Modeling of human muscle and its deformation.

There is a lack of volume preserving and reasonable deformation of human muscles during bones and joints movement in the field of digital orthopedics. A novel approach for modeling of human muscle and its deformation was put forward to effectively assist doctors in guiding patients to carry out rehabilitation exercises. Firstly, based on Magnetic Resonance Imaging (MRI) data, the generated slice images were used to extract the outer contour lines and then the corresponding contour lines and optimal matching points of the adjacent layer images were connected to construct the three-dimensional (3D) geometric models of the muscles; Secondly, the mapping relationship between parameters can be established through hierarchical definition of the muscle characteristics to realize the volume-preserving deformation of muscle; Finally, the movement of human joints can be realized based on the constraint range of joint movement, and the vector-valued dynamic fourth-order differential equation was proposed to make the characteristic curve dynamically simulate the process of muscle deformation, thereby forming the corresponding relationship between bone movement and muscle deformation. The effectiveness and feasibility of this method have been verified in our experiments with biceps brachii and triceps brachii as examples. The maximum volume errors of biceps brachii and triceps brachii during the deformation process were less than 0.6%, which can be ignored within a certain allowable error range, reflecting that the parametric method was used to realize the reasonable volume-preserving deformation of human muscle.

Lower Extremity Muscle Volume in Unilateral and Bilateral Patellofemoral Pain: A Cross-Sectional Exploratory Study Including Superficial and Deep Muscles Authors.

CONTEXT: Existing patellofemoral pain (PFP) literature has primarily focused on quadriceps muscle volume, with limited attention given to the lower limbs deep and superficial muscle volumes in individuals with unilateral and bilateral PFP. This research aims to fill this gap. OBJECTIVE: To explore superficial and deep lower extremity muscle volume in women with unilateral and bilateral PFP compared to a normative database of pain-free women. DESIGN: Cross-sectional study. SETTING: University imaging research center. PATIENTS OR OTHER PARTICIPANTS: Twenty women with PFP (10 unilateral and 10 bilateral) and 8 pain-free women. MAIN OUTCOME MEASURE(S): We quantified lower extremity muscle volume via 3.0 Tesla magnetic resonance imaging. Two separate one-way analyses of variance were performed: (1) unilateral PFP (painful vs. non-painful limb) vs. pain-free control and (2) bilateral PFP (more painful vs. less painful limb) vs. pain-free control. RESULTS: There were no differences in age and body mass index across groups (P >.05). Compared to pain-free women, both women with unilateral and bilateral PFP had bilaterally smaller volumes of the anterior (iliacus: P ≤ .0004, d = 2.12-2.65), medial (adductor brevis, adductor longus, gracilis, and pectineus: P ≤ .02, d = 1.25-2.24), posterior (obturator externus, obturator internus, and quadratus femoris: P < .05, d = 1.17-4.82), and lateral (gluteus minimus: P ≤ .03, d = 1.16-2.09) hip muscles, and knee extensors (rectus femoris: P ≤.003, d = 1.67-2.16) and flexors (biceps femoris: long and short head: P ≤ .01, d = 1.56-1.93). CONCLUSIONS: Both women with unilateral and bilateral PFP 25 displayed decreased volume of multiple superficial and deep muscles of the bilateral hips and knees compared with pain-free women. Interventions should bilaterally target lower limb muscles when treating PFP, and hypertrophy exercises for specific muscles should be explored to enhance interventional choices.

Influence of Treadmill Design on Gait: Does Treadmill Size Affect Muscle Activation Amplitude? A Musculoskeletal Calculation With Individualized Input Parameters of Gait Analysis.

With increasing age, gait changes often occur, leading to mobility problems and thus a higher risk of falling. Interest in training at home or at retirement homes has led to the development of "mobile treadmills." A difference in treadmill surface length may influence walking parameters (i.e., step length) and therefore may affect muscle activation. This led to the question: Does the treadmill size affect the muscle activation, i.e., with the length of the walking surface. The study aimed to investigate the influence of treadmill size, i.e., length of the walking surface, on gait pattern and to determine differences in the amplitude of muscle activation using a participant-specific musculoskeletal model (AnyBody Technology A/S, Aalborg, Denmark). For a prospective, randomized study gait parameters were collected from 47 healthy participants (aged 50.19 ± 20.58 years) while walking on two different treadmills, a small mobile treadmill (walking surface length 100 cm) and a conventional treadmill (walking surface length 150 cm), at their preferred speed, 2 km/h, and 4 km/h. Muscle activation amplitude patterns were similar between treadmills (M. gastrocnemius medialis: rmean = 0.94, M. gastrocnemius lateralis: rmean = 0.92, M. gluteus medius rmean = 0.90, M. gluteus minimus rmean = 0.94). However, the gait analysis showed a decreased preferred velocity (p < 0.001, z = 4.54), reduced stride length (preferred velocity: p = 0.03, z = -2.17; 2 km/h: p = 0.36, z = 2.10; 4 km/h: p = 0.006, z = 2.76), shorter stride time (2 km/h: p < 0.001, z = 4.65; 4 km/h: p < 0.001, z = 4.15), and higher cadence (2 km/h: p < 0.001, z = -4.20; 4 km/h: p = 0.029, z = -2.18) on the mobile treadmill than on the conventional treadmill. Our observations suggest that the treadmill design (e.g., a 50 cm difference in walking surface length) may not influence muscle activity amplitude during walking. However, the design of the treadmill may influence gait characteristics (e.g., stride length, cadence) of walking.

Correlating Skeletal Muscle Output Force and Intramuscular Pressure Via a Three-Dimensional Finite Element Muscle Model.

The inclusion of muscle pressure in muscle models may have important implications in biomechanics. This notion builds from the known correlation between muscle contractile force and internal pressure. However, this relation is often omitted in numerical models leveraged to study biomechanics. Thus, the purpose of this study was to develop and validate a method of modeling muscles, via finite elements, inclusive of the correlation between muscle contractile force and intramuscular pressure. A magnetic resonance imaging (MRI)-scanned tibialis anterior muscle was modeled via a simple, yet easily scalable, mixed shell and pressure finite element model. Then a validation study was conducted on intramuscular pressure, resulting from applied muscle contractile force, through leveraging special fluid elements type. The fluid-structure-based model and adopted methods exhibited muscle forces and intramuscular pressure that were highly linearly correlated. Indirect validation was achieved with a maximum discrepancy of 7.25%. Furthermore, force-length curves followed a trend similar to documented conventional muscle data, which added to the model's validity. Mesh, material properties, and tendon stiffness sensitivity studies supported the model's robustness. This study has introduced a novel three-dimensional finite element modeling method that respects the physiological force and intramuscular pressure relationship. Although similar models have been previously explored, their complex physiological representation and time-consuming solvers make their scalability and real-time implementation questionable. Thus, the developed model may address such limitations while improving the realism of volumetric finite element models inclusive of muscle contribution.

A Physiology-Guided Classification of Active-Stress and Active-Strain Approaches for Continuum-Mechanical Modeling of Skeletal Muscle Tissue.

The well-established sliding filament and cross-bridge theory explain the major biophysical mechanism responsible for a skeletal muscle's active behavior on a cellular level. However, the biomechanical function of skeletal muscles on the tissue scale, which is caused by the complex interplay of muscle fibers and extracellular connective tissue, is much less understood. Mathematical models provide one possibility to investigate physiological hypotheses. Continuum-mechanical models have hereby proven themselves to be very suitable to study the biomechanical behavior of whole muscles or entire limbs. Existing continuum-mechanical skeletal muscle models use either an active-stress or an active-strain approach to phenomenologically describe the mechanical behavior of active contractions. While any macroscopic constitutive model can be judged by it's ability to accurately replicate experimental data, the evaluation of muscle-specific material descriptions is difficult as suitable data is, unfortunately, currently not available. Thus, the discussions become more philosophical rather than following rigid methodological criteria. Within this work, we provide a extensive discussion on the underlying modeling assumptions of both the active-stress and the active-strain approach in the context of existing hypotheses of skeletal muscle physiology. We conclude that the active-stress approach resolves an idealized tissue transmitting active stresses through an independent pathway. In contrast, the active-strain approach reflects an idealized tissue employing an indirect, coupled pathway for active stress transmission. Finally the physiological hypothesis that skeletal muscles exhibit redundant pathways of intramuscular stress transmission represents the basis for considering a mixed-active-stress-active-strain constitutive framework.

Biomechanics of the human thumb and the evolution of dexterity.

Systematic tool production and use is one of humanity's defining characteristics, possibly originating as early as >3 million years ago.1-3 Although heightened manual dexterity is considered to be intrinsically intertwined with tool use and manufacture, and critical for human evolution, its role in the emergence of early culture remains unclear. Most previous research on this question exclusively relied on direct morphological comparisons between early hominin and modern human skeletal elements, assuming that the degree of a species' dexterity depends on its similarity with the modern human form. Here, we develop a new approach to investigate the efficiency of thumb opposition, a fundamental component of manual dexterity, in several species of fossil hominins. Our work for the first time takes into account soft tissue as well as bone anatomy, integrating virtual modeling of musculus opponens pollicis and its interaction with three-dimensional bone shape form. Results indicate that a fundamental aspect of efficient thumb opposition appeared approximately 2 million years ago, possibly associated with our own genus Homo, and did not characterize Australopithecus, the earliest proposed stone tool maker. This was true also of the late Australopithecus species, Australopithecus sediba, previously found to exhibit human-like thumb proportions. In contrast, later Homo species, including the small-brained Homo naledi, show high levels of thumb opposition dexterity, highlighting the increasing importance of cultural processes and manual dexterity in later human evolution.

InverseMuscleNET: Alternative Machine Learning Solution to Static Optimization and Inverse Muscle Modeling.

InverseMuscleNET, a machine learning model, is proposed as an alternative to static optimization for resolving the redundancy issue in inverse muscle models. A recurrent neural network (RNN) was optimally configured, trained, and tested to estimate the pattern of muscle activation signals. Five biomechanical variables (joint angle, joint velocity, joint acceleration, joint torque, and activation torque) were used as inputs to the RNN. A set of surface electromyography (EMG) signals, experimentally measured around the shoulder joint for flexion/extension, were used to train and validate the RNN model. The obtained machine learning model yields a normalized regression in the range of 88-91% between experimental data and estimated muscle activation. A sequential backward selection algorithm was used as a sensitivity analysis to discover the less dominant inputs. The order of most essential signals to least dominant ones was as follows: joint angle, activation torque, joint torque, joint velocity, and joint acceleration. The RNN model required 0.06 s of the previous biomechanical input signals and 0.01 s of the predicted feedback EMG signals, demonstrating the dynamic temporal relationships of the muscle activation profiles. The proposed approach permits a fast and direct estimation ability instead of iterative solutions for the inverse muscle model. It raises the possibility of integrating such a model in a real-time device for functional rehabilitation and sports evaluation devices with real-time estimation and tracking. This method provides clinicians with a means of estimating EMG activity without an invasive electrode setup.

Estimation of the force-velocity properties of individual muscles from measurement of the combined plantarflexor properties.

The force-velocity (F-V) properties of isolated muscles or muscle fibers have been well studied in humans and other animals. However, determining properties of individual muscles in vivo remains a challenge because muscles usually function within a synergistic group. Modeling has been used to estimate the properties of an individual muscle from the experimental measurement of the muscle group properties. While this approach can be valuable, the models and the associated predictions are difficult to validate. In this study, we measured the in situ F-V properties of the maximally activated kangaroo rat plantarflexor group and used two different assumptions and associated models to estimate the properties of the individual plantarflexors. The first model (Mdl1) assumed that the percent contributions of individual muscles to group force and power were based upon the muscles' cross-sectional area and were constant across the different isotonic loads applied to the muscle group. The second model (Mdl2) assumed that the F-V properties of the fibers within each muscle were identical, but because of differences in muscle architecture, the muscles' contributions to the group properties changed with isotonic load. We compared the two model predictions with independent estimates of the muscles' contributions based upon sonomicrometry measurements of muscle length. We found that predictions from Mdl2 were not significantly different from sonomicrometry-based estimates while those from Mdl1 were significantly different. The results of this study show that incorporating appropriate fiber properties and muscle architecture is necessary to parse the individual muscles' contributions to the group F-V properties.

Hierarchical modeling of force generation in cardiac muscle.

Performing physiologically relevant simulations of the beating heart in clinical context requires to develop detailed models of the microscale force generation process. These models, however, may reveal difficult to implement in practice due to their high computational costs and complex calibration. We propose a hierarchy of three interconnected muscle contraction models-from the more refined to the more simplified-that are rigorously and systematically related to each other, offering a way to select, for a specific application, the model that yields a good trade-off between physiological fidelity, computational cost and calibration complexity. The three model families are compared to the same set of experimental data to systematically assess what physiological indicators can be reproduced or not and how these indicators constrain the model parameters. Finally, we discuss the applicability of these models for heart simulation.

Characterization of Electromechanical Delay Based on a Biophysical Multi-Scale Skeletal Muscle Model.

Skeletal muscles can be voluntary controlled by the somatic nervous system yielding an active contractile stress response. Thereby, the active muscle stresses are transmitted to the skeleton by a cascade of connective tissue and thus enable motion. In the context of joint perturbations as well as the assessment of the complexity of neural control, the initial phase of the muscle-tendon system's stress response has a particular importance and is analyzed by means of electromechanical delay (EMD). EMD is defined as the time lag between the stimulation of a muscle and a measurable change in force output. While EMD is believed to depend on multiple structures / phenomena, it is hard to separate their contributions experimentally. We employ a physiologically detailed, three-dimensional, multi-scale model of an idealized muscle-tendon system to analyze the influence of (i) muscle and tendon length, (ii) the material behavior of skeletal muscle and tendon tissue, (iii) the chemo-electro-mechanical behavior of the muscle fibers and (iv) neural control on EMD. Comparisons with experimental data show that simulated EMD values are within the physiological range, i.e., between 6.1 and 68.6 ms, and that the model is able to reproduce the characteristic EMD-stretch curve, yielding the minimum EMD at optimal length. Simulating consecutive recruitment of motor units increases EMD by more than 20 ms, indicating that during voluntary contractions neural control is the dominant factor determining EMD. In contrast, the muscle fiber action potential conduction velocity is found to influence EMD even of a 27 cm long muscle by not more than 3.7 ms. We further demonstrate that in conditions where only little pre-stretch is applied to a muscle-tendon system, the mechanical behavior of both muscle and tendon tissue considerably impacts EMD. Predicting EMD for different muscle and tendon lengths indicates that the anatomy of a specific muscle-tendon system is optimized for its function, i.e., shorter tendon lengths are beneficial to minimize the neural control effort for muscles primary acting as motor in concentric contractions.

Stochastic modeling of chemical-mechanical coupling in striated muscles.

We propose a chemical-mechanical model of myosin heads in sarcomeres, within the classical description of rigid sliding filaments. In our case, myosin heads have two mechanical degrees-of-freedom (dofs)-one of which associated with the so-called power stroke-and two possible chemical states, i.e., bound to an actin site or not. Our major motivations are twofold: (1) to derive a multiscale coupled chemical-mechanical model and (2) to thus account-at the macroscopic scale-for mechanical phenomena that are out of reach for classical muscle models. This model is first written in the form of Langevin stochastic equations, and we are then able to obtain the corresponding Fokker-Planck partial differential equations governing the probability density functions associated with the mechanical dofs and chemical states. This second form is important, as it allows to monitor muscle energetics and also to compare our model with classical ones, such as the Huxley'57 model to which our equations are shown to reduce under two different types of simplifying assumptions. This provides insight and gives a Langevin form for Huxley'57. We then show how we can calibrate our model based on experimental data-taken here for skeletal muscles-and numerical simulations demonstrate the adequacy of the model to represent complex physiological phenomena, in particular the fast isometric transients in which the power stroke is known to have a crucial role, thus circumventing a limitation of many classical models.

Skeletal muscle mechanics, energetics and plasticity.

The following papers by Richard Lieber (Skeletal Muscle as an Actuator), Thomas Roberts (Elastic Mechanisms and Muscle Function), Silvia Blemker (Skeletal Muscle has a Mind of its Own: a Computational Framework to Model the Complex Process of Muscle Adaptation) and Sabrina Lee (Muscle Properties of Spastic Muscle (Stroke and CP) are summaries of their representative contributions for the session on skeletal muscle mechanics, energetics and plasticity at the 2016 Biomechanics and Neural Control of Movement Conference (BANCOM 2016). Dr. Lieber revisits the topic of sarcomere length as a fundamental property of skeletal muscle contraction. Specifically, problems associated with sarcomere length non-uniformity and the role of sarcomerogenesis in diseases such as cerebral palsy are critically discussed. Dr. Roberts then makes us aware of the (often neglected) role of the passive tissues in muscles and discusses the properties of parallel elasticity and series elasticity, and their role in muscle function. Specifically, he identifies the merits of analyzing muscle deformations in three dimensions (rather than just two), because of the potential decoupling of the parallel elastic element length from the contractile element length, and reviews the associated implications for the architectural gear ratio of skeletal muscle contraction. Dr. Blemker then tackles muscle adaptation using a novel way of looking at adaptive processes and what might drive adaptation. She argues that cells do not have pre-programmed behaviors that are controlled by the nervous system. Rather, the adaptive responses of muscle fibers are determined by sub-cellular signaling pathways that are affected by mechanical and biochemical stimuli; an exciting framework with lots of potential. Finally, Dr. Lee takes on the challenging task of determining human muscle properties in vivo. She identifies the dilemma of how we can demonstrate the effectiveness of a treatment, specifically in cases of muscle spasticity following stroke or in children with cerebral palsy. She then discusses the merits of ultrasound based elastography, and the clinical possibilities this technique might hold. Overall, we are treated to a vast array of basic and clinical problems in skeletal muscle mechanics and physiology, with some solutions, and many suggestions for future research.

Prediction of muscle activation for an eye movement with finite element modeling.

In this paper, a 3D finite element (FE) modeling is employed in order to predict extraocular muscles' activation and investigate force coordination in various motions of the eye orbit. A continuum constitutive hyperelastic model is employed for material description in dynamic modeling of the extraocular muscles (EOMs). Two significant features of this model are accurate mass modeling with FE method and stimulating EOMs for motion through muscle activation parameter. In order to validate the eye model, a forward dynamics simulation of the eye motion is carried out by variation of the muscle activation. Furthermore, to realize muscle activation prediction in various eye motions, two different tracking-based inverse controllers are proposed. The performance of these two inverse controllers is investigated according to their resulted muscle force magnitude and muscle force coordination. The simulation results are compared with the available experimental data and the well-known existing neurological laws. The comparison authenticates both the validation and the prediction results.

Skeletal muscle mechanics: questions, problems and possible solutions.

Skeletal muscle mechanics have been studied ever since people have shown an interest in human movement. However, our understanding of muscle contraction and muscle mechanical properties has changed fundamentally with the discovery of the sliding filament theory in 1954 and associated cross-bridge theory in 1957. Nevertheless, experimental evidence suggests that our knowledge of the mechanisms of contraction is far from complete, and muscle properties and muscle function in human movement remain largely unknown.In this manuscript, I am trying to identify some of the crucial challenges we are faced with in muscle mechanics, offer possible solutions to questions, and identify problems that might be worthwhile exploring in the future. Since it is impossible to tackle all (worthwhile) problems in a single manuscript, I identified three problems that are controversial, important, and close to my heart. They may be identified as follows: (i) mechanisms of muscle contraction, (ii) in vivo whole muscle mechanics and properties, and (iii) force-sharing among synergistic muscles. These topics are fundamental to our understanding of human movement and movement control, and they contain a series of unknowns and challenges to be explored in the future.It is my hope that this paper may serve as an inspiration for some, may challenge current beliefs in selected areas, tackle important problems in the area of muscle mechanics, physiology and movement control, and may guide and focus some of the thinking of future muscle mechanics research.

Chimpanzee super strength and human skeletal muscle evolution.

Since at least the 1920s, it has been reported that common chimpanzees (Pan troglodytes) differ from humans in being capable of exceptional feats of "super strength," both in the wild and in captive environments. A mix of anecdotal and more controlled studies provides some support for this view; however, a critical review of available data suggests that chimpanzee mass-specific muscular performance is a more modest 1.5 times greater than humans on average. Hypotheses for the muscular basis of this performance differential have included greater isometric force-generating capabilities, faster maximum shortening velocities, and/or a difference in myosin heavy chain (MHC) isoform content in chimpanzee relative to human skeletal muscle. Here, we show that chimpanzee muscle is similar to human muscle in its single-fiber contractile properties, but exhibits a much higher fraction of MHC II isoforms. Unlike humans, chimpanzee muscle is composed of ∼67% fast-twitch fibers (MHC IIa+IId). Computer simulations of species-specific whole-muscle models indicate that maximum dynamic force and power output is 1.35 times higher in a chimpanzee muscle than a human muscle of similar size. Thus, the superior mass-specific muscular performance of chimpanzees does not stem from differences in isometric force-generating capabilities or maximum shortening velocities-as has long been suggested-but rather is due in part to differences in MHC isoform content and fiber length. We propose that the hominin lineage experienced a decline in maximum dynamic force and power output during the past 7-8 million years in response to selection for repetitive, low-cost contractile behavior.

Mathematical model for isometric and isotonic muscle contractions.

A new mathematical model is presented to describe both the active and passive mechanics of muscles. In order to account for the active response, a two-layer kinematics that introduces both the visible and rest lengths of the muscle is presented within a rational mechanics framework. The formulation is based on an extended version of the principle of virtual power and the dissipation principle. By using an accurate constitutive description of muscle mobility under activation, details of microscopic processes that lead to muscle contraction are glossed over while macroscopic effects of chemical/electrical stimuli on muscle mechanics are retained. The model predictions are tested with isometric and isotonic experimental data collected from murine extensor digitorum muscle. It is shown that the proposed model captures experimental observations with only three scalar parameters.

Erratum: An action potential-driven model of soleus muscle activation dynamics for locomotor-like movements (2015 J. Neural. Eng. 12 046025).

We published our study on modelling ans simulation of force production in cat soleus muscles during locomotor-like movements. Unfortunately, we recently found several typographical errors in equation (15), table 1 and figure 3E in the published paper. Those errors arose from mistakes on our part during transitioning of our manuscript from the paper to electronic version. We have confirmed that correction of our errors does not influence any simulation results and conclusions published in our paper. However, we think that the errors and their corrections should be noticed publically to prevent the readers from having difficulties in implementing our muscle model.

Muscle wrapping on arbitrary meshes with the heat method.

Muscle paths play an important role in musculoskeletal simulations by determining a muscle's length and how its force is distributed to joints. Most previous approaches estimate the way in which muscles 'wrap' around bones and other structures with smooth analytical wrapping surfaces. In this paper, we employ Newton's method with discrete differential geometry to permit muscle wrapping over arbitrary polygonal mesh surfaces that represent underlying bones and structures. Precomputing distance fields allows us to speed up computations for the common situation where many paths cross the same wrapping surfaces. We found positive results for the accuracy, robustness, and efficiency of the method. However the method did not exhibit continuous changes in path length for dynamic simulations. Nonetheless this approach provides a valuable step toward fast muscle wrapping on arbitrary meshes.

Assessing the accuracy of subject-specific, muscle-model parameters determined by optimizing to match isometric strength.

Biomechanical models are sensitive to the choice of model parameters. Therefore, determination of accurate subject specific model parameters is important. One approach to generate these parameters is to optimize the values such that the model output will match experimentally measured strength curves. This approach is attractive as it is inexpensive and should provide an excellent match to experimentally measured strength. However, given the problem of muscle redundancy, it is not clear that this approach generates accurate individual muscle forces. The purpose of this investigation is to evaluate this approach using simulated data to enable a direct comparison. It is hypothesized that the optimization approach will be able to recreate accurate muscle model parameters when information from measurable parameters is given. A model of isometric knee extension was developed to simulate a strength curve across a range of knee angles. In order to realistically recreate experimentally measured strength, random noise was added to the modeled strength. Parameters were solved for using a genetic search algorithm. When noise was added to the measurements the strength curve was reasonably recreated. However, the individual muscle model parameters and force curves were far less accurate. Based upon this examination, it is clear that very different sets of model parameters can recreate similar strength curves. Therefore, experimental variation in strength measurements has a significant influence on the results. Given the difficulty in accurately recreating individual muscle parameters, it may be more appropriate to perform simulations with lumped actuators representing similar muscles.

Equivalent linear damping characterization in linear and nonlinear force-stiffness muscle models.

In the current research, the muscle equivalent linear damping coefficient which is introduced as the force-velocity relation in a muscle model and the corresponding time constant are investigated. In order to reach this goal, a 1D skeletal muscle model was used. Two characterizations of this model using a linear force-stiffness relationship (Hill-type model) and a nonlinear one have been implemented. The OpenSim platform was used for verification of the model. The isometric activation has been used for the simulation. The equivalent linear damping and the time constant of each model were extracted by using the results obtained from the simulation. The results provide a better insight into the characteristics of each model. It is found that the nonlinear models had a response rate closer to the reality compared to the Hill-type models.