Validity of the Force-Velocity Relation for Muscle Contraction in the Length Region, <i>l</i> ≤ <i>l</i>0

Matsumoto, Yorimi

doi:10.1085/jgp.50.5.1125

Cited by 23 publications

(9 citation statements)

References 4 publications

(6 reference statements)

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“…These values of about 1.8 kg/cm 2 are within the lower range of P o values generally obtained in mammalian skeletal muscle (11)(12)(13)(14)(15). Using the highest mean value for the P' o (1.08 kg/cm 2 ) as experimentally obtained in the heart muscle at the optimal length of the length-tension relation (15) and correcting this value for the SE extension by the factor 0.6 derived from the present study, a maximal isometric tension of 1.80 kg/cm 2 would be obtained in heart muscle.…”

Section: Discussionsupporting

confidence: 85%

Effects of Various Inotropic Interventions on the Dynamic Properties of the Contractile Elements in Heart Muscle of the Cat

Brutsaert

Parmley

Sonnenblick

1970

Circulation Research

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Force-velocity-length (FVL) relations were obtained by determining die phase-plane tracings of velocity of shortening vs. length during isotonic contractions. These measurements were then replotted in a three-dimensional graph after correction for the series elastic extension during the isometric phase of the contractions as derived from a quick release contraction. On examining the influence of temperature (29° and 37°), preload, frequency of stimulation (12/min and 24-30/min), paired stimulation (PS), calcium (2.5 B M and 7.5 HIM), and isoproterenol (10~5M), it was shown that the surface created by the three-dimensional FVL relations of the contractile element (CE) is unique for a given state of contractility. Furthermore, the course of velocity vs. length is determined only by the instantaneous CE length, regardless of the contractile state of die CE, and is independent of the time after stimulation over a large portion of the shortening. From the intersection of the linear load-shortening relation observed for the CE with the load axis the maximum force (P o ) development of the CE was derived. The highest values of this corrected P o (1.80 ±0.13 kg/cm 2 ) were seen following inotropic interventions such as PS, calcium, or isoproterenol. Using the corrected P o , truly hyperbolic force-velocity curves were constructed from which V max and the Hill equation constants a and b were derived for the various inotropic interventions.ADDITIONAL KEY WORDS cat papillary muscles contractility force-velocity-length relations • It has been shown that the surface created by the three-dimensional plot of the instantaneous force, velocity, and length of the contractile elements (CE) of the myocardium is unique for a given state of contractility (1). Thus the velocity-length relations of the CE for a given load during isotonic contractions are independent of initial muscle length and independent of the time after stimulation except at the terminal portions of shortening when the intensity of active state is falling. Further, the load-shortening relation of the CE has been shown to be linear. This permits an estimation of the maximum isometric force (P o ) which the CE could develop if there were no extension of the series elastic elements (SE) and hence no shortening of the CE during the development of force. Moreover, when corrected to this maximum isometric force, the force-velocity relation of heart muscle becomes hyperbolic in form. A. V. Hill (2) has demonstrated in skeletal muscle that there is an inverse relation between velocity of shortening (V) and load (P) which is described by the hyperbolic function: (P + a) (V + b) = (P o + a)b, where a and b are constants. This mechanical relation takes on added interest since the constant a can be related to the extent of energy release per unit of shortening and the constant b to the rate of energy release (3). Although such quantitative analysis has

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Section: Discussionsupporting

confidence: 85%

Effects of Various Inotropic Interventions on the Dynamic Properties of the Contractile Elements in Heart Muscle of the Cat

Brutsaert

Parmley

Sonnenblick

1970

Circulation Research

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“…On the other hand, it provides new interpretations of some experiments reported in the literature. Buchthal (1942), Mar~chal (1955), Del~ze (1961), and Matsumoto (1967) have shown that the 'isotonic' length-tension diagram is not the same as the 'isometric' length-tension diagram. The latter is obtained by tetanizing the muscle isometrically at various lengths, the former by recording the active shortening of muscles pulling a free-hanging load.…”

Section: Discussionmentioning

confidence: 99%

“…The tension-length diagram obtained" by tetanizing the muscle isometrically at various lengths is not the same as that obtained by recording the active shortening of muscles which pull a free-hanging load (Buchthal, 1942;Mar6chal, 1955;Delbze, 1961;Matsumoto, 1967). The velocity of isotonic shortening measured at some given length depends on the starting length (Carlson, 1957;Bahler et al, 1968).…”

Section: Introductionmentioning

confidence: 91%

The deficit of the isometric tetanic tension redeveloped after a release of frog muscle at a constant velocity.

Maréchal¹,

Plaghki²

1979

The Journal of General Physiology

197

214

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Frog sartorius muscles tetanized isometrically were released at a constant velocity from lengths lL to ls (A/ = l L -ls; ls >/0). The tension P~s redeveloped after the release was lower than the isometric tension Ps at Is, and higher than the isometric tension PL at lL. The tension deficit D is defined as the difference Ps-P*. The timing of the release during the tetanus did not influence D. D/Po was proportional to Al/lo. The proportionality constant k was equal to 1.35 -+ 0.19 (n = 8) when the velocity of release was 2.5 mm/s. When the muscles were released the same Al, D was found to be an exponential decreasing function of the velocity. The tension deficit was also found in experiments performed in the region ls < lo. The proportionality constant k was smaller, but the influence of the velocity of the release on D was not modified. When the velocity of the release was changed during the release, D changed accordingly, showing that the effects of Al and V are multiplicative. These facts suggest a working hypothesis based on the concept that the actin filaments which enter the overlap region during a release are strained by the tetanic stress and therefore unable to make normal cross-bridges.

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“…~la.6" F o r isometric tension developed at l e n g t h , / 0 , a n d isotonic contraction after- (Matsumoto, 1967), and T = 0.109 sec when l/lo = 1.0. Substituting these values in the above equation, l0 dP 30.6 P F-~o dl----~ = ~ + 7.65 (see Fig.…”

Section: If the Exponential Tension-time Course Is Approximately Corrmentioning

confidence: 99%

“…Isotonic contractions were studied with a series of afterloads and the shortenings were imposed at intervals no shorter than 10 rain. For each muscle, a whole family of shortening vs. time curves was obtained, each curve within the series differing from the others in the amount of afterload (Matsumoto, 1965(Matsumoto, , 1967.…”

Section: E X P E R I M E N T a Lmentioning

confidence: 99%

Theoretical Series Elastic Element Length in Rana pipiens Sartorius Muscles

Matsumoto

1967

The Journal of General Physiology

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A B S T R A C T Assuming a two component system for the muscle, a series elastic element and a contractile component, the analyses of the isotonic and isometric data points were related to obtain the series elastic stiffness, dP/dl,, from the relation, dP dP dt dP 1From the isometric data, dP/dt was obtained and shortening velocity, v, was a result of the isotonic experiments. Substituting (Po --P ) / T for dP/dt and (P0 --P ) / ( P + a) times b for v, dP/dl, = (P + a) /bT, where P < P0, and a, b are constants for any lengths l ~ l0 (Matsumoto, 1965). If the isometric tension and the shortening velocity are recorded for a given muscle length, 10, although the series elastic, l,, and the contractile component, 1,, are changing, the total muscle length, l0 remains fixed and therefore the time constant, T. Integrating, f v e dP 1 f z , o P + a -b T ~o dl~'the stress-strain relation for the series elastic element, is obtained; l,,0 ----ls + lo0 where /co equals the contractile component length for a muscle exerting a tension of P0-For a given P / P o , ls is uniquely determined and must be the same whether on the isotonic or isometric length-tensiontime curve. In fact, a locus on one surface curve can be associated with the corresponding locus on the other.

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

Cited by 23 publications

References 4 publications

Effects of Various Inotropic Interventions on the Dynamic Properties of the Contractile Elements in Heart Muscle of the Cat

Effects of Various Inotropic Interventions on the Dynamic Properties of the Contractile Elements in Heart Muscle of the Cat

The deficit of the isometric tetanic tension redeveloped after a release of frog muscle at a constant velocity.

Theoretical Series Elastic Element Length in Rana pipiens Sartorius Muscles

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