Muscle Synergies Heavily Influence the Neural Control of Arm Endpoint Stiffness and Energy Consumption

Much debate has arisen from research on muscle synergies with respect to both limb impedance control and energy consumption. Studies of limb impedance control in the context of reaching movements and postural tasks have produced divergent findings, and this study explores whether the use of synergies by the central nervous system (CNS) can resolve these findings and also provide insights on mechanisms of energy consumption. In this study, we phrase these debates at the conceptual level of interactions between neural degrees of freedom and tasks constraints. This allows us to examine the ability of experimentally-observed synergies—correlated muscle activations—to control both energy consumption and the stiffness component of limb endpoint impedance. In our nominal 6-muscle planar arm model, muscle synergies and the desired size, shape, and orientation of endpoint stiffness ellipses, are expressed as linear constraints that define the set of feasible muscle activation patterns. Quadratic programming allows us to predict whether and how energy consumption can be minimized throughout the workspace of the limb given those linear constraints. We show that the presence of synergies drastically decreases the ability of the CNS to vary the properties of the endpoint stiffness and can even preclude the ability to minimize energy. Furthermore, the capacity to minimize energy consumption—when available—can be greatly affected by arm posture. Our computational approach helps reconcile divergent findings and conclusions about task-specific regulation of endpoint stiffness and energy consumption in the context of synergies. But more generally, these results provide further evidence that the benefits and disadvantages of muscle synergies go hand-in-hand with the structure of feasible muscle activation patterns afforded by the mechanics of the limb and task constraints. These insights will help design experiments to elucidate the interplay between synergies and the mechanisms of learning, plasticity, versatility and pathology in neuromuscular systems.     

Measuring multi-joint stiffness during single movements: numerical validation of a novel time-frequency approach

This study presents and validates a Time-Frequency technique for measuring 2-dimensional multijoint arm stiffness throughout a single planar movement as well as during static posture. It is proposed as an alternative to current regressive methods which require numerous repetitions to obtain average stiffness on a small segment of the hand trajectory. The method is based on the analysis of the reassigned spectrogram of the arm's response to impulsive perturbations and can estimate arm stiffness on a trial-by-trial basis. Analytic and empirical methods are first derived and tested through modal analysis on synthetic data. The technique's accuracy and robustness are assessed by modeling the estimation of stiffness time profiles changing at different rates and affected by different noise levels. Our method obtains results comparable with two well-known regressive techniques. We also test how the technique can identify the viscoelastic component of non-linear and higher than second order systems with a non-parametrical approach. The technique proposed here is very impervious to noise and can be used easily for both postural and movement tasks. Estimations of stiffness profiles are possible with only one perturbation, making our method a useful tool for estimating limb stiffness during motor learning and adaptation tasks, and for understanding the modulation of stiffness in individuals with neurodegenerative diseases.     

Exploring novel objective functions for simulating muscle coactivation in the neck

Musculoskeletal modeling allows for analysis of individual muscles in various situations. However, current techniques to realistically simulate muscle response when significant amounts of intentional coactivation is required are inadequate. This would include stiffening the neck or spine through muscle coactivation in preparation for perturbations or impacts. Muscle coactivation has been modeled previously in the neck and spine using optimization techniques that seek to maximize the joint stiffness by maximizing total muscle activation or muscle force. These approaches have not sought to replicate human response, but rather to explore the possible effects of active muscle. Coactivation remains a challenging feature to include in musculoskeletal models, and may be improved by extracting optimization objective functions from experimental data. However, the components of such an objective function must be known before fitting to experimental data. This study explores the effect of components in several objective functions, in order to recommend components to be used for fitting to experimental data. Four novel approaches to modeling coactivation through optimization techniques are presented, two of which produce greater levels of stiffness than previous techniques. Simulations were performed using OpenSim and MATLAB cooperatively. Results show that maximizing the moment generated by a particular muscle appears analogous to maximizing joint stiffness. The approach of optimizing for maximum moment generated by individual muscles may be a good candidate for developing objective functions that accurately simulate muscle coactivation in complex joints. This new approach will be the focus of future studies with human subjects.     

Parameter identification of the human lower limb under dynamic, transient torsional loading

The response of the lower limb to dynamic, transient torsional loading applied at the foot has been measured for a male test subject. The dynamic loading was provided by a computer controlled pneumatic system which applied single haversine (i.e. half cycle of a sine wave) axial moment pulses of variable amplitude (0-100 Nm) and duration (50-600 ms). Potentiometers measured the absolute rotations of the three leg segments. Test variables included rotation direction, weight bearing and joint flexion. Two approaches were explored for specifying parameters (i.e. inertia, damping, stiffness) of a three degree-of-freedom dynamic system model which best duplicated the measured response. One approach involved identification of linear parameters by means of optimization while the other approach entailed estimation. Parameter estimates, which included non-linear, asymmetric stiffness functions, were derived from the literature. The optimization was undertaken so as to identify parameter dependence on test variables. Results indicate that parameter values are influenced by test variables. Results also indicate that the non-linear, estimated model better approximates the experimental data than the linear, identified model. In addition to identifying parameters of a three degree-of-freedom model, parameters were also identified for a single degree-of-freedom model where the motion variable was intended to indicate the rotation of the in vivo knee. It is concluded that the simpler model offers good accuracy in predicting both magnitude and time of occurrence of peak knee axial rotations. Model motion fails to track the measured knee rotation subsequent to the peak, however.     

Use of Self-Selected Postures to Regulate Multi-Joint Stiffness During Unconstrained Tasks

Background

The human motor system is highly redundant, having more kinematic degrees of freedom than necessary to complete a given task. Understanding how kinematic redundancies are utilized in different tasks remains a fundamental question in motor control. One possibility is that they can be used to tune the mechanical properties of a limb to the specific requirements of a task. For example, many tasks such as tool usage compromise arm stability along specific directions. These tasks only can be completed if the nervous system adapts the mechanical properties of the arm such that the arm, coupled to the tool, remains stable. The purpose of this study was to determine if posture selection is a critical component of endpoint stiffness regulation during unconstrained tasks.

Methodology/Principal Findings

Three-dimensional (3D) estimates of endpoint stiffness were used to quantify limb mechanics. Most previous studies examining endpoint stiffness adaptation were completed in 2D using constrained postures to maintain a non-redundant mapping between joint angles and hand location. Our hypothesis was that during unconstrained conditions, subjects would select arm postures that matched endpoint stiffness to the functional requirements of the task. The hypothesis was tested during endpoint tracking tasks in which subjects interacted with unstable haptic environments, simulated using a 3D robotic manipulator. We found that arm posture had a significant effect on endpoint tracking accuracy and that subjects selected postures that improved tracking performance. For environments in which arm posture had a large effect on tracking accuracy, the self-selected postures oriented the direction of maximal endpoint stiffness towards the direction of the unstable haptic environment.

Conclusions/Significance

These results demonstrate how changes in arm posture can have a dramatic effect on task performance and suggest that postural selection is a fundamental mechanism by which kinematic redundancies can be exploited to regulate arm stiffness in unconstrained tasks.     

Contribution of muscle short-range stiffness to initial changes in joint kinetics and kinematics during perturbations to standing balance: A simulation study

Simulating realistic musculoskeletal dynamics is critical to understanding neural control of muscle activity evoked in sensorimotor feedback responses that have inherent neural transmission delays. Thus, the initial mechanical response of muscles to perturbations in the absence of any change in muscle activity determines which corrective neural responses are required to stabilize body posture. Muscle short-range stiffness, a history-dependent property of muscle that causes a rapid and transient rise in muscle force upon stretch, likely affects musculoskeletal dynamics in the initial mechanical response to perturbations. Here we identified the contributions of short-range stiffness to joint torques and angles in the initial mechanical response to support surface translations using dynamic simulation. We developed a dynamic model of muscle short-range stiffness to augment a Hill-type muscle model. Our simulations show that short-range stiffness can provide stability against external perturbations during the neuromechanical response delay. Assuming constant muscle activation during the initial mechanical response, including muscle short-range stiffness was necessary to account for the rapid rise in experimental sagittal plane knee and hip joint torques that occurs simultaneously with very small changes in joint angles and reduced root mean square errors between simulated and experimental torques by 56% and 47%, respectively. Moreover, forward simulations lacking short-range stiffness produced unreasonably large joint angle changes during the initial response. Using muscle models accounting for short-range stiffness along with other aspects of history-dependent muscle dynamics may be important to advance our ability to simulate inherently unstable human movements based on principles of neural control and biomechanics.     

Identification of small scale biochemical networks based on general type system perturbations

New technologies enable acquisition of large data-sets containing genomic, proteomic and metabolic information that describe the state of a cell. These data-sets call for systematic methods enabling relevant information about the inner workings of the cell to be extracted. One important issue at hand is the understanding of the functional interactions between genes, proteins and metabolites. We here present a method for identifying the dynamic interactions between biochemical components within the cell, in the vicinity of a steady-state. Key features of the proposed method are that it can deal with data obtained under perturbations of any system parameter, not only concentrations of specific components, and that the direct effect of the perturbations does not need to be known. This is important as concentration perturbations are often difficult to perform in biochemical systems and the specific effects of general type perturbations are usually highly uncertain, or unknown. The basis of the method is a linear least-squares estimation, using time-series measurements of concentrations and expression profiles, in which system states and parameter perturbations are estimated simultaneously. An important side-effect of also employing estimation of the parameter perturbations is that knowledge of the system's steady-state concentrations, or activities, is not required and that deviations from steady-state prior to the perturbation can be dealt with. Time derivatives are computed using a zero-order hold discretization, shown to yield significant improvements over the widely used Euler approximation. We also show how network interactions with dynamics that are too fast to be captured within the available sampling time can be determined and excluded from the network identification. Known and unknown moiety conservation relationships can be processed in the same manner. The method requires that the number of samples equals at least the number of network components and, hence, is at present restricted to relatively small-scale networks. We demonstrate herein the performance of the method on two small-scale in silico genetic networks.     

Novel approaches to the calculation and comparison of thermoregulatory parameters: Non-linear regression of metabolic rate and evaporative water loss in Australian rodents

The calculation and comparison of physiological characteristics of thermoregulation has provided insight into patterns of ecology and evolution for over half a century. Thermoregulation has typically been explored using linear techniques; I explore the application of non-linear scaling to more accurately calculate and compare characteristics and thresholds of thermoregulation, including the basal metabolic rate (BMR), peak metabolic rate (PMR) and the lower (T_lc) and upper (T_uc) critical limits to the thermo-neutral zone (TNZ) for Australian rodents. An exponentially-modified logistic function accurately characterised the response of metabolic rate to ambient temperature, while evaporative water loss was accurately characterised by a Michaelis-Menten function. When these functions were used to resolve unique parameters for the nine species studied here, the estimates of BMR and TNZ were consistent with the previously published estimates. The approach resolved differences in rates of metabolism and water loss between subfamilies of Australian rodents that haven’t been quantified before. I suggest that non-linear scaling is not only more effective than the established segmented linear techniques, but also is more objective. This approach may allow broader and more flexible comparison of characteristics of thermoregulation, but it needs testing with a broader array of taxa than those used here.     

Trunk stiffness and dynamics during active extension exertions

Spinal stability is related to the recruitment and control of active muscle stiffness. Stochastic system identification techniques were used to calculate the effective stiffness and dynamics of the trunk during active trunk extension exertions. Twenty-one healthy adult subjects (10 males, 11 females) wore a harness with a cable attached to a servomotor such that isotonic flexion preloads of 100, 135, and 170 N were applied at the T10 level of the trunk. A pseudorandom stochastic force sequence (bandwidth 0-10 Hz, amplitude +/-30 N) was superimposed on the preload causing small amplitude trunk movements. Nonparametric impulse response functions of trunk dynamics were computed and revealed that the system exhibited underdamped second-order behavior. Second-order trunk dynamics were determined by calculating the best least-squares fit to the IRF. The quality of the model was quantified by comparing estimated and observed displacement variance accounted for (VAF), and quality of the second-order fits was calculated as a percentage and referred to as fit accuracy. Mean VAF and fit accuracy were 87.8 +/- 4.0% and 96.0 +/- 4.3%, respectively, indicating that the model accurately represented active trunk kinematic response. The accuracy of the kinematic representation was not influenced by preload or gender. Mean effective stiffness was 2.78 +/- 0.96 N/mm and increased significantly with preload (p < 0.001), but did not vary with gender (p = 0.425). Mean effective damping was 314 +/- 72 Ns/m and effective trunk mass was 37.0 +/- 9.3 kg. We conclude that stochastic system identification techniques should be used to calculate effective trunk stiffness and dynamics.     

Test of dynamic closed-loop baroreflex and autoregulatory control of total peripheral resistance in intact and conscious sheep

This is the first study able to examine and delineate the actual actions of the physiological mechanisms responsible for the dynamic couplings between cardiac output (CO), arterial pressure (Pa), right atrial pressure (PRA), and total peripheral resistance (TPR) in an individual subject without altering the underlying regulatory mechanisms. Eight conscious male sheep were used, where both types of baroreceptors were independently exposed to simultaneous beat-to-beat pressure perturbations under intact closed-loop conditions while CO, Pa, PRA, and TPR were measured. We applied the cardiovascular system identification method proposed in a companion paper (4) to quantitatively characterize the dynamic closed-loop transfer relations CO-->Pa, PRA-->Pa, Pa-->TPR, and PRA-->TPR from the measured signals. To validate the dynamic properties of the estimated transfer relations, the essential parts of the linear dynamics of the model were independently and comprehensively evaluated via error model cross-validation, and the overall model's steady-state behavior was compared with a separate random effects regression approach. In addition to numerous physiological findings, we found that the cardiovascular system identification results were exceptionally consistent with the analytically derived solutions previously discussed in Ref. 4. In conclusion, this study presents the first time validation of a cardiovascular system identification method by means of experimentally acquired animal data in the intact and conscious animal and offers a set of powerful quantitative tools essential to advancing our knowledge of cardiovascular regulatory physiology.     

Measuring the stiffness of bacterial cells from growth rates in hydrogels of tunable elasticity

Although bacterial cells are known to experience large forces from osmotic pressure differences and their local microenvironment, quantitative measurements of the mechanical properties of growing bacterial cells have been limited. We provide an experimental approach and theoretical framework for measuring the mechanical properties of live bacteria. We encapsulated bacteria in agarose with a user-defined stiffness, measured the growth rate of individual cells and fit data to a thin-shell mechanical model to extract the effective longitudinal Young's modulus of the cell envelope of Escherichia coli (50-150 MPa), Bacillus subtilis (100-200 MPa) and Pseudomonas aeruginosa (100-200 MPa). Our data provide estimates of cell wall stiffness similar to values obtained via the more labour-intensive technique of atomic force microscopy. To address physiological perturbations that produce changes in cellular mechanical properties, we tested the effect of A22-induced MreB depolymerization on the stiffness of E. coli. The effective longitudinal Young's modulus was not significantly affected by A22 treatment at short time scales, supporting a model in which the interactions between MreB and the cell wall persist on the same time scale as growth. Our technique therefore enables the rapid determination of how changes in genotype and biochemistry affect the mechanical properties of the bacterial envelope.     

Muscle mass in musculoskeletal models

Most current models of musculoskeletal dynamics lump a muscle's mass with its body segment, and then simulate the dynamics of these body segments connected by joints. As shown here, this popular approach leads to errors in the system's inertia matrix and hence in all aspects of the dynamics. Two simplified mathematical models were created to capture the relevant features of monoarticular and biarticular muscles, and the errors were analyzed. The models were also applied to two physiological examples: the triceps surae muscles that plantar flex the human ankle and the biceps femoris posterior muscle of the rat hind limb. The analysis of errors due to lumping showed that these errors can be large. Although the errors can be reduced in some postures, they cannot be easily eliminated in models that use segment lumping. Some options for addressing these errors are discussed.     

Successful Reconstruction of a Physiological Circuit with Known Connectivity from Spiking Activity Alone

Identifying the structure and dynamics of synaptic interactions between neurons is the first step to understanding neural network dynamics. The presence of synaptic connections is traditionally inferred through the use of targeted stimulation and paired recordings or by post-hoc histology. More recently, causal network inference algorithms have been proposed to deduce connectivity directly from electrophysiological signals, such as extracellularly recorded spiking activity. Usually, these algorithms have not been validated on a neurophysiological data set for which the actual circuitry is known. Recent work has shown that traditional network inference algorithms based on linear models typically fail to identify the correct coupling of a small central pattern generating circuit in the stomatogastric ganglion of the crab Cancer borealis. In this work, we show that point process models of observed spike trains can guide inference of relative connectivity estimates that match the known physiological connectivity of the central pattern generator up to a choice of threshold. We elucidate the necessary steps to derive faithful connectivity estimates from a model that incorporates the spike train nature of the data. We then apply the model to measure changes in the effective connectivity pattern in response to two pharmacological interventions, which affect both intrinsic neural dynamics and synaptic transmission. Our results provide the first successful application of a network inference algorithm to a circuit for which the actual physiological synapses between neurons are known. The point process methodology presented here generalizes well to larger networks and can describe the statistics of neural populations. In general we show that advanced statistical models allow for the characterization of effective network structure, deciphering underlying network dynamics and estimating information-processing capabilities.     

An adaptive system identification model of the biomechanical response of the human trunk during sudden loading

Sudden loading injuries to the low back are a concern. Current models are limited in their ability to quantify the time-varying nature of the sudden loading event. The method of approach used six males who were subjected to sudden loads. Response data (EMG and kinematics) were input into a system identification model to yield time-varying torso stiffness estimates. The results show estimates of system stiffness in good agreement with values in the literature. The average root mean square error of the model's predictions of sagittal motion was equal to 0.1 deg. In conclusion, system identification can be implemented with minimal error and used to gain more insight into the time-dependent trunk response to sudden loads.     

Effect of input resistance voltage-dependency on DC estimate of membrane capacitance in cardiac myocytes

The measure of membrane capacitance (C(m)) in cardiac myocytes is of primary importance as an index of their size in physiological and pathological conditions, and for the understanding of their excitability. Although a plethora of very accurate methods has been developed to access C(m) value in single cells, cardiac electrophysiologists still use, in the majority of laboratories, classical direct current techniques as they have been established in the early days of cardiac cellular electrophysiology. These techniques are based on the assumption that cardiac membrane resistance (R(m)) is constant, or changes negligibly, in a narrow potential range around resting potential. Using patch-clamp whole-cell recordings, both in current-clamp and voltage-clamp conditions, and numerical simulations, we document here the voltage-dependency of R(m), up to -45% of its resting value for 10-mV hyperpolarization, in resting rat ventricular myocytes. We show how this dependency makes classical protocols to misestimate C(m) in a voltage-dependent manner (up to 20% errors), which can dramatically affect C(m)-based calculations on cell size and on intracellular ion dynamics. We develop a simple mechanistic model to fit experimental data and obtain voltage-independent estimates of C(m), and we show that accurate estimates can also be extrapolated from the classical approach.     

A unified framework for unraveling the functional interaction structure of a biomolecular network based on stimulus-response experimental data

We propose a unified framework for the identification of functional interaction structures of biomolecular networks in a way that leads to a new experimental design procedure. In developing our approach, we have built upon previous work. Thus we begin by pointing out some of the restrictions associated with existing structure identification methods and point out how these restrictions may be eased. In particular, existing methods use specific forms of experimental algebraic equations with which to identify the functional interaction structure of a biomolecular network. In our work, we employ an extended form of these experimental algebraic equations which, while retaining their merits, also overcome some of their disadvantages. Experimental data are required in order to estimate the coefficients of the experimental algebraic equation set associated with the structure identification task. However, experimentalists are rarely provided with guidance on which parameters to perturb, and to what extent, to perturb them. When a model of network dynamics is required then there is also the vexed question of sample rate and sample time selection to be resolved. Supplying some answers to these questions is the main motivation of this paper. The approach is based on stationary and/or temporal data obtained from parameter perturbations, and unifies the previous approaches of Kholodenko et al. (PNAS 99 (2002) 12841-12846) and Sontag et al. (Bioinformatics 20 (2004) 1877-1886). By way of demonstration, we apply our unified approach to a network model which cannot be properly identified by existing methods. Finally, we propose an experiment design methodology, which is not limited by the amount of parameter perturbations, and illustrate its use with an in numero example.     

Coordinate Representations for Interference Reduction in Motor Learning

When opposing force fields are presented alternately or randomly across trials for identical reaching movements, subjects learn neither force field, a behavior termed ‘interference’. Studies have shown that a small difference in the endpoint posture of the limb reduces this interference. However, any difference in the limb’s endpoint location typically changes the hand position, joint angles and the hand orientation making it ambiguous as to which of these changes underlies the ability to learn dynamics that normally interfere. Here we examine the extent to which each of these three possible coordinate systems—Cartesian hand position, shoulder and elbow joint angles, or hand orientation—underlies the reduction in interference. Subjects performed goal-directed reaching movements in five different limb configurations designed so that different pairs of these configurations involved a change in only one coordinate system. By specifically assigning clockwise and counter-clockwise force fields to the configurations we could create three different conditions in which the direction of the force field could only be uniquely distinguished in one of the three coordinate systems. We examined the ability to learn the two fields based on each of the coordinate systems. The largest reduction of interference was observed when the field direction was linked to the hand orientation with smaller reductions in the other two conditions. This result demonstrates that the strongest reduction in interference occurred with changes in the hand orientation, suggesting that hand orientation may have a privileged role in reducing motor interference for changes in the endpoint posture of the limb.     

Modeling short-range stiffness of feline lower hindlimb muscles

The short-range stiffness (SRS) of skeletal muscles is a critical property for understanding muscle contributions to limb stability, since it represents a muscle's capacity to resist external perturbations before reflexes or voluntary actions can intervene. A number of studies have demonstrated that a simple model, consisting of a force-dependent active stiffness connected in series with a constant passive stiffness, is sufficient to characterize the SRS of individual muscles over the entire range of obtainable forces. The purpose of this study was to determine if such a model could be used to characterize the SRS-force relationship in a number of architecturally distinct muscles. Specifically, we hypothesized that the active and passive stiffness components for a specific muscle can be estimated from anatomical measurements, assuming uniform active and passive stiffness properties across all muscles. This hypothesis was evaluated in six feline lower hindlimb muscle types with different motor unit compositions and architectures. The SRS-force relationships for each muscle type were predicted based on anatomical measurements and compared to experimental data. The model predictions were accurate to within 30%, when uniform scaling properties were assumed across all muscles. Errors were the greatest for the extensor digitorum longus (EDL). When this muscle was removed from the analysis, prediction errors dropped to less than 8%. Subsequent analyses suggested that these errors might have resulted from differences in the tendon elastic modulus, as compared to the other muscles tested.     

Dispersal promotes compensatory dynamics and stability in forced metacommunities

Understanding the factors that govern the stability of populations and communities has gained increasing importance as habitat fragmentation and environmental perturbations continue to escalate due to human activities. Dispersal is commonly viewed as essential to the maintenance of diversity in spatially subdivided communities, but few experiments have explored how dispersal interacts with the spatiotemporal components of environmental perturbations to determine community-level stability. We examined these processes using an experimental planktonic system composed of three competing species of zooplankton. We subjected zooplankton metacommunities to varying levels of dispersal and pH perturbations that varied in their degree of spatial synchrony. We show that dispersal can reverse the destabilizing effects of environmental forcing when perturbations are spatially asynchronous. Asynchrony in pH perturbations generated spatially and temporally varying species refugia that promoted source-sink dynamics and allowed prolonged persistence of zooplankton species that were otherwise extirpated in synchronously varying metacommunities. This, in turn, increased local species diversity, promoted compensatory population dynamics, and enhanced local community-level stability. Our results indicate that patterns of spatial covariation in environmental variability are critical to predicting the effects of dispersal on the dynamics and persistence of communities.