Mechanical properties of the heart muscle in the passive state

J. &mechanics,

1973, Vol. 6. pp. W-616.

Pergamon Press.

Printed in Great Britain

MECHANICAL PROPERTIES OF THE HEART MUSCLE IN THE PASSIVE STATE* JOHN G. PINTO and Y. C. FUNG Department of AMES (Bioengineering), University of California, San Diego, La Jolla, California 92037, U.S.A. Abstract-The viscoelastic behaviour of the heart muscle (papillary muscle) in the passive unstimulated) state is studied by such methods as stress relaxation, creep, vibration and stressstrain testing. The tests are conducted on a newly developed electromechanical muscle testing device which is suitable for conducting active and passive tests on biological materials. INTRODUCTION

of the muscle. Various types of devices for testing heart muscle have been reported in literature. These devices may be roughly classified into three types: (a) Sonnenblick’s type of lever system capable of varying preload and afterload, and quick release to a specified condition (Sonnenblick, 1%2), (b) Hefier’s type using electromagnetic forces for loading the muscle (Hefner and Bowen, 1%7, Noyes, 1967) and (c) Brady’s type of dynamometer capable of imposing specific time history on the specimen (Brady, 1965). The equipment to be described below was specifically designed for testing cardiac muscles, and belongs to the Brady type with the addition of a feedback control system. It is a ‘high speed’ positioning servo-system, capable of performing all experiments reported earlier while removing some of the difficulties encountered.

CARDIAC

muscle can exist in two states-the stimulated (active) state and the unstimulated (passive) state (Huxley, 1969). To study the active contraction of the muscle, one must first know its behavior in the passive state. In the present article the passive behavior is discussed. Experimental results on the active contraction is presented in a companion article. From the mechanical point of view heart muscle in the passive state is an inhomogeneous, anisotropic and incompressible material. Its properties change with temperature and other environmental conditions. It exhibits a stress relaxation behavior under maintained stretch (Abbot and Lowy, 1957; Abbott and Mommaerts, 1959; Brady, 1%7; Calcote, 1%8; and Hoffman et al., 1%8) and creep under a maintained stress (Buchthal and Kaiser, 1951). It dissipates energy and exhibits hysteresis loop in cyclic loading and unloading (Buchthal and Kaiser, 1951 and Fung, 1%7, 1970). Thus, heart muscle in the passive state is viscoelastic. In recent years much attention has been focused on the health and disease of the heart. Much effort is devoted

to describe

THE TESTING EQUIPMENT

The general arrangement of the electromechanical system is shown in Fig. 1. The device consists of a linear vibrator (Ling Altec. Inc., Model 203 S/N 125) whose spindle motion is controlled using a feedback servo controller. A linearly variable differential transformer (HP 595 DT-100, 25 kHz carrier) is used to measure displacements. Force is measured by a modified pressure sensor (Pitran, Stow Labs., Boston, Mass.). The dis-

the perfor-

mance of the heart under normal and pathological conditions. Heart is a dynamic organ; its performance rests on the mechanics *Received 21 March 1973. 591

598

JOHN G. PINTO and Y. C. FUNG LINEAR VIBRATOR MOTOR

MUSCLE SPECIMEN

‘STATHAM FORCE GAUGE

Fig. 1. Mechanical arrangement of the system.

placement and force transducers are connected in series to the vibrator spindle. Steady state is achieved within 3 msec after a step change in displacements over a range of 0~25 mm. The displacement transducer is capable of 0.002 mm resolution. A force of 50 mg can be resolved with the force transducer. In active contraction (stimulated muscle) experiments on papillary muscle, force resolution of about 10 mg can be achieved by recording repetitive signals on a tape recorder and then using a signal averaging device (PAR TDM-9 waveform eductor) to obtain the average values from about 60 equivalent records. The system can be operated in a displacement mode or a force mode. In the former the length of the specimen is controlled. In the later the force acting on the specimen is controlled. Either mode can be programmed to follow a specific course in time. Transfer from one mode to another is possible by electronic control. The displacement mode is utilized for passive tests such as stress-strain, relaxation, vibration and active (stimulated) isometric test. The force mode is utilized for active isotonic tests. The displacement and force transducers are positioned at the same side of the muscle

specimen and move with the motor spindle in order to avoid instability in the fast-acting servo-system. Otherwise, the muscle itself becomes an element in the feedback loop and may cause instability by introducing an additional phase change in the feedback loop. The characteristic time of the controller is short relative to that of physical process; and the system is stable. The Pitran force transducer used to measure force is light weight and has a good frequency response (2 kHz); but is drift-prone at low frequencies. This difficulty is circumvented by using a double transducer system (Fig. 1). A stable transducer (Statham green cell, Frequency response 50 Hz) is mounted at the lower end of the specimen. By matching precisely the sensitivities of the Pitran and the green cell and using a cross-over network with suitable filters a uniform, drift-free gain can be obtained (Fig. 2). Details of the block diagram and operation procedure are described in the Appendix and in Pinto (1972).

Fig. 2. Crossover Filter Network. DATA RECORDING

In conducting the tests the step changes imposed on the muscle-in both displacement and force mode-occur at high speeds. Hence an FM 4 channel tape recorder was used to record the data. The recording head has a frequency response of 2-5 kHz. The force sensor has good sensitivity (150 MVlg), but noise due to various extraneous and spurious disturbances in the laboratory reduce the force resolution to only about 50 mg if additional measures were not taken to improve the situation. The resolution was increased by using a signal conditioning device known as the wave form eductor (Princeton Applied Re-

MECHANICAL

PROPERTIES

search Corp., New Jersey). The eductor finds the ensemble average of a large number of repetitive signals. In case of active muscle tests, the repetitive signals are .obtained easily by repeating a particular test a large number of times (150-200 times) and recording the signals on the magnetic tape. The recorded data can be played back to the eductor thus obtaining improvement in the signal to noise ratio. The system described above is used for testing the papillary muscles of rabbit. Specific tests and the corresponding results are discussed below. METHOD OF MOUNTING SPECIMEN AND EFFECT OF END CONDITIONS

Papillary muscles were obtained from adult -5 month, 2-5-3 kg) rabbit heart. To avoid the effect of drugs, the animal is knocked unconscious by a quick sharp blow at the root of the head, severing the spinal cord. The chest cavity is immediately opened and the vigorously beating heart is resected and placed on a breadboard immersed in a tray containing modified Kreb-Ringer solution (Sonnenblick, 1%2) at room temperature and pH 7.4. A 95 per cent O2 and 5 per cent CO, mixture of gas is continuously bubbled through the solution (l-l

OF THE

HEART

MUSCLE

(02 tension 600 mm IIg). The right ventricle is then dissected to expose the papillary muscles. Of the two or three papilIaries that are often seen, the one with a larger aspect ratio and good cylindrical geometry is chosen for test. The papillary is tied off at both ends using 5-O Deknatal black braided surgical silk thread. Hooks made of tempered stainless steel wire are strung beneath the thread knot at both ends (Fig. 3). The specimen is then resected off the ventricle and mounted in the specimen bath of the testing apparatus which contains Kreb-Ringer solution of desired temperature and pH. The entire surgical procedure is performed in the Kreb solution. The procedure generally takes 5-8 min. A tight knot produces a site of stress concentration. The constraint caused by the knots introduces artificial rigidity to the specimen. The effect of this rigidity on the longitudinal properties of the specimen cannot be quantified at present. The effect of end conditions may be reduced by employing specimen of larger aspect ratio; unfortunately, no such specimen can be obtained. In the initial stages of experimentation several types of end fixtures-alternate forms of hooks, thread loops, non slipping miniature

SPECIMEN ?

UPPER

HOOK 8mm Length I 0.127mm Diameter d L5mm Radius of Curvature 8mgm. Weight

LOWER

ASPECT

RATIO

= -

HOOK I.lCf?l Length t 0.127mm Diameter d 1.5mm Radius of Curvature Weight l2mgm

R

Lref dref

Fig. 3. Specimen

nomenclature

599

and specifications

of the hooks.

600

JOHN

G. PINTO

and Y. C. FUNG

clamps were tried. Our final choice was the ‘fish hook’ type of mounting shown in Fig. 3 which provided the plumbness, ease and speed of specimen preparation. In stringing the hook through the specimen, the hook pierces the specimen which might be torn under tension. Care was taken to minimize this tearing by stringing the hooks as close to the thread-tie as possible. Realizing the difficulty of holding the specimen and its importance in the interpretation of the data, we suggest that further study be made in the light of the constitutive equations obtained from the present study.

The homeostatic condition of the papillary muscle is disturbed upon resection. It needs a period of adjustment for a repeatable mechanical performance in a given test. In a particular test repeatability of performance is observed if the specimen is subjected to a few cycles of that test. For example, in a creep test, creep response tends to repeat if the specimen undergoes a few cycles of creep, or in a stress-strain test, a few cycles of repeated loading and unloading_ It is difficult to estimate the nature of changes occuring within the specimen during the preconditioning cycle. Aside from changes occuring within the specimen, preconditioning helps to remove any slacks or kinks that may exist in the connection between the hooks and the specimen. Appropriate preconditioning was performed on all specimen tested in this study. Figure 4 shows typical features of adjustment occuring in creep test. After preconditioning, measurement of a reference length (I,& and a reference dia. (L.) were made on all specimens. A reference state is a standard condition defined here as a slightly loaded state of the specimen caused by a 12mg hook hanging from the

‘PRECONDITIONING’ OF THE SPECIMEN The ultrastructure of complex materials such as high polymers and living tissues changes irreversibly under strain, hence their mechanical properties depend on strain history. A steady state may be reached under cyclic conditions. In a living animal a steady state condition is called a homeostatic condition. In vitro, an equivalent of homeostasis, if it exists, is called a ‘preconditioned’ state. 15.

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(2)

. . ..I”

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a

.

.

.

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.

A .

.

.

l

(41

. ..*.*d

. .**.w

32-

I 0.01

I I .o

I O-I

Time,

Fig. 4. Typical

features

I 10.0

I too.0

min

of preconditioning

in a creep test.

1000~0

MECHANICAL

PROPERTIES

lower end of the specimen which is suspended freely in a bath containing Kreb-Ringer solution. Thus the reference state referred here is not a stress-free state, but an arbitrarily defined state convenient for laboratory work. For a very flexible nonlinear specimen such as the papillary muscle of the rabbit, the specimen has no well defined geometry in the stress-free state, and an accurate measure of length and cross section is not possible. The reference state, however, while arbitrary, has the virtue of being definitely measurable. The length and diameter were measured using a cross-hair focusing device cathetometer (Griffins and George, England) capable of 0.01 mm resolution. The Lrer. is the length of the specimen between the hooks and the &., its diameter at mid-length (see Fig. 3). RELAXATION Displacement tranducer: Resolution: Force sensor:

Overall force resolution: Test duration: Stretch ratio: Temperature range: pH:

30 mg 1000 set after preconditioning h=l.05 to h=l*30 5, 10, 15, 20, 25, 30-37°C 74.

Relaxation tests were conducted after 5 cycles of preconditioning stretches, each lasting a duration of lo-15 set, and an equal period of rest between stretches. The magnitude of preconditioning stretch was same as that used in the particular relaxation test. During each test the constant temperature condition was maintained

within

limits

601

stretch magnitude. Transient oscillations of the force transducer persisted over 40-50 msec. In reducing the data, the relaxation curve was extrapolated to the t = t, point as shown dotted in the figure. Poor frequency response of the strip chart recorder was circumvented by recording initial portion of displacement and force curves on a magnetic tape.

+r +ss

TEST RESULTS

Linear variable differential transformer 0402 mm Statham green cell and Tektronix 3C66 Carrier System 283 mV/g Drift under 30mg Fast response-magnetic tape recorder, Slow response-strip chart (Hewlett Packard 7100 BM) recorder

Sensitivity: DC Stability: Recorder:

OF THE HEART MUSCLE

of * O-SC. Figure

5 shows

the transient displacement and force in a relaxation test. Rise times t, ranged between 0.8 msec and 3 msec, while the time to attain a steady state, t,,, was between 3 msec and 11 msec. Overshoot was under 15 per cent of

Fig. 5. Displacement

and force transducer laxation test.

signals in a re-

After completing a test run of 1000 set the specimen was allowed to rest for 5-10min. Stretch was then increased to the next higher level; the specimen was preconditioned for 5 cycles at the new stretch, and then relaxation test was performed. In this fashion each specimen was carried through strains from 5 to 30 per cent in 5 per cent increments. Temperature was maintained constant during the entire set of experiments on a given specimen. Likewise, a new specimen was tested at a new temperature. In all, seven sets of relaxation data corresponding to seven temperatures were obtained. In Fig. 6, relaxation data obtained at 15°C for 5 stretches (A = 1.05-1.30) performed on the same specimen is shown. The ordinate G(t) represents a normalized function of time known as the reduced relaxation function,

602

JOHN G. PINTO and Y. C. FUNG

0.5-

0.4

I 0.01

I

I I I I, I, 0.1

,

,

, , , , , I, I.0 Time,

,

,

, , , , , ,, IO.0

,

,

, , , , ,,,

,

,

I , ,

100.0

101 I.0

seconds

Fig. 6. Effects of stretch h on reduced relaxation function G(t).

which is defined (Fung, 1972) as T(t) G(t) = T(t,)

(1)

where T(t) is the Lagrangian stress (total load divided by the cross-sectional area at the reference state) in the specimen at time t corresponding to a stretch A imposed at t = t, and T(f,) is the Lagrangian stress in the specimen at the instant of time t = t,. The time t, corresponds to the rise time of the imposed stretch (Fig. 5). From Fig. 6 it is seen that G(t) is essentially independent of the stretch A. This independence is also observed at other temperatures. This feature has been alluded to by Fung (1972) and is the basis for considering the passive muscle as a quasi-linear material viscoelastically. Figure 7 shows a plot of G(r) vs time at h = 1.30 for 7 temperatures. The trend is not grossly temperature dependent-particularly in periods of time less than 1 sec. Thus in periods comparable with that of one heart beat, the relaxation function G(r) may be considered independent of temperature in the

range 5-37°C. Hill (1950), working on skeletal muscle fibers, also did not find measurable variation of the course of relaxation with temperature. Figure 8 is a plot of G(t) vs temperature for A = 1.15 at various times after the initiation of relaxation. It is seen that for periods of time up to 10 set, G(t) does not change markedly with temperature. The relaxation function (Fung, 1%5), the history of the stress response for a suddenly applied and maintained strain, is in general a function of many variables such as the stretch magnitude A, the temperature 8, the pH, the chemical composition of the fluid environment, and the time t: Thus K = K(h, 0, pH, N. . . . . t).

(2)

In the present study, only the effects of stretch A, the temperature 0, and the time t have been studied-pH and the osmolarity of the chemical environment being maintained constant throughout. With this restriction, K can be written as K = K(A, 8, t).

(3)

MECHANICAL

603

PROPERTIES OF THE HEART MUSCLE

Time,

seconds

Fig. 7. Temperature effects on G(t).

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-------o/

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.96 -

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A-.

0.01 0.1 1.0

IO.0 MC. 100.0 IS. 1000.0 WC-

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WC. sec. see.

.68 I

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50

IO.

150

20’

I

TEMPERATURE

I

I 300

25.

37.

(‘Cl

Fig. 8. Variation of G(t) with temperature 0.

EM.

Vol. 6 No. 6-B

I

604

JOHN G. PINTO and Y. C. FUNG

The experimental results shown in Figs. 6 and 7 suggest that K can be written in the form K(A, e, t) = G(t) P(A,

e)

(4)

where G(t) is a normalized function of time alone and is defined such that G(0) = 1. In (4), P(A, 0) is the so called elastic response (Fung, 1972)-a hypothetical Lagrangian stress as a function of stretch A and temperature 8. Fung (1972) has proposed that for soft tissues for which (4) is valid, the stress T(t) at any time t is linearly related to the elastic response P’[A(t), 01 for an arbitrary loading history A(t) by a convolution integral as follows: T(t) = G(t)*T”‘[A(t),

61

(5)

where * denotes the convolution operator. The linear operator in equation (5) allows the application of the theory of linear viscoelasticity to the nonlinear papillary muscle. The elastic response T(e) is discussed below. THEELASTIC RESPONSE T”‘(A, 0) By definition Fe’ (A, 0) is the tensile stress generated instantly in the tissue when a step stretch A is imposed on the specimen at temperature 8. Measurement of T”’ (A, (3) strictly according to the definition is not possible not only because a true step motion of the loading head is impossible to obtain in the laboratory, but also because, in rapid loading the inertia of the matter will cause stress waves to travel in the specimen so that uniform strain throughout the specimen cannot be obtained. For this reason P’ is a hypothetical quantity. A rational way to deduce T(e) from a stress-strain experiment is to apply equation (5) to a loading-unloading experiment at constant rate, then mathematically invert the operator to compute Fe’ (i.e. experimentally determine T(t), G(t) and compute p’). To see what can be obtained by attempting a step loading anyway, without regard to its true meaning, a series of ‘high speed’ stretches and

releases of varying magnitude were imposed on the papillary muscle. Each quick stretch was followed by a quick release of the same magnitude so that the muscle is unloaded to its reference dimensions (Lrer and d,,). Muscle relaxed about 10 set following the stretch before it was released. Rise time for these stretches varied from under 1 to 10 msec depending upon the magnitude of stretch. Results of such a ‘quick stretch,’ ‘quick release’ test are shown in Fig. 9. Force-extension curve obtained at the same temperature (20°C) and at an uniform rate of loading and unloading is also shown for comparison. Figure 9 shows that the differences between the two sets of curves is considerable. If the quick stretch results are taken as the elastic response then the difference can be interpreted as the effect of finite strain rate. Since the relaxation function G(t) is a monotonically decreasing function, stress response to straining-at a finite rate is expected to be lower than the elastic response. That the muscle response in loading and unloading is considerably different even under slow and uniform rates of stretch and release has been well documented (Fung, 1%7)-also see Fig. 10. It is of interest here to recall a salient point reported by Fung in his stress-strain studies of rabbit mesentery. In stress-strain tests performed at relatively slow rates Fung reported that when mesentery was stretched to an intermediate stress level and then subjected to a ‘high Speed,’ small amplitude perturbation about the intermediate position, small hysteresis loops were seen. The curves representing the small loops differed sharply from those of the larger hysteresis loop and had greater slope than those of the larger loop. It appears, therefore, that mesentery responds with a greater stiffness for transient disturbances of high speed. Similar behavior can be expected in the papillary muscle subjected to quick stretches and releases. The stiffer load-extension curve of the papillary muscle shown in Fig. 9 agrees with this observation.

MECHANICAL

PROPERTIES

OF THE HEART MUSCLE

Extension,

Fig. 9. The elastic

605

mm

response T”‘(A,0).

of elongation and the bottom trace, that of muscle force-both loading and unloading are shown. It is apparent from the figure that loading and unloading follow different time rates consequently giving rise to the hysteresis loops on a stress-strain diagram. Hysteresis Overall force loops were directly recorded using a x-y plotresolution: 30 mg Maximum ter for stretch rates up to 5 Hz. For higher strain: 30 per cent rates oscilloscope pictures of force-extension Rates of traces were taken. stretch: 0.01-20 Hz in 1-2-5-8 sequence All the hysteresis loops plotted showed inTemperature ranges: 5, 10, 15, 20, 25, 30 and 37°C sensitivity to rates of stretch and temperature. pH: 74. The area of the loop is proportional to the After preconditioning the specimen by a few energy dissipated in the loading-unloading the damping characteristic of cycles of repeated loading and unloading at process-thus 1 Hz, reference measurements of length and the muscle is found to be insensitive to the diameter were taken. The specimen was then ‘rate process.’ Hysteresis loop areas were measured with a planimeter and are plotted subjected to the test at uniform stretch rates ranging from 0.01 to 20Hz in l-2-5-8 se- against rates of stretch in Fig. 11. For 3 dequence. The test was repeated for 7 tem- cades of speed changes shown, the dissipated peratures. During each set of rates, pH and energy has hardly doubled. The rate insensitivity property of soft biological tissues temperature of the chemical environment (muscle, skin, mesentery) has been made the were maintained constant. A typical loadstresscentral point by Fung in postulating a noncurve from which extension strain diagram is deduced is shown in linear viscoelastic model for soft tissues. Fung (1%7) advocated the use of an expoFig. 10. The top trace shows the time history STRESS-STRAIN TEST RESULTS

Force sensor: Sensitivity: Recording:

Statham green cell 221 mV/g Fast rates (l-50 Hz )--magnetic tape; slow rates-Hewlett Pac7100 BM strip-chart kard recorder.

606

JOHN G. PINTO and Y. C. FUNG

. . 0.06.

Fig. 11.Effect of stretching rates on dissipated energy.

nential function to describe the stress-strain from experimental results is beset by inaccuracies encountered in the reduction of data behavior of biological tissues. Figure 12 shows the validity of the exponential law for papil- near the origin of the load-elongation plot. The lary muscle for strain up to 30 per cent used in stress-strain relationship can be expressed in the present study. In the figure, experimental terms of 4, fi and a known point (a*, A*) on points in loading and unloading are shown. the experimental stress-strain curve-as folThe line drawn through the set of points lows: Write the regression line shown in Fig. (loading) is the least squares fit. The vertical 12 as intercept on the line on the right hand side of da the figure shows the root mean square value of -= &(a+fi). dh the deviation of experimental points from the regression line when every experimental point is treated with equal weight. (see definition of Hence error in Table 1). The slope of the line is denoted by bi, which is a dimensionless *+&lp C number. The intercept on the vertical (daldh) axis, is denoted by &/.? and has the units of stress-g/mm’; and represents the extrapowhere C is the constant of integration. If u = U* when h = A*, then lated Young’s modulus of the muscle at the reference state. Table 1 is a catalogue of 4 and fi (T= (@*+ fi) e+**, - fi* values of the regression lines for the rates and (8) temperatures studied-both in loading and unloading obtained by least squares method. The This procedure is valid only in the range in unloading curve has a higher slope &, and which the regression line (6) can be trusted. Table 1 shows again the insensitivity of the sometimes shows a negative intercept (- ai& An accurate determination of the factor b, exponent & with respect to the strain rates and

Temp: Strain:

15OC, pH: 7.4, Rate: 30%, Lref: 3.66mm,

Top Trace: Bottom

Trace :

Extension,

I Hz, dref:

Force,

lOOmv/div.

Time,

50 msec/div.

Fig. 10. Force-extension curves of rabbit papikry under uniform rate of stretch and release.

(Facing p. 606)

1.38mm

20 mv/div.

muscle

(0) Force leads displacement in unloading. Freq.: 9OHt., DC Stmh 15%. Dynamic Strain: 3%, L,t: 4.16mm, d,f: l.l6mm, Temp.: 3VC, pHI 14

(b) Lissajous figure representing alternating extension (abscissa) versus force hrdtnate) at 90Hr. Fig. 13. Vibration test on rabbit papillary.

MECHANICAL

0

L 0, IO

I 020

I 0.30

PROPERTIES

I O-40

I 0.50

OF THE HEART

I 0 60

Eulerian stress

I 070

within the range of stretches and temperatures (5-37°C)

VIBRATION TEST RESULTS Force sensor:

Displacement sensor: Recording:

Stretch levels: Dynamic strain: Temperature: pH:

Bentley proximity sensor probe; sensitivity, 213 mV/g; frequency response flat to lOOHz, force resolution 30 mg Linear variable differential transformer resolution (LVDT), 0402 mm Above 1Hz, Tektronix dual beam oscilloscope, below 1 Hz, Hewlett Packard 7007B strip chart recorder A = 1.05, 1.15 and 1.30 1, 2 and 5 per cent of Lrcr 5, 10, 15, 25, 30 and 37°C 74.

Vibration tests were performed on the rabbit papillary muscle for pH and temperatures shown above. After preconditioning the specimen (approximately 50 cycles at 1 Hz) it was subjected to sinusoidal strains of 1,2 and 5 per cent of reference length at three levels of stretch (A= l-05, 1.15 and h = 1.30). Frequency of vibration was varied from 0.01 to 100 Hz. Force amplitude was measured from

I 0.90

I I.00

607

I

IIO

I

I.20

fl. g/mm2

Fig. 12. The exponential

the temperatures (30 per cent) studied.

L 0.80

MUSCLE

law.

the records traced on a strip chart recorder for frequencies up to 1 Hz. For frequencies above 1 Hz, amplitude of force oscillations were directly read off the oscilloscope screen. Frequency of vibration was limited to 100 Hz range because the force transducer used is effective only in that range. A typical record from a vibrational test is shown in Fig. 13. In the record shown, the amplitude of the two traces (displacement and force) are arbitrarily adjusted using the sensitivity control of the display channel and are superimposed to show the phase relationship between the imposed displacement and the muscle force response (see Fig. 13). In the ascending portion of the trace, the force lags behind the displacement by a small phase angle. (This phase lag in the ascending leg is not visible on the record shown)--Measurement of this lag angle in the ascending portion was difficult and as such has not been quantified in the present study. In the descending portion the force trace leads the displacement trace in the entire range of frequencies studied (0~01-100 Hz). After (1%8) has reported phase leading characteristics of the muscle in a

JOHN

608

G. PINTO

and Y. C. FUNG

Table 1. Value of & and b in the exponential law for the stress-strain behaviour of rabbit papillary muscle at various rates of stretch and temperature.

Specimen:

Rabbit papillary

error = da yi = dependent variable a

L =r: 366 mm d : 1.38 mm Gx stretch: 30 per cent pH: U

a g b

estimated by the regression line g

7.4

= Experimental value of

dependent variable m = Number of experimental points

Slope of regression line on

vs (CT)plot The intercept of the regression line on 0 axis, g/mm2

k = 1 for first degree polynomial (straight line) fit A* = 1.25

Loading Temp. (“0

Rate (I-W

5

0.01 0.02 0.05 O-08 0.10 0.20 050 0.80 1.00 ;:g

10

15

lO@l 0.01 0.02 0.05 0.08 0.10 0.20 0.50 0.80 1.00 2.00 5.00 lO*OO 0.01 0.02 0.05 0.08 0.10 0.20 0.50 0.80 1.00 2.00 5.00 10.00

& f error

s

10.48?0.18 11.38kO.22 10.98 + O-24

0.85 0.75 0.74

12.36kO.27 12.88~0.43 12.93 20.39 13.19kO.35 12*18+0.34 13.2OkO.46 8.11 t3.68

Unloading u* (g/mm’)

(+* (g/mm’)

ai *error

a

0.98 0.97 1.05

19.78& 1.07 19,862 1.09 18.25 +0*91

- o-40 - 0.53 - 0.49

0.76 0.76 0.83

0.55 0.34 0.36 0.34 0.79 0.46 1.65

1.01 0.86 1.32 1.32 1.27 1.39 1.70

19.23 50.78 18.66kO.69 18.862 1.10 19+0+1.36 18.23 f 1.15 26.39k4.71 15.2Ok6.36

- 0.14 - 0.30 - 0.36 - 066 - 0.27 - 2.01 -0.22

0.82 o-71 1.07 1.09 1.02 1.15 1.14

9.2OkO.20 9.47kO.19 9.41?0+16 990*0.19 10.16kO.34 9,74+0.14 11.82kO.12 12.49-cO.23 11.9220.13 12.11*0.14 11.88kO.14

0.62 0.53 0.59 0.49 0.38 0.46 0.33 0.19 0.33 0.21 0.31

0.56 0.59 0.61 0.63 064 066 0.54 0.54 0.55 0.54 060

13.6520.70 14.21 kO.63 14.8720~83 13.91?0*67 14.89kO.86 12*88+0.35 18.05*0.59 17.43 +0&l 17.84kO.43 17.86kO.35 18.08kO.43

- 0.16 - 0.28 - 0.28 -0.17 - 0.41 0.08 - 0.15 - 0.04 - 0.13 - 0.10 - 0.09

0.41 0.43 0.45 0.46 0.47 0.50 044 044 044 0.43 0.50

11.79kO.15 12~11_co-20 12.56kO.26 12.7920.21 12.79?0*41 11.84?0.17 11.74kO.14 12.3620.13 12.41 kO.27 12-3610.31 12.15kO.27 11.88kO.15

0.69 0.72 0.59 0.58 0.53 0.51 0.63 0.50 040 0.58 0.55 0.51

1.10 1.15 1.22 1.24 1.26 0.91 0.95 099 0.95 1.01 1.12 -

17.7OkO.73 18.01 kO.79 19.02 1.08 18.01 kO.74 18.75 * 1.03 16.82kO.69 16.10 kO.68 17.91 kO.87 17.19kO.89 19.73 &O+O 19.48? 1.27 19.20*0.%

-

0.97 1.02 1.10 1.13 1.13 0.75 0.78 0.80 0.80 0.78 090 -

0.17 0.19 0.30 0.09 0.23 0.12 0.06 - 0.19 -0-12 - 0.24 - 0.58 - 0.54

MECHANICAL

PROPERTIES

OF THE HEART

609

MUSCLE

Table 1. (contd.) Unloading

Loading Temp. (“C)

20

25

30

30

37

Rate (Hz) O-01 0.02 0.05 0.08 0.10 0.20 0.50 0.80 1.00 2.00 5.00 lOa_l 0.01 0.02 0.05 0.08 0.10 0.20 0.50 0.80 I.00 2.00 5.00 10.00 0.01 0.02 0.05 0.08 0.10 0.20 0.50 0.80 1.oo 2xKl 5.00 10@0 0.01 0.02 0.05 0.08 0.10 0.20 0.50 0.80

1.oo 2.00 5.00 10.00

cr* (g/mm’)

& -+error

B

11~80~0~08 11.7OkO.12 12.29-cO.20 12.58kO.19 12.78kO.14 12.35kO.15 12.31-t-0.19 11.32kO.19 11.82kO.20 12.77kO.43 11.94t0.23

O-68 064 0.47 0.50 0.48 0.41 046 0.65 0.49 0.48 0.42

0.99

9.9520.14 10.2620.27 10.39-cO.29 10.77kO.14 10.88+0.18 11.42kO.16 11.7OkO.27 12.73 20.25 12.08+0.31 12.2OkO.39 12.03 eO.36 12.72kO.24 9.45kO.13 9.57kO.11 10.27kO.22 10.78kO.15 10.94+0*19 10.96kO.23 12.25kO.17 13.03 20.27 11.59-to.33 13.52-1-0.30 12.72kO.23 -

0.54 0.47 0.39 0.43 0.45 0.41 0.39 0.26 0.20 0.13 0.29 0.13 0.59 0.52 0.52 0.41 0.29 0.32 0.41 0.25 0.55 0.17 0.13

0.58 0.60 0.63 0.63 0.63 0.66 0.68 0.64 0.72 0.78 0.80

1146+0.11 12.33kO.22 12.56t0.14 12.7OkO.20 12.7320.13 13.3720.14 12.1850.37 12.94kO.14 13.12kO.16 13.7220.17 14~00~0~30 13.52iO.14

0.58 0.50 0.54 0.60 0.52 044 0.55 0.49 0.24 0.43 0.20 0.17

0.74 0.77 0.81 0.83 0.84 0.87 066 0.66 0.66 0.70 0.75

limited band of frequencies; she suggests that this phase leading characteristics is due to an ‘energy producing’ process in the muscle. However, on the basis of stress-strain studies of the papillary muscle in loading and unload-

1.05 1.10 1.12 1.12 0.86 0.88 0.89 0.93 0.93 1%

0.50 0.53 0.53 0.55 0.56 0.58 0.74 0.74 0.79 0.80 0.83

& *error

B

u* (g/mm’)

17.06kO.60 17.65 20.88 18.41 kO.93 17.45 20.63 18.75 zkO.93 16.98-cO64 17.24~066 16.55 to.56 17.58r0.76 17-2920.80 17.65 kO.73

-

O-02 0.21 0.27 0.03 0.24 0.02 0.06 0.07 - 0.23 -0.12 - 0.13

0.88 0.93 0.98 1.02 1.04 0.72 0.72 0,71 0,77 0.79 0.89

14.68kO.51 14.501tro.53 14.81 to.53 15.56-eO60 15.49+060 15.2450.45 15.74eo.54 16.4220.45 16.10?044 16.59kO.62 16.84-cO.69 16.52 kO.63 14.32TO.44 144Or0.43 14.34-tO.46 15.11 to.50 1490+0~45 14+9t0.50 16.5750.53 1444t0,24 16.9850.54 15.7220.29 16.52 20.52 -

0.08 0.06 0.01 - 0.01 0.02 0.12 0.12 0.08 0.00 - 0.26 - 0.24 -0.11 - 0,08 0.08 O,lO 0.02 O-00 - 0.07 0.15 0.36 0.05 0.19 0.01 -

0.45 0.48 0.51 0.51 0.52 0.57 0.56 0.60 0.60 0.65 0.69

17.08-r-0.45 17.47-0.62 16.95+0&l 17.27eO.49 17.08kO.39 17.8420.38 16.00t0.57 17.47t0.39 16.99~0.36 18.4320.53 17.3420.45 16.98t0.33

0.01 0.06 0.13 0.18 0.25 0.24 0.34 0.31 0.29 0.12 0.02 0.05

0.37 0.39 0.42 0.39 o-39 0.47 0.62 0.63 0.62 0.67 0.68 066 0.69 0.74 0.77 0.78 0.84 0.54 0.56 0.55 0.61 0.63

ing it is clear that the ‘force lead’ characteristics is due to the ‘unloading’ of a highly nonlinear ‘spring.’ Apter’s observation of ‘energy production’ during a totally passive (unstimulated) vibration test may point

610

JOHN G. PINTO and Y. C. FLING

to the fact that the chemical environments used in the two studies (Apter’s vs the present one) are responsible for the conflicting observations. [Apter’s chemical environment might have been conducive to self stimulation when the muscle is strained at appropriate frequency]. This point therefore needs further scrutiny. A typical frequency response of the papillary muscle is shown in Fig. 14. Similar behavior is observed at other stretch ratios, vibrational amplitudes, and temperatures adopted in this study. Figure 15 shows the frequency response of the muscle for the range of temperature shown. The ordinate-dynamic stiffness-has been normalized with respect to the stiffness at 0.01 Hz. A point of particular interest here is that in covering a wide range of frequencies (4 decades) the dynamic stiffness has at best doubled. This remarkable insensitivity of the muscle to frequency of vibration once again points to the non-linear viscoelastic aspect of the papillary muscle. For a sinusoidal oscillations of small amplitude (2 per cent stretch) about an initial

61

I

lo-z

16’

Frequency,

Fig.

14.

Frequency

Fig. 15. Temperature

Hz

effect on the frequency

lo’

IO’

Hz

response of rabbit papillary muscle

I .6 -

Frequency.

IO0

response.

MECHANICAL

PROPERTIES

stretch of 10 or 15 per cent, the muscle exhibits a sinusoidal force response (linear characteristic). However, when amplitudes of the order of 5 per cent of reference length were superposed on initial stretches in the range of 20-30 per cent, responses shown in Fig. 16 resulted. Here for harmonic oscillations at AA = 5 per cent at h = l-30, force response became anharmonic. This is a typical example of the quasi-linear behavior of soft tissues described by Fung (1972). CREEP

TESTS

Creep (deformation with time under constant load) of the cardiac muscle over short durations of time has relevance to the intact heart muscle behavior (such as that during isovolumetric period) and is of particular importance in hypertrophied heart. Before the electromechanical muscle testing device was put into operation, some onedimensional creep tests were performed on rabbit papillary muscle using the test apparatus of Yin and Fung (1971). Following mounting of the specimen in the apparatus, it was preconditioned by subjecting it to four or 5 creep tests of 10 min duration each. Specimen was unloaded at the end of 10 min and allowed to ‘rest’ for 5 min before loading it again. Adjustments occuring in the

0.07 Hz

I

OF THE

HEART

MUSCLE

specimen due to creep-preconditioning are shown in Fig. 4. Within 4 or 5 ‘trials’ the specimen showed fairly repeatable performance. Reference measurements of length and diameter were then made, and long-term (1000 min) creep test was undertaken. For all creep tests, a load of 4.5 g was used, pH of the specimen bath was maintained at 7.4, and temperature of the bath was maintained at test temperature (? O.S’C) by a water jacket system. A typical creep curve of the rabbit papillary is shown in Fig. 17. In the figure, the ordinate is the strain (extension divided by reference length) at time t expressed as a percentage. Temperature effect on creep behavior was studied by subjecting some papillary specimen to a constant load (4.5 g) at different temperatures. Results are shown in Fig. 18. owing to variations in cross-sectional areas, the specimens experienced different stresses. The stress-levels are indicated in the figure. Figures 17 and 18 show that for a given stress and temperature creep is essentially a linear function of log time for the first 10 min. Beyond 10 min it increases rapidly with log t. In long duration tests such as those presented here, possible degradation of the specimen is a further complication and it is difficult to ascertain changes occuring in the specimen with time as those due to deterioration or

d

O.O9Hz

Time cotwse of the extenson h is harmonic whtle the corraspondmg the stress T ts asharmonic.

time

course of

Fig. 16. The quasi-linear

611

stress-strain

history relationship.

0.91mm

612

JOHN G. PINTO and Y. C. FUNG 26

1

2624 22-

0,0.01

I

I

I

I

0.1

I.0

IO .o

1000

Time,

1000~0

min

Fig. 17. Creep characteristics of rabbit papillary muscle.

otherwise. In a few cases electrical stimulation was tried and it did not elicit any active tension response. We conclude that the specimen had deteriorated. Short-term creep testing is planned for the near future. CONCLUSIONS ON THE PASSIVE BEHAVIOR OF THE PAPILLARY MUSCLE The following conclusions can be drawn

from the study on the passive behavior of the rabbit papillary muscle reported here: (a) Relaxation behavior (i) The reduced relaxation function G(t) is independent of the stretch A for strains up to 30 per cent of muscle length (Fig. 6). (ii) For time periods comparable with the heart beat (1 set) the function G(t) is independent of temperature in the temperature range of 5-37°C (Fig. 8). validate observations above (iii) The Fung’s hypothesis (1972) that the relaxation function K(h, 8, t) can be written in the separated form, G(t) T”‘(A, O), (see equation 4). This permits the application of the theory of

linear viscoelasticity muscle.

to the nonlinear papillary

(b) Stress-strain behavior in loading and unloading at a constant rate (i) An exponential law (Fung, 1%7) can be adopted to describe the stress-strain relation in either loading or unloading of the papillary muscle for strains up to 30 per cent of initial muscle length and in the temperature range 5-37°C. (ii) The exponent & (equation 6) is almost independent of the rate of uniform loading and unloading in the range of rates studied (0.01-20 Hz). (iii) The exponent & is also independent of temperature (Table 1). (iv) For rates and temperatures studied, the energy dissipated by the papillary muscle in cyclic loading and unloading is insensitive to rates and temperatures (Fig. 11). (c) Behavior in harmonic vibration (displacement) (i) For frequencies of vibration in the range

MECHANICAL

PROPERTIES

OF THE HEART

MUSCLE

613

26 .spedma” 24

p” hod

Rabbit Fvpmary 7.4 4.5 gm

22

Time,

Fig. 18. Temperature

and stress dependence

(0.01-100 Hz) the dynamic stiffness is insensitive to frequency (Fig. 14). (ii) The force leads the displacement in the unloading leg of the oscillation in the entire range of frequencies studied here. In the loading leg the force lags the displacement by a small amount. (iii) When harmonic displacements of 4-5 per cent of initial muscle lengths are superposed on a stretched muscle (25-30 per cent strain), the force response is anharmonic (Fig. 16). This demonstrates the quasi-linear behavior of the muscle for large strains. (d) Creep The cardiac muscle under a constant load.

creeps

considerably

CRITIQUE

OF THE PRESENT WORK ON PASSIVE PAPIL.LARY MUSCLE In the study presented here, a given

min

(i) test (defined in terms of type of test, temperature, pH, stretch ratio, etc.) was performed on a single, freshly excised rabbit papillary muscle. The tests were not repeated on several specimens to study the statistical aspects of the

of creep.

problem. To obtain meaningful statistical correlation, the sample size must be increased. An automatic digital data collection and data processing device is being installed in our laboratory to improve this aspect. (ii) In view of the small aspect ratio (length to diameter ratio), the experimental data is liable to be affected by the end conditions (knots and hooks). (iii) The deduction of the so-called elastic response I”“(& f3) requires a constitutive equation and an accurate relaxation function G(t). The presentation of the constitutive equation and the elastic response is reserved for a separate article. Acknowledgements-This work is supported by the National Science Foundation Grant No. GK 32972 X and by the U.S. PHS NIH Grant HE 12494 through the National Heart and Lung Institute. REFERENCES Abbot, B. C. and Lowy, J. (1957) Stress relaxation in muscle. Proc. R. Sot., Lomi Ser. B146, 281-288. Abbott, B. D. and Mommaerts, W. F. H. M. (1959) A study of inotropic mechanisms in the papillary muscle preparation.

614

JOHN G. PINTO and Y. C. FUNG

Apter, J. T. and Hassan, N. (1968) A test of tranplantability of animal hearts. JAMA 24I6(13), 2881-2882. Bloom, W. and Fawcett, D. W. (1%2) A Textbook of Histologv. -__ 9th Edn. Saunders. Philadelohia. Brady, Allan J. (1%5) Time and displacement dependence of cardiac contractility: problems in defining the active state and force velocity relations. Federation Proceedings 24, 1410-1420. July-December. Brady, Allan J. (1%7) The three element model of muscle mechanics: its applicability to cardiac muscle. Physiologist 75-86. Buchthal, F. and Kaiser, E. (1951) The rheology of the cross striated muscle fibre with particular reference to isotonic conditions. Copenhagen: Det Kongelige Danske Videnskemes Selskab. Dan. Biol. Medd. 21(7), 318. Calcote, L. R. (1%8) introduction to Continuum Mechanics. Van Nostrand. Edman, K. A. P. and Nilsson, E. (1968) The mechanical parameters of myocardial contraction studied at a constant length of the contractile element. Acta Physiol. Stand. 72, 205-219. Fung, Y. C. (1965) Foundations of Solid Mechanics. Prentice-Hall, New Jersey. Fung, Y. C. (1%7) Elasticity of soft tissues in simple elongation. Am. J. Physiol. 213, 1532-1544. Fung, Y. C. (1970) Mathematical representation of the mechanical properties of the heart muscle. J. Biomechanics 3, 381-404. Fung, Y. C. (1971) Comparison of different models of the heart muscle. J. Biomechanics 4, 289-297. Fung, Y. C. (1972) Stress-strain history relations of soft tissues in simple elongation. In Biomechanics: Its Foundations and Objectives, (Edited by Fung, Y. C., Perone, N. and Anliker, M.) Chap. 7, pp. 181-208. Prentice-Hall, New Jersey. Hefner, L. L. and Bowen, T. E., Jr. (1967) Elastic components of cat papillary muscle. Am. J. Physiol. 212, 1221-1227. Hill, A. V. (1950) The series elastic component of muscle. Froc. R. Sot. Lond. Ser. B. 137, 272-280. Hoffman, B. F., Bassett, A. L. and Bartlestone, H. J. (1%8) Some mechanical properties of isolated mammalian cardiac muscle. Circ. Res. 23, 291-312. Huxley, H. E. (1969) The mechanism of muscular contraction. Science 164, 13561361. Noyes, D. (1967) Muscle balance with electrical to mechanical loading transducer. J. appl. Physiol. 22, 177. Pinto, J. G. (1972) Mechanical properties of the papillary muscle in the passive and active state. Ph.D. Dissertation. San Diego: University of California. Pinto, J. G. and Fung Y. C. (1973) A dynamic testing device for the Active and Passive Mechanical Properties of the Heart Muscle. Presented at The 4th Annual Biomedical Eng. Sot. Meeting, 30 Jan, 1973. Sonnenblick, E. H. (1962) Force-velocity-relations in mammalian heart muscle. Am. .Z.Physiol. 202, 931. Sonnenblick, E. H. (1%5) Determinants of active state in heart muscle: force, velocity, instantaneous muscle length, time. Federation Proc. 24, 139f%1409. Yin, F. C. P. and Fung, Y. C. (1971) Mechanical properties of isolated mammalian ureteral segments. Am. Z. Physiol. 221 (5) 1484-1493.

APPENDIX Some details of the testing equipment The thermal environment of the test specimen is carefully controlled by a double bath. The Kreb solution flows from a reservoir into a cup where it is bubbled with a O&O, mixture. The temperature in the cup is controlled by circulating water at a desired temperature in a glass coil immersed in the cup. The Kreb solution then passes through an additional heat exchanger located in the water jacket and flows into the inner tank of the specimen bath (see Fig. 1). Its temperature is further maintained within close limits by water circulating through the outer tank. A suction hose, connected near the top of a standpipe communicating with the inner tank, maintains the level of the Kreb’s solution in the bath. O,CO, bubbling through the solution is done outside the specimen bath to avoid possible disturbances to the specimen. The arrangement provides for continuous circulation of fresh Kreb’s solution at a rate of about 50 ml/min with a minimum disturbance to the specimen. The PITRAN transducer is sensitive to mechanical movement caused by pressure or force and is capable of producing large signal voltages depending upon the model, typically in the range of + 0.25-k 1 for a f 1 pin. displacement of the diaphragm. It is a silicon planar N-P-N transistor that has its emitter-base junction mechanically coupled to a diaphragm. A point force applied to the diaphragm produces a large reversible change in the current gain of the transistor (anisotropic stress effect in semiconductors) so that the output is modulated by the mechanical variable. The details of the sensor, the transducer construction, transfer characteristics and other pertinent data are shown in Fig. 19. A servo controller continuously senses the displacement and force, compares them against reference values, determines the errors, and actuates the linear motor. The characteristic time of the controller is short relative to that of the physical process; and the system is stable.

c’

I

I

I

!

I

I

I

N-P-NTranr~rtor Diamond Dmphraqm STANDARD HOOK-UP CIRCUIT

PITRANSENSOR

f

P

; E

IO-

a

-

f F h

-

Luute Burhmg A, Holder

o5 _

PT.22 %nrar FORCE TRANSDUCER DETAILS

FORCE TRANSDUCER

Sensor PITRAN PI- 22 -j Senrltwty 150 MVfgm Tronrducer wt

I664 9m

,

Hook welqht 12 mgm 0

0

I I2

I

I

I

I

I

I

3

4

5

6

7

8

WEIGHT tgm

1

Fig. 19. The Pitran Sensor and the force transducer.

3

MECHANICAL

PROPERTIES

CANCELLATION OF INERTIA In view of the requirement of high frequency response, a duration of 3 msec is chosen as the upper limit to attain a new steady state following a step change in the controlled variable. Accordingly, a rise time of 700-800 psec to achieve 100 per cent of step change with a maximum overshoot of 10 per cent is considered acceptable for papillary muscle tests. For active tests of the muscle, the speed of the linear motor (200 mm/set) far exceeds any contractile velocity reported for papillary muscle. Brady (1%.5); Edman and Nilsson (1968); Sonnenblick (1%2, 1%5), and other investigators report a contractile velcoity in the range of l-20 mmlsec. In the conventional isometric-isotonic changeover method of determining contractile velocity using pivoted lever system, the muscle has to accelerate not only the afterload, but also the inertia of the lever system which is usually quite difficult to minimize. (Lever systems having an effective weight of 60 mg to over 500 mg have been reported in the literature, see Hefner and Bowen 1%7). In the present design the inertia is counteracted by the servo system. (Pinto and Fung, 1973). When the servo system operates in a chosen mode, either a force level or a displacement is chosen and held constant, the servo controller actuates the linear motor to compfy with the command. OPERATION OF THE SYSTEM Figure 20 is the block diagram of the servo system. When the switch is in the lower position, the system operates in displacement mode. The operation is best described by an example such as a quick release test shown in Fig. 21. With LVDT core positioned approximately in its central position the servo is switched on. The reference voltage E, is adjusted so that the error voltage l2 is zero thereby setting the entire system at a steady state. In this position the spindle of the vibrator will be automatically locked. The specimen is then mounted between the hooks (Fig. 1). Starting from an initial length Lo, the specimen is passively stretched (preloaded) to a new length L, (Fig. 21). The amount of passive stretch and the corresponding BACK

OF THE HEART

TIME

IN POSITION AA:

SWITCH

IN POSITION BB : FORCE

passive load are read off the dial gauge and the force transducer respectively. Relaxation of the specimen takes place at length L, as shown by the force curve. At time t, the muscle is stimulated. The spindle being locked, the muscle contracts isometrically. At time tz the reference voltage E., is suddenly changed using a programming device. Corresponding to the new reference voltage an error lZ (Ed-E,) is produced at the comparator. The error voltage is amplified and fed through a compensating network which corrects the phase of the feedback signal. The feedback signal then actuates the power amplifier which in turn actuates the linear motor to a new position. This new position of the spindle corresponds to a length L2 of the muscle. At the quick change in length, an abrupt change in force occurs. At time t, the reference voltage is so changed that the spindle of the vibrator moves back to its original position. After a refraction period of the muscle. it is stimulated again and the process can be repeated. In this way the series elasticity data are generated.

emf

DISPLACEMENT

-

Fig. 21. A typical quick release test.

LVDT

SWITCH

615

MUSCLE

MODE

MODE

Fig. 20. The block diagram of the servo-system

CIRCUIT

616

JOHN G. PINTO and Y. C. FWNG

Operation of the system in a force mode is similar. To convert the operation from the displacement mode to force mode, a switching has to be performed at the comparator stage, i.e. the force transducer signal has to be

fed-in for comparison instead of the LVDT signal. The switching operation is performed by an oscillator circuit triggered by the programing unit at a desired instant in time.