Abstract The most important paradigms in quantum mechanics are probably a twolevel system, a harmonic oscillator and an ideal (infinite) periodic potential. The first two provide a starting point for understanding the phenomena in systems where the spectrum of energy levels is discrete, whereas the last one results in continuous energy bands. Here an attempt is made to study the dynamics of the electrons in a narrow miniband of a semiconductor superlattice under electric and magnetic fields. Semiconductor superlattices are artificial periodic structures, where certain properties like the period and the energy band structure, defined in standard crystals by the nature, can be controlled. Electron dynamics in a single superlattice miniband is interesting both from the viewpoint of fundamental and applied physics. From the fundamental perspective superlattices serve as a model system for a wealth of phenomena resulting from the wavenature of charge carriers. On the other hand, superlattices can potentially be utilized in oscillators and amplifiers operating at THz frequencies. They can, in principle, provide a reasonable THz Bloch gain under dc bias and parametric amplification in the presence of ac pump field. Because of numerous scientific and technological applications in different areas of science and technology, including astrophysics and atmospheric science, biological and medical sciences, and detection of concealed weapons and biosecurity, a construction of compact tunable THz amplifiers and generators that can operate at room temperature is an important – but so far unrealized – task. This thesis focuses on the influence of electric and magnetic fields on small-signal absorption and gain in semiconductor superlattices in the presence of dissipation (scattering). We present several new ideas how the effects arising due to the wave nature of the electrons can be utilized in an operation of THz oscillators and amplifiers. In Papers I–V, we discuss the properties of superlattice sub-THz and THz parametric amplifiers, whereas the Papers VI–IX are devoted to the problem of domain instability in the realization of cw THz Bloch oscillator. In Paper IX we also establish a feasibility of new type of superlattice THz amplifier based on nonlinear cyclotron-like oscillations of the miniband electrons. The ideas presented in the Papers I–IX are supplemented here with a detailed discussion of the physical origin of the effects and more rigorous mathematical derivations of the main equations.

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Despite the vast myriad of applications and the long way it has come, MRI is still a relatively new field of knowledge with much prospect for more advancement and expansion. This work is mainly concerned with two gradient echo imaging methods which are directly or indirectly related to blood vessel imaging as well as iron depiction in the human brain. In each case, new methods are introduced that overcome existing limitations. For blood vessel imaging, 3D Time-of-Flight (TOF) MR angiography (MRA) with its known capability to image arteries as well as veins was implemented at 3.0 T. At this field strength, the significant RF profile variability due to RF inhomogeneity is a liability for circle-of-Willis imaging in the human brain that was overcome by introducing a new means to counter the RF effects through increased slope of the ramped pulse. In addition a new method is introduced for TOF MRA with two-in-one arterial and venous 3D TOF imaging to overcome the significant scan time overhead of a traditional second venous scan and for cutting down RF power utilization. Using this method, total scan time could be reduced by as much as 46% and specific absorption rate (SAR) due to spatial saturation could be reduced by as much as 92%. For iron sensitive imaging, Susceptibility Weighted Imaging (SWI) was developed at 4.7 T. The phase SWI method was used to visualize lesions in Multiple Sclerosis (MS) patients and was experimentally compared to the visibility on standard T2 weighting with results demonstrating visualization of new lesions, with 18% of total lesions exclusively visible on SWI. A new approach to 3D imaging was also introduced to enable accurate oblique SWI scanning while overcoming the current restriction to axial imaging to produce correct phase effects for oblique imaging. New results from oblique phase imaging were presented and the phase measurements from key brain structures were successfully validated against images obtained by the current standard of axial imaging.

Magnetic resonance imaging is an essential tool for assessing soft tissues. The desire for increased signal-to-noise and improved tissue contrast has spurred development of imaging systems operating at magnetic fields exceeding 3.0 Tesla (T). Unfortunately, traditional imaging methods are of limited utility on these systems. Novel imaging methods are required to exploit the potential of high field systems and enable innovative clinical studies. This thesis presents methodological advances for human brain imaging at 4.7 T. These methods are applied to assess sub-cortical gray matter in multiple sclerosis (MS) patients. Safety concerns regarding energy deposition in the patient precludes the use of traditional fast spin echo (FSE) imaging at 4.7 T. Reduced and variable refocusing angles were employed to effectively moderate this energy deposition while maintaining high signal levels; an assortment of time-efficient FSE images are presented. Contrast changes were observed at low angles, but images maintained a clinically useful appearance. Heterogeneous transmit fields hinder the measurement of transverse relaxation times. A post-processing technique was developed to model the salient signal behaviour and enable accurate transverse relaxometry. This method is robust to transmit variations observed at 4.7 T and improves multislice imaging efficiency. Gradient echo sequences can exploit the magnetic susceptibility difference between tissues to enhance contrast, but are corrupted near air/tissue interfaces. A correction method was developed and employed to reliably produce a multitude of quantitative and qualitative image sets. Using these techniques, transverse relaxation times and susceptibility field shifts were measured in sub-cortical nuclei of relapsing-remitting MS patients. Abnormalities in the globus pallidus and pulvinar nucleus were observed in all quantitative methods; most other regions differed on one or more measures. Correlations with disease duration were not observed, reaffirming that the disease process commences prior to symptom onset. The methods presented in this thesis enable efficient qualitative and quantitative imaging at high field strength. Unique challenges, notably patient safety and field variability, were overcome via sequence implementation and data processing. These techniques enable visualization and measurement of unique contrast mechanisms, which reveal insight into neurodegenerative diseases, including widespread sub-cortical gray matter damage in MS.

The hippocampus is a gray matter structure in the temporal lobe that plays a key role in memory processes and in many diseases (Alzheimer's disease, epilepsy, depression ...).The development of morphometric models is essential for the study of the functional anatomy and structure alterations associated with different pathologies. The objective of this thesis is to develop and validate methods for morphometry of the hippocampus in two contexts: the study of the external shape of the hippocampus from conventional MRI (1.5T or 3T) with millimeter resolution, and the study of its internal structure from 7T MRI with high spatial resolution. These two settings correspond to the two main parts of the thesis.In the first part, we propose a method for the automatic classification of patients from shape descriptors. This method is based on a spherical harmonic decomposition which is combined with a support vector machine classifier (SVM). The method is evaluated in the context of automatic classification of patients with Alzheimer's disease (AD) patients, mild cognitive impairment (MCI) patients and healthy elderly subjects. It is also compared to other approaches and a more comprehensive validation is available in a population of 509 subjects from the ADNI database. Finally, we present another application of morphometry to study structural alterations associated with the syndrome of Gilles de la Tourette.The second part of the thesis is devoted to the morphometry of the internal structure of the hippocampus from MRI at 7 Tesla. Indeed, the internal structure of the hippocampus is rich and complex but inaccessible to conventional MRI. We first propose an atlas of the internal structure of the hippocampus from postmortem data acquired at 9.4T. Then, we propose to model the Ammon's horn and the subiculum as a skeleton and a local measure thickness. To do this, we introduce a variational method using original Hilbert spaces reproducing kernels. The method is validated on the postmortem atlas and evaluated on in vivo data from healthy subjects and patients with epilepsy acquired at 7T.