Force-length Relationship Research Articles

Skeletal muscle contractile properties in a novel murine model for limb girdle muscular dystrophy 2i.

Limb-girdle muscular dystrophy (LGMD) 2i results from mutations in fukutin-related protein and aberrant α-dystroglycan glycosylation. Although this significantly compromises muscle function and ambulation, the comprehensive characteristics of contractile dysfunction are unknown. Therefore, we quantified the in situ contractile properties of the medial gastrocnemius in young adult P448L mice, an affected muscle of a novel model of LGMD2i. Normalized maximal twitch force, tetanic force, and power were significantly smaller in P448L mice, compared with sex-matched, wild-type mice. These differences were consistent with the replacement of contractile fibers by passive tissue. The shape of the active force-length relationships were similar in both groups, regardless of sex, consistent with an intact sarcomeric structure in P448L mice. Passive force-length curves normalized to maximal isometric force were steeper in P448L mice, and passive elements contribute disproportionately more to total contractile force in P448L mice. Sex differences were mostly noted in the force-velocity curves, as normalized values for maximal and optimal velocities were significantly slower in P448L males, compared with wild-type, but not in P448L females. This suggests that the dystrophic phenotype, which may include possible changes in cross-bridge kinetics and fiber-type proportions, progresses more quickly in P448L males. These results together indicate that active force and power generation are compromised in both sexes of P448L mice, while passive forces increase. More importantly, the results identified several functional markers of disease pathophysiology that could aid in developing and assessment of novel therapeutics for LGMD2i and possibly other dystroglycanopathies as well. NEW & NOTEWORTHY Comprehensive assessments of muscle contractile function have, until now, never been performed in an animal model for any dystroglycanopathy. This study suggests that skeletal muscle contractile properties are significantly compromised in a recently developed model for limb-girdle muscular dystrophy 2i, the P448L mouse. It further identifies novel pathological markers of muscle function that are suitable for developing therapeutics and for better understanding of disease pathogenesis.

Structure-function relationship of the human external anal sphincter.

Obstetrical external anal sphincter (EAS) injury and subsequent dysfunction are leading risk factors for femalefecal incontinence (FI). Limited knowledge of the EAS structure-function relationship hinders treatment optimization. We directly measured functionally relevant intrinsicparameters of human EAS and tested whether vaginal delivery alters the EAS structure-function relationship. Major predictors of in vivo EAS function were compared between specimens procured from vaginally nulliparous (VN, n=5) and vaginally parous (VP, n=7) cadaveric donors: operational sarcomere length (Ls), which dictates force-length relationship; physiological cross-sectional area (PCSA), which determines isometric force-generating capacity; fiber length (Lfn), responsible for muscle excursion and contractile velocity; and muscle stiffness. Data were analyzed using unpaired and paired t tests, α<0.05. Results are presented as mean±SEM. The VN and VP (median parity 3) groups were similar in age and BMI. No gross anatomical defects were identified. EAS Ls (2.36±0.05μm) was shorter than the optimal Lso (2.7μm), at which contractile force is maximal, P=0.0001. Stiffness was lower at Ls than Lso (5.4±14kPa/μm vs 35.3±12kPa/μm, P<0.0001). This structural design allows active and passive tension to increase with EAS stretching. EAS relatively long Lfn (106±24.8mm) permits rapid contraction without decreased force, whereas intermediate PCSA (1.3±0.3cm2) is conducive to maintaining resting tone. All parameters were similar between groups. This first direct examination of human EAS underscores how EAS intrinsic design matches its intended function. Knowledge of the EAS structure-function relationship is important for understanding the pathogenesis of FI and the optimization of treatments for EAS dysfunction.

Determination of individual knee-extensor properties from leg extensions and parameter identification

ABSTRACTNeural commands control skeletal muscles that act on passive structures and regulate voluntary movements. Mathematical models can simulate such movements and therefore require the knowledge of neuromuscular properties. In contrast to scaling these properties to the individual, we present a non-linear parameter identification method to determine them non-invasively and in vivo. The classic model A describes an excitable contractile element (CE) embedded in a geometrical representation of the leg. Its extension model B is used to study the effects of the force–length relationship and the serial elastic element (SEE). We show the validation of model B and discuss the quality of neuromuscular properties identified from simulations and experiments. The main finding is that identifications that consider CE–SEE dynamics result in increased and more realistic curvatures of the force–velocity relations. This shows that CE and SEE work interdependently and we recommend to co-ordinate the parameter values of muscle–tendon units.

Sarcomere mechanics in striated muscles: from molecules to sarcomeres to cells.

Muscle contraction is commonly associated with the cross-bridge and sliding filament theories, which have received strong support from experiments conducted over the years in different laboratories. However, there are studies that cannot be readily explained by the theories, showing 1) a plateau of the force-length relation extended beyond optimal filament overlap, and forces produced at long sarcomere lengths that are higher than those predicted by the sliding filament theory; 2) passive forces at long sarcomere lengths that can be modulated by activation and Ca2+, which changes the force-length relation; and 3) an unexplained high force produced during and after stretch of activated muscle fibers. Some of these studies even propose "new theories of contraction." While some of these observations deserve evaluation, many of these studies present data that lack a rigorous control and experiments that cannot be repeated in other laboratories. This article reviews these issues, looking into studies that have used intact and permeabilized fibers, myofibrils, isolated sarcomeres, and half-sarcomeres. A common mechanism associated with sarcomere and half-sarcomere length nonuniformities and a Ca2+-induced increase in the stiffness of titin is proposed to explain observations that derive from these studies.

The active force-length relationship is invisible during extensive eccentric contractions in skinned skeletal muscle fibres.

In contrast to experimentally observed progressive forces in eccentric contractions, cross-bridge and sliding-filament theories of muscle contraction predict that varying myofilament overlap will lead to increases and decreases in active force during eccentric contractions. Non-cross-bridge contributions potentially explain the progressive total forces. However, it is not clear whether underlying abrupt changes in the slope of the nonlinear force-length relationship are visible in long isokinetic stretches, and in which proportion cross-bridges and non-cross-bridges contribute to muscle force. Here, we show that maximally activated single skinned rat muscle fibres behave (almost across the entire working range) like linear springs. The force slope is about three times the maximum isometric force per optimal length. Cross-bridge and non-cross-bridge contributions to the muscle force were investigated using an actomyosin inhibitor. The experiments revealed a nonlinear progressive contribution of non-cross-bridge forces and suggest a nonlinear cross-bridge contribution similar to the active force-length relationship (though with increased optimal length and maximum isometric force). The linear muscle behaviour might significantly reduce the control effort. Moreover, the observed slight increase in slope with initial length is in accordance with current models attributing the non-cross-bridge force to titin.

Operating length and velocity of human M. vastus lateralis fascicles during vertical jumping.

Humans achieve greater jump height during a counter-movement jump (CMJ) than in a squat jump (SJ). However, the crucial difference is the mean mechanical power output during the propulsion phase, which could be determined by intrinsic neuro-muscular mechanisms for power production. We measured M. vastus lateralis (VL) fascicle length changes and activation patterns and assessed the force–length, force–velocity and power–velocity potentials during the jumps. Compared with the SJ, the VL fascicles operated on a more favourable portion of the force–length curve (7% greater force potential, i.e. fraction of VL maximum force according to the force–length relationship) and more disadvantageous portion of the force–velocity curve (11% lower force potential, i.e. fraction of VL maximum force according to the force–velocity relationship) in the CMJ, indicating a reciprocal effect of force–length and force–velocity potentials for force generation. The higher muscle activation (15%) could therefore explain the moderately greater jump height (5%) in the CMJ. The mean fascicle-shortening velocity in the CMJ was closer to the plateau of the power–velocity curve, which resulted in a greater (15%) power–velocity potential (i.e. fraction of VL maximum power according to the power–velocity relationship). Our findings provide evidence for a cumulative effect of three different mechanisms—i.e. greater force–length potential, greater power–velocity potential and greater muscle activity—for an advantaged power production in the CMJ contributing to the marked difference in mean mechanical power (56%) compared with SJ.

The influence of biophysical muscle properties on simulating fast human arm movements

Computational modeling provides a framework to understand human movement control. For this approach, physiologically motivated and experimentally validated models are required to predict the dynamic interplay of the neuronal controller with the musculoskeletal biophysics. Previous studies show, that an adequate model of arm movements should consider muscle fiber contraction dynamics, parallel and serial elasticities, and activation dynamics. Numerous validated macroscopic model representations of these structures and processes exist. In this study, the influence of these structures and processes on maximum movement velocity of goal-directed arm movements was investigated by varying their mathematical model descriptions. It was found that the movement velocity strongly depends on the pre-activation of the muscles (differences up to 91.6%) and the model representing activation dynamics (differences up to 43.3%). Looking at the influence of the active muscle fibers (contractile element), the simulations reveal that velocities systematically differ depending on the width of the force–length relation (differences up to 17.4%). The series elasticity of the tendon influences the arm velocity up to 7.6%. In conclusion, in fast goal-directed arm movements from an equilibrium position, the modeling of the biophysical muscle properties influences the simulation results. To reliably distinguish between mathematical formulations by experimental validation, the initial muscular activity and the activation dynamics have to be modeled validly, as their influence excels. To this end, further experiments systematically varying the initial muscular activity would be needed.

Residual force enhancement is regulated by titin in skeletal and cardiac myofibrils

When a skeletal muscle is stretched while it contracts, the muscle produces a relatively higher force than the force from an isometric contraction at the same length: a phenomenon referred to as residual force enhancement. Residual force enhancement is puzzling because it cannot be directly explained by the classical force-length relationship and the sliding filament theory of contraction, the main paradigms in the muscle field. We used custom-built instruments to measure residual force enhancement in skeletal myofibrils, and, for the first time, in cardiac myofibrils. Our data report that residual force enhancement is present in skeletal muscles, but not cardiac muscles, and is regulated by the different isoforms of the titin protein filaments. When a skeletal muscle contracts isometrically, the muscle produces a force that is relative to the final isometric sarcomere length (SL). However, when the same final SL is reached by stretching the muscle while it contracts, the muscle produces a relatively higher force: a phenomenon commonly referred to as residual force enhancement. In this study, we investigated residual force enhancement in rabbit skeletal psoas myofibrils and, for the first time, cardiac papillary myofibrils. A custom-built atomic force microscope was used in experiments that stretched myofibrils before and after inhibiting myosin and actin interactions to determine whether the different cardiac and skeletal titin isoforms regulate residual force enhancement. At SLs ranging from 2.24 to 3.13μm, the skeletal myofibrils enhanced the force by an average of 9.0%, and by 29.5% after hindering myosin and actin interactions. At SLs ranging from 1.80 to 2.29μm, the cardiac myofibrils did not enhance the force before or after hindering myosin and actin interactions. We conclude that residual force enhancement is present only in skeletal muscles and is dependent on the titin isoforms.

Linearity in force – length Relation and Determination of Muscle Forces

This paper examines the force–length relations of skeletal muscle actuators during normal human gait based on gait data analysis. Instead of time or gait cycle, the joint coordinates were taken as independent parameters in the study of force–length relations. Force–length relations are nonlinear and non-analytic functions in the domain of each gait cycle. We propose to carry out kinematic segmentation of each joint coordinate function into four kinematic states depending on its displacement, velocity and acceleration for studying the force–length relations. When considered segment-wise, linear fit to force–length curves were found statistically significant. Thus it was seen that the skeletal muscles behaved linearly when evaluated in terms of the kinematic segments in the gait cycle. Hence a method to evaluate muscle force distribution was proposed using linear equivalent static formulation based on strain energy minimization as a rapid procedure in comparison with static optimization algorithm. The method resulted in simplified modeling and analysis of musculo-skeletal system to draw interim conclusions before the fully fledged musculo-skeletal analysis is carried out. The proposed method was applied on a single degree of freedom case and was verified with established analysis procedure, namely static optimization using OpenSim, an open-source software system.

On the Functional Role of Valve Interstitial Cell Stress Fibers: A Continuum Modeling Approach.

The function of the heart valve interstitial cells (VICs) is intimately connected to heart valve tissue remodeling and repair, as well as the onset and progression of valvular pathological processes. There is yet only very limited knowledge and extant models for the complex three-dimensional VIC internal stress-bearing structures, the associated cell-level biomechanical behaviors, and how they change under varying activation levels. Importantly, VICs are known to exist and function within the highly dynamic valve tissue environment, including very high physiological loading rates. Yet we have no knowledge on how these factors affect VIC function. To this end, we extended our previous VIC computational continuum mechanics model (Sakamoto, et al., 2016, "On Intrinsic Stress Fiber Contractile Forces in Semilunar Heart Valve Interstitial Cells Using a Continuum Mixture Model," J. Mech. Behav. Biomed. Mater., 54(244-258)). to incorporate realistic stress-fiber geometries, force-length relations (Hill model for active contraction), explicit α-smooth muscle actin (α-SMA) and F-actin expression levels, and strain rate. Novel micro-indentation measurements were then performed using cytochalasin D (CytoD), variable KCl molar concentrations, both alone and with transforming growth factor β1 (TGF-β1) (which emulates certain valvular pathological processes) to explore how α-SMA and F-actin expression levels influenced stress fiber responses under quasi-static and physiological loading rates. Simulation results indicated that both F-actin and α-SMA contributed substantially to stress fiber force generation, with the highest activation state (90 mM KCL + TGF-β1) inducing the largest α-SMA levels and associated force generation. Validation was performed by comparisons to traction force microscopy studies, which showed very good agreement. Interestingly, only in the highest activation state was strain rate sensitivity observed, which was captured successfully in the simulations. These unique findings demonstrated that only VICs with high levels of αSMA expression exhibited significant viscoelastic effects. Implications of this study include greater insight into the functional role of α-SMA and F-actin in VIC stress fiber function, and the potential for strain rate-dependent effects in pathological states where high levels of α-SMA occur, which appear to be unique to the valvular cellular in vivo microenvironment.

Relationship between Hip Flexion Contracture and Hip-Joint Contact Force in Standing Posture: A Computer Simulation Study

Mechanical stress on articular cartilage and long-duration standing postures are risk factors for hip osteoarthritis progression. This study aims to examine the relationship between hip flexion contracture and the hip-joint contact force in standing postures using computer simulation. A musculoskeletal model composed of seven segments (Head, Arms, and Trunk (HAT) and thighs, shanks, and two feet) was created. Various standing postures (708 variations) were generated, and five hip flexion contracture conditions were set: zero contracture and flexions of 0°, 10°, 20°, and 30°. A standing posture satisfying the hip flexion contracture condition with the minimum sum of the muscle activations was obtained as the optimal standing posture, and the hip-joint contact force in the optimal standing posture was calculated. A sensitivity analysis was conducted by varying four parameters (the objective function, physiological cross-sectional area, force-length relation, and muscle moment arm length). The hip-joint contact force and hip extensor muscle forces (i.e., those of the gluteus maximus, semitendinosus, semimembranosus, and biceps femoris long head) during standing increased with the development of hip flexion contracture. The hip-joint contact force for the standing posture with a 30° hip flexion contracture was almost twice that for the no-contracture condition (8.7 and 3.7 N/kg, respectively). The sensitivity analysis showed that variation of the four parameters did not affect our main finding. The main finding of this study is that hip-joint contact force during standing increases with the development of hip flexion contracture. The findings of this study may help to prevent hip osteoarthritis progression.

EFFECTS OF SADDLE HEIGHT ON PERFORMANCE AND MUSCULAR ACTIVITY DURING THE WINGATE TEST

This study aimed to analyze the anaerobic performance and muscle activation during a supramaximal cycling test at three different saddle positions. Twelve competitive cyclists completed an incremental cycling test and three 30-s Wingate tests in three different saddle heights (reference, downward, and upward), in a random order, on different days. The saddle height was individually shifted downward and upward (seeing 2.5% of the distance from the pubic symphysis to ground) from the reference position. The electromyographic signal (EMG) data was obtained from the rectus femoris, vastus lateralis, biceps femoris (long head), and gastrocnemius lateralis in order to assess muscle activation during the entire test. The anaerobic variables and the EMG data were divided into six consecutive windows of 5-s. The EMG signals were normalized by the first 5-s window of the reference position to provide the percentage changes throughout the test. The results suggest that during a 30-s Wingate test small changes in saddle height result in greater peak power output (reference=1380±241 W; downward=1497±175 W, p=0.036; upward=1491±225 W, p=0.049) and greater activation period for vastus lateralis (reference=33.6%, downward=33.2%, upward=35.0%; p=0.001) in comparision to rectus femoris (reference=24.5%, downward=25.2%, upward=23.7%), biceps femoris (reference=20.7%, downward=20.8%, upward=19.9%), and gastrocnemius lateralis (reference=21.2%, downward=20.8%, upward=19.9%). The results suggest that small adjustments in saddle height may affect the force-length relationship of the muscles of the lower limb, and consequently their recruitment pattern and their ability to generate force.

Modeling and testing of a knitted-sleeve fluidic artificial muscle

The knitted-sleeve fluidic muscle is similar in design to a traditional McKibben muscle, with a separate bladder and sleeve. However, in place of a braided sleeve, it uses a tubular-knit sleeve made from a thin strand of flexible but inextensible yarn. When the bladder is pressurized, the sleeve expands by letting the loops of fiber slide past each other, changing the dimensions of the rectangular cells in the stitch pattern. Ideally, the internal volume of the sleeve would reach a maximum when its length has contracted by 2/3 from its maximum length, and although this is not reachable in practice, preliminary tests show that free contraction greater than 50% is achievable. The motion relies on using a fiber with a low coefficient of friction in order to reduce hysteresis to an acceptable level. In addition to increased stroke length, potential advantages of this technique include slower force drop-off during the stroke, more useable energy in certain applications, and greater similarity to the force–length relationship of skeletal muscle. Its main limitation is its potentially greater effect from friction compared to other fluidic muscle designs.

Mechanical Stress Conditioning and Electrical Stimulation Promote Contractility and Force Maturation of Induced Pluripotent Stem Cell-Derived Human Cardiac Tissue.

Tissue engineering enables the generation of functional human cardiac tissue with cells derived in vitro in combination with biocompatible materials. Human-induced pluripotent stem cell-derived cardiomyocytes provide a cell source for cardiac tissue engineering; however, their immaturity limits their potential applications. Here we sought to study the effect of mechanical conditioning and electric pacing on the maturation of human-induced pluripotent stem cell-derived cardiac tissues. Cardiomyocytes derived from human-induced pluripotent stem cells were used to generate collagen-based bioengineered human cardiac tissue. Engineered tissue constructs were subjected to different mechanical stress and electric pacing conditions. The engineered human myocardium exhibits Frank-Starling-type force-length relationships. After 2 weeks of static stress conditioning, the engineered myocardium demonstrated increases in contractility (0.63±0.10 mN/mm2 vs 0.055±0.009 mN/mm2 for no stress), tensile stiffness, construct alignment, and cell size. Stress conditioning also increased SERCA2 (Sarco/Endoplasmic Reticulum Calcium ATPase 2) expression, which correlated with a less negative force-frequency relationship. When electric pacing was combined with static stress conditioning, the tissues showed an additional increase in force production (1.34±0.19 mN/mm2), with no change in construct alignment or cell size, suggesting maturation of excitation-contraction coupling. Supporting this notion, we found expression of RYR2 (Ryanodine Receptor 2) and SERCA2 further increased by combined static stress and electric stimulation. These studies demonstrate that electric pacing and mechanical stimulation promote maturation of the structural, mechanical, and force generation properties of human-induced pluripotent stem cell-derived cardiac tissues.

How to model a muscle’s active force–length relation: A comparative study

The active isometric force–length relation (FLR) of mammalian skeletal muscle is one of the most investigated characteristics throughout biomechanics. Numerous experiments have been conducted that reveal insights on the mechanisms of muscle contraction. However, the entity of molecular processes is yet not fully understood. Modelers thus rely on a rather descriptive characterization of experimental findings. Starting with the well-known, piece-wise linear formulation by A. Gordon, A. Huxley and F. Julian in 1966, a variety of structurally distinguishable FLR models have been developed. Five decades later, the original idea was taken up to derive the first purely physiological FLR formulation, based on sliding filament and cross-bridge theory. This derivation offers us the opportunity to contrast a broad variety of 19 distinct FLR models. By comparing their ability to fit experimental data, we deduce qualitative as well as quantitative acceptance criteria such as symmetry, normalization, complexity, and physiological interpretability. Resultant, different models comprise different advantages. The new piece-wise linear model is the overall most favorable, a further piece-wise exponential model is mathematically more robust, a polynomial model of fourth order has the best optimization properties, and a certain purely exponential model is the computationally cheapest. This work gives a detailed overview, as well as a mathematical/physiological assessment of existing FLR models, and serves as a guideline for modelers to choose a proper formulation based on individual requirements.

Effects of Bladder Geometry in Pneumatic Artificial Muscles

Designing optimal pneumatic muscles for a particular application requires an accurate model of the hyperelastic bladder and how it influences contraction force. Previous work does not fully explain the influence of bladder prestrain on actuator characteristics. We present here modeling and experimental data on the actuation properties of artificial muscles constructed with varying bladder prestrain and wall thickness. The tests determine quasi-static force–length relationships during extension and contraction, for muscles constructed with unstretched bladder lengths equal to 55%, 66%, and 97% of the stretched muscle length and two different wall thicknesses. Actuator force and maximum contraction length are found to depend strongly on both the prestrain and the thickness of the rubber, making existing models inadequate for choosing bladder geometry. A model is presented to better predict force–length characteristics from geometric parameters, using a novel thick-walled tube calculation to account for the nonlinear elastic properties of the bladder. It includes axial force generated by stretching the bladder lengthwise, and it also describes the hoop stress created by radial expansion of the muscle that partially counteracts the internal fluid pressure exerted outward on the mesh. This effective reduction in pressure affects both axial muscle force and mesh-on-bladder friction. The rubber bladder is modeled as a Mooney–Rivlin incompressible solid. The axial force generated by the mesh is found directly from contact forces rather than from potential energy. Modeling the bladder as a thin-walled tube gives a close match to experimental data on wall thickness, but a thick-walled bladder model is found to be necessary for explaining the effects of prestrain.

Intermuscular pressure between synergistic muscles correlates with muscle force.

The purpose of the study was to examine the relationship between muscle force generated during isometric contractions (i.e. at a constant muscle-tendon unit length) and the intermuscular (between adjacent muscles) pressure in synergistic muscles. Therefore, the pressure at the contact area of the gastrocnemius and plantaris muscle was measured synchronously to the force of the whole calf musculature in the rabbit species Oryctolagus cuniculus Similar results were obtained when using a conductive pressure sensor, or a fibre-optic pressure transducer connected to a water-filled balloon. Both methods revealed a strong linear relationship between force and pressure in the ascending limb of the force-length relationship. The shape of the measured force-time and pressure-time traces was almost identical for each contraction (r=0.97). Intermuscular pressure ranged between 100 and 700 mbar (70,000 Pa) for forces up to 287 N. These pressures are similar to previous (intramuscular) recordings within skeletal muscles of different vertebrate species. Furthermore, our results suggest that the rise in intermuscular pressure during contraction may reduce the force production in muscle packages (compartments).

A musculoskeletal model of the lumbar spine using ArtiSynth – development and validation

A musculoskeletal model of the spine was created using ArtiSynth, an open-source biomechanical modelling toolkit. The model included the entire spine and rib cage, with the lumbar vertebrae being mobile and 210 muscle fascicles. Muscle parameters needed for a full Hill-type musculotendon model including tendon ratios and pennation angles along with muscle force-length and force-velocity curves were incorporated into the model, as were the nonlinear stiffness of the functional spinal units and the effect of intra-abdominal pressure. We used forward dynamics-assisted data tracking for the estimation of muscle forces and validated the solution method by comparing the predicted spinal forces vs. the results of two in vivo experiments in the literature. Our model produced larger maximum extension moment in flexion than extension, which is observed in in vivo experiments. These results could not be achieved without the inclusion of the muscle force-length relationship. The model was also able to predict the ratios of axial forces at L4–L5 as measured in vivo intradiscal pressures for three cases of upright standing, holding a crate close to and far from the chest. Due to the high stiffness of the spine, our solution method was sensitive to input kinematics, which hindered extensive validation of the model for body positions other than standing. Modifying the solution method, possibly by only tracking the angular motion of the vertebrae rather than their translational motion, should make the model less sensitive and enable further validation.

Human Leg Model Predicts Muscle Forces, States, and Energetics during Walking.

Humans employ a high degree of redundancy in joint actuation, with different combinations of muscle and tendon action providing the same net joint torque. Both the resolution of these redundancies and the energetics of such systems depend on the dynamic properties of muscles and tendons, particularly their force-length relations. Current walking models that use stock parameters when simulating muscle-tendon dynamics tend to significantly overestimate metabolic consumption, perhaps because they do not adequately consider the role of elasticity. As an alternative, we posit that the muscle-tendon morphology of the human leg has evolved to maximize the metabolic efficiency of walking at self-selected speed. We use a data-driven approach to evaluate this hypothesis, utilizing kinematic, kinetic, electromyographic (EMG), and metabolic data taken from five participants walking at self-selected speed. The kinematic and kinetic data are used to estimate muscle-tendon lengths, muscle moment arms, and joint moments while the EMG data are used to estimate muscle activations. For each subject we perform an optimization using prescribed skeletal kinematics, varying the parameters that govern the force-length curve of each tendon as well as the strength and optimal fiber length of each muscle while seeking to simultaneously minimize metabolic cost and maximize agreement with the estimated joint moments. We find that the metabolic cost of transport (MCOT) values of our participants may be correctly matched (on average 0.36±0.02 predicted, 0.35±0.02 measured) with acceptable joint torque fidelity through application of a single constraint to the muscle metabolic budget. The associated optimal muscle-tendon parameter sets allow us to estimate the forces and states of individual muscles, resolving redundancies in joint actuation and lending insight into the potential roles and control objectives of the muscles of the leg throughout the gait cycle.

Right Ventricular Contractile Reserve and Pulmonary Circulation Uncoupling During Exercise Challenge in Heart Failure: Pathophysiology and Clinical Phenotypes

ObjectivesRight ventricular (RV) exercise contractile reserve (RVECR), its phenotypes, and its functional correlates are among the unresolved issues with regard to the role of the right ventricle in heart failure (HF) syndrome, and understanding these issues constitutes the objective of this study. BackgroundAlthough the role of the right ventricle in HF syndrome might be fundamental, the pathophysiology of the failing right ventricle has not been extensively investigated. MethodsNinety-seven patients with HF (mean age 64 years, 70% men, mean left ventricular ejection fraction 33 ± 10%) underwent maximal exercise stress echocardiographic and cardiopulmonary exercise testing. RVECR and RV–to–pulmonary circulation (PC) coupling were assessed using the length-force relationship (tricuspid annular plane systolic excursion [TAPSE] vs. pulmonary artery systolic pressure) and the slope of mean pulmonary artery pressure versus cardiac output. On the basis of TAPSE, patients were categorized into 3 groups: those with TAPSE at rest ≥16 mm (group A, n = 60) and those with TAPSE at rest <16 mm, who were divided according to median TAPSE at peak exercise (15.5 mm) into 2 subgroups (group B, ≥15.5 mm, n = 19; group C, <15.5 mm, n = 18). ResultsAlthough they had similar left ventricular ejection fractions and rest RV impairment, compared with patients in group C, those in group B showed some degree of RVECR (upward shift of the length-force relationship), better RV-to-PC coupling (lower mean pulmonary artery pressure vs. cardiac output slope), and greater ventilatory efficiency (lower slope of minute ventilation to carbon dioxide output). Rest mitral regurgitation and net changes in pulmonary artery systolic pressure were the variables retained in the best regression model as correlates of RVECR. ConclusionsIn patients with HF, RVECR unmasks different phenotypes. Impaired RV function at rest might not invariably lead to unfavorable RVECR and exercise RV-to-PC coupling. Testing these variables appears useful even in more advanced stages of HF to define various clinical conditions and, most likely, to define different levels of risk.