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Skeletal muscle has a broad range of biomechanical functions, including power generation and energy absorption. These roles are underpinned by the force-velocity relationship, which comprises two distinct components: a concentric and an eccentric force-velocity relationship. The concentric component has been extensively studied across a wide range of muscles with different muscle properties. However, to date, little progress has been made in accurately characterising the eccentric force-velocity relationship in mammalian muscle with varying muscle properties. Consequently, mathematical models of this muscle behaviour are based on a poorly understood phenomenon. Here, we present a comprehensive assessment of the concentric force-velocity and eccentric force-velocity relationships of four mammalian muscles (soleus, extensor digitorum longus, diaphragm and digastric) with varying biomechanical functions, spanning three orders of magnitude in body mass (mouse, rat and rabbits). The force-velocity relationship was characterised using a hyperbolic-linear equation for the concentric component a hyperbolic equation for the eccentric component, at the same time as measuring the rate of force development in the two phases of force development in relation to eccentric lengthening velocity. We demonstrate that, despite differences in the curvature and plateau height of the eccentric force-velocity relationship, the rates of relative force development were consistent for the two phases of the force-time response during isovelocity lengthening ramps, in relation to lengthening velocity, in the four muscles studied. Our data support the hypothesis that this relationship depends on cross-bridge and titin activation. Hill-type musculoskeletal models of the eccentric force-velocity relationship for mammalian muscles should incorporate this biphasic force response. KEY POINTS: The capacity of skeletal muscle to generate mechanical work and absorb energy is underpinned by the force-velocity relationship. Despite identification of the lengthening (eccentric) force-velocity relationship over 80 years ago, no comprehensive study has been undertaken to characterise this relationship in skeletal muscle. We show that the biphasic force response seen during active muscle lengthening is conserved over three orders of magnitude of mammalian skeletal muscle mass. Using mice with a small deletion in titin, we show that part of this biphasic force profile in response to muscle lengthening is reliant on normal titin activation. The rate of force development during muscle stretch may be a more reliable way to describe the forces experienced during eccentric muscle contractions compared to the traditional hyperbolic curve fitting, and functions as a novel predictor of force-velocity characteristics that may be used to better inform hill-type musculoskeletal models and assess pathophysiological remodelling., (© 2024 The Authors. The Journal of Physiology published by John Wiley & Sons Ltd on behalf of The Physiological Society.)

This article aims to present some novel experimental approaches and computational methods providing detailed insights into the mechanical behavior of skeletal muscles relevant to clinical problems associated with managing and treating musculoskeletal diseases. The mechanical characterization of skeletal muscles in vivo is crucial for better understanding of, prevention of, or intervention in movement alterations due to exercise, aging, or pathologies related to neuromuscular diseases. To achieve this, we suggest an intraoperative experimental method including direct measurements of human muscle forces supported by computational methodologies. A set of intraoperative experiments indicated the major role of extracellular matrix (ECM) in spastic cerebral palsy. The force data linked to joint function are invaluable and irreplaceable for evaluating individual muscles however, they are not feasible in many situations. Three‐dimensional, continuum‐mechanical models provide a way to predict the exerted muscle forces. To obtain, however, realistic predictions, it is important to investigate the muscle not by itself, but embedded within the respective musculoskeletal system, for example, a 6‐muscle upper arm model, and the ability to obtain non‐invasively, or at least, minimally invasively material parameters for continuum‐mechanical skeletal muscle models, for example, by presently proposed homogenization methodologies. Botulinum toxin administration as a treatment option for spasticity is exemplified by combining experiments with modeling to find out the mechanical outcomes of altered ECM and the controversial effects of the toxin. The potentials and limitations of both experimental and modeling approaches and how they need each other are discussed. [ABSTRACT FROM AUTHOR]

Computational musculoskeletal modelling has emerged as an alternative, less-constrained technique to indirect calorimetry for estimating energy expenditure. However, predictions from modelling tools depend on many assumptions around muscle architecture and function and motor control. Therefore, these tools need to continue to be validated if we are to eventually develop subject-specific simulations that can accurately and reliably model rates of energy consumption for any given task. In this study, we used OpenSim software and experimental motion capture data to simulate muscle activations, muscle fascicle dynamics and whole-body metabolic power across mechanically and energetically disparate hopping tasks, and then evaluated these outputs at a group- and individual-level against experimental electromyography, ultrasound and indirect calorimetry data. Comparing simulated and experimental outcomes, we found weak to strong correlations for peak muscle activations, moderate to strong correlations for absolute fascicle shortening and mean shortening velocity, and strong correlations for gross metabolic power. These correlations tended to be stronger on a group-level rather than individual-level. We encourage the community to use our publicly available dataset from SimTK.org to experiment with different musculoskeletal models, muscle models, metabolic cost models, optimal control policies, modelling tools and algorithms, data filtering etc. with subject-specific simulations being a focal goal.

Abstract The following papers by Richard Lieber (Skeletal Muscle as an Actuator), Thomas Roberts (Elastic Mechanisms and Muscle Function), Silvia Blemker (Skeletal Muscle has a Mind of its Own: a Computational Framework to Model the Complex Process of Muscle Adaptation) and Sabrina Lee (Muscle Properties of Spastic Muscle (Stroke and CP) are summaries of their representative contributions for the session on skeletal muscle mechanics, energetics and plasticity at the 2016 Biomechanics and Neural Control of Movement Conference (BANCOM 2016). Dr. Lieber revisits the topic of sarcomere length as a fundamental property of skeletal muscle contraction. Specifically, problems associated with sarcomere length non-uniformity and the role of sarcomerogenesis in diseases such as cerebral palsy are critically discussed. Dr. Roberts then makes us aware of the (often neglected) role of the passive tissues in muscles and discusses the properties of parallel elasticity and series elasticity, and their role in muscle function. Specifically, he identifies the merits of analyzing muscle deformations in three dimensions (rather than just two), because of the potential decoupling of the parallel elastic element length from the contractile element length, and reviews the associated implications for the architectural gear ratio of skeletal muscle contraction. Dr. Blemker then tackles muscle adaptation using a novel way of looking at adaptive processes and what might drive adaptation. She argues that cells do not have pre-programmed behaviors that are controlled by the nervous system. Rather, the adaptive responses of muscle fibers are determined by sub-cellular signaling pathways that are affected by mechanical and biochemical stimuli; an exciting framework with lots of potential. Finally, Dr. Lee takes on the challenging task of determining human muscle properties in vivo. She identifies the dilemma of how we can demonstrate the effectiveness of a treatment, specifically in cases of muscle spasticity following stroke or in children with cerebral palsy. She then discusses the merits of ultrasound based elastography, and the clinical possibilities this technique might hold. Overall, we are treated to a vast array of basic and clinical problems in skeletal muscle mechanics and physiology, with some solutions, and many suggestions for future research.

Abstract Skeletal muscle mechanics have been studied ever since people have shown an interest in human movement. However, our understanding of muscle contraction and muscle mechanical properties has changed fundamentally with the discovery of the sliding filament theory in 1954 and associated cross-bridge theory in 1957. Nevertheless, experimental evidence suggests that our knowledge of the mechanisms of contraction is far from complete, and muscle properties and muscle function in human movement remain largely unknown. In this manuscript, I am trying to identify some of the crucial challenges we are faced with in muscle mechanics, offer possible solutions to questions, and identify problems that might be worthwhile exploring in the future. Since it is impossible to tackle all (worthwhile) problems in a single manuscript, I identified three problems that are controversial, important, and close to my heart. They may be identified as follows: (i) mechanisms of muscle contraction, (ii) in vivo whole muscle mechanics and properties, and (iii) force-sharing among synergistic muscles. These topics are fundamental to our understanding of human movement and movement control, and they contain a series of unknowns and challenges to be explored in the future. It is my hope that this paper may serve as an inspiration for some, may challenge current beliefs in selected areas, tackle important problems in the area of muscle mechanics, physiology and movement control, and may guide and focus some of the thinking of future muscle mechanics research.

Mass transport represents the most fundamental process in living organisms. It includes delivery of nutrients, oxygen, drugs, and other substances from the vascular system to tissue and transport of waste and other products from cells back to vascular and lymphatic network and organs. Furthermore, movement is achieved by mechanical forces generated by muscles in coordination with the nervous system. The signals coming from the brain, which have the character of electrical waves, produce activation within muscle cells. Therefore, from a physics perspective, there exist a number of physical fields within the body, such as velocities of transport, pressures, concentrations of substances, and electrical potential, which is directly coupled to biochemical processes of transforming the chemical into mechanical energy and further internal forces for motion. The overall problems of mass transport and electrophysiology coupled to mechanics can be investigated theoretically by developing appropriate computational models. Due to the enormous complexity of the biological system, it would be almost impossible to establish a detailed computational model for the physical fields related to mass transport, electrophysiology, and coupled fields. To make computational models feasible for applications, we here summarize a concept of smeared physical fields, with coupling among them, and muscle mechanics, which includes dependence on the electrical potential. Accuracy of the smeared computational models, also with coupling to muscle mechanics, is illustrated with simple example, while their applicability is demonstrated on a liver model with tumors present. The last example shows that the introduced methodology is applicable to large biological systems.

Many models have been developed to predict metabolic energy expenditure based on biomechanical proxies of muscle function. However, current models may only perform well for select forms of locomotion, not only because the models are rarely rigorously tested across subtle and broad changes in locomotor task but also because previous research has not adequately characterised different forms of locomotion to account for the potential variability in muscle function and thus metabolic energy expenditure. To help to address the latter point, the present study imposed frequency and height constraints to hopping and quantified gross metabolic power as well as the activation requirements of medial gastrocnemius (MG), lateral gastrocnemius (GL), soleus (SOL), tibialis anterior (TA), vastus lateralis (VL), rectus femoris (RF) and biceps femoris (BF), and the work requirements of GL, SOL and VL. Gross metabolic power increased with a decrease in hop frequency and increase in hop height. There was no hop frequency or hop height effect on the mean electromyography (EMG) data of ankle musculature; however, the mean EMG of VL and RF increased with a decrease in hop frequency and that of BF increased with an increase in hop height. With a reduction in hop frequency, GL, SOL and VL fascicle shortening, fascicle shortening velocity and fascicle to MTU shortening ratio increased, whereas with an increase in hop height, only SOL fascicle shortening velocity increased. Therefore, within the constraints that we imposed, decreases in hop frequency and increases in hop height resulted in increases in metabolic power that could be explained by increases in the activation requirements of knee musculature and/or increases in the work requirements of both knee and ankle musculature., Competing Interests: Competing interests The authors declare no competing or financial interests., (© 2023. Published by The Company of Biologists Ltd.)

Contraction in striated muscle is classically described as regulated by calcium-mediated structural changes in the actin-containing thin filaments, which release the binding sites for the interaction with myosin motors to produce force. In this view, myosin motors, arranged in the thick filaments, are basically always ready to interact with the thin filaments, which ultimately regulate the contraction. However, a new "dual-filament" activation paradigm is emerging, where both filaments must be activated to generate force. Growing evidence from the literature shows that the thick filament activation has a role on the striated muscle fine regulation, and its impairment is associated with severe pathologies. This review is focused on the proposed mechanical feedback that activates the inactive motors depending on the level of tension generated by the active ones, the so-called mechanosensing mechanism. Since the main muscle function is to generate mechanical work, the implications on muscle mechanics will be highlighted, showing: (i) how non-mechanical modulation of the thick filament activation influences the contraction, (ii) how the contraction influences the activation of the thick filament and (iii) how muscle, through the mechanical modulation of the thick filament activation, can regulate its own mechanics. This description highlights the crucial role of the emerging bi-directional feedback on muscle mechanical performance.

The secondary evolution of quadrupedality from bipedal ancestry is a rare evolutionary transition in tetrapods yet occurred convergently at least three times within ornithischian dinosaurs. Despite convergently evolving quadrupedal gait, ornithischians exhibited variable anatomy, particularly in the forelimbs, which underwent a major functional change from assisting in foraging and feeding in bipeds to becoming principal weight-bearing components of the locomotor system in quadrupeds. Here, we use three-dimensional multi-body dynamics models to demonstrate quantitatively that different quadrupedal ornithischian clades evolved distinct forelimb musculature, particularly around the shoulder. We find that major differences in glenohumeral abduction-adduction and long axis rotation muscle leverages were key drivers of mechanical disparity, thereby refuting previous hypotheses about functional convergence in major clades. Elbow muscle leverages were also disparate across the major ornithischian lineages, although high elbow extension muscle leverages were convergent between most quadrupeds. Unlike in ornithischian hind limbs, where differences are more closely tied to functional similarity than phylogenetic relatedness, mechanical disparity in ornithischian forelimbs appears to have been shaped primarily by phylogenetic constraints. Differences in ancestral bipedal taxa within each clade may have resulted in disparate ecomorphological constraints on the evolutionary pathways driving divergence in their quadrupedal descendants.

Skeletal muscle tissue has a highly complex and heterogeneous structure comprising several physical length scales. In the simplest model of muscle tissue, it can be represented as a one dimensional nonlinear spring in the direction of muscle fibres. However, at the finest level, muscle tissue includes a complex network of collagen fibres, actin and myosin proteins, and other cellular materials. This study shall derive an intermediate physical model which encapsulates the major contributions of the muscle components to the elastic response apart from activation-related along-fibre responses. The micro-mechanical factors in skeletal muscle tissue (eg. connective tissue, fluid, and fibres) can be homogenized into one material aggregate that will capture the behaviour of the combination of material components. In order to do this, the corresponding volume fractions for each type of material need to be determined by comparing the stress-strain relationship for a volume containing each material. This results in a model that accounts for the micro-mechanical features found in muscle and can therefore be used to analyze effects of neuro-muscular diseases such as cerebral palsy or muscular dystrophies. The purpose of this study is to construct a model of muscle tissue that, through choosing the correct material parameters based on experimental data, will accurately capture the mechanical behaviour of whole muscle. This model is then used to look at the impacts of the bulk modulus and material parameters on muscle deformation and strain energy-density distributions.

Despite decades of research, we lack a mechanistic framework capable of predicting how movement-related signals are transformed into the diversity of muscle spindle afferent firing patterns observed experimentally, particularly in naturalistic behaviors. Here, a biophysical model demonstrates that well-known firing characteristics of mammalian muscle spindle Ia afferents – including movement history dependence, and nonlinear scaling with muscle stretch velocity – emerge from first principles of muscle contractile mechanics. Further, mechanical interactions of the muscle spindle with muscle-tendon dynamics reveal how motor commands to the muscle (alpha drive) versus muscle spindle (gamma drive) can cause highly variable and complex activity during active muscle contraction and muscle stretch that defy simple explanation. Depending on the neuromechanical conditions, the muscle spindle model output appears to ‘encode’ aspects of muscle force, yank, length, stiffness, velocity, and/or acceleration, providing an extendable, multiscale, biophysical framework for understanding and predicting proprioceptive sensory signals in health and disease.

IntroductionThe passive stiffness of skeletal muscle can drastically affect muscle function in vivo, such as the case for fibrotic tissue or patients with cerebral palsy. The two constituents of skeletal muscle that dominate passive stiffness are the intracellular protein titin and the collagenous extracellular matrix (ECM). However, efforts to correlate stiffness and measurements of specific muscle constituents have been mixed, and thus the complete mechanisms for changes to muscle stiffness remain unknown. We hypothesize that biaxial stretch can provide an improved approach to evaluating passive muscle stiffness.MethodsWe performed planar biaxial materials testing of passively stretched skeletal muscle and identified three previously published datasets of uniaxial materials testing. We developed and employed a constitutive model of passive skeletal muscle that includes aligned muscle fibers and dispersed ECM collagen fibers with a bimodal von Mises distribution. Parametric modeling studies and fits to experimental data (both biaxial and previously published) were completed.ResultsBiaxial data exhibited differences in time dependent behavior based on orientation (p < 0.0001), suggesting different mechanisms supporting load in the direction of muscle fibers (longitudinal) and in the perpendicular (transverse) directions. Model parametric studies and fits to experimental data exhibited the robustness of the model (