Özet:
Magnetic resonance imaging (MRI) have been advanced signi cantly since its discovery, especially in imaging soft biological structures. One of the most studied and improved technique in this eld is di usion MRI consisting of two methods; namely, di usion weighted imaging (DWI) and di usion tensor imaging (DTI). This imaging modality is rather regarded with imaging tissues in micro environments,where restricted di usion occurs, such as neural networks and microscopically crowded media . In this thesis, we will investigate the in uence of di usion on nuclear magnetic resonance (NMR) experiments in two distinct parts. Firstly, we will study the NMR signal measured from molecules di using under the in uence of a parabolic (Hookean) potential. We will induce a Hookean potential into the free di usion state to restrict the random movements of the molecules. Then, a recently introduced method, con nement tensor model, is employed in the analytical measurements to validate the random walk simulations. The second part consists of rather a di erent investigation regarding the determination of energy landscapes of boundaries in which water molecules undergo random walk. A recently proposed pulse sequence, allowing us to perform an inverse Fourier transformation on the signal, is employed to image the potential energy landscape in which the water molecules di use. The energy landscape encodes information about heterogeneities of a domain as well as adhesiveness feature of boundaries. As an additional approach, we will give a brief discussion about the fractional Brownian motion (fBm) to bring more realistic perspective to the di usive motion of the particles in restricted regions.
