Hill Muscle Research Articles

Development of a musculoskeletal shoulder model considering anatomic joint structures and soft-tissue deformation for dynamic simulation.

The shoulder joint has a high degree of freedom and an extremely complex and unstable kinematic mechanism. Coordinated contraction of the rotator cuff muscles that stop around the humeral head and the deltoid muscles and the extensibility of soft tissues, such as the joint capsule, labrum, and ligaments, contribute to shoulder-joint stability. Understanding the mechanics of shoulder-joint movement, including soft-tissue characteristics, is important for disease prevention and the development of a device for disease treatment. This study aimed to create a musculoskeletal shoulder model to represent the realistic behavior of joint movement and soft-tissue deformation as a dynamic simulation using a rigid-body model for bones and a soft-body model for soft tissues via a spring-damper-mass system. To reproduce the muscle-contraction properties of organisms, we used a muscle-expansion representation and Hill's mechanical muscle model. Shoulder motion, including the movement of the center of rotation in joints, was reproduced, and the strain in the joint capsule during dynamic shoulder movement was quantified. Furthermore, we investigated narrowing of the acromiohumeral distance in several situations to induce tissue damage due to rotator cuff impingement at the anterior-subacromial border during shoulder abduction. Given that the model can analyze exercises under disease conditions, such as muscle and tendon injuries and impingement syndrome, the proposed model is expected to help elucidate disease mechanisms and develop treatment guidelines.

Physics-Informed Deep Learning for Muscle Force Prediction With Unlabeled sEMG Signals.

Computational biomechanical analysis plays a pivotal role in understanding and improving human movements and physical functions. Although physics-based modeling methods can interpret the dynamic interaction between the neural drive to muscle dynamics and joint kinematics, they suffer from high computational latency. In recent years, data-driven methods have emerged as a promising alternative due to their fast execution speed, but label information is still required during training, which is not easy to acquire in practice. To tackle these issues, this paper presents a novel physics-informed deep learning method to predict muscle forces without any label information during model training. In addition, the proposed method could also identify personalized muscle-tendon parameters. To achieve this, the Hill muscle model-based forward dynamics is embedded into the deep neural network as the additional loss to further regulate the behavior of the deep neural network. Experimental validations on the wrist joint from six healthy subjects are performed, and a fully connected neural network (FNN) is selected to implement the proposed method. The predicted results of muscle forces show comparable or even lower root mean square error (RMSE) and higher coefficient of determination compared with baseline methods, which have to use the labeled surface electromyography (sEMG) signals, and it can also identify muscle-tendon parameters accurately, demonstrating the effectiveness of the proposed physics-informed deep learning method.

The Problem with Inventing Molecular Mechanisms to Fit Thermodynamic Equations of Muscle.

Almost every model of muscle contraction in the literature to date is a molecular power stroke model, even though this corpuscular mechanism is opposed by centuries of science, by 85 years of unrefuted evidence that muscle is a thermodynamic system, and by a quarter century of direct observations that the molecular mechanism of muscle contraction is a molecular switch, not a molecular power stroke. An ensemble of molecular switches is a binary mechanical thermodynamic system from which A.V. Hill's muscle force-velocity relationship is directly derived, where Hill's parameter a is the internal force against which unloaded muscle shortens, and Hill's parameter b is the product of the switch displacement, d, and the actin-myosin ATPase rate. Ignoring this model and the centuries of thermodynamics that preceded it, corpuscularians continue to develop molecular power stroke models, adding to their 65-year jumble of "new", "innovative", and "unconventional" molecular mechanisms for Hill's a and b parameters, none of which resemble the underlying physical chemistry. Remarkably, the corpuscularian community holds the thermodynamicist to account for these discrepancies, which, as outlined here, I have done for 25 years. It is long past time for corpuscularians to be held accountable for their mechanisms, which by all accounts have no foundation in science. The stakes are high. Molecular power stroke models are widely used in research and in clinical decision-making and have, for over half a century, muddied our understanding of the inner workings of one of the most efficient and clean-burning machines on the planet. It is problematic that corpuscularians present these models to stakeholders as science when in fact corpuscularians have been actively defending these models against science for decades. The path forward for scientists is to stop baseless rejections of muscle thermodynamics and to begin testing corpuscular and thermodynamic mechanisms with the goal of disproving one or the other of these hypotheses.

Elbow Joint Stiffness Functional Scales Based on Hill's Muscle Model and Genetic Optimization.

The ultimate goal of rehabilitation engineering is to provide objective assessment tools for the level of injury and/or the degree of neurorehabilitation recovery based on a combination of different sensing technologies that enable the monitoring of relevant measurable variables, as well as the assessment of non-measurable variables (such as muscle effort/force and joint mechanical stiffness). This paper aims to present a feasibility study for a general assessment methodology for subject-specific non-measurable elbow model parameter prediction and elbow joint stiffness estimation. Ten participants without sensorimotor disorders performed a modified "Reach and retrieve" task of the Wolf Motor Function Test while electromyography (EMG) data of an antagonistic muscle pair (the triceps brachii long head and biceps brachii long head muscle) and elbow angle were simultaneously acquired. A complete list of the Hill's muscle model and passive joint structure model parameters was generated using a genetic algorithm (GA) on the acquired training dataset with a maximum deviation of 6.1% of the full elbow angle range values during the modified task 8 of the Wolf Motor Function Test, and it was also verified using two experimental test scenarios (a task tempo variation scenario and a load variation scenario with a maximum deviation of 8.1%). The recursive least square (RLS) algorithm was used to estimate elbow joint stiffness (Stiffness) based on the estimated joint torque and the estimated elbow angle. Finally, novel Stiffness scales (general patterns) for upper limb functional assessment in the two performed test scenarios were proposed. The stiffness scales showed an exponentially increasing trend with increasing movement tempo, as well as with increasing weights. The obtained general Stiffness patterns from the group of participants without sensorimotor disorders could significantly contribute to the further monitoring of motor recovery in patients with sensorimotor disorders.

Dynamic modeling of pneumatic braided muscle actuator based on Hill muscle model

This article presents a dynamic model of a pneumatic braided muscle (PBM) actuator which is inspired from skeletal muscle model. The behavior of the PBM actuator can be simulated as Hill muscle model and thus, it is modeled as an equivalent nonlinear spring dashpot system. Instead of empirical relations, the force-stretch relation of the actuator derived in our earlier work based on finite deformation theory is utilized. The nonlinear equation of motion is solved for both free and forced vibration cases numerically. The frequency analysis of the forced vibration is performed using the multiple scales method. Furthermore, the effect of various parameters like damping, material stiffness, and geometry on the nonlinear response of the actuator has been examined using time response, phase portrait, and frequency response at simple resonance condition. This study will assist researchers to determine safe system parameter range for diverse applications.

Hill-type, bioinspired actuation delivers energy economy in DC motors

Electromagnetic motors convert stored energy to mechanical work through a linear force–velocity (FV) relationship. In biological systems, however, muscle actuation is characterized by the hyperbolic FV mechanisms of the Hill muscle—in which a parameter α characterizes the degree of nonlinearity. Previous work has shown that bioinspiration in human-engineered systems can contribute favorable mechanical attributes—such as energy efficiency, self-stability, and flexibility, among others. In this study, we first construct an easily amendable, bioinspired electromagnetic motor which produces FV curves that mimic the Hill model of muscle with a high degree of accuracy. A proportional-integral-differential (PID) controller converges the characteristically linear FV relationship of a DC motor to nonlinear Hill-type force outputs. The bioinspired electric motor does a fixed amount of work by lifting a 147.5 g mass, and we record the translational velocity of the mass and the nonlinear applied force of the motor. Under optimized gain coefficients in the PID, the bioinspired motor achieves agreement of with the Hill muscle model. Studies have shown that designing biologically inspired actuators produce comparatively energy efficient systems. We investigate the energy economy of actuating our motor with nonlinear, Hill-type forces in direct comparison with conventional linear FV actuation techniques. We find that the bioinspired motor delivers energy economy with respect to energy consumption and conversion: the nonlinear, Hill-type DC motor reduces the energetic cost of actuation when delivering a fixed amount of mechanical work.

Validate the force-velocity relation of the Hill's muscle model from a molecular perspective.

Validate the force-velocity relation of the Hill's muscle model from a molecular perspective.

Construction and Simulation of Biomechanical Model of Human Hip Joint Muscle-Tendon Assisted by Elastic External Tendon by Hill Muscle Model.

Based on the Hill muscle model (HMM), a biomechanical model of human hip muscle tendon assisted by elastic external tendon (EET) was preliminarily established to investigate and analyze the biomechanical transition between the hip joint (HJ) and related muscle tendons. Using the HMM, the optimal muscle fiber length and muscle force scaling variables were introduced by means of constrained optimization problems and were optimized. The optimized HMM was constructed with human parameters of 170 cm and 70 kg. The biomechanical model simulation test of the hip muscle tendon was performed in the automatic dynamic analysis of mechanical systems (ADAMS) software to analyze and optimize the changes in the root mean square error (RMSE), biological moment, muscle moment distribution coefficient (MDC), muscle moment, muscle force, muscle power, and mechanical work of the activation curves of the hip major muscle, iliopsoas muscle, rectus femoris muscle, and hamstring muscle under analyzing the optimized HMM and under different EET auxiliary stiffnesses from the joint moment level, joint level, and muscle level, respectively. It was found that the trends of the output joint moment of the optimized HMM and the biological moment of the human HJ were basically the same, r2 = 0.883 and RMSE = 0.18 Nm/kg, and the average metabolizable energy consumption of the HJ was (243.77 ± 1.59) J. In the range of 35%∼65% of gait cycle (GC), the auxiliary moment showed a significant downward trend with the increase of EET stiffness, when the EET stiffness of the human body was less than 200 Nm/rad, the biological moment of the human HJ gradually decreased with the increase of EET stiffness, and the MDC of the iliopsoas and hamstring muscles gradually decreased; when the EET stiffness was greater than 200 Nm/rad, the increase of the total moment of the extensor muscles significantly increased, the MDC of the gluteus maximus and rectus muscles gradually increased, and the gluteus maximus and hamstring muscle moments and muscle forces gradually increased; the results show that the optimized muscle model based on Hill can reflect the law of human movement and complete the simulation test of HJ movements, which provides a new idea for the analysis of energy migration in the musculoskeletal system of the lower limb.

Single-motor driven multi-joints lower limb exoskeleton system based on controllable clamper

In this paper, a scheme of single-motor driven multi-joints lower limb exoskeleton based on controllable clamper is proposed in order to reduce the number of driving motors, overall weight and structural complexity of the lower limb exoskeleton. We propose a new type of tendon-sheath artificial muscle as the transmission method for exoskeleton according to the Hill muscle model. A controllable clamper is used to control the contraction and relaxation of the artificial muscle, and a pair of series and parallel springs is used to imitate the characteristics of the muscle. On this basis, we designed the mechanical structure of the system, and figure out the relationship between assistant force and driving motor’s angle, then planned the control timing sequence of the clampers. The driving motor’s angle curve is determined by theoretical calculation. A platform is built, and the experimental results verify that the scheme of single motor to drive multi-joints is feasible and effective.

Thorax Dynamic Modeling and Biomechanical Analysis of Chest Breathing in Supine Lying Position.

During respiration, the expansion and contraction of the chest and abdomen are coupled with each other, presenting a complex torso movement pattern. A finite element (FE) model of chest breathing based on the HUMOS2 human body model was developed. One-dimensional muscle units with active contraction functions were incorporated into the model based on Hill's active muscle model so as to generate muscle contraction forces that can change over time. The model was validated by comparing it to the surface displacement of the chest and abdomen during respiration. Then, the mechanism of the coupled motion of the chest and abdomen was analyzed. The analyses revealed that since the abdominal wall muscles are connected to the lower edge of the rib cage through tendons, the movement of the rib cage may cause the abdominal wall muscles to be stretched in both horizontal and vertical in a supine position. The anteroposterior and the right-left diameters of the chest will increase at inspiration, while the right-left diameter of the abdomen will decrease even though the anteroposterior diameter of the abdomen increases. The external intercostal muscles at different regions had different effects on the motion of the ribs during respiration. In particular, the external intercostal muscles at the lateral region had a larger effect on pump handle movement than bucket handle movement, and the external intercostal muscles at the dorsal region had a greater influence on bucket handle movement than pump handle movement.

A Musculoskeletal Multibody Algorithm Based on a Novel Rheonomic Constraints Definition Applied to the Lower Limb.

In this paper, a multibody model was developed in the framework of biotribology of lower limb artificial joints. The presented algorithm performs the inverse dynamics of musculoskeletal systems with the aim to achieve a tool for the calculation of the joint reaction forces. The revolute joint, the cam joint, the spherical joint and the free joint were considered in the analyzed lower limb system by introducing a novel analytical formulation of the rheonomic constraint equations based on the quaternions theory. Within the kinematical analysis, the curved muscle paths were modeled by simulating their geodesic wrapping over bony surfaces while the muscle actuations were formulated through the Hill muscle model. The developed theoretical model was developed in matlab environment allowing to follow the classical musculoskeletal analysis pipeline: kinematical analysis, inverse dynamics, and static optimization, applied to the lower limb during the gait kinematics. The validation of the results was obtained by comparing the calculated hip joint reactions with the ones obtained in vivo by Bergmann and calculated by Opensim software, showing a satisfactory agreement. The proposed model and algorithm represent a fully open and controllable synovial joint tribological configuration generator tool, useful to be coupled with numerical lubrication/contact models in the framework of the in silico artificial joints tribological optimization.

Estimation of the Continuous Pronation-Supination Movement by Using Multichannel EMG Signal Features and Kalman Filter: Application to Control an Exoskeleton.

The Hill muscle model can be used to estimate the human joint angles during continuous movement. However, adopting this model requires the knowledge of many parameters, such as the length and speed of contraction of muscle fibers, which are liable to change with different individuals, leading to errors in estimation. This study established the backpropagation neural network model based on surface electromyography (sEMG) features and human movement angle. First, the function of muscles in joint rotation is defined, and then, sensors are placed on muscle tissues to gain sEMG, and then, a relation model between the surface sEMG features and the joint angle is constructed. As integrated electromyography information cannot be well reflected through a single electromyography feature, a feature extraction method combining the time domain, frequency domain, and time–frequency domain was proposed. As the degree of freedom (DOF) of the pronation–supination movement was controlled by several muscles, it was difficult to make an angle prediction. A method of correcting the estimation error based on the Kalman filter was raised to cope with this problem. An exoskeleton robot with one DOF was designed and put into the tracking experiment. The results show that the proposed model was able to enhance the estimation of the joint angle during continuous pronation–supination movements.

Design and Control of a Nonlinear Series Elastic Cable Actuator Based on the Hill Muscle Model

The bionic design of muscles is a research hotspot at present. Many researchers have designed bionic elastic actuators based on the Hill muscle model, and most of them include an active contraction element, passive contraction element and series elastic element, but they need more parametric design of mechanical structure and control under the guidance of Hill muscle model. In this research, a nonlinear series elastic cable actuating mechanism is designed in which the parameters of the elastic mechanism are optimized based on the Hill muscle model to fit the nonlinear passive elasticity of a muscle. Through the force–position relationship determined by the Hill muscle model, the output force and position of a nonlinear series elastic cable actuator are controlled to simulate the active contraction performance of a muscle. The experiments show that the proposed design and control method can make the nonlinear cable actuator have good muscle-like output force–displacement characteristics.

Trajectory optimisation with musculoskeletal integration features for fracture reduction orthopaedic robot.

Human body is an integrated system of bones and muscles. To date, there are insufficient studies on the effect of muscles on the trajectory planning of orthopaedic robot. To this end, based on a Stewart-Gough platform (6-UPU) fracture reduction orthopaedic robot, a musculoskeletal trajectory optimisation method was constructed for the interference of soft tissue during the reduction process. Firstly, pose description of the fracture reduction orthopaedic robot was introduced, and its working space was analysed. Secondly, an improved Hill muscle theory was used to construct the musculoskeletal system, and finite element analysis (FEA) was carried out. Thirdly, particle swarm optimisation (PSO) with variable weights was imported, and fracture reduction trajectory planning was obtained by quintic polynomial in the workspace. Then mathematical model for trajectory optimisation was presented, and targets of musculoskeletal optimisation were extracted, which include muscle energy consumption, robot-assisted repositioning time and trajectory length. In this sense, musculoskeletal integration trajectory optimisation method was put forward. Finally, comparative optimisation simulation with skeleton only and bone and muscle together were tested, and safety experiment with musculoskeletal integration was conducted. A cone shape workspace was got, whose range can be defined as 635.14mm on the X axis, 720mm on the Y axis, and 240mm on the Z axis, respectively. Besides, different FEA displacements revealed the effect of bone and muscle on the movement of the robot. Moreover, the optimal results with and without muscle had showed different movement time: the former consumed about 27s, but the latter spent about 25s. Additionally, the speed and acceleration of the drive rods can be obtained from zero to zero during the reset. The results show that the optimised trajectory obtained with this method is safe and reliable. Furthermore, the presence of muscle has great influence on the trajectory of robot, which could prolong the reduction time so as to prevent the occurrence of uneven soft and hard traction rate problem. This paper could be helpful for the future trajectory planning study of fracture reduction orthopaedic robot.

Research on comfortable driving posture of car drivers based on muscle biomechanics

This paper aims to solve the problem of optimal design on a comfortable human-machine arrangement of car drivers with different physical signs under dynamic manipulation. Based on the biomechanical characteristic of human skeletal muscle and Hill muscle mechanics model, this paper constructs the human seat musculoskeletal model of 5th, 50th, and 95th percentile physical signs of Chinese car drivers under dynamic manipulation. The six-degree-of-freedom flexible test bench was set up and the center composite method was used to optimize the number of experiments. The consistency and relevance analysis of the actual measurement and dynamic manipulation simulation was carried out to comprehensively analyze the human-machine arrangement parameters such as vehicle seat, pedal, and steering wheel, so as to realize the optimization design of the hard point size of comfortable driving posture and verify the rationality and applicability of the test results through the vehicle road test.

Design, control, and experimental verification of a soft knee exoskeleton for rehabilitation during walking

Since the rigid constructions of the traditional exoskeletons are liable to increase inertia of the joint and limit wearer flexibility, the soft-type exoskeletons have been developed in recent years, which can reduce system inertia, increase interaction compliance, and ensure operation safety. In this article, we present the detailed design and preliminary control of a soft body-worn and tendon-sheath-driven exoskeleton that can apply appropriate torques to the biological knee joints during rehabilitation training. This article focuses on the design of compliance tendon-sheath actuation system based on Hill muscle model, which utilizes multi-wrap pulleys and Hill-based series elastic actuator to transmit effective forces. Besides, the overall control system and strategy architectures of knee soft exoskeleton are also proposed. A fuzzy proportional–integral–derivative controller is developed for the passive rehabilitation training. On this basis, a back-propagation-neural-network-based adaptive impedance control scheme is presented to provide adaptive force based on the disease condition of the patient. Finally, preliminary experiments are conducted to demonstrate the effectiveness of proposed exoskeleton and control strategies.

A Novel Explicit Analytical Multibody Approach for the Analysis of Upper Limb Dynamics and Joint Reactions Calculation Considering Muscle Wrapping

The aim of this paper is to present an explicit analytical biomechanical multibody procedure able to be implemented in the solution of the musculoskeletal systems inverse dynamics problems. The model is proposed in formal multibody analysis and implemented in the Matlab numerical environment. It is based on the constraint kinematical behaviour analysis and considers both linear muscle actuators and curved ones, by calculating the geodesic muscle path over wrapping surfaces fixed to the bodies. The model includes the Hill muscle approach in order to evaluate both the contractile elements’ actions and the passive ones. With the aim to have a first validation, the model was applied to the dynamical analysis of the “arm26” OpenSim model, an upper limb subjected to external forces of gravity and to known kinematics. The comparison of results shows interesting matching in terms of kinematical analysis, driving forces, muscles’ activations and joint reactions, proving the reliability of the proposed approach in all cases in which it is necessary to achieve in-silico explicit determinations of the upper limb dynamics and joint reactions (i.e., in joint tribological optimization).

Estimation of Trunk Muscle Forces Using a Bio-Inspired Control Strategy Implemented in a Neuro-Osteo-Ligamentous Finite Element Model of the Lumbar Spine

Low back pain (LBP), the leading cause of disability worldwide, remains one of the most common and challenging problems in occupational musculoskeletal disorders. The effective assessment of LBP injury risk, and the design of appropriate treatment modalities and rehabilitation protocols, require accurate estimation of the mechanical spinal loads during different activities. This study aimed to: (1) develop a novel 2D beam-column finite element control-based model of the lumbar spine and compare its predictions for muscle forces and spinal loads to those resulting from a geometrically matched equilibrium-based model; (2) test, using the foregoing control-based finite element model, the validity of the follower load (FL) concept suggested in the geometrically matched model; and (3) investigate the effect of change in the magnitude of the external load on trunk muscle activation patterns. A simple 2D continuous beam-column model of the human lumbar spine, incorporating five pairs of Hill’s muscle models, was developed in the frontal plane. Bio-inspired fuzzy neuro-controllers were used to maintain a laterally bent posture under five different external loading conditions. Muscle forces were assigned based on minimizing the kinematic error between target and actual postures, while imposing a penalty on muscular activation levels. As compared to the geometrically matched model, our control-based model predicted similar patterns for muscle forces, but at considerably lower values. Moreover, irrespective of the external loading conditions, a near (<3°) optimal FL on the spine was generated by the control-based predicted muscle forces. The variation of the muscle forces with the magnitude of the external load within the simulated range at the L1 level was found linear. This work presents a novel methodology, based on a bio-inspired control strategy, that can be used to estimate trunk muscle forces for various clinical and occupational applications toward shedding light on the ever-elusive LBP etiology.

Determining the Online Measurable Input Variables in Human Joint Moment Intelligent Prediction Based on the Hill Muscle Model.

Introduction: Human joint moment is a critical parameter to rehabilitation assessment and human-robot interaction, which can be predicted using an artificial neural network (ANN) model. However, challenge remains as lack of an effective approach to determining the input variables for the ANN model in joint moment prediction, which determines the number of input sensors and the complexity of prediction. Methods: To address this research gap, this study develops a mathematical model based on the Hill muscle model to determining the online input variables of the ANN for the prediction of joint moments. In this method, the muscle activation, muscle-tendon moment velocity and length in the Hill muscle model and muscle-tendon moment arm are translated to the online measurable variables, i.e., muscle electromyography (EMG), joint angles and angular velocities of the muscle span. To test the predictive ability of these input variables, an ANN model is designed and trained to predict joint moments. The ANN model with the online measurable input variables is tested on the experimental data collected from ten healthy subjects running with the speeds of 2, 3, 4 and 5 m/s on a treadmill. The variance accounted for (VAF) between the predicted and inverse dynamics moment is used to evaluate the prediction accuracy. Results: The results suggested that the method can predict joint moments with a higher accuracy (mean VAF = 89.67±5.56 %) than those obtained by using other joint angles and angular velocities as inputs (mean VAF = 86.27±6.6%) evaluated by jack-knife cross-validation. Conclusions: The proposed method provides us with a powerful tool to predict joint moment based on online measurable variables, which establishes the theoretical basis for optimizing the input sensors and detection complexity of the prediction system. It may facilitate the research on exoskeleton robot control and real-time gait analysis in motor rehabilitation.

Modeling and simulation of musculoskeletal system of human lower limb based on tensegrity structure

In this paper, a mechanical model of the skeletal muscle of human lower limb system is established by using the Hill muscle model and kinetic equation of the movement of lower extremities according to the attachment positions of skeletal muscle. State vector and neural control are delineated by the direct configuration method. Changes of gait and skeletal muscle stress during walking process are analyzed with energy consumption as objective function. Results illustrate that simulation data are in good agreement with actual walking gait data. Feasibility and correctness of the designed model and control behavior of skeletal muscle tension structure are also verified.