Optimising muscle parameters in musculoskeletal models using Monte Carlo simulation

The use of musculoskeletal simulation software has become a useful tool for modelling joint and muscle forces during human activity, including in reduced gravity because direct experimentation is difficult. Knowledge of muscle and joint loads can better inform the design of exercise protocols and exercise countermeasure equipment. In this study, the LifeModeler? (San Clemente, CA, USA) biomechanics simulation software was used to model a squat exercise. The initial model using default parameters yielded physiologically reasonable hip-joint forces but no activation was predicted in some large muscles such as rectus femoris, which have been shown to be active in 1-g performance of the activity. Parametric testing was conducted using Monte Carlo methods and combinatorial reduction to find a muscle parameter set that more closely matched physiologically observed activation patterns during the squat exercise. The rectus femoris was predicted to peak at 60.1% activation in the same test case compared to 19.2% activation using default parameters. These results indicate the critical role that muscle parameters play in joint force estimation and the need for exploration of the solution space to achieve physiologically realistic muscle activation.     

Estimation of non-linear growth models by linearization: a simulation study using a Gompertz function

A method based on Taylor series expansion for estimation of location parameters and variance components of non-linear mixed effects models was considered. An attractive property of the method is the opportunity for an easily implemented algorithm. Estimation of non-linear mixed effects models can be done by common methods for linear mixed effects models, and thus existing programs can be used after small modifications. The applicability of this algorithm in animal breeding was studied with simulation using a Gompertz function growth model in pigs. Two growth data sets were analyzed: a full set containing observations from the entire growing period, and a truncated time trajectory set containing animals slaughtered prematurely, which is common in pig breeding. The results from the 50 simulation replicates with full data set indicate that the linearization approach was capable of estimating the original parameters satisfactorily. However, estimation of the parameters related to adult weight becomes unstable in the case of a truncated data set.     

Estimation of musculotendon kinematics in large musculoskeletal models using multidimensional B-splines

We present a robust and computationally inexpensive method to estimate the lengths and three-dimensional moment arms for a large number of musculotendon actuators of the human lower limb. Using a musculoskeletal model of the lower extremity, a set of values was established for the length of each musculotendon actuator for different lower limb generalized coordinates (joint angles). A multidimensional spline function was then used to fit these data. Muscle moment arms were obtained by differentiating the musculotendon length spline function with respect to the generalized coordinate of interest. This new method was then compared to a previously used polynomial regression method. Compared to the polynomial regression method, the multidimensional spline method produced lower errors for estimating musculotendon lengths and moment arms throughout the whole generalized coordinate workspace. The fitting accuracy was also less affected by the number of dependent degrees of freedom and by the amount of experimental data available. The spline method only required information on musculotendon lengths to estimate both musculotendon lengths and moment arms, thus relaxing data input requirements, whereas the polynomial regression requires different equations to be used for both musculotendon lengths and moment arms. Finally, we used the spline method in conjunction with an electromyography driven musculoskeletal model to estimate muscle forces under different contractile conditions, which showed that the method is suitable for the integration into large scale neuromusculoskeletal models.     

A three-dimensional model of the rat hindlimb: musculoskeletal geometry and muscle moment arms

As a first step towards developing a dynamic model of the rat hindlimb, we measured muscle attachment and joint center coordinates relative to bony landmarks using stereophotogrammetry. Using these measurements, we analyzed muscle moment arms as functions of joint angle for most hindlimb muscles, and tested the hypothesis that postural change alone is sufficient to alter the function of selected muscles of the leg. We described muscle attachment sites as second-order curves. The length of the fit parabola and residual errors in the orthogonal directions give an estimate of muscle attachment sizes, which are consistent with observations made during dissection. We modeled each joint as a moving point dependent on joint angle; relative endpoint errors less than 7% indicate this method as accurate. Most muscles have moment arms with a large range across the physiological domain of joint angles, but their moment arms peak and vary little within the locomotion domain. The small variation in moment arms during locomotion potentially simplifies the neural control requirements during this phase. The moment arms of a number of muscles cross zero as angle varies within the quadrupedal locomotion domain, indicating they are intrinsically stabilizing. However, in the bipedal locomotion domain, the moment arms of these muscles do not cross zero and thus are no longer intrinsically stabilizing. We found that muscle function is largely determined by the change in moment arm with joint angle, particularly the transition from quadrupedal to bipedal posture, which may alter an intrinsically stabilizing arrangement or change the control burden.     

Higher medially-directed joint reaction forces are a characteristic of dysplastic hips: A comparative study using subject-specific musculoskeletal models

Acetabular dysplasia is a known cause of hip osteoarthritis. In addition to abnormal anatomy, changes in kinematics, joint reaction forces (JRFs), and muscle forces could cause tissue damage to the cartilage and labrum, and may contribute to pain and fatigue. The objective of this study was to compare lower extremity joint angles, moments, hip JRFs and muscle forces during gait between patients with symptomatic acetabular dysplasia and healthy controls. Marker trajectories and ground reaction forces were measured in 10 dysplasia patients and 10 typically developing control subjects. A musculoskeletal model was scaled in OpenSim to each subject and subject-specific hip joint centers were determined using reconstructions from CT images. Joint kinematics and moments were calculated using inverse kinematics and inverse dynamics, respectively. Muscle forces and hip JRFs were estimated with static optimization. Inter-group differences were tested for statistical significance (p ≤ 0.05) and large effect sizes (d ≥ 0.8). Results demonstrated that dysplasia patients had higher medially directed JRFs. Joint angles and moments were mostly similar between the groups, but large inter-group effect sizes suggested some restriction in range of motion by patients at the hip and ankle. Higher medially-directed JRFs and inter-group differences in hip muscle forces likely stem from lateralization of the hip joint center in dysplastic patients. Joint force differences, combined with reductions in range of motion at the hip and ankle may also indicate compensatory strategies by patients with dysplasia to maintain joint stability.     

Estimation of muscle forces in gait using a simulation of the electromyographic activity and numerical optimization

Clinical gait analysis provides great contributions to the understanding of gait patterns. However, a complete distribution of muscle forces throughout the gait cycle is a current challenge for many researchers. Two techniques are often used to estimate muscle forces: inverse dynamics with static optimization and computer muscle control that uses forward dynamics to minimize tracking. The first method often involves limitations due to changing muscle dynamics and possible signal artefacts that depend on day-to-day variation in the position of electromyographic (EMG) electrodes. Nevertheless, in clinical gait analysis, the method of inverse dynamics is a fundamental and commonly used computational procedure to calculate the force and torque reactions at various body joints. Our aim was to develop a generic musculoskeletal model that could be able to be applied in the clinical setting. The musculoskeletal model of the lower limb presents a simulation for the EMG data to address the common limitations of these techniques. This model presents a new point of view from the inverse dynamics used on clinical gait analysis, including the EMG information, and shows a similar performance to another model available in the OpenSim software. The main problem of these methods to achieve a correct muscle coordination is the lack of complete EMG data for all muscles modelled. We present a technique that simulates the EMG activity and presents a good correlation with the muscle forces throughout the gait cycle. Also, this method showed great similarities whit the real EMG data recorded from the subjects doing the same movement.     

Estimation of descriptive parameters of overlapping chromatographic peaks: a simulation study

The characteristics of a non-linear optimization technique for resolution of overlapping chromatographic peaks are examined. A modified Meiron-Marquardt method was used. The estimates of the parameters of overlapping peaks in simulated chromatograms were investigated to indicate the limitations of present mathematical methods and, hopefully, to improve their ultimate utility. Gaussian shapes as well as exponential-Gaussian convolutes were used to simulate the chromatographic peaks. Effects on the overall performance of varying heights, widths, and separation of two peaks were determined. Random additive noise and base line drift were also simulated. For illustrative purposes, the performance of the parameter estimation techniques was expressed in terms of relative errors in estimating the second (or smaller) peak's area, height and location. The results presented indicate the relative importance of noise, skewness, height and width ratios and peak separation on the maximum resolution achievable by numerical methods in an automated chromatographic system.     

Dynamic response of the brain with vasculature: a three-dimensional computational study

To date, the influence of the vasculature on the dynamic response of the brain has not been studied with a complete three-dimensional (3D) finite element head model. In this study, short duration rotational (10,000 rad/s(2) with a duration of 5 ms) and translational (100G with a duration of 5 ms) acceleration impulses were applied to the 3D finite element models to study the dynamic response of the brain. The hypothesis of this study was that due to the convoluted organization and non-linear material properties of cerebral vasculature, the difference in maximum principle strain between models with and without vasculature should be minimal. The effects of non-linear material properties and the convoluted structure of the vasculature were examined by comparing the results from the 3D finite element models. The peak average strain reduction in a model with non-linear elastic vasculature and a model with linear elastic vasculature compared to a model without vasculature was 2% and 5%, respectively, indicating that the influence of the vasculature on the dynamic response of the brain is minimal.     

Stabilisation of walking by intrinsic muscle properties revealed in a three-dimensional muscle-driven simulation

A fundamental question in movement science is how humans perform stable movements in the presence of disturbances such as contact with objects. It remains unclear how the nervous system, with delayed responses to disturbances, maintains the stability of complex movements. We hypothesised that intrinsic muscle properties (i.e. the force–length–velocity properties of muscle fibres and tendon elasticity) may help stabilise human walking by responding instantaneously to a disturbance and providing forces that help maintain the movement trajectory. To investigate this issue, we generated a 3D muscle-driven simulation of walking and analysed the changes in the simulation's motion when a disturbance was applied to models with and without intrinsic muscle properties. Removing the intrinsic properties reduced the stability; this was true when the disturbing force was applied at a variety of times and in different directions. Thus, intrinsic muscle properties play a unique role in stabilising walking, complementing the delayed response of the central nervous system.     

Estimation of accuracy of patient-specific musculoskeletal modelling: case study on a post polio residual paralysis subject

For patients with patterns ranging out of anthropometric standard values, patient-specific musculoskeletal modelling becomes crucial for clinical diagnosis and follow-up. However, patient-specific modelling using imaging techniques and motion capture systems is mainly subject to experimental errors. The aim of this study was to quantify these experimental errors when performing a patient-specific musculoskeletal model. CT scan data were used to personalise the geometrical model and its inertial properties for a post polio residual paralysis subject. After having performed a gait-based experimental protocol, kinematics data were measured using a VICON motion capture system with six infrared cameras. The musculoskeletal model was computed using a direct/inverse algorithm (LifeMod software). A first source of errors was identified in the segmentation procedure in relation to the calculation of personalised inertial parameters. The second source of errors was subject related, as it depended on the reproducibility of performing the same type of gait. The impact of kinematics, kinetics and muscle forces resulting from the musculoskeletal modelling was quantified using relative errors and the absolute root mean square error. Concerning the segmentation procedure, we found that the kinematics results were not sensitive to the errors (relative error < 1%). However, a strong influence was noted on the kinetics results (deviation up to 71%). Furthermore, the reproducibility error showed a significant influence (relative mean error varying from 5 to 30%). The present paper demonstrates that in patient-specific musculoskeletal modelling variations due to experimental errors derived from imaging techniques and motion capture need to be both identified and quantified. Therefore, the paper can be used as a guideline.     

Estimation of accuracy of patient-specific musculoskeletal modelling: case study on a post polio residual paralysis subject

For patients with patterns ranging out of anthropometric standard values, patient-specific musculoskeletal modelling becomes crucial for clinical diagnosis and follow-up. However, patient-specific modelling using imaging techniques and motion capture systems is mainly subject to experimental errors. The aim of this study was to quantify these experimental errors when performing a patient-specific musculoskeletal model. CT scan data were used to personalise the geometrical model and its inertial properties for a post polio residual paralysis subject. After having performed a gait-based experimental protocol, kinematics data were measured using a VICON motion capture system with six infrared cameras. The musculoskeletal model was computed using a direct/inverse algorithm (LifeMod software). A first source of errors was identified in the segmentation procedure in relation to the calculation of personalised inertial parameters. The second source of errors was subject related, as it depended on the reproducibility of performing the same type of gait. The impact of kinematics, kinetics and muscle forces resulting from the musculoskeletal modelling was quantified using relative errors and the absolute root mean square error. Concerning the segmentation procedure, we found that the kinematics results were not sensitive to the errors (relative error<1%). However, a strong influence was noted on the kinetics results (deviation up to 71%). Furthermore, the reproducibility error showed a significant influence (relative mean error varying from 5 to 30%). The present paper demonstrates that in patient-specific musculoskeletal modelling variations due to experimental errors derived from imaging techniques and motion capture need to be both identified and quantified. Therefore, the paper can be used as a guideline.     

Estimation of individual muscle force using elastography

Background

Estimation of an individual muscle force still remains one of the main challenges in biomechanics. In this way, the present study aimed: (1) to determine whether an elastography technique called Supersonic Shear Imaging (SSI) could be used to estimate muscle force, (2) to compare this estimation to that one provided by surface electromyography (EMG), and (3) to determine the effect of the pennation of muscle fibers on the accuracy of the estimation.

Methods and Results

Eleven subjects participated in two experimental sessions; one was devoted to the shear elastic modulus measurements and the other was devoted to the EMG recordings. Each session consisted in: (1) two smooth linear torque ramps from 0 to 60% and from 0 to 30% of maximal voluntary contraction, for the first dorsal interosseous and the abductor digiti minimi, respectively (referred to as “ramp contraction”); (2) two contractions done with the instruction to freely change the torque (referred to as “random changes contraction”). Multi-channel surface EMG recordings were obtained from a linear array of eight electrodes and the shear elastic modulus was measured using SSI. For ramp contractions, significant linear relationships were reported between EMG activity level and torque (R² = 0.949±0.036), and between shear elastic modulus and torque (R² = 0.982±0.013). SSI provided significant lower RMS_deviation between measured torque and estimated torque than EMG activity level for both types of contraction (1.4±0.7 vs. 2.8±1.4% of maximal voluntary contraction for “ramp contractions”, p<0.01; 4.5±2.3 vs. 7.9±5.9% of MVC for “random changes contractions”, p<0.05). No significant difference was reported between muscles.

Conclusion

The shear elastic modulus measured using SSI can provide a more accurate estimation of individual muscle force than surface EMG. In addition, pennation of muscle fibers does not influence the accuracy of the estimation.     

A three-dimensional model of the human cervical spine for impact simulation

A three-dimensional analytical model of the cervical spine is described. The cervical vertebrae and the head are modeled as rigid bodies which are interconnected by deformable elements representing the intervertebral disks, facet joints, ligaments and muscles. A special pentahedral continuum element for representing the articular facets is described which effectively maintains stability of the cervical spine in both lateral and frontal plane accelerations, which is very difficult with multi-spring models of the facets. A simplified representation is used for the spine and body below the level of T1. The neck musculature is modeled by over 100 muscle elements representing 22 major muscle groups in the neck. The model has been validated for frontal and sideways impact accelerations by simulating published experimental data. Results are also presented to show the effects of the stretch reflex response on the dynamics of the head and neck under moderate acceleration.     

Estimation of the mean waiting time of a customer subject to balking: a simulation study

To a customer, the waiting time for order processing for a product or service is important information for order placement. If the time foreseen for order fulfillment is long, the order might be lost to a competitor. In particular, modern principles of supply chain management highly suggest information sharing between entities in the chain and information technology has enabled customers to conveniently consider the waiting time for a potential balking decision. To help determine the design and operation of a manufacturing or service system in which a customer may balk based on the foreseen waiting time, this paper develops procedures to estimate the average waiting time of an order. Either the procedures allow the maximum waiting time for a balking decision to be random or do not require knowledge of the arrival process of customers before balking if the balking limit is known. For generality of the model, this paper considers general inter-arrival and service time distributions, and uses the simulation and regression approach.     

Effects of lumbo-pelvic rhythm on trunk muscle forces and disc loads during forward flexion: A combined musculoskeletal and finite element simulation study

Previous in-vivo studies suggest that the ratio of total lumbar rotation over pelvic rotation (lumbo-pelvic rhythm) during trunk sagittal movement is essential to evaluate spinal loads and discriminate between low back pain and asymptomatic population. Similarly, there is also evidence that the lumbo-pelvic rhythm is key for evaluation of realistic muscle and joint reaction forces and moments predicted by various computational musculoskeletal models. This study investigated the effects of three lumbo-pelvic rhythms defined based on in-vivo measurements on the spinal response during moderate forward flexion (60°) using a combined approach of musculoskeletal modeling of the upper body and finite element model of the lumbosacral spine. The muscle forces and joint loads predicted by the musculoskeletal model, together with the gravitational forces, were applied to the finite element model to compute the disc force and moment, intradiscal pressure, annular fibers strain, and load-sharing. The results revealed that a rhythm with high pelvic rotation and low lumbar flexion involves more global muscles and increases the role of the disc in resisting spinal loads, while its counterpart, with low pelvic rotation, recruits more local muscles and engages the ligaments to lower the disc loads. On the other hand, a normal rhythm that has balanced pelvic and lumbar rotations yields almost equal disc and ligament load-sharing and results in more balanced synergy between global and local muscles. The lumbo-pelvic rhythm has less effect on the intradiscal pressure and annular fibers strain. This work demonstrated that the spinal response during forward flexion is highly dependent on the lumbo-pelvic rhythm. It is therefore, essential to adapt this parameter instead of using the default values in musculoskeletal models for accurate prediction of muscle forces and joint reaction forces and moments. The findings provided by this work are expected to improve knowledge of spinal response during forward flexion, and are clinically relevant towards low back pain treatment and disc injury prevention.     

Validation of subject-specific musculoskeletal models using the anatomical reachable 3-D workspace

A novel metric for the validation of musculoskeletal models is proposed, the reachable 3-D workspace (RWS). This new metric was used to compare a generic model scaled in a standard manner to a more subject-specific model. An experimental protocol for assessing the RWS was performed by ten participants for four distinct hand-payload cases. In addition, isometric individual strength measurements were collected for 12 different directions. The strength of subject-specific musculoskeletal models was then computed using the following assumptions: (1) standard routines including the length-mass-fat (LMF) scaling law; (2) the isometric strengths of the muscle elements were optimized to the individual strength measurements using joint strength factors (JSF). The RWS of each participant was subsequently estimated from each of the scaling approaches, LMF and JSF, for the four load cases. The experimental RWS showed that the volume and shape decreased with increasing hand-payload for every participant. The lateral and frontal far-from-torso aspects of the RWS were reduced the most. These trends were reproduced by both strength scaling approaches, but the LMF-scaled models were not able to track the overall RWS volume decrease with increasing payload, since they proved to be weaker than the participants. On the other hand, the optimised JSF subject-specific models performed better on the prediction of the RWS for all payload cases across participants. The RWS can potentially be further used as a subject-specific musculoskeletal model validation, enabling quantification of the volume and shape differences between experimentally and model-predicted RWSs.     

臭氧对农作物影响的模型

对流层臭氧(O3)浓度增加对作物的不利影响已受到广泛关注,臭氧模型研究自然已成为该领域的热点之一。建立有效的模型对臭氧造成的作物产量损失进行评估和预测,能为中国臭氧污染的控制和农业安全提供科学依据。根据模型与作物生长关系的紧密程度,可将其分为统计模型和机理模型2大类。本文依据模型的研究进程,依次阐述了浓度响应、剂量响应、通量响应3个统计模型;重点分析国内外影响较大的CLASS、Martin和AFRCWHEAT2-O33个机理模型;指出各模型的局限性,并对相关研究发展方向的可行性措施进行讨论。