AMERICAN JOURNAL OF PHYSIOLOGY Vol. 213, No. 6, Ihcember 1967. Printed

in U.S.A.

Series elastic component of mammalian skeletal muscle1 ALAN

S. BAHLER2

Department of Biomedical Baltimore, Maryland

balance nonlinear

technique stress-strain

The Johns Hopkins

University,

series elastic component of the frog sartorius muscle using fast constant ve!ocity releases and has found the maximum extension of the series elastic component to be about 3 ‘% of rest length with maximum isometric tension. The damping of this element is less than 200 dyne/ cm per sec. The second (9) quicklv changes the force across the muscle from full isometric tension to a given isotonic level and measures the instantaneous shortening that occurs. During release there is an instantaneous shortening of the lightly damped series elastic component and negligible shortening of the slower contractile component. This method applied to the frog sartorius muscle yields a series elastic component that stretches up to 4 % of rest length at maximum isometric tension ( 10). The third (6, 7) assumes that during an isometric contraction the contractile component is stretching the series elastic component and thus the time derivative of developed force is

BAHLER, ALAN S. Series elastic component of mammalian skeletal 1967.-A method muscle. Am. J. Physiol. 213(6): 1560-1564. of modifying the Wilkie quick-release technique of determining the compliance of the series elastic component of mammalian muscle is described. This modification eliminates the effect of muscle and lever system mass by adding an additional factor related to the shortening of the contractile component. The compliance of the series elastic component of the rat gracilis anticus muscle varies from 1.1 X lo+ cm/dyne at maximum isometric tetanic tension to 17.6 X lOA cm/dyne at zero tension. The extension of this component was 0.07 rest length at maximum isometric tetanic tension. The damping of the series elastic component was calculated from an energy balance technique to be typically 300 dyne/cm per sec. The results of this study are compared with those obtained from other striated muscles.

method ; energy modified quick-release lightly damped series elastic component; relationship

Engineering,

;

6P

dP d7

=

6L’

dL’ l

6P

-$+G-

T

BEHAVIOR of mammalian skeletal can be explained by postulating the presence of three functionally different components of the muscle (2, 3). This three-component model of muscle consists of a nonlinear elastic element in series with a contractile component both bridged by another nonlinear elastic element. The active element of this model, the contractile component, is a function of length, external load, temperature, and real time. For most parallel-fibered mammalian skeletal muscles, the parallel elastic component can be neglected at lengths less than or equal to rest length, L, (length at which maximum isometric tetanic tension, PO, is devel oped). The characteristics of the series elastic component are commonly determined by three different methods. The f rst (4) has mapped out the force-length diagram of the HE

MECHANICAL

where P is the isometric tension, L’ is the length of the contractile component, and t is the time. If 6P/6t is zero, then

muscle

Received for publication 9 June 1967. 1 This work was supported by Public 5-F3-GM-23, 697-02, 5-Tl -GM-576, and 2 Special Fellow, Public Health Service. of Electrical Engineering and Bioengineering University, Houston, Texas 77001.

Health AM-05524. Present

Service address Laboratory,

dP -dL’

dP - dt

dt l

dL’

Therefore, dP/dL’, the compliance of the series elastic component, is determined from the experimental data (dP/dt and l/dL’/dt) obtained when the muscle is allowed to shorten after an initial period of isometric contraction. This technique has shown the frog sartorius muscle to have a series elastic component extension of from 3 to 5 % of rest length (6) and the cat papillary muscle to have a series elastic component extension of greater than 10 %) of rest length ( 7). The purpose of the present study is to define the series elastic component of a mammalian skeletal muscle, the rat gracilis anticus. The quick release technique has been used since this method is the most applicable with the

Grants : Dept. Rice 1560

MAMMALIAN

SERIES

1561

ELASTIC M

K SE tP

‘: b

SE

‘1

3 bL

FIG. 1. Linearized equivalent model of muscle quick-release method. (Note : since the contractile cannot change its length instantaneously, it has been this approximation.)

for Wilkie’s component neglected in

present muscle preparation and lever system. Rat skeletal muscle shortens rapidly; therefore, the quick release method has been modified to correct for the combined mass of the lever system and the muscle. The damping of the series elastic component was determined by applying the principle of conservation of energy to the quick release. METHODS

Preparution. The experiments were performed on the right gracilis anticus muscle from white male Wistar rats (Carworth Farms, Type CFN), approximately 50 days old, 140-165 g body wt, fed a normal balanced rat diet. The muscles had a mean weight of 60 mg and a mean rest length of 2.7 cm (fiber length).

The gracilis anticus, a thin parallel-fibered muscle which takes its origin from the posterior half of the pubic symphysis and is inserted into the upper part of the crest and medial border of the tibia, was surgically removed from anesthetized rats (45 mg/kg sodium pentobarbital ip). After removal, the muscle, with a portion of the tibia and pubis, was placed immediately in a 1,500 ml bath (17.5 C) containing oxygenated (95 % OL, 5 % COO) bicarbonate-buffered Krebs-Ringer solution pH 7.3 (NaCl, 116.8 InM; NaHCO,, 28 mM; CaClp, 2.5 mM; MgS04, 3.1 mM; KCl, 3.5 mM; KHtPO,, 1.2 mM; and glucose, 11.1 mM). The muscle was trimmed and small stainless steel yokes were attached to the pubis and tibia bones by means of “00” noncapillary braided black-silk suture. These yokes were then placed between the lever member and the force transducer. Lever system. The lever system used in this study (equivalent mass 350 mg) consists of an electromechanical torque source, lightweight magnesium lever, velocity and force transducers, control circuit, and low impedance pulse generator. A detailed description of this lever has been presented previously ( 1). The muscle was supramaximally stimulated by two platinum multielectrode assemblies which set up an electric field normal to the long axis of the muscle (current density = 0.08 amp/cm2). Stimulation consisted of a train of 32 2-msec pulses with a pulse separation of 10.5 msec. All records were displayed on a Tek-

PIG. 2. Records showing the effect of quick changes of load (from isometric to a fixed isotonic level). In each frame, a, force record; b, length record. Base lines are given for both. Initial length is 2.8 cm. Force sensitivity is 10 g/major vertical division. Sweep speed is 10 msec/major horizontal division. A: length sensitivity is I mm/major vertical division; AP = 29 g. B: length sensitivity is 0.4 mm/major vertical division; AP = 21.8 g. C. length sensitivity is 0.4 mm/ major vertical division; AP = 15.8 g. D: length sensitivity is 0.2 mm/major vertical division; AP = 6.2 g. Muscle wt = 68 mg; L, = 2.8 cm; P,, = 34 g; bath temperature = 17.7 C.

1562

A. S. BAHLER SION

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tronix RM561A oscilloscope and recorded on Polaroid type 107 film. Experimental details. Isometric experiments were performed at y