multimodality image registration by maximization of mutual information a new approach to the problem of multimodality medical image registration is proposed using a basic concept from information theory mutual information mi or relative entropy as a new matching criterion the method presented in this paper applies mi to measure the statistical dependence or information redundancy between the image intensities of corresponding voxels in both images which is assumed to be maximal if the images are geometrically aligned maximization of mi is a very general and powerful criterion because no assumptions are made regarding the nature of this dependence and no limiting constraints are imposed on the image content of the modalities involved the accuracy of the mi criterion is validated for rigid body registration of computed tomography ct magnetic resonance mr and photon emission tomography pet images by comparison with the stereotactic registration solution while robustness is evaluated with respect to implementation issues such as interpolation and optimization and image content including partial overlap and image degradation our results demonstrate that subvoxel accuracy with respect to the stereotactic reference solution can be achieved completely automatically and without any prior segmentation feature extraction or other preprocessing steps which makes this method very well suited for clinical applications

finite element methods for active contour models and balloons for 2 d and 3 d images the use of energy minimizing curves known as snakes to extract features of interest in images has been introduced by kass witkin and terzopoulos 1987 a balloon model was introduced by cohen 1991 as a way to generalize and solve some of the problems encountered with the original method a 3 d generalization of the balloon model as a 3 d deformable surface which evolves in 3 d images is presented it is deformed under the action of internal and external forces attracting the surface toward detected edgels by means of an attraction potential we also show properties of energy minimizing surfaces concerning their relationship with 3 d edge points to solve the minimization problem for a surface two simplified approaches are shown first defining a 3 d surface as a series of 2 d planar curves then after comparing finite element method and finite difference method in the 2 d problem we solve the 3 d model using the finite element method yielding greater stability and faster convergence this model is applied for segmenting magnetic resonance images

a smooth transition model between kinetic and diffusion equations this paper presents a model which provides a smooth transition between a kinetic and a diffusion domain the idea is to use a buffer zone in which both diffusion and kinetic equations will be solved the solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations we use an artificial connecting function which makes the equation on each domain degenerate at the end of the buffer zone thus no boundary condition is needed at the transition point this model avoids the delicate issue of finding the interface condition or iteration in a typical domain decomposition method that couples a kinetic equation with hydrodynamic equations a new asymptotic preserving method for this model is introduced and numerical examples are used to validate this new model and the new numerical method

stabilization to equilibria of compressible navier stokes equations with infinite mass we consider the compressible navier stokes equations in an exterior three dimensional domain with non zero constant density prescribed at infinity we assume that p r r c c 32 and that the force is potential we show that for time tending to infinity the density approaches the unique solution to the stationary problem provided the potential satisfies certain regularity and structural assumptions

cortical thickness analysis in autism with heat kernel smoothing we present a novel data smoothing and analysis framework for cortical thickness data defined on the brain cortical manifold gaussian kernel smoothing which weights neighboring observations according to their 3d euclidean distance has been widely used in 3d brain images to increase the signal to noise ratio when the observations lie on a convoluted brain surface however it is more natural to assign the weights based on the geodesic distance along the surface we therefore develop a framework for geodesic distance based kernel smoothing and statistical analysis on the cortical manifolds as an illustration we apply our methods in detecting the regions of abnormal cortical thickness in 16 high functioning autistic children via random field based multiple comparison correction that utilizes the new smoothing technique

strong convergence to global solutions for multidimensional flows of compressible viscous fluids with polytropic equations of state and discontinuous initial data we extend to general polytropic pressures p k 1 the existence theory of 8 for isothermal 1 flows of navier stokes fluids in two and three space dimensions with fairly general initial data specifically we require that the initial density be close to a constant in l2 and l and that the initial velocity be small in l2 and bounded in l2n in two dimensions the l2 norms must be weighted slightly solutions are obtained as limits of approximate solutions corresponding to mollified initial data the key point is that the approximate densities are shown to converge strongly so that nonlinear pressures can be accommodated even in the absence of any uniform regularity information for the approximate densities

local well posedness to the cauchy problem of the 2d compressible navier stokes smoluchowski equations with vacuum abstract this paper concerns the local strong solution to the compressible navier stokes smoluchowski equations with vacuum as far field density on the whole space r 2 without additional cho choe kim type compatibility conditions which provided the initial density and the initial particles density decay not too slow at infinity in particular we extend the results of ding et al 2016 13 and yang 2020 24 to the 2d case

cortical thickness analysis examined through power analysis and a population simulation we have previously developed a procedure for measuring the thickness of cerebral cortex over the whole brain using 3 d mri data and a fully automated surface extraction asp algorithm this paper examines the precision of this algorithm its optimal performance parameters and the sensitivity of the method to subtle focal changes in cortical thickness the precision of cortical thickness measurements was studied using a simulated population study and single subject reproducibility metrics cortical thickness was shown to be a reliable method reaching a sensitivity probability of a true positive of 0 93 six different cortical thickness metrics were compared the simplest and most precise method measures the distance between corresponding vertices from the white matter to the gray matter surface given two groups of 25 subjects a 0 6 mm 15 change in thickness can be recovered after blurring with a 3 d gaussian kernel full width half max 30 mm smoothing across the 2 d surface manifold also improves precision in this experiment the optimal kernel size was 30 mm

optimal surface segmentation in volumetric images a graph theoretic approach efficient segmentation of globally optimal surfaces representing object boundaries in volumetric data sets is important and challenging in many medical image analysis applications we have developed an optimal surface detection method capable of simultaneously detecting multiple interacting surfaces in which the optimality is controlled by the cost functions designed for individual surfaces and by several geometric constraints defining the surface smoothness and interrelations the method solves the surface segmentation problem by transforming it into computing a minimum s hbox t cut in a derived arc weighted directed graph the proposed algorithm has a low order polynomial time complexity and is computationally efficient it has been extensively validated on more than 300 computer synthetic volumetric images 72 ct scanned data sets of different sized plexiglas tubes and tens of medical images spanning various imaging modalities in all cases the approach yielded highly accurate results our approach can be readily extended to higher dimensional image segmentation

a stochastic model for studying the laminar structure of cortex from mri the human cerebral cortex is a laminar structure about 3 mm thick and is easily visualized with current magnetic resonance mr technology the thickness of the cortex varies locally by region and is likely to be influenced by such factors as development disease and aging thus accurate measurements of local cortical thickness are likely to be of interest to other researchers we develop a parametric stochastic model relating the laminar structure of local regions of the cerebral cortex to mr image data parameters of the model include local thickness and statistics describing white gray and cerebrospinal fluid csf image intensity values as a function of the normal distance from the center of a voxel to a local coordinate system anchored at the gray white matter interface our fundamental data object the intensity distance histogram idh is a two dimensional 2 d generalization of the conventional 1 d image intensity histogram which indexes voxels not only by their intensity value but also by their normal distance to the gray white interface we model the idh empirically as a marked poisson process with marking process a gaussian random field model of image intensity indexed against normal distance in this paper we relate the parameters of the idh model to the local geometry of the cortex a maximum likelihood framework estimates the parameters of the model from the data here we show estimates of these parameters for 10 volumes in the posterior cingulate and 6 volumes in the anterior and posterior banks of the central sulcus the accuracy of the estimates is quantified via cramer rao bounds we believe that this relatively crude model can be extended in a straightforward fashion to other biologically and theoretically interesting problems such as segmentation surface area estimation and estimating the thickness distribution in a variety of biologically relevant contexts

geometrically accurate topology correction of cortical surfaces using nonseparating loops in this paper we focus on the retrospective topology correction of surfaces we propose a technique to accurately correct the spherical topology of cortical surfaces specifically we construct a mapping from the original surface onto the sphere to detect topological defects as minimal nonhomeomorphic regions the topology of each defect is then corrected by opening and sealing the surface along a set of nonseparating loops that are selected in a bayesian framework the proposed method is a wholly self contained topology correction algorithm which determines geometrically accurate topologically correct solutions based on the magnetic resonance imaging mri intensity profile and the expected local curvature applied to real data our method provides topological corrections similar to those made by a trained operator

age related changes in the surface morphology of the central sulcus abstract we utilized a sulcus based computational approach to investigate the relationship between the three dimensional 3d morphology of the central sulcus cs and age the anterior and posterior walls of the cs were manually outlined using high resolution magnetic resonance images of 295 right handed healthy participants age range 18 94 years surface reconstruction and parameterization methods were employed to create anatomical correspondence of surface locations across participants four surface metrics including average sulcal length sl surface area fractal dimension fd and sulcal span were used to represent the 3d morphology of the cs we found significant age related decreases in the surface area for all walls of the cs the sl for posterior walls of the cs and the fd for posterior wall of right cs age related increases were found in the sulcal spans between the anterior and posterior walls these surface metrics except fd exhibited leftward asymmetries specifically age related changes in surface morphology progressed more rapidly in the posterior than in the anterior walls finally sex differences were found only in the fd of the right anterior wall of the cs taken together our results show age related changes in the surface morphology of the cs and therefore provide insights into the normal aging process

asymptotic induced domain decomposition methods for kinetic and drift diffusion semiconductor equations this paper deals with domain decomposition methods for kinetic and drift diffusion semiconductor equations in particular accurate coupling conditions at the interface between the kinetic and drift diffusion domain are given the cases of slight and strong nonequilibrium situations at the interface are considered and numerical examples are shown

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

feature based statistical analysis of structural mr data for automatic detection of focal cortical dysplastic lesions this paper presents a method for fully automated detection and localization of focal cortical dysplastic fcd lesions from anatomical magnetic resonance mr images of the human brain model based tissue classification of the image under study was applied first such that a gray matter gm segmentation map is obtained of which we demonstrate that it also includes possible fcd lesions cortical thickness was estimated at each voxel using an appropriate distance transform applied to the binarized gm object and an fcd specific feature map was constructed by computing the ratio of cortical thickness over absolute image intensity gradient at each voxel in absence of any prior anatomical hypothesis on the spatial location of the lesion a statistical parameter map was constructed by evaluating the evidence for each gray matter voxel against the null hypothesis of no difference in the feature map of the patient versus similar maps obtained for a group of normal controls voxel clusters for which the null hypothesis was found to be improbable at optimally selected thresholds for cluster height and extent were reported as lesions the method was applied to a surgical series of 17 fcd patient images that were compared against a group of 64 neurologically normal controls the method correctly detected and located the fcd lesion in 9 out of 17 fcd cases 53 using a threshold that minimized false positives and 12 of 17 71 using a threshold that allowed more false positive results the detected lesions had a median volume of 7 2 cm3 versus 2 9 cm3 for the non detected lesions the detected lesions more often had an increased cortical thickness on t1 than the non detected lesions p 0 015 fisher s exact test due to a high variance of the feature maps in the temporal lobes and insula detection of fcd lesions in these regions appeared more difficult than in other brain regions with lower variance

decay estimates for isentropic compressible navier stokes equations in bounded domain abstract in this paper under the hypothesis that is upper bounded we construct a lyapunov functional for the multidimensional isentropic compressible navier stokes equations and show that the weak solutions decay exponentially to the equilibrium state in l 2 norm this can be regarded as a generalization of matsumura and nishida s results a matsumura t nishida in computing methods in applied sciences and engineering vol v 1982 pp 389 406 since our analysis is done in the framework of lions p l lions oxford science publication 1998 and feireisl et al e fereisl a novotny h petzeltova j math fluid mech 3 2001 358 392 the higher regularity of u and the uniformly positive lower bound of are not necessary in our analysis and vacuum may be admitted indeed the upper bound of the density plays the essential role in our proof

global well posedness of classical solutions with large oscillations and vacuum to the three dimensional isentropic compressible navier stokes equations we establish the global existence and uniqueness of classical solutions to the cauchy problem for the isentropic compressible navier stokes equations in three spatial dimensions with smooth initial data that are of small energy but possibly large oscillations with constant state as far field which could be either vacuum or nonvacuum the initial density is allowed to vanish and the spatial measure of the set of vacuum can be arbitrarily large in particular the initial density can even have compact support these results generalize previous results on classical solutions for initial densities being strictly away from vacuum and are the first for global classical solutions that may have large oscillations and can contain vacuum states 2012 wiley periodicals inc

convergence and divergence of thickness correlations with diffusion connections across the human cerebral cortex cortical thickness correlation across individuals has been observed so far it remains unclear to what extent such a correlation in thickness is a reflection of underlying fiber connection here we explicitly compared the patterns of cortical thickness correlation and diffusion based fiber connection across the entire cerebral cortex in 95 normal adults interregional thickness correlations were extracted by using computational neuroanatomy algorithms based on structural mri and diffusion connections were detected by using diffusion probabilistic tractography approximately 35 40 of thickness correlations showed convergent diffusion connections across the cerebral cortex intriguingly the observed convergences between thickness correlation and diffusion connection are mostly focused on the positive thickness correlations while almost all of the negative correlations 90 did not have a matched diffusion connection suggesting different mechanisms behind the positive and negative thickness correlations the latter not being mediated by a direct fiber pathway furthermore graph theoretic analysis reveals that the thickness correlation network has a more randomized overall topology whereas the nodal characteristics of cortical regions in these two networks are statistically correlated these findings indicate that thickness correlations partly reflect underlying fiber connections but they contains exclusive information and therefore should not be simply taken as a proxy measure for fiber connections

universal dynamics for the defocusing logarithmic schrodinger equation we consider the nonlinear schrodinger equation with a logarithmic nonlinearity in a dispersive regime we show that the presence of the nonlinearity affects the large time behavior of the solution the dispersion is faster than usual by a logarithmic factor in time and the positive sobolev norms of the solution grow logarithmically in time moreover after rescaling in space by the dispersion rate the modulus of the solution converges to a universal gaussian profile these properties are suggested by explicit computations in the case of gaussian initial data and remain when an extra power like nonlinearity is present in the equation one of the key steps of the proof consists in using the madelung transform to reduce the equation to a variant of the isothermal compressible euler equation whose large time behavior turns out to be governed by a parabolic equation involving a fokker planck operator

efficient asymptotic preserving ap schemes for some multiscale kinetic equations many kinetic models of the boltzmann equation have a diffusive scaling that leads to the navier stokes type parabolic equations as the small scaling parameter approaches zero in practical applications it is desirable to develop a class of numerical schemes that can work uniformly with respect to this relaxation parameter from the rarefied kinetic regimes to the hydrodynamic diffusive regimes an earlier approach in s jin l pareschi and g toscani siam j numer anal 35 1998 pp 2405 2439 reformulates such systems into the common hyperbolic relaxation system by jin and xin for hyperbolic conservation laws used to construct the relaxation schemes and then uses a multistep time splitting method to solve the relaxation system here we observe that the combination of the two time split steps may yield hyperbolic parabolic systems that are more advantageous in both stability and efficiency for numerical computations we show that such an approach yields a class of asymptotic preserving ap schemes which are suitable for the computation of multiscale kinetic problems we use the goldstein taylor and carleman models to illustrate this approach

automated 3 d extraction and evaluation of the inner and outer cortical surfaces using a laplacian map and partial volume effect classification accurate reconstruction of the inner and outer cortical surfaces of the human cerebrum is a critical objective for a wide variety of neuroimaging analysis purposes including visualization morphometry and brain mapping the anatomic segmentation using proximity asp algorithm previously developed by our group provides a topology preserving cortical surface deformation method that has been extensively used for the aforementioned purposes however constraints in the algorithm to ensure topology preservation occasionally produce incorrect thickness measurements due to a restriction in the range of allowable distances between the gray and white matter surfaces this problem is particularly prominent in pediatric brain images with tightly folded gyri this paper presents a novel method for improving the conventional asp algorithm by making use of partial volume information through probabilistic classification in order to allow for topology preservation across a less restricted range of cortical thickness values the new algorithm also corrects the classification of the insular cortex by masking out subcortical tissues for 70 pediatric brains validation experiments for the modified algorithm constrained laplacian asp clasp were performed by three methods i volume matching between surface masked gray matter gm and conventional tissue classified gm ii surface matching between simulated and clasp extracted surfaces and iii repeatability of the surface reconstruction among 16 mri scans of the same subject in the volume based evaluation the volume enclosed by the clasp wm and gm surfaces matched the classified gm volume 13 more accurately than using conventional asp in the surface based evaluation using synthesized thick cortex the average difference between simulated and extracted surfaces was 4 6 t 1 4 mm for conventional asp and 0 5 t 0 4 mm for clasp in a repeatability study clasp produced a 30 lower rms error for the gm surface and a 8 lower rms error for the

combining anatomical manifold information via diffeomorphic metric mappings for studying cortical thinning of the cingulate gyrus in schizophrenia spatial normalization is a crucial step in assessing patterns of neuroanatomical structure and function associated with health and disease errors that occur during spatial normalization can influence hypothesis testing due to the dimensionalities of mapping algorithms and anatomical manifolds landmarks curves surfaces volumes used to drive the mapping algorithms the primary aim of this paper is to improve statistical inference using multiple anatomical manifolds and large deformation diffeomorphic metric mapping lddmm algorithms we propose that combining information generated by the various manifolds and algorithms improves the reliability of hypothesis testing we used this unified approach to assess variation in the thickness of the cingulate gyrus in subjects with schizophrenia and healthy comparison subjects three different lddmm algorithms for mapping landmarks curves and triangulated meshes were used to transform thickness maps of the cingulate surfaces into an atlas coordinate system we then tested for group differences by combining the information from the three types of anatomical manifolds and lddmm mapping algorithms the unified approach provided reliable statistical results and eliminated ambiguous results due to surface mismatches subjects with schizophrenia had non uniform cortical thinning over the left and right cingulate gyri especially in the anterior portion as compared to

automated 3 d extraction of inner and outer surfaces of cerebral cortex from mri automatic computer processing of large multidimensional images such as those produced by magnetic resonance imaging mri is greatly aided by deformable models which are used to extract identify and quantify specific neuroanatomic structures a general method of deforming polyhedra is presented here with two novel features first explicit prevention of self intersecting surface geometries is provided unlike conventional deformable models which use regularization constraints to discourage but not necessarily prevent such behavior second deformation of multiple surfaces with intersurface proximity constraints allows each surface to help guide other surfaces into place using model based constraints such as expected thickness of an anatomic surface these two features are used advantageously to identify automatically the total surface of the outer and inner boundaries of cerebral cortical gray matter from normal human mr images accurately locating the depths of the sulci even where noise and partial volume artifacts in the image obscure the visibility of sulci the extracted surfaces are enforced to be simple two dimensional manifolds having the topology of a sphere even though the data may have topological holes this automatic 3 d cortex segmentation technique has been applied to 150 normal subjects simultaneously extracting both the gray white and gray cerebrospinal fluid interface from each individual the collection of surfaces has been used to create a spatial map of the mean and standard deviation for the location and the thickness of cortical gray matter three alternative criteria for defining cortical thickness at each cortical location were developed and compared these results are shown to corroborate published postmortem and in vivo measurements of cortical thickness

a geometry driven optical flow warping for spatial normalization of cortical surfaces spatial normalization is frequently used to map data to a standard coordinate system by removing intersubject morphological differences thereby allowing for group analysis to be carried out the work presented in this paper is motivated by the need for an automated cortical surface normalization technique that will automatically identify homologous cortical landmarks and map them to the same coordinates on a standard manifold the geometry of a cortical surface is analyzed using two shape measures that distinguish the sulcal and gyral regions in a multiscale framework a multichannel optical flow warping procedure aligns these shape measures between a reference brain and a subject brain creating the desired normalization the partial differential equation that carries out the warping is implemented in a euclidean framework in order to facilitate a multiresolution strategy thereby permitting large deformations between the two surfaces the technique is demonstrated by aligning 33 normal cortical surfaces and showing both improved structural alignment in manually labeled sulci and improved functional alignment in positron emission tomography data mapped to the surfaces a quantitative comparison between our proposed surface based spatial normalization method and a leading volumetric spatial normalization method is included to show that the surface based spatial normalization performs better in matching homologous cortical anatomies

global existence and large time behavior of weak solutions to the compressible magnetohydrodynamic equations with coulomb force abstract in this paper we consider the equations of magnetohydrodynamics with coulomb force which is of hyperbolic parabolic elliptic mixed type by constructing the approximate solutions to the modified system with an artificial pressure term added global existence of finite energy weak solutions is established via the weak convergence method more careful argument has been paid to overcome the new difficulty arising from the poisson term of coulomb force in two dimensions when the adiabatic exponent is close to one we also investigate the large time behavior of such weak solutions after discussing the regularity and uniqueness of solutions to the stationary problem

anatomical mapping of functional activation in stereotactic coordinate space numerous applications have been reported for the stereotactic mapping of focal changes in cerebral blood flow during sensory and cognitive activation as measured with positron emission tomography pet subtraction images since these images lack significant anatomical information analysis of these kinds of data has been restricted to an automated search for peaks in the pet subtraction dataset and localization of the peak coordinates within a standardized stereotactic atlas this method is designed to identify isolated foci with dimensions smaller than the image resolution details of activation patterns that may extend over finite distances following the underlying anatomical structures will not be apparent we describe the combined mapping into stereotactic coordinate space of magnetic resonance imaging mri and pet information from each of a set of subjects such that the major features of the activation pattern particularly extended tracts of increased blood flow can be immediately assessed within their true anatomical context as opposed to that presumed using a standard atlas alone near areas of high anatomical variability e g central sulcus or of sharp curvature e g frontal and temporal poles this information can be essential to the localization of a focus to the correct gyrus or for the rejection of extracerebral peaks it also allows for the removal from further analysis of data from cognitively normal subjects with abnormal anatomy such as enlarged ventricles in patients with neuropathology e g alzheimer s disease arteriovenous malformation stroke or neoplasm the use of correlated mri is mandatory for correct localization of functional activation

global solutions of the navier stokes equations for multidimensional compressible flow with discontinuous initial data abstract we prove the global existence of weak solutions of the navier stokes equations for compressible isothermal flow in two and three space dimensions when the initial density is close to a constant in l 2 and l and the initial velocity is small in l 2 and bounded in l 2 n in two dimensions the l 2 norms must be weighted slightly a great deal of qualitative information about the solution is obtained for example we show that the velocity and vorticity are relatively smooth in positive time as is the effective viscous flux f which is the divergence of the velocity minus a certain multiple of the pressure we find that f plays a crucial role in the entire analysis particularly in closing the required energy estimates understanding rates of regularization near the initial layer and most important obtaining time independent pointwise bounds for the density

the initial value problem for the compressible navier stokes equations without heat conductivity abstract in this paper we are concerned with the global existence and convergence rates of strong solutions for the compressible navier stokes equations without heat conductivity in r 3 the global existence and uniqueness of strong solutions are established by the delicate energy method under the condition that the initial data are close to the constant equilibrium state in h 2 framework furthermore if additionally the initial data belong to l 1 the optimal convergence rates of the solutions in l 2 norm and convergence rates of their spatial derivatives in l 2 norm are obtained

on the energy inequality for weak solutions to the navier stokes equations of compressible fluids on unbounded domains abstract we consider the navier stokes equations of compressible isentropic viscous fluids on an unbounded three dimensional domain with a compact lipschitz boundary under the condition that the total mass of the fluid is finite we show the existence of globally defined weak solutions satisfying the energy inequality in differential form

a hybrid method for anisotropic elliptic problems based on the coupling of an asymptotic preserving method with the asymptotic limit model this paper presents a hybrid numerical method to solve efficiently a class of highly anisotropic elliptic problems the anisotropy is aligned with one coordinate axis and its strength is described by a parameter e 0 1 which can largely vary in the study domain our hybrid model is based on asymptotic techniques and couples spatially an asymptotic preserving model with its asymptotic limit model the latter being used in regions where the anisotropy parameter e is small adequate coupling conditions link the two models the aim of this hybrid procedure is to reduce the computational time for problems where the region of small e values extends over a significant part of the domain and this is due to the reduced complexity of the limit model

ordinary differential equations transport theory and sobolev spaces we obtain some new existence uniqueness and stability results for ordinary differential equations with coefficients in sobolev spaces these results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions

global existence and asymptotic behavior for the 3d compressible navier stokes equations without heat conductivity in a bounded domain abstract in this paper we investigate the global existence and uniqueness of strong solutions to the initial boundary value problem for the 3d compressible navier stokes equations without heat conductivity in a bounded domain with slip boundary the global existence and uniqueness of strong solutions are obtained when the initial data is near its equilibrium in h 2 furthermore the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods

cortex segmentation a fast variational geometric approach an automatic cortical gray matter segmentation from a three dimensional 3 d brain images magnetic resonance mr or computed tomography is a well known problem in medical image processing in this paper we first formulate it as a geometric variational problem for propagation of two coupled bounding surfaces an efficient numerical scheme is then used to implement the geodesic active surface model experimental results of cortex segmentation on real 3 d mr data are provided

estimating linear cortical magnification in human primary visual cortex via dynamic programming abstract human primary visual cortex is organized retinotopically with adjacent locations in cortex representing adjacent locations on the retina the spatial sampling in cortex is highly nonuniform the amount of cortex devoted to a unit area of retina decreases with increasing retinal eccentricity this sampling property can be quantified by the linear cortical magnification factor which is expressed in terms of millimeters of cortex per degree of visual angle in this paper we present a new method using dynamic programming and fmri retinotopic eccentricity mapping to estimate the linear cortical magnification factor in human primary visual cortex v1 we localized cortical activity while subjects viewed each of seven stationary contrast reversing radial checkerboard rings of equal thickness that tiled the visual field from 1 62 to 12 96 degrees of eccentricity imaging data from all epochs of each ring were contrasted with data from fixation epochs on a subject by subject basis the resulting t statistic maps were then superimposed on a local coordinate system constructed from the gray white matter boundary surface of each individual subject s occipital lobe separately for each ring smoothed maps of functional activity on the cortical surface were constructed using orthonormal bases of the laplace beltrami operator that incorporate the geometry of the cortical surface this allowed us to stably track the ridge of maximum activation due to each ring via dynamic programming optimization over all possible paths on the cortical surface we estimated the linear cortical magnification factor by calculating geodesic distances between activation ridges on the cortical surface in a population of five normal subjects the reliability of these estimates was assessed by comparing results based on data from one quadrant to those based on data from the full hemifield along with a split half reliability analysis

using a deformable surface model to obtain a shape representation of the cortex this paper examines the problem of obtaining a mathematical representation of the outer cortex of the human brain which is a key problem in several applications including morphological analysis of the brain and spatial normalization and registration of brain images a parameterization of the outer cortex is first obtained using a deformable surface algorithm which motivated by the structure of the cortex is constructed to find the central layer of thick surfaces based on this parameterization a hierarchical representation of the outer cortical structure is proposed through its depth map and its curvature maps at various scales various experiments on magnetic resonance data are presented

an asymptotic preserving method for highly anisotropic elliptic equations based on a micro macro decomposition the concern of the present work is the introduction of a very efficient asymptotic preserving scheme for the resolution of highly anisotropic diffusion equations the characteristic features of this scheme are the uniform convergence with respect to the anisotropy parameter 0 e 1 the applicability on cartesian grids to cases of non uniform and non aligned anisotropy fields b and the simple extension to the case of a non constant anisotropy intensity 1 e the mathematical approach and the numerical scheme are different from those presented in the previous work p degond f deluzet a lozinski j narski c negulescu duality based asymptotic preserving method for highly anisotropic diffusion equations communications in mathematical sciences 10 1 2012 1 31 and its considerable advantages are pointed out

segmentation of focal cortical dysplasia lesions on mri using level set evolution focal cortical dysplasia fcd is the most frequent malformation of cortical development in patients with medically intractable epilepsy on mri fcd lesions are not easily differentiable from the normal cortex and defining their spatial extent is challenging in this paper we introduce a method to segment fcd lesions on t1 weighted mri it relies on two successive three dimensional deformable models whose evolutions are based on the level set framework the first deformable model is driven by probability maps obtained from three mri features cortical thickness relative intensity and gradient these features correspond to the visual characteristics of fcd and allow discriminating lesions and normal tissues in a second stage the previous result is expanded towards the underlying and overlying cortical boundaries throughout the whole cortical section the method was quantitatively evaluated by comparison with manually traced labels in 18 patients with fcd the automated segmentations achieved a strong agreement with the manuals labels demonstrating the applicability of the method to assist the delineation of fcd lesions on mri this new approach may become a useful tool for the presurgical evaluation of patients with intractable epilepsy related to cortical dysplasia

adaptive reproducing kernel particle method for extraction of the cortical surface we propose a novel adaptive approach based on the reproducing kernel particle method rkpm to extract the cortical surfaces of the brain from three dimensional 3 d magnetic resonance images mris to formulate the discrete equations of the deformable model a flexible particle shape function is employed in the galerkin approximation of the weak form of the equilibrium equations the proposed support generation method ensures that support of all particles cover the entire computational domains the deformable model is adaptively adjusted by dilating the shape function and by inserting or merging particles in the high curvature regions or regions stopped by the target boundary the shape function of the particle with a dilation parameter is adaptively constructed in response to particle insertion or merging the proposed method offers flexibility in representing highly convolved structures and in refining the deformable models self intersection of the surface during evolution is prevented by tracing backward along gradient descent direction from the crest interface of the distance field which is computed by fast marching these operations involve a significant computational cost the initial model for the deformable surface is simple and requires no prior knowledge of the segmented structure no specific template is required e g an average cortical surface obtained from many subjects the extracted cortical surface efficiently localizes the depths of the cerebral sulci unlike some other active surface approaches that penalize regions of high curvature comparisons with manually segmented landmark data are provided to demonstrate the high accuracy of the proposed method we also compare the proposed method to the finite element method and to a commonly used cortical surface extraction approach the cruise method we also show that the independence of the shape functions of the rkpm from the underlying mesh enhances the convergence speed of the deformable model

initial boundary value problems for the equations of motion of compressible viscous and heat conductive fluids the equations of motion of compressible viscous and heat conductive fluids are investigated for initial boundary value problems on the half space and on the exterior domain of any bounded region the global solution in time is proved to exist uniquely and approach the stationary state ast provided the prescribed initial data and the external force are sufficiently small

global low energy weak solution and large time behavior for the compressible flow of liquid crystals abstract in this paper we consider the weak solution of the simplified ericksen leslie system modeling compressible nematic liquid crystal flows in r 3 when the initial data are of small energy and initial density is positive and essentially bounded we prove the existence of a global weak solution in r 3 the large time behavior of a global weak solution is also established

sense factors for reliable cortical thickness measurement the purposes of this study were to examine the effect of sensitivity encoding sense factors on cortical thickness measurements and to determine which sense factor to use to reliably measure cortical thickness in 3 0 t and 1 5 t t1 weighted mri images the 3d t1 tfe images were acquired from 11 healthy volunteers with 6 different sense acceleration factors from 1 0 without sense acceleration to 4 0 on a 1 5 t scanner and 9 different sense factors from 1 0 to 6 0 plus a second day 1 0 acquisition on a 3 0 t scanner cortical thickness was calculated for the entire cortical surface that was further subdivided into 33 regions repeated measures multivariate analysis of variance revealed that the main effect of sense factors f 12 485 df 7 p 0 006 was a significant underestimation of cortical thickness at sense 5 0 p 0 022 and 6 0 p 0 011 at 3 0 t and at sense 4 0 p 0 000 at 1 5 t repeated measures anova showed that thickness measurements at the insula superior temporal sulcus the medial part of the superior frontal lobe and cingulate cortex are highly affected by sense factors sense factors affect thickness estimation more significantly at 1 5 t and thus 1 5 t imaging provides less reliable estimates using sense techniques faster imaging can be done without too much loss of reliability using a high sense factor such as 3 0 at 3 0 t with acquisition time being inversely proportional to the sense factor

an eulerian pde approach for computing tissue thickness we outline an eulerian framework for computing the thickness of tissues between two simply connected boundaries that does not require landmark points or parameterizations of either boundary thickness is defined as the length of correspondence trajectories which run from one tissue boundary to the other and which follow a smooth vector field constructed in the region between the boundaries a pair of partial differential equations pdes that are guided by this vector field are then solved over this region and the sum of their solutions yields the thickness of the tissue region unlike other approaches this approach does not require explicit construction of any correspondence trajectories an efficient stable and computationally fast solution to these pdes is found by careful selection of finite differences according to an up winding condition the behavior and performance of our method is demonstrated on two simulations and two magnetic resonance imaging data sets in two and three dimensions these experiments reveal very good performance and show strong potential for application in tissue thickness visualization and quantification

automatic segmentation and reconstruction of the cortex from neonatal mri abstract segmentation and reconstruction of cortical surfaces from magnetic resonance mr images are more challenging for developing neonates than adults this is mainly due to the dynamic changes in the contrast between gray matter gm and white matter wm in both t1 and t2 weighted images t1w and t2w during brain maturation in particular in neonatal t2w images wm typically has higher signal intensity than gm this causes mislabeled voxels during cortical segmentation especially in the cortical regions of the brain and in particular at the interface between gm and cerebrospinal fluid csf we propose an automatic segmentation algorithm detecting these mislabeled voxels and correcting errors caused by partial volume effects our results show that the proposed algorithm corrects errors in the segmentation of both gm and wm compared to the classic expectation maximization em scheme quantitative validation against manual segmentation demonstrates good performance the mean dice value 0 758 0 037 for gm and 0 794 0 078 for wm the inner central and outer cortical surfaces are then reconstructed using implicit surface evolution a landmark study is performed to verify the accuracy of the reconstructed cortex the mean surface reconstruction error 0 73 mm for inner surface and 0 63 mm for the outer both segmentation and reconstruction have been tested on 25 neonates with the gestational ages ranging from 27 to 45 weeks this preliminary analysis confirms previous findings that cortical surface area and curvature increase with age and that surface area scales to cerebral volume according to a power law while cortical thickness is not related to age or brain growth

weighted fourier series representation and its application to quantifying the amount of gray matter we present a novel weighted fourier series wfs representation for cortical surfaces the wfs representation is a data smoothing technique that provides the explicit smooth functional estimation of unknown cortical boundary as a linear combination of basis functions the basic properties of the representation are investigated in connection with a self adjoint partial differential equation and the traditional spherical harmonic spharm representation to reduce steep computational requirements a new iterative residual fitting irf algorithm is developed its computational and numerical implementation issues are discussed in detail the computer codes are also available at http www stat wisc edu mchung softwares weighted spharm weighted spharm html as an illustration the wfs is applied in quantifying the amount of gray matter in a group of high functioning autistic subjects within the wfs framework cortical thickness and gray matter density are computed and compared

a smooth transition model between kinetic and hydrodynamic equations this paper presents a model which provides a smooth transition between a kinetic and a hydrodynamic domain the idea is to use a buffer zone in which both hydrodynamics and kinetic equations will be solved the solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations we use an artificial connecting function which makes the equation on each domain degenerate at the end of the buffer zone thus no boundary condition is needed at the transition point consequently this model avoids the delicate issue of finding the interface condition in a typical domain decomposition method that couples a kinetic equation with hydrodynamic equations a simple kinetic scheme is developed to discretize our model and numerical examples are used to validate the method

heritability estimates of cortical anatomy the influence and reliability of different estimation strategies twin study designs have been previously used to investigate the heritability of neuroanatomical measures such as regional cortical volumes volume can be fractionated into surface area and cortical thickness where both measures are considered to have independent genetic and environmental bases region of interest roi and vertex wise approaches have been used to calculate heritability of cortical thickness and surface area in twin studies in our study we estimate heritability using the human connectome project magnetic resonance imaging dataset composed of healthy young twin and non twin siblings mean age of 29 sample size of 757 both roi and vertex wise methods were used to compare regional heritability of cortical thickness and surface area heritability estimates were controlled for age sex and total ipsilateral surface area or mean cortical thickness in both approaches heritability estimates of cortical thickness and surface area were lower when accounting for average ipsilateral cortical thickness and total surface area respectively when comparing both approaches at a regional level the vertex wise approach showed higher surface area and lower cortical thickness heritability estimates compared to the roi approach the calcarine fissure had the highest surface area heritability estimate roi 44 vertex wise 50 and posterior cingulate gyrus had the highest cortical thickness heritability roi 50 vertex wise 40 we also observed that limitations in image processing and variability in spatial averaging errors based on regional size may make obtaining true estimates of cortical thickness and surface area challenging in smaller regions it is important to identify which approach is best suited to estimate heritability based on the research hypothesis and the size of the regions being investigated

artificial shifting of fmri activation localized by volume and surface based analyses spatial smoothing is an important post processing procedure that is used to increase the signal to noise ratio snr of blood oxygenation level dependent signals bold in common functional magnetic resonance imaging fmri applications however recent studies have shown that smoothing artificially shifts probabilistic local maxima of fmri activations in this study we show shifting of the localization of functional centers in hand motor areas of the cerebral cortex by three dimensional isotropic gaussian kernel smoothing or two dimensional heat kernel smoothing in volume and surface based fmri analyses activation maps derived from smoothed echo planar imaging epi data by volume and surface based analyses were assigned to the nodes of individual cortical surface models and local maxima in the primary motor area m1 and the primary somatosensory cortex s1 were compared with those derived from non smoothed risk map analysis which is commonly used in presurgical applications for each analysis the euclidean and geodesic distances between the correlation coefficients of local maxima derived from smoothed and non smoothed epi data were measured the results show that the correlation coefficients derived from the volume and surface based analyses were about 29 4 and 42 9 higher for smoothed than for non smoothed risk map analyses and show minimum shifting of localizations by 12 1 mm and 6 9 mm on average in euclidean distance respectively and about 9 5 mm and 5 7 mm on average in geodesic distance respectively