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Skeletal muscle–powered ventricle
Skeletal muscle-powered ventricle Effects of size and configuration on ventricular function The optimal size and configuration of skeletal muscle-powered ventricles are still undetermined. This study was aimed at comparing three types of skeletal muscle-powered ventricle: (A) a smaU size (15 mI capacity) double-layered pump, (B) a smaU size (15 mI capacity) single-layered pump, and (C) a large size (40 to 60 mI capacity) single-layered pump constructued sequentiaUy with the same untrained latissimus dorsi muscle of 12 mongrel dogs. The skeletal muscle-powered ventricle was connected to a mock circulation system, the stroke volumes against 40 to 160 mm Hg of afterload at 5 to 60 mm Hg of preload were measured, and the stroke work was computer analyzed on line. Raising the preload from 5 to 60 mm Hg increased the peak isovolumic developed pressure (A) from 91.3 ± 11.0 to 215.6 ± 26.1 mm Hg, (B) from 92.8 ± 12.0 to 166.3 ± 19.0 mm Hg, and (C) from 32.3 ± 5.2 to 121.4 ± 15.5 mm Hg (p < 0.05, C versus A and B). Similarly, the stroke volume (stroke work) against an afterload of 120 mm Hg increased (A) from 3.8 ± 0.5 mI (0.22 ± 0.04 X 1()6 ergs) to 14.5 ± 1.1 mI (1.05 ± 0.11 X 106 ergs), (B) from 4.5 ± 0.7 mI (0.30 ± 0.08 X 106 ergs) to 10.7 ± 0.9 mI (0.63 ± 0.08 X 106 ergs), and (C) from 1.8 ± 0.5 mI (0.09 ± 0.04 X 106 ergs) to 24.0 ± 3.6 mI (1.94 ± 0.41 X 106 ergs) (p < 0.05, C versus B at 5 mm Hg of preload; p < 0.05, C versus A and B at preloads ~30 mm Hg), At low preloads ( 5 to 15 mm Hg) both smaU pumps generated a significantly larger stroke volume (stroke work) than the large pump, whereas at high preloads (~30 mm Hg) the large pump generated a significantly larger stroke volume (stroke work) than the smaU pumps. It is concluded that under physiologic preload, B (smaU single-layered pump) performs better than or at least as weU as A (smaU double-layered pump) and C (large single-layered pump), despite being constructed with only one half of the muscle mass used for either A or C. (J THORAC CARDIOVASC SURG 1993;105:68-77)
Teiji ada, MD, Alfonso-Tadaomi Miyamoto, MD,* Yoshifumi Okamoto, MD, and Toshihiko Ban, MD, Kyoto, Japan
T
he contractile power per unit of cross-sectional area of the skeletal muscle has been reported to be four times that ofthe myocardium I and has been applied to assist the function of the heart in the form of cardiomyoplasty with the latissimus dorsi muscle.v" However, the stroke work From the Department of Cardiovascular Surgery, Kyoto University Faculty of Medicine, Kyoto, Japan. Received for publication July 24, 1991. Accepted for publication May 22, 1992. Address for reprints: Teiji Oda, MD, Kyoto University Faculty of Medicine, 54 Shougoin-Kawaramachi, Sakyo-ku, Kyoto 606, Japan. *Present address: Cardiovascular Research Institute, Kokura Memorial Hospital, Kitakyusyu, Japan.
12/1/39844
68
of an experimentally constructed skeletal muscle-powered pump or ventricle (SMPV) has been reported to be only one fifth to one half that of the left side of the heart.>'" This discrepancy has been attributed to differences in shape or wrapping of the muscle, but specific studies are lacking. In our recent study the single-layered large SMPV displayed larger output capabilities than the double-layered small SMPV, but this ability was greatly influenced by the preload and afterload conditions because of the limited pressure-generating capabilities. On the other hand, the double-layered small pump, generating greater pressure, was less affected by such changes. I I The purpose of this study was to elucidate the effects of pump volume or radius and muscle mass or wall thickness on function of the SMPV by comparing three kinds 0022-5223/93/$1.00/ + 0.10
Volume 105 Number 1
Skeletal muscle-powered ventricle 6 9
January 1993
Electrical stimulator
t
air pressure (after load)
t
---=",...,.-+---tf--
bladder (26ml x 4)
SMPV pressure Pressurized cannister (1L x 2) Fig. 1. Schematic representation of the experimental model. The used mock system allows independent manipulation of preload (adjusting the volume of saline solution introduced into the system) and afterload (air pressure in cannister) without the need of check valves. See text for full description.
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VOLUME (ml)
Fig. 2. Resting compliance (chamber distensibility) of SMPV. SSLV, Small single-layered ventricle; SDLV, small double-layered ventricle; LSLV, large single-layered ventricle.
of cylindrical SMPVs: two small SMPVs of the same capacity but constructed either with a single layer (SSLV) or a double layer (SDLV) of muscle, and a pump using the entire available muscle mass to construct only one large single-layered SMPV (LSLV).
Material and methods Short-term experiments with untrained latissimus dorsi musclewereperformed in 12 mongrel dogs (l0.5 to 17 kg; mean 12.9 kg} anesthetized with ketamine (10 mg/kg intramuscularly) and pentobarbital sodium (20 mg/kg intravenously). Anesthesia was maintained with a continuous pentobarbital drip after endotracheal intubation for ventilation with an Anesthesia Respirator (model-B3, Igarashi Inc., Tokyo, Japan) to maintain normal arterial oxygen and carbon dioxide tensions. The
10
20
30
40
50
60
PRELOAD (mmHg)
Fig. 3. Effects of varying preload on the isovolumic peak developed pressure (PDP). For abbreviations see Fig. 2.
surgical details have been described previously,11 the dissection being limited to mobilizing a muscular flap just large enough to construct the SDLV to preserve as many collateral vessels as possible to the muscle. The small pumps were constructed by wrapping the muscle concentrically around a cylindrical mandrel of 15 ml volume with a diameter of 16 mm using only one layer of the middle one half of the muscle for the SSLV and the entire available muscle mass (1.5 to 2.25 times concentric wrapping) for the SDLV. The LSL V was constructed with the available muscle as a single-layered cylinder without using a mandrel. Care was observed so that the muscle mass used for the SDLV was as close to that of the LSLV, and that of the SSL V to be about one half ofthe other two pumps. A Teflon cuff was sutured at one end of the muscular roll, and a thin-walled
70
The Journal of Thoracic and Cardiovascular Surgery
Oda et al.
AFTERLOAD =40 mmHg
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PRELOAD (mmHg)
Fig. 4. Effects of varying preload on the ejection time against specific afterloads. Observe the relatively small ejection time changes of both small pumps compared with the large pump in response to changing preloads and afterloads. For abbreviations see Fig. 2.
latex rubber condom attached to a 42F cannula was inserted into the muscular chamber. Standard temporary epicardial pacing wires (TAK-I, Matsuda Medical Inc., Tokyo, Japan), one placed at the thoracodorsal nerve trunk and the other 6 to 8 em distally into the muscular mass itself,'? were used to deliver a tetanic burst (9 pulses) type stimulus (pulse width of 210 /Lsec, 25 Hz, for 320 msec with supramaximal voltage of 10 to 40 volts; neurophysiological stimulator: SEN -3301, Nihon Kohden Corp., Tokyo, Japan). A mock circulation circuit was designed to allow independent control of preload and afterload as described by Acker and associates.v" It has two twin components (each consisted of a I L capacity cannister containing two side-by-side thin-walled polyvinylchloride balloons of 26 ml each) attached in parallel with a Y connector, the common limb of which was connected to the SMPV (Fig. I). The circuit was filled with isotonic saline solution to any specific filling pressure. The air chamber pressure was controlled to the desired afterload. Flow and pressures of the pump system and air chamber were measured by means of properly placed transducers (TP-IOIT, Nihon Kohden) or electromagnetic flow probe (FF type, Nihon Kohden). The same latissimus dorsi muscle was used to study the three
kinds of SMPV in a sequential manner by constructing these SMPVs in six different orders, every two dogs being studied in the same sequence. Care was observed to maintain adequate arterial oxygenation as well as acid-base balance. The pump muscle temperature was monitored and kept between 350 and 38 0 C with a heating lamp. The following variables were studied in order: (I) static volumetric measurements (resting compliance) were made by stepwise addition of isotonic saline solution to the empty pump up to a pressure of 60 mm Hg; (2) pressure generation function was evaluated by peak developed pressure during isovolumic contraction at five levels of preload (5,15,30,45, and 60 mm Hg); and (3) pumpingfunction was studied at those fivelevels'of preload and four levelsof afterload: 40,80, 120, and 160 mm Hg; the flow velocity wave was integrated and converted into stroke volume, which was looped to the pump pressure (pressure-volume loop), the area of which represents the stroke work, was computer calculated, displayed, and recorded (PC9801, NEe, Tokyo, Japan). The pump fluid volume was measured after each determination for calculation of the ejection fraction. Determinations were made on a single "beat," and 3 minutes' recovery time was allowed between measurements to prevent muscle fatigue. Data were recorded on a thermal array recorder (RTA-1300, Nihon Kohden). All data
Volume 105 Number 1
Skeletal muscle-powered ventricle 7 1
January 1993
AFTERLOAD =40 mmHg 20
160mmHg
120mmHg
80 mmHg 20
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PRELOAD (mmHg)
Fig. 5. Effects of varying preload on the peak flowvelocity against specific afterloads. Observe the drastic peak flow velocity decrease of the LSLV compared with that of smaller pumps. For abbreviations see Fig. 2. were expressed in mean ± standard error of the mean. Statistical analysis was performed by Scheffe's multiple comparison test, and p < 0.05 was considered to be significant. All animals received care in compliance with the "Principles of Laboratory Animal Care" formulated by the National Society for Medical Research and the "Guide for the Care and Use of Laboratory Animals" prepared by the National Academy of Sciences and published by the National Institutes of Health (NIH Publication No. 80-23, revised 1978).
Results Resting compliance. The capacity of the SDLV increased from 15.8 ± 2.2 to 35.1 ± 3.0 ml, that of the SSLV from 21.8 ± 2.1 to 37.9 ± 3.2 ml,and that of the LSLV from 72.1 ± 5.3 to 202.7 ± 13.1 ml when the filling pressure was increased from 5 to 60 mm Hg. The slopes of the pressure-volume curves for both small pumps were almost equal, steep and quite linear, whereas the slopeof the LSL V had a gradual ascent during the initial phase of relatively low pressures (10 to 30 mm Hg) (Fig. 2). The compliance of the condom itself used as the pump chamber was high, and filling it with 300 ml raised the pressure to only 6 to 7 mm Hg.
Pressure generating capabilities. Isovolumic contractions of the two small pumps produced higher peak developed pressures than the LSLV, the differences being significant at all preload levels for the SDLV and at preloads of 5 to 15 mm Hg for the SSLV (Fig. 3). The SDLV generated the same peak developed pressures as the SSLV at a preload of 5 mm Hg, but the SDLV generated a higher pressure at preloads over 15 mm Hg, although the differences were not statistically significant. The maximal peak developed pressures were 215.6 ± 26.1 mm Hg (SDLV), 166.3 ± 19.0 mm Hg (SSLV), and 121.4 ± 15.5 mm Hg (LSLV), all at the high preload of 60 mm Hg. Beyond preloads of 45 mm Hg both single-layered pumps failed to increase the peak developed pressure, whereas the SDLV continued to increase it even at the preload of 60 mm Hg. As anticipated, the pressure generation of the LSLV was the most strongly affected and the SSLV the least affected by the preload changes. Pumping function capabilities Stroke volume. The maximal stroke volume was 49.1 ± 3.4 ml for the LSLV, 19.4 ± 1.5 ml for the
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The Journal of Thoracic and Cardiovascular Surgery
Oda et al.
Table I. Stroke volume (milliliters) ofSMPVs against 40 to 160 mm Hg of afterload at 5 to 60 mm Hg of
preload Preload (mm Hf() 5 15 30 45 60
40 11.87 ± 2.63 27.79 ± 3.38**tt 49.07 ± 3.43**tt
LSLV
SDLV
afterload (mm Hg)
afterload (mm Hg)
3.52 10.03 29.32 36.23 40.09
160
120
80 0.80 1.78 3.53**tt 3.65**tt ± 3.99**tt
± ± ± ±
1.84 4.67 15.31 20.52 24.01
± 0.53t ± 1.21 ± 2.76t ± 3.01ott ± 3.56
2.20 3.02 6.71 11.46 14.46
± 0.62 ± 0.71 ± 1.19 ± 2.26 ± 2.96
40
80
8.74 ± 1.79 14.33 ± 1.95** 19.37 ± 2.04**
6.04 10.03 14.18 17.13 19.38
± 0.98 ± 1.11 ± 1.17** ± 1.31** ± 1.48**
Values are expressed as mean ± standard error. *p < 0.05 } LSLV versus SDLV. **p < 0.01 tp<0.05 } LSLV versus SSLV. ttp <0.01
Table II. Stroke work (X1if ergs) of SMPVs against 40 to 160 mm Hg of afterload at 5 to 60 mm Hg ofpreload SDLV
LSLV Preload (mm Hg) 5 15 30 45 60
afterload (mm Hg)
afterload (mm Hg)
80
40 0.41 ± 0.13 1.01 ± O.l8*tt 1.91 ± 0.26**tt
0.15 0.60 2.13 2.24 1.92
± ± ± ± ±
0.05 0.15 0.37**tt 0.33**tt 0.31 **tt
160
120 0.09 0.34 1.55 2.00 1.94
± ± ± ± ±
0.04t 0.14 0.40t 0.43*tt 0.41 ott
0.16 0.22 0.67 1.30 1.61
± ± ± ± ±
0.07 0.07* 0.18 0.36 0.45
40 0.28 ± 0.07 0.52 ± 0.08* 0.67 ± 0.07**
80 0.32 0.63 0.83 0.88 0.89
± 0.07 ± 0.09 ± 0.09** ± 0.07** ± 0.10**
Values are expressed as mean ± standard error. *p < 0.05 } LSLV versus SDLV. **p < 0.01 tp<0.05 } LSLV versus SSLV. ttp
SDLV, and 17.6 ± I.3mlfortheSSLV(TableI).Atany given afterload, increasing preload resulted in increasing stroke volume. The stroke volume of the LSLV with high preload (30 to 60 mm Hg) and low afterload (40 to 120 mm Hg) was significantly larger than that of the small SMPVs, but the opposite occurred against high afterloads (120 to 160 mm Hg) at low preloads (5 to 15 mm Hg). The stroke volume of the SSLV at low preload (5 to 15 mm Hg) was larger than, or at least equal to, that of SDLV; however, the reverse was true for high preloads (30 to 60 mm Hg). The increasing flowvelocity and ejection time account for the increasing stroke volume with increasing preload. In the large pump the longer ejection time seems to be the major contributor (Fig. 4), as opposed to the relatively greater role of flow velocity increase in the small pumps (Fig. 5). Stroke work. The maximal stroke work was 2.24 ± 0.33 X 106 ergs (LSLV), 1.05 ± 0.11 X 106 ergs (SDLV), and 0.65 ± 0.09 X 106 ergs (SSLV). Although the stroke work of the LSL V is significantly larger than that of the two small pumps against low afterloads (40 to
120 mm Hg) and at high preloads (30 to 60 mm Hg), the opposite occurs when afterloads are high (120 to 160 mm Hg) at low preloads (5 to 15 mm Hg) (Table 11). Ejection fraction. The maximal ejection fractions of 64.2% ± 3.6% (SDLV), 53.1% ± 3.6% (SSLV), and 31.1% ± 3.8% (LSLV) were obtained at 30 mm Hg of preload and 40 mm Hg of afterload, but ejection fraction decreased progressively with increasing afterloads, particularly for the LSLV. The two small pumps displayed a significantly larger ejection fraction than the LSLV regardless of the preload and afterload conditions; the SDLV had a larger ejection fraction than the SSLV, and the differences reached significance at some preload and afterload conditions (Fig. 6). To verify that muscle fatigue had not developed during the study period, we performed isovolumic contraction determinations at both the beginning and the end of each study. Muscle fatigue did not occur in the great majority of pumps. The muscle mass used for constructing the SDLV and the LSLV was 60 to 105 gm (80.8 ± 4.3) and that used for the SSLV was considered
Volume 105 Number 1
Skeletal muscle-powered ventricle
January 1993
73
SSLV afterload (mm Hg)
/20 3.85 ± 6.92 ± 10.21 ± 12.70 ± 14.46 ±
160
0.51 0.73 0.91 0.98* 1.14
3.09 5.12 7.23 9.12 10.70
± 0.39 ± 0.50 ± 0.55 ± 0.72 ± 0.85
80
40 10.34 ± 1.35 14.27 ± 1.36tt 17.63 ± 1.33tt
6.42 9.02 12.07 13.70 14.83
160
120
± 0.88 ± 1.02 ± 0.90tt ± 1.0Ut ± 1.09tt
4.49 6.16 8.38 9.73 10.72
± ± ± ± ±
0.73t 0.80 0.83t 0.91tt 0.89
3.25 4.43 6.32 7.07 8.06
± 0.58 ± 0.56 ± 0.66 ± 0.77 ± 0.82
SSLV after/oad (mm Hg)
120 0.22 ± 0.55 ± 0.86 ± 1.00 ± 1.05 ±
160
0.04 0.07 0.09 0.10* 0.11*
0.22 0.46 0.69 0.95 1.00
± ± ± ± ±
0.04 0.06* 0.07 0.10 0.10
80
40 0.35 ± 0.07 0.44 ± 0.05tt 0.50 ± 0.05tt
to be one half of that. The ratios of pump volume/muscle mass at the preload of 15 mm Hg were 0.76 ± 0.06 (SSLV), 0.30 ± 0.02 (SDLV), and 1.53 ± 0.14 (LSLV).
Discussion Pump function can be characterized by two properties: pressure generation and flow ejection. The pressure generation capability (isovolumic peak developed pressure) of a thick-walled cylinder is governed by the well-known equation: S = p(R02 + Ri 2) / (R0 2 - Ri 2) where Ro is the outer radius of the cylinder, Ri is the inner radius, S is the circumferential wall stress at its inner aspect, and P is the chamber pressure. Since the muscle fibers of our pumps were oriented perpendicular to the long axis of the cylindrical pump, the entire contractile forceof the muscle can be considered to be working circumferentially to determine the wall stress (S). The difference between the outer and inner radii
0.32 0.49 0.62 0.59 0.51
± ± ± ± ±
160
120
0.07 0.09 O.07tt 0.06tt 0.06tt
0.30 0.44 0.60 0.65 0.63
± ± ± ± ±
0.08t 0.09 0.09t 0.09tt 0.08tt
0.23 0.35 0.54 0.58 0.64
± ± ± ± ±
0.07 0.06 0.09 0.09 0.09
(Ro - Ri = Th) is wall thickness, and if we apply the concept of relative wall thickness (Rt)13 as defined by Ri/Th, which is another way to designate the volume/ mass ratio, the following expressions can be derived (see Appendix I): S = P(2Rt2 + 2Rt + 1)/(2Rt + I) P = S(2Rt + 1)/(2Rt2 + 2Rt + 1) The modulus of equation "S" (=[2Rt 2 + 2Rt + 1]/ [2Rt + 1]) increases (or decreases) as relative wall thickness increases (or decreases); that is, the diastolic wall stress (S), which will ultimately determine muscle fiber or sarcomere length, will increase or decrease as resting Ri/Th, that is, volume/mass ratio, increases or decreases. The SMPV with a lower resting volume/mass ratio such as the SDLV needs higher filling pressure to achieve an optimal sarcomere length compared to one with a higher volume/mass ratio such as the SSLV. This is in agreement with the fact that the SDLV needs high filling pressure (~ 30 mm Hg) to produce a larger peak developed pressure or stroke volume than the SSLV. Yoran,
74
The Journal of Thoracic and Cardiovascular Surgery
Oda et at.
AFTERLOAD =40 mmHg
80 mmHg
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LSLV vs SSLV SOL V vs SSL V
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30
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PRELOAD (mmHg) Fig. 6. Effects of varying preloadon the ejection fraction (E.F.) againstspecific afterloads. Observe the variability of the ejection fraction of the large pump with increasing afterloads. For abbreviations see Fig. 2.
Covell, and ROSS1 4 reported that the subepicardial (and the subendocardial) sarcomeres of the left ventricular wall are the most difficult to stretch, a preload of 20 mm Hg being necessary to achieve it. The hypertrophic left ventricle of the hypertensive rat has a stronger preload dependency than that of the normotensive rat. IS In this regard the SOLV could be compared with the hypertrophic heart of the rat with hypertension and the SSLV to the normotensive heart. The resting volume / mass ratio also determines the chamber compliance (dV /dP) of the left ventricle, as can be appreciated in the equation for a thick-walled sphere": dV /dP = VO
+ V /M)/E
where E is myocardial stiffness. Accordingly the compliance of the left ventricle will increase (or decrease) as volume/mass ratio or volume increase (or decrease) if myocardial stiffness remains constant. It is evident that the LSLV would be the most distensible one, because of its larger volume and higher volume/mass ratio (1.53 ± 0.14). Although theSSLV had a higher volume/ mass ratio (0.76 ± 0.06) than that of the SOLV (0.30 ± 0.02), the SSLV had almost the same compliance as the SOLV. The modulus of equation "P" (= [2Rt + 1J/
[2Rt2 + 2Rt + 1]) attains its maximal value (= 1) when relative wall thickness (Rt) is zero and thereafter decreases, gradually approaching zero as relative wall thickness increases. It seems to be apparent that the pressure generation will fall as relative wall thickness increases if systolic wall stress (S) remains constant. But the diastolic wall stress (S) determining sarcomere length will increase even at the same filling pressure as relative wall thickness increases, and accordingly muscle force per unit area, that is, systolic wall stress (S), will increase as relative wall thickness increases, which in turn offsets the above decrease of pressure generation. This implies that Laplace's law alone cannot be enough to explain the lower peak developed pressure of the LSLV with high volume/mass ratio (1.53) compared with the higher one of the SSLV with low volume/mass ratio (0.76) at the same filling pressure. It could be explained by characteristics of skeletal muscle itself, that is, by the well-known length-tension curve developed by graded stretching of a skeletal muscle in a linear model and measuring its active (isometric) force (F) and passive or resting force (f). I, 17, 18 Although isometric force (F) increases gradually to plateau at Fmax (at the optimal length), the resting force (f) increases exponentially without ceiling as the stretch is increased. It becomes apparent that the muscle
Volume 105 Number 1 January 1993
efficiency (isometric F/resting f) deteriorates as the resting force or muscle length increases. In an SMPV the isometric F /the resting f ratio could be considered to be the systolic wall stress / diastolic wall stress ratio; therefore this ratio will decrease as the diastolic wall stress (S) or muscle length increases. The SMPV working at a shorter muscle length or lower diastolic wall stress (S), the SDLV having the lowest volume/mass ratio (0.30 ± 0.02) would have the highest systolic wall stress/diastolic wall stress ratio and therefore could generate a higher peak developed pressure than the one working at a longer muscle length, that is, at higher diastolic wall stress (S) than the SSLV having a volume/mass ratio of 0.76 or the LSLV with the highest ratio of 1.53 (see Appendix 11). From all these considerations it becomes apparent that an adequate SMPV must meet two essential conditions: (1) The diastolic volume/mass ratio must be low enough to develop enough pressure to overcome the afterload but (2) high enough (that is, with a capacity large enough to be reasonably compliant) to allow loading it with sufficient volume to have an adequate output. Spotnitz, Sonnenblick, and Spiro'? reported a left ventricular volume/ mass ratio of 0.55 at the preload of 12 mm Hg for normal dogs. The SMPV with the volume/mass ratio closest to that was that of the SSLV with 0.76 ± 0.06. This is in agreement with the fact that the SSLV seems to be particularly well suited to operate under physiologic range preloads and systemic range afterloads. The stroke volume and work of the LSLV displayed a marked dependency on the filling pressure compared with the small SMPVs (SDLV, SSLV). At low filling pressure the large ventricle does not develop enough pressure, but as the preload is increased its pressure-generating capability is also increased and the output function changes accordingly. This large increase in stroke volume of the LSLV was found to be related to the increase of its ejection time, which was almost twice as long as that of the small SMPVs, rather than to the increase in its peak flow velocity. Afterload changes influenced markedly the stroke volume and work of the LSLV, whereas both small pumps were able to keep a relatively constant stroke work regardless of the afterload conditions because of their stronger pressure-generating capabilities. These results are in agreement with those of Acker and associates.t who also reported relatively unchanged stroke work against afterloads between 60 to 200 mm Hg using an SDLV. Glower and colleagues-" reported similar behavior of the normal intact canine heart of maintaining a relatively constant stroke work when the afterload is increased, as opposed to the decreasing stroke work that occurs in the depressed failing heart with such changes. In this sense
Skeletal muscle-powered ventricle 75
the performance of the LSLV resembles that of the failing heart and the two small ventricles that of the normal heart. On the basis of the large deformation elasticity theory, Bridges and coworkers-' calculated an output of 400 nil/min for a small ventricle (initial capacity of 17 m!) and an output of 800 ml/rnin for the large ventricle (initial capacity of 50 m!) when working against an afterload of 80 mm Hg with a filling pressure of 20 mm Hg at the rate of 54 beats/min. They suggested that at physiologic range preloads a large ventricle would have a better pump output. Indeed, a pump pressure of 54 ± 5 mm Hg and a stroke work of 0.89 ± 0.26 X 106 ergs in a right heart bypass study using a large pump (49 to 69 ml of initial capacity) at the central venous pressure of 11 to 13 mm Hg were reported.f Since the canine right ventricular stroke work is 0.22 ± 0.11 X 106 ergs"), the obtained stroke work is adequate for working in the pulmonary circulation, but not for a systemic type high-pressure system. It is not clear whether the pump used in their study was single layered or multilayered, but our single-layered large ventricle needed higher filling pressure than the small SMPVs. It might be possible that a multilayered large ventricle with a lower volume/mass ratio would have the capabilities of generating enough pressure to produce a large enough stroke volume against a higher afterload, in the range of systemic rather than pulmonary artery pressure. The stroke work of our LSLV exceeded left ventricular stroke work (1.83 ± 0.98 X 106 ergs") against afterloads of 40 to 120 mm Hg. However, for this LSLV to display the necessary two thirds of its ejecting capability, the required preloads (30 to 45 mm Hg) are far above the physiologic ones and indeed might be suited to work in a system with a high preload, like in a counterpulsation device, if it is to work against high afterloads. A number of questions remain unanswered regarding the SDLV and will be the subjects of further studies: (1) Will the described functional characteristics be retained once adhesions between the inner and outer muscular layer takes place in the chronic phase? (2) Will wrapping of the muscle under tension alter the function characteristics in anyway? We constructed theSDLVbywrapping the latissimus dorsi around the mandrel without tension. However, according to the well-known engineering concept of the "compound cylinder," better performance might be anticipated if some tension was to be applied to the muscle during the wrapping procedure. The wall stress distribution between the inner and outer cylinders of the "compound cylinder" (constructed by concentrically overlapping two cylinders, the outer cylinder having a smaller internal diameter than the external diameter of the inner cylinder) is relatively even despite the thicker
76
The Journal of Thoracic and Cardiovascular Surgery
Oda et af.
resulting wall. An SOLV constructed according to this concept might operate more effectively at a lower filling pressure. The SSLV exhibited similar output capabilities to the SOLV against changing afterloads and yet less preload dependency, which are highly desirable qualities. However, its potential maximal stroke work was about one half of the SOLV. Considering that only one half of the latissimus dorsi is used for making one SSLV, it could be possible to construct two SSLVs out of only one latissimus dorsi flap instead of one SOLV or one LSLV. In fact, studies with such an SMPV fashioned in a double barrel shape by arranging the two SSLVs in parallel indicate a larger output capability under physiologic preload and afterload conditions than an SOLV. 22 One last word of caution is that these experiments were performed with untrained muscle, which is known to generate a somewhat higher pressure than conditioned muscle, and in a preparation without vascular delay. Although every effort was made to prevent muscle fatigue, the data must be interpreted with these considerations in mind. Similar studies using trained muscle and muscular flaps with fully developed collateral circulation might be necessary before reaching final conclusions. Conclusions Our data, although obtained in nonconditioned muscle, does support the following conclusions. The SSLV being the least dependent on the preload seems to exhibit the best ejection performance under physiologic conditions. The SOLV has the greatest pressure-generating capabilities but only when preloads are far above the physiologic range. The LSLV displayed excellent volume-displacing capabilities, albeit greatly influenced by the preload and afterload conditions, but has the poorest pressure-generating capabilities. To maximize the efficiency of the pump, the ratio of pump volume or radius/muscle mass or thickness must be optimized for the type of work for which it is being designed-whether the pump is to function at low or high preloads and against low or high afterloads. We acknowledgeShigeru aka, Meiji Seika Inc., for the statistical evaluation, Tomohiro Shiroyama, Department of Mechanical Engineering, Kyoto University, for adviceon engineering, and YoshiakiAoki and Kenji Kawase, Nihon Kohden, for their technical assistance. REFERENCES 1. Spiro D, Sonnenblick EH. Comparison of the ultrastructural basis of the contractile process in heart and skeletal muscle. Circ Res 1964;14,15(Pt 2):14-37. 2. Grandjean PA, Austin L, Chan S, Terpstra B, Bourgeois
3.
4. 5.
6.
7.
8.
9.
10.
11.
12.
13. 14. 15.
16.
17.
18.
1M. Dynamic cardiomyop1asty: clinicalfollow-up results.J Cardiac Surg 1991;6(suppl):80-8. Molteni L, Almada H, Ferreira R. Synchronouslystimulated skeletal muscle graft for left ventricular assistance: case report. J THORAC CARDIOVASC SURG 1989;97:439-46. Magovern GJ, Heckler FR, Park SB, et al. Paced skeletal muscle for dynamic cardiomyoplasty. Ann Thorac Surg 1988;45:614-9. Acker MA, Hammond RL, Mannion JD, Salmons S, Stephenson LW. An autologous biologic pump motor. J THORAC CARDIOVASC SURG 1986;92:733-46. Mannion JD, Velchik MA, Acker A, et al. Transmural blood flowof multilayered latissimus dorsi skeletal muscle ventricles during circulatory assistance. Trans Am Soc Artif Intern Organs 1986;32:454-60. Acker MA, Hammond RL, Mannion JD, Salmons S, Stephenson LW. Skeletal muscle as the potential power source for a cardiovascular pump: assessmentin vivo. Science 1987;236:324-7. Bridges CR Jr, Hammond RL, Dimeo F, Anderson WA, Stephenson LW. Functional right-heart replacement with skeletal muscle ventricles. Circulation 1989;80(Pt 2):III 183-91. Mannion JD, Acker MA, Hammond RL, Faltemeyer W, Duckett S, Stephenson LW. Power output of skeletal muscle ventriclesin circulation: short-term studies.Circulation 1987;76: 155-62. Mannion JD, Acker MA, Hammond RL, StephensonLW. Four-hour circulatory assistance with canine skeletal muscle ventricles. Surg Forum 1986;37:211-3. ada T, Ban T, Okamoto Y, Miyamoto AT. Skeletal muscle poweredventricle: comparison of double layered small ventricleand singlelayered large ventricle.J Cardiac Surg 1991;6(suppl): 154-63. Chachques JC, Grandjean PA, Carpentier A. Latissimus dorsi dynamic cardiomyoplasty. Ann Thorac Surg 1989; 47:600-4. Gaasch WHoLeft ventricular radius to wallthicknessratio. Am J Cardiol1979;43:1189-94. Yoran C, Covell JW, Ross J Jr. Structural basis for the ascending limb of left ventricular function. Circ Res 1973;32:297-303. Noresson E, Ricksten SE, Nordlander MH, Thoren P. Performance of the hypertrophied left ventricle in spontaneously hypertensiverat: effectsof changes in preload and afterload. Acta Physiol Scand 1979;107:1-8. Mirsky 1. Assessment of diastolic function: suggested methods and future considerations. Circulation 1984; 69:836-41. Spotnitz HM, Merker C, Maim JR. Applied physiology of the canine rectus abdominis:force-lengthcurvescorrelated with functional characteristics of a rectus powered"ventricle." Potential for cardiac assistance.Trans Am Soc Artif Intern Organs 1974;20:747-55. Witzmann FA, Kim DH, Fitts RH. Hindlimb immobilization: length-tension and contractile propertiesof skeletal muscle. J Appl PhysioI1982;53:333-45.
Volume 105 Number 1 January 1993
Skeletal muscle-powered ventricle
19. Spotnitz HM, Sonnenblick EH, Spiro D. Relation of ultrastructure to function in the intact heart: sarcomere structure relative to pressure volume curves of intact left ventricles of dog and cat. Circ Res 1966;18:49-66. 20. Glower DD, Spratt JA, Snow ND, et al. Linearity of the Franck-Starling relationship in the intact heart: the concept of preload recruitable stroke work. Circulation 1985; 71:994-1009. 21. Bridges CR Jr, Anderson JS, Anderson WA, Hammond RL, Acker MA, Stephenson LW. Skeletal muscle ventricles: preliminary results and theoretical design considerations. In: Reichart B, ed. Recent advances in cardiovascular surgery. 1st ed. Munich: Verlag RS Schulz, 1989:182202. 22. Oda T, Miyamoto AT, Okamoto Y, Ban T. Skeletal muscle powered pump can work under low preload: design considerations. Trans Am Soc Artif Intern Organs 1992 [In press].
Appendixes Appendix I. Derivation of Laplace's equation for a thickwalled cylinder to include the concept of relative wall thickness (Ri/h): S = P (R0 2+ Ri 2)/(R02 - Ri 2) = P ([Ri + hj2+ Ri 2)/([Ri + hF- Ri 2 ) = P (2Ri 2+ 2hRi + h 2)/(2hRi + h 2) where h is wall thickness. Multiplying both numerator and denominator by h2: = P(2[Ri/hF + 2Ri/h + 1)/(2Ri/h + I)
If Ri/h is defined as Rt S = P (2Rt2 + 2Rt + 1)/(2Rt + I)
77
Appendix II. A diastolic (circumferential) wall stress (at its inner aspect) (= Sa) of pump A with a lower Ri/Th ratio (= Xa) at a given filling pressure (= Pd) can be calculated by modified Laplace's equation (S = P X f[Rt] = P[2Rt2 + 2Rt+ 1]/[2Rt + I]). Sa
= Pd X f(Xa)
A diastolic wall stress ( = Sb) of pump B, which is constructed from the same muscle and mass as pump A, with a higher Ri/Th ratio (= Xb > Xa) at the same filling pressure (Pd) can be similarly calculated Sb = Pd
X
f(Xb)
Because f(Xb) > f(Xa), Sb > Sa. Muscle fiber in pump B could be more stretched than one in pump A. According to the real length-tension curves of skeletal muscle,1.17,18 active (isometric) force per unit area/passive force per unit area ratio decreases as the muscle fiber length (or passive force) increases. In an SMPV, the active force/passive force ratio could be considered to be the systolic wall stress/diastolic wall stress ratio; therefore this ratio decreases as the muscle fiber length (or diastolic wall stress) increases. The systolic wall stress/diastolic wall stress ratio of the pump A( = Ra) is greater than the one of the pump B( = Rb). Ra>Rb Since the systolic wall stress can be equal to Ra X Sa (Rb X Sb), peak isovolumic pressure (pump A = Pa, pump B = Pb) at a filling pressure of Pd can be calculated by the modified Laplace equation. Pa
= l/f(Xa) X Ra
X f(Xa) X Pd
= Ra
X Pd
= l/f(Xb) X Rb
X f(Xb) X Pd
= Rb
X Pd
Similarly, Pb Therefore, Pa>Pb
Teiji ada, MD, Alfonso-Tadaomi Miyamoto, MD,* Yoshifumi Okamoto, MD, and Toshihiko Ban, MD, Kyoto, Japan
T
he contractile power per unit of cross-sectional area of the skeletal muscle has been reported to be four times that ofthe myocardium I and has been applied to assist the function of the heart in the form of cardiomyoplasty with the latissimus dorsi muscle.v" However, the stroke work From the Department of Cardiovascular Surgery, Kyoto University Faculty of Medicine, Kyoto, Japan. Received for publication July 24, 1991. Accepted for publication May 22, 1992. Address for reprints: Teiji Oda, MD, Kyoto University Faculty of Medicine, 54 Shougoin-Kawaramachi, Sakyo-ku, Kyoto 606, Japan. *Present address: Cardiovascular Research Institute, Kokura Memorial Hospital, Kitakyusyu, Japan.
12/1/39844
68
of an experimentally constructed skeletal muscle-powered pump or ventricle (SMPV) has been reported to be only one fifth to one half that of the left side of the heart.>'" This discrepancy has been attributed to differences in shape or wrapping of the muscle, but specific studies are lacking. In our recent study the single-layered large SMPV displayed larger output capabilities than the double-layered small SMPV, but this ability was greatly influenced by the preload and afterload conditions because of the limited pressure-generating capabilities. On the other hand, the double-layered small pump, generating greater pressure, was less affected by such changes. I I The purpose of this study was to elucidate the effects of pump volume or radius and muscle mass or wall thickness on function of the SMPV by comparing three kinds 0022-5223/93/$1.00/ + 0.10
Volume 105 Number 1
Skeletal muscle-powered ventricle 6 9
January 1993
Electrical stimulator
t
air pressure (after load)
t
---=",...,.-+---tf--
bladder (26ml x 4)
SMPV pressure Pressurized cannister (1L x 2) Fig. 1. Schematic representation of the experimental model. The used mock system allows independent manipulation of preload (adjusting the volume of saline solution introduced into the system) and afterload (air pressure in cannister) without the need of check valves. See text for full description.
.
soo '00
:r
E
..
.§ w
~
a
50
SDlV
200
:r
E
IE
-5
...
...
Q
100 50
100
150
200
VOLUME (ml)
Fig. 2. Resting compliance (chamber distensibility) of SMPV. SSLV, Small single-layered ventricle; SDLV, small double-layered ventricle; LSLV, large single-layered ventricle.
of cylindrical SMPVs: two small SMPVs of the same capacity but constructed either with a single layer (SSLV) or a double layer (SDLV) of muscle, and a pump using the entire available muscle mass to construct only one large single-layered SMPV (LSLV).
Material and methods Short-term experiments with untrained latissimus dorsi musclewereperformed in 12 mongrel dogs (l0.5 to 17 kg; mean 12.9 kg} anesthetized with ketamine (10 mg/kg intramuscularly) and pentobarbital sodium (20 mg/kg intravenously). Anesthesia was maintained with a continuous pentobarbital drip after endotracheal intubation for ventilation with an Anesthesia Respirator (model-B3, Igarashi Inc., Tokyo, Japan) to maintain normal arterial oxygen and carbon dioxide tensions. The
10
20
30
40
50
60
PRELOAD (mmHg)
Fig. 3. Effects of varying preload on the isovolumic peak developed pressure (PDP). For abbreviations see Fig. 2.
surgical details have been described previously,11 the dissection being limited to mobilizing a muscular flap just large enough to construct the SDLV to preserve as many collateral vessels as possible to the muscle. The small pumps were constructed by wrapping the muscle concentrically around a cylindrical mandrel of 15 ml volume with a diameter of 16 mm using only one layer of the middle one half of the muscle for the SSLV and the entire available muscle mass (1.5 to 2.25 times concentric wrapping) for the SDLV. The LSL V was constructed with the available muscle as a single-layered cylinder without using a mandrel. Care was observed so that the muscle mass used for the SDLV was as close to that of the LSLV, and that of the SSL V to be about one half ofthe other two pumps. A Teflon cuff was sutured at one end of the muscular roll, and a thin-walled
70
The Journal of Thoracic and Cardiovascular Surgery
Oda et al.
AFTERLOAD =40 mmHg
r.. . /
400
, - - - , LSLV _SDLV .0------ ... SSLV
400
[_J
n
[///[
, , '** [/ ##
Ul
J---..1
w
::E
tj200f
200
j
** ##
** ##
/
/l* ) ... -..1...--
1~1
I-
* =P
l
,,ft
1l 300 ** ##
5
160mmHg
T
/f
,/1
1/ ~ j ** ##
120mmHg
80 mmHg
l-
.>
300
200
200
100
100
1
~ ,
300
..-
1
ow -, w
100
100
5
15
30
5 15
30
45
60
5
15
30
45
60
5
15
30
45
60
PRELOAD (mmHg)
Fig. 4. Effects of varying preload on the ejection time against specific afterloads. Observe the relatively small ejection time changes of both small pumps compared with the large pump in response to changing preloads and afterloads. For abbreviations see Fig. 2.
latex rubber condom attached to a 42F cannula was inserted into the muscular chamber. Standard temporary epicardial pacing wires (TAK-I, Matsuda Medical Inc., Tokyo, Japan), one placed at the thoracodorsal nerve trunk and the other 6 to 8 em distally into the muscular mass itself,'? were used to deliver a tetanic burst (9 pulses) type stimulus (pulse width of 210 /Lsec, 25 Hz, for 320 msec with supramaximal voltage of 10 to 40 volts; neurophysiological stimulator: SEN -3301, Nihon Kohden Corp., Tokyo, Japan). A mock circulation circuit was designed to allow independent control of preload and afterload as described by Acker and associates.v" It has two twin components (each consisted of a I L capacity cannister containing two side-by-side thin-walled polyvinylchloride balloons of 26 ml each) attached in parallel with a Y connector, the common limb of which was connected to the SMPV (Fig. I). The circuit was filled with isotonic saline solution to any specific filling pressure. The air chamber pressure was controlled to the desired afterload. Flow and pressures of the pump system and air chamber were measured by means of properly placed transducers (TP-IOIT, Nihon Kohden) or electromagnetic flow probe (FF type, Nihon Kohden). The same latissimus dorsi muscle was used to study the three
kinds of SMPV in a sequential manner by constructing these SMPVs in six different orders, every two dogs being studied in the same sequence. Care was observed to maintain adequate arterial oxygenation as well as acid-base balance. The pump muscle temperature was monitored and kept between 350 and 38 0 C with a heating lamp. The following variables were studied in order: (I) static volumetric measurements (resting compliance) were made by stepwise addition of isotonic saline solution to the empty pump up to a pressure of 60 mm Hg; (2) pressure generation function was evaluated by peak developed pressure during isovolumic contraction at five levels of preload (5,15,30,45, and 60 mm Hg); and (3) pumpingfunction was studied at those fivelevels'of preload and four levelsof afterload: 40,80, 120, and 160 mm Hg; the flow velocity wave was integrated and converted into stroke volume, which was looped to the pump pressure (pressure-volume loop), the area of which represents the stroke work, was computer calculated, displayed, and recorded (PC9801, NEe, Tokyo, Japan). The pump fluid volume was measured after each determination for calculation of the ejection fraction. Determinations were made on a single "beat," and 3 minutes' recovery time was allowed between measurements to prevent muscle fatigue. Data were recorded on a thermal array recorder (RTA-1300, Nihon Kohden). All data
Volume 105 Number 1
Skeletal muscle-powered ventricle 7 1
January 1993
AFTERLOAD =40 mmHg 20
160mmHg
120mmHg
80 mmHg 20
x - - ~ LSLV _SDLV .. -- --- .. SSLV
I
-<,
...J
;
>-
[
1
1
I-
U
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s
1 1
~ 10
1//
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i
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##
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------1
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5
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SDLV
YS
SSLV
10
5
-' 11
i
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1 #
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'/1
15
30
5
15
30
45
60
5
15
30
45
60
5
15
30
45
60
PRELOAD (mmHg)
Fig. 5. Effects of varying preload on the peak flowvelocity against specific afterloads. Observe the drastic peak flow velocity decrease of the LSLV compared with that of smaller pumps. For abbreviations see Fig. 2. were expressed in mean ± standard error of the mean. Statistical analysis was performed by Scheffe's multiple comparison test, and p < 0.05 was considered to be significant. All animals received care in compliance with the "Principles of Laboratory Animal Care" formulated by the National Society for Medical Research and the "Guide for the Care and Use of Laboratory Animals" prepared by the National Academy of Sciences and published by the National Institutes of Health (NIH Publication No. 80-23, revised 1978).
Results Resting compliance. The capacity of the SDLV increased from 15.8 ± 2.2 to 35.1 ± 3.0 ml, that of the SSLV from 21.8 ± 2.1 to 37.9 ± 3.2 ml,and that of the LSLV from 72.1 ± 5.3 to 202.7 ± 13.1 ml when the filling pressure was increased from 5 to 60 mm Hg. The slopes of the pressure-volume curves for both small pumps were almost equal, steep and quite linear, whereas the slopeof the LSL V had a gradual ascent during the initial phase of relatively low pressures (10 to 30 mm Hg) (Fig. 2). The compliance of the condom itself used as the pump chamber was high, and filling it with 300 ml raised the pressure to only 6 to 7 mm Hg.
Pressure generating capabilities. Isovolumic contractions of the two small pumps produced higher peak developed pressures than the LSLV, the differences being significant at all preload levels for the SDLV and at preloads of 5 to 15 mm Hg for the SSLV (Fig. 3). The SDLV generated the same peak developed pressures as the SSLV at a preload of 5 mm Hg, but the SDLV generated a higher pressure at preloads over 15 mm Hg, although the differences were not statistically significant. The maximal peak developed pressures were 215.6 ± 26.1 mm Hg (SDLV), 166.3 ± 19.0 mm Hg (SSLV), and 121.4 ± 15.5 mm Hg (LSLV), all at the high preload of 60 mm Hg. Beyond preloads of 45 mm Hg both single-layered pumps failed to increase the peak developed pressure, whereas the SDLV continued to increase it even at the preload of 60 mm Hg. As anticipated, the pressure generation of the LSLV was the most strongly affected and the SSLV the least affected by the preload changes. Pumping function capabilities Stroke volume. The maximal stroke volume was 49.1 ± 3.4 ml for the LSLV, 19.4 ± 1.5 ml for the
72
The Journal of Thoracic and Cardiovascular Surgery
Oda et al.
Table I. Stroke volume (milliliters) ofSMPVs against 40 to 160 mm Hg of afterload at 5 to 60 mm Hg of
preload Preload (mm Hf() 5 15 30 45 60
40 11.87 ± 2.63 27.79 ± 3.38**tt 49.07 ± 3.43**tt
LSLV
SDLV
afterload (mm Hg)
afterload (mm Hg)
3.52 10.03 29.32 36.23 40.09
160
120
80 0.80 1.78 3.53**tt 3.65**tt ± 3.99**tt
± ± ± ±
1.84 4.67 15.31 20.52 24.01
± 0.53t ± 1.21 ± 2.76t ± 3.01ott ± 3.56
2.20 3.02 6.71 11.46 14.46
± 0.62 ± 0.71 ± 1.19 ± 2.26 ± 2.96
40
80
8.74 ± 1.79 14.33 ± 1.95** 19.37 ± 2.04**
6.04 10.03 14.18 17.13 19.38
± 0.98 ± 1.11 ± 1.17** ± 1.31** ± 1.48**
Values are expressed as mean ± standard error. *p < 0.05 } LSLV versus SDLV. **p < 0.01 tp<0.05 } LSLV versus SSLV. ttp <0.01
Table II. Stroke work (X1if ergs) of SMPVs against 40 to 160 mm Hg of afterload at 5 to 60 mm Hg ofpreload SDLV
LSLV Preload (mm Hg) 5 15 30 45 60
afterload (mm Hg)
afterload (mm Hg)
80
40 0.41 ± 0.13 1.01 ± O.l8*tt 1.91 ± 0.26**tt
0.15 0.60 2.13 2.24 1.92
± ± ± ± ±
0.05 0.15 0.37**tt 0.33**tt 0.31 **tt
160
120 0.09 0.34 1.55 2.00 1.94
± ± ± ± ±
0.04t 0.14 0.40t 0.43*tt 0.41 ott
0.16 0.22 0.67 1.30 1.61
± ± ± ± ±
0.07 0.07* 0.18 0.36 0.45
40 0.28 ± 0.07 0.52 ± 0.08* 0.67 ± 0.07**
80 0.32 0.63 0.83 0.88 0.89
± 0.07 ± 0.09 ± 0.09** ± 0.07** ± 0.10**
Values are expressed as mean ± standard error. *p < 0.05 } LSLV versus SDLV. **p < 0.01 tp<0.05 } LSLV versus SSLV. ttp
SDLV, and 17.6 ± I.3mlfortheSSLV(TableI).Atany given afterload, increasing preload resulted in increasing stroke volume. The stroke volume of the LSLV with high preload (30 to 60 mm Hg) and low afterload (40 to 120 mm Hg) was significantly larger than that of the small SMPVs, but the opposite occurred against high afterloads (120 to 160 mm Hg) at low preloads (5 to 15 mm Hg). The stroke volume of the SSLV at low preload (5 to 15 mm Hg) was larger than, or at least equal to, that of SDLV; however, the reverse was true for high preloads (30 to 60 mm Hg). The increasing flowvelocity and ejection time account for the increasing stroke volume with increasing preload. In the large pump the longer ejection time seems to be the major contributor (Fig. 4), as opposed to the relatively greater role of flow velocity increase in the small pumps (Fig. 5). Stroke work. The maximal stroke work was 2.24 ± 0.33 X 106 ergs (LSLV), 1.05 ± 0.11 X 106 ergs (SDLV), and 0.65 ± 0.09 X 106 ergs (SSLV). Although the stroke work of the LSL V is significantly larger than that of the two small pumps against low afterloads (40 to
120 mm Hg) and at high preloads (30 to 60 mm Hg), the opposite occurs when afterloads are high (120 to 160 mm Hg) at low preloads (5 to 15 mm Hg) (Table 11). Ejection fraction. The maximal ejection fractions of 64.2% ± 3.6% (SDLV), 53.1% ± 3.6% (SSLV), and 31.1% ± 3.8% (LSLV) were obtained at 30 mm Hg of preload and 40 mm Hg of afterload, but ejection fraction decreased progressively with increasing afterloads, particularly for the LSLV. The two small pumps displayed a significantly larger ejection fraction than the LSLV regardless of the preload and afterload conditions; the SDLV had a larger ejection fraction than the SSLV, and the differences reached significance at some preload and afterload conditions (Fig. 6). To verify that muscle fatigue had not developed during the study period, we performed isovolumic contraction determinations at both the beginning and the end of each study. Muscle fatigue did not occur in the great majority of pumps. The muscle mass used for constructing the SDLV and the LSLV was 60 to 105 gm (80.8 ± 4.3) and that used for the SSLV was considered
Volume 105 Number 1
Skeletal muscle-powered ventricle
January 1993
73
SSLV afterload (mm Hg)
/20 3.85 ± 6.92 ± 10.21 ± 12.70 ± 14.46 ±
160
0.51 0.73 0.91 0.98* 1.14
3.09 5.12 7.23 9.12 10.70
± 0.39 ± 0.50 ± 0.55 ± 0.72 ± 0.85
80
40 10.34 ± 1.35 14.27 ± 1.36tt 17.63 ± 1.33tt
6.42 9.02 12.07 13.70 14.83
160
120
± 0.88 ± 1.02 ± 0.90tt ± 1.0Ut ± 1.09tt
4.49 6.16 8.38 9.73 10.72
± ± ± ± ±
0.73t 0.80 0.83t 0.91tt 0.89
3.25 4.43 6.32 7.07 8.06
± 0.58 ± 0.56 ± 0.66 ± 0.77 ± 0.82
SSLV after/oad (mm Hg)
120 0.22 ± 0.55 ± 0.86 ± 1.00 ± 1.05 ±
160
0.04 0.07 0.09 0.10* 0.11*
0.22 0.46 0.69 0.95 1.00
± ± ± ± ±
0.04 0.06* 0.07 0.10 0.10
80
40 0.35 ± 0.07 0.44 ± 0.05tt 0.50 ± 0.05tt
to be one half of that. The ratios of pump volume/muscle mass at the preload of 15 mm Hg were 0.76 ± 0.06 (SSLV), 0.30 ± 0.02 (SDLV), and 1.53 ± 0.14 (LSLV).
Discussion Pump function can be characterized by two properties: pressure generation and flow ejection. The pressure generation capability (isovolumic peak developed pressure) of a thick-walled cylinder is governed by the well-known equation: S = p(R02 + Ri 2) / (R0 2 - Ri 2) where Ro is the outer radius of the cylinder, Ri is the inner radius, S is the circumferential wall stress at its inner aspect, and P is the chamber pressure. Since the muscle fibers of our pumps were oriented perpendicular to the long axis of the cylindrical pump, the entire contractile forceof the muscle can be considered to be working circumferentially to determine the wall stress (S). The difference between the outer and inner radii
0.32 0.49 0.62 0.59 0.51
± ± ± ± ±
160
120
0.07 0.09 O.07tt 0.06tt 0.06tt
0.30 0.44 0.60 0.65 0.63
± ± ± ± ±
0.08t 0.09 0.09t 0.09tt 0.08tt
0.23 0.35 0.54 0.58 0.64
± ± ± ± ±
0.07 0.06 0.09 0.09 0.09
(Ro - Ri = Th) is wall thickness, and if we apply the concept of relative wall thickness (Rt)13 as defined by Ri/Th, which is another way to designate the volume/ mass ratio, the following expressions can be derived (see Appendix I): S = P(2Rt2 + 2Rt + 1)/(2Rt + I) P = S(2Rt + 1)/(2Rt2 + 2Rt + 1) The modulus of equation "S" (=[2Rt 2 + 2Rt + 1]/ [2Rt + 1]) increases (or decreases) as relative wall thickness increases (or decreases); that is, the diastolic wall stress (S), which will ultimately determine muscle fiber or sarcomere length, will increase or decrease as resting Ri/Th, that is, volume/mass ratio, increases or decreases. The SMPV with a lower resting volume/mass ratio such as the SDLV needs higher filling pressure to achieve an optimal sarcomere length compared to one with a higher volume/mass ratio such as the SSLV. This is in agreement with the fact that the SDLV needs high filling pressure (~ 30 mm Hg) to produce a larger peak developed pressure or stroke volume than the SSLV. Yoran,
74
The Journal of Thoracic and Cardiovascular Surgery
Oda et at.
AFTERLOAD =40 mmHg
80 mmHg
120mmHg
160mmHg ......... SOLV ..-- .... SSLV
~
u: u.i
40
30 20
** ##
*
** ##
(/1
r/
60
60
60
50
50
50
40
40
40
30
10
5
15
* =P
t
20
10
"_·x LSLV
30
1-_--1---J
t
1/'/
L''
** ## ** ##
** ##
** ##
If
/
**
##
A·_·+---f
20 10
V
5 15
1,/
1-** ##
** ##
r·.-f' 30
45
60
5 15
1_--1---1
30
** ## ** ** ##
20
##
,.,1.---t-f --'
/
** ##
1// ** ##
** ##
45
60
5 15
** :: ##
_--f._...... L
,...-+.__ .---t.
30
LSLV vs SSLV SOL V vs SSL V
~
L/ 10
LSLV vs SOLV
30
45
60
PRELOAD (mmHg) Fig. 6. Effects of varying preloadon the ejection fraction (E.F.) againstspecific afterloads. Observe the variability of the ejection fraction of the large pump with increasing afterloads. For abbreviations see Fig. 2.
Covell, and ROSS1 4 reported that the subepicardial (and the subendocardial) sarcomeres of the left ventricular wall are the most difficult to stretch, a preload of 20 mm Hg being necessary to achieve it. The hypertrophic left ventricle of the hypertensive rat has a stronger preload dependency than that of the normotensive rat. IS In this regard the SOLV could be compared with the hypertrophic heart of the rat with hypertension and the SSLV to the normotensive heart. The resting volume / mass ratio also determines the chamber compliance (dV /dP) of the left ventricle, as can be appreciated in the equation for a thick-walled sphere": dV /dP = VO
+ V /M)/E
where E is myocardial stiffness. Accordingly the compliance of the left ventricle will increase (or decrease) as volume/mass ratio or volume increase (or decrease) if myocardial stiffness remains constant. It is evident that the LSLV would be the most distensible one, because of its larger volume and higher volume/mass ratio (1.53 ± 0.14). Although theSSLV had a higher volume/ mass ratio (0.76 ± 0.06) than that of the SOLV (0.30 ± 0.02), the SSLV had almost the same compliance as the SOLV. The modulus of equation "P" (= [2Rt + 1J/
[2Rt2 + 2Rt + 1]) attains its maximal value (= 1) when relative wall thickness (Rt) is zero and thereafter decreases, gradually approaching zero as relative wall thickness increases. It seems to be apparent that the pressure generation will fall as relative wall thickness increases if systolic wall stress (S) remains constant. But the diastolic wall stress (S) determining sarcomere length will increase even at the same filling pressure as relative wall thickness increases, and accordingly muscle force per unit area, that is, systolic wall stress (S), will increase as relative wall thickness increases, which in turn offsets the above decrease of pressure generation. This implies that Laplace's law alone cannot be enough to explain the lower peak developed pressure of the LSLV with high volume/mass ratio (1.53) compared with the higher one of the SSLV with low volume/mass ratio (0.76) at the same filling pressure. It could be explained by characteristics of skeletal muscle itself, that is, by the well-known length-tension curve developed by graded stretching of a skeletal muscle in a linear model and measuring its active (isometric) force (F) and passive or resting force (f). I, 17, 18 Although isometric force (F) increases gradually to plateau at Fmax (at the optimal length), the resting force (f) increases exponentially without ceiling as the stretch is increased. It becomes apparent that the muscle
Volume 105 Number 1 January 1993
efficiency (isometric F/resting f) deteriorates as the resting force or muscle length increases. In an SMPV the isometric F /the resting f ratio could be considered to be the systolic wall stress / diastolic wall stress ratio; therefore this ratio will decrease as the diastolic wall stress (S) or muscle length increases. The SMPV working at a shorter muscle length or lower diastolic wall stress (S), the SDLV having the lowest volume/mass ratio (0.30 ± 0.02) would have the highest systolic wall stress/diastolic wall stress ratio and therefore could generate a higher peak developed pressure than the one working at a longer muscle length, that is, at higher diastolic wall stress (S) than the SSLV having a volume/mass ratio of 0.76 or the LSLV with the highest ratio of 1.53 (see Appendix 11). From all these considerations it becomes apparent that an adequate SMPV must meet two essential conditions: (1) The diastolic volume/mass ratio must be low enough to develop enough pressure to overcome the afterload but (2) high enough (that is, with a capacity large enough to be reasonably compliant) to allow loading it with sufficient volume to have an adequate output. Spotnitz, Sonnenblick, and Spiro'? reported a left ventricular volume/ mass ratio of 0.55 at the preload of 12 mm Hg for normal dogs. The SMPV with the volume/mass ratio closest to that was that of the SSLV with 0.76 ± 0.06. This is in agreement with the fact that the SSLV seems to be particularly well suited to operate under physiologic range preloads and systemic range afterloads. The stroke volume and work of the LSLV displayed a marked dependency on the filling pressure compared with the small SMPVs (SDLV, SSLV). At low filling pressure the large ventricle does not develop enough pressure, but as the preload is increased its pressure-generating capability is also increased and the output function changes accordingly. This large increase in stroke volume of the LSLV was found to be related to the increase of its ejection time, which was almost twice as long as that of the small SMPVs, rather than to the increase in its peak flow velocity. Afterload changes influenced markedly the stroke volume and work of the LSLV, whereas both small pumps were able to keep a relatively constant stroke work regardless of the afterload conditions because of their stronger pressure-generating capabilities. These results are in agreement with those of Acker and associates.t who also reported relatively unchanged stroke work against afterloads between 60 to 200 mm Hg using an SDLV. Glower and colleagues-" reported similar behavior of the normal intact canine heart of maintaining a relatively constant stroke work when the afterload is increased, as opposed to the decreasing stroke work that occurs in the depressed failing heart with such changes. In this sense
Skeletal muscle-powered ventricle 75
the performance of the LSLV resembles that of the failing heart and the two small ventricles that of the normal heart. On the basis of the large deformation elasticity theory, Bridges and coworkers-' calculated an output of 400 nil/min for a small ventricle (initial capacity of 17 m!) and an output of 800 ml/rnin for the large ventricle (initial capacity of 50 m!) when working against an afterload of 80 mm Hg with a filling pressure of 20 mm Hg at the rate of 54 beats/min. They suggested that at physiologic range preloads a large ventricle would have a better pump output. Indeed, a pump pressure of 54 ± 5 mm Hg and a stroke work of 0.89 ± 0.26 X 106 ergs in a right heart bypass study using a large pump (49 to 69 ml of initial capacity) at the central venous pressure of 11 to 13 mm Hg were reported.f Since the canine right ventricular stroke work is 0.22 ± 0.11 X 106 ergs"), the obtained stroke work is adequate for working in the pulmonary circulation, but not for a systemic type high-pressure system. It is not clear whether the pump used in their study was single layered or multilayered, but our single-layered large ventricle needed higher filling pressure than the small SMPVs. It might be possible that a multilayered large ventricle with a lower volume/mass ratio would have the capabilities of generating enough pressure to produce a large enough stroke volume against a higher afterload, in the range of systemic rather than pulmonary artery pressure. The stroke work of our LSLV exceeded left ventricular stroke work (1.83 ± 0.98 X 106 ergs") against afterloads of 40 to 120 mm Hg. However, for this LSLV to display the necessary two thirds of its ejecting capability, the required preloads (30 to 45 mm Hg) are far above the physiologic ones and indeed might be suited to work in a system with a high preload, like in a counterpulsation device, if it is to work against high afterloads. A number of questions remain unanswered regarding the SDLV and will be the subjects of further studies: (1) Will the described functional characteristics be retained once adhesions between the inner and outer muscular layer takes place in the chronic phase? (2) Will wrapping of the muscle under tension alter the function characteristics in anyway? We constructed theSDLVbywrapping the latissimus dorsi around the mandrel without tension. However, according to the well-known engineering concept of the "compound cylinder," better performance might be anticipated if some tension was to be applied to the muscle during the wrapping procedure. The wall stress distribution between the inner and outer cylinders of the "compound cylinder" (constructed by concentrically overlapping two cylinders, the outer cylinder having a smaller internal diameter than the external diameter of the inner cylinder) is relatively even despite the thicker
76
The Journal of Thoracic and Cardiovascular Surgery
Oda et af.
resulting wall. An SOLV constructed according to this concept might operate more effectively at a lower filling pressure. The SSLV exhibited similar output capabilities to the SOLV against changing afterloads and yet less preload dependency, which are highly desirable qualities. However, its potential maximal stroke work was about one half of the SOLV. Considering that only one half of the latissimus dorsi is used for making one SSLV, it could be possible to construct two SSLVs out of only one latissimus dorsi flap instead of one SOLV or one LSLV. In fact, studies with such an SMPV fashioned in a double barrel shape by arranging the two SSLVs in parallel indicate a larger output capability under physiologic preload and afterload conditions than an SOLV. 22 One last word of caution is that these experiments were performed with untrained muscle, which is known to generate a somewhat higher pressure than conditioned muscle, and in a preparation without vascular delay. Although every effort was made to prevent muscle fatigue, the data must be interpreted with these considerations in mind. Similar studies using trained muscle and muscular flaps with fully developed collateral circulation might be necessary before reaching final conclusions. Conclusions Our data, although obtained in nonconditioned muscle, does support the following conclusions. The SSLV being the least dependent on the preload seems to exhibit the best ejection performance under physiologic conditions. The SOLV has the greatest pressure-generating capabilities but only when preloads are far above the physiologic range. The LSLV displayed excellent volume-displacing capabilities, albeit greatly influenced by the preload and afterload conditions, but has the poorest pressure-generating capabilities. To maximize the efficiency of the pump, the ratio of pump volume or radius/muscle mass or thickness must be optimized for the type of work for which it is being designed-whether the pump is to function at low or high preloads and against low or high afterloads. We acknowledgeShigeru aka, Meiji Seika Inc., for the statistical evaluation, Tomohiro Shiroyama, Department of Mechanical Engineering, Kyoto University, for adviceon engineering, and YoshiakiAoki and Kenji Kawase, Nihon Kohden, for their technical assistance. REFERENCES 1. Spiro D, Sonnenblick EH. Comparison of the ultrastructural basis of the contractile process in heart and skeletal muscle. Circ Res 1964;14,15(Pt 2):14-37. 2. Grandjean PA, Austin L, Chan S, Terpstra B, Bourgeois
3.
4. 5.
6.
7.
8.
9.
10.
11.
12.
13. 14. 15.
16.
17.
18.
1M. Dynamic cardiomyop1asty: clinicalfollow-up results.J Cardiac Surg 1991;6(suppl):80-8. Molteni L, Almada H, Ferreira R. Synchronouslystimulated skeletal muscle graft for left ventricular assistance: case report. J THORAC CARDIOVASC SURG 1989;97:439-46. Magovern GJ, Heckler FR, Park SB, et al. Paced skeletal muscle for dynamic cardiomyoplasty. Ann Thorac Surg 1988;45:614-9. Acker MA, Hammond RL, Mannion JD, Salmons S, Stephenson LW. An autologous biologic pump motor. J THORAC CARDIOVASC SURG 1986;92:733-46. Mannion JD, Velchik MA, Acker A, et al. Transmural blood flowof multilayered latissimus dorsi skeletal muscle ventricles during circulatory assistance. Trans Am Soc Artif Intern Organs 1986;32:454-60. Acker MA, Hammond RL, Mannion JD, Salmons S, Stephenson LW. Skeletal muscle as the potential power source for a cardiovascular pump: assessmentin vivo. Science 1987;236:324-7. Bridges CR Jr, Hammond RL, Dimeo F, Anderson WA, Stephenson LW. Functional right-heart replacement with skeletal muscle ventricles. Circulation 1989;80(Pt 2):III 183-91. Mannion JD, Acker MA, Hammond RL, Faltemeyer W, Duckett S, Stephenson LW. Power output of skeletal muscle ventriclesin circulation: short-term studies.Circulation 1987;76: 155-62. Mannion JD, Acker MA, Hammond RL, StephensonLW. Four-hour circulatory assistance with canine skeletal muscle ventricles. Surg Forum 1986;37:211-3. ada T, Ban T, Okamoto Y, Miyamoto AT. Skeletal muscle poweredventricle: comparison of double layered small ventricleand singlelayered large ventricle.J Cardiac Surg 1991;6(suppl): 154-63. Chachques JC, Grandjean PA, Carpentier A. Latissimus dorsi dynamic cardiomyoplasty. Ann Thorac Surg 1989; 47:600-4. Gaasch WHoLeft ventricular radius to wallthicknessratio. Am J Cardiol1979;43:1189-94. Yoran C, Covell JW, Ross J Jr. Structural basis for the ascending limb of left ventricular function. Circ Res 1973;32:297-303. Noresson E, Ricksten SE, Nordlander MH, Thoren P. Performance of the hypertrophied left ventricle in spontaneously hypertensiverat: effectsof changes in preload and afterload. Acta Physiol Scand 1979;107:1-8. Mirsky 1. Assessment of diastolic function: suggested methods and future considerations. Circulation 1984; 69:836-41. Spotnitz HM, Merker C, Maim JR. Applied physiology of the canine rectus abdominis:force-lengthcurvescorrelated with functional characteristics of a rectus powered"ventricle." Potential for cardiac assistance.Trans Am Soc Artif Intern Organs 1974;20:747-55. Witzmann FA, Kim DH, Fitts RH. Hindlimb immobilization: length-tension and contractile propertiesof skeletal muscle. J Appl PhysioI1982;53:333-45.
Volume 105 Number 1 January 1993
Skeletal muscle-powered ventricle
19. Spotnitz HM, Sonnenblick EH, Spiro D. Relation of ultrastructure to function in the intact heart: sarcomere structure relative to pressure volume curves of intact left ventricles of dog and cat. Circ Res 1966;18:49-66. 20. Glower DD, Spratt JA, Snow ND, et al. Linearity of the Franck-Starling relationship in the intact heart: the concept of preload recruitable stroke work. Circulation 1985; 71:994-1009. 21. Bridges CR Jr, Anderson JS, Anderson WA, Hammond RL, Acker MA, Stephenson LW. Skeletal muscle ventricles: preliminary results and theoretical design considerations. In: Reichart B, ed. Recent advances in cardiovascular surgery. 1st ed. Munich: Verlag RS Schulz, 1989:182202. 22. Oda T, Miyamoto AT, Okamoto Y, Ban T. Skeletal muscle powered pump can work under low preload: design considerations. Trans Am Soc Artif Intern Organs 1992 [In press].
Appendixes Appendix I. Derivation of Laplace's equation for a thickwalled cylinder to include the concept of relative wall thickness (Ri/h): S = P (R0 2+ Ri 2)/(R02 - Ri 2) = P ([Ri + hj2+ Ri 2)/([Ri + hF- Ri 2 ) = P (2Ri 2+ 2hRi + h 2)/(2hRi + h 2) where h is wall thickness. Multiplying both numerator and denominator by h2: = P(2[Ri/hF + 2Ri/h + 1)/(2Ri/h + I)
If Ri/h is defined as Rt S = P (2Rt2 + 2Rt + 1)/(2Rt + I)
77
Appendix II. A diastolic (circumferential) wall stress (at its inner aspect) (= Sa) of pump A with a lower Ri/Th ratio (= Xa) at a given filling pressure (= Pd) can be calculated by modified Laplace's equation (S = P X f[Rt] = P[2Rt2 + 2Rt+ 1]/[2Rt + I]). Sa
= Pd X f(Xa)
A diastolic wall stress ( = Sb) of pump B, which is constructed from the same muscle and mass as pump A, with a higher Ri/Th ratio (= Xb > Xa) at the same filling pressure (Pd) can be similarly calculated Sb = Pd
X
f(Xb)
Because f(Xb) > f(Xa), Sb > Sa. Muscle fiber in pump B could be more stretched than one in pump A. According to the real length-tension curves of skeletal muscle,1.17,18 active (isometric) force per unit area/passive force per unit area ratio decreases as the muscle fiber length (or passive force) increases. In an SMPV, the active force/passive force ratio could be considered to be the systolic wall stress/diastolic wall stress ratio; therefore this ratio decreases as the muscle fiber length (or diastolic wall stress) increases. The systolic wall stress/diastolic wall stress ratio of the pump A( = Ra) is greater than the one of the pump B( = Rb). Ra>Rb Since the systolic wall stress can be equal to Ra X Sa (Rb X Sb), peak isovolumic pressure (pump A = Pa, pump B = Pb) at a filling pressure of Pd can be calculated by the modified Laplace equation. Pa
= l/f(Xa) X Ra
X f(Xa) X Pd
= Ra
X Pd
= l/f(Xb) X Rb
X f(Xb) X Pd
= Rb
X Pd
Similarly, Pb Therefore, Pa>Pb