A probabilistic model of glenohumeral external rotation strength for healthy normals and rotator cuff tear cases

A comparative probabilistic analysis of human and chimpanzee rotator cuff functional capacity

Computational musculoskeletal modeling represents a valuable approach to examining biological systems in physical anthropology. Probabilistic modeling builds on computational musculoskeletal models by associating mathematical distributions of specific musculoskeletal features within known ranges of biological variability with functional outcomes. The purpose of this study was to determine if overlap in rotator cuff muscle force predictions would occur between species during the performance of an evolutionarily relevant horizontal bimanual arm suspension task. This necessitated creating novel probabilistic models of the human and chimpanzee glenohumeral joint through augmentation of previously published deterministic models. Glenohumeral musculoskeletal features of anthropological interest were probabilistically modeled to produce distributions of predicted human and chimpanzee rotator cuff muscle force that were representative of the specific anatomical manipulations. Musculoskeletal features modeled probabilistically included rotator cuff origins and deltoid insertion, glenoid inclination, and joint stability. Predicted human rotator cuff muscle force distributions were mostly limited to alternating between infraspinatus and teres minor, with both 100% and 0% muscle force predicted for both muscles. The chimpanzee model predicted low-to-moderate muscle force across all rotator cuff muscles. Rotator cuff muscle force predictions were most sensitive to changes of muscle origins and insertions. Results indicate that functional rotator cuff overlap is unlikely between chimpanzees and humans without greater modifications of the glenohumeral musculoskeletal phenotypes. The results also highlight the low efficacy of the human upper extremity in overhead, weight-bearing tasks, and propensity for rotator cuff injury.

From fibre to function: are we accurately representing muscle architecture and performance?

The size and arrangement of fibres play a determinate role in the kinetic and energetic performance of muscles. Extrapolations between fibre architecture and performance underpin our understanding of how muscles function and how they are adapted to power specific motions within and across species. Here we provide a synopsis of how this 'fibre to function' paradigm has been applied to understand muscle design, performance and adaptation in animals. Our review highlights the widespread application of the fibre to function paradigm across a diverse breadth of biological disciplines but also reveals a potential and highly prevalent limitation running through past studies. Specifically, we find that quantification of muscle architectural properties is almost universally based on an extremely small number of fibre measurements. Despite the volume of research into muscle properties, across a diverse breadth of research disciplines, the fundamental assumption that a small proportion of fibre measurements can accurately represent the architectural properties of a muscle has never been quantitatively tested. Subsequently, we use a combination of medical imaging, statistical analysis, and physics-based computer simulation to address this issue for the first time. By combining diffusion tensor imaging (DTI) and deterministic fibre tractography we generated a large number of fibre measurements (>3000) rapidly for individual human lower limb muscles. Through statistical subsampling simulations of these measurements, we demonstrate that analysing a small number of fibres (n < 25) typically used in previous studies may lead to extremely large errors in the characterisation of overall muscle architectural properties such as mean fibre length and physiological cross-sectional area. Through dynamic musculoskeletal simulations of human walking and jumping, we demonstrate that recovered errors in fibre architecture characterisation have significant implications for quantitative predictions of in-vivo dynamics and muscle fibre function within a species. Furthermore, by applying data-subsampling simulations to comparisons of muscle function in humans and chimpanzees, we demonstrate that error magnitudes significantly impact both qualitative and quantitative assessment of muscle specialisation, potentially generating highly erroneous conclusions about the absolute and relative adaption of muscles across species and evolutionary transitions. Our findings have profound implications for how a broad diversity of research fields quantify muscle architecture and interpret muscle function.

Scapulothoracic rhythm affects glenohumeral joint force

Hypothesis

Musculoskeletal computer models provide valuable insights into shoulder biomechanics. The shoulder is a complex joint composed of glenohumeral, scapulothoracic, acromioclavicular, and sternoclavicular articulations, whose function is largely dependent on the many muscles spanning these joints. However, the range of patient-to-patient variability in shoulder function is largely unknown. We therefore assessed the sensitivity of glenohumeral forces to population-based model input parameters that were likely to influence shoulder function.

Methods

We constructed musculoskeletal models of the shoulder in the AnyBody Modeling System (AnyBody Technology, Aalborg, Denmark). We used inverse dynamics and static optimization to solve for glenohumeral joint forces during a simulated shoulder elevation. We generated 1000 AnyBody models by uniformly distributing the following input parameters: subject height, scapulohumeral rhythm, humeral head radius, and acromiohumeral interval.

Results

Increasing body height increased glenohumeral joint forces. Increasing the ratio of scapulothoracic to glenohumeral elevation also increased forces. Increasing humeral head radius and acromiohumeral interval decreased forces. The relative sensitivity of glenohumeral joint forces to input parameters was dependent on the angle of shoulder elevation. We developed an efficient method of generating and simulating musculoskeletal models representing a large population of shoulder arthroplasty patients. We found that scapulohumeral rhythm had a significant influence on glenohumeral joint force.

Conclusions

This finding underscores the importance of more accurately measuring and simulating scapulothoracic motion rather than using fixed ratios or average scapulothoracic motion. This modeling approach can be used to generate virtual populations for conducting efficient simulations and generating statistical conclusions.

Using a Bayesian Network to Predict L5/S1 Spinal Compression Force from Posture, Hand Load, Anthropometry, and Disc Injury Status

Stochastic biomechanical modeling has become a useful tool most commonly implemented using Monte Carlo simulation, advanced mean value theorem, or Markov chain modeling. Bayesian networks are a novel method for probabilistic modeling in artificial intelligence, risk modeling, and machine learning. The purpose of this study was to evaluate the suitability of Bayesian networks for biomechanical modeling using a static biomechanical model of spinal forces during lifting. A 20-node Bayesian network model was used to implement a well-established static two-dimensional biomechanical model for predicting L5/S1 compression and shear forces. The model was also implemented as a Monte Carlo simulation in MATLAB. Mean L5/S1 spinal compression force estimates differed by 0.8%, and shear force estimates were the same. The model was extended to incorporate evidence about disc injury, which can modify the prior probability estimates to provide posterior probability estimates of spinal compression force. An example showed that changing disc injury status from false to true increased the estimate of mean L5/S1 compression force by 14.7%. This work shows that Bayesian networks can be used to implement a whole-body biomechanical model used in occupational biomechanics and incorporate disc injury.

Modeling people with motor disabilities to empower the automatic accessibility and ergonomic assessment of new products

Virtual User Models (VUMs) can be a valuable tool for accessibility and ergonomic evaluation of designs in simulation environments. As increasing the accessibility of a design is usually translated into additional costs and increased development time, the need for specifying the percentage of population for which the design will be accessible is crucial. This paper addresses the development of VUMs representing specific groups of people with disabilities. In order to create such VUMs, we need to know the functional limitations, i.e. disability parameters, caused by each disability and their variability over the population. Measurements were obtained from 90 subjects with motor disabilities and were analyzed using both parametric and nonparametric regression methods as well as a proposed hybrid regression method able to handle small sample sizes. Validation results showed that in most cases the proposed regression analysis can produce valid estimations on the variability of each disability parameter.

Comparison of rotator cuff muscle architecture between humans and other selected vertebrate species

In this study, we compare rotator cuff muscle architecture of typically used animal models with that of humans and quantify the scaling relationships of these muscles across mammals. The four muscles that correspond to the human rotator cuff - supraspinatus, infraspinatus, subscapularis and teres minor - of 10 commonly studied animals were excised and subjected to a series of comparative measurements. When body mass among animals was regressed against physiological cross-sectional area, muscle mass and normalized fiber length, the confidence intervals suggested geometric scaling but did not exclude other scaling relationships. Based on the architectural difference index (ADI), a combined measure of fiber length-to-moment arm ratio, fiber length-to-muscle length ratio and the fraction of the total rotator cuff physiological cross-sectional area contributed by each muscle, chimpanzees were found to be the most similar to humans (ADI=2.15), followed closely by capuchins (ADI=2.16). Interestingly, of the eight non-primates studied, smaller mammals such as mice, rats and dogs were more similar to humans in architectural parameters compared with larger mammals such as sheep, pigs or cows. The force production versus velocity trade-off (indicated by fiber length-to-moment arm ratio) and the excursion ability (indicated by fiber length-to-muscle length ratio) of humans were also most similar to those of primates, followed by the small mammals. Overall, primates provide the best architectural representation of human muscle architecture. However, based on the muscle architectural parameters of non-primates, smaller rather than larger mammals may be better models for studying muscles related to the human rotator cuff.

The Roles of Whole Body Balance, Shoe-Floor Friction, and Joint Strength During Maximum Exertions: Searching for the “Weakest Link”

Exerting manual forces is critical during occupational performance. Therefore, being able to estimate maximum force capacity is particularly useful for determining how these manual exertion demands relate to available capacity. To facilitate this type of prediction requires a complete understanding of how maximum force capacity is governed biomechanically. This research focused on identifying how factors including joint moment strength, balance and shoe-floor friction affected hand force capacity during pulling, pressing downward and pushing medially. To elucidate potential limiting factors, joint moments were calculated and contrasted with reporte joint strength capacities, the balancing point within the shoe-floor interface was calculated and expresess relative to the area defined by the shoe-floor interface, and the net applied horizontal forces were compare with the available friction. Each of these variables were calculated as participants exerted forces in a series o conditions designed to systematically control or restrict certain factors from limiting hand force capacity. The results demonstrated that hand force capacity, in all tested directions, was affected by the experimental conditions (up to 300%). Concurrently, biomechanical measures reached or surpassed reported criterion threshold inferring specific biomechanical limitations. Downward exertions were limited by elbow strength, wherea pulling exertions were often limited by balance along the anterior-posterior axis. No specific limitations wer identified for medial exertions.

Estimated Force and Moment of Shoulder External Rotation Muscles: Differences Between Transverse and Sagittal Planes

The aim of this study was to compare shoulder muscle force and moment production during external rotation performed in the transverse and sagittal planes. An optimization model was used for estimating shoulder muscle force production of infraspinatus, teres minor, supraspinatus, anterior deltoid, middle deltoid and posterior deltoid muscles. The model uses as input data the external rotation moment, muscle moment arm magnitude, muscle physiologic cross-sectional area and muscle specific tension. The external rotation moment data were gathered from eight subjects in transverse and six subjects in sagittal plane using an isokinetic dynamometer. In the sagittal plane, all studied muscles presented larger estimated force in comparison with the transverse plane. The infraspinatus, teres minor, supraspinatus and posterior deltoid muscles presented larger moment in sagittal when compared with transverse plane. When prescribing shoulder rehabilitation exercises, therapists should bear in mind the described changes in muscle force production.

A probabilistic finger biodynamic model better depicts the roles of the flexors during unloaded flexion

Previous deterministic finger biomechanical models predicted that the flexor digitorum superficialis (FDS) was silent and the flexor digitorum profundus (FDP) was the only active flexor during finger flexion. Experimental studies in vivo, however, recorded activities of both flexors. In this study, in an attempt to elucidate the roles of the flexors, a probabilistic biodynamic model of the index finger was constructed to estimate the muscle-tendon forces during an experimentally measured index finger flexion movement. A Monte-Carlo simulation was performed with four model parameters, including moment arms, physiological cross sectional areas (PCSA), passive torques, and anthropometric measures as independent random variables. The muscle-tendon forces at each time point were determined using a nonlinear optimization technique. The model predicted that both FDS and FDP contributed to sustaining the movement and the FDS was not necessarily silent. The two distinct force patterns observed in vivo in experimental studies were also corroborated by the simulation. These findings, contrary to previous deterministic models' predictions but in agreement with experimental measurements, explained the observed coactivation of FDS and FDP, and resolved the controversy regarding the roles of the flexors in finger movement dynamics.

A review of probabilistic analysis in orthopaedic biomechanics

Probabilistic analysis methods are being increasingly applied in the orthopaedics and biomechanics literature to account for uncertainty and variability in subject geometries, properties of various structures, kinematics and joint loading, as well as uncertainty in implant alignment. As a complement to experiments, finite element modelling, and statistical analysis, probabilistic analysis provides a method of characterizing the potential impact of variability in parameters on performance. This paper presents an overview of probabilistic analysis and a review of biomechanics literature utilizing probabilistic methods in structural reliability, kinematics, joint mechanics, musculoskeletal modelling, and patient-specific representations. The aim of this review paper is to demonstrate the wide range of applications of probabilistic methods and to aid researchers and clinicians in better understanding probabilistic analyses.

A comparison between two models of shoulder muscle force estimation

Shoulder injuries are often related to rotator cuff muscles. Although there are various models for muscle force estimation, it is difficult to ensure that the results obtained with such models are reliable. The aim of the current study was to compare two models of muscle force estimation. Eight subjects, seven male and one female (mean age of 24 yr; mean height of 1.83 m), performed five isokinetic maximum concentric contractions of internal and external shoulder rotation. Two models with different algorithms were used. In both, the input data consisted of the measured internal rotation moment. Comparisons were made between the difference and the average results obtained with each model of muscle force estimation. There was reasonable agreement among the results for force between the two models for subscapularis, pectoralis major, and anterior deltoideus muscles results. Conversely, poor correlation was found for the latissimus dorsi, teres major, and middle deltoid. These results suggest that the algorithm structure might have a strong effect on muscle force estimation results.

Improving the fitness of high-dimensional biomechanical models via data-driven stochastic exploration

The field of complex biomechanical modeling has begun to rely on Monte Carlo techniques to investigate the effects of parameter variability and measurement uncertainty on model outputs, search for optimal parameter combinations, and define model limitations. However, advanced stochastic methods to perform data-driven explorations, such as Markov chain Monte Carlo (MCMC), become necessary as the number of model parameters increases. Here, we demonstrate the feasibility and, what to our knowledge is, the first use of an MCMC approach to improve the fitness of realistically large biomechanical models. We used a Metropolis-Hastings algorithm to search increasingly complex parameter landscapes (3, 8, 24, and 36 dimensions) to uncover underlying distributions of anatomical parameters of a "truth model" of the human thumb on the basis of simulated kinematic data (thumbnail location, orientation, and linear and angular velocities) polluted by zero-mean, uncorrelated multivariate Gaussian "measurement noise." Driven by these data, ten Markov chains searched each model parameter space for the subspace that best fit the data (posterior distribution). As expected, the convergence time increased, more local minima were found, and marginal distributions broadened as the parameter space complexity increased. In the 36-D scenario, some chains found local minima but the majority of chains converged to the true posterior distribution (confirmed using a cross-validation dataset), thus demonstrating the feasibility and utility of these methods for realistically large biomechanical problems.

A stochastic analysis of glenoid inclination angle and superior migration of the humeral head

BACKGROUND

Superior glenoid inclination, which is a relatively upward facing of the glenoid in the plane of the scapula, has been associated with rotator cuff pathology. Increased glenoid inclination may cause superior humeral head migration, which can cause impingement of the supraspinatus tendon. The purpose of this study was to test the hypothesis that inclination angle affects the probability of superior humeral head migration.

METHODS

A three-dimensional model of the glenohumeral joint was developed in which muscle forces were modeled as random variables. Monte Carlo simulation was used to compute the probability that the glenohumeral reaction force was directed such that superior humeral head migration should occur. An electromyogram-driven model was used to estimate shoulder muscle forces in healthy volunteers performing arm elevation.

FINDINGS

The model predicted that the probability of superior humeral head migration increased as glenoid inclination angle was increased. This finding was independent of the assumed shape of the muscle force probability distributions.

INTERPRETATION

The results support the theory that glenoid inclination may be a risk factor for rotator cuff pathology.

Comparison of model-predicted and measured moment arms for the rotator cuff muscles

BACKGROUND

The ability of mathematical models of the shoulder to accurately replicate physiological muscle moment arms is unknown. The purpose of this study was to compare model-predicted and experimentally measured moment arms for the rotator cuff muscles during arm elevation.

METHODS

Moment arms obtained from six mathematical models and seven experimental studies were compared for the supraspinatus, infraspinatus, teres minor, and subscapularis for elevation in the scapular plane.

RESULTS

All of the included models generated moment arms that generally fell within the range of experimentally measured data.

INTERPRETATION

The quantitative agreement between model-predicted and experimentally measured moment arms supports the use of the included models for biomechanical shoulder analyses.