A lagrangian formulation for statistical fluid registration

We defined a new statistical fluid registration method with Lagrangian mechanics. Although several authors have suggested that empirical statistics on brain variation should be incorporated into the registration problem, few algorithms have included this information and instead use regularizers that guarantee diffeomorphic mappings. Here we combine the advantages of a large-deformation fluid matching approach with empirical statistics on population variability in anatomy. We reformulated the Riemannian fluid algorithmdeveloped in [4], and used a Lagrangian framework to incorporate 0 th and 1st order statistics in the regularization process. 92 2D midline corpus callosum traces from a twin MRI database were fluidly registered using the non-statistical version of the algorithm (algorithm 0), giving initial vector fields and deformation tensors. Covariance matrices were computed for both distributions and incorporated either separately (algorithm 1 and algorithm 2) or together (algorithm 3) in the registration. We computed heritability maps and two vector and tensorbased distances to compare the power and the robustness of the algorithms.

A nonconservative Lagrangian framework for statistical fluid registration - SAFIRA

In this paper, we used a nonconservative Lagrangian mechanics approach to formulate a new statistical algorithm for fluid registration of 3-D brain images. This algorithm is named SAFIRA, acronym for statistically-assisted fluid image registration algorithm. A nonstatistical version of this algorithm was implemented, where the deformation was regularized by penalizing deviations from a zero rate of strain. In, the terms regularizing the deformation included the covariance of the deformation matrices Σ and the vector fields (q). Here, we used a Lagrangian framework to reformulate this algorithm, showing that the regularizing terms essentially allow nonconservative work to occur during the flow. Given 3-D brain images from a group of subjects, vector fields and their corresponding deformation matrices are computed in a first round of registrations using the nonstatistical implementation. Covariance matrices for both the deformation matrices and the vector fields are then obtained and incorporated (separately or jointly) in the nonconservative terms, creating four versions of SAFIRA. We evaluated and compared our algorithms' performance on 92 3-D brain scans from healthy monozygotic and dizygotic twins; 2-D validations are also shown for corpus callosum shapes delineated at midline in the same subjects. After preliminary tests to demonstrate each method, we compared their detection power using tensor-based morphometry (TBM), a technique to analyze local volumetric differences in brain structure. We compared the accuracy of each algorithm variant using various statistical metrics derived from the images and deformation fields. All these tests were also run with a traditional fluid method, which has been quite widely used in TBM studies. The versions incorporating vector-based empirical statistics on brain variation were consistently more accurate than their counterparts, when used for automated volumetric quantification in new brain images. This suggests the advantages of this approach for large-scale neuroimaging studies.

Fluid registration of diffusion tensor images using information theory

We apply an information-theoretic cost metric, the symmetrized Kullback-Leibler (sKL) divergence, or $J$-divergence, to fluid registration of diffusion tensor images. The difference between diffusion tensors is quantified based on the sKL-divergence of their associated probability density functions (PDFs). Three-dimensional DTI data from 34 subjects were fluidly registered to an optimized target image. To allow large image deformations but preserve image topology, we regularized the flow with a large-deformation diffeomorphic mapping based on the kinematics of a Navier-Stokes fluid. A driving force was developed to minimize the $J$-divergence between the deforming source and target diffusion functions, while reorienting the flowing tensors to preserve fiber topography. In initial experiments, we showed that the sKL-divergence based on full diffusion PDFs is adaptable to higher-order diffusion models, such as high angular resolution diffusion imaging (HARDI). The sKL-divergence was sensitive to subtle differences between two diffusivity profiles, showing promise for nonlinear registration applications and multisubject statistical analysis of HARDI data.

Quantitative genetic modeling of lateral ventricular shape and volume using multi-atlas fluid image alignment in twins

Despite substantial progress in measuring the 3D profile of anatomical variations in the human brain, their genetic and environmental causes remain enigmatic. We developed an automated system to identify and map genetic and environmental effects on brain structure in large brain MRI databases . We applied our multi-template segmentation approach ("Multi-Atlas Fluid Image Alignment") to fluidly propagate hand-labeled parameterized surface meshes into 116 scans of twins (60 identical, 56 fraternal), labeling the lateral ventricles. Mesh surfaces were averaged within subjects to minimize segmentation error. We fitted quantitative genetic models at each of 30,000 surface points to measure the proportion of shape variance attributable to (1) genetic differences among subjects, (2) environmental influences unique to each individual, and (3) shared environmental effects. Surface-based statistical maps revealed 3D heritability patterns, and their significance, with and without adjustments for global brain scale. These maps visualized detailed profiles of environmental versus genetic influences on the brain, extending genetic models to spatially detailed, automatically computed, 3D maps.

Improving fluid registration through white matter segmentation in a twin study design

Robust and automatic non-rigid registration depends on many parameters that have not yet been systematically explored. Here we determined how tissue classification influences non-linear fluid registration of brain MRI. Twin data is ideal for studying this question, as volumetric correlations between corresponding brain regions that are under genetic control should be higher in monozygotic twins (MZ) who share 100% of their genes when compared to dizygotic twins (DZ) who share half their genes on average. When these substructure volumes are quantified using tensor-based morphometry, improved registration can be defined based on which method gives higher MZ twin correlations when compared to DZs, as registration errors tend to deplete these correlations. In a study of 92 subjects, higher effect sizes were found in cumulative distribution functions derived from statistical maps when performing tissue classification before fluid registration, versus fluidly registering the raw images. This gives empirical evidence in favor of pre-segmenting images for tensor-based morphometry.

Automated ventricular mapping with multi-atlas fluid image alignment reveals genetic effects in Alzheimer's disease

We developed and validated a new method to create automated 3D parametric surface models of the lateral ventricles in brain MRI scans, providing an efficient approach to monitor degenerative disease in clinical studies and drug trials. First, we used a set of parameterized surfaces to represent the ventricles in four subjects' manually labeled brain MRI scans (atlases). We fluidly registered each atlas and mesh model to MRIs from 17 Alzheimer's disease (AD) patients and 13 age- and gender-matched healthy elderly control subjects, and 18 asymptomatic ApoE4-carriers and 18 age- and gender-matched non-carriers. We examined genotyped healthy subjects with the goal of detecting subtle effects of a gene that confers heightened risk for Alzheimer's disease. We averaged the meshes extracted for each 3D MR data set, and combined the automated segmentations with a radial mapping approach to localize ventricular shape differences in patients. Validation experiments comparing automated and expert manual segmentations showed that (1) the Hausdorff labeling error rapidly decreased, and (2) the power to detect disease- and gene-related alterations improved, as the number of atlases, N, was increased from 1 to 9. In surface-based statistical maps, we detected more widespread and intense anatomical deficits as we increased the number of atlases. We formulated a statistical stopping criterion to determine the optimal number of atlases to use. Healthy ApoE4-carriers and those with AD showed local ventricular abnormalities. This high-throughput method for morphometric studies further motivates the combination of genetic and neuroimaging strategies in predicting AD progression and treatment response. © 2007 Elsevier Inc. All rights reserved.

Automated 3D mapping & shape analysis of the lateral ventricles via fluid registration of multiple surface-based atlases

We developed and validated a new method to create automated 3D parametric surface models of the lateral ventricles, designed for monitoring degenerative disease effects in clinical neuroscience studies and drug trials. First we used a set of parameterized surfaces to represent the ventricles in a manually labeled set of 9 subjects' MRIs (atlases). We fluidly registered each of these atlases and mesh models to a set of MRIs from 12 Alzheimer's disease (AD) patients and 14 matched healthy elderly subjects, and we averaged the resulting meshes for each of these images. Validation experiments on expert segmentations showed that (1) the Hausdorff labeling error rapidly decreased, and (2) the power to detect disease-related alterations monotonically improved as the number of atlases, N, was increased from 1 to 9. We then combined the segmentations with a radial mapping approach to localize ventricular shape differences in patients. In surface-based statistical maps, we detected more widespread and intense anatomical deficits as we increased the number of atlases, and we formulated a statistical stopping criterion to determine the optimal value of N. Anterior horn anomalies in Alzheimer's patients were only detected with the multi-atlas segmentation, which clearly outperformed the standard single-atlas approach.

Double diffusive Marangoni convection flow of electrically conducting fluid in a square cavity with chemical reaction

Double diffusive Marangoni convection flow of viscous incompressible electrically conducting fluid in a square cavity is studied in this paper by taking into consideration of the effect of applied magnetic field in arbitrary direction and the chemical reaction. The governing equations are solved numerically by using alternate direct implicit (ADI) method together with the successive over relaxation (SOR) technique. The flow pattern with the effect of governing parameters, namely the buoyancy ratio W, diffusocapillary ratio w, and the Hartmann number Ha, is investigated. It is revealed from the numerical simulations that the average Nusselt number decreases; whereas the average Sherwood number increases as the orientation of magnetic field is shifted from horizontal to vertical. Moreover, the effect of buoyancy due to species concentration on the flow is stronger than the one due to thermal buoyancy. The increase in diffusocapillary parameter, w caus

Geochronological (U–Pb, U–Th–total Pb, Sm–Nd) and geochemical (REE, 87Sr/86Sr, δ18O, δ13C) tracing of intraplate tectonism and associated fluid flow in the Warburton Basin, Australia

The Warburton Basin of central Australia has experienced a complex tectonic and fluid-flow history, resulting in the formation of various authigenic minerals. Geochemical and geochronological analyses were undertaken on vein carbonates from core samples of clastic sediments. Results were then integrated with zircon U–Pb dating and uraninite U–Th–total Pb dating from the underlying granite. Stable and radiogenic isotopes (δ18O, Sr and εNd), as well as trace element data of carbonate veins indicate that >200 °C basinal fluids of evolved meteoric origin circulated through the Warburton Basin. Almost coincidental ages of these carbonates (Sm–Nd; 432 ± 12 Ma) with primary zircon (421 ± 3.8 Ma) and uraninite (407 ± 16 Ma) ages from the granitic intrusion point towards a substantial period of active tectonism and an elevated thermal regime during the mid Silurian. We hypothesise that such a thermal regime may have resulted from extensional tectonism and concomitant magmatic activity following regional orogenesis. This study shows that the combined application of geochemical and geochronological analyses of both primary and secondary species may constrain the timing of tectonomagmatic events and associated fluid flow in intraplate sedimentary basins. Furthermore, this work suggests that the Sm–Nd-isotopic system is surprisingly robust and can record geologically meaningful age data from hydrothermal mineral species.

Unsteady-Flow Of A Viscous-Fluid Between 2 Parallel Disks With A Time-Varying Gap Width And A Magnetic-Field

The unsteady incompressible viscous fluid flow between two parallel infinite disks which are located at a distance h(t*) at time t* has been studied. The upper disk moves towards the lower disk with velocity h'(t*). The lower disk is porous and rotates with angular velocity Omega(t*). A magnetic field B(t*) is applied perpendicular to the two disks. It has been found that the governing Navier-Stokes equations reduce to a set of ordinary differential equations if h(t*), a(t*) and B(t*) vary with time t* in a particular manner, i.e. h(t*) = H(1 - alpha t*)(1/2), Omega(t*) = Omega(0)(1 - alpha t*)(-1), B(t*) = B-0(1 - alpha t*)(-1/2). These ordinary differential equations have been solved numerically using a shooting method. For small Reynolds numbers, analytical solutions have been obtained using a regular perturbation technique. The effects of squeeze Reynolds numbers, Hartmann number and rotation of the disk on the flow pattern, normal force or load and torque have been studied in detail

Experiments on a plume with off-source heating: Implications for cloud fluid dynamics

We report here on a series of laboratory experiments on plumes, undertaken with the object of simulating the effect of the heat release that occurs in clouds on condensation of water vapor. The experimental technique used for this purpose relies on ohmic heating generated in an electrically conducting plume fluid subjected to a suitable alternating voltage across specified axial stations in the plume flow [Bhat et al., 1989]. The present series of experiments achieves a value of the Richardson number that is toward the lower end of the range that characteristics cumulus clouds. It is found that the buoyancy enhancement due to heating disrupts the eddy structures in the flow and reduces the dilution owing to entrainment of ambient fluid that would otherwise have occurred in the central region of the plume. Heating also reduces the spread rate of the plume, but as it accelerates the flow as well, the overall specific mass flux in the plume does not show a very significant change at the heat input employed in the experiment. However, there is some indication that the entrainment rate (proportional to the streamwise derivative of the mass flux) is slightly higher immediately after heat injection and slightly lower farther downstream. The measurements support a previous proposal for a cloud scenario [Bhat and Narasimha, 1996] and demonstrate how fresh insights into certain aspects of the fluid dynamics of clouds may be derived from the experimental techniques employed here.

Unsteady flow over a stretching surface with a magnetic field in a rotating fluid

The effect of the magnetic field on the unsteady flow over a stretching surface in a rotating fluid has been studied. The unsteadiness in the flow field is due to the time-dependent variation of the velocity of the stretching surface and the angular velocity of the rotating fluid. The Navier-Stokes equations and the energy equation governing the flow and the heat transfer admit a self-similar solution if the velocity of the stretching surface and the angular velocity of the rotating fluid vary inversely as a linear function of time. The resulting system of ordinary differential equations is solved numerically using a shooting method. The rotation parameter causes flow reversal in the component of the velocity parallel to the strerching surface and the magnetic field tends to prevent or delay the flow reversal. The surface shear stresses dong the stretching surface and in the rotating direction increase with the rotation parameter, but the surface heat transfer decreases. On the other hand, the magnetic field increases the surface shear stress along the stretching surface, but reduces the surface shear stress in the rotating direction and the surface heat transfer. The effect of the unsteady parameter is more pronounced on the velocity profiles in the rotating direction and temperature profiles.

Dynamics of a dilute sheared inelastic fluid. I. Hydrodynamic modes and velocity correlation functions

The hydrodynamic modes and the velocity autocorrelation functions for a dilute sheared inelastic fluid are analyzed using an expansion in the parameter epsilon=(1-e)(1/2), where e is the coefficient of restitution. It is shown that the hydrodynamic modes for a sheared inelastic fluid are very different from those for an elastic fluid in the long-wave limit, since energy is not a conserved variable when the wavelength of perturbations is larger than the ``conduction length.'' In an inelastic fluid under shear, there are three coupled modes, the mass and the momenta in the plane of shear, which have a decay rate proportional to k(2/3) in the limit k -> 0, if the wave vector has a component along the flow direction. When the wave vector is aligned along the gradient-vorticity plane, we find that the scaling of the growth rate is similar to that for an elastic fluid. The Fourier transforms of the velocity autocorrelation functions are calculated for a steady shear flow correct to leading order in an expansion in epsilon. The time dependence of the autocorrelation function in the long-time limit is obtained by estimating the integral of the Fourier transform over wave number space. It is found that the autocorrelation functions for the velocity in the flow and gradient directions decay proportional to t(-5/2) in two dimensions and t(-15/4) in three dimensions. In the vorticity direction, the decay of the autocorrelation function is proportional to t(-3) in two dimensions and t(-7/2) in three dimensions.

Dynamics of a dilute sheared inelastic fluid. II. The effect of correlations

The effect of correlations on the viscosity of a dilute sheared inelastic fluid is analyzed using the ring-kinetic equation for the two-particle correlation function. The leading-order contribution to the stress in an expansion in epsilon=(1-e)(1/2) is calculated, and it is shown that the leading-order viscosity is identical to that obtained from the Green-Kubo formula, provided the stress autocorrelation function in a sheared steady state is used in the Green-Kubo formula. A systemmatic extension of this to higher orders is also formulated, and the higher-order contributions to the stress from the ring-kinetic equation are determined in terms of the terms in the Chapman-Enskog solution for the Boltzmann equation. The series is resummed analytically to obtain a renormalized stress equation. The most dominant contributions to the two-particle correlation function are products of the eigenvectors of the conserved hydrodynamic modes of the two correlated particles. In Part I, it was shown that the long-time tails of the velocity autocorrelation function are not present in a sheared fluid. Using those results, we show that correlations do not cause a divergence in the transport coefficients; the viscosity is not divergent in two dimensions, and the Burnett coefficients are not divergent in three dimensions. The equations for three-particle and higher correlations are analyzed diagrammatically. It is found that the contributions due to the three-particle and higher correlation functions to the renormalized viscosity are smaller than those due to the two-particle distribution function in the limit epsilon -> 0. This implies that the most dominant correlation effects are due to the two-particle correlations.

A follow up MRI-based geometry and computational fluid dynamics study of carotid bifurcation

Cardiovascular disease is the leading causes of death in the developed world. Wall shear stress (WSS) is associated with the initiation and progression of atherogenesis. This study combined the recent advances in MR imaging and computational fluid dynamics (CFD) and evaluated the patient-specific carotid bifurcation. The patient was followed up for 3 years. The geometry changes (tortuosity, curvature, ICA/CCA area ratios, central to the cross-sectional curvature, maximum stenosis) and the CFD factors (Velocity distribute, Wall Shear Stress (WSS) and Oscillatory Shear Index (OSI)) were compared at different time points.The carotid stenosis was a slight increase in the central to the cross-sectional curvature, and it was minor and variable curvature changes for carotid centerline. The OSI distribution presents ahigh-values in the same region where carotid stenosis and normal border, indicating complex flow and recirculation.The significant geometric changes observed during the follow-up may also cause significant changes in bifurcation hemodynamics.