Reliability and Uncertainty in Diffusion MRI Modelling

Current Diffusion MRI studies often utilise more complex models beyond the single exponential decay model used in clinical standards. As this thesis shows, however, two of these models, biexponential and kurtosis, experience mathematical, ill-conditioning issues that can arise when used with regression algorithms, causing extreme bias and/or variance in the parameter estimates. Using simulated noisy data measurements from known truth, the magnitude of the bias and variance was shown to vary based on signal parameters as well as SNR, and increasing the SNR did not reduce this uncertainty for all data. Parameter estimate reliability could not be assessed from a single regression fit in all cases unless bootstrap resampling was performed, in which case measurements with high parameter estimate uncertainty were successfully identified. Prior to data analysis, current studies may use information criteria or cross-validation model selection methods to establish the best model to assess a specific tissue condition. While the best selection method to use is currently unclear in the literature, when testing simulated data in this thesis, no model selection method performed more reliably than the others and these methods were merely biased toward either simpler or more complex models. When a specific model was used to generate simulated noisy data, no model selection method selected this true model for all signals, and the ability of these methods to select the true model also varied depending on the true signal parameters. The results from these simulated data analyses were applied to ex vivo data from excised prostate tissue, and both information criteria measures and bootstrap sample distributions were able to identify image voxels whose parameter estimates had likely reliability issues. Removing these voxels from analysis improved sample variance of the parameter estimates

The structural connectivity of higher order association cortices reflects human functional brain networks

AbstractHuman higher cognition arises from the main tertiary association cortices including the frontal, temporal and parietal lobes. Many studies have suggested that cortical functions must be shaped or emerge from the pattern of underlying physical (white matter) connectivity. Despite the importance of this hypothesis, there has not been a large-scale analysis of the white-matter connectivity within and between these associative cortices. Thus, we explored the pattern of intra- and inter-lobe white matter connectivity between multiple areas defined in each lobe. We defined 43 regions of interest on the lateral associative cortex cytoarchitectonically (6 regions of interest – ROIs in the frontal lobe and 17 ROIs in the parietal lobe) and anatomically (20 ROIs in the temporal lobe) on individuals' native space. The results demonstrated that intra-region connectivity for all 3 lobes was dense and graded generally. In contrary, the inter-lobe connectivity was relatively discrete and regionally specific such that only small sub-regions exhibited long-range connections to another lobe. The long-range connectivity was mediated by 6 major associative white matter tracts, consistent with the notion that these higher cognitive functions arises from brain-wide distributed connectivity. Using graph-theory network analysis we revealed five physically-connected sub-networks, which correspond directly to five known functional networks. This study provides strong and direct evidence that core functional brain networks mirror the brain's structural connectivity

Derivation of Fiber Orientations From Oblique Views Through Human Brain Sections in 3D-Polarized Light Imaging

3D-Polarized Light Imaging (3D-PLI) enables high-resolution three-dimensional mapping of the nerve fiber architecture in unstained histological brain sections based on the intrinsic birefringence of myelinated nerve fibers. The interpretation of the measured birefringent signals comes with conjointly measured information about the local fiber birefringence strength and the fiber orientation. In this study, we present a novel approach to disentangle both parameters from each other based on a weighted least squares routine (ROFL) applied to oblique polarimetric 3D-PLI measurements. This approach was compared to a previously described analytical method on simulated and experimental data obtained from a post mortem human brain. Analysis of the simulations revealed in case of ROFL a distinctly increased level of confidence to determine steep and flat fiber orientations with respect to the brain sectioning plane. Based on analysis of histological sections of a human brain dataset, it was demonstrated that ROFL provides a coherent characterization of cortical, subcortical, and white matter regions in terms of fiber orientation and birefringence strength, within and across sections. Oblique measurements combined with ROFL analysis opens up new ways to determine physical brain tissue properties by means of 3D-PLI microscopy

Computing and visualising intra-voxel orientation-specific relaxation-diffusion features in the human brain

Diffusion MRI techniques are used widely to study the characteristics of the human brain connectome in vivo. However, to resolve and characterise white matter (WM) fibres in heterogeneous MRI voxels remains a challenging problem typically approached with signal models that rely on prior information and constraints. We have recently introduced a 5D relaxation–diffusion correlation framework wherein multidimensional diffusion encoding strategies are used to acquire data at multiple echo‐times to increase the amount of information encoded into the signal and ease the constraints needed for signal inversion. Nonparametric Monte Carlo inversion of the resulting datasets yields 5D relaxation–diffusion distributions where contributions from different sub‐voxel tissue environments are separated with minimal assumptions on their microscopic properties. Here, we build on the 5D correlation approach to derive fibre‐specific metrics that can be mapped throughout the imaged brain volume. Distribution components ascribed to fibrous tissues are resolved, and subsequently mapped to a dense mesh of overlapping orientation bins to define a smooth orientation distribution function (ODF). Moreover, relaxation and diffusion measures are correlated to each independent ODF coordinate, thereby allowing the estimation of orientation‐specific relaxation rates and diffusivities. The proposed method is tested on a healthy volunteer, where the estimated ODFs were observed to capture major WM tracts, resolve fibre crossings, and, more importantly, inform on the relaxation and diffusion features along with distinct fibre bundles. If combined with fibre‐tracking algorithms, the methodology presented in this work has potential for increasing the depth of characterisation of microstructural properties along individual WM pathways

End to End Brain Fiber Orientation Estimation Using Deep Learning

In this work, we explore the various Brain Neuron tracking techniques, one of the most significant applications of Diffusion Tensor Imaging. Tractography is a non-invasive method to analyze underlying tissue micro-structure. Understanding the structure and organization of the tissues facilitates a diagnosis method to identify any aberrations which can occur within tissues due to loss of cell functionalities, provides acute information on the occurrences of brain ischemia or stroke, the mutation of certain neurological diseases such as Alzheimer, multiple sclerosis and so on. Under all these circumstances, accurate localization of the aberrations in efficient manner can help save a life. Following up with the limitations introduced by the current Tractography techniques such as computational complexity, reconstruction errors during tensor estimation and standardization, we aim to elucidate these limitations through our research findings. We introduce an End to End Deep Learning framework which can accurately estimate the most probable likelihood orientation at each voxel along a neuronal pathway. We use Probabilistic Tractography as our baseline model to obtain the training data and which also serve as a Tractography Gold Standard for our evaluations. Through experiments we show that our Deep Network can do a significant improvement over current Tractography implementations by reducing the run-time complexity to a significant new level. Our architecture also allows for variable sized input DWI signals eliminating the need to worry about memory issues as seen with the traditional techniques. The advantage of this architecture is that it is perfectly desirable to be processed on a cloud setup and utilize the existing multi GPU frameworks to perform whole brain Tractography in minutes rather than hours. The proposed method is a good alternative to the current state of the art orientation estimation technique which we demonstrate across multiple benchmarks

Transferring principles of solid-state and Laplace NMR to the field of in vivo brain MRI

Magnetic resonance imaging (MRI) is the primary method for non-invasive investigations of the human brain in health, disease, and development, but yields data that are difficult to interpret whenever the millimeter scale voxels contain multiple microscopic tissue environments with different chemical and structural properties. We propose a novel MRI framework to quantify the microscopic heterogeneity of the living human brain as spatially resolved five-dimensional relaxation-diffusion distributions by augmenting a conventional diffusion-weighted imaging sequence with signal encoding principles from multidimensional solid-state nuclear magnetic resonance (NMR) spectroscopy, relaxation-diffusion correlation methods from Laplace NMR of porous media, and Monte Carlo data inversion. The high dimensionality of the distribution space allows resolution of multiple microscopic environments within each heterogeneous voxel as well as their individual characterization with novel statistical measures that combine the chemical sensitivity of the relaxation rates with the link between microstructure and the anisotropic diffusivity of tissue water. The proposed framework is demonstrated on a healthy volunteer using both exhaustive and clinically viable acquisition protocols

Microscale Measurements of Cell and Tissue Mechanics in Three Dimensions

Two-dimensional (2D) studies have revealed that mechanical forces drive cell migration and can feedback to regulate proliferation, differentiation and the synthesis/remodeling of extracellular matrix (ECM) proteins. Whether these observations can be translated to clinical settings or be utilized for tissue engineering will depend critically on our ability to translate these findings into physiologically relevant three-dimensional (3D) environments. The general goal of this dissertation has been to develop and apply new technologies capable of extending studies of cell and tissue mechanics into 3D environments. In the first project, we measured both shear and normal traction forces exerted by cells cultured on planar substrates. We observed that focal adhesions serve as pivots about which cells generate rotational moments. In the second project, we combined enzymatically degradable synthetic hydrogels with finite element models to measure the mechanical tractions exerted by cells fully encapsulated within 3D matrices. We found that cells reach out thin protrusions and pull back inward towards the cell body with the highest forces at the tip. Cellular extensions that were invading into the surrounding matrix displayed a strong inward force 10-15 microns behind the leading tip, suggesting that growing extensions may establish a contractile waypoint, before invading further. To study the forces cells exert during tissue remodeling, we utilized photolithograpy to generate arrays of microtissues consisting of cells encapsulated in 3D collagen matrices. Microcantilevers were used to constrain the remodeling of the collagen gel and to report the forces generated during this process. We used this technique to explore the effects of boundary stiffness and matrix density within model tendon and cardiac tissues. Finally, we combined this system with a Foerster radius energy transfer (FRET) based biosensor of fibronectin conformation to reveal how tissue geometry and cell-genereated tractions cooperate to pattern matrix conformation during tissue remodeling. Together, these studies highlight novel approaches to understand the nature of cell-ECM interactions in 3D matrices. Such mechanical insights will help us to understand how physical forces drive cell migration and behavior within physiologically relevant environments