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

1967 ◽  
Vol 50 (5) ◽  
pp. 1125-1137 ◽  
Author(s):  
Yorimi Matsumoto
Keyword(s):  
Length Change ◽  
Hill Equation ◽  
Isometric Tension ◽  
Resting Tension ◽  
Reference Length ◽  
Velocity Relation ◽  
Force Velocity ◽  
Almost All ◽  
The Hill ◽  
Isotonic Shortening

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.

Contractile properties of bronchial smooth muscle with and without cartilage

1990 ◽  
Vol 69 (1) ◽  
pp. 120-126 ◽  
Author(s):  
H. Jiang ◽  
N. L. Stephens
Keyword(s):  
Smooth Muscle ◽  
Bronchial Tree ◽  
Isometric Tension ◽  
Bronchial Smooth Muscle ◽  
Optimal Length ◽  
Resting Tension ◽  
Force Velocity ◽  
Later Phase ◽  
Isotonic Shortening

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)

Maximum shortening velocity of smooth muscle: zero load-clamp vs. afterloaded method

1983 ◽  
Vol 55 (5) ◽  
pp. 1630-1633 ◽  
Author(s):  
R. W. Mitchell ◽  
N. L. Stephens
Keyword(s):  
Smooth Muscle ◽  
Direct Measurement ◽  
Hill Equation ◽  
Shortening Velocity ◽  
Optimal Length ◽  
Lever System ◽  
Technical Advances ◽  
Force Velocity ◽  
The Hill ◽  
Isotonic Shortening

Previous reports from this laboratory of force-velocity relationships of canine tracheal smooth muscle (TSM) have presented maximum shortening velocities (Vmax) mathematically derived from the linearized transformation of the Hill equation (A. V. Hill, Proc. Roy. Soc. London, Ser. B., 126:136-195, 1938). Recent technical advances enable us to measure Vmax directly using an electromagnetic lever system that can instantaneously clamp to a zero load, thus we compared values of Vmax derived mathematically and those directly measured on the same TSM strips. Derived Vmax values from afterloaded isotonic shortening curves for loads greater than preload were 0.328 +/- 0.021 optimal length (lO)/s and were not significantly different from zero load-clamp measurements of 0.301 +/- 0.022 lO/s from the same (n = 15) muscles. These data indicate that Vmax values mathematically derived for TSM from conventional isotonic afterloaded force-velocity curves are valid estimates of zero load velocity, because they were not significantly different from values obtained by direct measurement using the zero load-clamp technique.

Effects of active shortening on tension development of rabbit papillary muscle

1980 ◽  
Vol 238 (1) ◽  
pp. H8-H13 ◽  
Author(s):  
J. K. Leach ◽  
A. J. Brady ◽  
B. J. Skipper ◽  
D. L. Millis
Keyword(s):  
Isometric Tension ◽  
Isometric Contractions ◽  
Tension Development ◽  
Velocity Of Shortening ◽  
Tension Time ◽  
Shortening Deactivation ◽  
Force Velocity ◽  
Stimulus Length ◽  
The Right ◽  
The Hill

Duration and intensity of force development have been shown to be less during active muscle shortening than during isometric contraction. The purpose of this study was to compare force developed during controlled shortening with that predicted by the Frank-Starling relation. Paillary muscles from the right ventricles of rabbits were arranged for isometric tension recording, and isometric contractions were recorded at several lengths. The muscles were then permitted to shorten at velocities of 0.2--6 mm/s, shortening beginning 150--200 ms after the stimulus. Length-tension-time curves constructed from the isometric contractions were used to determine predicted shortening tension (Pp), which was compared with actual tension during shortening (Ps) at corresponding times and lengths. Ps was significantly less than Pp and the ratio Ps/Pp decreased with increasing velocity of shortening. The decrease in Ps/Pp was directly related to the duration of shortening (P less than 0.001), suggesting that the fall of shortening tension reflected both the Hill force-velocity relation and shortening deactivation.

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

1992 ◽  
Vol 73 (5) ◽  
pp. 2105-2111 ◽  
Author(s):  
B. T. Ameredes ◽  
W. F. Brechue ◽  
G. M. Andrew ◽  
W. N. Stainsby
Keyword(s):  
Muscle Length ◽  
Isometric Tension ◽  
Maximal Velocity ◽  
Velocity Of Shortening ◽  
Low Load ◽  
Before And After ◽  
Force Velocity ◽  
The Hill ◽  
Isotonic Contractions

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.

scholarly journals Hill’s equation of muscle performance and its hidden insight on molecular mechanisms

2013 ◽  
Vol 142 (6) ◽  
pp. 561-573 ◽  
Author(s):  
Chun Y. Seow
Keyword(s):  
Molecular Mechanisms ◽  
Muscle Mechanics ◽  
Hill Equation ◽  
Muscle Performance ◽  
Shortening Velocity ◽  
Force Velocity ◽  
Protein Isoform ◽  
Heavy Loads ◽  
The Hill ◽  
The Relationship

Muscles shorten faster against light loads than they do against heavy loads. The hyperbolic equation first used by A.V. Hill over seven decades ago to illustrate the relationship between shortening velocity and load is still the predominant method used to characterize muscle performance, even though it has been regarded as purely empirical and lacking precision in predicting velocities at high and low loads. Popularity of the Hill equation has been sustained perhaps because of historical reasons, but its simplicity is certainly attractive. The descriptive nature of the equation does not diminish its role as a useful tool in our quest to understand animal locomotion and optimal design of muscle-powered devices like bicycles. In this Review, an analysis is presented to illustrate the connection between the historic Hill equation and the kinetics of myosin cross-bridge cycle based on the latest findings on myosin motor interaction with actin filaments within the structural confines of a sarcomere. In light of the new data and perspective, some previous studies of force–velocity relations of muscle are revisited to further our understanding of muscle mechanics and the underlying biochemical events, specifically how extracellular and intracellular environment, protein isoform expression, and posttranslational modification of contractile and regulatory proteins change the interaction between myosin and actin that in turn alter muscle force, shortening velocity, and the relationship between them.

Graded activation in rabbit mesotubarium smooth muscle

1975 ◽  
Vol 229 (2) ◽  
pp. 455-465 ◽  
Author(s):  
RA Meiss
Keyword(s):  
Smooth Muscle ◽  
Phase Plane ◽  
Isometric Force ◽  
Stimulus Frequency ◽  
Hill Equation ◽  
Electrical Field ◽  
First Derivative ◽  
Force Velocity ◽  
The Hill ◽  
Slow Onset

The outer margin of the mesotubarium superius, an accessory ligament from the femal rabbit reproductive system, contains a long and slender bundle of smooth muscle fibers well aligned with the long axis of the tissue. Very little connective tissue is present. Massive alternating-current electrical field stimuli (variable in frequency, amplitude, and duration) applied to isolated mesotubaria from mature, nonpregnant animals produced contractions in which isometric force (P) and its first derivative (dP/dt) could be continuously graded; an optimum existed for stimulus frequency and amplitude, but not for its duration. Twitchlike contractions could not be produced. Isometric contractions in which P was plotted against dP/dt to generate a phase-plane trajectory were used to predict the ultimate (time = infinity) force (Po) in graded contractions; this value agreed with the Po derived from isotonic force-velocity curves fitted to the Hill equation. Quick stretches applied during the rise of contractile force revealed a slow onset of the ability to bear the Po force.

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