Kinematic construction of the trajectory of sequential arm movements

A kinematic construction rule determining the trajectory of human sequential movements is formulated using minimum-jerk and minimum-angular-jerk trajectories. The kinematic construction rule states that the observed trajectory of sequential movements coincides with a weighted average of the minimum-jerk trajectory and the segmented minimum-angular-jerk trajectory. This rule covers not only point-to-point movements but also simple sequential movements. Five kinds of experiments that measure the trajectories in planar, multijoint sequential arm movements were conducted. The measured trajectories coincide with the predictions made on the basis of the kinematic construction rule presented here. Moreover, predictions of previous models such as the minimum-jerk, the equilibrium-trajectory, and the minimum-torque-change models are shown to be incompatible with our observations of sequential movements. Received: 31 October 1997 /Accepted in revised form: 18 November 1998     

End-point constraints in aiming movements: effects of approach angle and speed

 The present study focuses on two trajectory-formation models of point-to-point aiming movements, viz., the minimum-jerk and the minimum torque-change model. To date, few studies on minimum-jerk and minimum torque-change trajectories have incorporated self- or externally imposed end-point constraints, such as the direction and velocity with which a target area is approached. To investigate which model accounts best for the effects on movement trajectories of such – in many circumstances – realistic end-point constraints, we adjusted both the minimum-jerk and the minimum torque-change model so that they could generate trajectories of which the final part has a specific direction and speed. The adjusted models yield realistic trajectories with a high curvature near movement completion. Comparison of simulated and measured movement trajectories show that pointing movements that are constrained with respect to final movement direction and speed can be described in terms of minimization of joint-torque changes. Received: 7 July 1999 / Accepted in revised form: 8 January 2001     

Prediction of Three-Dimensional Arm Trajectories Based on ECoG Signals Recorded from Human Sensorimotor Cortex

Brain-machine interface techniques have been applied in a number of studies to control neuromotor prostheses and for neurorehabilitation in the hopes of providing a means to restore lost motor function. Electrocorticography (ECoG) has seen recent use in this regard because it offers a higher spatiotemporal resolution than non-invasive EEG and is less invasive than intracortical microelectrodes. Although several studies have already succeeded in the inference of computer cursor trajectories and finger flexions using human ECoG signals, precise three-dimensional (3D) trajectory reconstruction for a human limb from ECoG has not yet been achieved. In this study, we predicted 3D arm trajectories in time series from ECoG signals in humans using a novel preprocessing method and a sparse linear regression. Average Pearson’s correlation coefficients and normalized root-mean-square errors between predicted and actual trajectories were 0.44∼0.73 and 0.18∼0.42, respectively, confirming the feasibility of predicting 3D arm trajectories from ECoG. We foresee this method contributing to future advancements in neuroprosthesis and neurorehabilitation technology.     

Quantization of human motions and learning of accurate movements

This paper presents a mathematical model for the learning of accurate human arm movements. Its main features are that the movement is the superposition of smooth submovements, the intrinsic deviation of arm movements is considered, visual and kinesthetic feedback are integrated in the motion control, and the movement duration and accuracy are optimized with practice. This model is consistent with the jerky arm movements of infants, and may explain how the adult motion behavior emerges from the infant behavior. Comparison with measurements of adult movements shows that the kinematics of accurate movements are well predicted by the model. Received: 15 May 1997 / Accepted 5 December 1997     

Equilibrium point control of a monkey arm simulator by a fast learning tree structured artificial neural network

A planar 17 muscle model of the monkey's arm based on realistic biomechanical measurements was simulated on a Symbolics Lisp Machine. The simulator implements the equilibrium point hypothesis for the control of arm movements. Given initial and final desired positions, it generates a minimum-jerk desired trajectory of the hand and uses the backdriving algorithm to determine an appropriate sequence of motor commands to the muscles (Flash 1987; Mussa-Ivaldi et al. 1991; Dornay 1991b). These motor commands specify a temporal sequence of stable (attractive) equilibrium positions which lead to the desired hand movement. A strong disadvantage of the simulator is that it has no memory of previous computations. Determining the desired trajectory using the minimum-jerk model is instantaneous, but the laborious backdriving algorithm is slow, and can take up to one hour for some trajectories. The complexity of the required computations makes it a poor model for biological motor control. We propose a computationally simpler and more biologically plausible method for control which achieves the benefits of the backdriving algorithm. A fast learning, tree-structured network (Sanger 1991c) was trained to remember the knowledge obtained by the backdriving algorithm. The neural network learned the nonlinear mapping from a 2-dimensional cartesian planar hand position {x, y} to a 17-dimensional motor command space {u ₁, ..., u ₁₇}. Learning 20 training trajectories, each composed of 26 sample points {{x y{,{u ₁, ..., u ₁₇} took only 20 min on a Sun-4 Spare workstation. After the learning stage, new, untrained test trajectories as well as the original trajectories of the hand were given to the neural network as input. The network calculated the required motor commands for these movements. The resulting movements were close to the desired ones for both the training and test cases.     

Trajectory formation based on physiological characteristics of skeletal muscles

Human arm trajectories in natural unrestricted reaching movements were studied. They have particular properties such that a hand path is a rather simple straight or curved line, and a tangential velocity profile of hand is bell-shaped. Also these properties are invariant, independent of movement duration and hand-held load. In this study, trajectory formation is investigated on the basis of physiological characteristics of skeletal muscles, and a criterion prescribed by a derivative of isometric muscle torque is proposed. Subsequently, optimal trajectories are formulated under various conditions of movement to account for a planning strategy of human arm trajectories. In addition to such a theoretical approach, human arm trajectories are experimentally observed by a measuring system which provides a visual sensor and a target tracking device, enabling totally unrestricted movements. Then, optimal trajectories are quantitatively evaluated in comparison with experimental data in which essential properties of human arm trajectories are demonstrated. These results support the idea that human arm trajectories are planned in order to minimize the proposed criterion which is determined from physiological aspects. Finally, the physiological advantages of human arm trajectories are discussed with regard to the analysis of observed and optimal trajectories. Received: 2 December 1997 / Accepted in revised form: 20 March 1998     

Virtual trajectory and stiffness ellipse during multijoint arm movement predicted by neural inverse models

We predict the virtual trajectories and stiffness ellipses during multijoint arm movements by computer simulations. A two-link manipulator with four single-joint muscles and two double-joint muscles is used as a model of the human arm. Physical parameters of the model are derived from several experimental data. Among them, special emphasis is put on low values of the dynamic hand stiffness recently measured during single joint and multijoint movements. The feedback-error-learning scheme to acquire the inverse dynamics model and the inverse statics model is utilized for this prediction. The virtual trajectories are much more complex than the actual trajectories. This indicates that planning the virtual trajectory is as difficult as solving the inverse dynamics problem for medium and fast movements, and simply falsifies the advocated computational advantage of the virtual trajectory control hypothesis. Thus, we conclude that learning inverse models is essential even in the virtual trajectory control framework. Finally, we propose a new computational model to learn the complicated shape of the virtual trajectories by integrating the virtual trajectory control and the feedback-error-learning scheme.     

Invariant characteristics of horizontal-plane minimum-torque-change movements with one mechanical degree of freedom

 Uno et al. (1989) suggested that movements are organized such that the squared change of torque is minimized over time. Although influential, this theory has attracted much less attention from experimental researchers than the competing minimum-jerk model (Flash and Hogan 1985). One reason for this relative neglect has been the lack of general quantitative predictions, which results from the belief that minimum-torque-change trajectories have to be computed numerically for individual movements and arm-dynamical parameters. In the present paper, we show that for an important special case, that of planar horizontal movements with one mechanical degree of freedom (DOF), it is actually possible to find an analytic expression for the predicted minimum-torque-change trajectories. Based on this mathematical result, we derive a set of properties which are characteristic of these trajectories and compare them to experimental data which have not previously been related to the minimum-torque-change model. Certain discrepancies between these experimental data and minimum-torque-change model predictions are revealed. Received: 3 September 1996 / Accepted in revised form: 7 January 1997     

Analysis of Nidogen-1/Laminin γ1 Interaction by Cross-Linking,Mass Spectrometry,and Computational Modeling Reveals Multiple Binding Modes

We describe the detailed structural investigation of nidogen-1/laminin γ1 complexes using full-length nidogen-1 and a number of laminin γ1 variants. The interactions of nidogen-1 with laminin variants γ1 LEb2–4, γ1 LEb2–4 N836D, γ1 short arm, and γ1 short arm N836D were investigated by applying a combination of (photo-)chemical cross-linking, high-resolution mass spectrometry, and computational modeling. In addition, surface plasmon resonance and ELISA studies were used to determine kinetic constants of the nidogen-1/laminin γ1 interaction. Two complementary cross-linking strategies were pursued to analyze solution structures of laminin γ1 variants and nidogen-1. The majority of distance information was obtained with the homobifunctional amine-reactive cross-linker bis(sulfosuccinimidyl)glutarate. In a second approach, UV-induced cross-linking was performed after incorporation of the diazirine-containing unnatural amino acids photo-leucine and photo-methionine into laminin γ1 LEb2–4, laminin γ1 short arm, and nidogen-1. Our results indicate that Asn-836 within laminin γ1 LEb3 domain is not essential for complex formation. Cross-links between laminin γ1 short arm and nidogen-1 were found in all protein regions, evidencing several additional contact regions apart from the known interaction site. Computational modeling based on the cross-linking constraints indicates the existence of a conformational ensemble of both the individual proteins and the nidogen-1/laminin γ1 complex. This finding implies different modes of interaction resulting in several distinct protein-protein interfaces.     

Characterization of Information-Based Learning Benefits with Submovement Dynamics and Muscular Rhythmicity

For skill advancement, motor variability must be optimized based on target information during practice sessions. This study investigated structural changes in kinematic variability by characterizing submovement dynamics and muscular oscillations after practice with visuomotor tracking under different target conditions. Thirty-six participants were randomly assigned to one of three groups (simple, complex, and random). Each group practiced tracking visual targets with trajectories of varying complexity. The velocity trajectory of tracking was decomposed into 1) a primary contraction spectrally identical to the target rate and 2) an intermittent submovement profile. The learning benefits and submovement dynamics were conditional upon experimental manipulation of the target information. Only the simple and complex groups improved their skills with practice. The size of the submovements was most greatly reduced by practice with the least target information (simple > complex > random). Submovement complexity changed in parallel with learning benefits, with the most remarkable increase in practice under a moderate amount of target information (complex > simple > random). In the simple and complex protocols, skill improvements were associated with a significant decline in alpha (8–12 Hz) muscular oscillation but a potentiation of gamma (35–50 Hz) muscular oscillation. However, the random group showed no significant change in tracking skill or submovement dynamics, except that alpha muscular oscillation was reduced. In conclusion, submovement and gamma muscular oscillation are biological markers of learning benefits. Effective learning with an appropriate amount of target information reduces the size of submovements. In accordance with the challenge point hypothesis, changes in submovement complexity in response to target information had an inverted-U function, pertaining to an abundant trajectory-tuning strategy with target exactness.     

Use of Artificial Neural Networks and a Gamma-Concept-Based Approach To Model Growth of and Bacteriocin Production by Streptococcus macedonicus ACA-DC 198 under Simulated Conditions of Kasseri Cheese Production

Growth of and bacteriocin production by Streptococcus macedonicus ACA-DC 198 were assessed and modeled under conditions simulating Kasseri cheese production. Controlled fermentations were performed in milk supplemented with yeast extract at different combinations of temperature (25, 40, and 55°C), constant pH (pHs 5 and 6), and added NaCl (at concentrations of 0, 2, and 4%, wt/vol). The data obtained were used to construct two types of predictive models, namely, a modeling approach based on the gamma concept, as well as a model based on artificial neural networks (ANNs). The latter computational methods were used on 36 control fermentations to quantify the complex relationships between the conditions applied (temperature, pH, and NaCl) and population behavior and to calculate the associated biokinetic parameters, i.e., maximum specific growth and cell count decrease rates and specific bacteriocin production. The functions obtained were able to estimate these biokinetic parameters for four validation fermentation experiments and obtained good agreement between modeled and experimental values. Overall, these experiments show that both methods can be successfully used to unravel complex kinetic patterns within biological data of this kind and to predict population kinetics. Whereas ANNs yield a better correlation between experimental and predicted results, the gamma-concept-based model is more suitable for biological interpretation. Also, while the gamma-concept-based model has not been designed for modeling of other biokinetic parameters than the specific growth rate, ANNs are able to deal with any parameter of relevance, including specific bacteriocin production.     

Prediction of Muscle Activities from Electrocorticograms in Primary Motor Cortex of Primates

Electrocorticography (ECoG) has drawn attention as an effective recording approach for brain-machine interfaces (BMI). Previous studies have succeeded in classifying movement intention and predicting hand trajectories from ECoG. Despite such successes, however, there still remains considerable work for the realization of ECoG-based BMIs as neuroprosthetics. We developed a method to predict multiple muscle activities from ECoG measurements. We also verified that ECoG signals are effective for predicting muscle activities in time varying series when performing sequential movements. ECoG signals were band-pass filtered into separate sensorimotor rhythm bands, z-score normalized, and smoothed with a Gaussian filter. We used sparse linear regression to find the best fit between frequency bands of ECoG and electromyographic activity. The best average correlation coefficient and the normalized root-mean-square error were 0.92±0.06 and 0.06±0.10, respectively, in the flexor digitorum profundus finger muscle. The δ (1.5∼4Hz) and γ2 (50∼90Hz) bands contributed significantly more strongly than other frequency bands (P<0.001). These results demonstrate the feasibility of predicting muscle activity from ECoG signals in an online fashion.     

Dependence of Brain Intravoxel Incoherent Motion Perfusion Parameters on the Cardiac Cycle

Measurement of microvascular perfusion with Intravoxel Incoherent Motion (IVIM) MRI is gaining interest. Yet, the physiological influences on the IVIM perfusion parameters (“pseudo-diffusion” coefficient D*, perfusion fraction f, and flow related parameter fD*) remain insufficiently characterized. In this article, we hypothesize that D* and fD*, which depend on blood speed, should vary during the cardiac cycle. We extended the IVIM model to include time dependence of D* = D*(t), and demonstrate in the healthy human brain that both parameters D* and fD* are significantly larger during systole than diastole, while the diffusion coefficient D and f do not vary significantly. The results non-invasively demonstrate the pulsatility of the brain’s microvasculature.     

Seeing More by Showing Less: Orientation-Dependent Transparency Rendering for Fiber Tractography Visualization

Fiber tractography plays an important role in exploring the architectural organization of fiber trajectories, both in fundamental neuroscience and in clinical applications. With the advent of diffusion MRI (dMRI) approaches that can also model “crossing fibers”, the complexity of the fiber network as reconstructed with tractography has increased tremendously. Many pathways interdigitate and overlap, which hampers an unequivocal 3D visualization of the network and impedes an efficient study of its organization. We propose a novel fiber tractography visualization approach that interactively and selectively adapts the transparency rendering of fiber trajectories as a function of their orientation to enhance the visibility of the spatial context. More specifically, pathways that are oriented (locally or globally) along a user-specified opacity axis can be made more transparent or opaque. This substantially improves the 3D visualization of the fiber network and the exploration of tissue configurations that would otherwise be largely covered by other pathways. We present examples of fiber bundle extraction and neurosurgical planning cases where the added benefit of our new visualization scheme is demonstrated over conventional fiber visualization approaches.     

Submovement Composition of Head Movement

Limb movement is smooth and corrections of movement trajectory and amplitude are barely noticeable midflight. This suggests that skeletomuscular motor commands are smooth in transition, such that the rate of change of acceleration (or jerk) is minimized. Here we applied the methodology of minimum-jerk submovement decomposition to a member of the skeletomuscular family, the head movement. We examined the submovement composition of three types of horizontal head movements generated by nonhuman primates: head-alone tracking, head-gaze pursuit, and eye-head combined gaze shifts. The first two types of head movements tracked a moving target, whereas the last type oriented the head with rapid gaze shifts toward a target fixed in space. During head tracking, the head movement was composed of a series of episodes, each consisting of a distinct, bell-shaped velocity profile (submovement) that rarely overlapped with each other. There was no specific magnitude order in the peak velocities of these submovements. In contrast, during eye-head combined gaze shifts, the head movement was often comprised of overlapping submovements, in which the peak velocity of the primary submovement was always higher than that of the subsequent submovement, consistent with the two-component strategy observed in goal-directed limb movements. These results extend the previous submovement composition studies from limb to head movements, suggesting that submovement composition provides a biologically plausible approach to characterizing the head motor recruitment that can vary depending on task demand.     

Impact of regulatory light chain mutation K104E on the ATPase and motor properties of cardiac myosin

Mutations in the cardiac myosin regulatory light chain (RLC, MYL2 gene) are known to cause inherited cardiomyopathies with variable phenotypes. In this study, we investigated the impact of a mutation in the RLC (K104E) that is associated with hypertrophic cardiomyopathy (HCM). Previously in a mouse model of K104E, older animals were found to develop cardiac hypertrophy, fibrosis, and diastolic dysfunction, suggesting a slow development of HCM. However, variable penetrance of the mutation in human populations suggests that the impact of K104E may be subtle. Therefore, we generated human cardiac myosin subfragment-1 (M2β-S1) and exchanged on either the wild type (WT) or K104E human ventricular RLC in order to assess the impact of the mutation on the mechanochemical properties of cardiac myosin. The maximum actin-activated ATPase activity and actin sliding velocities in the in vitro motility assay were similar in M2β-S1 WT and K104E, as were the detachment kinetic parameters, including the rate of ATP-induced dissociation and the ADP release rate constant. We also examined the mechanical performance of α-cardiac myosin extracted from transgenic (Tg) mice expressing human wild type RLC (Tg WT) or mutant RLC (Tg K104E). We found that α-cardiac myosin from Tg K104E animals demonstrated enhanced actin sliding velocities in the motility assay compared with its Tg WT counterpart. Furthermore, the degree of incorporation of the mutant RLC into α-cardiac myosin in the transgenic animals was significantly reduced compared with wild type. Therefore, we conclude that the impact of the K104E mutation depends on either the length or the isoform of the myosin heavy chain backbone and that the mutation may disrupt RLC interactions with the myosin lever arm domain.     

Switching of Swimming Modes in Magnetospirillium gryphiswaldense

The microaerophilic magnetotactic bacterium Magnetospirillum gryphiswaldense swims along magnetic field lines using a single flagellum at each cell pole. It is believed that this magnetotactic behavior enables cells to seek optimal oxygen concentration with maximal efficiency. We analyze the trajectories of swimming M. gryphiswaldense cells in external magnetic fields larger than the earth’s field, and show that each cell can switch very rapidly (in <0.2 s) between a fast and a slow swimming mode. Close to a glass surface, a variety of trajectories were observed, from straight swimming that systematically deviates from field lines to various helices. A model in which fast (slow) swimming is solely due to the rotation of the trailing (leading) flagellum can account for these observations. We determined the magnetic moment of this bacterium using a to our knowledge new method, and obtained a value of (2.0 ± 0.6) × 10^?16 A · m². This value is found to be consistent with parameters emerging from quantitative fitting of trajectories to our model.     

A Dynamic Energy Budget (DEB) Model for the Keystone Predator Pisaster ochraceus

We present a Dynamic Energy Budget (DEB) model for the quintessential keystone predator, the rocky-intertidal sea star Pisaster ochraceus. Based on first principles, DEB theory is used to illuminate underlying physiological processes (maintenance, growth, development, and reproduction), thus providing a framework to predict individual-level responses to environmental change. We parameterized the model for P. ochraceus using both data from the literature and experiments conducted specifically for the DEB framework. We devoted special attention to the model’s capacity to (1) describe growth trajectories at different life-stages, including pelagic larval and post-metamorphic phases, (2) simulate shrinkage when prey availability is insufficient to meet maintenance requirements, and (3) deal with the combined effects of changing body temperature and food supply. We further validated the model using an independent growth data set. Using standard statistics to compare model outputs with real data (e.g. Mean Absolute Percent Error, MAPE) we demonstrated that the model is capable of tracking P. ochraceus’ growth in length at different life-stages (larvae: MAPE = 12.27%; post-metamorphic, MAPE = 9.22%), as well as quantifying reproductive output index. However, the model’s skill dropped when trying to predict changes in body mass (MAPE = 24.59%), potentially because of the challenge of precisely anticipating spawning events. Interestingly, the model revealed that P. ochraceus reserves contribute little to total biomass, suggesting that animals draw energy from structure when food is limited. The latter appears to drive indeterminate growth dynamics in P. ochraceus. Individual-based mechanistic models, which can illuminate underlying physiological responses, offer a viable framework for forecasting population dynamics in the keystone predator Pisaster ochraceus. The DEB model herein represents a critical step in that direction, especially in a period of increased anthropogenic pressure on natural systems and an observed recent decline in populations of this keystone species.     

Evidence against a Looped Structure of the Inactive Human X-Chromosome Territory

Multicolor fluorescencein situhybridization with a whole chromosome composite probe for the X-chromosome and microdissection probes for the Xp and Xq arms, as well as for the Xp terminal, Xq terminal, and X centromer specific subregional probes, was applied to three-dimensional (3D) preserved human female amniotic fluid cell nuclei. Confocal laser scanning microscopy and three-dimensional image analysis demonstrated distinctly separated Xp arm and Xq arm domains. 3D distance measurements revealed a high variability of intrachromosomal distances between Xpter, Xcen, and Xqter specific probes within both X territories. A 3D distance measurement error of ±70 nm was found in control experiments using quartz glass microspheres labeled with different fluorochromes. Our data argue against the hypothesis of Walkeret al.(1991,Proc. Natl. Acad. Sci. USA88, 6191–6195) that a looped structure of the inactive X territory is formed by tight telomere–telomere associations.