Active length-tension relation and the effect of muscle pinnation on fiber lengthening

The active length-tension relation was determined for the left digastric muscle of seven New Zealand White rabbits anesthetized with pentobarbital. Measurements of muscle length and fiber architecture were made from photographs of resting and actively contracting muscle. There was a marked difference between length-tension curves based upon resting as compared to active muscle length. The active length-tension relation had a longer descending limb than ascending limb, whereas the length-tension relation based on passive muscle length tended to be symmetrical around optimum length. On the average, muscle fibers lengthened 0.77 mm for each 1 mm of extension of the muscle belly. Since the rabbit digastric muscle is unipinnate, this suggests that pinnation serves to enhance the range of muscle excursion in this muscle.     

Distributed Representations for Actin-Myosin Interaction in the Oscillatory Contraction of Muscle

In this paper we suggest and test a specific hypothesis relating the attachment-detachment cycle of cross bridges between actin (I) and myosin (A) filaments to the measured length-tension dynamics of active insect fibrillar flight muscle. It is first shown that if local A-filament strain perturbs the rate constants in the cross-bridge cycle appropriately, then exponentially delayed tension changes can follow imposed changes of length; the latter phenomenon is sufficient for the work-producing property of fibrillar muscle, as measured with small-signal forcing of length and at low Ca²⁺ concentration, and possibly for related effects described recently in frog striated muscle. It is not clear a priori that the above explanation of work production by fibrillar muscle will remain tenable when the viscoelastic complexity of the heterogeneous sarcomere is taken into account. However, White's (1967) recent mechanical and electron microscope study of the passive dynamics of glycerinated fibrillar muscle has produced a model of the distributed viscoeleastic structure sufficiently explicit that alternative schemes for cross-bridge force generation in this muscle can now be tested more critically than previously. Therefore, we derive and solve third-order partial-differential equations which relate local interfilament shear forces associated with the perturbed cross-bridge cycles to the over-all length-tension dynamics of an idealized sarcomere. We then show (a) that the starting hypothesis can account approximately for the small-signal dynamics of glycerinated muscle in the work-producing state over two decades of frequency and (b) that the rate constants for cross-bridge formation and breakage, restricted solely by fitting of the model to the mechanical data, determine a cycling rate of cross bridges in the model compatible with recent measurements of ATP hydrolysis rate vs. stretch in this muscle. Finally, the formulation is extended tentatively to the large-signal nonlinear case, and shown to compare favorably with previous suggestions for the origin of the work-producing dynamics of fibrillar flight muscle.     

Response of arterial smooth muscle to length perturbation.

The ability of arterial smooth muscle to generate tension is influenced by muscle length. An unsettled question is whether the length-tension relationship is a simple reflection of the contractile filament overlap, as it is in skeletal muscle. There are several factors that could potentially affect tension generation in arterial smooth muscle; these include stretch-induced myogenic response and length-oscillation-induced disruption of the contractile filament organization. In this study, in which rabbit carotid arterial preparations were used, we found that different length-tension curves could be obtained at different times after a length change. In addition, length oscillation at a frequency of normal pulse rate and with small to moderate oscillation amplitude was found to potentiate tension generation but reduced tension at large amplitudes. The observed response could be attributed to adaptation of the muscle to length change over time and to myogenic potentiation associated with stretching of the muscle.     

A Model for the Transient and Steady-State Mechanical Behavior of Contracting Muscle

A model was developed which can simulate both the transient and steady-state mechanical behavior of contracting skeletal striated muscle. Thick filament cross-bridges undergo cycles of attachment to and detachment from thin filament sites. Cross-bridges can attach only while in the first of two stable states. Force is then generated by a transition to the second state after which detachment can occur. Cross-bridges are assumed to be connected to the thin filaments by an elastic element whose extension or compression influences the rate constants for attachment, detachment, and changes between states. The model was programmed for a digital computer and attempts made to match both the transient and the steady-state responses of the model to that of real muscle in two basic types of experiment: force response to sudden change in length and length response to sudden reduction of load from P_o. Values for rate constants and other parameters were chosen to try to match the model's output to results from real muscles, while at the same time trying to accommodate structural and biochemical information.     

Adaptation to chronic length change in explanted airway smooth muscle.

It has been shown that airway smooth muscle in vitro is able to maintain active force over a large length range by adaptation in the absence of periodic stimulations at 4 degrees C (Wang L, Paré PD, and Seow CY. J Appl Physiol 90: 734-740, 2001). In this study, we show that such adaptation also takes place at body temperature and that long-term adaptation results in irreversible functional change in the muscle that could lead to airway hyperresponsiveness. Rabbit tracheal muscle explants were passively maintained at shortened and in situ length for 3 and 7-8 days in culture media; the length-tension relationship was then examined. The length associated with maximal force generation decreased by 10.5 +/- 3.8% (SE) after 3 days and 37.7 +/- 8.5% after 7 or 8 days of passive shortening. At day 3, the left shift in the length-tension curve due to adaptation at short lengths was reversible by readapting the muscle at a longer length. The shift was, however, not completely reversible after 7 days. The results suggest that long-term adaptation of airway smooth muscle could lead to increased muscle stiffness and force-generating ability at short lengths. Under in vivo condition, this could translate into resistance to stretch-induced relaxation and excessive airway narrowing.     

A Phenomenological Theory of Muscular Contraction: II. Generalized Length Variations

In part I of this series, the theory of irreversible thermodynamics was applied to the sliding filament model to obtain rate equations for a contracting muscle at the in situ length l_o. In this paper we extend the theory to include length variations derived from the sliding filament model of contracting muscle using the work of Gordon, Huxley, and Julian (1). Accepting the validity of Hill's forcevelocity relation (2) at the in situ length, we show that Hill's equation is valid for any length provided that the values of the parameters, a, b, and V_m vary with length as derived herein. The predicted variation with length of the velocity for a lightly loaded isotonic contraction is shown to agree well with that measured by Gordon, Huxley, and Julian (1). Chemical rates are derived as functions of length using parameters that can be obtained experimentally.     

Adjustable passive length-tension curve in rabbit detrusor smooth muscle.

Until the 1990s, the passive and active length-tension (L-T) relationships of smooth muscle were believed to be static, with a single passive force value and a single maximum active force value for each muscle length. However, recent studies have demonstrated that the active L-T relationship in airway smooth muscle is dynamic and adapts to length changes over a period of time. Furthermore, our prior work showed that the passive L-T relationship in rabbit detrusor smooth muscle (DSM) is also dynamic and that in addition to viscoelastic behavior, DSM displays strain-softening behavior characterized by a loss of passive stiffness at shorter lengths following a stretch to a new longer length. This loss of passive stiffness appears to be irreversible when the muscle is not producing active force and during submaximal activation but is reversible on full muscle activation, which indicates that the stiffness component of passive force lost to strain softening is adjustable in DSM. The present study demonstrates that the passive L-T curve for DSM is not static and can shift along the length axis as a function of strain history and activation history. This study also demonstrates that adjustable passive stiffness (APS) can modulate total force (35% increase) for a given muscle length, while active force remains relatively unchanged (4% increase). This finding suggests that the structures responsible for APS act in parallel with the contractile apparatus, and the results are used to further justify the configuration of modeling elements within our previously proposed mechanical model for APS.     

Rises in whole muscle passive tension of mammalian muscle after eccentric contractions at different lengths.

This is a report of experiments carried out on the medial gastrocnemius muscle of the anesthetized cat, investigating the effects of eccentric contractions carried out at different muscle lengths on the passive and active length-tension relationships. In one series of experiments, the motor supply to the muscle was divided into three approximately equal parts; in the other, whole muscles were used. Fifty eccentric contractions were carried out over different regions of the active length-tension curve for each partial or whole muscle. Active and passive length-tension curves were measured before and after the eccentric contractions. When eccentric contractions were carried out at longer lengths, there was a larger shift of the optimum length for active tension in the direction of longer muscle lengths and a larger fall in peak isometric tension. Passive tension was higher immediately after the eccentric contractions, and if the muscle was left undisturbed for 40 min, it increased further to higher values, particularly after contractions at longer lengths. A series of 20 passive stretches of the same speed and amplitude and covering the same length range as the active stretches, reduced the passive tension which redeveloped over a subsequent 40-min period. It is hypothesized that there are two factors influencing the level of passive tension in a muscle after a series of eccentric contractions. One is injury contractures in damaged muscle fibers tending to raise passive tension; the other is the presence of disrupted sarcomeres in series with still-functioning sarcomeres tending to reduce it.     

OBLIQUELY STRIATED MUSCLE : III. Contraction Mechanism of Ascaris Body Muscle

Segments of the obliquely striated body muscle of Ascaris were fixed at minimum body length after treatment with acetylcholine and at maximum body length after treatment with piperazine citrate and then studied by light and electron microscopy. Evidence was found for two mechanisms of length change: sliding of thin filaments with respect to thick filaments such as occurs in cross-striated muscle, and shearing of thick filaments with respect to each other such that the degree of their stagger increases with extension and decreases with shortening. The shearing mechanism could account for great extensibility in this muscle and in nonstriated muscles in general and could underlie other manifestations of "plasticity" as well. In addition, it is suggested that the contractile apparatus is attached to the endomysium in such a way that the sarcomeres can act either in series, as in cross-striated muscle, or individually. Since the sarcomeres are virtually longitudinal in orientation and are almost coextensive with the muscle fiber, it would, therefore, be possible for a single sarcomere contracting independently to develop tension effectively between widely separated points on the fiber surface, thus permitting very efficient maintenance of isometric tension.     

Active contractions of ureteral segments

The first step in the analysis of the biomechanics of any organ is to obtain its constitutive equation. In pursuit of a constitutive equation describing the peristalsis of the ureter, we measured the relationship between the length of the muscle, the velocity of contraction, and the active tension development of isolated ureter segments. The results of length-tension measurements (giving the maximum tension developed in isometric contraction of a ureter segment of specific length) were similar to those obtained by previous investigators and reflected the behavior of length-tension relationship for other smooth muscles. Two aspects of the force-velocity relationship of the ureter were examined: the effect of releasing the ureter at different times after stimulation, and that at different levels of afterload. Measurements were analyzed using the hyperbolic Hill's equation in the form T/T0 = (1-v/v0) (l + cv/v0)-1 where v is the velocity of contraction, v0 is the velocity of contraction when T = 0, T is the tension in the muscle after release, T0 is the tension in the muscle immediately prior to release, and c is the dimensionless constant. The results of force-velocity measurements showed that the so-called "maximum" velocity v0, is the largest if the tension is released at a time of contraction, early in the rise portion of the contraction cycle. Further, if tension is released from an isometric contraction at a fixed time in the rise portion of the contraction cycle, the largest value of v0 is obtained when the muscle length is in the range of 0.85-0.90 Lmax. Interestingly, the in vivo length of the ureter lies also in this range, 0.85-0.90 Lmax.     

The motor units of cat medial gastrocnemius: electrical and mechanical properties as a function of muscle length.

The effects of changing muscle length on the mechanical properties of 89 motor units from adult cat medial gastrocnemius have been studied in eight experiments. Few differences were found between the effects of length on tetanic tension, twitch tension, twitch-tetanus ratio, twitch contraction time, twitch half relaxation time, rate of force development and electrical activity for fast contracting (twitch contraction time less than or equal to 45 msec) and slowly contracting (greater than 45 msec) units. Those differences that did appear did not persist when these two groups were matched by tetanic tension. It is concluded that the biophysical mechanisms responsible for the changes in mechanical and electrical properties with length must be similar for fast and slow twitch units and not related to potential differences in their muscle fiber type. The effects of changing muscle length on the mechanical properties of the eight whole muscles suggest that changes in force output with length are of minor importance during normal movements as the muscle is found to be electrically active over a relatively narrow range of lengths close to the optimum length for tetanus of the whole muscle. The very shortest muscle lengths at which there is only minimal force development are not used in natural movements, while the declining limb of the length tension curve is at muscle lengths beyond the maximum in situ length.     

An intrinsic mechanism for the oscillatory contraction of muscle

A new model based on the theory of dynamical systems is proposed for the intrinsic random or pscudo-random mechanism underlying certain types of muscular tremor. The active length-tension curve of the individual sarcomere, in conjunction with the passive length-tension relation is a map from length to tension with an observed time delay between length change and resulting tension change. The passive length tension relation is assumed to instantaneously relate this tension change back to a change in length. The stability properties of this iterated interval map are investigated by means of computer simulation and computation of the Lyapunov exponent and the bifurcation tree. The resulting analysis is related to experimental tremor data in the literature in terms of period doubling, bifurcation points, and chaotic behavior. The model appears to have its most fruitful application in understanding the insect type and isometric mammalian types of tremor.     

Length-tension relationships are altered in regenerating muscles of the rat after bupivacaine injection.

Intramuscular injection of bupivacaine causes complete degeneration of fibers in extensor digitorum longus (EDL) muscles of rats, followed by complete regeneration within 60 days. Previous studies have shown that regenerated EDL muscles are protected from contraction-induced injury 60 days after bupivacaine injection. It is possible that these regenerated muscles have altered length-tension relations because of fiber remodeling. We tested the hypothesis that length-tension relations are different in bupivacaine-injected and noninjected control muscles. EDL and soleus muscles of the right hindlimb of deeply anesthetized rats were injected with bupivacaine and then allowed to recover for 7, 14, 21, or 60 days (7D, 14D, 21D, 60D), and isometric contractile properties were assessed. Muscles of the contralateral limb were not injected and served as control. EDL muscles recovered from bupivacaine injection more rapidly than soleus muscles, with mass restored to control levels at 21D, and isometric tetanic force (P(o)) restored to control at 60D. In contrast, mass and P(o) of injected soleus muscles was not restored to control even at 60D. In 7D EDL muscles, length-tension curves were shifted leftward compared with control, but in 21D and 60D EDL muscles length-tension curves were right shifted significantly (treatment x muscle length: P < 0.001). Although no clear shift in the position of the length-tension curve was observed in regenerating soleus muscles, force production was enhanced on the descending limb of the curve in 60D soleus muscles (treatment x relative muscle length: P < 0.01). The rightward shift in the length-tension curve of EDL muscles 60 days after bupivacaine injection is likely to contribute to the mechanism for their previously observed protection from contraction-induced injury.     

Correlation between active and passive isometric force and intramuscular pressure in the isolated rabbit tibialis anterior muscle

The purpose of this study was to quantify the relationship between intramuscular pressure (IMP) and muscle force during isometric muscle contraction of the rabbit tibialis anterior (TA) absent the effect of either bone or fascia. To quantify this relationship, length-tension experiments were performed on the isolated TA of the New Zealand White rabbit (mass=2.5+/-0.5kg, n=12). The knee was fixed in a custom jig, the distal tendon of the TA was attached to a servomotor, and a 360 microm fiber optic pressure transducer was inserted into the TA. The peroneal nerve was stimulated to define optimal length (L(0)). The length-tension curve was created using 40Hz isometric contractions with 2-min rest intervals between each contraction. Measurements began at L(0)-50%L(f) and progressed to L(0)+50%L(f), changing the length-tension in 5% L(f) increments after each contraction. Qualitatively, the length-tension curve for isometric contractions was mimicked by the length-pressure curve for both active and passive conditions. Linear regression was performed individually for each animal for the ascending and descending limb of the length-tension curve and for active and passive conditions. Pressure-force coefficients of determination ranged from 0.138-0.963 for the active ascending limb and 0.343-0.947 for the active descending limb. Passive pressure coefficients of determination ranged from 0.045-0.842 for the ascending limb and 0.672-0.982 for the descending limb. These data indicate that IMP measurement provide a fairly accurate index of relative muscle force, especially at muscle lengths longer than optimal.     

A comparison of two Hill-type skeletal muscle models on the construction of medial gastrocnemius length-tension curves in humans in vivo

Human length-tension curves are traditionally constructed using a model that assumes passive tension does not change during contraction (model A) even though the animal literature suggests that passive tension can decrease (model B). The study's aims were threefold: 1) measure differences in human medial gastrocnemius length-tension curves using model A vs. model B, 2) test the reliability of ultrasound constructed length-tension curves, and 3) test the robustness of fascicle length-generated length-tension curves to variations between the angle and fascicle length relationship. An isokinetic dynamometer manipulated and measured ankle angle while ultrasound was used to measure medial gastrocnemius fascicle length. Supramaximal tibial nerve stimulation was used to evoke resting muscle twitches. Length-tension curves were constructed using model A {angle-torque [A-T((A))], length-torque [L-T((A))]} or model B {length-torque [L-T((B))]} in three conditions: baseline, heel-lift (where the muscle was shortened at each angle), and baseline repeated 2 h later (+2 h). Length-tension curves constructed from model B differed from those produced via model A, indicated by a significant increase in maximum torque (≈23%) when using L-T((B)) vs. L-T((A)). No parameter measured was different between baseline and +2 h for any method, indicating good reliability when using ultrasound. Length-tension curves were unaffected by the heel-lift condition when using L-T((A)) or L-T((B)) but were affected when using A-T((A)). Since the muscle model used significantly alters human length-tension curves, and given animal data indicate model B to be more accurate when passive tension is present, we recommend that model B should be used when constructing medial gastrocnemius length-tension curves in humans in vivo.     

Active tension adaptation at a shortened arterial muscle length: inhibition by cytochalasin-D

Unlike the static length-tension curve of striated muscle, airway and urinary bladder smooth muscles display a dynamic length-tension curve. Much less is known about the plasticity of the length-tension curve of vascular smooth muscle. The present study demonstrates that there were significant increases of ～15% in the phasic phase and ～10% in the tonic phase of a third KCl-induced contraction of a rabbit femoral artery ring relative to the first contraction after a 20% decrease in length from an optimal muscle length (L(0)) to 0.8-fold L(0). Typically, three repeated contractions were necessary for full length adaptation to occur. The tonic phase of a third KCl-induced contraction was increased by ～50% after the release of tissues from 1.25-fold to 0.75-fold L(o). The mechanism for this phenomenon did not appear to lie in thick filament regulation because there was no increase in myosin light chain (MLC) phosphorylation to support the increase in tension nor was length adaptation abolished when Ca(2+) entry was limited by nifedipine and when Rho kinase (ROCK) was blocked by H-1152. However, length adaptation of both the phasic and tonic phases was abolished when actin polymerization was inhibited through blockade of the plus end of actin by cytochalasin-D. Interestingly, inhibition of actin polymerization when G-actin monomers were sequestered by latrunculin-B increased the phasic phase and had no effect on the tonic phase of contraction during length adaptation. These data suggest that for a given level of cytosolic free Ca(2+), active tension in the femoral artery can be sensitized not only by regulation of MLC phosphatase via ROCK and protein kinase C, as has been reported by others, but also by a nonmyosin regulatory mechanism involving actin polymerization. Dysregulation of this form of active tension modulation may provide insight into alterations of large artery stiffness in hypertension.     

A new method for measuring passive length-tension properties of human gastrocnemius muscle in vivo

The study of muscle growth and muscle length adaptations requires measurement of passive length-tension properties of individual muscles, but until now such measurements have only been made in animal muscles. We describe a new method for measuring passive length-tension properties of human gastrocnemius muscles in vivo. Passive ankle torque and ankle angle data were obtained as the ankle was rotated through its full range with the knee in a range of positions. To extract gastrocnemius passive length-tension curves from passive torque-angle data it was assumed that passive ankle torque was the sum of torque due to structures which crossed only the ankle joint (this torque was a 6-parameter function of ankle joint angle) and a torque due to the gastrocnemius muscle (a 3-parameter function of knee and ankle angle). Parameter values were estimated with non-linear regression and used to reconstruct passive length-tension curves of the gastrocnemius. The reliability of the method was examined in 11 subjects by comparing three sets of measurements: two on the same day and the other at least a week later. Length-tension curves were reproducible: the average root mean square error was 5.1+/-1.1 N for pairs of measurements taken within a day and 7.3+/-1.2 N for pairs of measurements taken at least a week apart (about 3% and 6% of maximal passive tension, respectively). Length-tension curves were sensitive to mis-specification of moment arms, but changes in length-tension curves were not. The new method enables reliable measurement of passive length-tension properties of human gastrocnemius in vivo, and is likely to be useful for investigation of changes in length-tension curves over time.     

Length-tension relationship of abdominal expiratory muscles: effect of emphysema

The present study examined the active and passive length-tension relationship of the abdominal expiratory muscles in vitro during electrically stimulated contractions. Studies were performed on isolated strips of transverse abdominis and external oblique muscle from nine adult hamsters with normal lung function. The effect of chronic hyperinflation on the two muscles was assessed in eight hamsters with elastase-induced emphysema. In normal animals the maximal active tension per cross-sectional area (Po) was equal in the two muscles. The absolute muscle fiber length at which Po occurred (Lo) was less for the external oblique than the transverse abdominis and the length-tension curve operated at shorter fiber lengths. However, the change in tension produced by an increase or decrease in muscle length expressed in relative terms (i.e., as %Lo) was greater for the transverse abdominis than the external oblique. Mean total lung capacity of emphysematous animals was 198% of control. Po of the transverse abdominis and external oblique were the same in emphysematous and control animals. However, Lo and the length-tension curve of the transverse abdominis occurred at shorter fiber lengths in emphysematous animals because of a reduction in the number of sarcomeres in series along the fiber. The length-tension curve and the number of sarcomeres in the external oblique was the same in emphysematous and control animals. These results in normal animals indicate that the magnitude of the change in active and passive tension produced by a change in muscle length differs in the transverse abdominis and external oblique. Moreover, chronic hyperinflation of the thorax produced by elastase injection alters the length-tension relationships of some but not all the expiratory muscles.     

Intrinsic Feedback Factors Producing Inertial Compensation in Muscle

An attempt was made to determine the factors causing the load-inertia compensation that has been observed in skeletal muscle. Cat skeletal muscle force output was determined as a function of the two variables, length and stimulus pulse rate. The results were represented in a system diagram from which it becomes apparent that: (a) the length-tension relationship in muscle forms a functional, non-neural servo feedback; (b) the force-velocity curve appears as an oscillation-damping, velocity feedback in the muscle servo; (c) the nonlinear action of pulse rate on response is, in effect, in the input element to the muscle servo system. For purpose of analysis of the motor system it appears that these signal handling characteristics of muscle make it more nearly a “position servo” than a “force motor.”