Dynamic Decomposition of Spatiotemporal Neural Signals

Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to specific types of information processing. Here we present a data analysis framework that uses a linearized model of these dynamic states in order to decompose the measured neural signal into a series of components that capture both rhythmic and non-rhythmic neural activity. The method is based on stochastic differential equations and Gaussian process regression. Through computer simulations and analysis of magnetoencephalographic data, we demonstrate the efficacy of the method in identifying meaningful modulations of oscillatory signals corrupted by structured temporal and spatiotemporal noise. These results suggest that the method is particularly suitable for the analysis and interpretation of complex temporal and spatiotemporal neural signals

Reconstructing anatomy from electro-physiological data

Here we show how it is possible to make estimates of brain structure based on MEG data. We do this by reconstructing functional estimates onto distorted cortical manifolds parameterised in terms of their spherical harmonics. We demonstrate that both empirical and simulated MEG data give rise to consistent and plausible anatomical estimates. Importantly, the estimation of structure from MEG data can be quantified in terms of millimetres from the true brain structure. We show, for simulated data, that the functional assumptions which are closer to the functional ground-truth give rise to anatomical estimates that are closer to the true anatomy

Does function fit structure? A ground truth for non-invasive neuroimaging.

There are now a number of non-invasive methods to image human brain function in-vivo. However, the accuracy of these images remains unknown and can currently only be estimated through the use of invasive recordings to generate a functional ground truth. Neuronal activity follows grey matter structure and accurate estimates of neuronal activity will have stronger support from accurate generative models of anatomy. Here we introduce a general framework that, for the first time, enables the spatial distortion of a functional brain image to be estimated empirically. We use a spherical harmonic decomposition to modulate each cortical hemisphere from its original form towards progressively simpler structures, ending in an ellipsoid. Functional estimates that are not supported by the simpler cortical structures have less inherent spatial distortion. This method allows us to compare directly between magnetoencephalography (MEG) source reconstructions based upon different assumption sets without recourse to functional ground truth

Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface.Comment: Accepted in Medical Image Analysi

The Unique Determination of Neuronal Currents in the Brain via Magnetoencephalography

The problem of determining the neuronal current inside the brain from measurements of the induced magnetic field outside the head is discussed under the assumption that the space occupied by the brain is approximately spherical. By inverting the Geselowitz equation, the part of the current which can be reconstructed from the measurements is precisely determined. This actually consists of only certain moments of one of the two functions specifying the tangential part of the current. The other function specifying the tangential part of the current as well as the radial part of the current are completely arbitrary. However, it is also shown that with the assumption of energy minimization, the current can be reconstructed uniquely. A numerical implementation of this unique reconstruction is also presented

Spherical harmonic based noise rejection and neuronal sampling with multi-axis OPMs

In this study we explore the interference rejection and spatial sampling properties of multi-axis Optically Pumped Magnetometer (OPM) data. We use both vector spherical harmonics and eigenspectra to quantify how well an array can separate neuronal signal from environmental interference while adequately sampling the entire cortex. We found that triaxial OPMs have superb noise rejection properties allowing for very high orders of interference (L=6) to be accounted for while minimally affecting the neural space (2dB attenuation for a 60-sensor triaxial system). We show that at least 11th order (143 spatial degrees of freedom) irregular solid harmonics or 95 eigenvectors of the lead field are needed to model the neural space for OPM data (regardless of number of axes measured). This can be adequately sampled with 75-100 equidistant triaxial sensors (225-300 channels) or 200 equidistant radial channels. In other words, ordering the same number of channels in triaxial (rather than purely radial) configuration may give significant advantages not only in terms of external noise rejection but also by minimizing cost, weight and cross-talk

Development and Evaluation of Data Processing Techniques in Magnetoencephalography

With MEG, the tiny magnetic fields produced by neuronal currents within the brain can be measured completely non-invasively. But the signals are very small (~100 fT) and often obscured by spontaneous brain activity and external noise. So, a recurrent issue in MEG data analysis is the identification and elimination of this unwanted interference within the recordings. Various strategies exist to meet this purpose. In this thesis, two of these strategies are scrutinized in detail. The first is the commonly used procedure of averaging over trials which is a successfully applied data reduction method in many neurocognitive studies. However, the brain does not always respond identically to repeated stimuli, so averaging can eliminate valuable information. Alternative approaches aiming at single trial analysis are difficult to realize and many of them focus on temporal patterns. Here, a compromise involving random subaveraging of trials and repeated source localization is presented. A simulation study with numerous examples demonstrates the applicability of the new method. As a result, inferences about the generators of single trials can be drawn which allows deeper insight into neuronal processes of the human brain. The second technique examined in this thesis is a preprocessing tool termed Signal Space Separation (SSS). It is widely used for preprocessing of MEG data, including noise reduction by suppression of external interference, as well as movement correction. Here, the mathematical principles of the SSS series expansion and the rules for its application are investigated. The most important mathematical precondition is a source-free sensor space. Using three data sets, the influence of a violation of this convergence criterion on source localization accuracy is demonstrated. The analysis reveals that the SSS method works reliably, even when the convergence criterion is not fully obeyed. This leads to utilizing the SSS method for the transformation of MEG data to virtual sensors on the scalp surface. Having MEG data directly on the individual scalp surface would alleviate sensor space analysis across subjects and comparability with EEG. A comparison study of the transformation results obtained with SSS and those produced by inverse and subsequent forward computation is performed. It shows strong dependence on the relative position of sources and sensors. In addition, the latter approach yields superior results for the intended purpose of data transformation

Disturbances in primary visual processing as a function of healthy aging

For decades, visual entrainment paradigms have been widely used to investigate basic visual processing in healthy individuals and those with neurological disorders. While healthy aging is known to be associated with alterations in visual processing, whether this extends to visual entrainment responses and the precise cortical regions involved is not fully understood. Such knowledge is imperative given the recent surge in interest surrounding the use of flicker stimulation and entrainment in the context of identifying and treating Alzheimer’s disease (AD). In the current study, we examined visual entrainment in eighty healthy aging adults using magnetoencephalography (MEG) and a 15 Hz entrainment paradigm, while controlling for age-related cortical thinning. MEG data were imaged using a time-frequency resolved beamformer and peak voxel time series were extracted to quantify the oscillatory dynamics underlying the processing of the visual flicker stimuli. We found that, as age increased, the mean amplitude of entrainment responses decreased and the latency of these responses increased. However, there was no effect of age on the trial-to-trial consistency in phase (i.e., inter-trial phase locking) nor amplitude (i.e., coefficient of variation) of these visual responses. Importantly, we discovered that the relationship between age and response amplitude was fully mediated by the latency of visual processing. These results indicate that aging is associated with robust changes in the latency and amplitude of visual entrainment responses within regions surrounding the calcarine fissure, which should be considered in studies examining neurological disorders such as AD and other conditions associated with increased age