Feasibility And Reproducibility Of Diffusion-weighted Magnetic Resonance Imaging Of The Fetal Brain In Twin-twin Transfusion Syndrome.

The aim of this study is to test the feasibility and reproducibility of diffusion-weighted magnetic resonance imaging (DW-MRI) evaluations of the fetal brains in cases of twin-twin transfusion syndrome (TTTS). From May 2011 to June 2012, 24 patients with severe TTTS underwent MRI scans for evaluation of the fetal brains. Datasets were analyzed offline on axial DW images and apparent diffusion coefficient (ADC) maps by two radiologists. The subjective evaluation was described as the absence or presence of water diffusion restriction. The objective evaluation was performed by the placement of 20-mm(2) circular regions of interest on the DW image and ADC maps. Subjective interobserver agreement was assessed by the kappa correlation coefficient. Objective intraobserver and interobserver agreements were assessed by proportionate Bland-Altman tests. Seventy-four DW-MRI scans were performed. Sixty of them (81.1%) were considered to be of good quality. Agreement between the radiologists was 100% for the absence or presence of diffusion restriction of water. For both intraobserver and interobserver agreement of ADC measurements, proportionate Bland-Altman tests showed average percentage differences of less than 1.5% and 95% CI of less than 18% for all sites evaluated. Our data demonstrate that DW-MRI evaluation of the fetal brain in TTTS is feasible and reproducible.

Spin-charge coupling in quantum wires at zero magnetic field

We discuss an approximation for the dynamic charge response of nonlinear spin-1/2 Luttinger liquids in the limit of small momentum. Besides accounting for the broadening of the charge peak due to two-holon excitations, the nonlinearity of the dispersion gives rise to a two-spinon peak, which at zero temperature has an asymmetric line shape. At finite temperature the spin peak is broadened by diffusion. As an application, we discuss the density and temperature dependence of the Coulomb drag resistivity due to long-wavelength scattering between quantum wires.

Travelling wave profiles in some models with nonlinear diffusion

We study some properties of the monotone solutions of the boundary value problem (p(u'))' - cu' + f(u) = 0, u(-infinity) = 0, u(+infinity) = 1, where f is a continuous function, positive in (0, 1) and taking the value zero at 0 and 1, and P may be an increasing homeomorphism of (0, 1) or (0, +infinity) onto [0, +infinity). This problem arises when we look for travelling waves for the reaction diffusion equation partial derivative u/partial derivative t = partial derivative/partial derivative x [p(partial derivative u/partial derivative x)] + f(u) with the parameter c representing the wave speed. A possible model for the nonlinear diffusion is the relativistic curvature operator p(nu)= nu/root 1-nu(2). The same ideas apply when P is given by the one- dimensional p- Laplacian P(v) = |v|(p-2)v. In this case, an advection term is also considered. We show that, as for the classical Fisher- Kolmogorov- Petrovski- Piskounov equations, there is an interval of admissible speeds c and we give characterisations of the critical speed c. We also present some examples of exact solutions. (C) 2014 Elsevier Inc. All rights reserved.

Semidiscretization and long-time asymptotics of nonlinear diffusion equations

We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero.

Investigation of field and diffusion time dependence of the diffusion-weighted signal at ultrahigh magnetic fields.

Over the last decade, there has been a significant increase in the number of high-magnetic-field MRI magnets. However, the exact effect of a high magnetic field strength (B0 ) on diffusion-weighted MR signals is not yet fully understood. The goal of this study was to investigate the influence of different high magnetic field strengths (9.4 T and 14.1 T) and diffusion times (9, 11, 13, 15, 17 and 24 ms) on the diffusion-weighted signal in rat brain white matter. At a short diffusion time (9 ms), fractional anisotropy values were found to be lower at 14.1 T than at 9.4 T, but this difference disappeared at longer diffusion times. A simple two-pool model was used to explain these findings. The model describes the white matter as a first hindered compartment (often associated with the extra-axonal space), characterized by a faster orthogonal diffusion and a lower fractional anisotropy, and a second restricted compartment (often associated with the intra-axonal space), characterized by a slower orthogonal diffusion (i.e. orthogonal to the axon direction) and a higher fractional anisotropy. Apparent T2 relaxation time measurements of the hindered and restricted pools were performed. The shortening of the pseudo-T2 value from the restricted compartment with B0 is likely to be more pronounced than the apparent T2 changes in the hindered compartment. This study suggests that the observed differences in diffusion tensor imaging parameters between the two magnetic field strengths at short diffusion time may be related to differences in the apparent T2 values between the pools. Copyright © 2013 John Wiley & Sons, Ltd.

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

An introduction to model-independent diffusion magnetic resonance imaging.

ABSTRACT: q-Space-based techniques such as diffusion spectrum imaging, q-ball imaging, and their variations have been used extensively in research for their desired capability to delineate complex neuronal architectures such as multiple fiber crossings in each of the image voxels. The purpose of this article was to provide an introduction to the q-space formalism and the principles of basic q-space techniques together with the discussion on the advantages as well as challenges in translating these techniques into the clinical environment. A review of the currently used q-space-based protocols in clinical research is also provided.

On the analysis of travelling waves to a nonlinear flux limited reaction-diffusion equation

In this paper we study the existence and qualitative properties of travelling waves associated to a nonlinear flux limited partial differential equation coupled to a Fisher-Kolmogorov-Petrovskii-Piskunov type reaction term. We prove the existence and uniqueness of finite speed moving fronts of C2 classical regularity, but also the existence of discontinuous entropy travelling wave solutions.

Diffusion-weighted magnetic resonance imaging in metastatic gastrointestinal stromal tumor (GIST): a pilot study on the assessment of treatment response in comparison with 18F-FDG PET/CT.

BACKGROUND: Diffusion-weighted magnetic resonance imaging (MRI) is increasingly being used for assessing the treatment succes in oncology, but the real clinical value needs to evaluated by comparison with other, already established, metabolic imaging techniques. PURPOSE: To prospectively evaluate the clinical potential of diffusion-weighted MRI with apparent diffusion coefficient (ADC) mapping for gastrointestinal stromal tumor (GIST) response to targeted therapy compared with 18F-fluorodeoxyglucose positron emission tomography/computed tomography (18F-FDG PET/CT). MATERIAL AND METHODS: Eight patients (mean age, 56 ± 11 years) known to have metastatic GIST underwent 18F-FDG PET/CT and MRI (T1Gd, DWI [b = 50,300,600], ADC mapping) simultaneously, before and after change in targeted therapy. MR and PET/CT examinations were first analyzed blindly. Second, PET/CT images were co-registered with T1Gd-MR images for lesion detection. Only 18F-FDG avid lesions were considered. Maximum standardized uptake value (SUVmax) and the corresponding minimum ADCmin were measured for the six largest lesions per patient, if any, on baseline and follow-up examinations. The relationship between changes in SUVmax and ADCmin was analyzed (Spearman's correlation). RESULTS: Twenty-four metastases (12 hepatic, 12 extra-hepatic) were compared on PET/CT and MR images. SUVmax decreased from 7.7 ± 8.1 g/mL to 5.5 ± 5.4 g/mL (P = 0.20), while ADCmin increased from 1.2 ± 0.3 × 10(-3)mm(2)/s to 1.5 ± 0.3 × 10(-3)mm(2)/s (P = 0.0002). There was a significant association between changes in SUVmax and ADCmin (rho = - 0.62, P = 0.0014), but not between changes in lesions size (P = 0.40). CONCLUSION: Changes in ADCmin correlated with the response of 18F-FDG avid GIST to targeted therapy. Thus, diffusion-weighted MRI may represent a radiation-free alternative for follow-up treatment for metastatic GIST patients.

Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging.

Methods are presented to map complex fiber architectures in tissues by imaging the 3D spectra of tissue water diffusion with MR. First, theoretical considerations show why and under what conditions diffusion contrast is positive. Using this result, spin displacement spectra that are conventionally phase-encoded can be accurately reconstructed by a Fourier transform of the measured signal's modulus. Second, studies of in vitro and in vivo samples demonstrate correspondence between the orientational maxima of the diffusion spectrum and those of the fiber orientation density at each location. In specimens with complex muscular tissue, such as the tongue, diffusion spectrum images show characteristic local heterogeneities of fiber architectures, including angular dispersion and intersection. Cerebral diffusion spectra acquired in normal human subjects resolve known white matter tracts and tract intersections. Finally, the relation between the presented model-free imaging technique and other available diffusion MRI schemes is discussed.

3-d residual eddy current field characterisation: applied to diffusion weighted magnetic resonance imaging.

Clinical use of the Stejskal-Tanner diffusion weighted images is hampered by the geometric distortions that result from the large residual 3-D eddy current field induced. In this work, we aimed to predict, using linear response theory, the residual 3-D eddy current field required for geometric distortion correction based on phantom eddy current field measurements. The predicted 3-D eddy current field induced by the diffusion-weighting gradients was able to reduce the root mean square error of the residual eddy current field to ~1 Hz. The model's performance was tested on diffusion weighted images of four normal volunteers, following distortion correction, the quality of the Stejskal-Tanner diffusion-weighted images was found to have comparable quality to image registration based corrections (FSL) at low b-values. Unlike registration techniques the correction was not hindered by low SNR at high b-values, and results in improved image quality relative to FSL. Characterization of the 3-D eddy current field with linear response theory enables the prediction of the 3-D eddy current field required to correct eddy current induced geometric distortions for a wide range of clinical and high b-value protocols.

Diffusion spectrum magnetic resonance imaging (DSI) tractography of crossing fibers.

MRI tractography is the mapping of neural fiber pathways based on diffusion MRI of tissue diffusion anisotropy. Tractography based on diffusion tensor imaging (DTI) cannot directly image multiple fiber orientations within a single voxel. To address this limitation, diffusion spectrum MRI (DSI) and related methods were developed to image complex distributions of intravoxel fiber orientation. Here we demonstrate that tractography based on DSI has the capacity to image crossing fibers in neural tissue. DSI was performed in formalin-fixed brains of adult macaque and in the brains of healthy human subjects. Fiber tract solutions were constructed by a streamline procedure, following directions of maximum diffusion at every point, and analyzed in an interactive visualization environment (TrackVis). We report that DSI tractography accurately shows the known anatomic fiber crossings in optic chiasm, centrum semiovale, and brainstem; fiber intersections in gray matter, including cerebellar folia and the caudate nucleus; and radial fiber architecture in cerebral cortex. In contrast, none of these examples of fiber crossing and complex structure was identified by DTI analysis of the same data sets. These findings indicate that DSI tractography is able to image crossing fibers in neural tissue, an essential step toward non-invasive imaging of connectional neuroanatomy.

From lattice-gas models to nonlinear diffusion models: A derivation of macroscopic equations and fluctuations

We derive nonlinear diffusion equations and equations containing corrections due to fluctuations for a coarse-grained concentration field. To deal with diffusion coefficients with an explicit dependence on the concentration values, we generalize the Van Kampen method of expansion of the master equation to field variables. We apply these results to the derivation of equations of phase-separation dynamics and interfacial growth instabilities.