Microstructure imaging using MRI: diffusion MRI and biophysical models under the influence of noise

Abstract

The microstructure of white matter in the human brain plays a central role in healthy human development and non-invasive imaging of it is crucial for understanding the neurological function as well as disorders. While ex vivo microscopy provides detailed insights into the microstructure of nervous tissue, in vivo imaging of nervous tissue and its changes remains a challenge. Diffusion magnetic resonance imaging (dMRI) is a non-invasive, in vivo imaging technique built around diffusion of water molecules in nervous tissue which is sensitive to the tissue microstructure. Hereby, dMRI offers a non-invasive alternative to ex vivo microscopy. Diffusion kurtosis imaging (DKI) is a physical framework used to interpret the measured dMRI signal. DKI shows promise for clinical use due to its ability to capture restricted diffusion which is typical for diffusion in nervous tissue due to the complex, cellular microstructure hindering it. Axisymmetric DKI, a modification of DKI, reduces complexity by introducing additional symmetry assumptions, theoretically making it more noise-robust and data efficient. Both DKI variants are diffusion models used to estimate physical diffusion properties of the investigated tissue which are "only" correlated to the tissue microstructure. Here, biophysical models go one step further and enhance the interpretability of the dMRI signal by connecting it to specific metrics of the actual biological tissue microstructure. For both DKI and biophysical models, noise in dMRI images poses a critical hurdle for accurate and precise parameter estimation. For example, noise in dMRI can lead to a bias in the parameter estimates, the so-called "Rician bias" which burdens parameter estimation for both DKI and biophysical models. This thesis investigates the effects of the Rician bias and how to mitigate them, axisymmetric DKI’s inherent bias, caused by violation of its additional symmetry assumptions, as well as the performance and accuracy of a variety of currently used biophysical models under the influence of noise. Through published, peer-reviewed articles, insights into bias-free parameter estimation at low signal to noise ratios are presented. Furthermore, the severity of the axisymmetric DKI inherent bias is quantified and ways to deal with it are explored. Finally, bias propagation of DKI parameters used to compute the biophysical parameters are investigated and the accuracy of various biophysical models are evaluated against a biological gold standard. Through this, the role of the combination of axisymmetric DKI and Rician bias correction as an highly effective "all-rounder" for reducing the Rician bias in DKI parameter estimation is demonstrated. Furthermore, the potential of a Bayesian-enhanced machine learning based approach for biophysical parameter estimation named "Baydiff" for becoming an accurate tool used for microstructure imaging under the influence of noise is highlighted.