Modeling and inference of multisubject fMRI data

Functional magnetic resonance imaging (fMRI) is a rapidly growing technique for studying the brain in action. Since its creation [1], [2], cognitive scientists have been using fMRI to understand how we remember, manipulate, and act on information in our environment. Working with magnetic resonance physicists, statisticians, and engineers, these scientists are pushing the frontiers of knowledge of how the human brain works. The design and analysis of single-subject fMRI studies has been well described. For example, [3], chapters 10 and 11 of [4], and chapters 11 and 14 of [5] all give accessible overviews of fMRI methods for one subject. In contrast, while the appropriate manner to analyze a group of subjects has been the topic of several recent papers, we do not feel it has been covered well in introductory texts and review papers. Therefore, in this article, we bring together old and new work on so-called group modeling of fMRI data using a consistent notation to make the methods more accessible and comparable

Data-driven haemodynamic response function extraction using Fourier-wavelet regularised deconvolution

Background: We present a simple, data-driven method to extract haemodynamic response functions (HRF) from functional magnetic resonance imaging (fMRI) time series, based on the Fourier-wavelet regularised deconvolution (ForWaRD) technique. HRF data are required for many fMRI applications, such as defining region-specific HRFs, effciently representing a general HRF, or comparing subject-specific HRFs. Results: ForWaRD is applied to fMRI time signals, after removing low-frequency trends by a wavelet-based method, and the output of ForWaRD is a time series of volumes, containing the HRF in each voxel. Compared to more complex methods, this extraction algorithm requires few assumptions (separability of signal and noise in the frequency and wavelet domains and the general linear model) and it is fast (HRF extraction from a single fMRI data set takes about the same time as spatial resampling). The extraction method is tested on simulated event-related activation signals, contaminated with noise from a time series of real MRI images. An application for HRF data is demonstrated in a simple event-related experiment: data are extracted from a region with significant effects of interest in a first time series. A continuous-time HRF is obtained by fitting a nonlinear function to the discrete HRF coeffcients, and is then used to analyse a later time series. Conclusion: With the parameters used in this paper, the extraction method presented here is very robust to changes in signal properties. Comparison of analyses with fitted HRFs and with a canonical HRF shows that a subject-specific, regional HRF significantly improves detection power. Sensitivity and specificity increase not only in the region from which the HRFs are extracted, but also in other regions of interest.

Sparse machine learning methods with applications in multivariate signal processing

This thesis details theoretical and empirical work that draws from two main subject areas: Machine Learning (ML) and Digital Signal Processing (DSP). A unified general framework is given for the application of sparse machine learning methods to multivariate signal processing. In particular, methods that enforce sparsity will be employed for reasons of computational efficiency, regularisation, and compressibility. The methods presented can be seen as modular building blocks that can be applied to a variety of applications. Application specific prior knowledge can be used in various ways, resulting in a flexible and powerful set of tools. The motivation for the methods is to be able to learn and generalise from a set of multivariate signals. In addition to testing on benchmark datasets, a series of empirical evaluations on real world datasets were carried out. These included: the classification of musical genre from polyphonic audio files; a study of how the sampling rate in a digital radar can be reduced through the use of Compressed Sensing (CS); analysis of human perception of different modulations of musical key from Electroencephalography (EEG) recordings; classification of genre of musical pieces to which a listener is attending from Magnetoencephalography (MEG) brain recordings. These applications demonstrate the efficacy of the framework and highlight interesting directions of future research

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

The foundations of lesion-function inference in the human brain

Understanding the functional architecture of the brain has long been a challenge in neuroscience with a variety of techniques having been developed to explore this structure-function relationship. However, in order to be able to accurately identify the underlying system we require techniques that have the capabilities of describing the complexities therein. In order to perform lesion-function studies a cohort of brain scans with the location of the lesion identified must be collected. Utilising diffusion weighted magnetic resonance imaging, normally collected in the clinical setting, I propose a new unsupervised lesion segmentation routine. The cohort of brain scans also need to be spatially normalised such that homologous regions of the brain are brought into register with each other. However, this process can be perturbed by the presence of a lesion within the scan. Though a series of simulations I evaluate the performance of 12 different spatial normalisation routines on brains scans that possess a lesion. Historically lesion-function mapping studies have tended to use a univariate statistical approach, where different locations within the brain are treated as being spatially independent from each other. Here I show that biases within the structure of the data have the potential to distort the lesion-function inferences we draw. Though a series of simulations, I show that a mass univariate technique is vulnerable to these biases and assess three different multivariate methods (Support Vector Machines, Relevance Vector Machines and Flexible Bayesian Modelling) as potential solutions to this problem. Asides from making lesion-function inferences, these multivariate models can be used to predict future events. Using a data set of paired admission diffusion weighted magnetic resonance imaging scans and functional outcome scores I apply these techniques to the clinical scenario of predicting the functional outcome of patients after a cerebral vascular event

Towards Patient-Specific Brain Networks Using Functional Magnetic Resonance Imaging

fMRI applications are rare in translational medicine and clinical practice. What can be inferred from a single fMRI scan is often unreliable due to the relative low signal-to-noise ratio compared to other neuroimaging modalities. However, the potential of fMRI is promising. It is one of the few neuroimaging modalities to obtain functional brain organisation of an individual during task engagement and rest. This work extends on current fMRI image processing approaches to obtain robust estimates of functional brain organisation in two resting-state fMRI cohorts. The first cohort comprises of young adults who were born at extremely low gestations and age-matched healthy controls. Group analysis between term- and preterm-born adults revealed differences in functional organisation, which were discovered to be predominantly caused by underlying structural and physiological differences. The second cohort comprises of elderly adults with young onset Alzheimer’s disease and age-matched controls. Their corresponding resting-state fMRI scans are short in scanning time resulting in unreliable spatial estimates with conventional dual regression analysis. This problem was addressed by the development of an ensemble averaging of matrix factorisations approach to compute single subject spatial maps characterised by improved spatial reproducibility compared to maps obtained by dual regression. The approach was extended with a haemodynamic forward model to obtain surrogate neural activations to examine the subject’s task behaviour. This approach applied to two task-fMRI cohorts showed that these surrogate neural activations matched with original task timings in most of the examined fMRI scans but also revealed subjects with task behaviour different than intended by the researcher. It is hoped that both the findings in this work and the novel matrix factorisation approach itself will benefit the fMRI community. To this end, the derived tools are made available online to aid development and validation of methods for resting-state and task fMRI experiments

Structured low-rank methods for robust 3D multi-shot EPI

Magnetic resonance imaging (MRI) has inherently slow acquisition speed, and Echo-Planar Imaging (EPI), as an efficient acquisition scheme, has been widely used in functional magnetic resonance imaging (fMRI) where an image series with high temporal resolution is needed to measure neuronal activity. Recently, 3D multi-shot EPI which samples data from an entire 3D volume with repeated shots has been drawing growing interest for fMRI with its high isotropic spatial resolution, particularly at ultra-high fields. However, compared to single-shot EPI, multi-shot EPI is sensitive to any inter-shot instabilities, e.g., subject movement and even physiologically induced field fluctuations. These inter-shot inconsistencies can greatly negate the theoretical benefits of 3D multi-shot EPI over conventional 2D multi-slice acquisitions. Structured low-rank image reconstruction which regularises under-sampled image reconstruction by exploiting the linear dependencies in MRI data has been successfully demonstrated in a variety of applications. In this thesis, a structured low-rank reconstruction method is optimised for 3D multi-shot EPI imaging together with a dedicated sampling pattern termed seg-CAIPI, in order to enhance the robustness to physiological fluctuations and improve the temporal stability of 3D multi-shot EPI for fMRI at 7T. Moreover, a motion compensated structured low-rank reconstruction framework is also presented for robust 3D multi-shot EPI which further takes into account inter-shot instabilities due to bulk motion. Lastly, this thesis also investigates into the improvement of structured low-rank reconstruction from an algorithmic perspective and presents the locally structured low-rank reconstruction scheme

A multi-scale cortical wiring space links cellular architecture and functional dynamics in the human brain.

The vast net of fibres within and underneath the cortex is optimised to support the convergence of different levels of brain organisation. Here, we propose a novel coordinate system of the human cortex based on an advanced model of its connectivity. Our approach is inspired by seminal, but so far largely neglected models of cortico-cortical wiring established by postmortem anatomical studies and capitalises on cutting-edge in vivo neuroimaging and machine learning. The new model expands the currently prevailing diffusion magnetic resonance imaging (MRI) tractography approach by incorporation of additional features of cortical microstructure and cortico-cortical proximity. Studying several datasets and different parcellation schemes, we could show that our coordinate system robustly recapitulates established sensory-limbic and anterior-posterior dimensions of brain organisation. A series of validation experiments showed that the new wiring space reflects cortical microcircuit features (including pyramidal neuron depth and glial expression) and allowed for competitive simulations of functional connectivity and dynamics based on resting-state functional magnetic resonance imaging (rs-fMRI) and human intracranial electroencephalography (EEG) coherence. Our results advance our understanding of how cell-specific neurobiological gradients produce a hierarchical cortical wiring scheme that is concordant with increasing functional sophistication of human brain organisation. Our evaluations demonstrate the cortical wiring space bridges across scales of neural organisation and can be easily translated to single individuals