Somatotopy of the sensory thalamus: inputs from directional deep brain stimulation in pain patients.

OBJECTIVE: The sensory ventroposterior (VP) thalamic nuclei display a mediolateral somatotopic organization (respectively head, arm, and leg). We studied this somatotopy using directional VP deep brain stimulation (DBS) in patients treated for chronic neuropathic pain. METHODS: Six patients with central (four) or peripheral (two) neuropathic pain were treated by VP DBS using directional leads in a prospective study (clinicaltrials.gov NCT03399942). Lead-DBS toolbox was used for leads localization, visualization, and modeling of the volume of tissue activated (VTA). Stimulation was delivered in each direction, 1 month after surgery and correlated to the location of stimulation-induced paresthesias. The somatotopy was modeled by correlating the respective locations of paresthesias and VTAs. We recorded 48 distinct paresthesia maps corresponding to 48 VTAs (including 36 related to directional stimulation). RESULTS: We observed that, in each patient, respective body representations of the trunk, upper limb, lower limb, and head were closely located around the lead. These representations differed across patients, did not follow a common organization and were not concordant with the previously described somatotopic organization of the sensory thalamus. INTERPRETATION: Thalamic reorganization has been reported in chronic pain patients compared to non-pain patients operated for movement disorders in previous studies using intraoperative recordings and micro-stimulation. Using a different methodology, namely 3D representation of the VTA by the directional postoperative stimulation through a stationary electrode, our study brings additional arguments in favor of a reorganization of the VP thalamic somatotopy in patients suffering from chronic neuropathic pain of central or peripheral origin.

Improvement of diffusion tensor imaging-based tractography by free-water correction in nonedematous gliomas: assessment with brain mapping.

OBJECTIVE: The free-water correction algorithm (Freewater Estimator Using Interpolated Initialization [FERNET]) can be applied to standard diffusion tensor imaging (DTI) tractography to improve visualization of subcortical bundles in the peritumoral area of highly edematous brain tumors. Interest in its use for presurgical planning in purely infiltrative gliomas without peritumoral edema has never been evaluated. Using subcortical maps obtained with direct electrostimulation (DES) in awake surgery as a reference standard, the authors sought to 1) assess the accuracy of preoperative DTI-based tractography with FERNET in a series of nonedematous glioma patients, and 2) determine its potential usefulness in presurgical planning. METHODS: Based on DES-induced functional disturbances and tumor topography, the authors retrospectively reconstructed the putatively stimulated bundles and the peritumoral tracts of interest (various associative and projection pathways) of 12 patients. The tractography data obtained with and without FERNET were compared. RESULTS: The authors identified 21 putative tracts from 24 stimulation sites and reconstituted 49 tracts of interest. The number of streamlines of the putative tracts crossing the DES area was 26.8% higher (96.04 vs 75.75, p = 0.016) and their volume 20.4% higher (13.99 cm3 vs 11.62 cm3, p < 0.0001) with FERNET than with standard DTI. Additionally, the volume of the tracts of interest was 22.1% higher (9.69 cm3 vs 7.93 cm3, p < 0.0001). CONCLUSIONS: Free-water correction significantly increased the anatomical plausibility of the stimulated fascicles and the volume of tracts of interest in the peritumoral area of purely infiltrative nonedematous gliomas. Because of the functional importance of the peritumoral zone, applying FERNET to DTI could have potential implications on surgical planning and the safety of glioma resection.

Classification of BCI-EEG Based on the Augmented Covariance Matrix.

OBJECTIVE: Electroencephalography signals are recorded as multidimensional datasets. We propose a new framework based on the augmented covariance that stems from an autoregressive model to improve motor imagery classification. METHODS: From the autoregressive model can be derived the Yule-Walker equations, which show the emergence of a symmetric positive definite matrix: the augmented covariance matrix. The state-of the art for classifying covariance matrices is based on Riemannian Geometry. A fairly natural idea is therefore to apply this Riemannian Geometry based approach to these augmented covariance matrices. The methodology for creating the augmented covariance matrix shows a natural connection with the delay embedding theorem proposed by Takens for dynamical systems. Such an embedding method is based on the knowledge of two parameters: the delay and the embedding dimension, respectively related to the lag and the order of the autoregressive model. This approach provides new methods to compute the hyper-parameters in addition to standard grid search. RESULTS: The augmented covariance matrix performed ACMs better than any state-of-the-art methods. We will test our approach on several datasets and several subjects using the MOABB framework, using both within-session and cross-session evaluation. CONCLUSION: The improvement in results is due to the fact that the augmented covariance matrix incorporates not only spatial but also temporal information. As such, it contains information on the nonlinear components of the signal through the embedding procedure, which allows the leveraging of dynamical systems algorithms. SIGNIFICANCE: These results extend the concepts and the results of the Riemannian distance based classification algorithm.

Graph alignment exploiting the spatial organization improves the similarity of brain networks.

Every brain is unique, having its structural and functional organization shaped by both genetic and environmental factors over the course of its development. Brain image studies tend to produce results by averaging across a group of subjects, under the common assumption that it is possible to subdivide the cortex into homogeneous areas while maintaining a correspondence across subjects. We investigate this assumption: can the structural properties of a specific region of an atlas be assumed to be the same across subjects? This question is addressed by looking at the network representation of the brain, with nodes corresponding to brain regions and edges to their structural relationships. Using an unsupervised graph matching strategy, we align the structural connectomes of a set of healthy subjects, considering parcellations of different granularity, to understand the connectivity misalignment between regions. First, we compare the obtained permutations with four different algorithm initializations: Spatial Adjacency, Identity, Barycenter, and Random. Our results suggest that applying an alignment strategy improves the similarity across subjects when the number of parcels is above 100 and when using Spatial Adjacency and Identity initialization (the most plausible priors). Second, we characterize the obtained permutations, revealing that the majority of permutations happens between neighbors parcels. Lastly, we study the spatial distribution of the permutations. By visualizing the results on the cortex, we observe no clear spatial patterns on the permutations and all the regions across the context are mostly permuted with first and second order neighbors.

Pseudo-online framework for BCI evaluation: a MOABB perspective using various MI and SSVEP datasets.

Objective. BCI (Brain-Computer Interfaces) operate in three modes:online,offline, andpseudo-online. Inonlinemode, real-time EEG data is constantly analyzed. Inofflinemode, the signal is acquired and processed afterwards. Thepseudo-onlinemode processes collected data as if they were received in real-time. The main difference is that theofflinemode often analyzes the whole data, while theonlineandpseudo-onlinemodes only analyze data in short time windows.Offlineprocessing tends to be more accurate, whileonlineanalysis is better for therapeutic applications.Pseudo-onlineimplementation approximatesonlineprocessing without real-time constraints. Many BCI studies beingofflineintroduce biases compared to real-life scenarios, impacting classification algorithm performance.Approach. The objective of this research paper is therefore to extend the current MOABB framework, operating inofflinemode, so as to allow a comparison of different algorithms in apseudo-onlinesetting with the use of a technology based on overlapping sliding windows. To do this will require the introduction of a idle state event in the dataset that takes into account all different possibilities that are not task thinking. To validate the performance of the algorithms we will use the normalized Matthews correlation coefficient and the information transfer rate.Main results. We analyzed the state-of-the-art algorithms of the last 15 years over several motor imagery and steady state visually evoked potential multi-subjects datasets, showing the differences between the two approaches from a statistical point of view.Significance. The ability to analyze the performance of different algorithms inofflineandpseudo-onlinemodes will allow the BCI community to obtain more accurate and comprehensive reports regarding the performance of classification algorithms.

Free-water correction DTI-based tractography in brain tumor surgery: assessment with functional and electrophysiological mapping of the white matter.

Peritumoral edema prevents fiber tracking from diffusion tensor imaging (DTI). A free-water correction may overcome this drawback, as illustrated in the case of a patient undergoing awake surgery for brain metastasis. The anatomical plausibility and accuracy of tractography with and without free-water correction were assessed with functional mapping and axono-cortical evoked-potentials (ACEPs) as reference methods. The results suggest a potential synergy between corrected DTI-based tractography and ACEPs to reliably identify and preserve white matter tracts during brain tumor surgery.

Identifying subcortical connectivity during brain tumor surgery: a multimodal study.

Bipolar direct electrical stimulation (DES) of an awake patient is the reference technique for identifying brain structures to achieve maximal safe tumor resection. Unfortunately, DES cannot be performed in all cases. Alternative surgical tools are, therefore, needed to aid identification of subcortical connectivity during brain tumor removal. In this pilot study, we sought to (i) evaluate the combined use of evoked potential (EP) and tractography for identification of white matter (WM) tracts under the functional control of DES, and (ii) provide clues to the electrophysiological effects of bipolar stimulation on neural pathways. We included 12 patients (mean age of 38.4 years) who had had a dMRI-based tractography and a functional brain mapping under awake craniotomy for brain tumor removal. Electrophysiological recordings of subcortical evoked potentials (SCEPs) were acquired during bipolar low frequency (2 Hz) stimulation of the WM functional sites identified during brain mapping. SCEPs were successfully triggered in 11 out of 12 patients. The median length of the stimulated fibers was 43.24 ± 19.55 mm, belonging to tracts of median lengths of 89.84 ± 24.65 mm. The electrophysiological (delay, amplitude, and speed of propagation) and structural (number and lengths of streamlines, and mean fractional anisotropy) measures were correlated. In our experimental conditions, SCEPs were essentially limited to a subpart of the bundles, suggesting a selectivity of action of the DES on the brain networks. Correlations between functional, structural, and electrophysiological measures portend the combined use of EPs and tractography as a potential intraoperative tool to achieve maximum safe resection in brain tumor surgery.

Long Multi-Stage Training for a Motor-Impaired User in a BCI Competition.

In a Mental Imagery Brain-Computer Interface the user has to perform a specific mental task that generates electroencephalography (EEG) components, which can be translated in commands to control a BCI system. The development of a high-performance MI-BCI requires a long training, lasting several weeks or months, in order to improve the ability of the user to manage his/her mental tasks. This works aims to present the design of a MI-BCI combining mental imaginary and cognitive tasks for a severely motor impaired user, involved in the BCI race of the Cybathlon event, a competition of people with severe motor disability. In the BCI-race, the user becomes a pilot in a virtual race game against up to three other pilots, in which each pilot has to control his/her virtual car by his/her mental tasks. We present all the procedures followed to realize an effective MI-BCI, from the user's first contact with a BCI technology to actually controlling a video-game through her EEG. We defined a multi-stage user-centered training protocol in order to successfully control a BCI, even in a stressful situation, such as that of a competition. We put a specific focus on the human aspects that influenced the long training phase of the system and the participation to the competition.

Towards linking diffusion MRI based macro- and microstructure measures with cortico-cortical transmission in brain tumor patients.

We aimed to link macro- and microstructure measures of brain white matter obtained from diffusion MRI with effective connectivity measures based on a propagation of cortico-cortical evoked potentials induced with intrasurgical direct electrical stimulation. For this, we compared streamline lengths and log-transformed ratios of streamlines computed from presurgical diffusion-weighted images, and the delays and amplitudes of N1 peaks recorded intrasurgically with electrocorticography electrodes in a pilot study of 9 brain tumor patients. Our results showed positive correlation between these two modalities in the vicinity of the stimulation sites (Pearson coefficient 0.54±0.13 for N1 delays, and 0.47±0.23 for N1 amplitudes), which could correspond to the neural propagation via U-fibers. In addition, we reached high sensitivities (0.78±0.07) and very high specificities (0.93±0.03) in a binary variant of our comparison. Finally, we used the structural connectivity measures to predict the effective connectivity using a multiple linear regression model, and showed a significant role of brain microstructure-related indices in this relation.

Structural connectivity to reconstruct brain activation and effective connectivity between brain regions.

OBJECTIVE: Understanding how brain regions interact to perform a specific task is very challenging. EEG and MEG are two non-invasive imaging modalities that allow the measurement of brain activation with high temporal resolution. Several works in EEG/MEG source reconstruction show that estimating brain activation can be improved by considering spatio-temporal constraints but only few of them use structural information to do so. APPROACH: In this work, we present a source reconstruction algorithm that uses brain structural connectivity, estimated from diffusion MRI (dMRI), to constrain the EEG/MEG source reconstruction. Contrarily to most source reconstruction methods which reconstruct activation for each time instant, the proposed method estimates an initial reconstruction for the first time instants and a multivariate autoregressive model that explains the data in further time instants. This autoregressive model can be thought as an estimation of the effective connectivity between brain regions. We called this algorithm iterative Source and Dynamics reconstruction (iSDR). MAIN RESULTS: This paper presents the overall iSDR approach and how the proposed model is optimized to obtain both brain activation and brain region interactions. The accuracy of our method is demonstrated using synthetic data in which it shows a good capability to reconstruct both activation and connectivity. iSDR is also tested with real data obtained from (Wakeman D and Henson R 2015 A multi-subject, multi-modal human neuroimaging dataset Scientific Data 2 15001) (face recognition task). The results are in phase with other works published with the same data and others that used different imaging modalities with the same task showing that the choice of using an autoregressive model gives relevant results. SIGNIFICANCE: This work shows that complex EEG/MEG datasets can be explained by an initial state and a MAR model for effective connectivity. This is a compact way to describe brain dynamics and offers a direct access to effective connectivity.

Fast Approximation of EEG Forward Problem and Application to Tissue Conductivity Estimation.

Bioelectric source analysis in the human brain from scalp electroencephalography (EEG) signals is sensitive to the conductivities of different head tissues. The conductivity of tissues is subject dependent, so non-invasive methods for conductivity estimation are necessary to fine tune EEG models. To do so, the EEG forward problem solution (so-called lead field matrix) must be computed for a large number of conductivity configurations. Computing a lead field requires a matrix inversion which is computationally intensive for realistic head models. Thus, the required time for computing a large number of lead fields can become impractical. In this work, we propose to approximate the lead field matrix for a set of conductivity configurations, using the exact solution only for a small set of support points in the conductivity space. Our approach accelerates the computation time, while controlling the approximation error. Our method is tested on simulated and measured EEG data for brain and skull conductivity estimation. This test demonstrates that the approximation does not introduce any bias and runs significantly faster than if exact lead field were to be computed.

Using diffusion MRI to discriminate areas of cortical grey matter.

Cortical area parcellation is a challenging problem that is often approached by combining structural imaging (e.g., quantitative T1, diffusion-based connectivity) with functional imaging (e.g., task activations, topological mapping, resting state correlations). Diffusion MRI (dMRI) has been widely adopted to analyse white matter microstructure, but scarcely used to distinguish grey matter regions because of the reduced anisotropy there. Nevertheless, differences in the texture of the cortical 'fabric' have long been mapped by histologists to distinguish cortical areas. Reliable area-specific contrast in the dMRI signal has previously been demonstrated in selected occipital and sensorimotor areas. We expand upon these findings by testing several diffusion-based feature sets in a series of classification tasks. Using Human Connectome Project (HCP) 3T datasets and a supervised learning approach, we demonstrate that diffusion MRI is sensitive to architectonic differences between a large number of different cortical areas defined in the HCP parcellation. By employing a surface-based cortical imaging pipeline, which defines diffusion features relative to local cortical surface orientation, we show that we can differentiate areas from their neighbours with higher accuracy than when using only fractional anisotropy or mean diffusivity. The results suggest that grey matter diffusion may provide a new, independent source of information for dividing up the cortex.

Brain computer interface with the P300 speller: Usability for disabled people with amyotrophic lateral sclerosis.

OBJECTIVES: Amyotrophic lateral sclerosis (ALS), a progressive neurodegenerative disease, restricts patients' communication capacity a few years after onset. A proof-of-concept of brain-computer interface (BCI) has shown promise in ALS and "locked-in" patients, mostly in pre-clinical studies or with only a few patients, but performance was estimated not high enough to support adoption by people with physical limitation of speech. Here, we evaluated a visual BCI device in a clinical study to determine whether disabled people with multiple deficiencies related to ALS would be able to use BCI to communicate in a daily environment. METHODS: After clinical evaluation of physical, cognitive and language capacities, 20 patients with ALS were included. The P300 speller BCI system consisted of electroencephalography acquisition connected to real-time processing software and separate keyboard-display control software. It was equipped with original features such as optimal stopping of flashes and word prediction. The study consisted of two 3-block sessions (copy spelling, free spelling and free use) with the system in several modes of operation to evaluate its usability in terms of effectiveness, efficiency and satisfaction. RESULTS: The system was effective in that all participants successfully achieved all spelling tasks and was efficient in that 65% of participants selected more than 95% of the correct symbols. The mean number of correct symbols selected per minute ranged from 3.6 (without word prediction) to 5.04 (with word prediction). Participants expressed satisfaction: the mean score was 8.7 on a 10-point visual analog scale assessing comfort, ease of use and utility. Patients quickly learned how to operate the system, which did not require much learning effort. CONCLUSION: With its word prediction and optimal stopping of flashes, which improves information transfer rate, the BCI system may be competitive with alternative communication systems such as eye-trackers. Remaining requirements to improve the device for suitable ergonomic use are in progress.

Spatial regularization based on dMRI to solve EEG/MEG inverse problem.

In this paper, we present a new approach to reconstruct dipole magnitudes of a distributed source model for magnetoencephalographic (MEG) and electroencephalographic (EEG). This approach is based on the structural homogeneity of the cortical regions which are obtained using diffusion MRI (dMRI). First, we parcellate the cortical surface into functional regions using structural information. Then, we use a weighting matrix that relates the dipoles' magnitudes of sources inside these functional regions. The weights are based on the region's structural homogeneity. Results of the simulated and real MEG measurement are presented and compared to classical source reconstruction methods.

Multivariate autoregressive model constrained by anatomical connectivity to reconstruct focal sources.

In this paper, we present a framework to reconstruct spatially localized sources from Magnetoencephalography (MEG)/Electroencephalography (EEG) using spatiotemporal constraint. The source dynamics are represented by a Multivariate Autoregressive (MAR) model whose matrix elements are constrained by the anatomical connectivity obtained from diffusion Magnetic Resonance Imaging (dMRI). The framework assumes that the whole brain dynamic follows a constant MAR model in a time window of interest. The source activations and the MAR model parameters are estimated iteratively. We could confirm the accuracy of the framework using simulation experiments in both high and low noise levels. The proposed framework outperforms the two-stage approach.

Modeling of the neurovascular coupling in epileptic discharges.

Despite the interest in simultaneous EEG-fMRI studies of epileptic spikes, the link between epileptic discharges and their corresponding hemodynamic responses is poorly understood. In this context, biophysical models are promising tools for investigating the mechanisms underlying observed signals. Here, we apply a metabolic-hemodynamic model to simulated epileptic discharges, in part generated by a neural mass model. We analyze the effect of features specific to epileptic neuronal activity on the blood oxygen level dependent (BOLD) response, focusing on the issues of linearity in neurovascular coupling and on the origin of negative BOLD signals. We found both sub- and supra-linearity in simulated BOLD signals, depending on whether one observes the early or the late part of the BOLD response. The size of these non-linear effects is determined by the spike frequency, as well as by the amplitude of the excitatory activity. Our results additionally indicate a minor deviation from linearity at the neuronal level. According to a phase space analysis, the possibility to obtain a negative BOLD response to an epileptic spike depends on the existence of a long and strong excitatory undershoot. Moreover, we strongly suggest that a combined EEG-fMRI modeling approach should include spatial assumptions. The present study is a step towards an increased understanding of the link between epileptic spikes and their BOLD responses, aiming to improve the interpretation of simultaneous EEG-fMRI recordings in epilepsy.

Forward field computation with OpenMEEG.

To recover the sources giving rise to electro- and magnetoencephalography in individual measurements, realistic physiological modeling is required, and accurate numerical solutions must be computed. We present OpenMEEG, which solves the electromagnetic forward problem in the quasistatic regime, for head models with piecewise constant conductivity. The core of OpenMEEG consists of the symmetric Boundary Element Method, which is based on an extended Green Representation theorem. OpenMEEG is able to provide lead fields for four different electromagnetic forward problems: Electroencephalography (EEG), Magnetoencephalography (MEG), Electrical Impedance Tomography (EIT), and intracranial electric potentials (IPs). OpenMEEG is open source and multiplatform. It can be used from Python and Matlab in conjunction with toolboxes that solve the inverse problem; its integration within FieldTrip is operational since release 2.0.

Tracking cortical activity from M/EEG using graph cuts with spatiotemporal constraints.

This work proposes to use magnetoencephalography (MEG) and electroencephalography (EEG) source imaging to provide cinematic representations of the temporal dynamics of cortical activations. Cortical activation maps, seen as images of the active brain, are scalar maps defined at the vertices of a triangulated cortical surface. They can be computed from M/EEG data using a linear inverse solver every millisecond. Taking as input these activation maps and exploiting both the graph structure of the cortical mesh and the high sampling rate of M/EEG recordings, neural activations are tracked over time using an efficient graph cut based algorithm. The method estimates the spatiotemporal support of the active brain regions. It consists in computing a minimum cut on a particularly designed weighted graph imposing spatiotemporal regularity constraints on the activation patterns. Each node of the graph is assigned a label (active or non active). The method works globally on the full time-period of interest, can cope with spatially extended active regions and allows the active domain to exhibit topology changes over time. The algorithm is illustrated and validated on synthetic data. Results of the method are provided on two MEG cognitive experiments in the visual and somatosensory cortices, demonstrating the ability of the algorithm to handle various types of data.

OpenMEEG: opensource software for quasistatic bioelectromagnetics.

BACKGROUND: Interpreting and controlling bioelectromagnetic phenomena require realistic physiological models and accurate numerical solvers. A semi-realistic model often used in practise is the piecewise constant conductivity model, for which only the interfaces have to be meshed. This simplified model makes it possible to use Boundary Element Methods. Unfortunately, most Boundary Element solutions are confronted with accuracy issues when the conductivity ratio between neighboring tissues is high, as for instance the scalp/skull conductivity ratio in electro-encephalography. To overcome this difficulty, we proposed a new method called the symmetric BEM, which is implemented in the OpenMEEG software. The aim of this paper is to present OpenMEEG, both from the theoretical and the practical point of view, and to compare its performances with other competing software packages. METHODS: We have run a benchmark study in the field of electro- and magneto-encephalography, in order to compare the accuracy of OpenMEEG with other freely distributed forward solvers. We considered spherical models, for which analytical solutions exist, and we designed randomized meshes to assess the variability of the accuracy. Two measures were used to characterize the accuracy. the Relative Difference Measure and the Magnitude ratio. The comparisons were run, either with a constant number of mesh nodes, or a constant number of unknowns across methods. Computing times were also compared. RESULTS: We observed more pronounced differences in accuracy in electroencephalography than in magnetoencephalography. The methods could be classified in three categories: the linear collocation methods, that run very fast but with low accuracy, the linear collocation methods with isolated skull approach for which the accuracy is improved, and OpenMEEG that clearly outperforms the others. As far as speed is concerned, OpenMEEG is on par with the other methods for a constant number of unknowns, and is hence faster for a prescribed accuracy level. CONCLUSIONS: This study clearly shows that OpenMEEG represents the state of the art for forward computations. Moreover, our software development strategies have made it handy to use and to integrate with other packages. The bioelectromagnetic research community should therefore be able to benefit from OpenMEEG with a limited development effort.

Consensus Matching Pursuit for multi-trial EEG signals.

Time-frequency representations are commonly used to analyze the oscillatory nature of brain signals in EEG, MEG or intracranial EEG. In the signal processing literature, there is growing interest in sparse time-frequency representations, where the data are described using few components. A popular algorithm is Matching Pursuit (MP) [Mallat SG, Zhang Z. Matching pursuits with time-frequency dictionaries. IEEE Trans Sig Proc 1993;41:3397-415], which iteratively subtracts from the signal its projection on atoms selected from a dictionary. The MP algorithm was recently adapted for multivariate datasets [Durka PJ, Matysiak A, Martinez-Montes E, Sosa PV, Blinowska KJ. Multichannel matching pursuit and EEG inverse solutions. J Neurosci Methods 2005;148:49-59; Gribonval R. Piecewise linear source separation. Proc SPIE'03 2003. p. 297-310], which is relevant for brain signals that are typically recorded using many channels and trials. So far, most approaches have assumed a stable pattern across channels or trials, even though cross-trial variability is often observed in brain signals. In this study, we adapt Matching Pursuit for brain signals with cross-trial variability in all their characteristics (time, frequency, number of oscillations). The originality of our method is to select each atom using a voting technique that is robust to variability, and to subtract it by adapting the parameters to each trial. Because the inter-trial variability is handled using a voting technique, the method is called Consensus Matching Pursuit (CMP). The CMP method is validated on simulated and real data, and shown to be robust to variability. Compared to existing multivariate Matching Pursuit algorithms, it (i) estimates atoms that are more representative of single-trial waveforms, (ii) leads to a sparser representation of the data, and (iii) permits to quantify the amount of variability across trials.