Parallel Elastic Elements Research Articles

Postischemic Ventricular Function of Stunned Myocardium: A Modeling Perspective

Myocardial stunning is a prolonged postischemic dysfunction that compromises ventricular performance. Several contributing factors have been identified, but the exact mechanism of myocardial stunning remains unclear. A computer model of the ventricle can be effective in modeling the dominant observable features of myocardial stunning. A regional ventricular model is first introduced here, followed by a single cardiac muscle fiber model. The regional model is based on a previously developed multicompartment model with normal and ischemic zones incorporating time-varying elastance and viscoelastic properties. The mathematical model of the single cardiac muscle fiber consisted of three elements: a contractile element, a series elastic element, and a parallel elastic element. On the basis of the classic force-velocity-length relations, the single muscle model could generate muscle length waveforms based on time-dependent force and contractile stiffness functions. By entering the same parameter values used in the regional ventricular model, and by reducing contractile stiffness function or the rates of activation and deactivation, the three-element model could mimic similar results observed in canine experiments.

Modelling of knee joint muscles during the swing phase of gait––a forward dynamics approach using MATLAB/Simulink

The present study primarily aims to predict the force (both active and passive) of eight main muscle–tendon actuators crossing the knee joint during the swing cycle. The knee-joint model was restricted and simplified to motion in the sagittal plane only. It was largely built in mathematical notation and was simulated using a high-performance computing and programming tool, MATLAB, along with Simulink. The eight muscles––Biceps Femoris Short Head (BFSH), three heads of Vasti (VL, VM and VI), Rectus Femoris (RF) and the Hamstrings (BFLH, SemiM and SemiT) were each modelled as a two-element, lumped-parameter entity, in series with tendon, which was assumed to be elastic with a known stress–strain relationship. The mechanical behaviour of muscle was described by a Hill-type contractile element which models the active force–length characteristic of muscle fascicles, and a parallel-elastic element which models its passive properties. The knee joint model was simulated for a swing period of 0.4 s and the knee flexed to a maximum of approximately 63°, providing safe toe clearance, and eventually extended to about 4° to prepare for the next heel strike. A comparison of the simulation results in this study with reported data warrants confidence in the prediction of muscle and tendon force. Based on further analysis and quantitative comparison of simulation results, functionally and anatomically similar muscles were eventually approximated with a muscle group and fusiform muscle fibres were favoured over pennate fibres in the muscle–tendon model.

Can a Single Muscle Fiber Model the Features of Myocardial Stunning

The exact mechanisms that cause myocardial stunning are still unclear. We previously utilized a computer model of the ventricle that was effective in modeling the dominant observable features of stunning, but it was not simple to implement. This led to the design of a single muscle fiber model. The mathematical model of a muscle fiber consisted of three elements: a contractile element, a series elastic element, and a parallel elastic element. The model created length waveforms based on time-dependent force and contractile stiffness functions. This model was initially evaluated by entering the same regional parameter values used in the global dual region ventricular model. First a reduction of the contractile stiffness function was applied by reducing the peak stiffness by 30%, and then the rates of activation and deactivation were reduced by 20% while maintaining the peak values constant. The three-element model produced results very similar to the canine and ventricular model. Thus, it is concluded that the simpler three-element model provides an accurate model of the myocardial tissue and its deficiencies during stunning.

A musculoskeletal model of the knee for evaluating ligament forces during isometric contractions

A model of the knee in the sagittal plane was developed to study the forces in the ligaments induced by isometric contractions of the extensor and flexor muscles. The geometry of the distal femur was obtained from cadaver data. The tibial plateau and patellar facet were modeled as flat surfaces. Eleven elastic elements were used to describe the mechanical behavior of the anterior and posterior cruciate ligaments (ACL and PCL), the medial and lateral collateral ligaments (MCL and LCL), and the posterior capsule. The model knee was actuated by 11 musculotendinous units, each muscle represented by a Hill-type contractile element, a series-elastic element, and a parallel-elastic element. Tendon was assumed to be elastic. The response of the model to anterior-posterior drawer suggests that the geometrical and mechanical properties of the model ligaments approximate the behavior of real ligaments in the intact knee. Calculations for a simulated quadriceps leg raise indicate further that the two-dimensional model reproduces the response of the three-dimensional knee under similar conditions of loading and constraint. During maximum isometric contractions of the quadriceps, the model ACL is loaded from full extension to 80°C of flexion; the model PCL is loaded at 70° of flexion and greater. For maximum isometric extension, ACL forces in the range 0–20° of flexion depend most heavily upon the force-length properties of the quadriceps. At flexion angles greater than 20°, cruciate ligament forces are determined by the geometry of the articulating surfaces of the bones. During isolated contractions of the hamstrings and gastrocnemius muscles, the model ACL is loaded from full extension to 10° of flexion; the model PCL is loaded at all flexion angles greater than 10°. Isolated contractions of the flexor muscles cannot unload the ACL near full extension, as the behavior of the ACL in this region is governed by the shapes of the bones. At 10° of flexion or greater, the overall pattern of PCL force is explained by the force-length properties of the hamstrings and by the geometrical arrangement of the flexor muscles about the knee.

Influence of the parameters of a human triceps surae muscle model on the isometric torque-angle relationship.

This study investigates the influence of parameter values of the human triceps surae muscle on the torque-angle relationship. The model used consisted of three units, each containing a contractile, a series elastic and a parallel elastic element. Parameter values were based on morphological characteristics, which made it possible to model individual units. However, for a number of parameters the values reported in the literature vary considerably. It was investigated how sensitive model results were for variation of these parameters. Slack length of the series elastic element, mean moment arm, maximum force, and length of the contractile element appeared to be the most important determinants of the behavior. For mean moment arm and contractile element length, morphology-based methods of estimation could be recommended. Slack length and maximum force were obtained through optimization. It was concluded that the model does not contain parameters on which its output depends strongly and which are difficult to estimate as well, with two exceptions: slack length of the series elastic element and maximum force.

Identification of nonlinear model of ankle joint dynamics during electrical stimulation of soleus.

The mechanical impedance of the ankle joint was estimated in two conditions: during submaximal surface electrical stimulation of the soleus muscle, and with no stimulation applied. Both neurologically intact (n = 5) and spinal cord injured subjects (n = 4) were used. The mechanical impedance was measured by applying angular step and constant velocity (13-100 degrees s-1) perturbations at 10 degrees to the ankle and measuring the resulting changes in torque. A five-element lumped model consisting of an inertial element, a parallel elastic element, and an elastic element in series with a viscous element and a pure tension generator produced a good fit for predicting the compliance characteristics of the ankle for both the relaxed and stimulated conditions. The elastic elements were piecewise linear with different values for the dorsiflexion and plantarflexion directions. The viscous element was velocity-dependent and it decreased in value as the velocity increased. The average torque error between the measured and model's response during soleus stimulation was 10.56% for the dorsiflexed and 11.93% for the plantarflexed perturbations. However, the average error was skewed by several subjects who had excessive error, due to volitional intervention or flexor withdrawal reflex. The average model error for the perturbations without stimulation was 7.12% for dorsiflexed and 5.58% for plantarflexed perturbations.

Storage and utilization of elastic strain energy during jumping.

Based upon the optimal control solutions to a maximum-height countermovement jump (CMJ) and a maximum-height squat jump (SJ), this paper provides a quantitative description of how tendons and the elastic elements of muscle store and deliver energy during vertical jumping. After confirming the ability of the model to replicate the major features of each jump (i.e. muscle activation patterns, body-segmental motions, ground reaction forces, jump height, and total ground contact time), the time histories of the forces and shortening velocities of all the musculotendon actuators in the model were used to calculate the work done on the skeleton by tendons as well as the series-elastic elements, the parallel-elastic elements, and the contractile elements of muscle. We found that all the elastic tissues delivered nearly the same amount of energy to the skeleton during a CMJ and an SJ. The reason is twofold: first, nearly as much elastic strain energy was stored during the SJ as the CMJ; second, more stored elastic strain energy was lost as heat during the CMJ. There was also a difference in the way energy was stored during each jump. During the CMJ, strain energy stored in the elastic tissues came primarily from the gravitational potential energy of the skeleton as the more proximal extensor muscles were stretched during the downward phase of the jump. During the SJ, on the other hand, energy stored in the elastic tissues came primarily from the contractile elements as they did work to stretch the tendons and the series-elastic elements of the muscles. Increasing tendon compliance in the model led to an increase in elastic energy storage and utilization, but it also decreased the amount of energy delivered by the contractile elements to the skeleton. Jump height therefore remained almost the same for both jumps. These results suggest that elastic energy storage and utilization enhance jumping efficiency much more than overall jumping performance.

A musculotendon model of the fatigue profiles of paralyzed quadriceps muscle under FES.

In a previous work, we studied the mechanical and the metabolic profiles of fatigue of paralyzed quadriceps muscle under activation by FES. The metabolic state of the muscle during stimulation of paraplegic patients was monitored, simultaneously with the decaying force, by using 31P nuclear magnetic resonance spectroscopy. In the present work, a musculotendon model was developed to enable prediction of the force output during continuous electrical stimulation. The model consisted of five elements, including the tendon, the parallel elastic, contractile and damper muscle elements, as well as the muscle mass. The mechanism of the contractile element was based upon the length-tension and the velocity-tension curves, the activation trajectory, and the experimentally obtained relationship between force and intracellular pH. In the equations obtained, three sets of parameters were used: 1) general muscle parameters, associated with the length-tension curves of tendon, fascia, and muscle and the velocity-tension curve of the contractile element; 2) specific anthropometric parameters of the muscle; and 3) fatigue parameters which were obtained from our previously recorded experimental data. The model was formulated to allow prediction of the quadriceps muscle force under dynamic activation and at various levels of stimulation. The model solution was for isometric contraction in supermaximal stimulation, and it provided the force decaying profiles, which were compared to those obtained experimentally. The parameters yielding the best fit between the model and the experimental results were indicated. Particularly, two muscle nonspecific parameters, namely, the muscle stress parameter and the parameter representing the ratio between the muscle's slack length and its length in vivo at various knee angles, were determined using the model. The muscle stress parameter was found to be between 60 and 64 N/cm2, and the length ratio was 0.952, 0.935, 0.920, and 0.901 for the 0, 30, 60, and 90 degrees knee angle, respectively. Finally, a sensitivity analysis was conducted of the model to perturbations of these two estimated parameters, revealing that the model was sensitive to these parameters.

Elastic energy storage in vertical jumping

s-International Society of Biomechanics XIII Congress 1991 691 ELASTIC ENERGY STORAGE IN VERTICAL JUMPING Frank C. Anderson and Marcus G. Pandy Department of Kinesiology and Health Education The University of Texas at Austin, Austin, Texas 787 12, USA. Based upon the optimal control solutions to a maximum-height countermovement jump (CMJ) and squat jump (SJ), the mechanisms by which energy is stored in the elastic tissues and subsequently delivered to the skeleton during jumping were investigated. The body was modeled as a four-segment, planar linkage, actuated by eight musculotendinous units. After confirming the ability of the model to replicate the major features of each jump, the time histories of the actuator forces and velocities derived from the model were used to calculate the work done on the skeleton by tendon, as well as the series-elastic elements, parallel-elastic elements, and contractile elements of muscle. The elastic tissues were found to deliver nearly the same amount of energy to the skeleton during both jumps, which explains why our model predicted only a 1 cm difference in jump height between a CMJ and SJ. However, the mechanism of elastic energy storage during each jump was different. During a CMJ, strain energy in the elastic tissues originated mainly as gravitational potential energy of the skeleton. During a SJ, on the other hand, strain energy was stored in the elastic tissues as the contractile elements did work to stretch both tendon and the series elastic elements. Our results suggest, therefore, that elastic energy storage and utilization is a determinant of jumping efficiency rather than of overall performance. Supported by the Whitaker Foundation and NASA/Ames Research Center. STRATEGIES IN HUMAN JUMPING Michael Voigt, Erik B. Simonsen, Poul Dyhre-Poulsen’ and Finn Bojsen-Moller. Laboratory for Functional Anatomy, Dept. Anat. C., *Institute of Neurophysiology, Universiry of Copenhagen. Denmark. The purpose of this work was to study the individual differences in jumping tasks performed by highly skilled jumpers. Four male elite volleyball players participated in the study. The performed 6 different explosive jumping tasks. The jumps was filmed with 500 frames pr. second in the sag&al plane. Maximal voluntary contractions, ground reaction forces and muscle activity (EMG) from 7 muscles of the right leg was reco&d. The subjects showed extreme and opposite characteristics. One with very fast movements, and a high net extensor power output from the knee joints compared to the ankle and hip joints. The other had longer take off times, a lower net extensor power output from the knee joints and with the total net power output more evenly distributed between ankle, knee and hip joints. The differences in mechanical net power output were reflected in the EMG patterns and indicated a pronounced transportation of mechanical power from the hip to the knee via b&attic&r muscles. The two other subjects showed coordination patterns between these two extremes. It was conch&d that even highly special&d jumpers show very different coordination patterns during jumping, especially with respect co-activation of monoand biarticular muscles. MODEL OF MUSCLE FIBRS WITH CONTROLLABLE RECRUITING A. Guskov, A.Eliutin Thomas Alva Research Centre, Moscow, USSR A. Vorobiev Central Research Institute of Sport, Moscow, USSR G. Ariel Ariel Life Systems Inc., La Jolla, CA, USA A finite muscle fiber model is proposed. As distinctive features the model incorporates: a formalized rule of recruiting of elementary motor units (EMU) along the fibre and a scheme of EMU with an absolutely rigid shell. Two internal panmters are introduced: the deformation of a contracted fiber and of a passive visco-elastic fiber, which determine the parameters of an EMU and the fiber. Thus, the 3-D diagram of static deformation of a model fibre in co-ordinates extension force is constituted. A significant feature of the diagram is it's dependence of the activation level. The model discriminates free length and natural length of the fibre. It is shown that the isotonic mode for an EMU is not isotonic for the fibre. A possible model with four structural parameters is described, incorporating 2 parameters of the viscoelastic state of an RM'IJ, linear percentage of fiber contraction and the recruitment law of the EMU. This set of parameters allows describing the existing experimental data with fair precision.

The biophysics and biochemistry of smooth muscle contraction.

In this review the biophysics and biochemistry of smooth muscle contraction are dealt with. We describe a new model for the study of bronchial smooth muscle, which facilitates study of cellular contractile mechanisms. A new concept emerging is that study of steady-state mechanical parameters such as maximal isometric force (Po) velocity is inadequate because two types of crossbridges (normally cycling (NBR) and latch) seem to be sequentially active during smooth muscle contraction. Thus quick-release techniques are required to characterize the force-velocity properties of the two types of bridges. Pathophysiological processes that affect the muscle's shortening ability seem to affect the early NBRs only. With respect to maximal shortening capacity of the smooth muscle, the role of loading is very important. The differences between isotonic, elastic, and viscous loading are considerable. Ultimately, the time course and magnitude of loading should exactly resemble that operative in vivo. Once again, it is the characteristic of loading in the early phase of contraction that is crucial, as most of the shortening in smooth muscle occurs early in the contraction. While the maximum force developed by smooth muscle per unit cross-sectional area is the same as for striated muscle, the velocity is 50 times less. The properties of the series and parallel elastic elements of smooth muscle are described. The latter, when in compression mode, acts as an internal resistance to shortening and probably limits it. Isotonic relaxation has therefore not been studied in smooth muscle. We have developed a shortening parameter that is independent of the load on the muscle and of the initial length of the muscle's contractile element. We report the novel observation that isotonically relaxing smooth muscle reactivates itself, resulting in terminal slowing of the relaxation process. With respect to the biochemistry of smooth muscle contraction, contractile (actin isoforms, myosin heavy and light chains and their isoforms), regulatory (calmodulin-4 Ca2+, myosin light chain kinase, myosin light chain and its phosphorylation, tropomyosin, caldesmon, and calponin), and cytoskeletal (chiefly desmin and vimentin) proteins are discussed. While the kinase activates the contractile system, caldesmon and calponin modulate the activity downward. The cytoskeletal proteins desmin, vimentin, and alpha-actinin could constitute the muscle cell's internal resistor.

A mathematical study of the plasticity effects in muscle contraction

Hill's three-element model of contracting muscle is expanded by replacing the series and the parallel elastic elements with elastoplastic elements. The contractile element is structurally described making use of the sliding filament theory. The resulting mathematical model is formulated in terms of an evolution variational inequality for a nonlinear and nonlocal transport-type operator. The existence and uniqueness of the solution are described along with a numerical approach.

The effects of tonicity on tension and stiffness of tetanized skeletal muscle fibres of the frog.

Tension and stiffness of tetanically activated skeletal muscle fibres of the frog were studied at varied tonicity of the extracellular medium (1.7-3.2 degrees C; sarcomere length, 2.13-2.22 microns). The stiffness was measured from the change in peak tension in response to fast (0.2 ms) stretches and releases of small amplitude (0.11-0.15% of the fibre length). The bathing solution was made hypotonic by reduction of NaCl and hypertonic by addition of sucrose. The osmotic strength of the solutions tested varied from 81 to 168% of the isotonic value. Maximum tetanic tension decreased markedly with increased tonicity. The active stiffness, on the other hand, increased as the tonicity was raised, and the tension/stiffness ratio (the total extension of the undamped fibre elasticity) was thus greatly reduced under these conditions. Evidence is presented to show that the change in the tension/stiffness ratio is due neither to the development of rigor cross-bridges nor to the recruitment of passive parallel-elastic elements in response to increased tonicity. Neither are viscous-like components important for explaining the effect. A change in the tension/stiffness ratio, similar to that seen in response to increased tonicity, did not occur as fibre width was reduced by increasing the sarcomere length. This suggests that the changes in the fibre volume affect this ratio mainly by mechanisms that are unrelated to changes in lateral spacing between the myofilaments.

Nonlinear stiffness--force relationships in whole mammalian skeletal muscles.

Small, sinusoidal length changes were superimposed on isometric contractions of fast- and slow-twitch mouse muscles, which were stimulated maximally via their nerves. Stiffness increased with increasing frequency of sinusoidal stimulation, but the relative time course of force and stiffness changes during twitch, tetanic, or partially fused contractions was quite invariant over a range of frequencies in both muscles. Typically, stiffness increases more rapidly than force during contraction and decreases less rapidly during relaxation. This pattern was observed at various temperatures and with various numbers of stimuli. It can be described by a nonlinear relation between stiffness and force with some hysteresis. The presence in the muscle of parallel and series elastic elements, whose stiffness varies with force, may account for the nonlinear relation. This nonlinearity can be used to relate the patterns for summation of force and stiffness observed with brief trains of stimuli under a variety of conditions.

Is the SII portion of the cross-bridge in glycerinated rabbit psoas fibers compliant in the rigor state?

To see whether the SII portion of the cross-bridge in rigor fibers is longitudinally compliant, we chemically cross-linked with dimethyl suberimidate the entire rod portion (including the SII portion) of myosin onto the surface of thick filaments in glycerinated rabbit psoas fibers, and studied the effect of the SII fixation on the stiffness of the rigor fibers. The cross-linking of fiber segments with full filament overlap increased the rigor stiffness by approximately 25%. Almost the same absolute amount of the stiffness increase was also observed in rigor fibers with half- or no filament overlap after the cross-linking, and a similar but somewhat larger increment of stiffness was observed in fiber segments cross-linked in relaxing solution. These results indicate that the stiffness increase is not produced by the fixation of the SII portion onto the thick filament surface, but is caused instead by the cross-linking of some parallel elastic elements in muscle, and therefore indicate that the SII portion of the cross-bridge is hardly longitudinally compliant in rigor fibers.

Connecting filaments, core filaments, and side-struts: a proposal to add three new load-bearing structures to the sliding filament model.

This report concerns structural forces in resting muscle and proposes three additions to the sliding filament model to account for these mechanical properties. The proposal includes: connecting filaments (C-filaments) which connect the ends of each thick filament to the neighboring Z-lines, core filaments which support the myosin of the thick filament and which attach to the C-filaments, and side-struts which bind the thick filaments together along their length and restrict their radial movement. C-filaments would act as the parallel elastic element and transmit the passive tension to the thick filaments. Isolated myofibrils (mechanically-skinned and detergent-treated frog semitendinosus fibers) when stretched progressively showed exponentially-increasing passive tension which did not disappear when filament overlap was exceeded, but continued to rise. SL was monitored with a HeNe laser. Passive tension phasically exceeded 3 X 10(5) N/M2. Electron microscopy (thin-sectioned and freeze-fracture/deep-etch specimens) of non-overlap fibers showed orderly fibril structure with clear separation of A- and I-bands. In the gap between them could be seen filaments, 40-50 A in diameter, connected to the thick filament ends. Unlike actin, these filaments did not become decorated by myosin S-1. Equatorial X-ray measurements showed that stretching relaxed skinned muscles squeezed the thick filaments closer; this radial compression continued beyond filament overlap. Extreme stretch of fibers caused the thick filaments to strain several-fold. Treatment of non-overlap fibers with a high ionic strength pyrophosphate myosin solvent caused a large drop in passive tension and stiffness, but no change in SL was detected nor was myofibril continuity detectably affected. Non-overlap fibrils, when treated with elastase, released A-segments which retain three-dimensional coherency . Deep-etch EM's of non-overlap fibers disclosed abundant structures (about 75 A) wide attaching adjacent thick filaments.

Systolic mechanical properties of the left ventricle. Effects of volume and contractile state.

To characterize the mechanical properties of the contracting left ventricle, we studied the changes in left ventricular systolic pressure following step-like perturbations (+/- 3 ml) in ventricular volume, using an isovolumically beating, isolated canine heart preparation. Three mechanical properties (elasticity, resistance, and a deactivation effect) were identified. The elastic property differs from the traditional parallel and series elastic elements; it is a time-varying elasticity that includes active and passive effects of volume changes. Furthermore, it could not be represented by a simple time-varying elasticity, but required a second factor to express the dependence of end-systolic elasticity on the timing of the volume step. This effect was represented by a "volume influence factor," which may arise from length-dependent activation. The resistive property appeared to be related to force-velocity behavior of the myocardium. Each mechanical property reacted characteristically to steady state changes in ventricular filling volume or contractile state produced by dobutamine (2-13 micrograms/min). Our findings indicate that elasticity was the property most sensitive to changes in contractile state; these changes increased peak isovolumetric pressure 54% on average, and raised elastic stiffness 40% above control (which was 5.1 mm Hg/ml). Changes in ventricular filling volume only prolonged, but did not alter, the level of elastic stiffness attained at peak pressure. These results support the view that elasticity--or the end-systolic pressure-volume relationship--serves in a given heart to quantify contractility. The "volume influence factor" was not affected by either filling volume or contractile state. Resistance increased in direct proportion with ventricular pressure, but this linear relation was not altered greatly by changes in contractile state or in ventricular filling volume. At 100 mm Hg, ventricular resistance averaged 0.11 mm Hg/ml per sec. Finally, deactivation was greater the later in systole a volume step was imposed, and this pattern was independent of changes in ventricular filling volume and in contractile state.

The velocity of unloaded shortening and its relation to sarcomere length and isometric force in vertebrate muscle fibres.

1. The velocity of shortening at zero load was studied during fused tetanic contractions and single twitches in isolated skeletal muscle fibres of Rana temporaria. 2. The technique used for determination of the speed of unloaded shortening consisted of a series of quick releases of different amplitudes applied at a given instant during activity. The time, delta t, needed for the fibre to take up the slack was plotted against the amplitude of release, delta L. The slope of the straight line relating delta t-delta L provided a measure of the velocity of shortening at zero load, V0. 3. V0 was compared with force-velocity data obtained at finite loads (load-clamp recordings). The predicted velocity of shortening at zero load, derived by hyperbolic extrapolation from velocities at low and intermediate loads, was not significantly different from V0. 4. The temperature dependence of isometric force and of shortening velocity was investigated between 2 and 12 degrees C in the same fibres. Q10 was 2.67 +/- 0.07 (S.E. of mean, n = 6) for V0 and 1.24 +/- 0.01 for tetanic force. 5. The velocity of unloaded shortening was determined at different sarcomere lengths in the range 1.4--3.1 microns. V0 was constant between 1.65 microns and approximately 2.7 microns. It decreased below 1.65 microns and increased above 2.7 microns. 6. The decrease in velocity at short sarcomere lengths probably reflects an increase of the passive resistance to shortening. The increase in velocity at long sarcomere lengths can be accounted for by the passive compressive force that is produced by the parallel elastic elements of the prestretched fibre. 7. V0 was determined at the peak of the twitch and during the plateau of the fused tetanus in the same fibre. Whereas the peak twitch force varied between 38 and 85% of the tetanic tension in the different fibres (mean: 71 +/- 5%, n = 8), V0 during the twitch was 99 +/- 2% of the value recorded during the tetanus. Depression of the isometric twitch amplitude to 10% of the control value by dantrolene did not cause any significant reduction of V0.

Myofilament-generated tension oscillations during partial calcium activation and activation dependence of the sarcomere length-tension relation of skinned cardiac cells.

During partial Ca2+ activation, skinned cardiac cells with sarcoplasmic reticulum destroyed by detergent developed spontaneous tension oscillations consisting of cycles (0.1-1 Hz) of rapid decrease of tension corresponding to the yield of some sarcomeres and slow redevelopment of tension corresponding to the reshortening of these sarcomeres. Such myofilament-generated tension oscillations were never observed during the full activation induced by a saturating [free Ca2+] or during the rigor tension induced by decreasing [MgATP] in the absence of free Ca2+ or when the mean sarcomere length (SL) of the preparation was greater than 3.10 microm during partial Ca2+ activation. A stiff parallel elastic element borne by a structure that could be digested by elastase hindered the study of the SL--active tension diagram in 8-13-microm-wide skinned cells from the rat ventricle, but this study was possible in 2-7-microm-wide myofibril bundles from the frog or dog ventricle. During rigor the tension decreased linearly when SL was increased from 2.35 to 3.80 microm. During full Ca2+ activation the tension decreased by less than 20% when SL was increased from 2.35 to approximately 3.10 microm. During partial Ca2+ activation the tension increased when SL was increased from 2.35 to 3.00 microm. From this observation of an apparent increase in the sensitivity of the myofilaments to Ca2+ induced by increasing SL during partial Ca2+ activation, a model was proposed that describes the tension oscillations and permits the derivation of the maximal velocity of shortening (Vmax). Vmax was increased by increasing [free Ca2+] or decreasing [free Mg2+] but not by increasing SL.

Regional variation of series elasticity in canine arterial smooth muscles.

Segments of carotid, iliac, renal, mesenteric, coronary, and internal thoracic arteries were studied in vitro to correlate the mechanical properties of series (SE) and parallel (PE) elastic elements with connective tissue (CT) composition and with active responses to potassium activation. The PE properties were determined using pressure-diameter data with passive smooth muscle (SM). SE properties were determined from periodic incremental releases imposed during isometric responses to [K+]O at a diameter corresponding to Lmax, the optimum muscle length. Active stress responses and diameter responses were determined using pressure-diameter data for active and passive conditions. Collagen and elastin contents were determined for each sample. No correlation was found between CT content and PE or SE properties for the various sites. A close correlation was found to exist between SE and PE properties at each site, i.e., the sites with the stiffest PE also had the stiffest SE. SM, with stiffer SE, had a larger diameter response with the same active stress response and the same diameter response with a smaller active stress response, compared to SM with more compliant SE. This suggests that passive properties of SM can have a significant influence on the external manifestations of contractile element properties.

The temperature dependence of parallel and series elastic elements in the vascular smooth muscle of the rat portal vein

The stiffness of a parallel (PE) as well as of a series elastic element (SE) in the isolated rat portal vein was determined at 37 degrees C and at 25 degrees C. The length-tension curve of the PE was obtained by a stepwise lengthening of the preparation and showed no temperature dependence for the element: the mean extension of the PE was 48.8% of the optimum length L0 at 37 degrees C, and 47.3% of L0 at 25 degrees C when loaded with the maximum active force T0. The maximum force occurred at both temperatures with the same muscle length. Even the stiffness factor, i.e. the slope 'k' of the linear function dT/dL = k . T + c showed no temperature dependence. The series elasticity was determined by means of the quick-release technique from afterloaded isometric contractions of the tetanized preparation. A distinct temperature influence was revealed by the decrease of the mean SE extension from 13.5% of L0 at 37 degrees C to 10.9% of L0 at 25 degrees C (P less than 0.0005). The stiffness factor, normalized to the actual muscle length, was 12.0 per ML at 37 degrees C and 14.7 per ML at 25 degrees C (P less than 0.025). The values obtained for the portal vein are equivalent to those calculated for other smooth muscle preparations but the stiffness of series elasticity is well below that found in the cardiac and skeletal muscle.