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

A benchmark of muscle models to length changes great and small

Digital human body models are used to simulate injuries that occur as a result of vehicle collisions, vibration, sports, and falls. Given enough time the body's musculature can generate force, affect the body's movements, and change the risk of some injuries. The finite-element code LS-DYNA is often used to simulate the movements and injuries sustained by the digital human body models as a result of an accident. In this work, we evaluate the accuracy of the three muscle models in LS-DYNA (MAT_156, EHTM, and the VEXAT) when simulating a range of experiments performed on isolated muscle: force-length-velocity experiments on maximally and sub-maximally stimulated muscle, active-lengthening experiments, and vibration experiments. The force-length-velocity experiments are included because these conditions are typical of the muscle activity that precedes an accident, while the active-lengthening and vibration experiments mimic conditions that can cause injury. The three models perform similarly during the maximally and sub-maximally activated force-length-velocity experiments, but noticeably differ in response to the active-lengthening and vibration experiments. The VEXAT model is able to generate the enhanced forces of biological muscle during active lengthening, while both the MAT_156 and EHTM produce too little force. In response to vibration, the stiffness and damping of the VEXAT model closely follows the experimental data while the MAT_156 and EHTM models differ substantially. The accuracy of the VEXAT model comes from two additional mechanical structures that are missing in the MAT_156 and EHTM models: viscoelastic cross-bridges, and an active titin filament. To help others build on our work we have made our simulation code publicly available.

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.

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.

An investigation of tendon strains in jersey finger injury load cases using a finite element neuromuscular human body model

Introduction: A common hand injury in American football, rugby and basketball is the so-called jersey finger injury (JFI), in which an eccentric overextension of the distal interphalangeal joint leads to an avulsion of the connected musculus flexor digitorum profundus (FDP) tendon. In the field of automotive safety assessment, finite element (FE) neuromuscular human body models (NHBMs) have been validated and are employed to evaluate different injury types related to car crash scenarios. The goal of this study is to show, how such a model can be modified to assess JFIs by adapting the hand of an FE-NHBM for the computational analysis of tendon strains during a generalized JFI load case. Methods: A jersey finger injury criterion (JFIC) covering the injury mechanisms of tendon straining and avulsion was defined based on biomechanical experiments found in the literature. The hand of the Total Human Model for Safety (THUMS) version 3.0 was combined with the musculature of THUMS version 5.03 to create a model with appropriate finger mobility. Muscle routing paths of FDP and musculus flexor digitorum superficialis (FDS) as well as tendon material parameters were optimized using literature data. A simplified JFI load case was simulated as the gripping of a cylindrical rod with finger flexor activation levels between 0% and 100%, which was then retracted with the velocity of a sprinting college football player to forcefully open the closed hand. Results: The optimization of the muscle routing node positions and tendon material parameters yielded good results with minimum normalized mean absolute error values of 0.79% and 7.16% respectively. Tendon avulsion injuries were detected in the middle and little finger for muscle activation levels of 80% and above, while no tendon or muscle strain injuries of any kind occurred. Discussion: The presented work outlines the steps necessary to adapt the hand model of a FE-NHBM for the assessment of JFIs using a newly defined injury criterion called the JFIC. The injury assessment results are in good agreement with documented JFI symptoms. At the same time, the need to rethink commonly asserted paradigms concerning the choice of muscle material parameters is highlighted.

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.

Finite element human body models with active reflexive muscles suitable for sex based whiplash injury prediction

Previous research has not produced a satisfactory resource to study reflexive muscle activity for investigating potentially injurious whiplash motions. Various experimental and computational studies are available, but none provided a comprehensive biomechanical representation of human response during rear impacts. Three objectives were addressed in the current study to develop female and male finite element human body models with active reflexive neck muscles: 1) eliminate the buckling in the lower cervical spine of the model observed in earlier active muscle controller implementations, 2) evaluate and quantify the influence of the individual features of muscle activity, and 3) evaluate and select the best model configuration that can be used for whiplash injury predictions. The current study used an open-source finite element model of the human body for injury assessment representing an average 50th percentile female anthropometry, together with the derivative 50th percentile male morphed model. Based on the head-neck kinematics and CORelation and Analyis (CORA) tool for evaluation, models with active muscle controller and parallel damping elements showed improved head-neck kinematics agreement with the volunteers over the passive models. It was concluded that this model configuration would be the most suitable for gender-based whiplash injury prediction when different impact severities are to be studied.

Evaluation of muscle strain injury severity in active human body models

Even though significant efforts in the field of injury detection with finite element active human body models (FE AHBMs) have been made, injuries of the muscle-tendon unit (MTU) have not yet been taken into consideration. Therefore, the goal of this study was to define a muscle strain injury criterion (MSIC) to evaluate the damage sustained by the musculature during muscle driven movement scenarios. The MSIC was derived from biomechanical tests found in the literature and the proposed threshold values were substantiated through a comparison to an estimate of the ultimate tensile strength of human skeletal muscle and the forces acting on the biceps femoris long head muscle during one sprinting gait cycle. The application of the MSIC to state-of-the-art FE AHBMs was demonstrated by evaluating the strain injury severity of selected neck muscles of a full-body AHBM during two seat rotation load cases. The results of the MSIC substantiation suggest that all three injury threshold values proposed in this work fall in a plausible corridor of forces acting on the MTU. The combined results of the AHBM simulations indicate that neither of the two examined seat rotations are likely to cause strain injury to the neck muscles and that the proposed MSIC can easily be applied to current AHBMs without further modification of the model architecture or the muscle parameters. The MSIC was also used to formulate a hypothesis on the aetiology of muscle strain injuries, through which it was demonstrated that material inhomogeneities in the MTU might be the cause for strain injuries sustained during otherwise physiological movements. This work is a first step in the direction of the definition of a wholistic injury criterion for the human skeletal muscle fibre.

Analysis of control strategies for VIVA OpenHBM with active reflexive neck muscles

Modeling muscle activity in the neck muscles of a finite element (FE) human body model can be based on two biological reflex systems. One approach is to approximate the Vestibulocollic reflex (VCR) function, which maintains the head orientation relative to a fixed reference in space. The second system tries to maintain the head posture relative to the torso, similar to the Cervicocolic reflex (CCR). Strategies to combine these two neck muscle controller approaches in a single head-neck FE model were tested, optimized, and compared to rear-impact volunteer data. The first approach, Combined-Control, assumed that both controllers simultaneously controlled all neck muscle activations. In the second approach, Distributed-Control, one controller was used to regulate activation of the superficial muscles while a different controller acted on deep neck muscles. The results showed that any muscle controller that combined the two approaches was less effective than only using one of VCR- or CCR-based systems on its own. A passive model had the best objective rating for cervical spine kinematics, but the addition of a single active controller provided the best response for both head and cervical spine kinematics. The present study demonstrates the difficulty in completely capturing representative head and cervical spine responses to rear-impact loading and identified a controller capturing the VCR reflex as the best candidate to investigate whiplash injury mechanisms through FE modeling.

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, r 2 = 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.

‘Falling heads’: investigating reflexive responses to head–neck perturbations

Background

Reflexive responses to head–neck perturbations affect the injury risk in many different situations ranging from sports-related impact to car accident scenarios. Although several experiments have been conducted to investigate these head–neck responses to various perturbations, it is still unclear why and how individuals react differently and what the implications of these different responses across subjects on the potential injuries might be. Therefore, we see a need for both experimental data and biophysically valid computational Human Body Models with bio-inspired muscle control strategies to understand individual reflex responses better.

Methods

To address this issue, we conducted perturbation experiments of the head–neck complex and used this data to examine control strategies in a simulation model. In the experiments, which we call ’falling heads’ experiments, volunteers were placed in a supine and a prone position on a table with an additional trapdoor supporting the head. This trapdoor was suddenly released, leading to a free-fall movement of the head until reflexive responses of muscles stopped the downwards movement.

Results

We analysed the kinematic, neuronal and dynamic responses for all individuals and show their differences for separate age and sex groups. We show that these results can be used to validate two simple reflex controllers which are able to predict human biophysical movement and modulate the response necessary to represent a large variability of participants.

Conclusions

We present characteristic parameters such as joint stiffness, peak accelerations and latency times. Based on this data, we show that there is a large difference in the individual reflexive responses between participants. Furthermore, we show that the perturbation direction (supine vs. prone) significantly influences the measured kinematic quantities. Finally, ’falling heads’ experiments data are provided open-source to be used as a benchmark test to compare different muscle control strategies and to validate existing active Human Body Models directly.

How muscle stiffness affects human body model behavior

BACKGROUND

Active human body models (AHBM) consider musculoskeletal movement and joint stiffness via active muscle truss elements in the finite element (FE) codes in dynamic application. In the latest models, such as THUMS™ Version 5, nearly all human muscle groups are modeled in form of one-dimensional truss elements connecting each joint. While a lot of work has been done to improve the active and passive behavior of this 1D muscle system in the past, the volumetric muscle system of THUMS was modeled in a much more simplified way based on Post Mortem Human Subject (PMHS) test data. The stiffness changing effect of isometric contraction was hardly considered for the volumetric muscle system of whole human body models so far. While previous works considered this aspect for single muscles, the effect of a change in stiffness due to isometric contraction of volumetric muscles on the AHBM behavior and computation time is yet unknown.

METHODS

In this study, a simplified frontal impact using the THUMS Version 5 AM50 occupant model was simulated. Key parameters to regulate muscle tissue stiffness of solid elements in THUMS were identified for the material model MAT_SIMPLIFIED_FOAM and different stiffness states were predefined for the buttock and thigh.

RESULTS

During frontal crash, changes in muscle stiffness had an effect on the overall AHBM behavior including expected injury outcome. Changes in muscle stiffness for the thigh and pelvis, as well as for the entire human body model and for strain-rate-dependent stiffness definitions based on literature data had no significant effect on the computation time.

DISCUSSION

Kinematics, peak impact force and stiffness changes were in general compliance with the literature data. However, different experimental setups had to be considered for comparison, as this topic has not been fully investigated experimentally in automotive applications in the past. Therefore, this study has limitations regarding validation of the frontal impact results.

CONCLUSION

Variations of default THUMS material model parameters allow an efficient change in stiffness of volumetric muscles for whole AHBM applications. The computation time is unaffected by altering muscle stiffness using the method suggested in this work. Due to a lack of validation data, the results of this work can only be validated with certain limitations. In future works, the default material models of THUMS could be replaced with recently published models to achieve a possibly more biofidelic muscle behavior, which would even allow a functional dependency of the 1D and 3D muscle systems. However, the effect on calculation time and model stability of these models is yet unknown and should be considered in future studies for efficient AHBM applications.

Vestibulocollic and Cervicocollic Muscle Reflexes in a Finite Element Neck Model During Multidirectional Impacts

Active neck musculature plays an important role in the response of the head and neck during impact and can affect the risk of injury. Finite element Human Body Models (HBM) have been proposed with open and closed-loop controllers for activation of muscle forces; however, controllers are often calibrated to specific experimental loading cases, without considering the intrinsic role of physiologic muscle reflex mechanisms under different loading conditions. This study aimed to develop a single closed-loop controller for neck muscle activation in a contemporary male HBM based on known reflex mechanisms and assess how this approach compared to current open-loop controllers across a range of impact directions and severities. Controller parameters were optimized using volunteer data and independently assessed across twelve impact conditions. The kinematics from the closed-loop controller simulations showed good average CORA rating to the experimental data (0.699) for the impacts following the ISO/TR9790 standard. Compared to previously optimized open-loop activation strategy, the average difference was less than 9%. The incorporation of the reflex mechanisms using a closed-loop controller can provide robust performance for a range of impact directions and severities, which is critical to improving HBM response under a larger spectrum of automotive impact simulations.