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Computational models of the musculoskeletal system are scientific tools used to study human movement, quantify the effects of injury and disease, plan surgical interventions, or control realistic high-dimensional articulated prosthetic limbs. If the models are sufficiently accurate, they may embed complex relationships within the sensorimotor system. These potential benefits are limited by the challenge of implementing fast and accurate musculoskeletal computations. A typical hand muscle spans over 3 degrees of freedom (DOF), wrapping over complex geometrical constraints that change its moment arms and lead to complex posture-dependent variation in torque generation. Here, we report a method to accurately and efficiently calculate musculotendon length and moment arms across all physiological postures of the forearm muscles that actuate the hand and wrist. Then, we use this model to test the hypothesis that the functional similarities of muscle actions are embedded in muscle structure. The posture dependent muscle geometry, moment arms and lengths of modeled muscles were captured using autogenerating polynomials that expanded their optimal selection of terms using information measurements. The iterative process approximated 33 musculotendon actuators, each spanning up to 6 DOFs in an 18 DOF model of the human arm and hand, defined over the full physiological range of motion. Using these polynomials, the entire forearm anatomy could be computed in <10 μs, which is far better than what is required for real-time performance, and with low errors in moment arms (below 5%) and lengths (below 0.4%). Moreover, we demonstrate that the number of elements in these autogenerating polynomials does not increase exponentially with increasing muscle complexity; complexity increases linearly instead. Dimensionality reduction using the polynomial terms alone resulted in clusters comprised of muscles with similar functions, indicating the high accuracy of approximating models. We propose that this novel method of describing musculoskeletal biomechanics might further improve the applications of detailed and scalable models to describe human movement.

[This corrects the article DOI: 10.1371/journal.pone.0164050.].

The sensorimotor integration during unconstrained reaching movements in the presence of variable environmental forces remains poorly understood. The objective of this study was to quantify how much the primary afferent activity of muscle spindles can contribute to shaping muscle coactivation patterns during reaching movements with complex dynamics. To achieve this objective, we designed a virtual reality task that guided healthy human participants through a set of planar reaching movements with controlled kinematic and dynamic conditions that were accompanied by variable muscle co-contraction. Next, we approximated the Ia afferent activity using a phenomenological model of the muscle spindle and muscle lengths derived from a musculoskeletal model. The parameters of the spindle model were altered systematically to evaluate the effect of fusimotor drive on the shape of the temporal profile of afferent activity during movement. The experimental and simulated data were analyzed with hierarchical clustering. We found that the pattern of co-activation of agonistic and antagonistic muscles changed based on whether passive forces in each movement played assistive or resistive roles in limb dynamics. The reaching task with assistive limb dynamics was associated with the most muscle co-contraction. In contrast, the simulated Ia afferent profiles were not changing between tasks and they were largely reciprocal with homonymous muscle activity. Simulated physiological changes to the fusimotor drive were not sufficient to reproduce muscle co-contraction. These results largely rule out the static set and α-γ coactivation as the main types of fusimotor drive that transform the monosynaptic Ia afferent feedback into task-dependent co-contraction of antagonistic muscles. We speculate that another type of nonlinear transformation of Ia afferent signals that is independent of signals modulating the activity of α motoneurons is required for Ia afferent-based co-contraction. This transformation could either be applied through a complex nonlinear profile of fusimotor drive that is not yet experimentally observed or through presynaptic inhibition.

Neural control of movement can only be realized though the interaction between the mechanical properties of the limb and the environment. Thus, a fundamental question is whether anatomy has evolved to simplify neural control by shaping these interactions in a beneficial way. This inductive data-driven study analyzed the patterns of muscle actions across multiple joints using the musculoskeletal model of the human upper limb. This model was used to calculate muscle lengths across the full range of motion of the arm and examined the correlations between these values between all pairs of muscles. Musculoskeletal coupling was quantified using hierarchical clustering analysis. Muscle lengths between multiple pairs of muscles across multiple postures were highly correlated. These correlations broadly formed two proximal and distal groups, where proximal muscles of the arm were correlated with each other and distal muscles of the arm and hand were correlated with each other, but not between groups. Using hierarchical clustering, between 11 and 14 reliable muscle groups were identified. This shows that musculoskeletal anatomy does indeed shape the mechanical interactions by grouping muscles into functional clusters that generally match the functional repertoire of the human arm. Together, these results support the idea that the structure of the musculoskeletal system is tuned to solve movement complexity problem by reducing the dimensionality of available solutions.

The stabilizing role of sensory feedback in relation to realistic 3-dimensional movement dynamics remains poorly understood. The objective of this study was to quantify how primary afferent activity contributes to shaping muscle activity patterns during reaching movements. To achieve this objective, we designed a virtual reality task that guided healthy human subjects through a set of planar reaching movements with controlled kinematic and dynamic conditions that minimized inter-subject variability. Next, we integrated human upper-limb models of musculoskeletal dynamics and proprioception to analyze motion and major muscle activation patterns during these tasks. We recorded electromyographic and motion-capture data and used the integrated model to simulate joint kinematics, joint torques due to muscle contractions, muscle length changes, and simulated primary afferent feedback. The parameters of the primary afferent model were altered systematically to evaluate the effect of fusimotor drive. The experimental and simulated data were analyzed with hierarchical clustering. We found that the muscle activity patterns contained flexible task-dependent groups that consisted of co-activating agonistic and antagonistic muscles that changed with the dynamics of the task. The activity of muscles spanning only the shoulder generally grouped into a proximal cluster, while the muscles spanning the wrist grouped into a distal cluster. The bifunctional muscle spanning the shoulder and elbow were flexibly grouped with either proximal or distal cluster based on the dynamical requirements of the task. The composition and activation of these groups reflected the relative contribution of active and passive forces to each motion. In contrast, the simulated primary afferent feedback was most related to joint kinematics rather than dynamics, even though the primary afferent models had nonlinear dynamical components and variable fusimotor drive. Simulated physiological changes to the fusimotor drive were not sufficient to reproduce the dynamical features in muscle activity pattern. Altogether, these results suggest that sensory feedback signals are in a different domain from that of muscle activation signals. This indicates that to solve the neuromechanical problem, the central nervous system controls limb dynamics through task-dependent co-activation of muscles and non-linear modulation of monosynaptic primary afferent feedback. Footnotes * Parameter exploration for the primary afferent model was performed to simulate the effect of the fusimotor drive. The results are summarized in the manuscript and in the new Figure 7.

Computational models of the musculoskeletal system are scientific tools used to study human movement, quantify the effects of injury and disease, and plan surgical interventions. Additionally, these models could also be used to intuitively link biological control signals and realistic high-dimensional articulated prosthetic limbs. However, implementing fast and accurate musculoskeletal computations that can be used to control a prosthetic limb in real-time is a challenging problem. As muscles typically span multiple joints, the wrapping over complex geometrical constraints changes their moment arms and length as a function of joint angle and, thus, their ability to generate joint torques. As a result of these biomechanical complexities, calculating these muscle state variables in real-time is a difficult simulation problem. Here, we report a method to accurately and efficiently calculate these variables for the forearm muscles that actuate the hand and wrist across multiple postures. The posture dependent muscle geometry, moment arms and lengths of modeled muscles, were captured using autogenerating polynomials that expanded their optimal selection of terms using information measurements. The iterative process approximated 33 musculotendon actuators, each spanning up to 6 DOFs in an 18 DOF model of the human arm and hand, defined over the full physiological range of motion. Using these polynomials, the entire forearm anatomy could be computed in <10 μs, which is far better than what is required for real-time performance, and with low errors in moment arms (below 5%) and lengths (below 0.4%). Moreover, we demonstrate that the number of elements in these autogenerating polynomials does not increase exponentially with the increase in complexity of muscles, increasing linearly instead. The similar structure and function of muscles are represented with specific invariant polynomial terms. Dimensionality reduction using the polynomial terms alone resulted in clusters comprised of muscles with similar functions, suggesting that the polynomials themselves captured biologically relevant features of muscle structure and function. We propose that this novel method of describing musculoskeletal biomechanics might further improve the applications of detailed and scalable models for the description of human movement.

Abstract The development of realistic musculoskeletal models is a fundamental goal for the theoretical progress in sensorimotor control and its engineering applications, e.g., in the biomimetic control of artificial limbs. Yet, accurate models require extensive experimental measures to validate structural and functional parameters describing muscle state over the full physiological range of motion. However, available experimental measurements of, for example, muscle moment arms are sparse and often disparate. Validation of these models is not trivial because of the highly complex anatomy and behavior of human limbs. In this study, we developed a method to validate and scale kinematic muscle parameters using posture-dependent moment arm profiles, isometric force measurements, and a computational detection of assembly errors. We used a previously published model with 18 degrees of freedom (DOFs) and 32 musculotendon actuators with force generated from a Hill-type muscle model. The muscle path from origin to insertion with wrapping geometry was used to model the muscle lengths and moment arms. We simulated moment arm profiles across the full physiological range of motion and compared them to an assembled dataset of published and merged experimental profiles. The muscle paths were adjusted using custom metrics based on root-mean-square and correlation coefficient of the difference between simulated and experimental values. Since the available measurements were sparse and the examination of high-dimensional muscles is challenging, we developed analyses to identify common failures, i.e., moment arm functional flipping due to the sign reversal in simulated moments and the imbalance of force generation between antagonistic groups in postural extremes. The validated model was used to evaluate the expected errors in torque generation with the assumption of constant instead of the posture-dependent moment arms at the wrist flexion-extension DOF, which is the critical joint in our model with the largest number of crossing muscles. We found that there was a reduction of joint torques by about 35% in the extreme quartiles of the wrist DOF. The use of realistic musculoskeletal models is essential for the reconstruction of hand dynamics. These models may improve the understanding of muscle actions and help in the design and control of artificial limbs in future applications. New & Noteworthy Realistic models of human limbs are a development goal required for the understanding of motor control and its applications in biomedical fields. However, developing accurate models is restrained by the lack of accurate and reliable musculoskeletal measurements in humans. Here, we have overcome this challenge by using multi-stage validation of simulated structures using both experimental data and the identification of structural failures in the high-dimensional muscle paths. We demonstrate that the rigorous structural and functional validation method is essential for the understanding of force generation at the wrist. Competing Interest Statement The authors have declared no competing interest. Footnotes * The placement of figures has been fixed by removing the automatic figure numbering fields and repeating graphics. The ORCID IDs are now added. The supplementary data URL is linked. * https://github.com/neurowired/ms_moment_arms_2020

Contact networks, behavioral interactions, and shared use of space can all have important implications for the spread of disease in animals. Social networks enable the quantification of complex patterns of interactions; therefore, network analysis is becoming increasingly widespread in the study of infectious disease in animals, including wildlife. We present an introductory guide to using social-network-analytical approaches in wildlife disease ecology, epidemiology, and management. We focus on providing detailed practical guidance for the use of basic descriptive network measures by suggesting the research questions to which each technique is best suited and detailing the software available for each. We also discuss how using network approaches can be used beyond the study of social contacts and across a range of spatial and temporal scales. Finally, we integrate these approaches to examine how network analysis can be used to inform the implementation and monitoring of effective disease management strategies.

The emergence and spread of infections can contribute to the decline and extinction of populations, particularly in conjunction with anthropogenic environmental change. The importance of heterogeneity in processes of transmission, resistance and tolerance is increasingly well understood in theory, but empirical studies that consider both the demographic and behavioural implications of infection are scarce. Non-random mixing of host individuals can impact the demographic thresholds that determine the amplification or attenuation of disease prevalence. Risk assessment and management of disease in threatened wildlife populations must therefore consider not just host density, but also the social structure of host populations. Here we integrate the most recent developments in epidemiological research from a demographic and social network perspective, and synthesize the latest developments in social network modelling for wildlife disease, to explore their applications to disease management in populations in decline and at risk of extinction. We use simulated examples to support our key points and reveal how disease-management strategies can and should exploit both behavioural and demographic information to prevent or control the spread of disease. Our synthesis highlights the importance of considering the combined impacts of demographic and behavioural processes in epidemics to successful disease management in a conservation context. This article is part of the theme issue ‘Linking behaviour to dynamics of populations and communities: application of novel approaches in behavioural ecology to conservation’.

Background Carbon nanotubes and nanofibers (CNT/F) have known toxicity but simultaneous comparative studies of the broad material class, especially those with a larger diameter, with computational analyses linking toxicity to their fundamental material characteristics was lacking. It was unclear if all CNT/F confer similar toxicity, in particular, genotoxicity. Nine CNT/F (MW #1–7 and CNF #1–2), commonly found in exposure assessment studies of U.S. facilities, were evaluated with reported diameters ranging from 6 to 150 nm. All materials were extensively characterized to include distributions of physical dimensions and prevalence of bundled agglomerates. Human bronchial epithelial cells were exposed to the nine CNT/F (0–24 μg/ml) to determine cell viability, inflammation, cellular oxidative stress, micronuclei formation, and DNA double-strand breakage. Computational modeling was used to understand various permutations of physicochemical characteristics and toxicity outcomes. Results Analyses of the CNT/F physicochemical characteristics illustrate that using detailed distributions of physical dimensions provided a more consistent grouping of CNT/F compared to using particle dimension means alone. In fact, analysis of binning of nominal tube physical dimensions alone produced a similar grouping as all characterization parameters together. All materials induced epithelial cell toxicity and micronuclei formation within the dose range tested. Cellular oxidative stress, DNA double strand breaks, and micronuclei formation consistently clustered together and with larger physical CNT/F dimensions and agglomerate characteristics but were distinct from inflammatory protein changes. Larger nominal tube diameters, greater lengths, and bundled agglomerate characteristics were associated with greater severity of effect. The portion of tubes with greater nominal length and larger diameters within a sample was not the majority in number, meaning a smaller percentage of tubes with these characteristics was sufficient to increase toxicity. Many of the traditional physicochemical characteristics including surface area, density, impurities, and dustiness did not cluster with the toxicity outcomes. Conclusion Distributions of physical dimensions provided more consistent grouping of CNT/F with respect to toxicity outcomes compared to means only. All CNT/F induced some level of genotoxicity in human epithelial cells. The severity of toxicity was dependent on the sample containing a proportion of tubes with greater nominal lengths and diameters.