Mechanical properties of diaphragm muscle in dogs* B. R. V a c h o n and H. K u n o v
W . Zingg
Institute of Biomedical Electronics & Engineering, University of Toronto, Toronto, Ont., Canada
Research Institute, Hospital for Sick Children, Toronto, Ont., Canada
A b s t r a c t - - T h e mechanical properties of diaphragm muscle in dogs were measured. A portion of the diaphragm was isolated and formed into a pouch which in turn was connected to various hydraufic circuits. We measured pressure response to electrical stimulation for various voltages, frequencies and baseline pressures; and also contraction time. Further, we obtained pressure-volume curves and estimated the power output of the actively contracting muscle. From the results we conclude that the properties of the diaphragm muscle do not exclude its use as a myocardial substitute. K e y w o r d s - - M e c h a n i c a l properties of muscle
Introduction
NUMEROUS attempts have been made to provide myocardial assistance by artificial means. In the child, however, the use of an artificial implanted device is accompanied by major problems due to the growth of the heart and the circulatory system throughout childhood. F o r this reason and others, use of the autologous transplant is attractive. The diaphragm muscle was suggested by KANTROWITZ and McKINNON (1958) and NAKAMURAand GLENN (1964) as a possible source of tissue. Both teams of investigators have attempted to utilise the diaphragm muscle to provide myocardial assistance but have met with very limited success. SHEPHERD (1969) gave an extensive review of the relevant literature covering both the anatomical and histological properties of the diaphragm muscle which make it a logical choice for a myocardial substitute. In addition she reviewed the various attempts at providing such assistance to the heart. Although there has been limited success in providing a viable graft of a portion of the diaphragm on to the heart, such a procedure has still to demonstrate that it can give useful assistance in the form of increased cardiac output. Central to the problem of evaluating the performance of a diaphragmatic graft to the heart is a proper understanding of the electrical-mechanical properties of the isolated diaphragm muscle itself. In short, is the diaphragm muscle capable of contracting under the conditions to be encountered in the heart ? The pressures that the muscle is required to withstand and generate, as well as the rate at which it will be required to contract, may be excessive. The present study of diaphragm muscle was undertaken to evaluate the relevant properties * First received 14th December 1972 andin final form 8th November 1973
252
under conditions which would parallel those to be encountered in the heart. Materials and methods Dogs were used in the experiments. A portion of the diaphragm was formed into a pouch (KuNov, ZINo6 and VACHON, 1975) which in turn was connected to various hydraulic circuits for the measurement and recording of the muscle response to stimuli. Electrical stimulation of various voltages and frequencies was applied to the muscle and the pressure response measured. Approximately 15 experiments were performed, with a success rate of 100K once the surgical techniques had been established.
Surgical technique of the pedicle graft The isolated piece of diaphragm muscle which can be used to replace part of the right ventricle receives its blood supply through a pedicle consisting of the mobilised internal mammary vessels and their surrounding connective tissue. The surgical technique has been described in detail by SHEPHERD (1969). Both sides of the diaphragm are exposed through a right lateral thoracotomy, which is extended as a midline abdominal incision. Branches of the internal mammary artery and vein are identified and divided. Following identification of the blood supply, the graft is outlined from below and excised. The nerve supplying the graft is divided and the defect in the diaphragm is closed. The procedure results in a denervated pedicle graft of diaphragm muscle.
Measurement system To evaluate the properties of such a pedicle of diaphragm muscle, a technique was devised whereby the pedicle is formed into a pouch instead of being implanted on to the myocardium. The pouch thus
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consists entirely of diaphragm muscle. A fluidfilled flaccid balloon is inserted into the pouch. The balloon and the catheter to which it is attached are filled with fluid (saline) and the free end of the catheter is connected to an appropriate hydraulic measurement circuit. Either active or passive properties of the muscle may be studied under conditions which are either isometric (isovolumetric) or which permit the muscle to contract with a resultant fluid flow. Provision is made for injecting (or withdrawing) fluid from the system and thus control the static pressure in the pouch. A diagram of a typical set-up along with its electrical analogue is given in Fig. 1.
Measurements made Keeping the baseline pressure at 10 mmHg, we measured the pressure response produced by a single stimulus of 6 V (single pulse, 1 m s pulse duration, 1 Hz repetitition rate). Also, keeping the
I I i i I, l/Ill Balellne Pressure = I0 mmHg
IOmmHg
DIAPHRAGM
MUSCLE
Stimulus: Single Pulse Imsec Duration 6,0v
Fig. 2 Twitch contraction--a representative response illustrating the measured parameters (unretouched photograph of record) Stimulus: 6 V, 1 ms, 1 Hz, baseline pressure -10 mmHg pcv.t I ("~ Vtt)
Fig. 1 Muscle pouch and electrical analogue
A detailed description of the measurement system and techniques is given in a previous paper (KuNov, Z i y c c and VACHON, 1975). Stimulation to the pouch is provided by a pair of stainless-steel braided-wire electrodes which are sewn into the muscle on opposite sides of the pouch, in such a way as not to interfere with the blood supply. When the response of the muscle to stimulation is being studied, the configuration of the experiment is always isometric (isovolumetric), except for measurement of power output. For isometric determinations in both twitch and tetanic contractions, the catheter leading from the pouch is connected directly to a pressure transducer and, upon stimulation and contraction of the muscle no fluid is allowed to flow out from the pouch. Filling the system with a given volume of fluid produces in the pouch a static pressure referred to as the baseline pressure. This baseline pressure is varied by injecting fluid into or withdrawing fluid from the system using a syringe. The exact volume of fluid in the pouch is thus controlled. Using the simple system comprising pouch, catheter, pressure transducer and syringe (with valve), we can study tetanic and twitch contractions with the option of independently varying both the static baseline pressure and the stimulus parameters (voltage, frequency, pulse duration). In the measurement of the power produced by the actively contracting muscle the fluid is forced out of the pouch and flows through a known hydraulic resistance placed in the catheter. The pressure drop across the resistance is monitored, allowing calculations to be made of the power output. Medical and Biological Engineering
baseline pressure at 6 mmHg we measured the pressure response to a stimulus producing a tetanic contraction (2 V, 50 Hz). In addition, we studied the effect on risetime of variations in frequency, and the effect on the pressure response of variations in baseline pressure. The results of these experiments are given below. When we refer to 'pressure response' we mean the peak pressure rise above the baseline pressure. Fig. 2 illustrates a pressure response of 40 mmHg for a twitch contraction produced by a single-pulse stimulus of 6 V, 1 ms in duration, repeated once per second, the baseline pressure being 10 mmHg.
Reliability of method The measurements made on any given dog were reproducible for the duration of the experiment (up to 4-5 h) provided that care was taken not to overstress the diaphragm muscle. For example, maintaining a high pressure (740 mmHg) would cause an impairment of circulation with resultant deterioration of the muscle which might not be reversible. If excessive voltages were applied, tissue burning at the electrode site could occur. If these and other similar stresses were avoided, the results were repeatable. The differences in results obtained from different dogs reflect the differences in the muscles of the two animals. Care must be taken to normalise the results to account for the different pouch sizes. Results and discussion
Among the first questions to be answered is whether or not the diaphragm muscle, upon being stimulated, is capable of producing a sufficient increase of pressure inside the pouch to make the pressure compatible with those normally encountered in the heart.
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For the dog, the mean pulmonary arterial pressure is about 23 mmHg, while the systolic pressure is 40 mmHg and the diastolic pressure about 10 mmHg (DUKES, 1955, p. 188). Can the diaphragm pouch produce a peak pressure of approximately 40 mmHg in response to a 'reasonable' stimulus when there is a baseline pressure of about 1 0 m m H g ? Fig. 2 shows that the required pressure can be p r o d u c e d - in response to a stimulus of 6.0 V (single pulse, 1.0 ms pulse duration, 1.0 Hz repetition rate) the pressure is approximately 40 mmHg when the baseline pressure is 10mmHg. One might question whether the stimulus is 'reasonable'. However, in answer it may be said that voltages for bladder stimulation of about 10 V, with a 1.0 ms or longer pulse duration, have been recommended as being optimum (TALml 1970) in direct stimulation of a muscle with an implanted device. Tetanic contraction Fig. 3A shows the pressure response to a stimulus producing a tetanic contraction (voltage, 2 . 0 V ; frequency, 50Hz). F o r a baseline pressure of 6 mmHg the pressure response is approximately
Response risetime Varying the frequency of the stimulus used to produce the tetanic contraction yields differences in the risetime of the response (Figs. 4 and 5), so some control can be exercised over the waveform of the. pressure response of the diaphragm pouch. i
IO~mH
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Tetanic contraction--a representative response (unretouched photograph of record) Stimulus ." 2 V, 1 ms, 50 Hz pulse train, baseline pressure -~ 6 mmHg Diaphragm
Pouch-~- ~ .................
.... ~-I
s..o.d--~
Fig. 4 Tetanic contraction--variation of the response against stimulus frequency (unretouched photograph of record) Stimulus : 2 V, I ms, baseline pressure = 8 mmHg RISE TIME see 1210-
Fig. 3B Comparison of contraction waveforms of heart (human) and the diaphragm pouch (dog)
\|
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47 mmHg. Comparing the rising portion of the curve with the pressure rise in the right ventricle (Fig. 3B), one sees that the two wave shapes are quite similar: all that would be required to make the curves match would be to reduce the voltage to the diaphragm pouch in a graded fashion. Differences in peak pressures would of course be adjusted by changes in the voltage. (It must be noted that, in this case, the pressure wave of the diaphragm pouch is being compared to the cardiac wave of a man, not that of a dog.) 254
04020
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STIMULUS FREQUENCY Hz
Fig. 5 Risetime against stimulus frequency--tetanic contraction (derived from Fig. 4) Stimulus : 2 V, 1 ms, baseline pressure = 8 mmHg
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March 1975
This variation of the risetime with the stimulus frequency is not just due to an increase in the peak response and a lengthening of the time taken to reach the peak. In Fig. 6 (derived from Fig. 4) the
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Fig. 6 Pressure response against stimulus frequency-tetanic contraction (derived from Fig. 4) Stimulus: 2 V, I ms, baseline pressure = 8 mmHg
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Fig. 8 Response against baseline pressure--tetanic contraction (unretouched photograph of record) Stimulus: 2 V, 1 ms, 50 Hz
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Fig. 7 Initial slope of pressure response against stimulus frequency--tetanic contraction (derived from Fig. 4) Stimulus: 2 V, I ms, baseline pressure = 8 mmHg
pressure response is seen to level off after the stimulus frequency is increased above 50Hz. Fig. 7 (derived from Fig. 4) shows that the initial slope of the pressure response increases in a approximately linear fashion to the log of the frequency. The response of the muscle when it is stimulated to contract tetanically varies in both peak response amplitude and also in waveform (Fig. 8). The waveform changes considerably as the baseline pressure is increased above 10 mmHg. This fact could be used for controlling the wave form of the pressure rise as the diaphragm pouch is stimulated, if it were possible to vary the baseline pressure (i.e. the diastolic pressure) of the heart. Of course this is not possible and one is forced to make do with the waveform obtained at the pressures in the heart. Medical and Biological Engineering
mser
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S TIMULUS:SINGLE PULSE Imser
Fig. 9 Pressure response--twitch contraction; expanded time scale (unretouched photograph of record) Stimulus: I mA, I ms, baseline pressure = 16 mmHg
If a recording of the pressure response is made with an expanded time scale, as shown in Fig. 9, then, besides the risetime, the delay between stimulus application and muscle response can be determined.
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Table 1 Risetime and stimulus configuration Baseline Voltage pressure Risetime V 6 6 3 8 2 1 '5 4 2 4 2
mmHg 10 42 42 95 42 17 17 10 10 4
muscle. Increasing the volume of the pouch to obtain increased pressure results in a stretching of the muscle fibres. Fig. 11 shows how voltage affects the response/ baseline-pressure relationship. As in the tetanic contraction, each curve has a peak value for pressure response. If the diaphragm muscle were transplanted to heart muscle then the portion of Fig. 11 which is
Stimulus configuration
ms 50 .... 50 45 50 50 50 50 50 55 55
Single pulse, - - t w i t c h contraction
Pulse train, tetaniccontraction
For a stimulus of 1 mA, 1.0 ms, and a baseline pressure of 16 mmHg, there is a 25 ms delay from the time of the stimulus application until the response has reached 1 0 ~ of the peak value. Between the 1 0 ~ and 9 0 ~ points of the response, 30 ms elapse. Between the start of the response and the peak we find a delay of 50 ms. This is comparable to the risetime of the contractions shown in Fig. 4. Table 1 gives the risetime obtained in a series of experiments with different voltages and baseline pressures. In each experiment the risetime was close to 50 ms, indicating that it is independent of strength of stimulus and baseline pressure.
Response against baseline pressure A plot of the peak response against the baseline pressure (Fig. 10) shows that there is an optimum PRESSURE RESPONSE mmHg
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Fig. 10 Pressure response against baseline pressure-tetanic contraction (derived from Fig. 8) Stimulus: 2 V, I ms, 50 Hz
value of baseline pressure at which the peak response i s a maximum. This pattern is characteristic of both tetanic and twitch contractions. The variation of response with baseline pressure is due to the effects of stretching the muscle fibres and involves a length/tension relationship as is found in skeletal 256
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Fig. 11 Pressure response against baseline pressure-twitch contraction Stimulus: 2, 6 and 10 V, 1 ms, 1 Hz
of interest is that where the baseline pressure corresponds to the end diastolic pressure (5 mmHg), i.e. near the beginning of the ascending portion of the curves. At the end diastolic pressure the diaphragm muscle will. not be working at its optimum but, on the other hand, its response will be similar to that of the heart muscle. Starling's Law states that, if there is increased filling of the ventricles, then the heart contracts with more force to produce an increased stroke volume, and the diaphragm muscle would do the same under those circumstances.
Transdiaphragmatic pressures
20- / 00
PRESSURE RESPONSE mmHg 50-
The diaphragm muscle is ultimately limited in the amount of differential pressure which it can sustain, since the blood supply will eventually be cut off. At what baseline pressures can the diaphragm pouch operate for prolonged periods? In its normal function of assisting respiration the diaphragm is subjected to pressure differentials. Normally the peak differential pressure across the diaphragm is about 6.4 mmHg, which is only about 25 ~o of the peak systolic pressure in the right heart (24 mmHg). On the other hand, the diaphragm muscle is capable of withstanding much greater pressure differentials during exertion, and with maximal effort the transdiaphragmatic pressure may be maintained around the value of 82 mmHg, which is much greater than the pressures to be encountered in the heart. In our experimental setup, the baseline pressure is equivalent to the transdiaphragmatic pressure. N o long-term studies were performed. Even in our short-term studies we found that damage can
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be done to the muscle by subjecting it to very high pressures. In one experiment the pressure in the pouch was increased to 200mmHg for a few minutes. The muscle response then decreased to less than a tenth of the initial value while the muscle appeared to be very cyanotic. It required some minutes of rest, at zero pressure, to return to a normal state. This effect is a gradual one, of course, there being an ever increasing amount of blood cut off the higher the pressure. Also, in the heart the diaphragm muscle would be subject to rhythmic fluctuations of pressure which tend to stimulate the circulation. The behaviour of the diaphragm muscle under high pressures is what would be expected of the heart muscle (or any other muscle for that matter) under similar circumstances, and so does not indicate an incompatibility of the diaphragm and heart muscles.
Stimulus frequency
Stimulus voltage
Fig. 13 Pressure response against baseline pressure-twitch contraction Stimulus: 2 V, I ms, 1 Hz
The response of the diaphragm pouch to continuous, increasing stimuli is shown in Fig. 12. Very high pressures are achieved with high voltages, he response being 176 mmHg at 30 V. The general
PRESSURE RESPONSE mmHg 200-
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agrees closely with the value of 1 2 . 5 m m H g obtained with a single-pulse stimulus at the same baseline pressure of 8 mmHg (Fig. 13). Fig. 6 shows that the peak response is three times the response at zero frequency, and the long broad plateau extending from about 50 Hz to 200 Hz indicates that any frequency above 50 Hz would serve to produce a maximum contraction.
Stimulus pulse width
120-
In Fig. 14, the response is plotted as a function of the width of the stimulus pulse. The general shape of the curve is what one would expect, since, as the pulse width is increased, more fibres will be stimulated. There is a limit to this process, however, since, at some point, all of the available fibres at that particular stimulus voltage are being stimulated and in effect there is direct current stimulation.
8040-
Fig. 6 gives some idea of the effect that the stimulus frequency has upon the response. Extrapolating the graph in Fig. 6 shows that at zero frequency the pressure-response value is 14.5mmHg, which
/./'~
0
STIMULUS-VOLTS Fig. 12 Pressure response against stimulus voltage-twitch contraction Stimulus: I ms, I Hz, baseline pressure = 15 mmHg
PRESSURE RESPONSE ; mmH I0030 V
8 0 - ~ , shape of the curve is characteristic for all the dogs used, and can be explained as follows: the initial rise is due to the stimulation of the nerves lying near the electrodes. As the voltage is increased from 0.4 to 1.0 V more nerves are stimulated, as is shown by the increase in pressure response. Between 1.0 and 1.5 V the pressure response increases suddenly because of the direct stimulation of the muscle fibres. Further increases in voltage result in increased pressure response due to the spread of the stimulus through the tissue. Medical and Biological Engineering
20 V
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Fig. 14 Peak pressure against stimulus pulse w i d t h - twitch contraction Stimulus: 1, 2 and 3 V, 1 Hz, baseline pressure -- 2 mmHg
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Passive pressure/volume relationship A typical plot of the volume against the pressure inside the diaphragm pouch (when passive) is shown in Fig. 15 plotted on semilogarithmic co-ordinates. This curve has the exponential shape P=O.95e ~ The initial volume to produce PASSIVE PRESSURE rnmH~ 80-
/
40-
20-
10-
/
/
e
64-
2-
/
!
-
! VOLUME cm 3
Fig. 15 Intrapouch pressure as a function of pouch volume--passive response, semilogarithmic plot
zero pressure will not be zero, since, if the pouch is completely collapsed, the muscle is not in a relaxed state.
Muscle stress The stress in the muscle wall depends not only on the pressure in the pouch, i.e. the force on the muscle fibres, but also on the wall cross-sectional area, which changes as the muscle is stretched. We investigated muscle stress to see whether it would yield more information than the pressure/volume curves. We had to make a number of assumptions PASSIVE PRESSURE
STRESS N/rn2• 3
mmH
60 ~
-60
./
40-
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-8
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6 B VOLUME cm 3
10
112
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Fig. 16 Pressure/volume relationship compared with the stress/volume relationship--passive response 258
to arrive at an estimate of the change in the wall cross-sectional area with volume. The empty pouch consists of two roughly square pieces of tissue lying flat against each other. When the pouch is filled enough to produce a pressure of say 100 mmHg, then it is approximately spherical. We decided to consider the pouch as consisting o f two equal spherical surfaces, such as would result from the intersection of a plane and a sphere (not into hemispheres--the two sections only constitute a complete sphere at large volumes). The approximate diameter of the pouch was measured photographically for each increment of volume. Knowing the volume and the diameter we could compute the approximate cross-sectional area of the muscle at the midplane and use this value, along with the simultaneously recorded pouch pressure, to compute the stress in the muscle wall. The results of these computations are shown in Fig. 16 which plots stress against volume and compares the curve with the pressure/volume curve for the same pouch. A semilog plot was used here to facilitate comparison of the two exponential curves. Since the shapes of the two curves were not significantly different we conclude that there is no additional information to be gathered from the stress. Perhaps this is to be expected, since diaphragm muscle has no property, such as a storage property, that would preclude a close correlation between the pressure in the pouch and the stress in the muscle wall. In contrast, DROLET(1971), working on the urinary bladder of dogs (which has a storage function), found that, while the pressure/volume curve has a definite plateau where the volume increases but the pressure does not, the stress in the bladder wall increases steadily with increasing volume.
Muscle fatigue Can the diaphragm muscle undergo long-term stimulation at a rate comparable]to that of the heart ? The present short-term investigations cannot answer the question with any finality. In our experiments, the pouch of diaphragm muscle has been stimulated continuously for periods of up to 4 h only. A number of observations can be made from the results of these experiments, however. Within any given experiment, the lower the baseline pressure the longer the muscle seems ab/e to maintain a given level of response. The repetition rate at which the muscle is stimulated is a limiting factor: the increased response of the muscle to increased frequency generally declines over time. However, in one experiment where the diaphragm pouch was stimulated (2 V) continuously for a period of 3" 5 h, the stimulus rate was 80 per minute for the first 2 h and then 150 per minute for the remaining 1" 5 h (the baseline pressure was 4 m m H g and the initial peak response 15 mmHg). The
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response at the end of the experiment was the same as the initial response. The muscle would thus appear to have some capacity for working at a relatively high rate (i.e. at a rate compatible with that required from heart muscle) for somewhat extended periods of time. Crucial to the muscle contracting for a prolonged period is the maintenance of an adequate blood supply. This was not always feasible with the surgical procedure used here. In an autologous transplant a patient blood supply is a minimal requirement and would be maintained if the graft were viable. The question as to whether or not a proper response can be maintained for prolonged periods is the subject of further investigation.
Power output of diaphragm muscle The power output of the heart can be estimated from the average values for the volume output and the arterial pressure. F o r dogs, calculations using a minute volume of 1" 5 litres (DuKEs, 1955, p. 113) and a mean arterial diastolic blood pressure of 100 mmHg (SPEcTOR, 1956, p. 232) give the power output of the left heart as 335 m W and that of the right heart (assuming the pulmonary arterial diastolic pressure to be 10 mmHg, i.e. one-tenth that of the left heart) as 33-5 roW. By calculating the approximate area of the right and left ventricles an estimate of the power per unit area for the myocardium call be obtained. F o r dogs the area is estimated to be about 30 cm 2, giving a power output of approximately 1 m W / c m 2. Measurements of the power output of the diaphragm pouch show the peak power to be about 50 roW. F o r a pouch size of about 30 cm 2, the power output per unit area would be 1.66 m W / c m 2. Comparing this figure with the figure for dog myocardium, it is reasonable to expect that the diaphragm muscle could provide some assistance to the heart if it were implanted. Comparing the normal power output of the diaphragm in respiration with that of the power output of the diaphragm pouch, we find the following results for man. During quiet breathing the respiratory muscles produce about 70 mW of power (CAMPBELL 1970, p. 121). This is a measure of the work performed as determined by external measurements. If we assume that the diaphragm contributes about 75 ~ of this work, the power output of this muscle is 52 mW. If, further, we assume that the approximate area of the intact diaphragm is 500cm 2, the power output per unit area is 0.1 m W / c m 2. During exercise the power output of the respiratory system can be increased as much as a hundredfold (CAMPBELL, 1970, p. 122). The relative contribution of the diaphragm muscle is probably not as great in these circumstances but a fiftyfold increase is probably realistic, giving a power output per unit area of 5 m W / c m 2 for diaphragm muscle at maximum respiratory effort. Medical and Biological Engineering
These data are all for man but it is reasonable to expect values of the same order of magnitude for the dog. The power output of the pouch then is about 16 times that of the normally functioning diaphragm during quiet breathing but is only about 31 ~ of the peak power obtainable.
Comparison with other investigators Only SANT'AMBROGIOand SAIBENE(1970) appear to have reported on the mechanical properties of the diaphragm muscle in dogs. They gave a number of parameters for dogs cats, rabbits, and rats, the first of these parameters being the contraction time of the muscle, defined as the time from the start of the pressure rise to the peak (our rise time). For dogs the contraction time was 64.7 + 5.6 ms for a twitch contraction. The risetime for a twitch contraction in our experiments with dogs is about 50 ms. SANT'AMBROGIOand SAIBENE also gave the time taken to reach one half of the peak response (T,) for a tetanic contraction. F o r dogs T, was 57+ 5.6ms. We measured T, on the curves of Fig. 4 and found that it varies somewhat with the stimulus frequency, as is shown in Fig. 17. However, T1/2 TIME TO ~ PEAK RESPONSE msec 100-
8060-
\
~020.
0 STIMULUS FREQUENCY Hz
Fig. 17 Risetime (expressed as T, against stimulus frequency--tetanie contraction (derived from Fig. 4) Stimulus: 2 V, I ms, baseline pressure = 8 mmHg
a value of 45 ms would be about average for a completely fused tetanic response, and is in reasonable agreement with the value found by the other investigators, although somewhat less, as was the value for the risetime of the twitch response. The discrepancies are most certainly due to the differences in the methods used to measure the muscle properties. SANT'AMBROGIO and SAIBENE used an in vivo experimental setup in which the phrenic nerve was exposed in the neck of the animal but there was no preparation of the diaphragm muscle itself. The response was measured by recording the pressure
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rise in the pulmonary system through a tracheal cannula. This method, while certainly not disturbing the diaphragm in any way, does not isolate the muscle from the rest of the respiratory system. It is reasonable to expect a distortion (in the direction of lengthening of response time) in the response, because of the compliance of the respiratory system and also the inertia of the tissue and organs which must be moved. It must also be kept in mind that SANT'AMBROGIO and his colleague used nerve stimulation; in our studies the electrodes were placed directly in the muscle. The frequency of stimulation producing a fused contraction was about 100Hz, according to the other investigators, but we found that complete fusion takes place at about 30 Hz (Fig. 4). Again this discrepancy may in part be explained by the different methods of stimulation. GLEBOVSKII (1961) discussed the contractile properties of respiratory muscles in cats. Specifically, the diaphragm muscle was investigated by isolating a portion extending from and including the central tendon and the appropriate ribs. Thus GLEBOVSKII'S study corresponds closely to ours. He found the risetime of the diaphragm muscle under these conditions to be 48.8 ms, a value in good agreement with the 50 ms we found in dogs. He found the frequency at which complete tetany occurs to be in the range of 18-20 Hz, a value again in agreement with ours (30 Hz). He found the optimum frequency for tetanic stimulation to be 100-150 Hz, comparable with our finding of a very broad peak between 50 and 200 Hz (Fig. 6). The agreement between the results obtained on both cats and dogs suggests that these two animals have similar diaphragm muscles and leads one to suspect the method used by SANT'AMBROGIOand SAIBENE to obtain their data. Also the differences they reported between dog and cat may be due primarily to differences in the total respiratory system (for example, rib cage) rather than to intrinsic differences in the diaphragm muscles themselves. Conclusion While our results do not prove that permanent
myocardial assistance can be achieved by means of a pedicled diaphragm graft, they reveal nothing which indicates it to be impossible. The risetime, pressures attained and the power output are all within the order of magnitude required for the heart. This information is encouraging in view of the early failures at providing myocardial assistance, and indicates that new attempts should be made. Acknowledgment--This work was supported by the Medical Research Council of Canada, under grant MA 4384. References
CAMPBELL,E. J. M. (1970) in: The respiratory muscles: mechanics and neural control. Eds. CAMPBELL,E. J. M., AGOSTINI, E., and DAvis, J. D. W. B. Saunders, London. DROLET, R. (1971) Introduction to the bladder control system of the dog--characterization--theory--application. Ph.D. thesis. University of Toronto, Ont., Canada. DUKES, H. H. (1955) in: Duke's physiology of domestic animals. Ed. SWENSON, M. J. 7th edn. Comstock Publishing Associates, New York. GLEBOVSKn(1961) Contractile properties of respiratory muscles in fully grown and neonate animals. Sechenov Physiol. J. 47, 470-480. KANTROWITZ,A. and McKINNON,W. M. P. (1958) The experimental use of the diaphragm as an auxiliary myocardium. Surg. Forum 9, 266-268. KUNOV, H., VACHON,B. R. and ZINGG,W. (1975) An hydraulic-pouch method for assessing muscle dynamics Med. & Biol. Engng. 13, 65-70. NAKAMURA,K. and GLENN, W. L. (1964) Graft of the diaphragm as a functioning substitute for the myocardium: An experimental study. J. Surg. Res. 4, 435-439. SANT'AMBROGIO,G. and SAIBENE,F. (1970) Contractile properties of the diaphragm in some mammals. Resp. Physiol. 10, 349-357. SHEPHERD, M. P. (1969) Diaphragmatic muscle and cardiac surgery. Ann. R. Coll. Surg. Engl. 45, 212-231. SPECTOR, W. S. (1956)in: Handbook of biological data. Ed. SPECTOR,W. S. W. B. Saunders, Philadelphia. TALIBI, M. A., DROLET, R., KUNOV, H. and ROBSON, C. J. (1970) A model for studying the electrical stimulation of the urinary bladder of dogs. Br. J. Urol. 42, 56-65.
Propridtds mdcaniques du muscle du diaphragme du chien Sommaire--Nous avons mesur6 les propri6t6s m6caniques du muscle du diaphragme du chien. Une portion du diaphragme fut isol6e et fagonn6e en forme de poche avant d'6tre reli6e ~t divers circuits hydrauliques. Nous avons mesur6 la r6ponse b. la pression cr66e par stimulation 61ectrique b. divers voltages, fr6quences et pressions de base ainsi qu'h la dur6e de contraction. De plus, nous avons obtenu les courbes de pression-volume et avons estim6 le rendement d'6nergie du muscle en contraction active. Nous concluons d'apr6s ces r6sultats que les propri6t6s du muscle du diaphragme n'61iminent pas son usage en tant que substituant du myocarde.
Mechanische Eigenschaften des Zwerchfellmuskels yon Hunden Zusammenfassung--Die mechanischen Eigenschaften von Zwerchfellmuskeln von Hunden wurden gemessen. Ein Tell des Zwerchfells wurde isoliert und zu eiDer Tasehe geformt, die wiederum an verschiedene hydraulische Kreisl~iufe angesehlossen wurde. Wit malden die Druckreaktion auf elektrische Stimulation durch verschiedene Spannungen, Frequenzen und MelDbasisdriicke,ferner die Kontraktionszeit. Wir erhielten ferner Druck-Volumen-Kurven und sch~itzten die abgegebene Leistung des aktiv kontrahierenden Muskels. Wir schlossen aus den Ergebnissen, dal3 die Eigenschaften des Zwerchfellmuskels seineDGebrauch als Ersatz fiir den Herzmuskel nicht ausschlieBen. 260
Medical and Biological Engineering
March 1975
W . Zingg
Institute of Biomedical Electronics & Engineering, University of Toronto, Toronto, Ont., Canada
Research Institute, Hospital for Sick Children, Toronto, Ont., Canada
A b s t r a c t - - T h e mechanical properties of diaphragm muscle in dogs were measured. A portion of the diaphragm was isolated and formed into a pouch which in turn was connected to various hydraufic circuits. We measured pressure response to electrical stimulation for various voltages, frequencies and baseline pressures; and also contraction time. Further, we obtained pressure-volume curves and estimated the power output of the actively contracting muscle. From the results we conclude that the properties of the diaphragm muscle do not exclude its use as a myocardial substitute. K e y w o r d s - - M e c h a n i c a l properties of muscle
Introduction
NUMEROUS attempts have been made to provide myocardial assistance by artificial means. In the child, however, the use of an artificial implanted device is accompanied by major problems due to the growth of the heart and the circulatory system throughout childhood. F o r this reason and others, use of the autologous transplant is attractive. The diaphragm muscle was suggested by KANTROWITZ and McKINNON (1958) and NAKAMURAand GLENN (1964) as a possible source of tissue. Both teams of investigators have attempted to utilise the diaphragm muscle to provide myocardial assistance but have met with very limited success. SHEPHERD (1969) gave an extensive review of the relevant literature covering both the anatomical and histological properties of the diaphragm muscle which make it a logical choice for a myocardial substitute. In addition she reviewed the various attempts at providing such assistance to the heart. Although there has been limited success in providing a viable graft of a portion of the diaphragm on to the heart, such a procedure has still to demonstrate that it can give useful assistance in the form of increased cardiac output. Central to the problem of evaluating the performance of a diaphragmatic graft to the heart is a proper understanding of the electrical-mechanical properties of the isolated diaphragm muscle itself. In short, is the diaphragm muscle capable of contracting under the conditions to be encountered in the heart ? The pressures that the muscle is required to withstand and generate, as well as the rate at which it will be required to contract, may be excessive. The present study of diaphragm muscle was undertaken to evaluate the relevant properties * First received 14th December 1972 andin final form 8th November 1973
252
under conditions which would parallel those to be encountered in the heart. Materials and methods Dogs were used in the experiments. A portion of the diaphragm was formed into a pouch (KuNov, ZINo6 and VACHON, 1975) which in turn was connected to various hydraulic circuits for the measurement and recording of the muscle response to stimuli. Electrical stimulation of various voltages and frequencies was applied to the muscle and the pressure response measured. Approximately 15 experiments were performed, with a success rate of 100K once the surgical techniques had been established.
Surgical technique of the pedicle graft The isolated piece of diaphragm muscle which can be used to replace part of the right ventricle receives its blood supply through a pedicle consisting of the mobilised internal mammary vessels and their surrounding connective tissue. The surgical technique has been described in detail by SHEPHERD (1969). Both sides of the diaphragm are exposed through a right lateral thoracotomy, which is extended as a midline abdominal incision. Branches of the internal mammary artery and vein are identified and divided. Following identification of the blood supply, the graft is outlined from below and excised. The nerve supplying the graft is divided and the defect in the diaphragm is closed. The procedure results in a denervated pedicle graft of diaphragm muscle.
Measurement system To evaluate the properties of such a pedicle of diaphragm muscle, a technique was devised whereby the pedicle is formed into a pouch instead of being implanted on to the myocardium. The pouch thus
Medical and Biological Engineering
March 1975
consists entirely of diaphragm muscle. A fluidfilled flaccid balloon is inserted into the pouch. The balloon and the catheter to which it is attached are filled with fluid (saline) and the free end of the catheter is connected to an appropriate hydraulic measurement circuit. Either active or passive properties of the muscle may be studied under conditions which are either isometric (isovolumetric) or which permit the muscle to contract with a resultant fluid flow. Provision is made for injecting (or withdrawing) fluid from the system and thus control the static pressure in the pouch. A diagram of a typical set-up along with its electrical analogue is given in Fig. 1.
Measurements made Keeping the baseline pressure at 10 mmHg, we measured the pressure response produced by a single stimulus of 6 V (single pulse, 1 m s pulse duration, 1 Hz repetitition rate). Also, keeping the
I I i i I, l/Ill Balellne Pressure = I0 mmHg
IOmmHg
DIAPHRAGM
MUSCLE
Stimulus: Single Pulse Imsec Duration 6,0v
Fig. 2 Twitch contraction--a representative response illustrating the measured parameters (unretouched photograph of record) Stimulus: 6 V, 1 ms, 1 Hz, baseline pressure -10 mmHg pcv.t I ("~ Vtt)
Fig. 1 Muscle pouch and electrical analogue
A detailed description of the measurement system and techniques is given in a previous paper (KuNov, Z i y c c and VACHON, 1975). Stimulation to the pouch is provided by a pair of stainless-steel braided-wire electrodes which are sewn into the muscle on opposite sides of the pouch, in such a way as not to interfere with the blood supply. When the response of the muscle to stimulation is being studied, the configuration of the experiment is always isometric (isovolumetric), except for measurement of power output. For isometric determinations in both twitch and tetanic contractions, the catheter leading from the pouch is connected directly to a pressure transducer and, upon stimulation and contraction of the muscle no fluid is allowed to flow out from the pouch. Filling the system with a given volume of fluid produces in the pouch a static pressure referred to as the baseline pressure. This baseline pressure is varied by injecting fluid into or withdrawing fluid from the system using a syringe. The exact volume of fluid in the pouch is thus controlled. Using the simple system comprising pouch, catheter, pressure transducer and syringe (with valve), we can study tetanic and twitch contractions with the option of independently varying both the static baseline pressure and the stimulus parameters (voltage, frequency, pulse duration). In the measurement of the power produced by the actively contracting muscle the fluid is forced out of the pouch and flows through a known hydraulic resistance placed in the catheter. The pressure drop across the resistance is monitored, allowing calculations to be made of the power output. Medical and Biological Engineering
baseline pressure at 6 mmHg we measured the pressure response to a stimulus producing a tetanic contraction (2 V, 50 Hz). In addition, we studied the effect on risetime of variations in frequency, and the effect on the pressure response of variations in baseline pressure. The results of these experiments are given below. When we refer to 'pressure response' we mean the peak pressure rise above the baseline pressure. Fig. 2 illustrates a pressure response of 40 mmHg for a twitch contraction produced by a single-pulse stimulus of 6 V, 1 ms in duration, repeated once per second, the baseline pressure being 10 mmHg.
Reliability of method The measurements made on any given dog were reproducible for the duration of the experiment (up to 4-5 h) provided that care was taken not to overstress the diaphragm muscle. For example, maintaining a high pressure (740 mmHg) would cause an impairment of circulation with resultant deterioration of the muscle which might not be reversible. If excessive voltages were applied, tissue burning at the electrode site could occur. If these and other similar stresses were avoided, the results were repeatable. The differences in results obtained from different dogs reflect the differences in the muscles of the two animals. Care must be taken to normalise the results to account for the different pouch sizes. Results and discussion
Among the first questions to be answered is whether or not the diaphragm muscle, upon being stimulated, is capable of producing a sufficient increase of pressure inside the pouch to make the pressure compatible with those normally encountered in the heart.
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253
For the dog, the mean pulmonary arterial pressure is about 23 mmHg, while the systolic pressure is 40 mmHg and the diastolic pressure about 10 mmHg (DUKES, 1955, p. 188). Can the diaphragm pouch produce a peak pressure of approximately 40 mmHg in response to a 'reasonable' stimulus when there is a baseline pressure of about 1 0 m m H g ? Fig. 2 shows that the required pressure can be p r o d u c e d - in response to a stimulus of 6.0 V (single pulse, 1.0 ms pulse duration, 1.0 Hz repetition rate) the pressure is approximately 40 mmHg when the baseline pressure is 10mmHg. One might question whether the stimulus is 'reasonable'. However, in answer it may be said that voltages for bladder stimulation of about 10 V, with a 1.0 ms or longer pulse duration, have been recommended as being optimum (TALml 1970) in direct stimulation of a muscle with an implanted device. Tetanic contraction Fig. 3A shows the pressure response to a stimulus producing a tetanic contraction (voltage, 2 . 0 V ; frequency, 50Hz). F o r a baseline pressure of 6 mmHg the pressure response is approximately
Response risetime Varying the frequency of the stimulus used to produce the tetanic contraction yields differences in the risetime of the response (Figs. 4 and 5), so some control can be exercised over the waveform of the. pressure response of the diaphragm pouch. i
IO~mH
-
~ J30
Stimulus : 50 Hz I mS~r duration 2.Or
20turn g
Ap= / 47mmHg /
Baselln, p r e s ~ H g
JSO
I i ~-~1
tl/, -
i
100
$er ~
Z ,~ 200
Fig. 3A
Tetanic contraction--a representative response (unretouched photograph of record) Stimulus ." 2 V, 1 ms, 50 Hz pulse train, baseline pressure -~ 6 mmHg Diaphragm
Pouch-~- ~ .................
.... ~-I
s..o.d--~
Fig. 4 Tetanic contraction--variation of the response against stimulus frequency (unretouched photograph of record) Stimulus : 2 V, I ms, baseline pressure = 8 mmHg RISE TIME see 1210-
Fig. 3B Comparison of contraction waveforms of heart (human) and the diaphragm pouch (dog)
\|
\
0806-
47 mmHg. Comparing the rising portion of the curve with the pressure rise in the right ventricle (Fig. 3B), one sees that the two wave shapes are quite similar: all that would be required to make the curves match would be to reduce the voltage to the diaphragm pouch in a graded fashion. Differences in peak pressures would of course be adjusted by changes in the voltage. (It must be noted that, in this case, the pressure wave of the diaphragm pouch is being compared to the cardiac wave of a man, not that of a dog.) 254
04020
~o
~o
,~o
260
STIMULUS FREQUENCY Hz
Fig. 5 Risetime against stimulus frequency--tetanic contraction (derived from Fig. 4) Stimulus : 2 V, 1 ms, baseline pressure = 8 mmHg
Medical and Biological Engineering
March 1975
This variation of the risetime with the stimulus frequency is not just due to an increase in the peak response and a lengthening of the time taken to reach the peak. In Fig. 6 (derived from Fig. 4) the
_s
I.SmmHg
L_
PRESSURE RESPONSE rnmH
3.0
50" 40-
/
/
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i
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~b
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Fig. 6 Pressure response against stimulus frequency-tetanic contraction (derived from Fig. 4) Stimulus: 2 V, I ms, baseline pressure = 8 mmHg
15
Z
INITIAL SLOPE OF RESPONSE mmHg/(sec•
t'
3O
........ I*o"
10-
Fig. 8 Response against baseline pressure--tetanic contraction (unretouched photograph of record) Stimulus: 2 V, 1 ms, 50 Hz
8-
..i:1"//
,-
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0
~ ,~
~
1;
2'o
5b
~;o 2~o
STIMULUS FREQUENCY log Hz
25
Fig. 7 Initial slope of pressure response against stimulus frequency--tetanic contraction (derived from Fig. 4) Stimulus: 2 V, I ms, baseline pressure = 8 mmHg
pressure response is seen to level off after the stimulus frequency is increased above 50Hz. Fig. 7 (derived from Fig. 4) shows that the initial slope of the pressure response increases in a approximately linear fashion to the log of the frequency. The response of the muscle when it is stimulated to contract tetanically varies in both peak response amplitude and also in waveform (Fig. 8). The waveform changes considerably as the baseline pressure is increased above 10 mmHg. This fact could be used for controlling the wave form of the pressure rise as the diaphragm pouch is stimulated, if it were possible to vary the baseline pressure (i.e. the diastolic pressure) of the heart. Of course this is not possible and one is forced to make do with the waveform obtained at the pressures in the heart. Medical and Biological Engineering
mser
S0m~ec
S TIMULUS:SINGLE PULSE Imser
Fig. 9 Pressure response--twitch contraction; expanded time scale (unretouched photograph of record) Stimulus: I mA, I ms, baseline pressure = 16 mmHg
If a recording of the pressure response is made with an expanded time scale, as shown in Fig. 9, then, besides the risetime, the delay between stimulus application and muscle response can be determined.
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255
Table 1 Risetime and stimulus configuration Baseline Voltage pressure Risetime V 6 6 3 8 2 1 '5 4 2 4 2
mmHg 10 42 42 95 42 17 17 10 10 4
muscle. Increasing the volume of the pouch to obtain increased pressure results in a stretching of the muscle fibres. Fig. 11 shows how voltage affects the response/ baseline-pressure relationship. As in the tetanic contraction, each curve has a peak value for pressure response. If the diaphragm muscle were transplanted to heart muscle then the portion of Fig. 11 which is
Stimulus configuration
ms 50 .... 50 45 50 50 50 50 50 55 55
Single pulse, - - t w i t c h contraction
Pulse train, tetaniccontraction
For a stimulus of 1 mA, 1.0 ms, and a baseline pressure of 16 mmHg, there is a 25 ms delay from the time of the stimulus application until the response has reached 1 0 ~ of the peak value. Between the 1 0 ~ and 9 0 ~ points of the response, 30 ms elapse. Between the start of the response and the peak we find a delay of 50 ms. This is comparable to the risetime of the contractions shown in Fig. 4. Table 1 gives the risetime obtained in a series of experiments with different voltages and baseline pressures. In each experiment the risetime was close to 50 ms, indicating that it is independent of strength of stimulus and baseline pressure.
Response against baseline pressure A plot of the peak response against the baseline pressure (Fig. 10) shows that there is an optimum PRESSURE RESPONSE mmHg
6o~
20-,0_ /'~'~'~~. 30-
_
/
10- / I
~
i~
1'6
2'0
2',
2'8
3~
BASELINEPRESSUREmmHg
Fig. 10 Pressure response against baseline pressure-tetanic contraction (derived from Fig. 8) Stimulus: 2 V, I ms, 50 Hz
value of baseline pressure at which the peak response i s a maximum. This pattern is characteristic of both tetanic and twitch contractions. The variation of response with baseline pressure is due to the effects of stretching the muscle fibres and involves a length/tension relationship as is found in skeletal 256
30- /
x
20- . ~ x
60 V ~" ~ ~ ~
o
;
) ~;
~
2'o
2'5
3'0
3'5
,'0
BASELINEPRESSURErnmHg
Fig. 11 Pressure response against baseline pressure-twitch contraction Stimulus: 2, 6 and 10 V, 1 ms, 1 Hz
of interest is that where the baseline pressure corresponds to the end diastolic pressure (5 mmHg), i.e. near the beginning of the ascending portion of the curves. At the end diastolic pressure the diaphragm muscle will. not be working at its optimum but, on the other hand, its response will be similar to that of the heart muscle. Starling's Law states that, if there is increased filling of the ventricles, then the heart contracts with more force to produce an increased stroke volume, and the diaphragm muscle would do the same under those circumstances.
Transdiaphragmatic pressures
20- / 00
PRESSURE RESPONSE mmHg 50-
The diaphragm muscle is ultimately limited in the amount of differential pressure which it can sustain, since the blood supply will eventually be cut off. At what baseline pressures can the diaphragm pouch operate for prolonged periods? In its normal function of assisting respiration the diaphragm is subjected to pressure differentials. Normally the peak differential pressure across the diaphragm is about 6.4 mmHg, which is only about 25 ~o of the peak systolic pressure in the right heart (24 mmHg). On the other hand, the diaphragm muscle is capable of withstanding much greater pressure differentials during exertion, and with maximal effort the transdiaphragmatic pressure may be maintained around the value of 82 mmHg, which is much greater than the pressures to be encountered in the heart. In our experimental setup, the baseline pressure is equivalent to the transdiaphragmatic pressure. N o long-term studies were performed. Even in our short-term studies we found that damage can
Medical and Biological Engineering
March 1975
be done to the muscle by subjecting it to very high pressures. In one experiment the pressure in the pouch was increased to 200mmHg for a few minutes. The muscle response then decreased to less than a tenth of the initial value while the muscle appeared to be very cyanotic. It required some minutes of rest, at zero pressure, to return to a normal state. This effect is a gradual one, of course, there being an ever increasing amount of blood cut off the higher the pressure. Also, in the heart the diaphragm muscle would be subject to rhythmic fluctuations of pressure which tend to stimulate the circulation. The behaviour of the diaphragm muscle under high pressures is what would be expected of the heart muscle (or any other muscle for that matter) under similar circumstances, and so does not indicate an incompatibility of the diaphragm and heart muscles.
Stimulus frequency
Stimulus voltage
Fig. 13 Pressure response against baseline pressure-twitch contraction Stimulus: 2 V, I ms, 1 Hz
The response of the diaphragm pouch to continuous, increasing stimuli is shown in Fig. 12. Very high pressures are achieved with high voltages, he response being 176 mmHg at 30 V. The general
PRESSURE RESPONSE mmHg 200-
f
160-
ie,-"
PRESSURE ~ESPONSE mm~o~ 16-
o~~
~*'~'~
8-
4-
o
~'
1'2 ~ 2'o 2', 2's BASELINEPRESSUREmmHg
~
3'2
agrees closely with the value of 1 2 . 5 m m H g obtained with a single-pulse stimulus at the same baseline pressure of 8 mmHg (Fig. 13). Fig. 6 shows that the peak response is three times the response at zero frequency, and the long broad plateau extending from about 50 Hz to 200 Hz indicates that any frequency above 50 Hz would serve to produce a maximum contraction.
Stimulus pulse width
120-
In Fig. 14, the response is plotted as a function of the width of the stimulus pulse. The general shape of the curve is what one would expect, since, as the pulse width is increased, more fibres will be stimulated. There is a limit to this process, however, since, at some point, all of the available fibres at that particular stimulus voltage are being stimulated and in effect there is direct current stimulation.
8040-
Fig. 6 gives some idea of the effect that the stimulus frequency has upon the response. Extrapolating the graph in Fig. 6 shows that at zero frequency the pressure-response value is 14.5mmHg, which
/./'~
0
STIMULUS-VOLTS Fig. 12 Pressure response against stimulus voltage-twitch contraction Stimulus: I ms, I Hz, baseline pressure = 15 mmHg
PRESSURE RESPONSE ; mmH I0030 V
8 0 - ~ , shape of the curve is characteristic for all the dogs used, and can be explained as follows: the initial rise is due to the stimulation of the nerves lying near the electrodes. As the voltage is increased from 0.4 to 1.0 V more nerves are stimulated, as is shown by the increase in pressure response. Between 1.0 and 1.5 V the pressure response increases suddenly because of the direct stimulation of the muscle fibres. Further increases in voltage result in increased pressure response due to the spread of the stimulus through the tissue. Medical and Biological Engineering
20 V
6040-
10 V
200-
o
~
~
~
~ b ~ ~ STIMULUSPULSEWIDTH
I~
?8
2~
rnsec
Fig. 14 Peak pressure against stimulus pulse w i d t h - twitch contraction Stimulus: 1, 2 and 3 V, 1 Hz, baseline pressure -- 2 mmHg
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257
Passive pressure/volume relationship A typical plot of the volume against the pressure inside the diaphragm pouch (when passive) is shown in Fig. 15 plotted on semilogarithmic co-ordinates. This curve has the exponential shape P=O.95e ~ The initial volume to produce PASSIVE PRESSURE rnmH~ 80-
/
40-
20-
10-
/
/
e
64-
2-
/
!
-
! VOLUME cm 3
Fig. 15 Intrapouch pressure as a function of pouch volume--passive response, semilogarithmic plot
zero pressure will not be zero, since, if the pouch is completely collapsed, the muscle is not in a relaxed state.
Muscle stress The stress in the muscle wall depends not only on the pressure in the pouch, i.e. the force on the muscle fibres, but also on the wall cross-sectional area, which changes as the muscle is stretched. We investigated muscle stress to see whether it would yield more information than the pressure/volume curves. We had to make a number of assumptions PASSIVE PRESSURE
STRESS N/rn2• 3
mmH
60 ~
-60
./
40-
,/ -20
-8
-,4
-2
,/,/
. . . . 2
4
6 B VOLUME cm 3
10
112
I
Fig. 16 Pressure/volume relationship compared with the stress/volume relationship--passive response 258
to arrive at an estimate of the change in the wall cross-sectional area with volume. The empty pouch consists of two roughly square pieces of tissue lying flat against each other. When the pouch is filled enough to produce a pressure of say 100 mmHg, then it is approximately spherical. We decided to consider the pouch as consisting o f two equal spherical surfaces, such as would result from the intersection of a plane and a sphere (not into hemispheres--the two sections only constitute a complete sphere at large volumes). The approximate diameter of the pouch was measured photographically for each increment of volume. Knowing the volume and the diameter we could compute the approximate cross-sectional area of the muscle at the midplane and use this value, along with the simultaneously recorded pouch pressure, to compute the stress in the muscle wall. The results of these computations are shown in Fig. 16 which plots stress against volume and compares the curve with the pressure/volume curve for the same pouch. A semilog plot was used here to facilitate comparison of the two exponential curves. Since the shapes of the two curves were not significantly different we conclude that there is no additional information to be gathered from the stress. Perhaps this is to be expected, since diaphragm muscle has no property, such as a storage property, that would preclude a close correlation between the pressure in the pouch and the stress in the muscle wall. In contrast, DROLET(1971), working on the urinary bladder of dogs (which has a storage function), found that, while the pressure/volume curve has a definite plateau where the volume increases but the pressure does not, the stress in the bladder wall increases steadily with increasing volume.
Muscle fatigue Can the diaphragm muscle undergo long-term stimulation at a rate comparable]to that of the heart ? The present short-term investigations cannot answer the question with any finality. In our experiments, the pouch of diaphragm muscle has been stimulated continuously for periods of up to 4 h only. A number of observations can be made from the results of these experiments, however. Within any given experiment, the lower the baseline pressure the longer the muscle seems ab/e to maintain a given level of response. The repetition rate at which the muscle is stimulated is a limiting factor: the increased response of the muscle to increased frequency generally declines over time. However, in one experiment where the diaphragm pouch was stimulated (2 V) continuously for a period of 3" 5 h, the stimulus rate was 80 per minute for the first 2 h and then 150 per minute for the remaining 1" 5 h (the baseline pressure was 4 m m H g and the initial peak response 15 mmHg). The
Medical and Biological Engineering
March 1975
response at the end of the experiment was the same as the initial response. The muscle would thus appear to have some capacity for working at a relatively high rate (i.e. at a rate compatible with that required from heart muscle) for somewhat extended periods of time. Crucial to the muscle contracting for a prolonged period is the maintenance of an adequate blood supply. This was not always feasible with the surgical procedure used here. In an autologous transplant a patient blood supply is a minimal requirement and would be maintained if the graft were viable. The question as to whether or not a proper response can be maintained for prolonged periods is the subject of further investigation.
Power output of diaphragm muscle The power output of the heart can be estimated from the average values for the volume output and the arterial pressure. F o r dogs, calculations using a minute volume of 1" 5 litres (DuKEs, 1955, p. 113) and a mean arterial diastolic blood pressure of 100 mmHg (SPEcTOR, 1956, p. 232) give the power output of the left heart as 335 m W and that of the right heart (assuming the pulmonary arterial diastolic pressure to be 10 mmHg, i.e. one-tenth that of the left heart) as 33-5 roW. By calculating the approximate area of the right and left ventricles an estimate of the power per unit area for the myocardium call be obtained. F o r dogs the area is estimated to be about 30 cm 2, giving a power output of approximately 1 m W / c m 2. Measurements of the power output of the diaphragm pouch show the peak power to be about 50 roW. F o r a pouch size of about 30 cm 2, the power output per unit area would be 1.66 m W / c m 2. Comparing this figure with the figure for dog myocardium, it is reasonable to expect that the diaphragm muscle could provide some assistance to the heart if it were implanted. Comparing the normal power output of the diaphragm in respiration with that of the power output of the diaphragm pouch, we find the following results for man. During quiet breathing the respiratory muscles produce about 70 mW of power (CAMPBELL 1970, p. 121). This is a measure of the work performed as determined by external measurements. If we assume that the diaphragm contributes about 75 ~ of this work, the power output of this muscle is 52 mW. If, further, we assume that the approximate area of the intact diaphragm is 500cm 2, the power output per unit area is 0.1 m W / c m 2. During exercise the power output of the respiratory system can be increased as much as a hundredfold (CAMPBELL, 1970, p. 122). The relative contribution of the diaphragm muscle is probably not as great in these circumstances but a fiftyfold increase is probably realistic, giving a power output per unit area of 5 m W / c m 2 for diaphragm muscle at maximum respiratory effort. Medical and Biological Engineering
These data are all for man but it is reasonable to expect values of the same order of magnitude for the dog. The power output of the pouch then is about 16 times that of the normally functioning diaphragm during quiet breathing but is only about 31 ~ of the peak power obtainable.
Comparison with other investigators Only SANT'AMBROGIOand SAIBENE(1970) appear to have reported on the mechanical properties of the diaphragm muscle in dogs. They gave a number of parameters for dogs cats, rabbits, and rats, the first of these parameters being the contraction time of the muscle, defined as the time from the start of the pressure rise to the peak (our rise time). For dogs the contraction time was 64.7 + 5.6 ms for a twitch contraction. The risetime for a twitch contraction in our experiments with dogs is about 50 ms. SANT'AMBROGIOand SAIBENE also gave the time taken to reach one half of the peak response (T,) for a tetanic contraction. F o r dogs T, was 57+ 5.6ms. We measured T, on the curves of Fig. 4 and found that it varies somewhat with the stimulus frequency, as is shown in Fig. 17. However, T1/2 TIME TO ~ PEAK RESPONSE msec 100-
8060-
\
~020.
0 STIMULUS FREQUENCY Hz
Fig. 17 Risetime (expressed as T, against stimulus frequency--tetanie contraction (derived from Fig. 4) Stimulus: 2 V, I ms, baseline pressure = 8 mmHg
a value of 45 ms would be about average for a completely fused tetanic response, and is in reasonable agreement with the value found by the other investigators, although somewhat less, as was the value for the risetime of the twitch response. The discrepancies are most certainly due to the differences in the methods used to measure the muscle properties. SANT'AMBROGIO and SAIBENE used an in vivo experimental setup in which the phrenic nerve was exposed in the neck of the animal but there was no preparation of the diaphragm muscle itself. The response was measured by recording the pressure
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rise in the pulmonary system through a tracheal cannula. This method, while certainly not disturbing the diaphragm in any way, does not isolate the muscle from the rest of the respiratory system. It is reasonable to expect a distortion (in the direction of lengthening of response time) in the response, because of the compliance of the respiratory system and also the inertia of the tissue and organs which must be moved. It must also be kept in mind that SANT'AMBROGIO and his colleague used nerve stimulation; in our studies the electrodes were placed directly in the muscle. The frequency of stimulation producing a fused contraction was about 100Hz, according to the other investigators, but we found that complete fusion takes place at about 30 Hz (Fig. 4). Again this discrepancy may in part be explained by the different methods of stimulation. GLEBOVSKII (1961) discussed the contractile properties of respiratory muscles in cats. Specifically, the diaphragm muscle was investigated by isolating a portion extending from and including the central tendon and the appropriate ribs. Thus GLEBOVSKII'S study corresponds closely to ours. He found the risetime of the diaphragm muscle under these conditions to be 48.8 ms, a value in good agreement with the 50 ms we found in dogs. He found the frequency at which complete tetany occurs to be in the range of 18-20 Hz, a value again in agreement with ours (30 Hz). He found the optimum frequency for tetanic stimulation to be 100-150 Hz, comparable with our finding of a very broad peak between 50 and 200 Hz (Fig. 6). The agreement between the results obtained on both cats and dogs suggests that these two animals have similar diaphragm muscles and leads one to suspect the method used by SANT'AMBROGIOand SAIBENE to obtain their data. Also the differences they reported between dog and cat may be due primarily to differences in the total respiratory system (for example, rib cage) rather than to intrinsic differences in the diaphragm muscles themselves. Conclusion While our results do not prove that permanent
myocardial assistance can be achieved by means of a pedicled diaphragm graft, they reveal nothing which indicates it to be impossible. The risetime, pressures attained and the power output are all within the order of magnitude required for the heart. This information is encouraging in view of the early failures at providing myocardial assistance, and indicates that new attempts should be made. Acknowledgment--This work was supported by the Medical Research Council of Canada, under grant MA 4384. References
CAMPBELL,E. J. M. (1970) in: The respiratory muscles: mechanics and neural control. Eds. CAMPBELL,E. J. M., AGOSTINI, E., and DAvis, J. D. W. B. Saunders, London. DROLET, R. (1971) Introduction to the bladder control system of the dog--characterization--theory--application. Ph.D. thesis. University of Toronto, Ont., Canada. DUKES, H. H. (1955) in: Duke's physiology of domestic animals. Ed. SWENSON, M. J. 7th edn. Comstock Publishing Associates, New York. GLEBOVSKn(1961) Contractile properties of respiratory muscles in fully grown and neonate animals. Sechenov Physiol. J. 47, 470-480. KANTROWITZ,A. and McKINNON,W. M. P. (1958) The experimental use of the diaphragm as an auxiliary myocardium. Surg. Forum 9, 266-268. KUNOV, H., VACHON,B. R. and ZINGG,W. (1975) An hydraulic-pouch method for assessing muscle dynamics Med. & Biol. Engng. 13, 65-70. NAKAMURA,K. and GLENN, W. L. (1964) Graft of the diaphragm as a functioning substitute for the myocardium: An experimental study. J. Surg. Res. 4, 435-439. SANT'AMBROGIO,G. and SAIBENE,F. (1970) Contractile properties of the diaphragm in some mammals. Resp. Physiol. 10, 349-357. SHEPHERD, M. P. (1969) Diaphragmatic muscle and cardiac surgery. Ann. R. Coll. Surg. Engl. 45, 212-231. SPECTOR, W. S. (1956)in: Handbook of biological data. Ed. SPECTOR,W. S. W. B. Saunders, Philadelphia. TALIBI, M. A., DROLET, R., KUNOV, H. and ROBSON, C. J. (1970) A model for studying the electrical stimulation of the urinary bladder of dogs. Br. J. Urol. 42, 56-65.
Propridtds mdcaniques du muscle du diaphragme du chien Sommaire--Nous avons mesur6 les propri6t6s m6caniques du muscle du diaphragme du chien. Une portion du diaphragme fut isol6e et fagonn6e en forme de poche avant d'6tre reli6e ~t divers circuits hydrauliques. Nous avons mesur6 la r6ponse b. la pression cr66e par stimulation 61ectrique b. divers voltages, fr6quences et pressions de base ainsi qu'h la dur6e de contraction. De plus, nous avons obtenu les courbes de pression-volume et avons estim6 le rendement d'6nergie du muscle en contraction active. Nous concluons d'apr6s ces r6sultats que les propri6t6s du muscle du diaphragme n'61iminent pas son usage en tant que substituant du myocarde.
Mechanische Eigenschaften des Zwerchfellmuskels yon Hunden Zusammenfassung--Die mechanischen Eigenschaften von Zwerchfellmuskeln von Hunden wurden gemessen. Ein Tell des Zwerchfells wurde isoliert und zu eiDer Tasehe geformt, die wiederum an verschiedene hydraulische Kreisl~iufe angesehlossen wurde. Wit malden die Druckreaktion auf elektrische Stimulation durch verschiedene Spannungen, Frequenzen und MelDbasisdriicke,ferner die Kontraktionszeit. Wir erhielten ferner Druck-Volumen-Kurven und sch~itzten die abgegebene Leistung des aktiv kontrahierenden Muskels. Wir schlossen aus den Ergebnissen, dal3 die Eigenschaften des Zwerchfellmuskels seineDGebrauch als Ersatz fiir den Herzmuskel nicht ausschlieBen. 260
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