Diffusion-weighted magnetic resonance imaging (DW-MRI) permits in-vivo measurements of water diffusion, from which we can infer the orientation of white matter fibres in the brain. We show that by ordering the measurements, we can improve the reproducibility of the fibre-orientation estimate from partially-completed DW-MRI scans, without altering the complete data set. Tractography methods reconstruct entire fibre pathways from the local fibre-orientation estimates. Because the local fibre-orientation measurements are subject to uncertainty, the reconstructed fibre pathways are best described with a probabilistic algorithm. One way to estimate the connection probabilities is by defining a probability density function (PDF) in each voxel, and sampling from the PDF in a Monte-Carlo fashion. We propose new models of the PDF based on standard spherical statistical methods. The models improve previous work by closely modelling the dispersion of repeated noisy estimates of the fibre orientation. We compare a simple PDF (the Watson PDF) that models circular cluster of axes to a more general PDF (the Bingham PDF) that models circular or elliptical clusters of axes. We also propose models of the PDF in regions of crossing fibres, where there are two distinct fibre populations in the voxel. We validate the PDFs by comparing them to the uncertainty in fibre orientation calculated from bootstrap resampling of a repeated brain MR acquisition. We find mat the Bingham PDF produces connection probabilities that are closer to the bootstrap results man the Watson PDF. We use the new PDF models to perform a connectivity-based segmentation of the corpus callosum in eight different subjects. The results are similar to those of previous studies on corpus callosum connectivity, despite the use of finer cortical labelling, suggesting that the dominant connections from the corpus callosum project to the superior frontal gyrus, the superior parietal gyrus and the occipital gyrus.

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Diffuse Optical Tomography (DOT) is a relatively new medical imaging modality which allows the simultaneous monitoring of both oxyhaemoglobin and deoxyhaemoglobin, and this is achieved without requiring external contrast agents, because in DOT, the intrinsic absorption and scattering properties of tissue are exploited. Other important features include the fast data acquisition, the relatively low cost, the portability and compactness of the equipment and the non-ionizing radiation which is harmless to the human being. All these features make DOT, an excellent candidate for the continuous monitoring of brain oxymetry. On the other hand, DOT also presents some important disadvantages such as the low spatial resolution and the high computational power required to produce images. The aim of this research was to apply non linear signal processing techniques and analysis methods to obtain significant improvements in brain imaging. The main contributions include: the establishment of a methodology for the incorporation of functional and anatomical a priori information based on MRI scans and physiology assessments; the development of a novel method for fast image reconstruction in DOT based on the use of reduced-order models of the propagation of light; a comparative study of two model representation, namely polynomial and Radial Basis Function (RBF) reduced- order models and an investigation on the applicability of these methods in three-dimensional imaging. Several examples demonstrate the effectiveness and applicability of the new methods, including the experimental validation of the proposed algorithms. Results indicate significant improvement on the spatial resolution and localization accuracy of brain haemodynamics, but more importantly, the feasibility of real-time tomographic monitoring of brain functioning. This work is a contribution to make the use of DOT possible in clinical environments. The ultimate purpose is to develop an inexpensive noninvasive device, whose portability and compactness allows real-time monitoring of brain oxymetry at the patient's bedside for extended periods.

The work described in this thesis was performed by the author, except where indicated. All the studies were accomplished on the 3 Tesla system within the Magnetic Resonance Centre at the University of Nottingham, and the Wellcome Trust MEG Laboratory at the Aston University during the period between October 1999 and June 2005. Functional Magnetic Resonance Imaging (fMRI) and Magnetoencephalography (MEG) are two promising brain function research modalities, sensitive to the hemodynamic and electrophysiological responses respectively during brain activites. The feasibility of joint employment of both modalities was examined in both spatial and temporal domains. A somatosensory tactile stimulus was adopted to induce simple functional reaction. It was shown that a reasonable spatial correspondence between fMRI and MEG can be established. Attempts were made on MEG recordings to extract suitable aspects for temporal features matching fMRI with a method reflecting the physical principles. It was shown that the this method is capable of exposing the nature of neural electric activities, although further development is required to perfect the strategy.

The partial volume effect is an imaging artefact associated with tomographic biomedical imaging data. Three-dimensional volumetric data points (voxels) enclose finite sized regions so that they may contain a mixture of signals which are then known as partial volume voxels. The limited spatial resolution of tomographic biomedical imaging data, due to the complex biomedical image acquisition processes, often results in large numbers of these partial volume voxels. Clinical applications of biomedical imaging data often require accurate estimates of tissues or metabolic activity, where many voxels in the data are partial volume voxels. Therefore accurate modelling of the partial volume effect can be very important for such quantitative applications. The probabilistic models discussed and presented in this thesis provide a generic mathematically consistent framework in which the partial volume effect is modelled. Novel developments include an improved model of an intensity and gradient magnitude feature space to model the PV effect; a novel analytically derived formulation of the ground truth (prior) description of the PV effect; a novel gradient controlled spatially regulated classifier that utilises Markov Chain Monte Carlo simulations; and a fully automatic brain isolation technique that identifies brain voxels in neurological MRI data. Simulated partial volume data and data from anatomical (MRI) and functional (PET) biomedical imaging modalities are utilized to assess the classification performance of the partial volume models. The data sets include: an imaged PET/CT phantom provided by the Royal Marsden Hospital, UK; publicly available simulated MR brain data together with the associated ground truths from the Montreal Neurological Institute, McGill University, Canada; and 20 normal MR data sets from the Center for Morphometric Analysis at Massachusetts General Hospital, USA. The performance of the developed classifiers were found to be competitive and in some cases superior to existing published quantitative estimation techniques.

High magnetic field strengths (4.7 Tesla) promise improved MRI quality but also pose technical challenges. The research described here aims to optimise imaging techniques to generate artifact-free human brain images. Radio frequency (RF) B1 magnetic field homogeneity is worse at high field. Progress towards reducing the effect of the inhomogeneity at 4.7 T has been made in a novel spin-echo sequence using Hyperbolic Secant (HS) RF pulses. The properties of HS pulses when used for excitation and refocusing are investigated and exploited using simulations and experiments to yield a pulse sequence in which the HS pulse refocusing is B1-insensitive. This sequence has one less RF pulse than a similar commonly used technique and produces an improved slice profile compared with a previous sequence. High resolution diffusion-weighted imaging in reasonable scan times and without severe distortion proves challenging at high magnetic field strength. A volume-selective Stimulated Echo Acquisition Mode Echo-Planar Imaging sequence developed here shows potential for overcoming these challenges. The technique is shown to give similar diffusion coefficients to standard sequences in phantoms. It is designed for application in brain regions in which the higher resolution could allow nerve fibre tracts to be followed in greater detail. The construction of an anthropomorphic head phantom as a tool for comparing susceptibility artifact reduction techniques is described. The aim is for the phantom to accurately reproduce the magnetic environment of the brain and allow quantification of susceptibility-induced distortion and drop-out, which are worse at high field strength. The phantom is based on a water-filled plastic skull with realistic air spaces and wax to mimic soft tissues and has been used to evaluate a new technique that recovers signal in areas of drop-out in gradient-echo images. Magnetic field maps show that the field pattern in the phantom is similar to that in real brains.

The work presented in this thesis is intended to contribute towards the understanding of the cerebral vascular behaviour in response to changes in neuronal activation. The blood oxygenation-level dependent (BOLD) functional magnetic resonance imaging (fMRI) signal provides an indirect measure of neuronal activation, arising from a combination of metabolic and vascular (blood flow and blood volume) changes local to the activation. Therefore the BOLD signal is dependent on local vascular properties as well as on the neuronal activation, leading to a variability of the BOLD signal, based on the underlying vascular structure. It has become an important goal to improve understanding of the mechanisms underlying the BOLD signal in order to separate out this vascular variability from the underlying correspondence with the neuronal activation. The effect of field strength on the temporal characteristics of the BOLD haemodynamic response function is investigated. An earlier BOLD response onset has been measured with increasing static magnetic field strength, consistent with an earlier microvascular (compared with macrovascular) signal response. This result can be used to improve haemodynamic models of the BOLD signal. Hypercapnia, a vasodilator, has been used both to assess the relationship between transverse relaxation and blood oxygenation at 3 and 7 Tesla and to identify vascular heterogeneity between two equivalent brain regions. A tight, linear relationship was found between the level of hypercapnia and transverse relaxation at both 3 and 7 Tesla, whilst the change in transverse relaxation due to hypercapnia increased 2.1 ± 0.5 fold from 3 to 7 Tesla, indicating an approximately linear relationship across field strength. In a separate experiment, a vascular asymmetry was found between the left and right precentral gyri using hypercapnia. This result highlights the need to account for the vascular contribution to the BOLD signal before using this BOLD signal to make comparisons of neuronal activity across brain regions. Finally, an improved model for calibrated BOLD has been proposed and implemented, which requires fewer assumptions than existing approaches. This uses the BOLD response to some task, repeated both at normoxia and hyperoxia. To assess the validity of this model, the effects of paramagnetic oxygen molecules are considered, both dissolved in blood plasma and in airspaces adjacent to the brain. These effects were found to be small, except for in the frontal cortex.

Multimodal neuroimaging using a combination of Magnetoencephalography (MEG) and ultra-high-field fMRI are used in order to gain further insight into the neural oscillations and haemodynamic responses in the somatosensory cortex. Single pulse electrical median nerve stimulation (MNS) with regular and jittered intervals is used in MEG. A preliminary study is used to determine acceptable trial number and length, and highlights points to be considered in paradigm optimization. Time-frequency analysis shows that the largest activities are beta event-related desynchronization (ERD) and event-related synchronization (ERS) between 13Hz and 30Hz. No significant difference in both the induced oscillations and evoked responses are found. Paired pulse MNS with varying ISIs are studied using MEG and 7T fMRI. The beta ERD is suggested to have a gating role with a magnitude irrespective of the starting point of stimulus. Non-linearity effects both in beta ERD/ERS and P35m are shown for ISIs of up to 2s, implying that the non-linear neural responses to the stimulus may still contribute to the BOLD non-linearity even when the evoked response has returned to baseline. Multiple pulse MNS with varying pulse train length and frequency are also investigated using MEG and MEG-fMRI. The gating role of beta ERD is further confirmed and the N160m is suggested to be modulated under this role. No accumulative effect is seen in the ERS with increasing pulse number but the amplitude of the ERS is modulated by the frequency. This can be explained by a Cortical Activation Model (CAM). Efforts to spatially separate the beta ERD and ERS are shown for all three studies. Group averaged SAM images suggest a separation of activation areas along the central gyrus. Significant difference are found in the z MNI coordinate between beta ERD and ERS peak locations, suggesting that these two effects could arise from different generators. In the multiple pulse frequency study, by including the temporal signature of beta ERD and ERS as a regressor in BOLD fMRI analysis, delayed BOLD responses are located posterior to the standard BOLD response. However, the exact nature of the relationship between this delayed BOLD response and the ERS effects requires further work.

The work undertaken involves the use of functional magnetic resonance imaging (fMRI) and magnetoencephalography (MEG) as separate but complementary non-invasive functional brain imaging modalities. The aim in combining fMRI and MEG is centred around exploitation of the high temporal resolution available in MEG, and the high spatial resolution available in fMRI. However, whilst MEG represents a direct measure of neuronal activity, BOLD fMRI is an indirect measure and this makes the two modalities truly complementary. In both cases, the imaging signals measured are relatively poorly understood and so the fundamental question asked here is: How are the neuromagnetic effects detectable using MEG related to the metabolic effects reflected in the fMRI BOLD response? Initially, a novel technique is introduced for the detection and spatial localisation of neuromagnetic effects in MEG. This technique, based on a beamforming approach to the MEG inverse problem, is shown to yield accurate results both in simulation and using experimental data. The technique introduced is applied to MEG data from a simple experiment involving stimulation of the visual cortex. A number of heterogeneous neuromagnetic effects are shown to be detectable, and furthermore, these effects are shown to be spatially and temporally correlated with the fMRI BOLD response. The limitations to comparing only two measures of brain activity are discussed, and the use of arterial spin labelling (ASL) to make quantitative measurements of physiological parameters supplementing these two initial metrics is introduced. Finally, a novel technique for accurate quantification of arterial cerebral blood volume using ASL is described and shown to produce accurate results. A concluding chapter then speculates on how these aCBV measurements might be combined with those from MEG in order to better understand the fMRI BOLD response.