Evaluation of a combination of continuum and truss finite elements in a model of passive and active muscle tissue

Biomechanical study of the effect of traction on elbow joint capsule contracture

Dynamic orthoses have a significant effect on the treatment of elbow capsular contracture. Because of the lack of quantitative research on traction forces, determining the appropriate traction force to help stretch soft tissues and maintain the joint's range of motion is a challenge in the rehabilitation process. We developed a human elbow finite element (FE) model incorporating the activity behavior of the muscles and considering different capsular contracture locations, including total, anterior and posterior capsular contractures, to analyze the internal biomechanical responses of different capsular contracture models during flexion (30 to 80 degrees). Traction loads of 10, 20, 30 and 40 N were applied to the ulna and radius at the maximum flexion angle (80 degrees) to explore the appropriate traction loads at week 4 after a joint capsule injury. We observed a significant increase in posterior capsule stress with anterior capsular contracture (ACC), and the maximum peak stress was 1.3 times higher than that in the healthy model. During the fourth week after elbow capsule injury, the appropriate traction forces for total capsule contracture (TCC), ACC and posterior capsule contracture (PCC) were 20, 10 and 20 N, respectively; these forces maintained a stable biomechanical environment for the elbow joint and achieved a soft tissue pulling effect, thus increasing elbow mobility. The results can be used as a quantitative guide for the rehabilitation physicians to determine the traction load for a specific patient.

Neck stabilization through sensory integration of vestibular and visual motion cues

BACKGROUND

To counteract gravity, trunk motion, and other perturbations, the human head-neck system requires continuous muscular stabilization. In this study, we combine a musculoskeletal neck model with models of sensory integration (SI) to unravel the role of vestibular, visual, and muscle sensory cues in head-neck stabilization and relate SI conflicts and postural instability to motion sickness.

METHOD

A 3D multisegment neck model with 258 Hill-type muscle elements was extended with postural stabilization using SI of vestibular (semicircular and otolith) and visual (rotation rate, verticality, and yaw) cues using the multisensory observer model (MSOM) and the subjective vertical conflict model (SVC). Dynamic head-neck stabilization was studied using empirical datasets, including 6D trunk perturbations and a 4 m/s2 slalom drive inducing motion sickness.

RESULTS

Recorded head translation and rotation are well matched when using all feedback loops with MSOM or SVC or assuming perfect perception. A basic version of the model, including muscle, but omitting vestibular and visual perception, shows that muscular feedback can stabilize the neck in all conditions. However, this model predicts excessive head rotations in conditions with trunk rotation and in the slalom. Adding feedback of head rotational velocity sensed by the semicircular canals effectively reduces head rotations at mid-frequencies. Realistic head rotations at low frequencies are obtained by adding vestibular and visual feedback of head rotation based on the MSOM or SVC model or assuming perfect perception. The MSOM with full vision well captures all conditions, whereas the MSOM excluding vision well captures all conditions without vision. The SVC provides two estimates of verticality, with a vestibular estimate SVCvest, which is highly effective in controlling head verticality, and an integrated vestibular/visual estimate SVCint which can complement SVCvest in conditions with vision. As expected, in the sickening drive, SI models imprecisely estimate verticality, resulting in sensory conflict and postural instability.

CONCLUSION

The results support the validity of SI models in postural stabilization, where both MSOM and SVC provide credible results. The results in the sickening drive show imprecise sensory integration to enlarge head motion. This uniquely links the sensory conflict theory and the postural instability theory in motion sickness causation.

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.

Biomechanical study of the male lower urinary tract: Simulation of internal and external sphincters dyssynergia

Urethral sphincter dysfunction is an important cause of stress urinary incontinence (SUI). The most effective treatment is the insertion of an artificial urethral sphincter (AUS), which relies to a large extent on the surgeon's experience. However, there is no quantitative standard for cuff tightness, resulting in frequent postoperative complications. This study aimed to investigate the effect of internal and external sphincter dyssynergia on urodynamic parameters in the lower urinary tract. A geometric model of male lower urinary tract tissue was constructed from collodion slices, accounting for the active behavior of the internal and external sphincters. Normal and dyssynergic internal and external sphincters (active sphincter behavior was individually injured by 25%, 50%, 75%, or 100%) were simulated with fluid-structure interactions and changes in urethral stress, displacement, and urine flow rate were detected. We found that when the internal sphincter was injured by 25%, 50%, 75%, and 100%, urethral stress near the internal sphincter decreased by 8.3%, 15.6%, 24.3%, and 35.7%, respectively. Additionally, when the external sphincter was injured by 25%, 50%, 75%, and 100%, urethral stress near the external sphincter was reduced by 13.3%, 24.3%, 38.6%, and 46.6%, respectively. Internal sphincter injury primarily affects positions near the internal sphincter and prostate, while external sphincter injury affects the area between the prostate and urethral outlet. These data could facilitate the standardized evaluation of internal and external sphincter dysfunction and lead to novel methods of preoperative assessment for AUS surgery.

The role of the joint capsule in the stability of the elbow joint

Existing studies lack a clear understanding of the interaction of the joint capsule with surrounding tissues and the local mechanical environment. Particularly, a finite element model of human elbow joint incorporating active behavior of muscle was constructed. The simulation was performed during the elbow joint flexion movement under different injury conditions of capsule (anterior capsule, posterior capsule, medial anterior capsule, lateral anterior capsule, medial posterior capsule, and lateral posterior capsule). The stress distribution and transfer of the joint capsule, ulnar cartilage, and ligaments were obtained under different injuries and flexion angles, to explore the influence of capsule injures on the stability of the elbow joint. In medial injury posterior capsule, the peak stress of the ulnar cartilage occurred at 60° flexion and shifted from posteromedial to anteromedial. And the stress was about 1.8 times that of no injury capsule. In several cases of posterior capsule injury, the stress of capsule decreased significantly and the peak stress was 40% of that in no injury joint capsule. In the case of anterior capsular injury, the cartilage stress did not change significantly, and the stress of anterior bundle and annular ligament changed slightly in the late flexion movement. These findings provide some help for doctors to treat elbow injury and understand the interaction of tissues around the joint after trauma.

One step further in biomechanical models in palaeontology: a nonlinear finite element analysis review

Finite element analysis (FEA) is no longer a new technique in the fields of palaeontology, anthropology, and evolutionary biology. It is nowadays a well-established technique within the virtual functional-morphology toolkit. However, almost all the works published in these fields have only applied the most basic FEA tools i.e., linear materials in static structural problems. Linear and static approximations are commonly used because they are computationally less expensive, and the error associated with these assumptions can be accepted. Nonetheless, nonlinearities are natural to be used in biomechanical models especially when modelling soft tissues, establish contacts between separated bones or the inclusion of buckling results. The aim of this review is to, firstly, highlight the usefulness of non-linearities and secondly, showcase these FEA tool to researchers that work in functional morphology and biomechanics, as non-linearities can improve their FEA models by widening the possible applications and topics that currently are not used in palaeontology and anthropology.

Influence of nonlinear soft tissue modeling on the external and internal forces during lateral hip impacts

Soft tissues in the hip region, which are typically considered the natural shock-absorbers during falls, attenuate the applied forces to the underlying hard tissue. The soft tissue thickness is, therefore, a significant parameter in the force attenuation. Another factor that could affect the assessment of the force attenuation in numerical simulations is the choice of constitutive model and material parameters for the soft tissue. Several constitutive models and parameters for muscle and adipose tissue were suggested in the published literature; however, the biofidelity of the proposed models for the lateral impacts has not been assessed yet. To achieve this purpose, we used a previously developed human body model named THUMS v4.02 and modified the mechanical properties and geometry of the soft tissues in the hip region. The simulations consisted of regional hip models and whole-body models. The biofidelity of the constitutive models of muscle and adipose tissue was determined objectively using the CORrelation and Analysis (CORA) rating. Moreover, the potential force attenuating effect of the adipose tissue thickness was investigated in the regional models. We collected and fitted several available nonlinear material models for muscle and adipose tissue and implemented them. The CORA ratings for several constitutive models for adipose tissue in the regional model were above 0.8. Among the muscle constitutive models, three Ogden models consistently rated above 0.58 for the whole-body model. Moreover, the impact forces in the selected adipose tissue model attenuated 47 N for every 1 mm increase in thickness. Overall, the choice of the nonlinear material model for the adipose and muscle tissue influences the external and internal force, and the difference between the material models is more pronounced when the thickness of the soft tissue increases.

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.

Importance of passive muscle, skin, and adipose tissue mechanical properties on head and neck response in rear impacts assessed with a finite element model

OBJECTIVE

The objective of this study was to improve head-neck kinematic predictions of a contemporary finite element (FE) head-neck model, assessed in rear impact scenarios (3-10 g), by including an accurate representation of the skin, adipose tissue, and passive muscle mechanical properties. The soft tissues of the neck have a substantial contribution to kinematic response, with the contribution being inversely proportional to the impact severity. Thus accurate representation of these passive tissues is critical for the assessment of kinematic response and the potential for crash induced injuries. Contemporary Human Body Models (HBMs) often incorporate overly stiff mechanical properties of passive tissues for numerical stability, which can affect the predicted kinematic response of the head and neck.

METHODS

Soft tissue material properties including non-linearity, compression-tension asymmetry, and viscoelasticity were implemented in constitutive models for the skin, adipose, and passive muscle tissues, based on experimental data in the literature. A quasi-linear viscoelastic formulation was proposed for the skin, while a phenomenological hyper-viscoelastic model was used for the passive muscle and adipose tissues. A head-neck model extracted from a contemporary FE HBM was updated to include the new tissue models and assessed using head rotation angle for rear impact scenarios (3 g, 7 g, and 10 g peak accelerations), and compared to postmortem human surrogate (PMHS) data for 7 g impacts.

RESULTS

The head rotation angle increased with the new material models for all three rear impact cases: (3 g: +43%, 7 g: +52%, 10 g: +71%), relative to the original model. The increase in head rotation was primarily attributed to the improved skin model, with the passive muscle being a secondary contributor to the increase in response. A 52% increase in head rotation for the 7 g impact improved the model response with respect to PMHS data, placing it closer to the experimental average, compared to the original model.

CONCLUSIONS

The improved skin, adipose tissue, and passive muscle material model properties, based on published experimental data, increased the neck compliance in rear impact, with improved correspondence to published PMHS test data for medium severity impacts. Future studies will investigate the coupled effect of passive and active muscle tissue for low severity impacts.

Importance of the cervical capsular joint cartilage geometry on head and facet joint kinematics assessed in a Finite element neck model

Finite element human neck models (NMs) aim to predict neck response and injury at the tissue level; however, contemporary models are most often assessed using global response such as head kinematics. Additionally, many NMs are developed from subject-specific imaging with limited soft tissue resolution in small structures such as the facet joints in the neck. Such details may be critical to enable NMs to predict tissue-level response. In the present study, the capsular joint cartilage (CJC) geometry in a contemporary NM was enhanced (M50-CJC) based on literature data. The M50-CJC was validated at the segment and full neck levels and assessed using relative facet joint kinematics (FJK), capsular ligament (CL) and intervertebral disc (IVD) strains, a relative vertebral rotation assessment (IV-NIC) and head kinematics in frontal and rear impact. The validation ratings at the segment level increased from 0.60 to 0.64, with improvements for modes of deformation associated with the facet joints, while no difference was noted at the head kinematic level. The improved CJC led to increased FJK rotation (188%) and IVD strain (152.2%,) attributed to the reduced facet joint gap. Further enhancements of the capsular joint representation or a link between the FJK and CL injury risk are recommended. Enhancements at the tissue level demonstrated a large effect on the IVD strain, but were not apparent in global metrics such as head kinematics. This study demonstrated that a biofidelic and detailed geometrical representation of the CJC contributes significantly to the predicted joint response, which is critical to investigate neck injury risk at the tissue level.

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.

Modeling of muscular activation of the muscle-tendon complex using discrete element method

The tearing of a muscle-tendon complex (MTC) is caused by an eccentric contraction; however, the structures involved and the mechanisms of rupture are not clearly identified. The passive mechanical behavior the MTC has already been modeled and validated with the discrete element method. The muscular activation is the next needed step. The aim of this study is to model the muscle fiber activation and the muscular activation of the MTC to validate their active mechanical behaviors. Each point of the force/length relationship of the MTC (using a parabolic law for the force/length relationship of muscle fibers) is obtained with two steps: 1) a passive tensile (or contractile) test until the desired elongation is reached and 2) fiber activation during a position holding that can be managed thanks to the Discrete Element model. The muscular activation is controlled by the activation of muscle fiber. The global force/length relationship of a single fiber and of the complete MTC during muscular activation is in agreement with literature. The influence of the external shape of the structure and the pennation angle are also investigated. Results show that the different constituents of the MTC (extracellular matrix, tendon), and the geometry, play an important role during the muscular activation and enable to decrease the maximal isometric force of the MTC. Moreover, the maximal isometric force decreases when the pennation angle increases. Further studies will combine muscular activation with a stretching of the MTC, until rupture, in order to numerically reproduce the tearing of the MTC.

Multilevel Validation of a Male Neck Finite Element Model With Active Musculature

Computational models of the human neck have been developed to assess human response in impact scenarios; however, the assessment and validation of such models is often limited to a small number of experimental data sets despite being used to evaluate the efficacy of safety systems and potential for injury risk in motor vehicle collisions. In this study, a full neck model (NM) with active musculature was developed from previously validated motion segment models of the cervical spine. Tissue mechanical properties were implemented from experimental studies, and were not calibrated. The neck model was assessed with experimental studies at three levels of increasing complexity: ligamentous cervical spine in axial rotation, axial tension, frontal impact, and rear impact; postmortem human subject (PMHS) rear sled impact; and human volunteer frontal and lateral sled tests using an open-loop muscle control strategy. The neck model demonstrated good correlation with the experiments ranging from quasi-static to dynamic, assessed using kinematics, kinetics, and tissue-level response. The contributions of soft tissues, neck curvature, and muscle activation were associated with higher stiffness neck response, particularly for low severity frontal impact. Experiments presenting single-value data limited assessment of the model, while complete load history data and cross-correlation enabled improved evaluation of the model over the full loading history. Tissue-level metrics demonstrated higher variability and therefore lower correlation relative to gross kinematics, and also demonstrated a dependence on the local tissue geometry. Thus, it is critical to assess models at the gross kinematic and the tissue levels.

In vitro compressive properties of skeletal muscles and inverse finite element analysis: Comparison of human versus animals

Virtual finite element human body models have been widely used in biomedical engineering, traffic safety injury analysis, etc. Soft tissue modeling like skeletal muscle accounts for a large portion of a human body model establishment, and its modeling method is not enough explored. The present study aims to investigate the compressive properties of skeletal muscles due to different species, loading rates and fiber orientations, in order to obtain available parameters of specific material laws as references for building or improving the human body model concerning both modeling accuracy and computational cost. A series of compressive experiments of skeletal muscles were implemented for human gastrocnemius muscle, bovine and porcine hind leg muscle. To avoid long-time preservation effects, all experimental tests were carried out in 24 h after that the samples were harvested. Considering computational cost and generally used in the previous human body models, one-order hyperelastic Ogden model and three-term simplified viscoelastic quasi-linear viscoelastic (QLV) were selected for numerical analysis. Inverse finite element analysis was employed to obtain corresponding material parameters. With good fitting records, the simulation results presented available material parameters for human body model establishment, and also indicated significant differences of muscle compressive properties due to species, loading rates and fiber orientations. When considering one-order Ogden law, it is worthy of noting that the inversed material parameters of the porcine muscles are similar to those of the human gastrocnemius regardless of fiber orientations. In conclusion, the obtained material parameters in the present study can be references for global human body and body segment modeling.

Implementation of controlling strategy in a biomechanical lower limb model with active muscles for coupling multibody dynamics and finite element analysis

Computational biomechanics for human body modeling has generally been categorized into two separated domains: finite element analysis and multibody dynamics. Combining the advantages of both domains is necessary when tissue stress and physical body motion are both of interest. However, the method for this topic is still in exploration. The aim of this study is to implement unique controlling strategies in finite element model for simultaneously simulating musculoskeletal body dynamics and in vivo stress inside human tissues. A finite element lower limb model with 3D active muscles was selected for the implementation of controlling strategies, which was further validated against in-vivo human motion experiments. A unique feedback control strategy that couples together a basic Proportion-Integration-Differentiation (PID) controller and generic active signals from Computed Muscle Control (CMC) method of the musculoskeletal model or normalized EMG singles was proposed and applied in the present model. The results show that the new proposed controlling strategy show a good correlation with experimental test data of the normal gait considering joint kinematics, while stress distribution of local lower limb tissue can be also detected in real-time with lower limb motion. In summary, the present work is the first step for the application of active controlling strategy in the finite element model for concurrent simulation of both body dynamics and tissue stress. In the future, the present method can be further developed to apply it in various fields for human biomechanical analysis to monitor local stress and strain distribution by simultaneously simulating human locomotion.

A comprehensive and volumetric musculoskeletal model for the dynamic simulation of the shoulder function

We present a volumetric and extensive finite element model of the shoulder usable in the context of inverse control, in which the scapula is left unconstrained on the ribcage. Such a model allows for exploring various shoulder movements, which are essential for making patient-specific decisions. The proposed model consists of 23 volumetric muscles parts modelled using the finite element method. The glenohumeral, acromioclavicular and sternoclavicular joints are modelled with soft ball-socket constraints. The musculoskeletal model can be controlled by a tracking-based algorithm, finding the excitations values in the muscles needed to follow some target points. The moment arms obtained during abduction and rotation are compared with the literature, which includes results from cadaveric data and a fine FE model of the rotator cuff and the deltoid. We simulated the paralysis of serratus anterior, a main reason of scapular winging, and compared it with its physiological counterpart. A deficiency in the range of motion as well as a reduction in upward rotation were observed, which both corroborate clinical observations. This is one of the most comprehensive model of the shoulder, which can be used to study complex pathologies of the shoulder and their impact on functional outcome such as range-of-motion.

Dynamic head-neck stabilization and modulation with perturbation bandwidth investigated using a multisegment neuromuscular model

The human head-neck system requires continuous stabilization in the presence of gravity and trunk motion. We investigated contributions of the vestibulocollic reflex (VCR), the cervicocollic reflex (CCR), and neck muscle co-contraction to head-in-space and head-on-trunk stabilization, and investigated modulation of the stabilization strategy with the frequency content of trunk perturbations and the presence of visual feedback. We developed a multisegment cervical spine model where reflex gains (VCR and CCR) and neck muscle co-contraction were estimated by fitting the model to the response of young healthy subjects, seated and exposed to anterior-posterior trunk motion, with frequency content from 0.3 up to 1, 2, 4 and 8Hz, with and without visual feedback. The VCR contributed to head-in-space stabilization with a strong reduction of head rotation (<8Hz) and a moderate reduction of head translation (>1Hz). The CCR contributed to head-on-trunk stabilization with a reduction of head rotation and head translation relative to the trunk (<2Hz). The CCR also proved essential to stabilize the individual intervertebral joints and prevent neck buckling. Co-contraction was estimated to be of minor relevance. Control strategies employed during low bandwidth perturbations most effectively reduced head rotation and head relative displacement up to 3Hz while control strategies employed during high bandwidth perturbations reduced head global translation between 1 and 4Hz. This indicates a shift from minimizing head-on-trunk rotation and translation during low bandwidth perturbations to minimizing head-in-space translation during high bandwidth perturbations. Presence of visual feedback had limited effects suggesting increased usage of vestibular feedback.

SIMULATION OF MUSCLE ACTIVATION WITH COUPLED NONLINEAR FE MODELS

Muscle activation plays an important role in head–neck dynamic response in vehicle accidents, especially in low speed impacts. The aim of the present study was to analyze the mechanical characteristics and dynamic stability of the muscle using coupled non-linear finite element model, which could be further applied for biomechanical study of head–neck system in car crash accidents. A rabbit tibialis anterior (TA) geometry model was developed. Two finite element models of TA were developed with coupled constitutive models. One coupled model was developed combining quasi-linear viscoelastic (QLV) elements and Hill type elements, and the other was developed combining hyperelastic rubber elements and Hill type elements, representing the passive behavior and active behavior, respectively. The models were validated via eccentric contractions tests under different strain rates published by Myers et al. Isometric Contraction and axial compression were also simulated via both models to evaluate the computational stability. The results showed that the coupled constitutive muscle models had a good biofidelity for the simulation of muscle activation. Both muscle models can fulfill the requirement of neck muscle system modeling for biomechanical study.

Injury mechanisms of the ligamentous cervical C2-C3 Functional Spinal Unit to complex loading modes: Finite Element study

The cervical spine sustains high rate complex loading modes during Motor Vehicle Crashes (MVCs) which may produce severe injuries accompanied with soft and/or hard tissue failure. Although previous numerical and experimental studies have provided insights on the cervical spine behavior under various loading scenarios, its response to complex impact loads and the resulting injury mechanisms are not fully understood. A validated Finite Element (FE) model of the ligamentous cervical C2-C3 Functional Spinal Unit (FSU) was utilized to assess the spinal response to six combined impact loading modes; flexion-extension combined with compression and distraction, and lateral bending and axial rotation combined with distraction. The FE model used time and rate-dependent material laws which permit assessing bone fracture and ligament failure. Spinal load-sharing, stresses in the spinal components, intradiscal pressure (IDP) change in the nucleus as well as contact pressure in the facet joints were predicted. Bone and ligaments failure occurrence and initiation instants were investigated. Results showed that spinal load-sharing varied with loading modes. Lateral bending combined with distraction was the most critical loading mode as it increased stresses and strains significantly and produced failure in most of the spinal components compared to other modes. The facet joints and surrounding cancellous bone as well as ligaments particularly the capsular (CL) and flavum (FL) ligaments were the most vulnerable structures to rapid flexion-extension, axial rotation and lateral bending combined with distraction or compression. The excessive stress and strain resulted from these loading modes produced rupture of the CL and FL ligaments and failure in the cancellous bone. The detection of failure initiation as well as fracture assessment demonstrated the vulnerability of ligaments to tensile combined loads and the major contribution of the bony structures in resisting compressive combined loads. Findings of this study may potentially assist in the development of injury prevention and treatment strategies.

On Using Model Populations to Determine Mechanical Properties of Skeletal Muscle. Application to Concentric Contraction Simulation

In the field of computational biomechanics, the experimental evaluation of the material properties is crucial for the development of computational models that closely reproduce real organ systems. When simulations of muscle tissue are concerned, stress/strain relations for both passive and active behavior are required. These experimental relations usually exhibit certain variability. In this study, a set of material parameters involved in a 3D skeletal muscle model are determined by using a system biology approach in which the parameters are randomly varied leading to a population of models. Using a set of experimental results from an animal model, a subset of the entire population of models was selected. This reduced population predicted the mechanical response within the window of experimental observations. Hence, a range of model parameters, instead of a single set of them, was determined. Rat Tibialis Anterior muscle was selected for this study. Muscles ([Formula: see text]) were activated through the sciatic nerve and during contraction the tissue pulled a weight fixed to the distal tendon (concentric contraction). Three different weights 1, 2 and 3 N were used and the time course of muscle stretch was analyzed obtaining values of (mean [Formula: see text] standard deviation): [Formula: see text], [Formula: see text] and [Formula: see text] respectively. A paired two-sided sign rank test showed significant differences between the muscle response for the three weights ([Formula: see text]). This study shows that the Monte Carlo method could be used for determine muscle characteristic parameters considering the variability of the experimental population.

Experimental characterization of post rigor mortis human muscle subjected to small tensile strains and application of a simple hyper-viscoelastic model

In models developed for impact biomechanics, muscles are usually represented with one-dimensional elements having active and passive properties. The passive properties of muscles are most often obtained from experiments performed on animal muscles, because limited data on human muscle are available. The aim of this study is thus to characterize the passive response of a human muscle in tension. Tensile tests at different strain rates (0.0045, 0.045, and 0.45 s−1) were performed on 10 extensor carpi ulnaris muscles. A model composed of a nonlinear element defined with an exponential law in parallel with one or two Maxwell elements and considering basic geometrical features was proposed. The experimental results were used to identify the parameters of the model. The results for the first- and second-order model were similar. For the first-order model, the mean parameters of the exponential law are as follows: Young’s modulus E (6.8 MPa) and curvature parameter α (31.6). The Maxwell element mean values are as follows: viscosity parameter η (1.2 MPa s) and relaxation time τ (0.25 s). Our results provide new data on a human muscle tested in vitro and a simple model with basic geometrical features that represent its behavior in tension under three different strain rates. This approach could be used to assess the behavior of other human muscles.

A physically motivated constitutive model for 3D numerical simulation of skeletal muscles

A detailed numerical implementation within the FEM is presented for a physically motivated three-dimensional constitutive model describing the passive and active mechanical behaviors of the skeletal muscle. The derivations for the Cauchy stress tensor and the consistent material tangent are provided. For nearly incompressible skeletal muscle tissue, the strain energy function may be represented either by a coupling or a decoupling of the distortional and volumetric material response. In the present paper, both functionally different formulations are introduced allowing for a direct comparison between the coupled and decoupled isochoric-volumetric approach. The numerical validation of both implementations revealed significant limitations for the decoupled approach. For an extensive characterization of the model response to different muscle contraction modes, a benchmark model is introduced. Finally, the proposed implementation is shown to provide a reliable tool for the analysis of complex and highly nonlinear problems through the example of the human mastication system by studying bite force and three-dimensional muscle shape changes during mastication.

A viscoelastic laryngeal muscle model with active components

Accurate definitions of both passive and active tissue characteristics are important to laryngeal muscle modeling. This report tested the efficacy of a muscle model which added active stress components to an accurate definition of passive properties. Using the previously developed three-network Ogden model to simulate passive stress, a Hill-based contractile element stress equation was utilized for active stress calculations. Model input parameters were selected based on literature data for the canine cricothyroid muscle, and simulations were performed in order to compare the model behavior to published results for the same muscle. The model results showed good agreement with muscle behavior, including appropriate tetanus response and contraction time for isometric conditions, as well as accurate stress predictions in response to dynamic strain with activation.

Validation of simulated chestband data in frontal and lateral loading using a human body finite element model

OBJECTIVE

Finite element (FE) computer models are an emerging tool to examine the thoracic response of the human body in the simulated environment. In this study, a recently developed human body model, the Global Human Body Models Consortium (GHBMC) mid-sized male, was used to examine chestband contour deformations in a frontal and lateral impact. The objective of this study was 2-fold. First, a methodology for extracting and analyzing virtual chestband data from a full-body FE model is presented. Then, this method is applied to virtual chestband data from 2 simulations to evaluate the model's performance against experimental data.

METHODS

One frontal and one lateral impact case were simulated using the FE model, which was preprogrammed with upper, middle, and lower chestbands. Maximum compression was determined using established techniques. Furthermore, a quadrant-based analysis technique for the results was introduced that enabled regional comparisons between the model and the experimental data in the anterior, posterior, right, and left sections of the chestband.

RESULTS

For the frontal case at 13.3 m/s, the model predicted a peak compression of 13.6 and 12.9 percent for the upper and middle chestbands. For the lateral case at 6.7 m/s, the model predicted peak compression of the upper, middle, and lower chestbands of 27.9, 26.0, and 20.4 percent. Regional analysis showed average differences at maximum deformation between the model and experiments ranging from 0.9 percent (posterior) to 6.3 percent (anterior) in the frontal case and 2.3 percent (posterior) to 10.8 percent (anterior) in the lateral case. The greatest difference between model and experimental findings was found in the anterior quadrant.

CONCLUSIONS

Though this work was focused on techniques to extract and analyze chestband data from FE models, the comparative results provide further validation of the model used in this study. The results suggest the importance of evaluating comparisons between virtual and experimental chestband data on a regional basis. These data also provide the potential to correlate chestband deformations to the loading of underlying thoraco-abdominal structures. Supplemental materials are available for this article. Go to the publisher's online edition of Traffic Injury Prevention to view the supplemental file.

Computational modeling of electromechanical propagation in the helical ventricular anatomy of the heart

The classical interpretation of myocardial activation assumes that the myocardium is homogeneous and that the electrical propagation is radial. However, anatomical studies have described a layered anatomical structure resulting from a continuous anatomical helical disposition of the myocardial fibers. To further investigate the sequence of electromechanical propagation based on the helical architecture of the heart, a simplified computational model was designed. This model was then used to test four activation patterns, which were generated by propagating the action potential along the myocardial band from different activation sites.

Simulation of active skeletal muscle tissue with a transversely isotropic viscohyperelastic continuum material model

Human body models with biofidelic kinematics in vehicle pre-crash and crash simulations require a constitutive model of muscle tissue with both passive and active properties. Therefore, a transversely isotropic viscohyperelastic continuum material model with element-local fiber definition and activation capability is suggested for use with explicit finite element codes. Simulations of experiments with New Zealand rabbit's tibialis anterior muscle at three different strain rates were performed. Three different active force-length relations were used, where a robust performance of the material model was observed. The results were compared with the experimental data and the simulation results from a previous study, where the muscle tissue was modeled with a combination of discrete and continuum elements. The proposed material model compared favorably, and integrating the active properties of the muscle into a continuum material model opens for applications with complex muscle geometries.

Parametric study of a Hill-type hyperelastic skeletal muscle model

Hill's one-dimensional three-element model has often been used for formulating a three-dimensional skeletal muscle constitutive model, which generally involves several material parameters. However, only few of these parameters have physical meanings and can be experimentally determined. In this paper, a parametric study of a Hill-type hyperelastic skeletal muscle model is performed. First, the Hill-type hyperelastic skeletal muscle model is formulated, containing 13 material parameters. The values or value ranges of these parameters are discussed. The muscle model is then used to predict the behaviour of New Zealand white rabbit hind leg muscle tibialis anterior and a sensitivity study of several parameters is performed. Results show that some parameters in the muscle model can be experimentally determined, some parameters have their own value ranges and the muscle model can predict the experimental data by tuning the parameters within their value ranges. The results from the sensitivity study can help understand how some parameters influence the total muscle stress.

Muscle mechanism: The acceleration of the load

The load (force/cross-section) determines the response of muscle power output, force and speed of contraction). The force is the product of the mass by the acceleration, thus the same force is generated by an infinite number of mass and acceleration couples and each one of these couples displays different physical and biological effects. Therefore, the load must be defined both by the mass and by the acceleration. Early muscle investigators were well aware of this situation as it is indicated by the work of Hill on the flexion of the arm against the "heavy fly-wheel". By making use of a model of sarcomere contraction we show here that the acceleration of the load is the first determinant of the time course of the process of generation of the isometric tension. We also propose that, in order to reproduce the rapid release, it is not necessary to invoke the presence of a distinct elastic element in the contractile machinery. It is sufficient to assume that the stiffness of the same machinery increases with the contractile force.

A visco-hyperelastic model for skeletal muscle tissue under high strain rates

In this paper, a visco-hyperelastic skeletal muscle model is developed. The constitutive relation is based on the definition of a Helmholtz free energy function. It is assumed that the Helmholtz energy can be decomposed into volumetric and isochoric parts; furthermore, the isochoric energy can be decoupled into hyperelastic and viscous parts. The model developed involves 14 material parameters and its performance is evaluated by comparing the finite element simulation results with the published experimental studies on the New Zealand white rabbit tibialis anterior muscle. Results show that this model is able to describe the visco-hyperelastic behaviour of both passive and active skeletal muscle tissues under high strain rates (10/s and 25/s).

Neck muscle load distribution in lateral, frontal, and rear-end impacts: a three-dimensional finite element analysis

STUDY DESIGN

A finite element (FE) model of the human neck was used to study the distribution of neck muscle loads during multidirectional impacts. The computed load distributions were compared to experimental electromyography (EMG) recordings.

OBJECTIVE

To quantify passive muscle loads in nonactive cervical muscles during impacts of varying direction and energy, using a three-dimensional (3D) continuum FE muscle model.

SUMMARY OF BACKGROUND DATA

Experimental and numerical studies have confirmed the importance of muscles in the impact response of the neck. Although EMG has been used to measure the relative activity levels in neck muscles during impact tests, this technique has not been able to measure all neck muscles and cannot directly quantify the force distribution between the muscles. A numerical model can give additional insight into muscle loading during impact.

METHODS

An FE model with solid element musculature was used to simulate frontal, lateral, and rear-end vehicle impacts at 4 peak accelerations. The peak cross-sectional forces, internal energies, and effective strains were calculated for each muscle and impact configuration. The computed load distribution was compared with experimental EMG data.

RESULTS

The load distribution in the cervical muscles varied with load direction. Peak sectional forces, internal energies, and strains increased in most muscles with increasing impact acceleration. The dominant muscles identified by the model for each direction were splenius capitis, levator scapulae, and sternocleidomastoid in lateral impacts, splenius capitis, and trapezoid in frontal impacts, and sternocleidomastoid, rectus capitis posterior minor, and hyoids in rear-end impacts. This corresponded with the most active muscles identified by EMG recordings, although within these muscles the distribution of forces and EMG levels were not the same.

CONCLUSION

The passive muscle forces, strains, and energies computed using a continuum FE model of the cervical musculature distinguished between impact directions and peak accelerations, and on the basis of prior studies, isolated the most important muscles for each direction.