Diffusion MRI of Brain Tissue: Importance of Axonal Trajectory

Obtaining microstructural information non-invasively on brain tissue remains a challenge. Diffusion magnetic resonance imaging (dMRI) is an imaging method that can provide such information. That includes geometrical considerations of nerve cells projections, axons, that are present in the white matter of the human brain. Axons carry information encoded into electrical impulses to other cells. The thesis deals with estimating parameters of the axonal trajectories, modeled as one-dimensional pathways, from the dMRI signal. That is achieved in two steps: constructing a forward model to predict the dMRI signal and, vice versa, estimating the tissue parameters from dMRI signal by solving the so-called inverse problem. The proposed forward model employs a spectral analysis of dMRI signal. This formulation enables signal prediction for any gradient waveform and helps to identify the physical characteristics of the underlying system that are preserved in the dMRI signal. The physical properties are represented in so-called diffusion spectra whereas gradient waveforms, that sensitizes the signal, are in the encoding spectra. To mimic biologically plausible axonal trajectories, axonal trajectories were modeled by a 1D-toy model that incorporates harmonic waves with variable degree of randomness. Different numerical methods for computation of diffusion spectra were compared, and the resulting spectra were characterized by a phenomenological model incorporating three parameters. It was not possible to estimate the exact parameters of the 1D-toy model from diffusion spectra. Nonetheless, it was possible to estimate their statistical descriptors, namely microscopic orientation dispersion and dispersion-weighted wavelength. Solving the inverse problem posed a major challenge. The phenomenological model of the diffusion spectra was incorporated in a forward model of the diffusion-weighted signal perpendicular to the trajectory and applied to a state-of-the-art data acquired in human brain white matter of a healthy volunteer. It was not possible to estimate all the parameters of the phenomenological model but by constraining the parameters to plausible values we could estimate the last that was within the range predicted by histology. Incorporating trajectory-parameters in the model of white matter diffusion yielded fit residuals as small as those obtained with current state-of-the-art models assuming parallel, straight, and cylindrical cylinders. However, the cylinder model predicted axon diameters far outside the range expected from histology. We conclude that neglecting the axonal trajectories leads to biased models of axons in brain white matter.MRI can serve as an example of successfully applied fundamental research from physics to biological sciences, humanities, chemistry or medicine. Biomolecules in biochemistry can be probed with atomic resolution. Nanomaterials in material sciences, porous rocks in geology, cell structures or tissues in biology and medicine can be examined. Statistical analysis of MRI signal can reveal functional state of the brain and is relevant in e.g. psychology. This thesis deals mainly with applications within medical sciences. Diffusion magnetic resonance imaging (dMRI) unravels the tissue microstructure, i.e. the structure of tissue on the micrometer length scale. At this scale, the arrangement of cells and other biologically relevant structures emerges as a new property from a deeper, biochemical, scale. Microstructural appearance is often defining feature of biological tissues and is intertwined with their biological behavior, which is a highly interesting information from a medical point of view. In this project, we study in a systematic way, often neglected, geometrical aspects of axons called axonal trajectories. Axons are the wiring of the brain. Based on microscopical images we proposed their representation, inspected their properties and forecasted the outcome of a diffusion measurement. The inverse question, whether the information on the axonal trajectories can be inferred from the outcome of measurement, and whether they could be neglected, was answered as well. The results suggest that non-straight axonal trajectories need to be considered in the of representations of axons, although to estimate them reliably the practical diffusion measurements need to be improved. The estimated properties of axonal trajectories were congruent to the gold-standard method, microscopy. Same methodology applied to the investigation of axonal trajectories can be employed in other problems in the dMRI field and may also lead to better understanding of the nature of the results of the diffusion measurements in the human tissue. Potentially, novel biomarkers that could help to diagnose diseases could be discovered. Generally, dMRI is an interesting research field where potential breakthrough could be made. It probes the microstructural region that is highly important from the biological point of view, has a solid foundation in physical theory, allows for large variety of possible arrangements of the dMRI experiments and is not as widespread as other imaging modalities

Novel methods and analysis of B0 and B1 gradients in magnetic resonance imaging

Ankara : The Department of Electrical and Electronics Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013.Thesis (Ph. D.) -- Bilkent University, 2013.Includes bibliographical references leaves 65-71.In this thesis, analysis of B0 gradients and B1 fields are performed and novel methods using B1 gradients instead of B0 gradients are proposed. The first contribution of this dissertation is expressing the nature of the interaction between the B0 gradient fields and the active implantable medical devices (AIMD). By utilizing the fact that gradient coils produce linear magnetic field in a volume of interest, the simplified closed form electric field expressions are defined inside a homogeneous cylindrical volume. Using these simplified expressions, the induced potential on an implant electrode has been computed approximately for various lead positions on a cylindrical phantom and verified by comparing with the measured potentials for these sample conditions. In addition, the validity of the method has been tested with isolated frog leg stimulation experiments. The results of both phantom and ex vivo experiments show that if the path of the implant lead is known, the induced voltage on the lead can be estimated analytically. The second topic in this dissertation is the Bloch-Siegert (BS) shift based B1 mapping method. The method is analyzed in terms of the effects of the off-resonance frequency, the RF pulse shape, and the duration of the RF pulse. Based on these analyses, a new theoretical model that relates the Fourier transform of the off-resonant BS RF pulse envelope to the phase shift is proposed. Utilizing Bloch simulations and phantom experiments the proposed frequency domain expression is verified. The results indicates that the proposed expression works well even for short pulse durations (< 2ms) and low offset frequencies (fRF < 500Hz) when the ratio of the RF field and the frequency offset of the RF pulse is smaller than 0.5. The last topic of this dissertation is on flow and shear wave imaging with B1 gradients instead of B0 gradients. In flow imaging, a novel sequence using a Bloch-Siegert pulse generated by a spatially dependent B1 field is proposed. The proposed method is experimentally verified by comparing the resultant velocity measurements with those obtained by using bipolar flow encoding B0 gradients. This comparison demonstrates the feasibility of using BS shift with B1 gradients in detecting the flow. The usage of B1 gradients is also proposed to detect shear waves at frequencies in kilohertz range and this method is experimentaly verified for 2kHz, 3kHz and 4kHz shear frequencies. The studies in this thesis indicate that extensive analysis of B0 gradients in Magnetic Resonance Imaging (MRI) is important for safety issues, and for scenarios where B0 gradients prove insufficient in encoding due to hardware limitations, utilizing B1 gradients can be considered as an alternative.Türk, Esra AbacıPh.D

Adaption in Dynamic Contrast-Enhanced MRI

In breast DCE MRI, dynamic data are acquired to assess signal changes caused by contrast agent injection in order to classify lesions. Two approaches are used for data analysis. One is to fit a pharmacokinetic model, such as the Tofts model, to the data, providing physiological information. For accurate model fitting, fast sampling is needed. Another approach is to evaluate architectural features of the contrast agent distribution, for which high spatial resolution is indispensable. However, high temporal and spatial resolution are opposing aims and a compromise has to be found. A new area of research are adaptive schemes, which sample data at combined resolutions to yield both, accurate model fitting and high spatial resolution morphological information. In this work, adaptive sampling schemes were investigated with the objective to optimize fitting accuracy, whilst providing high spatial resolution images. First, optimal sampling design was applied to the Tofts model. By that it could be determined, based on an assumed parameter distribution, that time points during the onset and the initial fast kinetics, lasting for approximately two minutes, are most relevant for fitting. During this interval, fast sampling is required. Later time points during wash-out can be exploited for high spatial resolution images. To achieve fast sampling during the initial kinetics, data acquisition has to be accelerated. A common way to increase imaging speed is to use view-sharing methods, which omit certain k-space data and interpolate the missing data from neighboring time frames. In this work, based on phantom simulations, the influence of different view-sharing techniques during the initial kinetics on fitting accuracy was investigated. It was found that all view-sharing methods imposed characteristic systematic errors on the fitting results of Ktrans. The best fitting performance was achieved by the scheme ``modTRICKS'', which is a combination of the often used schemes keyhole and TRICKS. It is not known prior to imaging, when the contrast agent will arrive in the lesion or when the wash-out begins. Currently used adaptive sequences change resolutions a fixed time points. However, missing time points on the upslope may cause fitting errors and missing the signal peak may lead to a loss in morphological information. This problem was addressed with a new automatic resolution adaption (AURA) sequence. Acquired dynamic data were analyzed in real-time to find the onset and the beginning of the wash-out and consequently the temporal resolution was automatically adapted. Using a perfusion phantom it could be shown that AURA provides both, high fitting accuracy and reliably high spatial resolution images close to the signal peak. As alternative approach to AURA, a sequence which allows for retrospective resolution adaption, was assesses. Advantages are that adaption does not have to be a global process, and can be tailored regionally to local sampling requirements. This can be useful for heterogeneous lesions. For that, a 3D golden angle radial sequence was used, which acquires contrast information with each line and the golden angles allow arbitrary resolutions at arbitrary time points. Using a perfusion phantom, it could be shown that retrospective resolution adaption yields high fitting accuracy and relatively high spatial resolution maps