Impact of within-voxel heterogeneity in fibre geometry on spherical deconvolution

Axons in white matter have been shown to have varying geometries within a bundle using ex vivo imaging techniques, but what does this mean for diffusion MRI (dMRI) based spherical deconvolution (SD)? SD attempts to estimate the fibre orientation distribution function (fODF) by assuming a single dMRI fibre response function (FRF) for all white matter populations and deconvolving this FRF from the dMRI signal at each voxel to estimate the fODF. Variable fibre geometry within a bundle however suggests the FRF might not be constant even within a single voxel. We test what impact realistic fibre geometry has on SD by simulating the dMRI signal in a range of realistic white matter numerical phantoms, including synthetic phantoms and real axons segmented from electron microscopy. We demonstrate that variable fibre geometry leads to a variable FRF across axons and that in general no single FRF is effective to recover the underlying fibre orientation distribution function (fODF). This finding suggests that assuming a single FRF can lead to misestimation of the fODF, causing further downstream errors in techniques such as tractography

Modeling the orientation distribution function by mixtures of angular central Gaussian distributions

In this paper we develop a tensor mixture model for diffusion weighted imaging data using an automatic model selection criterion for the order of tensor components in a voxel. We show that the weighted orientation distribution function for this model can be expanded into a mixture of angular central Gaussian distributions. We show properties of this model in extensive simulations and in a high angular resolution experimental data set. The results suggest that the model may improve imaging of cerebral fiber tracts. We demonstrate how inference on canonical model parameters may give rise to new clinical applications

Impact of within-voxel heterogeneity in fibre geometry on spherical deconvolution

Axons in white matter have been shown to have varying geometries within a bundle using ex vivo imaging techniques, but what does this mean for diffusion MRI (dMRI) based spherical deconvolution (SD)? SD attempts to estimate the fibre orientation distribution function (fODF) by assuming a single dMRI fibre response function (FRF) for all white matter populations and deconvolving this FRF from the dMRI signal at each voxel to estimate the fODF. Variable fibre geometry within a bundle however suggests the FRF might not be constant even within a single voxel. We test what impact realistic fibre geometry has on SD by simulating the dMRI signal in a range of realistic white matter numerical phantoms, including synthetic phantoms and real axons segmented from electron microscopy. We demonstrate that variable fibre geometry leads to a variable FRF across axons and that in general no single FRF is effective to recover the underlying fibre orientation distribution function (fODF). This finding suggests that assuming a single FRF can lead to misestimation of the fODF, causing further downstream errors in techniques such as tractography

FiberBlender: A Realistic Computer Model of Nerve Bundles for Simulating and Validating the Acquisition of Diffusion Tensor Imaging

Diffusion Tensor Imaging (DTI) is a powerful medical imaging technique that provides a unique method to investigate the structure and connectivity of neural pathways. DTI is a special magnetic resonance imaging (MRI) modality that combines the principles of magnetic resonance with molecular diffusion to trace the motion of water molecules. In the central nervous system, where nerve fibers are packed in highly-directional bundles, these molecules diffuse along the orientation of the fibers. Hence, characterizing the motion of water with DTI delivers a non-invasive in vivo technique to capture the connectivity of nerves themselves. Despite its promises and successful clinical applications for nearly thirty years, problems with validation and interpretation of measurements still persist. Most validation studies attempt to generate ground-truth data from animal models, phantoms, and computer models. This dissertation proposes a novel validation system, FiberBlender, capable of reproducing three-dimensional fiber structures and simulating the diffusion of water molecules to generate ground-truth synthetic DTI data. In particular FiberBlender contributes to: (i) creating more biologically accurate representations of fiber bundles with the inclusion of myelin and glial cells, (ii) examining the effect of demyelination and gliosis on DTI measurements, (iii) optimizing acquisition sequences, and (iv) evaluating the performance of multi-tensor models for the study of crossing fibers. FiberBlender strays away from the “one size fits all” approach taken by previous studies and uses computer algorithms in conjunction with some limited manual operations to produce brain-like geometries that take into account the random spatial location of axons and correct distributions of axon diameters, myelin to axon radius, and myelin to glia ratio. In this way no two models are the same and the system is capable of generating structures that can potentially represent any region of the brain and encompass the heterogeneity between human subjects. This feature is essential for optimization as the performance of DTI acquisition sequences may vary among subjects and the type of scanner used. In addition to better accuracy, the system offers a high degree of flexibility as the geometry can be modified to simulate events that cause drastic changes to the fiber structure. Specially, this dissertation looks at demyelination (an extensive loss of myelin volume), gliosis (a proliferation of glial cells), and axon compaction (a condensation of axons due to a loss of total brain volume) to determine their effects on the observed DTI signal. Simulation results confirm that axon compaction and partial remyelination have similar characteristics. Results also show that some standard clinically used acquisition sequences are incapable of capturing the effects of demyelination, gliosis and compaction when performing longitudinal studies. A novel sequence optimization technique based on Shannon entropy and mutual information is proposed to better capture demyelination. Optimized sequences are tested on a number of non-identical models to confirm their validity and can be used to improve the quality of DTI diagnostics. Finally this work looks at crossing fibers for the validation of multi-tensor models in their ability to characterize crossing diffusion profiles. The performance of multi-tensor models from CHARMED, Q-ball and spherical deconvolution that are widely used in both research and clinical settings are evaluated against ground-truth data generated with FiberBlender. The study is performed on a number of different crossing geometries and preliminary results show that the CHARMED model is the most comprehensive approach