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.     

Assessing Movement Factors in Upper Limb Kinematics Decoding from EEG Signals

The past decades have seen the rapid development of upper limb kinematics decoding techniques by performing intracortical recordings of brain signals. However, the use of non-invasive approaches to perform similar decoding procedures is still in its early stages. Recent studies show that there is a correlation between electroencephalographic (EEG) signals and hand-reaching kinematic parameters. From these studies, it could be concluded that the accuracy of upper limb kinematics decoding depends, at least partially, on the characteristics of the performed movement. In this paper, we have studied upper limb movements with different speeds and trajectories in a controlled environment to analyze the influence of movement variability in the decoding performance. To that end, low frequency components of the EEG signals have been decoded with linear models to obtain the position of the volunteer’s hand during performed trajectories grasping the end effector of a planar manipulandum. The results confirm that it is possible to obtain kinematic information from low frequency EEG signals and show that decoding performance is significantly influenced by movement variability and tracking accuracy as continuous and slower movements improve the accuracy of the decoder. This is a key factor that should be taken into account in future experimental designs.     

Toward electrocorticographic control of a dexterous upper limb prosthesis: building brain-machine interfaces

One of the most exciting and compelling areas of research and development is building brain machine interfaces (BMIs) for controlling prosthetic limbs. Prosthetic limb technology is advancing rapidly, and the modular prosthetic limb (MPL) of the Johns Hopkins University/ Applied Physics Laboratory (JHU/APL) permits actuation with 17 degrees of freedom in 26 articulating joints. There are many signals from the brain that can be leveraged, including the spiking rates of neurons in the cortex, electrocorticographic (ECoG) signals from the surface of the cortex, and electroencephalographic (EEG) signals from the scalp. Unlike microelectrodes that record spikes, ECoG does not penetrate the cortex and has a higher spatial specificity, signal-to-noise ratio, and bandwidth than EEG signals. We have implemented an ECoG-based system for controlling the MPL in the Johns Hopkins Hospital Epilepsy Monitoring Unit, where patients are implanted with ECoG electrode grids for clinical seizure mapping and asked to perform various recorded finger or grasp movements. We have shown that low-frequency local motor potentials (LMPs) and ECoG power in the high gamma frequency (70,150 Hz) range correlate well with grasping parameters, and they stand out as good candidate features for closed-loop control of the MPL.     

A neural network model for limb trajectory formation

This paper deals with the problem of representing and generating unconstrained aiming movements of a limb by means of a neural network architecture. The network produced time trajectories of a limb from a starting posture toward targets specified by sensory stimuli. Thus the network performed a sensory-motor transformation. The experimenters trained the network using a bell-shaped velocity profile on the trajectories. This type of profile is characteristic of most movements performed by biological systems. We investigated the generalization capabilities of the network as well as its internal organization. Experiments performed during learning and on the trained network showed that: (i) the task could be learned by a three-layer sequential network; (ii) the network successfully generalized in trajectory space and adjusted the velocity profiles properly; (iii) the same task could not be learned by a linear network; (iv) after learning, the internal connections became organized into inhibitory and excitatory zones and encoded the main features of the training set; (v) the model was robust to noise on the input signals; (vi) the network exhibited attractor-dynamics properties; (vii) the network was able to solve the motorequivalence problem. A key feature of this work is the fact that the neural network was coupled to a mechanical model of a limb in which muscles are represented as springs. With this representation the model solved the problem of motor redundancy.     

Unscented Kalman Filter for Brain-Machine Interfaces

Brain machine interfaces (BMIs) are devices that convert neural signals into commands to directly control artificial actuators, such as limb prostheses. Previous real-time methods applied to decoding behavioral commands from the activity of populations of neurons have generally relied upon linear models of neural tuning and were limited in the way they used the abundant statistical information contained in the movement profiles of motor tasks. Here, we propose an n-th order unscented Kalman filter which implements two key features: (1) use of a non-linear (quadratic) model of neural tuning which describes neural activity significantly better than commonly-used linear tuning models, and (2) augmentation of the movement state variables with a history of n-1 recent states, which improves prediction of the desired command even before incorporating neural activity information and allows the tuning model to capture relationships between neural activity and movement at multiple time offsets simultaneously. This new filter was tested in BMI experiments in which rhesus monkeys used their cortical activity, recorded through chronically implanted multielectrode arrays, to directly control computer cursors. The 10th order unscented Kalman filter outperformed the standard Kalman filter and the Wiener filter in both off-line reconstruction of movement trajectories and real-time, closed-loop BMI operation.     

Envelope reconstruction of speech and music highlights stronger tracking of speech at low frequencies

The human brain tracks amplitude fluctuations of both speech and music, which reflects acoustic processing in addition to the encoding of higher-order features and one’s cognitive state. Comparing neural tracking of speech and music envelopes can elucidate stimulus-general mechanisms, but direct comparisons are confounded by differences in their envelope spectra. Here, we use a novel method of frequency-constrained reconstruction of stimulus envelopes using EEG recorded during passive listening. We expected to see music reconstruction match speech in a narrow range of frequencies, but instead we found that speech was reconstructed better than music for all frequencies we examined. Additionally, models trained on all stimulus types performed as well or better than the stimulus-specific models at higher modulation frequencies, suggesting a common neural mechanism for tracking speech and music. However, speech envelope tracking at low frequencies, below 1 Hz, was associated with increased weighting over parietal channels, which was not present for the other stimuli. Our results highlight the importance of low-frequency speech tracking and suggest an origin from speech-specific processing in the brain.     

Linear correlation between fractal dimension of EEG signal and handgrip force

Fractal dimension (FD) has been proved useful in quantifying the complexity of dynamical signals in biology and medicine. In this study, we measured FDs of human electroencephalographic (EEG) signals at different levels of handgrip forces. EEG signals were recorded from five major motor-related cortical areas in eight normal healthy subjects. FDs were calculated using three different methods. The three physiological periods of handgrip (command preparation, movement and holding periods) were analyzed and compared. The results showed that FDs of the EEG signals during the movement and holding periods increased linearly with handgrip force, whereas FD during the preparation period had no correlation with force. The results also demonstrated that one method (Katz’s) gave greater changes in FD, and thus, had more power in capturing the dynamic changes in the signal. The linear increase of FD, together with results from other EEG and neuroimaging studies, suggest that under normal conditions the brain recruits motor neurons at a linear progress when increasing the force.     

Quantitative underwater 3D motion analysis using submerged video cameras: accuracy analysis and trajectory reconstruction

In this study we aim at investigating the applicability of underwater 3D motion capture based on submerged video cameras in terms of 3D accuracy analysis and trajectory reconstruction. Static points with classical direct linear transform (DLT) solution, a moving wand with bundle adjustment and a moving 2D plate with Zhang's method were considered for camera calibration. As an example of the final application, we reconstructed the hand motion trajectories in different swimming styles and qualitatively compared this with Maglischo's model. Four highly trained male swimmers performed butterfly, breaststroke and freestyle tasks. The middle fingertip trajectories of both hands in the underwater phase were considered. The accuracy (mean absolute error) of the two calibration approaches (wand: 0.96 mm – 2D plate: 0.73 mm) was comparable to out of water results and highly superior to the classical DLT results (9.74 mm). Among all the swimmers, the hands' trajectories of the expert swimmer in the style were almost symmetric and in good agreement with Maglischo's model. The kinematic results highlight symmetry or asymmetry between the two hand sides, intra- and inter-subject variability in terms of the motion patterns and agreement or disagreement with the model. The two outcomes, calibration results and trajectory reconstruction, both move towards the quantitative 3D underwater motion analysis.     

Surrogate data analysis of sleep electroencephalograms reveals evidence for nonlinearity

 We tested the hypothesis of whether sleep electroencephalographic (EEG) signals of different time windows (164 s, 82 s, 41 s and 20.5 s) are in accordance with linear stochastic models. For this purpose we analyzed the all-night sleep electroencephalogram of a healthy subject and corresponding Gaussian-rescaled phase randomized surrogates with a battery of five nonlinear measures. The following nonlinear measures were implemented: largest Lyapunov exponent L1, correlation dimension D2, and the Green-Savit measures δ2, δ4 and δ6. The hypothesis of linear stochastic data was rejected with high statistical significance. L1 and D2 yielded the most pronounced effects, while the Green-Savit measures were only partially successful in differentiating EEG epochs from the phase randomized surrogates. For L1 and D2 the efficiency of distinguishing EEG signals from linear stochastic data decreased with shortening of the time window. Altogether, our results indicate that EEG signals exhibit nonlinear elements and cannot completely be described by linear stochastic models. Received: 21 December 1995/Accepted in revised form: 19 March 1996     

Correlation dimension based lossless compression of EEG signals

Transmission of long duration EEG signals without loss of information is essential for telemedicine based applications. In this work, a lossless compression scheme for EEG signals based on neural network predictors using the concept of correlation dimension (CD) is proposed. EEG signals which are considered as irregular time series of chaotic processes can be characterized by the non-linear dynamic parameter CD which is a measure of the correlation among the EEG samples. The EEG samples are first divided into segments of 1 s duration and for each segment, the value of CD is calculated. Blocks of EEG samples are then constructed such that each block contains segments with closer CD values. By arranging the EEG samples in this fashion, the accuracy of the predictor is improved as it makes use of highly correlated samples. As a result, the magnitude of the prediction error decreases leading to less number of bits for transmission. Experiments are conducted using EEG signals recorded under different physiological conditions. Different neural network predictors as well as classical predictors are considered. Experimental results show that the proposed CD based preprocessing scheme improves the compression performance of the predictors significantly.     

Tree-ring width based streamflow reconstruction for the Kaidu River originating from the central Tianshan Mountains since A.D. 1700

In this study, a 310-year pSeptember–August record of streamflow (where p denotes a month from the previous year) for the Kaidu River was reconstructed based on tree-ring-width from 137 Schrenk spruces (Picea schrenkiana). Spatial correlation showed that this streamflow reconstruction contains local hydroclimatic signals that approximately overlap the Kaidu River watershed. A comparison between the streamflow reconstruction for the Kaidu River and five tree-ring-based hydrological reconstructions for the surrounding areas revealed similar variations in the low-frequency domain. The results of comparison analyses between this reconstruction and other hydrological reconstructions indicated that the hydrological characteristics of the Kaidu River in the 1910s (the driest decade for the Kaidu River in the last 310 years), and the increasing trend of streamflow that began in the 1980s, might have occurred in other areas of the Tianshan Mountains and covered an even larger area. Furthermore, the highest and lowest values of this reconstructed streamflow series capture five flood or snowfall events (1803, 1804, 1836, 1923, and 1959) and six drought events (1894, 1916, 1917, 1918, 1931, and 1944) that were noted in historical documents. The 10.8- and 3.5–5.4-year cycles of this reconstruction coincided with the observed data and other tree-ring based hydrometeorological reconstructions, and revealed the possible influences of solar activity and the atmosphere–ocean system.     

Sleep EEG as a nonlinear dynamic process: a comparison of global correlation dimension of human EEG and measures of linear interdependence between channels

The goal of this work was to study (1) whether the estimation of correlation dimension (D2) using spatial embedding distinguishes between sleep stages and (2) whether information gained from the application of global D2 is redundant to measures of linear interdependence between channels. Twenty one-channel EEG segments of 12 healthy male subjects recorded during waking and sleep stages REM, I, II, and III-IV (according to the Rechtshaffen and Kales criteria) were analyzed with global (multichannel) D2, mean square correlation coefficients (MS) and proportion of variance accounted for by the first principal component (PC1). D2 was found to decrease progressively from stage I to stage III-IV with D2 values of waking and REM being close to those of stages I and II. MS and PC1 did not distinguish among sleep stages but yielded significant differences between waking and sleep. The results suggest that global D2 extracts information from human EEG. That sort of evidence cannot be obtained with measures of linear interdependence between channels.     

Hip and knee joint kinematics during a diagonal jump landing in anterior cruciate ligament reconstructed females

Anterior cruciate ligament (ACL) injury is a common injury encountered by sport medicine clinicians. Surgical reconstruction is the recommended treatment of choice for those athletes wishing to return to full-contact sports participation and for sports requiring multi-directional movement patterns. The aim of ACL reconstruction is to restore knee joint mechanical stability such that the athlete can return to sporting participation. However, knowledge regarding the extent to which lower limb kinematic profiles are restored following ACL reconstruction is limited. In the present study the hip and knee joint kinematic profiles of 13 ACL reconstructed (ACL-R) and 16 non-injured control subjects were investigated during the performance of a diagonal jump landing task. The ACL-R group exhibited significantly less peak knee joint flexion (P=0.01). Significant between group differences were noted for time averaged hip joint sagittal plane (P<0.05) and transverse plane (P<0.05) kinematic profiles, as well as knee joint frontal plane (P<0.05) and sagittal plane (P<0.05) kinematic profiles. These results suggest that aberrant hip and knee joint kinematic profiles are present following ACL reconstruction, which could influence future injury risk.     

Decoding hand movement velocity from electroencephalogram signals during a drawing task

Background  

Decoding neural activities associated with limb movements is the key of motor prosthesis control. So far, most of these studies have been based on invasive approaches. Nevertheless, a few researchers have decoded kinematic parameters of single hand in non-invasive ways such as magnetoencephalogram (MEG) and electroencephalogram (EEG). Regarding these EEG studies, center-out reaching tasks have been employed. Yet whether hand velocity can be decoded using EEG recorded during a self-routed drawing task is unclear.     

The Extratropical Northern Hemisphere Temperature Reconstruction during the Last Millennium Based on a Novel Method

Large-scale climate history of the past millennium reconstructed solely from tree-ring data is prone to underestimate the amplitude of low-frequency variability. In this paper, we aimed at solving this problem by utilizing a novel method termed “MDVM”, which was a combination of the ensemble empirical mode decomposition (EEMD) and variance matching techniques. We compiled a set of 211 tree-ring records from the extratropical Northern Hemisphere (30–90°N) in an effort to develop a new reconstruction of the annual mean temperature by the MDVM method. Among these dataset, a number of 126 records were screened out to reconstruct temperature variability longer than decadal scale for the period 850–2000 AD. The MDVM reconstruction depicted significant low-frequency variability in the past millennium with evident Medieval Warm Period (MWP) over the interval 950–1150 AD and pronounced Little Ice Age (LIA) cumulating in 1450–1850 AD. In the context of 1150-year reconstruction, the accelerating warming in 20^th century was likely unprecedented, and the coldest decades appeared in the 1640s, 1600s and 1580s, whereas the warmest decades occurred in the 1990s, 1940s and 1930s. Additionally, the MDVM reconstruction covaried broadly with changes in natural radiative forcing, and especially showed distinct footprints of multiple volcanic eruptions in the last millennium. Comparisons of our results with previous reconstructions and model simulations showed the efficiency of the MDVM method on capturing low-frequency variability, particularly much colder signals of the LIA relative to the reference period. Our results demonstrated that the MDVM method has advantages in studying large-scale and low-frequency climate signals using pure tree-ring data.     

高维混沌降维的投影追踪主分量分析法

一些生理信号,例如脑电是源自于高维混沌系统,因此低维混沌理论和方法不适用于分析这类高维混沌。采用投影追踪主分量分析法（Princiopal Component Analysis based on Projection Pursuit,PP PCA）对高维Lorenz模型系统进行了降维的研究。在用上述方法成功地对线性和非线性噪声－周期模型分别进行了PP PCA分析的基础上,对Lorenz高维混沌系统进行了PPPCA降维的研究。结果表明,正确选用非线性的投影追踪主分量分析法,可以通过简化原系统达到降维的目的,并能保留研究所关心的原系统的主要动态特性。同时也阐明了方法的稳定性和将该方法应用于高维脑电降维的可行性。     

Speed-dependent reference joint trajectory generation for robotic gait support

For the control of actuated orthoses, or gait rehabilitation robotics, kinematic reference trajectories are often required. These trajectories, consisting of joint angles, angular velocities and accelerations, are highly dependent on walking-speed. We present and evaluate a novel method to reconstruct body-height and speed-dependent joint trajectories. First, we collected gait kinematics in fifteen healthy (middle) aged subjects (47–68), at a wide range of walking-speeds (0.5–5 kph). For each joint trajectory multiple key-events were selected (among which its extremes). Second, we derived regression-models that predict the timing, angle, angular velocity and acceleration for each key-event, based on walking-speed and the subject?s body-height. Finally, quintic splines were fitted between the predicted key-events to reconstruct a full gait cycle. Regression-models were obtained for hip ab-/adduction, hip flexion/extension, knee flexion/extension and ankle plantar-/dorsiflexion. Results showed that the majority of the key-events were dependent on walking-speed, both in terms of timing and amplitude, whereas the body-height had less effect. The reconstructed trajectories matched the measured trajectories very well, in terms of angle, angular velocity and acceleration. For the angles the RMSE between the reconstructed and measured trajectories was 2.6°. The mean correlation coefficient between the reconstructed and measured angular trajectories was 0.91. The method and the data presented in this paper can be used to generate speed-dependent gait patterns. These patterns can be used for the control of several robotic gait applications. Alternatively they can assist the assessment of pathological gait, where they can serve as a reference for “normal” gait.     

Analysis of kinematic invariances of multijoint reaching movement

 There is a no unique relationship between the trajectory of the hand, represented in cartesian or extrinsic space, and its trajectory in joint angle or intrinsic space in the general condition of joint redundancy. The goal of this work is to analyze the relation between planning the trajectory of a multijoint movement in these two coordinate systems. We show that the cartesian trajectory can be planned based on the task parameters (target coordinates, etc.) prior to and independently of angular trajectories. Angular time profiles are calculated from the cartesian trajectory to serve as a basis for muscle control commands. A unified differential equation that allows planning trajectories in cartesian and angular spaces simultaneously is proposed. Due to joint redundancy, each cartesian trajectory corresponds to a family of angular trajectories which can account for the substantial variability of the latter. A set of strategies for multijoint motor control following from this model is considered; one of them coincides with the frog wiping reflex model and resolves the kinematic inverse problem without inversion. The model trajectories exhibit certain properties observed in human multijoint reaching movements such as movement equifinality, straight end-point paths, bell-shaped tangential velocity profiles, speed-sensitive and speed-insensitive movement strategies, peculiarities of the response to double-step targets, and variations of angular trajectory without variations of the limb end-point trajectory in cartesian space. In humans, those properties are almost independent of limb configuration, target location, movement duration, and load. In the model, these properties are invariant to an affine transform of cartesian space. This implies that these properties are not a special goal of the motor control system but emerge from movement kinematics that reflect limb geometry, dynamics, and elementary principles of motor control used in planning. All the results are given analytically and, in order to compare the model with experimental results, by computer simulations. Received: 6 April 1994/Accepted in revised form: 25 April 1995     

Quantitative comparison of CFD predicted and MRI measured velocity fields in a carotid bifurcation phantom

Steady flow of a blood mimicking fluid in a physiologically realistic model of the human carotid bifurcation was studied using both magnetic resonance imaging (MRI) and computational fluid dynamics (CFD) modelling techniques. Quantitative comparisons of the 3D velocity field in the bifurcation phantom were made between phase contrast MRI measurements and CFD predictions. The geometry for the CFD model was reconstructed from T(1) weighted MR imaging of the test phantom. It was found that the predicted velocity fields were in fair agreement with MR measured velocities. In both the internal and external carotid arteries, the agreement between CFD predictions and MRI measurements was better along the inner-outer wall axis with a correlation factor C>0.897 (average 0.939) where the velocity profiles were skewed, than along the anterior-posterior axis (average correlation factor 0.876) where the velocity profiles were in M-shape.     

A 2917-year tree-ring-based reconstruction of precipitation for the Buerhanbuda Mts., Southeastern Qaidam Basin,China

In this study, we developed the tree-ring width chronology for the period of 1404 BCE to 2015 CE using Qilian juniper (Sabina przewalskii Kom.) trees collected from the Buerhanbuda Mts. in the southeastern Qaidam Basin (QB) near Nuomuhong Village, Qinghai Province. This is the first and longest chronology to date in this region. Based on the relationships between the tree-ring width chronology and climate data, the annual precipitation from previous July to current June (July-June) was reconstructed for the past 2917 years from 902 BCE to 2015 CE. This reconstruction accounted for 47.9% of the total variance in the actual July-June precipitation in the calibration period (1957–2015). The full reconstruction captured distinct wet and dry variability, and contained evidence of some low-frequency climate signals. We identified 13 wet and 12 dry periods, of which 1443–1503 CE and 1789–1836 CE were the two longest dry periods. General agreements in the low-frequency variations between the July-June precipitation and other moisture-sensitive records for the northeastern Tibetan Plateau (TP) suggested that the reconstruction in this study represented a regional signal. Spatial correlations with gridded precipitation data also indicated that the reconstructed July-June precipitation could adequately represent climate fluctuations over a large area of the northeastern TP. The new tree-ring width chronology and precipitation reconstruction are important for understanding natural climate change in the southeastern QB.