Variational Approaches to the Estimation, Regularization and Segmentation of Diffusion Tensor Images

Diffusion magnetic resonance imaging probes and quantifies the anisotropic diffusion of water molecules in biological tissues, make it possible to non-invasively infer the architecture of the underlying structures. In this chapter, we present a set of new techniques for the robust estimation and regularization of diffusion tensor images (DTI) as well as a novel statistical framework for the segmentation of cerebral white matter structures from this type of dataset. Numerical experiments conducted on real diffusion weighted MRI illustrate the technique and exhibit promising results

Diffusion-weighted imaging: basic concepts and application in cerebral stroke and head trauma

Diffusion-weighted imaging (DWI) of the brain represents a new imaging technique that extends imaging from depiction of neuroanatomy to the level of function and physiology. DWI measures a fundamentally different physiological parameter compared with conventional MRI. Image contrast is related to differences in the diffusion rate of water molecules rather than to changes in total tissue water. DWI can reveal pathology in cases where conventional MRI remains unremarkable. DWI has proven to be highly sensitive in the early detection of acute cerebral ischemia and seems promising in the evaluation of traumatic brain injury. DWI can differentiate between lesions with decreased and increased diffusion. In addition, full-tensor DWI can evaluate the microscopic architecture of the brain, in particular white matter tracts, by measuring the degree and spatial distribution of anisotropic diffusion within the brain. This article reviews the basic concepts of DWI and its application in cerebral ischemia and traumatic brain injur

Orientation of Sticks and Spheres - Estimating Tensor Shape and Orientation Distribution using Diffusion NMR

The diffusion characteristics of water can be measured by using NMR methods. Specifically, the diffusion profiles in samples containing domains of water barriers are of major importance to be able to describe in applications such as diffusion tensor imaging or diffusion MRI-sequences. These sequences can be used to study the internal structure of samples of complex diffusion profiles. The diffusion characteristics can be described by a diffusion tensor matrix which can be parameterised by the isotropic diffusion coefficient and the level of anisotropy. This thesis work aims to measure diffusion weighted NMR signals from a triple-stimulated spin-echo pulse sequence to simultaneously determine both the diffusion tensor characteristics and the orientation density function, ODF. Traditionally, obtaining the ODF is based on assuming a fixed diffusion tensor in a diffusion-weighted NMR experiment to describe the different signal attenuations along different directions as differences in the shape of the microscopic water domains. By the work presented in this report, it is proven by measurements on lyotropic liquid crystal systems that the shape of the diffusion tensor and the ODF indeed can be extracted from the same measurement. This is shown for samples having either prolate or oblate diffusion tensors.Mapping the inside: Study of water diffusion using NMR experiment This work shows how the internal structures of samples, which for instance could be cells or crystals, containing microscopic water channels and other structures where the water molecules can move in some directions but not in others can be determined in detail by looking at the magnetic properties of atomic nuclei. In order to see the structures in which the water molecules can move, two kinds of information about how the molecules move around are needed. First, the way in which the water molecules can move inside of the channels, i.e. the diffusion of water, must be known. Second, the difference in how the water molecules can move around depending on the direction within the sample must be known. Older ways of finding out the latter depends on guessing the former. The technique described in this work shows a way to determine both in the same measurement. When you measure temperature with a thermometer it is the motion of molecules that is measured. Every molecule in a liquid moves around freely and randomly while still bumping into other molecules. This motion of molecules is called diffusion. Nuclear magnetic resonance (NMR) spectroscopy is the study of how the magnetic properties of atomic nuclei change from the influences of magnetic fields. As all nuclei are found within molecules and the molecules move around, it is understandable that the NMR signal can change if the molecules move around. In my work, I have shown that a NMR method can be used to map the diffusion of water molecules inside samples that have thin channels or corridors that the water molecules can move around in. Similar methods are used to map diffusion of water in the neurons in the brain, which among other things can show how the neurons are connected. The new thing that I showcase in my report, is that it is possible to determine two important features of the sample; both how much the water diffusion only can occur in one direction and also which directions the channels and corridors are oriented in. Previously, it has not been possible to determine both based on the same measurement. This improvement is important as it helps to make the map of the channel orientations more reliable. In the future, this might be used to study samples which is has a complex microscopical environment where the water molecules move around in wide or narrow corridors, big halls, and across planes. One very important application of this could be to gain more understanding of both the types, conditions, and structure of cells and tissues of the brain if the experiment could be performed in a clinical MRI scanner

On High Order Tensor-based Diffusivity Profile Estimation

Diffusion weighted magnetic resonance imaging (dMRI) is used to measure, in vivo, the self-diffusion of water molecules in biological tissues. High order tensors (HOTs) are used to model the apparent diffusion coefficient (ADC) profile at each voxel from the dMRI data. In this paper we propose: (i) A new method for estimating HOTs from dMRI data based on weighted least squares (WLS) optimization; and (ii) A new expression for computing the fractional anisotropy from a HOT that does not suffer from singularities and spurious zeros. We also present an empirical evaluation of the proposed method relative to the two existing methods based on both synthetic and real human brain dMRI data. The results show that the proposed method yields more accurate estimation than the competing methods

Effects of microperfusion in hepatic diffusion weighted imaging

Clinical hepatic diffusion weighted imaging (DWI) generally relies on mono-exponential diffusion. The aim was to demonstrate that mono-exponential diffusion in the liver is contaminated by microperfusion and that the bi-exponential model is required. Nineteen fasting healthy volunteers were examined with DWI (seven b-values) using fat suppression and respiratory triggering (1.5 T). Five different regions in the liver were analysed regarding the mono-exponentially fitted apparent diffusion coefficient (ADC), and the bi-exponential model: molecular diffusion (D (slow) ) microperfusion (D (fast) ) and the respective fractions (f (slow/fast)). Data were compared using ANOVA and Kruskal-Wallis tests. Simulations were performed by repeating our data analyses, using just the DWI series acquired with b-values approximating those of previous studies. Median mono-exponentially fitted ADCs varied significantly (P <0.001) between 1.107 and 1.423 x 10(-3) mm(2)/s for the five regions. Bi-exponential fitted D-slow varied between 0.923 and 1.062 x 10(-3) mm(2)/s without significant differences (P = 0.140). D (fast) varied significantly, between 17.8 and 46.8 x 10(-3) mm(2)/s (P <0.001). F-tests showed that the diffusion data fitted the bi-exponential model significantly better than the mono-exponential model (F > 21.4, P <0.010). These results were confirmed by the simulations. ADCs of normal liver tissue are significantly dependent on the measurement location because of substantial microperfusion contamination; therefore the bi-exponential model should be used. Diffusion weighted MR imaging helps clinicians to differentiate tumours by diffusion properties Fast moving water molecules experience microperfusion, slow molecules diffusion Hepatic diffusion should be measured by bi-exponential models to avoid microperfusion contamination Mono-exponential models are contaminated with microperfusion, resulting in apparent regional diffusion differences Bi-exponential models are necessary to measure diffusion and microperfusion in the liver