from the linear force-velocity
data. We also used the model to predict the pressure-flow relation for
ventricles made from the same muscles but with the dimensions of a dog
left ventricle (Fig 12), for which the actual pressure-flow relation
has been published.15 The left ventricle had a lower
resistance than that predicted by the model despite the fact that the
latter was based on the assumption of no losses in configuring the
muscle as an SMV.
The model thus predicted the isovolumetric performance of SMVs fairly closely but showed that the pressure loss caused by flow in the real SMVs was greater than would be expected if SMV performance were determined solely by the linear force-velocity properties of the constituent muscle. Moreover, the reduction in pressure resulting from movement appeared to be much lower for a natural cardiac ventricle than for an SMV. It is this low resistance, or low reduction in driving pressure caused by ejection, that emerges as the most striking feature of the natural left ventricle, and it is a feature that concentrically wrapped SMVs lack. Since the shape of the force-velocity curve of isolated cardiac trabecular or papillary muscle is not greatly different from that of isolated skeletal muscle fibers, it may be that the complex fiber geometry of the natural ventricle22 contributes to this remarkable property.
The greatest difference, then, between the predicted and the actual performance of the SMVs, lay in their ability to generate flow. Since the pressure-generating properties were modeled with reasonable fidelity, we conclude that the loss of power arises mainly from the effect of the wrapping procedure on the ability of the muscle to move rather than on some aspect of the geometry that we were unable to simulate. The reduced performance may be due to shear resistance between fiber layers within the wall of the SMVs.
Clearly, it will be important to optimize not only the state of transformation of the muscle graft but also the surgical configuration of the SMV if an adequate hydraulic performance is to be assured in clinical use.
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Acknowledgments |
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This study was supported by the British Heart Foundation (RG25). Dr Jarvis held a Beit Memorial Research Fellowship. Dr Kwende was supported by a Wellcome Prize Studentship. We thank J. Yates, R. Galvin, and J. Blackhurst for their technical assistance.
Received January 21, 1997; revision received April 24, 1997; accepted May 1, 1997.
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