Multi-dimensional connectivity: a conceptual and mathematical review.

The estimation of functional connectivity between regions of the brain, for example based on statistical dependencies between the time series of activity in each region, has become increasingly important in neuroimaging. Typically, multiple time series (e.g. from each voxel in fMRI data) are first reduced to a single time series that summarises the activity in a region of interest, e.g. by averaging across voxels or by taking the first principal component; an approach we call one-dimensional connectivity. However, this summary approach ignores potential multi-dimensional connectivity between two regions, and a number of recent methods have been proposed to capture such complex dependencies. Here we review the most common multi-dimensional connectivity methods, from an intuitive perspective, from a formal (mathematical) point of view, and through a number of simulated and real (fMRI and MEG) data examples that illustrate the strengths and weaknesses of each method. The paper is accompanied with both functions and scripts, which implement each method and reproduce all the examples

Disclosing large-scale directed functional connections in MEG with the multivariate phase slope index.

Abstract The phase slope index (PSI) is a method to disclose the direction of frequency-specific neural interactions from magnetoencephalographic (MEG) time series. A fundamental property of PSI is that of vanishing for linear mixing of independent neural sources. This property allows PSI to cope with the artificial instantaneous connectivity among MEG sensors or brain sources induced by the field spread. Nevertheless, PSI is limited by being a bivariate estimator of directionality as opposite to the multidimensional nature of brain activity as revealed by MEG. The purpose of this work is to provide a multivariate generalization of PSI. We termed this measure as the multivariate phase slope index (MPSI). In order to test the ability of MPSI in estimating the directionality, and to compare the MPSI results to those obtained by bivariate PSI approaches based on maximizing imaginary part of coherency and on canonical correlation analysis, we used extensive simulations. We proved that MPSI achieves the highest performance and that in a large number of simulated cases, the bivariate methods, as opposed to MPSI, do not detect a statistically significant directionality. Finally, we applied MPSI to assess seed-based directed functional connectivity in the alpha band from resting state MEG data of 61 subjects from the Human Connectome Project. The obtained results highlight a directed functional coupling in the alpha band between the primary visual cortex and several key regions of well-known resting state networks, e.g. dorsal attention network and fronto-parietal network

Analysing linear multivariate pattern transformations in neuroimaging data.

Most connectivity metrics in neuroimaging research reduce multivariate activity patterns in regions-of-interests (ROIs) to one dimension, which leads to a loss of information. Importantly, it prevents us from investigating the transformations between patterns in different ROIs. Here, we applied linear estimation theory in order to robustly estimate the linear transformations between multivariate fMRI patterns with a cross-validated ridge regression approach. We used three functional connectivity metrics that describe different features of these voxel-by-voxel mappings: goodness-of-fit, sparsity and pattern deformation. The goodness-of-fit describes the degree to which the patterns in an input region can be described as a linear transformation of patterns in an output region. The sparsity metric, which relies on a Monte Carlo procedure, was introduced in order to test whether the transformation mostly consists of one-to-one mappings between voxels in different regions. Furthermore, we defined a metric for pattern deformation, i.e. the degree to which the transformation rotates or rescales the input patterns. As a proof of concept, we applied these metrics to an event-related fMRI data set consisting of four subjects that has been used in previous studies. We focused on the transformations from early visual cortex (EVC) to inferior temporal cortex (ITC), fusiform face area (FFA) and parahippocampal place area (PPA). Our results suggest that the estimated linear mappings explain a significant amount of response variance in the three output ROIs. The transformation from EVC to ITC shows the highest goodness-of-fit, and those from EVC to FFA and PPA show the expected preference for faces and places as well as animate and inanimate objects, respectively. The pattern transformations are sparse, but sparsity is lower than would have been expected for one-to-one mappings, thus suggesting the presence of one-to-few voxel mappings. The mappings are also characterised by different levels of pattern deformations, thus indicating that the transformations differentially amplify or dampen certain dimensions of the input patterns. While our results are only based on a small number of subjects, they show that our pattern transformation metrics can describe novel aspects of multivariate functional connectivity in neuroimaging data.This work was funded by a British Academy Postdoctoral Fellowship (PS140117) to MM, by the Medical Research Council UK (SUAG/058 G101400) to OH, and conducted under the framework of the Departments of Excellence 2018–2022 initiative of the Italian Ministry of Education, University and Research for the Department of Neuroscience, Imaging and Clinical Sciences (DNISC) of the University of Chieti-Pescara

Non-linear Analysis of Scalp EEG by Using Bispectra: The Effect of the Reference Choice

Bispectral analysis is a signal processing technique that makes it possible to capture the non-linear and non-Gaussian properties of the EEG signals. It has found various applications in EEG research and clinical practice, including the assessment of anesthetic depth, the identification of epileptic seizures, and more recently, the evaluation of non-linear cross-frequency brain functional connectivity. However, the validity and reliability of the indices drawn from bispectral analysis of EEG signals are potentially biased by the use of a non-neutral EEG reference. The present study aims at investigating the effects of the reference choice on the analysis of the non-linear features of EEG signals through bicoherence, as well as on the estimation of cross-frequency EEG connectivity through two different non-linear measures, i.e., the cross-bicoherence and the antisymmetric cross-bicoherence. To this end, four commonly used reference schemes were considered: the vertex electrode (Cz), the digitally linked mastoids, the average reference, and the Reference Electrode Standardization Technique (REST). The reference effects were assessed both in simulations and in a real EEG experiment. The simulations allowed to investigated: (i) the effects of the electrode density on the performance of the above references in the estimation of bispectral measures; and (ii) the effects of the head model accuracy in the performance of the REST. For real data, the EEG signals recorded from 10 subjects during eyes open resting state were examined, and the distortions induced by the reference choice in the patterns of alpha-beta bicoherence, cross-bicoherence, and antisymmetric cross-bicoherence were assessed. The results showed significant differences in the findings depending on the chosen reference, with the REST providing superior performance than all the other references in approximating the ideal neutral reference. In conclusion, this study highlights the importance of considering the effects of the reference choice in the interpretation and comparison of the results of bispectral analysis of scalp EEG

Looking through the windows: a study about the dependency of phase-coupling estimates on the data length

| openaire: EC/H2020/810377/EU//ConnectToBrainObjective. Being able to characterize functional connectivity (FC) state dynamics in a real-time setting, such as in brain-computer interface, neurofeedback or closed-loop neurostimulation frameworks, requires the rapid detection of the statistical dependencies that quantify FC in short windows of data. The aim of this study is to characterize, through extensive realistic simulations, the reliability of FC estimation as a function of the data length. In particular, we focused on FC as measured by phase-coupling (PC) of neuronal oscillations, one of the most functionally relevant neural coupling modes.Approach. We generated synthetic data corresponding to different scenarios by varying the data length, the signal-to-noise ratio (SNR), the phase difference value, the spectral analysis approach (Hilbert or Fourier) and the fractional bandwidth. We compared seven PC metrics, i.e. imaginary part of phase locking value (iPLV), PLV of orthogonalized signals, phase lag index (PLI), debiased weighted PLI, imaginary part of coherency, coherence of orthogonalized signals and lagged coherence.Main results. Our findings show that, for a SNR of at least 10 dB, a data window that contains 5-8 cycles of the oscillation of interest (e.g. a 500-800 ms window at 10 Hz) is generally required to achieve reliable PC estimates. In general, Hilbert-based approaches were associated with higher performance than Fourier-based approaches. Furthermore, the results suggest that, when the analysis is performed in a narrow frequency range, a larger window is required.Significance. The achieved results pave the way to the introduction of best-practice guidelines to be followed when a real-time frequency-specific PC assessment is at target.Peer reviewe

Genetic dynamics in untreated CLL patients with either stable or progressive disease: a longitudinal study.

Clonal evolution of chronic lymphocytic leukemia (CLL) often follows chemotherapy and is associated with adverse outcome, but also occurs in untreated patients, in which case its predictive role is debated. We investigated whether the selection and expansion of CLL clone(s) precede an aggressive disease shift. We found that clonal evolution occurs in all CLL patients, irrespective of the clinical outcome, but is faster during disease progression. In particular, changes in the frequency of nucleotide variants (NVs) in specific CLL-related genes may represent an indicator of poor clinical outcome

Tracker-in-Calorimeter (TIC) Project: A Calorimetric New Solution for Space Experiments

A space-based detector dedicated to measurements of γ-rays and charged particles has to achieve a balance between different instrumental requirements. A good angular resolution is necessary for the γ-rays, whereas an excellent geometric factor is needed for the charged particles. The tracking reference technique of γ-ray physics is based on a pair-conversion telescope made of passive material (e.g., tungsten) coupled with sensitive layers (e.g., silicon microstrip). However, this kind of detector has a limited acceptance because of the large lever arm between the active layers, needed to improve the track reconstruction capability. Moreover, the passive material can induce fragmentation of nuclei, thus worsening charge reconstruction performances. The Tracker-In-Calorimeter (TIC) project aims to solve all these drawbacks. In the TIC proposal, the silicon sensors are moved inside a highly-segmented isotropic calorimeter with a couple of external scintillators dedicated to charge reconstruction. In principle, this configuration has a good geometrical factor, and the angle of the γ-rays can be precisely reconstructed from the lateral profile of the electromagnetic shower sampled, at different depths in the calorimeter, by silicon strips. The effectiveness of this approach has been studied with Monte Carlo simulations and validated with beam test data of a small prototype

A New Approach to Calorimetry in Space-Based Experiments for High-Energy Cosmic Rays

Precise measurements of the energy spectra and of the composition of cosmic rays in the PeV region could improve our knowledge regarding their origin, acceleration mechanism, propagation, and composition. At the present time, spectral measurements in this region are mainly derived from data collected by ground-based detectors, because of the very low particle rates at these energies. Unfortunately, these results are affected by the high uncertainties typical of indirect measurements, which depend on the complicated modeling of the interaction of the primary particle with the atmosphere. A space experiment dedicated to measurements in this energy region has to achieve a balance between the requirements of lightness and compactness, with that of a large acceptance to cope with the low particle rates. CaloCube is a four-year-old R&D project, approved and financed by the Istituto Nazionale di Fisica Nucleare (INFN) in 2014, aiming to optimize the design of a space-borne calorimeter. The large acceptance needed is obtained by maximizing the number of entrance windows, while thanks to its homogeneity and high segmentation this new detector achieves an excellent energy resolution and an enhanced separation power between hadrons and electrons. In order to optimize detector performances with respect to the total mass of the apparatus, comparative studies on different scintillating materials, different sizes of crystals, and different spacings among them have been performed making use of MonteCarlo simulations. In parallel to simulations studies, several prototypes instrumented with CsI(Tl) (Caesium Iodide, Tallium doped) cubic crystals have been constructed and tested with particle beams. Moreover, the last development of CaloCube, the Tracker-In-Calorimeter (TIC) project, financed by the INFN in 2018, is focused on the feasibility of including several silicon layers at different depths in the calorimeter in order to reconstruct the particle direction. In fact, an important requirement for γ -ray astronomy is to have a good angular resolution in order to allow precise identification of astrophysical sources in space. In respect to the traditional approach of using a tracker with passive material in front of the calorimeter, the TIC solution can save a significant amount of mass budget in a space satellite experiment, which can then be exploited to improve the acceptance and the resolution of the calorimeter. In this paper, the status of the project and perspectives for future developments are presented