Hill-type Model Research Articles

Neuromuscular mechanisms for the fast decline in rate of force development with muscle disuse - a narrative review.

The removal of skeletal muscle tension (unloading or disuse) is followed by many changes in the neuromuscular system, including muscle atrophy and loss of isometric maximal strength (measured by maximal force, Fmax). Explosive strength, i.e. the ability to develop the highest force in the shortest possible time, to maximise rate of force development (RFD), is a fundamental neuromuscular capability, often more functionally relevant than maximal muscle strength. In the present review, we discuss data from studies that looked at the effect of muscle unloading on isometric maximal versus explosive strength. We present evidence that muscle unloading yields a greater decline in explosive relative to maximal strength. The longer the unloading duration, the smaller the difference between the decline in the two measures. Potential mechanisms that may explain the greater decline in measures of RFD relative to Fmax after unloading are higher recruitment thresholds and lower firing rates of motor units, slower twitch kinetics, impaired excitation-contraction coupling, and decreased tendon stiffness. Using a Hill-type force model, we showed that this ensemble of adaptations minimises the loss of force production at submaximal contraction intensities, at the expense of a disproportionately lower RFD. With regard to the high functional relevance of RFD on one hand, and the boosted detrimental effects of inactivity on RFD on the other hand, it seems crucial to implement specific exercises targeting explosive strength in populations that experience muscle disuse over a longer time.

A three filament mechanistic model of musculotendon force and impedance

The force developed by actively lengthened muscle depends on different structures across different scales of lengthening. For small perturbations, the active response of muscle is well captured by a linear-time-invariant (LTI) system: a stiff spring in parallel with a light damper. The force response of muscle to longer stretches is better represented by a compliant spring that can fix its end when activated. Experimental work has shown that the stiffness and damping (impedance) of muscle in response to small perturbations is of fundamental importance to motor learning and mechanical stability, while the huge forces developed during long active stretches are critical for simulating and predicting injury. Outside of motor learning and injury, muscle is actively lengthened as a part of nearly all terrestrial locomotion. Despite the functional importance of impedance and active lengthening, no single muscle model has all these mechanical properties. In this work, we present the viscoelastic-crossbridge active-titin (VEXAT) model that can replicate the response of muscle to length changes great and small. To evaluate the VEXAT model, we compare its response to biological muscle by simulating experiments that measure the impedance of muscle, and the forces developed during long active stretches. In addition, we have also compared the responses of the VEXAT model to a popular Hill-type muscle model. The VEXAT model more accurately captures the impedance of biological muscle and its responses to long active stretches than a Hill-type model and can still reproduce the force-velocity and force-length relations of muscle. While the comparison between the VEXAT model and biological muscle is favorable, there are some phenomena that can be improved: the low frequency phase response of the model, and a mechanism to support passive force enhancement.

A three filament mechanistic model of musculotendon force and impedance.

The force developed by actively lengthened muscle depends on different structures across different scales of lengthening. For small perturbations, the active response of muscle is well captured by a linear-time-invariant (LTI) system: a stiff spring in parallel with a light damper. The force response of muscle to longer stretches is better represented by a compliant spring that can fix its end when activated. Experimental work has shown that the stiffness and damping (impedance) of muscle in response to small perturbations is of fundamental importance to motor learning and mechanical stability, while the huge forces developed during long active stretches are critical for simulating and predicting injury. Outside of motor learning and injury, muscle is actively lengthened as a part of nearly all terrestrial locomotion. Despite the functional importance of impedance and active lengthening, no single muscle model has all these mechanical properties. In this work, we present the viscoelastic-crossbridge active-titin (VEXAT) model that can replicate the response of muscle to length changes great and small. To evaluate the VEXAT model, we compare its response to biological muscle by simulating experiments that measure the impedance of muscle, and the forces developed during long active stretches. In addition, we have also compared the responses of the VEXAT model to a popular Hill-type muscle model. The VEXAT model more accurately captures the impedance of biological muscle and its responses to long active stretches than a Hill-type model and can still reproduce the force-velocity and force-length relations of muscle. While the comparison between the VEXAT model and biological muscle is favorable, there are some phenomena that can be improved: the low frequency phase response of the model, and a mechanism to support passive force enhancement.

Advancements in Patient Care and Safety: Integrating Nursing Innovations for Enhanced Healthcare Outcomes

In the realm of virtual environments, hand haptic technology plays a crucial role in capturing the nuanced movements of a user’s hands and fingers. This is complemented by a haptic sleeve that bridges the gap between the arm and hand, effectively translating these movements into corresponding actions performed by a robot avatar within the virtual space. Furthermore, these innovative devices are adept at relaying the force and texture felt by the robot avatar as it interacts with objects in the virtual environment back to the user. This interaction crafts an immersive experience, mirroring the sensation of physically touching and manipulating the objects. The prediction of wearer's joint torques uses the Hill-type model and is made through the flexion movement of the elbow joint. As the user engages in object manipulation through the robot avatar, the haptic feedback disseminates throughout the entire arm, enriching the user experience with a wide spectrum of tactile sensations. This advancement in haptic technology significantly enhances the realism of robot operation, thereby improving the dynamics of human-robot interaction.

Finite Element Analysis of Cervical Spine Kinematic Response during Ejection Utilising a Hill-Type Dynamic Muscle Model.

To determine the impact of active muscle on the dynamic response of a pilot's neck during simulated emergency ejection, a detailed three-dimensional (3D) cervical spine (C0-T1) finite element (FE) model integrated with active muscles was constructed. Based on the Hill-type model characterising the muscle force activation mechanics, 13 major neck muscles were modelled. The active force generated by each muscle was simulated as functions of (i) active state (Na), (ii) velocity (Fv(v)), and (iii) length (FL(L)). An acceleration-time profile with an initial acceleration rate of 125 G·s-1 in the 0-80 ms period, reaching peak acceleration of 10 G, then kept constant for a further 70 ms, was applied. The rotational angles of each cervical segment under these ejection conditions were compared with those without muscles and with passive muscles derived from the previous study. Similar trends of segmental rotation were observed with S- and C-curvature of the cervical spine in the 150 ms span analysed. With active muscles, the flexion motion of the C0-C2 segments exhibited higher magnitudes of rotation compared to those without muscle and passive muscle models. The flexion motion increased rapidly and peaked at about 95-105 ms, then decreased rapidly to a lower magnitude. Lower C2-T1 segments exhibited less variation in flexion and extension motions. Overall, during emergency ejections, active muscle activities effectively reduce the variability in rotational angles across cervical segments, except C0-C2 segments in the 60-120 ms period. The role of the active state dynamics of the muscles was crucial to the magnitude of the muscle forces demonstrated. This indicates that it is crucial for pilots to consciously contract their muscles before ejection to prevent cervical spine injuries.

Full Hill-type muscle model of the I1/I3 retractor muscle complex in Aplysia californica.

The coordination of complex behavior requires knowledge of both neural dynamics and the mechanics of the periphery. The feeding system of Aplysia californica is an excellent model for investigating questions in soft body systems' neuromechanics because of its experimental tractability. Prior work has attempted to elucidate the mechanical properties of the periphery by using a Hill-type muscle model to characterize the force generation capabilities of the key protractor muscle responsible for moving Aplysia's grasper anteriorly, the I2 muscle. However, the I1/I3 muscle, which is the main driver of retractions of Aplysia's grasper, has not been characterized. Because of the importance of the musculature's properties in generating functional behavior, understanding the properties of muscles like the I1/I3 complex may help to create more realistic simulations of the feeding behavior of Aplysia, which can aid in greater understanding of the neuromechanics of soft-bodied systems. To bridge this gap, in this work, the I1/I3 muscle complex was characterized using force-frequency, length-tension, and force-velocity experiments and showed that a Hill-type model can accurately predict its force-generation properties. Furthermore, the muscle's peak isometric force and stiffness were found to exceed those of the I2 muscle, and these results were analyzed in the context of prior studies on the I1/I3 complex's kinematics in vivo.

Conserved mammalian muscle mechanics during eccentric contractions.

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 80years 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.

A physiologically enhanced muscle spindle model: using a Hill-type model for extrafusal fibers as template for intrafusal fibers

The muscle spindle is an essential proprioceptor, significantly involved in sensing limb position and movement. Although biological spindle models exist for years, the gold-standard for motor control in biomechanics are still sensors built of homogenized spindle output models due to their simpler combination with neuro-musculoskeletal models. Aiming to improve biomechanical simulations, this work establishes a more physiological model of the muscle spindle, aligned to the advantage of easy integration into large-scale musculoskeletal models. We implemented four variations of a spindle model in Matlab/Simulink®: the Mileusnic et al. (2006) model, Mileusnic model without mass, our enhanced Hill-type model, and our enhanced Hill-type model with parallel damping element (PDE). Different stretches in the intrafusal fibers were simulated in all model variations following the spindle afferent recorded in previous experiments in feline soleus muscle. Additionally, the enhanced Hill-type models had their parameters extensively optimized to match the experimental conditions, and the resulting model was validated against data from rats’ triceps surae muscle. As result, the Mileusnic models present a better overall performance generating the afferent firings compared to the common data evaluated. However, the enhanced Hill-type model with PDE exhibits a more stable performance than the original Mileusnic model, at the same time that presents a well-tuned Hill-type model as muscle spindle fibers, and also accounts for real sarcomere force-length and force-velocity aspects. Finally, our activation dynamics is similar to the one applied to Hill-type model for extrafusal fibers, making our proposed model more easily integrated in multi-body simulations.

Motoneuron-driven computational muscle modelling with motor unit resolution and subject-specific musculoskeletal anatomy.

The computational simulation of human voluntary muscle contraction is possible with EMG-driven Hill-type models of whole muscles. Despite impactful applications in numerous fields, the neuromechanical information and the physiological accuracy such models provide remain limited because of multiscale simplifications that limit comprehensive description of muscle internal dynamics during contraction. We addressed this limitation by developing a novel motoneuron-driven neuromuscular model, that describes the force-generating dynamics of a population of individual motor units, each of which was described with a Hill-type actuator and controlled by a dedicated experimentally derived motoneuronal control. In forward simulation of human voluntary muscle contraction, the model transforms a vector of motoneuron spike trains decoded from high-density EMG signals into a vector of motor unit forces that sum into the predicted whole muscle force. The motoneuronal control provides comprehensive and separate descriptions of the dynamics of motor unit recruitment and discharge and decodes the subject's intention. The neuromuscular model is subject-specific, muscle-specific, includes an advanced and physiological description of motor unit activation dynamics, and is validated against an experimental muscle force. Accurate force predictions were obtained when the vector of experimental neural controls was representative of the discharge activity of the complete motor unit pool. This was achieved with large and dense grids of EMG electrodes during medium-force contractions or with computational methods that physiologically estimate the discharge activity of the motor units that were not identified experimentally. This neuromuscular model advances the state-of-the-art of neuromuscular modelling, bringing together the fields of motor control and musculoskeletal modelling, and finding applications in neuromuscular control and human-machine interfacing research.

Evaluation of a Fused Sonomyography and Electromyography-Based Control on a Cable-Driven Ankle Exoskeleton

This article presents an assist-as-needed (AAN) control framework for exoskeleton assistance based on human volitional effort prediction via a Hill-type neuromuscular model. A sequential processing algorithm-based multirate observer is applied to continuously estimate muscle activation levels by fusing surface electromyography (sEMG) and ultrasound (US) echogenicity signals from the ankle muscles. An adaptive impedance controller manipulates the exoskeleton's impedance for a more natural behavior by following a desired intrinsic impedance model. Two neural networks provide robustness to uncertainties in the overall ankle joint-exoskeleton model and the prediction error in the volitional ankle joint torque. A rigorous Lyapunov-based stability analysis proves that the AAN control framework achieves uniformly ultimately bounded tracking for the overall system. Experimental studies on five participants with no neurological disabilities walking on a treadmill validate the effectiveness of the designed ankle exoskeleton and the proposed AAN approach. Results illustrate that the AAN control approach with fused sEMG and US echogenicity signals maintained a higher human volitional effort prediction accuracy, less ankle joint trajectory tracking error, and less robotic assistance torque than the AAN approach with the sEMG-based volitional effort prediction alone. The findings support our hypotheses that the proposed controller increases human motion intent prediction accuracy, improves the exoskeleton's control performance, and boosts voluntary participation from human subjects. The new framework potentially paves a foundation for using multimodal biological signals to control rehabilitative or assistive robots.

Development of Modernized Acinetobacter baumannii Susceptibility Test Interpretive Criteria for Recommended Antimicrobial Agents Using Pharmacometric Approaches.

Acinetobacter baumannii-Acinetobacter calcoaceticus complex (referred to herein as A. baumannii) treatment guidelines contain numerous older antimicrobial agents with susceptibility test interpretive criteria (STIC, also known as susceptibility breakpoints) set using only epidemiological data. We utilized a combination of in vitro surveillance data, preclinical murine thigh and lung infection models, population pharmacokinetics, simulation, and pharmacokinetic/pharmacodynamic (PK/PD) target attainment analyses to evaluate A. baumannii STIC for four commonly recommended antimicrobials from different classes (amikacin, ceftazidime, ciprofloxacin, and minocycline). Antimicrobial in vitro surveillance data were based on 1,647 clinical A. baumannii isolates obtained from 109 centers in the United States and Europe. Among these isolates, 5 were selected for evaluation in murine infection models based on fitness and MIC variability. PK and dose-ranging studies were conducted using neutropenic murine thigh and lung infection models The MIC ranges for the 5 isolates evaluated were as follows: amikacin, 2 to 32 μg/mL; ceftazidime, 4 to 16 μg/mL; ciprofloxacin, 0.12 to 2 μg/mL; minocycline, 0.25 to 4 μg/mL. All organisms grew ≥1.5 log10 CFU in both models in untreated controls. Plasma and epithelial lining fluid (ELF) pharmacokinetics for all drugs were determined in mice using liquid chromatography-tandem mass spectrometry (LC-MS/MS) methods. For each isolate, 5 dose levels of each drug were tested individually in the thigh and lung infection model. The inoculum ranged from 7.9 to 8.4 and 6.8 to 7.7 log10 CFU/mL for the lung and thigh models, respectively. PK/PD targets associated with net bacterial stasis and 1- and 2-log10 CFU reductions from baseline were identified for each organism/infection model using Hill-type models. Population pharmacokinetic models for each agent were identified from the literature. Using demographic variables for simulated patients with hospital-acquired or ventilator-associated bacterial pneumonia or urinary tract infections (including acute pyelonephritis) who were administered maximal dosing regimens of each agent, estimates of protein binding, and ELF penetration ratios based on data from the literature, free-drug plasma and total-drug concentration-time profiles were generated, and PK/PD indices by MIC were calculated. Percent probabilities of attaining median and randomly assigned PK/PD targets associated with the above-described endpoints were determined. Recommended susceptible breakpoints for each agent were those representing the highest MIC at which the percent probabilities of achieving PK/PD targets associated with a 1-log10 CFU reduction from baseline approached or were ≥90%. The following susceptible breakpoints for A. baumannii were identified: amikacin, ≤8 μg/mL for pneumonia; ceftazidime, ≤32 and ≤8 μg/mL for pneumonia; ciprofloxacin, ≤1 μg/mL; and minocycline, ≤0.5/≤1 μg/mL which correspond to the standard and high minocycline dosing regimens of 200 mg per day and 200 mg every 12 h, respectively. Implementation of appropriate STIC will help clinicians optimally use the above-described agents and improve the likelihood of successful patient outcomes.

Limiting radial pedal forces greatly reduces maximal power output and efficiency in sprint cycling: an optimal control study.

A cyclist's performance depends critically on the generated average mechanical power output (AMPO). The instantaneous mechanical power output equals the product of crank angular velocity, crank length, and the tangential pedal force. Radial pedal forces do not contribute to mechanical power. It has been suggested that radial pedal forces arise from suboptimal pedaling technique and that limiting these would increase AMPO and efficiency. Here, we presented an optimal control musculoskeletal model of a cyclist (consisting of five segments driven by nine Hill-type muscle-tendon units) to predict maximal AMPO during sprint cycling at different levels of allowed radial pedal forces. Our findings showed that limiting radial pedal forces has a detrimental effect on maximal AMPO; it dropped from 1,115 W without a limit on radial forces to 528 W when no radial forces were allowed (both at 110 rpm). We explained that avoiding radial pedal forces causes ineffective use of muscles: muscles deliver less positive power and have a higher muscle power dissipation ratio (average mechanical power dissipated per unit of average positive power delivered). We concluded that radial pedal forces are an unavoidable by-product when optimizing for maximal AMPO and that limiting these leads to a performance decrease.NEW & NOTEWORTHY In the literature, but also in the "cycling field" [e.g., trainers, coaches, and (professional) cyclists], it is often suggested that trying to limit/avoid radial pedal forces enhances cycling technique and with that maximal average power output and efficiency. In this paper, we introduce an optimal control model of a human cyclists (consisting of five segments and driven by nine Hill-type muscle-tendon complex models). With that we not only show, but also explain why limiting radial forces is a bad idea: it will decrease maximal attainable AMPO and will decrease efficiency.

Numerical instability of Hill-type muscle models.

Hill-type muscle models are highly preferred as phenomenological models for musculoskeletal simulation studies despite their introduction almost a century ago. The use of simple Hill-type models in simulations, instead of more recent cross-bridge models, is well justified since computationally 'light-weight'-although less accurate-Hill-type models have great value for large-scale simulations. However, this article aims to invite discussion on numerical instability issues of Hill-type muscle models in simulation studies, which can lead to computational failures and, therefore, cannot be simply dismissed as an inevitable but acceptable consequence of simplification. We will first revisit the basic premises and assumptions on the force-length and force-velocity relationships that Hill-type models are based upon, and their often overlooked but major theoretical limitations. We will then use several simple conceptual simulation studies to discuss how these numerical instability issues can manifest as practical computational problems. Lastly, we will review how such numerical instability issues are dealt with, mostly in an ad hoc fashion, in two main areas of application: musculoskeletal biomechanics and computer animation.

The Impact of Hill-Type Actuator Components on the Performance of Reinforcement Learning Controllers to Reverse Upper-Limb Paralysis.

Functional electrical stimulation (FES) may allow people who are paralyzed due to spinal cord injuries (SCIs) to regain the ability to move. Deep neural networks (DNNs) trained with reinforcement learning (RL) have been recently explored as a promising methodology to control FES systems to restore upper-limb movements. However, previous studies suggested that large asymmetries in antagonistic upper-limb muscle strengths could impair RL controller performance. In this work, we investigated the underlying causes of asymmetry-associated decreases in controller performance by comparing different Hill-type models of muscle atrophy, and by characterizing RL controller sensitivity to passive mechanical properties of the arm. Simulations indicated that RL controller performance is relatively insensitive to moderate (up to 50%) changes in tendon stiffness and in flexor muscle stiffness. However, the viable workspace for RL control was substantially affected by flexor muscle weakness and by extensor muscle stiffness. Furthermore, we uncovered that RL controller performance issues previously attributed to asymmetrical antagonistic muscle strength resulted from flexor muscle active forces that were insufficient to counteract extensor muscle passive resistance. The simulations supported the adoption of rehabilitation protocols for reaching tasks that prioritize decreasing muscle passive resistance, and counteracting passive resistance with increased antagonistic muscle strength.

A Simple Integrated Mathematical Model of Neuromuscular Activation

In the present work, we propose a new integrated mathematical model of neuromuscular activation. It combines the Izhikevich model of neural activity with the Williams model of calcium activity inside the muscle cell and a Hill-type model for the resultant muscle force. The coupling is done using a heuristic approach. The aim is to construct a simple model, which has biophysically meaningful parameters and is applicable to the study of neuromuscular diseases. Then, we study numerically the properties of the model solutions with respect to the main parameters. To that end, we study the effect of various firing patterns of the motoneuron, variations in the properties of the end-plate as well as the rates, corresponding to the calcium dynamics inside the muscle cell.

Development and Validation of an Active Muscle Simplified Finite Element Human Body Model in a Standing Posture.

Active muscles play an important role in postural stabilization, and muscle-induced joint stiffening can alter the kinematic response of the human body, particularly that of the lower extremities, under dynamic loading conditions. There are few full-body human body finite element models with active muscles in a standing posture. Thus, the objective of this study was to develop and validate the M50-PS+Active model, an average-male simplified human body model in a standing posture with active musculature. The M50-PS+Active model was developed by incorporating 116 skeletal muscles, as one-dimensional beam elements with a Hill-type material model and closed-loop Proportional Integral Derivative (PID) controller muscle activation strategy, into the Global Human Body Models Consortium (GHBMC) simplified pedestrian model M50-PS. The M50-PS+Active model was first validated in a gravity standing test, showing the effectiveness of the active muscles in maintaining a standing posture under gravitational loading. The knee kinematics of the model were compared against volunteer kinematics in unsuited and suited step-down tests from NASA's active response gravity offload system (ARGOS) laboratory. The M50-PS+Active model showed good biofidelity with volunteer kinematics with an overall CORA score of 0.80, as compared to 0.64 (fair) in the passive M50-PS model. The M50-PS+Active model will serve as a useful tool to study the biomechanics of the human body in vehicle-pedestrian accidents, public transportation braking, and space missions piloted in a standing posture.

Adaptive cooperative control of a soft elbow rehabilitation exoskeleton based on improved joint torque estimation

A current challenge with robot-assisted rehabilitation is to combine the active involvement and voluntary participation of patients into the rehabilitation training process to enhance therapy outcome. This paper presents a soft elbow exoskeleton for the rehabilitation training of disabled patients. An adaptive cooperative control strategy is investigated to promote active participation based on an improved joint torque estimation method and a time-delay sliding mode control scheme. The surface electromyography signals from biceps and triceps are input into a Hill-type musculoskeletal model and a Gaussian radial basis functional network to estimate human elbow joint torque and motion intention. The joint torque estimation experiment, intention-based trajectory following experiment and patient-active free-motion training experiment are carried out by five healthy volunteers and five stroke patients to evaluate the performance of proposed control strategy. The results indicate that the proposed scheme can guarantee the joint torque estimation accuracy and position control accuracy. Moreover, it allow patients to actively dominate the training path based on their motion intention with different training intensity.

Huxley muscle model surrogates for high-speed multi-scale simulations of cardiac contraction

The computational requirements of the Huxley-type muscle models are substantially higher than those of Hill-type models, making large-scale simulations impractical or even impossible to use. We constructed a data-driven surrogate model that operates similarly to the original Huxley muscle model but consumes less computational time and memory to enable efficient usage in multiscale simulations of the cardiac cycle. The data was collected from numerical simulations to train deep neural networks so that the neural networks’ behavior resembles that of the Huxley model. Since the Huxley muscle model is history-dependent, time series analysis is required to take the previous states of the muscle model into account. Recurrent and temporal convolutional neural networks are typically used for time series analysis. These networks were trained to produce stress and instantaneous stiffness. Once the networks have been trained, we compared the similarity of the produced stresses and achieved speed-up to the original Huxley model, which indicates the potential of the surrogate model to replace the model efficiently. We presented the creation procedure of the surrogate model and integration of the surrogate model into the finite element solver. Based on similarities between the surrogate model and the original model in several types of numerical experiments, and also achieved speed-up of an order of magnitude, it can be concluded that the surrogate model has the potential to replace the original model within multiscale simulations. Finally, we used our surrogate model to simulate a full cardiac cycle in order to demonstrate the application of the surrogate model in larger-scale problems.

Contribution of stroke-related changes in neuromuscular factors to gear ratio during isometric contraction of medial gastrocnemius muscle: A simulation study

BackgroundIt is not clear which neuromuscular factors are most closely associated with the loss of variable fascicle gearing after chronic stroke. The purpose of this simulation study is to determine the effects of stroke-related changes in key neuromuscular factors on the gear ratio. MethodsA modified Hill-type model of the medial gastrocnemius was developed to determine the gear ratio for a given muscle activation level and musculotendon length. Model parameters were then systematically adjusted to simulate known stroke-related changes in neuromuscular factors, and the gear ratio was computed for each change in the parameters. A Monte Carlo simulation was performed to understand which neuromuscular factors and fiber behavior-related parameters are most relevant to the loss of variable gearing. Dominance analyses were also conducted to quantify the relative importance of fiber behavior-related parameters on the gear ratio. FindingsThe gear ratio decreases significantly with smaller pennation angle and with shorter optimal fiber length. In addition, muscle thickness and pennation angle at optimal fiber length appear to be the most important muscle architectural parameters. Dominance analyses further suggest that primary determinants of gear ratio include initial pennation angle, fiber rotation-shortening ratio, initial muscle thickness, and fiber rotation. InterpretationOur findings provide insight that the pennation angle may play an important role for efficient muscular contraction, implying that maintaining muscle architecture and/or improving fiber/fascicle rotation could a key goal in rehabilitation interventions. Our findings will help us to better interpret altered gearing behavior in aging and pathological muscles.

Medial gastrocnemius muscle–tendon unit ratios of young females and males

A muscle’s contractile element length relative to its muscle–tendon unit (MTU) length is a fundamental design feature affecting MTU function, with high (0.9) or low ratios (0.1) favouring either rapid or economical force production, respectively. Despite the importance for MTU function, little in vivo work has been done to understand contractile element-MTU length ratio variability between individuals and sexes. We therefore compared the medial gastrocnemius (MG) MTU ratios of thirteen females and eighteen males, and explored whether individual ratios could be predicted based on anatomical features.At the presumed tendon slack length ankle joint angle, lengths of MG’s MTU, Achilles tendon, muscle belly and its muscle fascicles were measured from B-mode ultrasound images. Contractile element length was represented by the in-series muscle fascicle length (FL) and was calculated by multiplying FL by the cosine of fascicle angle.The mean ± standard deviation in-series FL-MTU length ratio was 0.09 ± 0.02 and ranged from 0.06 to 0.11, whereas the muscle belly length-MTU length ratio was 0.54 ± 0.38 and ranged from 0.47 to 0.60. Neither ratio was significantly different between females and males (p ≥ 0.116). In-series FL was not significantly correlated with MTU length (r = -0.115, p =.538), muscle belly length (r = 0.05, p =.788), or shank length (r = 0.169, p =.364), but MTU length was significantly correlated with muscle belly length (r = 0.641, p <.001), and shank length (r = 0.575, p =.001).A low in-series FL-MTU length ratio suggests that the MG of young, healthy individuals is specialised for energy-efficient stretch–shortening cycles. These findings provide useful inputs for the MTU actuator design of Hill-type models.