Models of Postural Control: Shared Variance in Joint and COM Motions

This paper investigated the organization of the postural control system in human upright stance. To this aim the shared variance between joint and 3D total body center of mass (COM) motions was analyzed using multivariate canonical correlation analysis (CCA). The CCA was performed as a function of established models of postural control that varied in their joint degrees of freedom (DOF), namely, an inverted pendulum ankle model (2DOF), ankle-hip model (4DOF), ankle-knee-hip model (5DOF), and ankle-knee-hip-neck model (7DOF). Healthy young adults performed various postural tasks (two-leg and one-leg quiet stances, voluntary AP and ML sway) on a foam and rigid surface of support. Based on CCA model selection procedures, the amount of shared variance between joint and 3D COM motions and the cross-loading patterns we provide direct evidence of the contribution of multi-DOF postural control mechanisms to human balance. The direct model fitting of CCA showed that incrementing the DOFs in the model through to 7DOF was associated with progressively enhanced shared variance with COM motion. In the 7DOF model, the first canonical function revealed more active involvement of all joints during more challenging one leg stances and dynamic posture tasks. Furthermore, the shared variance was enhanced during the dynamic posture conditions, consistent with a reduction of dimension. This set of outcomes shows directly the degeneracy of multivariate joint regulation in postural control that is influenced by stance and surface of support conditions.     

Translational and rotational joint power terms in a six degree-of-freedom model of the normal ankle complex

We hypothesized that defining joint power (JP) merely on the basis of joint rotations ignores important translational power terms, and may not adequately represent the energy flow profile for a given muscle group. A novel six degree-of-freedom (6 DOF) model of the ankle complex was implemented, accounting for previously ignored joint translations as well as traditional rotations. Foot and shank kinematic and kinetic data were collected over a stride cycle on five male and five female adults, walking five trials each at 0.69 statures s⁻¹. During intra-subject analyses, ensemble averages were calculated (n=5) for JP associated with each DOF, and for related velocity and force/moment data. Translational joint velocities typically peaked below 10% of the mean walking velocity. The largest peak in JP occurred for the rotational DOF associated with dorsi/planter flexion (360 W). The next largest peak in JP was for the vertical translational DOF, and was nearly 10% of the predominant peak. Positive work during push-off was significantly less p≤0.05) for the 6 DOF model (27.9 J) than for either 1 or 3 DOF rotational models (30.3 and 29.9 J, respectively). Negative work during early stance was significantly less for the 6 DOF model (−10.3 J) than for either the 1 or 3 DOF models (−13.1 and −12.6 J, respectively). Inter-subject analyses (n=50) were conducted for JP data only, with similar results. We conclude that translational JP terms are of practical importance in mechanical energy studies, and may be of particular concern when evaluating energy storing prostheses, when summing total power at several joints, and when studying pathologies that disturb joint geometry.     

Effect of implementing magnetic resonance imaging for patient-specific OpenSim models on lower-body kinematics and knee ligament lengths

BackgroundOpenSim models are typically based on cadaver findings that are generalized to represent a wide range of populations, which curbs their validity. Patient-specific modelling through incorporating magnetic resonance imaging (MRI) improves the model’s biofidelity with respect to joint alignment and articulations, muscle wrapping, and ligament insertions. The purpose of this study was to determine if the inclusion of an MRI-based knee model would elicit differences in lower limb kinematics and resulting knee ligament lengths during a side cut task.MethodsEleven participants were analyzed with the popular Rajagopal OpenSim model, two variations of the same model to include three and six degrees of freedom knee (DOF), and a fourth version featuring a four DOF MRI-based knee model. These four models were used in an inverse kinematics analysis of a side cut task and the resulting lower limb kinematics and knee ligament lengths were analyzed.ResultsThe MRI-based model was more responsive to the movement task than the original Rajagopal model while less susceptible to soft tissue artifact than the unconstrained six DOF model. Ligament isometry was greatest in the original Rajagopal model and smallest in the six DOF model.ConclusionsWhen using musculoskeletal modelling software, one must acutely consider the model choice as the resulting kinematics and ligament lengths are dependent on this decision. The MRI-based knee model is responsive to the kinematics and ligament lengths of highly dynamic tasks and may prove to be the most valid option for continuing with late-stage modelling operations such as static optimization.     

Modeling differences in the vibration response characteristics of the human body

Mathematical models may provide a useful tool for the development and evaluation of seating systems for vibration mitigation. A five-degree-of-freedom (DOF) model was formulated based on the measured driving-point impedance and transmissibilities of major anatomical structures contributing to the observed resonance behaviors. The model was limited in its ability to simulate differences observed in the resonance behaviors of a broader population and was unable to simulate the multiple resonances observed in the thigh. This paper describes the effectiveness of a modified five DOF model in simulating the major resonance behaviors observed in the population using representative data from a 56 kg female and 75 kg male. In addition, the model was also evaluated for its ability to predict the effects of selected seat cushions. The modified lumped-parameter model improved the peak chest and spine transmissibility simulations. The model was effective in simulating both the lower impedance peak observed in the primary resonance region (4-8 Hz) and the prevalent impedance peak observed in the second resonance region (7-10 Hz) in the smaller subjects. However, the model was not effective in predicting the dampening observed in the second resonance peak with the use of cushions. Redistribution of the model coefficients for the legs and the consideration of coupling between the legs and other anatomical structures may further improve the ability of the lumped-parameter model to predict the effects of seating systems on vibration transmission in the human body.     

EMG-Driven Forward-Dynamic Estimation of Muscle Force and Joint Moment about Multiple Degrees of Freedom in the Human Lower Extremity

This work examined if currently available electromyography (EMG) driven models, that are calibrated to satisfy joint moments about one single degree of freedom (DOF), could provide the same musculotendon unit (MTU) force solution, when driven by the same input data, but calibrated about a different DOF. We then developed a novel and comprehensive EMG-driven model of the human lower extremity that used EMG signals from 16 muscle groups to drive 34 MTUs and satisfy the resulting joint moments simultaneously produced about four DOFs during different motor tasks. This also led to the development of a calibration procedure that allowed identifying a set of subject-specific parameters that ensured physiological behavior for the 34 MTUs. Results showed that currently available single-DOF models did not provide the same unique MTU force solution for the same input data. On the other hand, the MTU force solution predicted by our proposed multi-DOF model satisfied joint moments about multiple DOFs without loss of accuracy compared to single-DOF models corresponding to each of the four DOFs. The predicted MTU force solution was (1) a function of experimentally measured EMGs, (2) the result of physiological MTU excitation, (3) reflected different MTU contraction strategies associated to different motor tasks, (4) coordinated a greater number of MTUs with respect to currently available single-DOF models, and (5) was not specific to an individual DOF dynamics. Therefore, our proposed methodology has the potential of producing a more dynamically consistent and generalizable MTU force solution than was possible using single-DOF EMG-driven models. This will help better address the important scientific questions previously approached using single-DOF EMG-driven modeling. Furthermore, it might have applications in the development of human-machine interfaces for assistive devices.     

Benchmarking novel approaches for modelling species range dynamics

Increasing biodiversity loss due to climate change is one of the most vital challenges of the 21st century. To anticipate and mitigate biodiversity loss, models are needed that reliably project species’ range dynamics and extinction risks. Recently, several new approaches to model range dynamics have been developed to supplement correlative species distribution models (SDMs), but applications clearly lag behind model development. Indeed, no comparative analysis has been performed to evaluate their performance. Here, we build on process‐based, simulated data for benchmarking five range (dynamic) models of varying complexity including classical SDMs, SDMs coupled with simple dispersal or more complex population dynamic models (SDM hybrids), and a hierarchical Bayesian process‐based dynamic range model (DRM). We specifically test the effects of demographic and community processes on model predictive performance. Under current climate, DRMs performed best, although only marginally. Under climate change, predictive performance varied considerably, with no clear winners. Yet, all range dynamic models improved predictions under climate change substantially compared to purely correlative SDMs, and the population dynamic models also predicted reasonable extinction risks for most scenarios. When benchmarking data were simulated with more complex demographic and community processes, simple SDM hybrids including only dispersal often proved most reliable. Finally, we found that structural decisions during model building can have great impact on model accuracy, but prior system knowledge on important processes can reduce these uncertainties considerably. Our results reassure the clear merit in using dynamic approaches for modelling species’ response to climate change but also emphasize several needs for further model and data improvement. We propose and discuss perspectives for improving range projections through combination of multiple models and for making these approaches operational for large numbers of species.     

A comparison of optimisation methods and knee joint degrees of freedom on muscle force predictions during single-leg hop landings

The aim of this paper was to compare the effect of different optimisation methods and different knee joint degrees of freedom (DOF) on muscle force predictions during a single legged hop. Nineteen subjects performed single-legged hopping manoeuvres and subject-specific musculoskeletal models were developed to predict muscle forces during the movement. Muscle forces were predicted using static optimisation (SO) and computed muscle control (CMC) methods using either 1 or 3 DOF knee joint models. All sagittal and transverse plane joint angles calculated using inverse kinematics or CMC in a 1 DOF or 3 DOF knee were well-matched (RMS error<3°). Biarticular muscles (hamstrings, rectus femoris and gastrocnemius) showed more differences in muscle force profiles when comparing between the different muscle prediction approaches where these muscles showed larger time delays for many of the comparisons. The muscle force magnitudes of vasti, gluteus maximus and gluteus medius were not greatly influenced by the choice of muscle force prediction method with low normalised root mean squared errors (<48%) observed in most comparisons. We conclude that SO and CMC can be used to predict lower-limb muscle co-contraction during hopping movements. However, care must be taken in interpreting the magnitude of force predicted in the biarticular muscles and the soleus, especially when using a 1 DOF knee. Despite this limitation, given that SO is a more robust and computationally efficient method for predicting muscle forces than CMC, we suggest that SO can be used in conjunction with musculoskeletal models that have a 1 or 3 DOF knee joint to study the relative differences and the role of muscles during hopping activities in future studies.     

Stimulus design for model selection and validation in cell signaling

Mechanism-based chemical kinetic models are increasingly being used to describe biological signaling. Such models serve to encapsulate current understanding of pathways and to enable insight into complex biological processes. One challenge in model development is that, with limited experimental data, multiple models can be consistent with known mechanisms and existing data. Here, we address the problem of model ambiguity by providing a method for designing dynamic stimuli that, in stimulus–response experiments, distinguish among parameterized models with different topologies, i.e., reaction mechanisms, in which only some of the species can be measured. We develop the approach by presenting two formulations of a model-based controller that is used to design the dynamic stimulus. In both formulations, an input signal is designed for each candidate model and parameterization so as to drive the model outputs through a target trajectory. The quality of a model is then assessed by the ability of the corresponding controller, informed by that model, to drive the experimental system. We evaluated our method on models of antibody–ligand binding, mitogen-activated protein kinase (MAPK) phosphorylation and de-phosphorylation, and larger models of the epidermal growth factor receptor (EGFR) pathway. For each of these systems, the controller informed by the correct model is the most successful at designing a stimulus to produce the desired behavior. Using these stimuli we were able to distinguish between models with subtle mechanistic differences or where input and outputs were multiple reactions removed from the model differences. An advantage of this method of model discrimination is that it does not require novel reagents, or altered measurement techniques; the only change to the experiment is the time course of stimulation. Taken together, these results provide a strong basis for using designed input stimuli as a tool for the development of cell signaling models.     

Validation of a non-invasive fluoroscopic imaging technique for the measurement of dynamic knee joint motion

The accurate measurement of the in vivo knee joint kinematics in six degrees-of-freedom (6DOF) remains a challenge in biomedical engineering. We have adapted a dual fluoroscopic imaging system (DFIS) to investigate the various in vivo dynamic knee joint motions. This paper presents a thorough validation of the accuracy and repeatability of the DFIS system when used to measure 6DOF dynamic knee kinematics. First, the validation utilized standard geometric spheres made from different materials to demonstrate the capability of the DFIS technique to determine the object positions under changing speeds. The translational pose of the spheres could be recreated to less than 0.15±0.09 mm for velocities below 300 mm/s. Next, tantalum beads were inserted into the femur and tibia of two fresh frozen cadaver knees to compare the dynamic kinematics measured by matching knee models to the kinematics from the tantalum bead matching—a technique similar to Roentgen stereophotogrammetric analysis (RSA). Each cadaveric knee was attached to the crosshead of a tensile testing machine and vertically translated at a rate of 16.66 mm/s while images were captured with the DFIS. Subsequently, the tibia was held fixed and the femur manually flexed from full extension to 90° of flexion, as the DFIS acquired images. In vitro translation of the cadaver knee using the tensile testing machine deviated from predicted values by 0.08±0.14 mm for the matched knee models. The difference between matching the knee and tantalum bead models during the dynamic flexion–extension motion of the knee was 0.1±0.65°/s in flexion speed; 0.24±0.16 mm in posterior femoral translation; and 0.16±0.61° in internal–external tibial rotation. Finally, we applied the method to investigate the knee kinematics of a living subject during a step ascent and treadmill gait. High repeatability was demonstrated for the in vivo application. Thus, the DFIS provides an easy and powerful tool for accurately determining 6DOF positions of the knee when performing daily functional activities.     

Rib fractures under anterior–posterior dynamic loads: Experimental and finite-element study

The purpose of this study was to investigate whether using a finite-element (FE) mesh composed entirely of hexahedral elements to model cortical and trabecular bone (all-hex model) would provide more accurate simulations than those with variable thickness shell elements for cortical bone and hexahedral elements for trabecular bone (hex–shell model) in the modeling human ribs. First, quasi-static non-injurious and dynamic injurious experiments were performed using the second, fourth, and tenth human thoracic ribs to record the structural behavior and fracture tolerance of individual ribs under anterior–posterior bending loads. Then, all-hex and hex–shell FE models for the three ribs were developed using an octree-based and multi-block hex meshing approach, respectively. Material properties of cortical bone were optimized using dynamic experimental data and the hex–shell model of the fourth rib and trabecular bone properties were taken from the literature. Overall, the reaction force–displacement relationship predicted by both all-hex and hex–shell models with nodes in the offset middle-cortical surfaces compared well with those measured experimentally for all the three ribs. With the exception of fracture locations, the predictions from all-hex and offset hex–shell models of the second and fourth ribs agreed better with experimental data than those from the tenth rib models in terms of reaction force at fracture (difference <15.4%), ultimate failure displacement and time (difference <7.3%), and cortical bone strains. The hex–shell models with shell nodes in outer cortical surfaces increased static reaction forces up to 16.6%, compared to offset hex–shell models. These results indicated that both all-hex and hex–shell modeling strategies were applicable for simulating rib responses and bone fractures for the loading conditions considered, but coarse hex–shell models with constant or variable shell thickness were more computationally efficient and therefore preferred.     

Prediction of the structural response of the femoral shaft under dynamic loading using subject-specific finite element models

The goal of this study was to predict the structural response of the femoral shaft under dynamic loading conditions using subject-specific finite element (SS-FE) models and to evaluate the prediction accuracy of the models in relation to the model complexity. In total, SS-FE models of 31 femur specimens were developed. Using those models, dynamic three-point bending and combined loading tests (bending with four different levels of axial compression) of bare femurs were simulated, and the prediction capabilities of five different levels of model complexity were evaluated based on the impact force time histories: baseline, mass-based scaled, structure-based scaled, geometric SS-FE, and heterogenized SS-FE models. Among the five levels of model complexity, the geometric SS-FE and the heterogenized SS-FE models showed statistically significant improvement on response prediction capability compared to the other model formulations whereas the difference between two SS-FE models was negligible. This result indicated the geometric SS-FE models, containing detailed geometric information from CT images with homogeneous linear isotropic elastic material properties, would be an optimal model complexity for prediction of structural response of the femoral shafts under the dynamic loading conditions. The average and the standard deviation of the RMS errors of the geometric SS-FE models for all the 31 cases was 0.46 kN and 0.66 kN, respectively. This study highlights the contribution of geometric variability on the structural response variation of the femoral shafts subjected to dynamic loading condition and the potential of geometric SS-FE models to capture the structural response variation of the femoral shafts.     

Derivation of the first clinical diagnostic models for dehydration severity in patients over five years with acute diarrhea

Diarrheal diseases lead to an estimated 1.3 million deaths each year, with the majority of those deaths occurring in patients over five years of age. As the severity of diarrheal disease can vary widely, accurately assessing dehydration status remains the most critical step in acute diarrhea management. The objective of this study is to empirically derive clinical diagnostic models for assessing dehydration severity in patients over five years with acute diarrhea in low resource settings. We enrolled a random sample of patients over five years with acute diarrhea presenting to the icddr,b Dhaka Hospital. Two blinded nurses independently assessed patients for symptoms/signs of dehydration on arrival. Afterward, consecutive weights were obtained to determine the percent weight change with rehydration, our criterion standard for dehydration severity. Full and simplified ordinal logistic regression models were derived to predict the outcome of none (<3%), some (3–9%), or severe (>9%) dehydration. The reliability and accuracy of each model were assessed. Bootstrapping was used to correct for over-optimism and compare each model’s performance to the current World Health Organization (WHO) algorithm. 2,172 patients were enrolled, of which 2,139 (98.5%) had complete data for analysis. The Inter-Class Correlation Coefficient (reliability) was 0.90 (95% CI = 0.87, 0.91) for the full model and 0.82 (95% CI = 0.77, 0.86) for the simplified model. The area under the Receiver-Operator Characteristic curve (accuracy) for severe dehydration was 0.79 (95% CI: 0.76–0.82) for the full model and 0.73 (95% CI: 0.70, 0.76) for the simplified model. The accuracy for both the full and simplified models were significantly better than the WHO algorithm (p<0.001). This is the first study to empirically derive clinical diagnostic models for dehydration severity in patients over five years. Once prospectively validated, the models may improve management of patients with acute diarrhea in low resource settings.     

An EMG-based, muscle driven forward simulation of single support phase of gait

This paper describes the process used to generate lower limb kinematics during single limb stance phase of gait, using musculoskeletal modelling, muscle driven forward simulation and gradient based optimisation techniques (including design of experiment techniques).Initial inputs to the forward simulation process were the normalised quantified muscle activation patterns of 22 muscles, and the initial segmental configuration (both angles and angular velocity) derived from Winter (The biomechanics and motor control of human gait, 1987, University of Waterloo Press, pp. 1-72). Two distinct musculoskeletal models (one including 6 DOF, the other 7 DOF) were defined and a muscle driven forward simulation was implemented.A series of optimisation sequences then were executed to modify the muscle activation patterns and initial segmental configuration, until the system output of the forward simulation approximated the angle data reported by. The accuracy and effectiveness of the analysis sequence proposed and the model response obtained using two distinct musculoskeletal models were verified and analysed with respect to the kinesiology of normal walking.     

The influence of the way the muscle force is modeled on the predicted results obtained by solving indeterminate problems for a fast elbow flexion

A critical point in models of the human limbs when the aim is to investigate the motor control is the muscle model. More often the mechanical output of a muscle is considered as one musculotendon force that is a design variable in optimization tasks solved predominantly by static optimization. For dynamic conditions, the relationship between the developed force, the length and the contraction velocity of a muscle becomes important and rheological muscle models can be incorporated in the optimization tasks. Here the muscle activation can be a design variable as well. Recently a new muscle model was proposed. A muscle is considered as a mixture of motor units (MUs) with different peculiarities and the muscle force is calculated as a sum of the MUs twitches. The aim of the paper is to compare these three ways for presenting the muscle force. Fast elbow flexion is investigated using a planar model with five muscles. It is concluded that the rheological models are suitable for calculation of the current maximal muscle forces that can be used as weight factors in the objective functions. The model based on MUs has many advantages for precise investigations of motor control. Such muscle presentation can explain the muscle co-contraction and the role of the fast and the slow MUs. The relationship between the MUs activation and the mechanical output is more clear and closer to the reality.     

Study of Biomechanical Response of Human Hand-Arm to Random Vibrations of Steering Wheel of Tractor

This paper reports a study on the biomechanical response of a human hand-arm model to random vibrations of the steering wheel of a tractor. An anatomically accurate bone-only hand-arm model from TurboSquidTM was used to obtain a finite element (FE) model to understand the Hand-arm vibration syndrome (HAVS), which is a neurological and vascular disorder caused by exposure of the human hand-arm to prolonged vibrations. Modal analysis has been done to find out the first few natural frequencies and mode shapes of the system. Coupling of degrees of freedom (DOF) had to be done in the FE idealization to do modal analysis, as the bones were not attached to each other in the TurboSquidTM model. The shoulder bone, scapula, has been constrained at one end for eigenvalue analysis. It was observed that the first five natural frequencies were in the range of 0-250 Hz, which is the range in which the effect of HAVS is the highest. Harmonic analysis was done by giving a swept sine excitation in the frequency range 0 to 200 Hz. For this, a force input of 25 N was imparted at nodes perpendicular to the hand, the force value chosen being the nominal force in most applications involving powered hand-held tools and steering wheels of tractors. The nodes chosen for force application were determined experimentally from observations made by gripping the steering wheel. The frequency response function (FRF) plots were obtained in the x, y and z directions. Random vibration analysis was done next by giving force power spectral densities (PSD) in the form of nodal excitation as input to the FE model of hand-arm, and computing the output acceleration PSDs. The input force PSDs were measured using FlexiForce® sensors along the three axes. The acceleration responses at the steering wheel were also measured using tri-axial accelerometers for validating the computed results. The output acceleration PSDs were then weighted using the frequency weighting curves for hand-arm vibration and the total daily exposure A(8), computed using ISO 5349-1 standards, was compared with the vibration action and limit values. The A(8) values obtained are found to be higher than the vibration limit values.     

An efficient approach to collaborative simulation of variable structure systems on multi-core machines

Complex variable-structure systems (CVSSs) are a common type of complex systems that exhibit changes both at structural and behavior levels. Simulations of CVSSs challenge current collaborative execution methods with increasingly big and complex models. The emergence of multi-core paradigm presents an exciting opportunity to address such challenge, so an advanced parallel simulator under multi-core environments is proposed. The simulator: (1) provides thread simulation kernels and five kinds of management services to support dynamic model structure flexibly; (2) can explore both inherent and dynamic parallelism among models based on interaction relations, and employ the multi-thread paradigm to gain good speedup; (3) adopts an efficient dynamic load-balancing method, which can migrate models among cores with very low cost and support dynamic core allocation on demand, to address evident load-imbalance problems brought by variable-structure. The experiments show that structure changes can be supported while up to 23 % performance increase can be gained.     

Maximum Likelihood Estimation of Long‐Term HIV Dynamic Models and Antiviral Response

Summary HIV dynamics studies, based on differential equations, have significantly improved the knowledge on HIV infection. While first studies used simplified short‐term dynamic models, recent works considered more complex long‐term models combined with a global analysis of whole patient data based on nonlinear mixed models, increasing the accuracy of the HIV dynamic analysis. However statistical issues remain, given the complexity of the problem. We proposed to use the SAEM (stochastic approximation expectation‐maximization) algorithm, a powerful maximum likelihood estimation algorithm, to analyze simultaneously the HIV viral load decrease and the CD4 increase in patients using a long‐term HIV dynamic system. We applied the proposed methodology to the prospective COPHAR2–ANRS 111 trial. Very satisfactory results were obtained with a model with latent CD4 cells defined with five differential equations. One parameter was fixed, the 10 remaining parameters (eight with between‐patient variability) of this model were well estimated. We showed that the efficacy of nelfinavir was reduced compared to indinavir and lopinavir.