Validity of the Force-Velocity Relation for Muscle Contraction in the Length Region, l ≤ l0

Considerable attention has been directed to the characteristic force-velocity relation discovered by A. V. Hill in the study of muscle kinematics. Models of contractile process were tested on the basis of their compatibility with the Hill equation. However, almost all the isotonic data have been restricted to one length, l₀, the maximum length with almost no resting tension; the velocities measured are those initial values when the load begins to move. The force-velocity curve extrapolates to zero velocity for isometric tension, but only for the tension at that one length. Very few efforts have been made to study the profiles of the curves throughout the range of lengths over which shortening takes place. In examining the length region, l ≤ l₀, for an isotonically contracting muscle, not only is the force-velocity relation valid for the initial reference length, l₀, but also for any other length. The analysis in this report indicates that the constants a/P₀ and b/l₀ remain fixed throughout the length change of afterloaded isotonic shortening in the Rana pipiens sartorius muscles.     

Force-velocity constants in smooth muscle: afterloaded isotonic and quick-release methods

In using pharmacologic stimuli, force-velocity (FV) curves are usually obtained by the method of quick release (QR) and redevelopment of shortening at peak tetanic tension; the advantage of the method being that the active state is at maximum. However, the QR may itself reduce the intensity of the active state and result in reduced values of FV constants. We tested this by delineating FV curves in canine tracheal smooth muscle using both conventional afterloaded isotonic contractions (ALI), and redevelopment of shortening after QR methods. For both these studies a supramaximal tetanizing electrical stimulus was used. The analysis of 11 experiments revealed that the latter method resulted in statistically significant reductions of all FV constants except for Po (maximum isometric tetanic tension). The means and standard errors for the sets of constants for the ALI and QR, respectively, are as follows: Vmax (maximum velocity of shortening) = 0.275 lo (optimal muscle length)/s +/- 0.024 (SE), and 0.216 lo/s + 0.023; a (hyperbolic constant with units of force) = 294 g/cm2 +/- 35 and 236 g/cm2 +/- 32; b (hyperbolic constant with units of velocity) = 0.059 lo +/- 0.004 and 0.039 lo/s +/- 0.005; a/Po = 0.214 +/- 0.028 and 0.182 +/- 0.026; and Po = 1.362 kg/cm2 +/- 0.106 and 1.294 kg/cm2 +/- 0.097. These data clearly show that the quick-release method for measuring force-velocity relationships in canine smooth muscle results in significant underestimates of muscle shortening properties.     

Force-velocity shifts with repetitive isometric and isotonic contractions of canine gastrocnemius in situ.

The force-velocity (F-V) relationships of canine gastrocnemius-plantaris muscles at optimal muscle length in situ were studied before and after 10 min of repetitive isometric or isotonic tetanic contractions induced by electrical stimulation of the sciatic nerve (200-ms trains, 50 impulses/s, 1 contraction/s). F-V relationships and maximal velocity of shortening (Vmax) were determined by curve fitting with the Hill equation. Mean Vmax before fatigue was 3.8 +/- 0.2 (SE) average fiber lengths/s; mean maximal isometric tension (Po) was 508 +/- 15 g/g. With a significant decrease of force development during isometric contractions (-27 +/- 4%, P < 0.01, n = 5), Vmax was unchanged. However, with repetitive isotonic contractions at a low load (P/Po = 0.25, n = 5), a significant decrease in Vmax was observed (-21 +/- 2%, P < 0.01), whereas Po was unchanged. Isotonic contractions at an intermediate load (P/Po = 0.5, n = 4) resulted in significant decreases in both Vmax (-26 +/- 6%, P < 0.05) and Po (-12 +/- 2%, P < 0.01). These results show that repeated contractions of canine skeletal muscle produce specific changes in the F-V relationship that are dependent on the type of contractions being performed and indicate that decreases in other contractile properties, such as velocity development and shortening, can occur independently of changes in isometric tension.     

Contractile properties of bronchial smooth muscle with and without cartilage

The majority of in vitro studies on airway smooth muscle have used the trachealis (TSM) as a convenient substitute for muscle from airways that constitute the flow-limiting segment. The latter are technically difficult to work with. However, because the site of maximum resistance to airflow is at the third to seventh generations of the bronchial tree, the trachealis preparation is of limited value. Length-tension and force-velocity properties were therefore studied at optimal length (lo) of canine bronchial smooth muscle (BSM) from which cartilage had been carefully removed. Normalized maximum isometric tension or stress (Po x 10(4) N/m2) for BSM was 7.1 +/- 0.19 (SE), which was similar to that of BSM with cartilage (BSM+C, 6.8 +/- 0.21) but lower than for TSM (18.2 +/- 0.81). At length greater than lo, the BSM+C was stiffer than the BSM. The values of maximum shortening capacity (delta Lmax), obtained directly from isotonic shortening at a load equal to the resting tension at lo, were 0.76 lo +/- 0.03, 0.41 lo +/- 0.02, and 0.24 +/- 0.02 lo for TSM, BSM, and BSM+C, respectively. The BSM and BSM+C delta Lmaxs were different (P less than 0.05). Maximal shortening velocities (Vo) for BSM, elicited at 2, 4, and 8 s by quick release in the course of an isometric contraction were significantly higher than for the BSM+C. Vos showed gradual decreases in all three groups in the later phase of contraction, suggesting the operation of latch bridges.(ABSTRACT TRUNCATED AT 250 WORDS)     

The maximum shortening velocity of muscle should be scaled with activation.

The purpose of this study was to determine whether the maximum shortening velocity (Vmax) in Hill's mechanical model (A. V. Hill. Proc. R. Soc. London Ser. B. 126: 136-195, 1938) should be scaled with activation, measured as a fraction of the maximum isometric force (Fmax). By using the quick-release method, force-velocity (F-V) relationships of the wrist flexors were gathered at five different activation levels (20-100% of maximum at intervals of 20%) from four subjects. The F-V data at different activation levels can be fitted remarkably well with Hill's characteristic equation. In general, the shortening velocity decreases with activation. With the assumption of nonlinear relationships between Hill constants and activation level, a scaled Vmax model was developed. When the F-V curves for submaximal activation were forced to converge at the Vmax obtained with maximum activation (constant Vmax model), there were drastic changes in the shape of the curves. The differences in Vmax values generated by the scaled and constant Vmax models were statistically significant. These results suggest that, when a Hill-type model is used in musculoskeletal modeling, the Vmax should be scaled with activation.     

Effects of aging on force, velocity, and power in the elbow flexors of males

The effect of aging on muscular power development was investigated by determining the force-velocity relationship. The muscle cross-sectional area (CSA) was estimated by the thickness of the elbow flexors. The subjects were 19 elderly males aged 69.1+/-3.7 years old (G-70 group), 15 middle-aged males aged 50.9+/-3.5 years old (G-50), and 19 young males aged 21.2+/-1.3 years old (G-20). The G-70 group had the slowest shortening velocities under various load conditions, resulting in the lowest force-velocity relationship. The maximum values for force (Fmax), velocity (Vmax), power (Pmax), dynamic constants (a, b), and the a/Fmax ratio were determined using Hill's equation. The a/Fmax ratio determines the degree of concavity in the force-velocity curve. The a/Fmax ratio was greatest in G-70, followed by those in G-50 and G-20, while the maximum values for force (Fmax), velocity (Vmax), and power (Pmax) were significantly lower in G-70 than in the other groups. Fmax and Pmax per CSA were lowest in G-70, and Vmax per unit muscle length was also lowest in G-70 as compared to the other age groups. The ratio of G-70/G-20 was greatest in Pmax (69.6%), followed by Fmax (75.3%) and Vmax (83.4%). However, there were no significant differences in CSA among the 3 age groups. Our findings suggest that muscle force and shortening velocity may decline gradually in the process of aging attributed to declining muscle function rather than CSA.     

Calculation of muscle maximal shortening velocity by extrapolation of the force-velocity relationship: afterloaded versus isotonic release contractions

The maximal shortening velocity of a muscle (V(max)) provides a link between its macroscopic properties and the underlying biochemical reactions and is altered in some diseases. Two methods that are widely used for determining V(max) are afterloaded and isotonic release contractions. To determine whether these two methods give equivalent results, we calculated V(max) in 9 intact single fibres from the lumbrical muscles of the frog Xenopus laevis (9.5-15.5 °C, stimulation frequency 35-70 Hz). The data were modelled using a 3-state cross-bridge model in which the states were inactive, detached, and attached. Afterloaded contractions gave lower predictions of Vmax than did isotonic release contractions in all 9 fibres (3.20 ± 0.84 versus 4.11 ± 1.08 lengths per second, respectively; means ± SD, p = 0.001) and underestimated unloaded shortening velocity measured with the slack test by an average of 29% (p = 0.001, n = 6). Excellent model predictions could be obtained by assuming that activation is inhibited by shortening. We conclude that under the experimental conditions used in this study, afterloaded and isotonic release contractions do not give equivalent results. When a change in the V(max) measured with afterloaded contractions is observed in diseased muscle, it is important to consider that this may reflect differences in either activation kinetics or cross-bridge cycling rates.     

Nitric oxide effects on force-velocity characteristics of the rat diaphragm

The present experiments tested nitric oxide (NO) effects on shortening velocity and power production in maximally activated rat diaphragm at 37 degrees C. Diaphragm fiber bundles (n = 10/group) were incubated at 37 degrees C in Krebs-Ringer solution containing no added drug (control), the NO synthase inhibitor Nomega-nitro-L-arginine (L-NNA; 10 mM), the NO donor sodium nitroprusside (SNP; 1 mM), or a combination (L-NNA + SNP). Loaded shortening velocity was measured via the load-clamp technique over a range of afterloads. Unloaded shortening velocity (Vo) was measured in control and L-NNA-treated bundles (n = 12/group) by using the slack test. Force-velocity data fitted to the Hill equation determined a Vmax of 13.7+/-0.4 lengths/s, contradicting the notion that rat diaphragm Vmax declines at temperatures > 35 degrees C. In contrast, L-NNA decreased Vmax (P < 0.05), loaded shortening velocity (P < 0.001), and power production (P < 0.001), but did not change Vo or maximal isometric force. All L-NNA effects were prevented by coincubating fiber bundles with L-NNA + SNP. SNP alone had no effect on any variable. These data indicate that endogenous NO is essential for optimal myofilament function during active shortening.     

A simple Hill element-nonlinear spring model of muscle contraction biomechanics

The purpose of this study was to develop a model to predict the mechanical response of muscles during isometric tetanic, afterloaded isotonic and isovelocity shortening contractions. Two versions of the model were developed. Both incorporated a contractile element that obeyed a Hill force-velocity relationship and a series elastic element. In a quadratic spring version, the series elastic element force was represented as proportional to the square of the stretch; in a cubic spring version, it was represented as proportional to the cube of the stretch. Both versions provided closed-form equations for response predictions that involved four independent parameters. Once the four parameters were chosen, each of these responses could be predicted. Model validity was established by comparing predicted and observed responses in slow and fast hindlimb muscles of rodents. Significant model-predicted responses seldom differed by more than 15% from experimental values. The model can provide insights into how changes in individual properties affect the overall mechanical behavior of muscles in a variety of circumstances and reduce the need for collection of experimental data.     

Dependency of the force-velocity relationships on Mg ATP in different types of muscle fibers from Xenopus laevis.

MgATP binding to the actomyosin complex is followed by the dissociation of actin and myosin. The rate of this dissociation process was determined from the relationship between the maximum velocity of shortening and the MgATP concentration. It is shown here that the overall dissociation rate is rather similar in different types of muscle fibers. The relation between MgATP concentration and the maximum shortening velocity was investigated in fast and slow fibers and bundles of myofibrils of the iliofibularis muscle of Xenopus laevis at 4 degrees C from which the sarcolemma was either removed mechanically or made permeable by means of a detergent. A small segment of each fiber was used for a histochemical determination of fiber type. At 5 mM MgATP, the fast fibers had a maximum shortening velocity (Vmax) of 1.74 +/- 0.12 Lo/s (mean +/- SEM) (Lo: segment length at a sarcomere length of 2.2 microns). For the slow fibers Vmax was 0.41 +/- 0.15 Lo/s. In both cases, the relationship between Vmax and the ATP concentration followed the hyperbolic Michaelis-Menten relation. A Km of 0.56 +/- 0.06 mM (mean +/- SD) was found for the fast fibers and of 0.16 +/- 0.03 mM for the slow fibers. Assuming that Vmax is mainly determined by the crossbridge detachment rate, the apparent second order dissociation rate for the actomyosin complex in vivo would be 3.8.10(5) M-1s-1 for the fast fibers and 2.9.10(5) M-1 s-1 for the slow fibers. Maximum power output as a function of the MgATP concentration was derived from the force-velocity relationships.(ABSTRACT TRUNCATED AT 250 WORDS)     

Ca2+-dependent facilitated shortening in isotonic contraction of trachealis muscle

We compared isotonic shortening with isometric force generation as a function of external Ca2+ in 166 tracheal smooth muscle (TSM) strips from 27 mongrel dogs in vitro. Concentration-response curves were generated with muscarinic stimulation (acetylcholine, ACh), alpha-adrenergic receptor activation (norepinephrine after beta-adrenoceptor blockade, NE), serotonin (5-HT), and KCl-substituted Krebs-Henseleit solution. The concentrations of 5-HT causing half-maximal shortening (ECS50, 1.54 +/- 0.14 X 10(-7) M) and half-maximal active isometric tension (ECT50, 1.72 +/- 0.30 X 10(-7) M) were similar (P = NS). Likewise, ECS50 (21.9 +/- 0.7 mM) and ECT50, (22.0 +/- 0.9 mM) were similar for KCl. In contrast, facilitated isotonic shortening (i.e., greater isotonic shortening for comparable degrees of force generation) was elicited with ACh and NE for all levels of force generation between 15 and 85% of maximum and for all concentrations of ACh from 3 X 10(-8) to 3 X 10(-5) M (P less than 0.05 for all points). Facilitated isotonic shortening also was elicited for all concentrations of NE from 10(-8) to 10(-6) M (P less than 0.05 for all points). Removal of Ca2+ from the perfusate substantially reduced the potency of ACh (P less than 0.001) and abolished differences between ECS50 (2.23 +/- 0.28 X 10(-5) M) and ECT50 (2.50 +/- 0.46 X 10(-5) M, P = NS). We demonstrate that for comparable degrees of force generation, muscarinic and alpha-adrenergic receptor activation cause greater isotonic shortening than KCl or 5-HT and that this facilitated shortening is associated with the concentration of external Ca2+.     

Sarcomere length dependence of the force-velocity relation in single frog muscle fibers.

The force-velocity relation of single frog fibers was measured at sarcomere lengths of 2.15, 2.65, and 3.15 microns. Sarcomere length was obtained on-line with a system that measures the distance between two markers attached to the surface of the fiber, approximately 800 microns apart. Maximal shortening velocity, determined by extrapolating the Hill equation, was similar at the three sarcomere lengths: 6.5, 6.0, and 5.7 microns/s at sarcomere lengths of 2.15, 2.65, and 3.15 microns, respectively. For loads not close to zero the shortening velocity decreased with increasing sarcomere length. This was the case when force was expressed as a percentage of the maximal force at optimal fiber length or as a percentage of the sarcomere-isometric force at the respective sarcomere lengths. The force-velocity relation was discontinuous around zero velocity: load clamps above the level that kept sarcomeres isometric resulted in stretch that was much slower than when the load was decreased below isometric by a similar amount. We fitted the force-velocity relation for slow shortening (less than 600 nm/s) and for slow stretch (less than 200 nm/s) with linear regression lines. At a sarcomere length of 2.15 microns the slopes of these lines was 8.6 times higher for shortening than for stretch. At 2.65 and 3.15 microns the values were 21.8 and 14.1, respectively. At a sarcomere length of 2.15 microm, the velocity of stretch abruptly increased at loads that were 160-170% of the sarcomere isometric load, i.e., the muscle yielded. However, at a sarcomere length of 2.65 and 3.15 microm yield was absent at such loads. Even the highest loads tested (260%) resulted in only slow stretch.(ABSTRACT TRUNCATED AT 250 WORDS)     

The biphasic force-velocity relationship in whole rat skeletal muscle in situ.

Edman has reported that the force-velocity relationship (FVR) departs from Hill's classic hyperbola near 0.80 of measured isometric force (J Physiol 404: 301-321, 1988). The purpose of this study was to investigate the biphasic nature of the FVR in the rested state and after some recovery from fatigue in the rat medial gastrocnemius muscle in situ. Force-velocity characteristics were determined before and during recovery from fatigue induced by intermittent stimulation at 170 Hz for 100 ms each second for 6 min. Force-velocity data were obtained for isotonic contractions with 100 ms of 200-Hz stimulation, including several measurements with loads above 0.80 of measured isometric force. The force-velocity data obtained in this study were fit well by a double-hyperbolic equation. A departure from Hill's classic hyperbola was found at 0.88+/-0.01 of measured isometric force, which is higher than the approximately 0.80 reported by Edman et al. for isolated frog fibers. After 45 min of recovery, maximum shortening velocity was 86+/-2% of prefatigue, but neither curvature nor predicted isometric force was significantly different from prefatigue. The location of the departure from Hill's classic hyperbola was not different after this recovery from the fatiguing contractions. Including an isometric point in the data set will not yield the same values for maximal velocity and the degree of curvature as would be obtained using the double hyperbola approach. Data up to 0.88 of measured isometric force can be used to fit data to the Hill equation.     

Isotonic relaxation of control and sensitized airway smooth muscle

Smooth muscle relaxation has most often been studied in isometric mode. However, this only tells us about the stiffness properties of the bronchial wall and thus only about wall capacitative properties. It tells us little about airflow. To study the latter, which of course is the meaningful parameter in regulation of ventilation and in asthma, we studied isotonic shortening of bronchial smooth muscle (BSM) strips. Failure of BSM to relax could be another important factor in maintaining high airway resistance. To analyze relaxation curves, we developed an index of isotonic relaxation, t1/2(P, lCE), which is the half-time for relaxation that is independent of muscle load (P) and of initial contractile element length (lCE). This index was measured in curves of relaxation initiated at 2 s (normally cycling crossbridges) and at 10 s (latch-bridges). At 10 s no difference was seen for adjusted t1/2(P, lCE) between curves obtained from control and sensitized BSM, (8.38 +/- 0.92 s vs. 7.78 +/- 0.93 s, respectively). At 2 s the half-time was almost doubled in the sensitized BSM (6.98 +/- 0.01 s (control) vs. 12.74 +/- 2.5 s (sensitized)). Thus, changes in isotonic relaxation are only seen during early contraction. Using zero load clamps, we monitored the time course of velocity during relaxation and noted that it varied according to 3 phases. The first phase (phase i) immediately followed cessation of electrical field stimulation (EFS) at 10 s and showed almost the same velocity as during the latter 1/3 of shortening; the second phase (phase ii) was linear in shape and is associated with zero load velocity, we speculate it could stem from elastic recoil of the cells' internal resistor; and the third phase (phase iii) was convex downwards. The zero load velocities in phase iii showed a surprising spontaneous increase suggesting reactivation of the muscle. Measurements of intracellular calcium (Fura-2 study) and of phosphorylation of the 20 kDa myosin light chain showed simultaneous increments, indicating phase iii represented an active process. Studies are under way to determine what changes occur in these 3 phases in a sensitized muscle. And of course, in the context of this conference, just what role the plastic properties of the muscle play in relaxation requires serious consideration.     

Some proposals in cardiac muscle mechanics and energetics

Based on A. V. Hill's three-component model, mechanical properties of the contractile element (CE), such as velocity and tension, were determined as muscle shortening and loads in quick-release or afterloaded isotonic contraction. The method is applicable for studying cardiac mechanics, to obtain force-velocity data of the same CE length at varous afterloads. Analysis of the energetics of cardiac muscle was based on simulation studies of cardiac mechanics (Wong 1971, 1972). By proper derivation, the conventional contractile element work (CEW) was found to be a minor energy determinant. The tension-time integral and tension-independent heat (Ricchiuti and Gibbs, 1965) represent energy utilization for activation and maintenance of tension, the primary energy determinant.     

Force-velocity properties of two avian hindlimb muscles

Recent work has provided measurements of power output in avian skeletal muscles during running and flying, but little is known about the contractile properties of avian skeletal muscle. We used an in situ preparation to characterize the force-velocity properties of two hind limb muscles, the lateral gastrocnemius (LG) and peroneus longus (PL), in Wild Turkeys (Meleagris gallopavo). A servomotor measured shortening velocity for at least six different loads over the plateau region of the length-tension curve. The Hill equation was fit to the data to determine maximum shortening velocity and peak instantaneous power. Maximum unloaded shortening velocity was 13.0+/-1.6 L s(-1) for the LG muscle and 14.8+/-1.0 L s(-1) for the PL muscle (mean+/-S.E.M.). These velocities are within the range of values published for reptilian and mammalian muscles. Values recorded for maximum isometric force per cross-sectional area, 271+/-28 kPa for the LG and 257+/-30.5 kPa for the PL, and peak instantaneous power output, 341.7+/-36.4 W kg(-1) for the LG and 319.4+/-42.5 W kg(-1) for the PL, were also within the range of published values for vertebrate muscle. The force-velocity properties of turkey LG and PL muscle do not reveal any extreme differences in the mechanical potential between avian and other vertebrate muscle.     

Loaded shortening and power output in cardiac myocytes are dependent on myosin heavy chain isoform expression

The purpose of this study was to examine the role of myosin heavy chain (MHC) in determining loaded shortening velocities and power output in cardiac myocytes. Cardiac myocytes were obtained from euthyroid rats that expressed alpha-MHC or from thyroidectomized rats that expressed beta-MHC. Skinned myocytes were attached to a force transducer and a position motor, and isotonic shortening velocities were measured at several loads during steady-state maximal Ca(2+) activation (P(pCa4.5)). MHC expression was determined after mechanical measurements using SDS-PAGE. Both alpha-MHC and beta-MHC myocytes generated similar maximal Ca(2+)-activated force, but alpha-MHC myocytes shortened faster at all loads and generated approximately 170% greater peak normalized power output. Additionally, the curvature of force-velocity relationships was less, and therefore the relative load optimal for power output (F(opt)) was greater in alpha-MHC myocytes. F(opt) was 0.31 +/- 0.03 P(pCa4.5) and 0.20 +/- 0.06 P(pCa4.5) for alpha-MHC and beta-MHC myocytes, respectively. These results indicate that MHC expression is a primary determinant of the shape of force-velocity relationships, velocity of loaded shortening, and overall power output-generating capacity of individual cardiac myocytes.     

Relations between force-velocity characteristics of the knee-hip extension movement and vertical jump performance

Relations between force-velocity characteristics of the multijoint movement of the lower limbs and vertical jump performance were investigated. A total of 67 untrained subjects (age: 19.54 +/- 2.38 years; height: 166.88 +/- 8.53 cm; body mass: 59.14 +/- 10.82 kg, mean +/- SD) performed isometric and isotonic knee-hip extension movements on a servo-controlled dynamometer, and the force-velocity relations were determined. Also, vertical jump (VJ) performance was measured with a jump gauge. The force-velocity relation was described with a linear function so that the maximum isometric force (Fmax) and the maximum unloaded velocity (Vmax) for the knee-hip extension movement were estimated by extrapolation. Maximum isometric force coincided with maximum isometric force, F(0) (F(0)/Fmax = 1.03 +/- 0.24). Maximum isometric force, Vmax, and maximum power output (Pmax) were positively correlated with VJ (r = 0.48, 0.68, and 0.76, respectively; p < 0.001). However, when Fmax, Vmax, and Pmax were normalized with body mass (BM), leg length (LL), and BM, respectively, no correlation was seen between Fmax/BM and VJ (r = 0.24, p > 0.05), and significant correlations were seen between Vmax/LL and VJ (r = 0.56, p < 0.001) and between Pmax/BM and VJ (r = 0.65, p < 0.001). On the other hand, Fmax and Vmax (r = 0.12, p > 0.05) and Fmax/BM and Vmax/LL (r = 0.05, p > 0.05) were not significantly correlated, indicating that Fmax and Vmax were independent variables. The present estimates of Fmax, Vmax, and Pmax can be useful for evaluating the actual performance of multijoint movement of the lower limbs. It is suggested that, although in untrained individuals the speed of movement might be a more important determinant of jump performance, jump performance ability has a potential to improve with increases in strength of the lower limb.     

The dynamic properties of mammalian skeletal muscle

The dynamic characteristics of the rat gracilis anticus muscle at 17.5°C have been determined by isotonic and isometric loading. For a fixed initial length these characteristics were represented either as a family of length-velocity phase trajectories at various isotonic afterloads or as a series of force-velocity curves at different lengths. An alternate method of viewing these data, the length-external load-velocity phase space, was also generated. When the muscle was allowed to shorten from different initial lengths, the velocity of shortening achieved at a given length was lower for longer initial lengths. The amount of departure was also dependent upon the isotonic load, the greater the load the greater the departure. The departures were not caused by changes in the elastic elements of the muscle or fatigue in the ordinary sense. When the behavior of the muscle was investigated at different frequencies of stimulation, the shortening velocity was a function of the number of stimulating pulses received by the muscle at a given frequency. The shortening velocity of the rat gracilis anticus muscle is, therefore, not only a function of load and length, but also of an additional variable related to the time elapsed from onset of stimulation.     

In vivo and in vitro correlation of trachealis muscle contraction in dogs.

Maximal trachealis muscle shortening in vivo was compared with that in vitro in seven anesthetized dogs. In addition, the effect of graded elastic loads on the muscle was evaluated in vitro. In vivo trachealis muscle shortening, as measured using sonomicrometry, revealed maximal active shortening to be 28.8 +/- 11.7% (SD) of initial length. Trachealis muscle preparations from the same animals were studied in vitro to evaluate isometric force generation, isotonic shortening, and the effect of applying linear elastic loads to the trachealis muscle during contraction from optimal length. Maximal isotonic shortening was 66.8 +/- 8.4% of optimal length in vitro. Increasing elastic loads decreased active shortening and velocity of shortening in vitro in a hyperbolic manner. The elastic load required to decrease in vitro shortening to the extent of the shortening observed in vivo was similar to the estimated load provided by the tracheal cartilage. We conclude that decreased active shortening in vivo is primarily due to the elastic afterload provided by cartilage.