Proton magnetic resonance with parahydrogen induced polarization : Imaging strategies and continuous generation

A major challenge in imaging is the detection of small amounts of molecules of interest. In the case of magnetic resonance imaging (MRI) their signals are typically concealed by the large background signal of e.g. the tissue of the body. This problem can be tackled by hyperpolarization which increases the NMR signals up to several orders of magnitude. However, this strategy is limited for 1H, the most widely used nucleus in NMR andrnMRI, because the enormous number of protons in the body screen the small amount of hyperpolarized ones.Here, I describe a method giving rise to high 1H MRI contrast for hyperpolarized molecules against a large background signal. The contrast is based on the J-coupling induced rephasing of the NMR signal of molecules hyperpolarized via parahydrogen induce polarization (PHIP) and it can easily be implemented in common pulse sequences.rnrnHyperpolarization methods typically require expensive technical equipment (e.g. lasers or microwaves) and most techniques work only in batch mode, thus the limited lifetime of the hyperpolarization is limiting its applications. Therefore, the second part of my thesis deals with the simple and efficient generation of an hyperpolarization.These two achievements open up alternative opportunities to use the standard MRI nucleus 1H for e.g. metabolic imaging in the future.

Inverse problems in classical and quantum physics

The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from tau-decay data and the inverse conductivity problem. Despite a concentrated effort by physicists extending over many years, an understanding of QCD from first principles continues to be elusive. Fortunately, data continues to appear which provide a rather direct probe of the inner workings of the strong interactions. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the time-like experimental data with asymptotic space-like results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. EIT is a technology developed to image the electrical conductivity distribution of a conductive medium. The technique works by performing simultaneous measurements of direct or alternating electric currents and voltages on the boundary of an object. These are the data used by an image reconstruction algorithm to determine the electrical conductivity distribution within the object. In this thesis, two approaches of EIT image reconstruction are proposed. The first is based on reformulating the inverse problem in terms of integral equations. This method uses only a single set of measurements for the reconstruction. The second approach is an algorithm based on linearisation which uses more then one set of measurements. A promising result is that one can qualitatively reconstruct the conductivity inside the cross-section of a human chest. Even though the human volunteer is neither two-dimensional nor circular, such reconstructions can be useful in medical applications: monitoring for lung problems such as accumulating fluid or a collapsed lung and noninvasive monitoring of heart function and blood flow.