Energy Production in Cardiac Isotonic Contractions

The energy output of rabbit papillary muscle is examined and it is shown that there is more energy liberated in an afterloaded isotonic contraction than in an "equivalent" isometric contraction. This statement holds true regardless of whether equivalence is based on the proposition that tension or the time integral of tension is the best index of muscle energy expenditure. Besides the external work performed there is additional heat production in isotonic contractions and this heat increases as the afterload is decreased. The additional heat is more evident when tension rather than the time integral of tension is made the determinant of energy expenditure. It is shown in single contractions that the rate of isotonic heat production, regardless of afterload size, never exceeds the heat rate recorded in an isometric contraction at the same initial length. Experiments reveal no simple linear correlation between isotonic energy output and contractile element work. Problems associated with the compartmentalization of the energy output of a contraction are discussed.     

A phenomenological model for estimating metabolic energy consumption in muscle contraction

A phenomenological model for muscle energy consumption was developed and used in conjunction with a simple Hill-type model for muscle contraction. The model was used to address two questions. First, can an empirical model of muscle energetics accurately represent the total energetic behavior of frog muscle in isometric, isotonic, and isokinetic contractions? And second, how does such a model perform in a large-scale, multiple-muscle model of human walking? Four simulations were conducted with frog sartorius muscle under full excitation: an isometric contraction, a set of isotonic contractions with the muscle shortening a constant distance under various applied loads, a set of isotonic contractions with the muscle shortening over various distances under a constant load, and an isokinetic contraction in lengthening. The model calculations were evaluated against results of similar thermal in vitro experiments performed on frog sartorius muscle. The energetics model was then incorporated into a large-scale, multiple-muscle model of the human body for the purpose of predicting energy consumption during normal walking. The total energy estimated by the model accurately reflected the observed experimental behavior of frog muscle for an isometric contraction. The model also accurately reproduced the experimental behavior of frog muscle heat production under isotonic shortening and isokinetic lengthening conditions. The estimated rate of metabolic energy consumption for walking was 29% higher than the value typically obtained from gait measurements.     

A Monte Carlo analysis of muscle force estimation sensitivity to muscle-tendon properties using a Hill-based muscle model

Surface electromyography driven models are desirable for estimating subject-specific muscle forces. However, these models include parameters that come from an array of sources, thus creating uncertainty in the model-estimated force. In this study, we used Monte-Carlo simulations to evaluate the sensitivity of Hill-based model muscle forces to changes in 11 parameters in the muscle-tendon unit morphological properties and in the model force-length and force-velocity relationships. We decomposed the force variability and ranked the sensitivity of the model to the underlying parameters using the Variogram Analysis of Response Surfaces. For the analyzed running experiments and the adopted Hill model structure, our results show that the parameters are separable into four groups, where the parameters in each group have a synergistic contribution to the model global sensitivity. The first group consists of the maximum isometric force and the pennation angle. The second group contains the optimal fiber length, the tendon slack length, the tendon reference strain and the tendon shape factor. The third group contains the width and shape at the extremities of the active contractile element, along with the maximum contraction velocity and the curvature constant in the force-velocity curve. The fourth group consisted only of the force enhancement during eccentric contraction. The first two groups revealed the largest influence on the output force sensitivity. As many input parameters are difficult to measure and impact estimated forces, we propose that model estimates be presented with confidence intervals as well as inter-parameter relationships, to encourage users to explicitly consider the model uncertainty.     

A dynamic model of smooth muscle contraction

A dynamic model of smooth muscle contraction is presented and is compared with the mechanical properties of vascular smooth muscle in the rat portal vein. The model is based on the sliding filament theory and the assumption that force is produced by cross-bridges extending from the myosin to the actin filaments. Thus, the fundamental aspects of the model are also potentially applicable to skeletal muscle. The main concept of the model is that the transfer of energy via the cross-bridges can be described as a 'friction clutch' mechanism. It is shown that a mathematical formulation of this concept gives rise to a model that agrees well with experimental observations on smooth muscle mechanics under isotonic as well as isometric conditions. It is noted that the model, without any ad hoc assumptions, displays a nonhyperbolic force-velocity relationship in its high-force portion and that it is able to maintain isometric force in conditions of reduced maximum contraction velocity. Both these findings are consistent with new experimental observations on smooth muscle mechanics cannot be accounted for by the classical Hill model.     

Calcium dynamics and vasomotion in arteries subject to isometric, isobaric, and isotonic conditions

In vitro, different techniques are used to study the smooth muscle cells’ calcium dynamics and contraction/relaxation mechanisms on arteries. Most experimental studies use either an isometric or an isobaric setup. However, in vivo, a blood vessel is neither isobaric nor isometric nor isotonic, as it is continuously submitted to intraluminal pressure variations arising from heart beat. We use a theoretical model of the smooth muscle calcium and arterial radius dynamics to determine whether results may be considerably different depending on the experimental conditions (isometric, isobaric, isotonic, or cyclic pressure variations). We show that isobaric conditions appear to be more realistic than isometric or isotonic situations, as the calcium dynamics is similar under cyclic intraluminal pressure variations (in vivo-like situation) and under a constant pressure (isobaric situation). The arterial contraction is less pronounced in isotonic than in isobaric conditions, and the vasoconstrictor sensitivity higher in isometric than isobaric or isotonic conditions, in agreement with experimental observations. Interestingly, the model predicts that isometric conditions may generate artifacts like the coexistence of multiple stable states. We have verified this model prediction experimentally using rat mesenteric arteries mounted on a wire myograph and stimulated with phenylephrine.     

A model of muscle contraction based on the Langevin equation with actomyosin potentials

We propose a muscle contraction model that is essentially a model of the motion of myosin motors as described by a Langevin equation. This model involves one-dimensional numerical calculations wherein the total force is the sum of a viscous force proportional to the myosin head velocity, a white Gaussian noise produced by random forces and other potential forces originating from the actomyosin structure and intra-molecular charges. We calculate the velocity of a single myosin on an actin filament to be 4.9–49 μm/s, depending on the viscosity between the actomyosin molecules. A myosin filament with a hundred myosin heads is used to simulate the contractions of a half-sarcomere within the skeletal muscle. The force response due to a quick release in the isometric contraction is simulated using a process wherein crossbridges are changed forcibly from one state to another. In contrast, the force response to a quick stretch is simulated using purely mechanical characteristics. We simulate the force–velocity relation and energy efficiency in the isotonic contraction and adenosine triphosphate consumption. The simulation results are in good agreement with the experimental results. We show that the Langevin equation for the actomyosin potentials can be modified statistically to become an existing muscle model that uses Maxwell elements.     

Muscle contraction history: modified Hill versus an exponential decay model

In recent years, it has been recognised that improvements to classic models of muscle mechanical behaviour are often necessary for properly modelling co-ordinated multi-joint actions. In this respect, the purpose of the present study was to improve on modelling stretch-induced force enhancement and shortening-induced force depression of muscle contraction. For this purpose, two models were used: a modified Hill model and a model based loosely on mechano-chemistry of the cross-bridge cycle (exponential decay model). The models were compared with a classic Hill model and experimental data. Parameter values were based, as much as possible, on experimental findings in the literature, and tested with new experiments on the gastrocnemius of the rat. Both models describe many features of slow-ramp movements well during short contractions (300–500 ms), but long-duration behaviour is described only partly. The exponential decay model does not incorporate a force–velocity curve. Therefore, its good performance indicates that the status of the classic force–velocity characteristic may have to be reconsidered. Like movement-induced force depression and enhancement, it seems a particular manifestation of time-dependent force behaviour of muscle, rather than a fundamental property of muscle (like the length–tension curve). It is argued that a combination of the exponential decay model (or other models based on the mechano-chemistry of contraction) and structurally based models may be fruitful in explaining this time-dependent contraction behaviour. Furthermore, not in the least because of its relative simplicity, the exponential decay model may prove more suitable for modelling multi-joint movements than the Hill model. Received: 19 March 1999 / Accepted in revised form: 9 June 2000     

A new model for calculating muscle forces from electromyograms

A muscle model is described that uses electromyogram (EMG), muscle length and speed of contraction to predict muscle force. Physiological parameters are the Hill constants and the shape of the twitch response to a single stimulus. The model was incorporated in a jaw model of the rabbit and tested by predicting the bite force produced by the jaw muscles during mastication. The time course of the calculated force appeared to match the bite force, measured in vivo by a strain gauge, applied to the bone below the teeth. The variation in peak strain amplitude from cycle to cycle correlated with the variation predicted by the model. The peak amplitude of the integrated EMGs of individual jaw muscles showed an average correlation with peak strain of 0.41. Use of the sum of the available peak amplitudes, weighted according to their effect upon the bite force increased the correlation to 0.46; the model predicted bite forces showed a correlation of 0.57 with the strain. The increase in correlation was statistically significant. The muscle forces were calculated using a minimum number of easily obtainable constants.     

A 3D skeletal muscle model coupled with active contraction of muscle fibres and hyperelastic behaviour

This paper presents a three-dimensional finite element model of skeletal muscle which was developed to simulate active and passive non-linear mechanical behaviours of the muscle during lengthening or shortening under either quasi-static or dynamic condition. Constitutive relation of the muscle was determined by using a strain energy approach, while active contraction behaviour of the muscle fibre was simulated by establishing a numerical algorithm based on the concept of the Hill's three-element muscle model. The proposed numerical algorithm could be used to predict concentric, eccentric, isometric and isotonic contraction behaviours of the muscle. The proposed numerical algorithm and constitutive model for the muscle were derived and implemented into a non-linear large deformation finite element programme ABAQUS by using user-defined material subroutines. A number of scenarios have been used to demonstrate capability of the model for simulating both quasi-static and dynamic response of the muscle. Validation of the proposed model has been performed by comparing the simulated results with the experimental ones of frog gastrocenemius muscle deformation. The effects of the fusiform muscle geometry and fibre orientation on the stress and fibre stretch distributions of frog muscle during isotonic contraction have also been investigated by using the proposed model. The predictability of the present model for dynamic response of the muscle has been demonstrated by simulating the extension of a squid tentacle during a strike to catch prey.     

Adenosine 5''-triphosphate consumption by smooth muscle as predicted by the coupled four-state crossbridge model.

We have proposed a four-state crossbridge model to explain contraction and the latch state in arterial smooth muscle. Ca(2+)-dependent crossbridge phosphorylation was the only postulated regulatory mechanism and the latchbridge (a dephosphorylated, attached crossbridge) was the only novel element in the model. In this study, we used the model to predict rates of ATP consumption by crossbridge phosphorylation (JPhos) and cycling (JCycle) during isometric and isotonic contractions in arterial smooth muscle; then we compared model predictions with experimental data. The model predicted that JPhos and JCycle were similar in magnitude in isometric contractions, and both increased almost linearly with myosin phosphorylation. The predicted relationship between isometric stress and ATP consumption was quasihyperbolic, but approximately linear when myosin phosphorylation was below 35%, in agreement with most of the available data. Muscle shortening increased the predicted values of JCycle up to 3.7-fold depending on shortening velocity and the level of myosin phosphorylation. The predicted maximum work output per ATP was 7.4-7.8 kJ/mol ATP and was relatively insensitive to changes in myosin phosphorylation. The predicted increase in JCycle with shortening was in agreement with available data, but the model prediction that work output per ATP was insensitive to changes in myosin phosphorylation was unexpected and remains to be tested in future experiments.     

Muscles as a chain of the Hill three element model for calculating asynchronicity of excitation in assessing the "active state" during isotonic contraction

The muscle is described by the chain of Hill three-element models. The expression is obtained of the index of chemical energy transformation into the mechanical one ("active state") as a function of the velocity of the excitation wave propagation along the chain under isotonic contraction.     

Maximum force production: why are crabs so strong?

Durophagous crabs successfully hunt hard-shelled prey by subjecting them to extremely strong biting forces using their claws. Here I show that, for a given body mass, six species of Cancer crabs (Cancer antennarius, Cancer branneri, Cancer gracilis, Cancer magister, Cancer oregonensis and Cancer productus) were able to exert mean maximum biting forces greater than the forces exerted in any other activity by most other animals. These strong biting forces were in part a result of the high stresses (740-1350 kN m(-2)) generated by the claw closer muscle. Furthermore, the maximum muscle stress increased with increasing mean resting sarcomere length (10-18 microm) for the closer muscle of the claws of these six Cancer species. A more extensive analysis incorporating published data on muscle stresses in other animal groups revealed that stress scales isometrically with the resting sarcomere length among species, as predicted by the sliding filament model of muscle contraction. Therefore, muscle or filament traits other than a very long mean sarcomere length need not be invoked in explaining the high stresses generated by crustacean claws.     

Optimal design of vertebrate and insect sarcomeres

This paper offers a model for the normalized length-tension relation of a muscle fiber based upon sarcomere design. Comparison with measurements published by Gordon et al. ('66) shows an accurate fit as long as the inhomogeneity of sarcomere length in a single muscle fiber is taken into account. Sequential change of filament length and the length of the cross-bridge-free zone leads the model to suggest that most vertebrate sarcomeres tested match the condition of optimal construction for the output of mechanical energy over a full sarcomere contraction movement. Joint optimization of all three morphometric parameters suggests that a slightly better (0.3%) design is theoretically possible. However, this theoretical sarcomere, optimally designed for the conversion of energy, has a low normalized contraction velocity; it provides a poorer match to the combined functional demands of high energy output and high contraction velocity than the real sarcomeres of vertebrates. The sarcomeres in fish myotomes appear to be built suboptimally for isometric contraction, but built optimally for that shortening velocity generating maximum power. During swimming, these muscles do indeed contract concentrically only. The sarcomeres of insect asynchronous flight muscles contract only slightly. They are not built optimally for maximum output of energy across the full range of contraction encountered in vertebrate sarcomeres, but are built almost optimally for the contraction range that they do in fact employ.     

An innovative work-loop calorimeter for in vitro measurement of the mechanics and energetics of working cardiac trabeculae

We describe a unique work-loop calorimeter with which we can measure, simultaneously, the rate of heat production and force-length work output of isolated cardiac trabeculae. The mechanics of the force-length work-loop contraction mimic those of the pressure-volume work-loops experienced by the heart. Within the measurement chamber of a flow-through microcalorimeter, a trabecula is electrically stimulated to respond, under software control, in one of three modes: fixed-end, isometric, or isotonic. In each mode, software controls the position of a linear motor, with feedback from muscle force, to adjust muscle length in the desired temporal sequence. In the case of a work-loop contraction, the software achieves seamless transitions between phases of length control (isometric contraction, isometric relaxation, and restoration of resting muscle length) and force control (isotonic shortening). The area enclosed by the resulting force-length loop represents the work done by the trabecula. The change of enthalpy expended by the muscle is given by the sum of the work term and the associated amount of evolved heat. With these simultaneous measurements, we provide the first estimation of suprabasal, net mechanical efficiency (ratio of work to change of enthalpy) of mammalian cardiac trabeculae. The maximum efficiency is at the vicinity of 12%.     

Hill's equation applied to reconstituted contractile collagen.

A new type of automatic force-displacement recording myograph has been developed to measure the contraction–relaxation characteristics of contractile systems. The device produces a polytonic (variable-force) load and therefore provides a more realistic measurement than either isometric or isotonic apparatus. Measurements on collagen that was first well ground and then extruded into a reconstituted thin tape show contraction and relaxation behaviour that can be characterized by a slightly modified form of Hill's 1938 equation. The characteristic parameters of the Hill equation determined for the reconstituted collagen were remarkably similar to those of intact muscle tissue.     

Complex myograph allows the examination of complex muscle contractions for the assessment of muscle force, shortening, velocity, and work in vivo

Background

The devices used for in vivo examination of muscle contractions assess only pure force contractions and the so-called isokinetic contractions. In isokinetic experiments, the extremity and its muscle are artificially moved with constant velocity by the measuring device, while a tetanic contraction is induced in the muscle, either by electrical stimulation or by maximal voluntary activation. With these systems, experiments cannot be performed at pre-defined, constant muscle length, single contractions cannot be evaluated individually and the separate examination of the isometric and the isotonic components of single contractions is not possible.

Methods

The myograph presented in our study has two newly developed technical units, i.e. a). a counterforce unit which can load the muscle with an adjustable, but constant force and b). a length-adjusting unit which allows for both the stretching and the contraction length to be infinitely adjustable independently of one another. The two units support the examination of complex types of contraction and store the counterforce and length-adjusting settings, so that these conditions may be accurately reapplied in later sessions.

Results

The measurement examples presented show that the muscle can be brought to every possible pre-stretching length and that single isotonic or complex isometric-isotonic contractions may be performed at every length. The applied forces act during different phases of contraction, resulting into different pre- and after-loads that can be kept constant - uninfluenced by the contraction. Maximal values for force, shortening, velocity and work may be obtained for individual muscles. This offers the possibility to obtain information on the muscle status and to monitor its changes under non-invasive measurement conditions.

Conclusion

With the Complex Myograph, the whole spectrum of a muscle's mechanical characteristics may be assessed.     

肌肉收缩Hill特性式的理论研究

从肌球蛋白工作循环的机械化学偶联模型出发,利用化学动力学方法和生物化学热力学原理,结合肌球蛋白单分子实验结果,从能量转化的观点给出了肌肉收缩的Hill特性式,加深了对Hill特性式及肌肉收缩过程中能量转化的理解,在整合肌球蛋白单分子性质与肌肉收缩宏观性质的信息方面做了尝试。     

Mechanical control of the rising phase of contraction of frog skeletal and cardiac muscle

The effect of shortening on contractile activity was studied in experiments in which shortening during the rising phase of an isotonic contraction was suddenly stopped. At the same muscle length and the same time after stimulation the rise in tension was much faster, if preceded by shortening, than during an isometric contraction, demonstrating an increase in contractile activity. In this experiment the rate of tension rise determined in various phases of contraction was proportional to the rate of isotonic shortening at the same time after stimulation. Therefore, the time course of the isotonic rising phase could be derived from the tension rise after shortening. The rate of isotonic shortening was found to be unrelated to the tension generated at various lengths and to correspond closely to the activation process induced by shortening. The length response explains differences between isotonic and isometric contractions with regard to energy release (Fenn effect) and time relations. These results extend previous work which showed that shortening during later phases of a twitch prolongs, while lengthening abbreviates contraction. Thus the length responses, which have been called shortening activation and lengthening deactivation, control activity throughout an isotonic twitch.     

Methodological aspects of SEMG recordings for force estimation – A tutorial and review

Insight into the magnitude of muscle forces is important in biomechanics research, for example because muscle forces are the main determinants of joint loading. Unfortunately muscle forces cannot be calculated directly and can only be measured using invasive procedures. Therefore, estimates of muscle force based on surface EMG measurements are frequently used. This review discusses the problems associated with surface EMG in muscle force estimation and the solutions that novel methodological developments provide to this problem. First, some basic aspects of muscle activity and EMG are reviewed and related to EMG amplitude estimation. The main methodological issues in EMG amplitude estimation are precision and representativeness. Lack of precision arises directly from the stochastic nature of the EMG signal as the summation of a series of randomly occurring polyphasic motor unit potentials and the resulting random constructive and destructive (phase cancellation) superimpositions. Representativeness is an issue due the structural and functional heterogeneity of muscles. Novel methods, i.e. multi-channel monopolar EMG and high-pass filtering or whitening of conventional bipolar EMG allow substantially less variable estimates of the EMG amplitude and yield better estimates of muscle force by (1) reducing effects of phase cancellation, and (2) adequate representation of the heterogeneous activity of motor units within a muscle. With such methods, highly accurate predictions of force, even of the minute force fluctuations that occur during an isometric and isotonic contraction have been achieved. For dynamic contractions, EMG-based force estimates are confounded by the effects of muscle length and contraction velocity on force producing capacity. These contractions require EMG amplitude estimates to be combined with modeling of muscle contraction dynamics to achieve valid force predictions.     

The influence of the way the muscle force is modeled on the predicted results obtained by solving indeterminate problems for a fast elbow flexion

A critical point in models of the human limbs when the aim is to investigate the motor control is the muscle model. More often the mechanical output of a muscle is considered as one musculotendon force that is a design variable in optimization tasks solved predominantly by static optimization. For dynamic conditions, the relationship between the developed force, the length and the contraction velocity of a muscle becomes important and rheological muscle models can be incorporated in the optimization tasks. Here the muscle activation can be a design variable as well. Recently a new muscle model was proposed. A muscle is considered as a mixture of motor units (MUs) with different peculiarities and the muscle force is calculated as a sum of the MUs twitches. The aim of the paper is to compare these three ways for presenting the muscle force. Fast elbow flexion is investigated using a planar model with five muscles. It is concluded that the rheological models are suitable for calculation of the current maximal muscle forces that can be used as weight factors in the objective functions. The model based on MUs has many advantages for precise investigations of motor control. Such muscle presentation can explain the muscle co-contraction and the role of the fast and the slow MUs. The relationship between the MUs activation and the mechanical output is more clear and closer to the reality.