Application of Time-Fractional Order Bloch Equation in Magnetic Resonance Fingerprinting

Magnetic resonance fingerprinting (MRF) is one novel fast quantitative imaging framework for simultaneous quantification of multiple parameters with pseudo-randomized acquisition patterns. The accuracy of the resulting multi-parameters is very important for clinical applications. In this paper, we derived signal evolutions from the anomalous relaxation using a fractional calculus. More specifically, we utilized time-fractional order extension of the Bloch equations to generate dictionary to provide more complex system descriptions for MRF applications. The representative results of phantom experiments demonstrated the good accuracy performance when applying the time-fractional order Bloch equations to generate dictionary entries in the MRF framework. The utility of the proposed method is also validated by in-vivo study.Comment: Accepted at 2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI 2019

Fractional order magnetic resonance fingerprinting in the human cerebral cortex

Mathematical models are becoming increasingly important in magnetic resonance imaging (MRI), as they provide a mechanistic approach for making a link between tissue microstructure and signals acquired using the medical imaging instrument. The Bloch equations, which describes spin and relaxation in a magnetic field, is a set of integer order differential equations with a solution exhibiting mono-exponential behaviour in time. Parameters of the model may be estimated using a non-linear solver, or by creating a dictionary of model parameters from which MRI signals are simulated and then matched with experiment. We have previously shown the potential efficacy of a magnetic resonance fingerprinting (MRF) approach, i.e. dictionary matching based on the classical Bloch equations, for parcellating the human cerebral cortex. However, this classical model is unable to describe in full the mm-scale MRI signal generated based on an heterogenous and complex tissue micro-environment. The time-fractional order Bloch equations has been shown to provide, as a function of time, a good fit of brain MRI signals. We replaced the integer order Bloch equations with the previously reported time-fractional counterpart within the MRF framework and performed experiments to parcellate human gray matter, which is cortical brain tissue with different cyto-architecture at different spatial locations. Our findings suggest that the time-fractional order parameters, {\alpha} and {\beta}, potentially associate with the effect of interareal architectonic variability, hypothetically leading to more accurate cortical parcellation

Pulse sequences for measuring exchange rates between proton species: From unlocalised NMR spectroscopy to chemical exchange saturation transfer imaging

Within the field of NMR spectroscopy, the study of chemical exchange processes through saturation transfer techniques has a long history. In the context of MRI, chemical exchange techniques have been adapted to increase the sensitivity of imaging to small fractions of exchangeable protons, including the labile protons of amines, amides and hydroxyls. The MR contrast is generated by frequency-selective irradiation of the labile protons, which results in a reduction of the water signal associated with transfer of the labile protons’ saturated magnetization to the protons of the surrounding free water. The signal intensity depends on the rate of chemical exchange and the concentration of labile protons as well as on the properties of the irradiation field. This methodology is referred to as CEST (chemical exchange saturation transfer) imaging. Applications of CEST include imaging of molecules with short transverse relaxation times and mapping of physiological parameters such as pH, temperature, buffer concentration and chemical composition due to the dependency of this chemical exchange effect on all these parameters. This article aims to describe these effects both theoretically and experimentally. In depth analysis and mathematical modelling are provided for all pulse sequences designed to date to measure the chemical exchange rate. Importantly, it has become clear that the background signal from semi-solid protons and the presence of the Nuclear Overhauser Effect (NOE), either through direct dipole-dipole mechanisms or through exchange-relayed signals, complicates the analysis of CEST effects. Therefore, advanced methods to suppress these confounding factors have been developed, and these are also reviewed. Finally, the experimental work conducted both in vitro and in vivo is discussed and the progress of CEST imaging towards clinical practice is presented

Precision spectroscopy by photon-recoil signal amplification

Precision spectroscopy of atomic and molecular ions offers a window to new physics, but is typically limited to species with a cycling transition for laser cooling and detection. Quantum logic spectroscopy has overcome this limitation for species with long-lived excited states. Here, we extend quantum logic spectroscopy to fast, dipole-allowed transitions and apply it to perform an absolute frequency measurement. We detect the absorption of photons by the spectroscopically investigated ion through the photon recoil imparted on a co-trapped ion of a different species, on which we can perform efficient quantum logic detection techniques. This amplifies the recoil signal from a few absorbed photons to thousands of fluorescence photons. We resolve the line center of a dipole-allowed transition in 40Ca+ to 1/300 of its observed linewidth, rendering this measurement one of the most accurate of a broad transition. The simplicity and versatility of this approach enables spectroscopy of many previously inaccessible species.Comment: 25 pages, 6 figures, 1 table, updated supplementary information, fixed typo

Generation of realistic white matter substrates with controllable morphology for diffusion MRI simulations

Numerical phantoms have played a key role in the development of diffusion MRI (dMRI) techniques seeking to estimate features of the microscopic structure of tissue by providing a ground truth for simulation experiments against which we can validate and compare techniques. One common limitation of numerical phantoms which represent white matter (WM) is that they oversimplify the true complex morphology of the tissue which has been revealed through ex vivo studies. It is important to try to generate WM numerical phantoms that capture this realistic complexity in order to understand how it impacts the dMRI signal. This thesis presents work towards improving the realism of WM numerical phantoms by generating fibres mimicking natural fibre genesis. A novel phantom generator is presented which was developed over two works, resulting in Contextual Fibre Growth (ConFiG). ConFiG grows fibres one-by-one, following simple rules motivated by real axonal guidance mechanisms. These simple rules enable ConFiG to generate phantoms with tuneable microstructural features by growing fibres while attempting to meet morphological targets such as user-specified density and orientation distribution. We compare ConFiG to the state-of-the-art approach based on packing fibres together by generating phantoms in a range of fibre configurations including crossing fibre bundles and orientation dispersion. Results demonstrate that ConFiG produces phantoms with up to 20% higher densities than the state-of-the-art, particularly in complex configurations with crossing fibres. We additionally show that the microstructural morphology of ConFiG phantoms is comparable to real tissue, producing diameter and orientation distributions close to electron microscopy estimates from real tissue as well as capturing complex fibre cross sections. ConFiG is applied to investigate the intra-axonal diffusivity and probe assumptions in a family of dMRI modelling techniques based on spherical deconvolution (SD), demonstrating that the microscopic variations in fibres’ shapes affects the diffusion within axons. This leads to variations in the per-fibre signal contrary to the assumptions inherent in SD which may have a knock-on effect in popular techniques such as tractography

Development and Optimization of Methods for Accelerated Magnetic Resonance Imaging

Magnetic resonance imaging (MRI) has yielded great success as a medical imaging modality in the past decades, and its excellent soft tissue contrast is used in clinical routine to support diagnosis today. However, MRI is still facing challenges. For example, the acquisition time is long in comparison to computed tomography, especially when directly measuring tissue properties with quantitative MRI. This thesis presents new approaches to accelerate quantitative MRI acquisitions without decreasing the accuracy, using analytical and numerical signal models. A quantitative acquisition to map the transverse relaxation T2 was first accelerated by combining parallel imaging with model-based reconstruction. It was demonstrated that the combination leads to an improved artifact behavior in comparison to a model-based reconstruction alone, facilitating higher acceleration factors. The technique was optimized to obtain T2 maps from the brain, knee, prostate and liver, with good initial results. The idea of combining methods was continued by introducing simultaneous multi slice acquisition to the T2 mapping approach. Furthermore, a numerical simulation rather than an analytical solution was used in the model-based reconstruction, resulting in a fast undersampled acquisition that also accounts for transmit field inhomogeneity. This approach yielded more accurate and faster acquired T2 values. Magnetic resonance fingerprinting (MRF) is a recently introduced model-based reconstruction that promises to provide multiple quantitative maps using a fast pseudo-random acquisition. However, similar to other model-based approaches, MRF depends on how well the model describes the measured signal. It was demonstrated in this work that the estimated quantitative maps may be systematically biased if the model does not account for magnetization transfer effects. To this end, a simplified numerical model was proposed, that includes magnetization transfer, and yields more accurate quantitative values. The same approach was translated to bSSFP acquisitions, where banding artifacts are a major limitation: the analytical model of a phase-cycle bSSFP acquisition was used to separate signal effects of the human tissue from signal effects due to magnetic field inhomogeneity. The separation allowed the removal of typical signal voids in bSSFP images. A compressed sensing reconstruction was employed to avoid additional acquisition time. In summary, this thesis has introduced new approaches to employ signal models in different applications, with the aim of either accelerating an acquisition, or improving the accuracy of an existing fast method. These approaches may help to make the next step away from qualitative towards a fully quantitative MR imaging modality, facilitating precision medicine and personalized treatment