Static versus dynamic muscle modelling in extinct species: a biomechanical case study of the Australopithecus afarensis pelvis and lower extremity

The force a muscle generates is dependent on muscle structure, in which fibre length, pennation angle and tendon slack length all influence force production. Muscles are not preserved in the fossil record and these parameters must be estimated when constructing a musculoskeletal model. Here, we test the capability of digitally reconstructed muscles of the Australopithecus afarensis model (specimen AL 288-1) to maintain an upright, single-support limb posture. Our aim was to ascertain the influence that different architectural estimation methods have on muscle specialisation and on the subsequent inferences that can be extrapolated about limb function. Parameters were estimated for 36 muscles in the pelvis and lower limb and seven different musculoskeletal models of AL 288-1 were produced. These parameters represented either a 'static' Hill-type muscle model (n = 4 variants) which only incorporated force, or instead a 'dynamic' Hill-type muscle model with an elastic tendon and fibres that could vary force-length-velocity properties (n = 3 variants). Each muscle's fibre length, pennation angle, tendon slack length and maximal isometric force were calculated based upon different input variables. Static (inverse) simulations were computed in which the vertical and mediolateral ground reaction forces (GRF) were incrementally increased until limb collapse (simulation failure). All AL 288-1 variants produced somewhat similar simulated muscle activation patterns, but the maximum vertical GRF that could be exerted on a single limb was not consistent between models. Three of the four static-muscle models were unable to support >1.8 times body weight and produced models that under-performed. The dynamic-muscle models were stronger. Comparative results with a human model imply that similar muscle group activations between species are needed to sustain single-limb support at maximally applied GRFs in terms of the simplified static simulations (e.g., same walking pose) used here. This approach demonstrated the range of outputs that can be generated for a model of an extinct individual. Despite mostly comparable outputs, the models diverged mostly in terms of strength.

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.

Development and verification of a physiologically motivated internal controller for the open-source extended Hill-type muscle model in LS-DYNA

Nowadays, active human body models are becoming essential tools for the development of integrated occupant safety systems. However, their broad application in industry and research is limited due to the complexity of incorporated muscle controllers, the long simulation runtime, and the non-regular use of physiological motor control approaches. The purpose of this study is to address the challenges in all indicated directions by implementing a muscle controller with several physiologically inspired control strategies into an open-source extended Hill-type muscle model formulated as LS-DYNA user-defined umat41 subroutine written in the Fortran programming language. This results in increased usability, runtime performance and physiological accuracy compared to the standard muscle material existing in LS-DYNA. The proposed controller code is verified with extensive experimental data that include findings for arm muscles, the cervical spine region, and the whole body. Selected verification experiments cover three different muscle activation situations: (1) passive state, (2) open-loop and closed-loop muscle activation, and (3) reflexive behaviour. Two whole body finite element models, the 50th percentile female VIVA OpenHBM and the 50th percentile male THUMS v5, are used for simulations, complemented by the simplified arm model extracted from the 50th percentile male THUMS v3. The obtained results are evaluated additionally with the CORrelation and Analysis methodology and the mean squared error method, showing good to excellent biofidelity and sufficient agreement with the experimental data. It was shown additionally how the integrated controller allows simplified mimicking of the movements for similar musculoskeletal models using the parameters transfer method. Furthermore, the Hill-type muscle model presented in this paper shows better kinematic behaviour even in the passive case compared to the existing one in LS-DYNA due to its improved damping and elastic properties. These findings provide a solid evidence base motivating the application of the enhanced muscle material with the internal controller in future studies with Active Human Body Models under different loading conditions.

Modeling of active skeletal muscles: a 3D continuum approach incorporating multiple muscle interactions

Skeletal muscles have a highly organized hierarchical structure, whose main function is to generate forces for movement and stability. To understand the complex heterogeneous behaviors of muscles, computational modeling has advanced as a non-invasive approach to evaluate relevant mechanical quantities. Aiming to improve musculoskeletal predictions, this paper presents a framework for modeling 3D deformable muscles that includes continuum constitutive representation, parametric determination, model validation, fiber distribution estimation, and integration of multiple muscles into a system level for joint motion simulation. The passive and active muscle properties were modeled based on the strain energy approach with Hill-type hyperelastic constitutive laws. A parametric study was conducted to validate the model using experimental datasets of passive and active rabbit leg muscles. The active muscle model with calibrated material parameters was then implemented to simulate knee bending during a squat with multiple quadriceps muscles. A computational fluid dynamics (CFD) fiber simulation approach was utilized to estimate the fiber arrangements for each muscle, and a cohesive contact approach was applied to simulate the interactions among muscles. The single muscle simulation results showed that both passive and active muscle elongation responses matched the range of the testing data. The dynamic simulation of knee flexion and extension showed the predictive capability of the model for estimating the active quadriceps responses, which indicates that the presented modeling pipeline is effective and stable for simulating multiple muscle configurations. This work provided an effective framework of a 3D continuum muscle model for complex muscle behavior simulation, which will facilitate additional computational and experimental studies of skeletal muscle mechanics. This study will offer valuable insight into the future development of multiscale neuromuscular models and applications of these models to a wide variety of relevant areas such as biomechanics and clinical research.

The impact of age-related increase in passive muscle stiffness on simulated upper limb reaching

Ageing changes the musculoskeletal and neural systems, potentially affecting a person's ability to perform daily living activities. One of these changes is increased passive stiffness of muscles, but its contribution to performance is difficult to separate experimentally from other ageing effects such as loss of muscle strength or cognitive function. A computational upper limb model was used to study the effects of increasing passive muscle stiffness on reaching performance across the model's workspace (all points reachable with a given model geometry). The simulations indicated that increased muscle stiffness alone caused deterioration of reaching accuracy, starting from the edges of the workspace. Re-tuning the model's control parameters to match the ageing muscle properties does not fully reverse ageing effects but can improve accuracy in selected regions of the workspace. The results suggest that age-related muscle stiffening, isolated from other ageing effects, impairs reaching performance. The model also exhibited oscillatory instability in a few simulations when the controller was tuned to the presence of passive muscle stiffness. This instability is not observed in humans, implying the presence of natural stabilizing strategies, thus pointing to the adaptive capacity of neural control systems as a potential area of future investigation in age-related muscle stiffening.

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 intrinsic muscle properties on simulated reaching performance

Musculoskeletal modelling is used widely for studying limb motion and its control, but simulation outcomes may depend heavily on the underlying muscle model used. The aim of this study was to investigate how intrinsic muscle properties affect reaching movements in a simple upper limb model. The simulations suggest that more realistic, higher-order activation dynamics requires longer prediction from a forward model and gives rise to a higher level of unplanned co-contraction than simple activation models. Consistent with prior work, muscle force-length-velocity properties stabilised and smoothed limb movements and furthermore helped promote accurate reaching performance with the high-order activation model.

Muscle-driven and torque-driven centrodes during modeled flexion of individual lumbar spines are disparate

Lumbar spine biomechanics during the forward-bending of the upper body (flexion) are well investigated by both in vivo and in vitro experiments. In both cases, the experimentally observed relative motion of vertebral bodies can be used to calculate the instantaneous center of rotation (ICR). The timely evolution of the ICR, the centrode, is widely utilized for validating computer models and is thought to serve as a criterion for distinguishing healthy and degenerative motion patterns. While in vivo motion can be induced by physiological active structures (muscles), in vitro spinal segments have to be driven by external torque-applying equipment such as spine testers. It is implicitly assumed that muscle-driven and torque-driven centrodes are similar. Here, however, we show that centrodes qualitatively depend on the impetus. Distinction is achieved by introducing confidence regions (ellipses) that comprise centrodes of seven individual multi-body simulation models, performing flexion with and without preload. Muscle-driven centrodes were generally directed superior–anterior and tail-shaped, while torque-driven centrodes were located in a comparably narrow region close to the center of mass of the caudal vertebrae. We thus argue that centrodes resulting from different experimental conditions ought to be compared with caution. Finally, the applicability of our method regarding the analysis of clinical syndromes and the assessment of surgical methods is discussed.

Force and deformation transmission characteristics of a compliant tendon-sheath actuation system based on Hill-type muscle model

Artificial muscle is a kind of transmission actuator widely used in rehabilitation robots and wearable devices. However, there are some restrictions on the usage of these artificial muscles, including the short stroke length, complex structure, special power sources, and high nonlinear characteristics. Inspired by Hill-type muscle model, in this article, a new kind of artificial muscle using tendon-sheath and compliant springs is proposed to perform muscle-like characteristics. Force and deformation transmission models are proposed and validated by simulations and experiments. The experimental and simulation output results show nice goodness-of-fit and the R-square values are 0.9876 and 0.9046, respectively. Moreover, experiments are carried out in groups to analyze the transmission characteristics using different parameters, including variations of series springs, velocities, tendon diameters, and bending angles. The best R-square value of force-elongation curve and fitness curve could reach 0.9845, which indicates that the transmission model of the compliant artificial muscle can be used to express the transmission characteristics of the skeleton muscles.

Model-based analysis of fatigued human knee extensors : Effects of isometrically induced fatigue on Hill-type model parameters and ballistic contractions

This study investigated the effect of isometrically induced fatigue on Hill-type muscle model parameters and related task-dependent effects. Parameter identification methods were used to extract fatigue-related parameter trends from isometric and ballistic dynamic maximum voluntary knee extensions. Nine subjects, who completed ten fatiguing sets, each consisting of nine 3 s isometric maximum voluntary contractions with 3 s rest plus two ballistic contractions with different loads, were analyzed. Only at the isometric task, the identified optimized model parameter values of muscle activation rate and maximum force generating capacity of the contractile element decreased from [Formula: see text] to [Formula: see text] Hz and from [Formula: see text] to [Formula: see text] N, respectively. For all tasks, the maximum efficiency of the contractile element, mathematically related to the curvature of the force-velocity relation, increased from [Formula: see text] to [Formula: see text]. The model parameter maximum contraction velocity decreased from [Formula: see text] to [Formula: see text] m/s and the stiffness of the serial elastic element from [Formula: see text] to [Formula: see text] N/mm. Thus, models of fatigue should consider fatigue dependencies in active as well as in passive elements, and muscle activation dynamics should account for the task dependency of fatigue.

Why are Antagonist Muscles Co-activated in My Simulation? A Musculoskeletal Model for Analysing Human Locomotor Tasks

Existing "off-the-shelf" musculoskeletal models are problematic when simulating movements that involve substantial hip and knee flexion, such as the upstroke of pedalling, because they tend to generate excessive passive fibre force. The goal of this study was to develop a refined musculoskeletal model capable of simulating pedalling and fast running, in addition to walking, which predicts the activation patterns of muscles better than existing models. Specifically, we tested whether the anomalous co-activation of antagonist muscles, commonly observed in simulations, could be resolved if the passive forces generated by the underlying model were diminished. We refined the OpenSim™ model published by Rajagopal et al. (IEEE Trans Biomed Eng 63:1-1, 2016) by increasing the model's range of knee flexion, updating the paths of the knee muscles, and modifying the force-generating properties of eleven muscles. Simulations of pedalling, running and walking based on this model reproduced measured EMG activity better than simulations based on the existing model-even when both models tracked the same subject-specific kinematics. Improvements in the predicted activations were associated with decreases in the net passive moments; for example, the net passive knee moment during the upstroke of pedalling decreased from 36.9 N m (existing model) to 6.3 N m (refined model), resulting in a dramatic decrease in the co-activation of knee flexors. The refined model is available from SimTK.org and is suitable for analysing movements with up to 120° of hip flexion and 140° of knee flexion.

Implementation and validation of the extended Hill-type muscle model with robust routing capabilities in LS-DYNA for active human body models

BACKGROUND

In the state of the art finite element AHBMs for car crash analysis in the LS-DYNA software material named *MAT_MUSCLE (*MAT_156) is used for active muscles modeling. It has three elements in parallel configuration, which has several major drawbacks: restraint approximation of the physical reality, complicated parameterization and absence of the integrated activation dynamics. This study presents implementation of the extended four element Hill-type muscle model with serial damping and eccentric force-velocity relation including [Formula: see text] dependent activation dynamics and internal method for physiological muscle routing.

RESULTS

Proposed model was implemented into the general-purpose finite element (FE) simulation software LSDYNA as a user material for truss elements. This material model is verified and validated with three different sets of mammalian experimental data, taken from the literature. It is compared to the *MAT_MUSCLE (*MAT_156) Hill-type muscle model already existing in LS-DYNA, which is currently used in finite element human body models (HBMs). An application example with an arm model extracted from the FE ViVA OpenHBM is given, taking into account physiological muscle paths.

CONCLUSION

The simulation results show better material model accuracy, calculation robustness and improved muscle routing capability compared to *MAT_156. The FORTRAN source code for the user material subroutine dyn21.f and the muscle parameters for all simulations, conducted in the study, are given at https://zenodo.org/record/826209 under an open source license. This enables a quick application of the proposed material model in LS-DYNA, especially in active human body models (AHBMs) for applications in automotive safety.

Muscle-tendon unit scaling methods of Hill-type musculoskeletal models: An overview

This article gives an overview of the state of the art in scaling methods of generic Hill-type muscle model parameters in view of different applications and implementation of experimental data. This article establishes the requirements used to alter a generic model toward subject-specific musculoskeletal models. This article aims to improve model transparency by a structured description of scaling methods and the associated limitations in musculoskeletal models and highlight the importance of selecting a scaling method supporting the purpose of the model.