The Funk-Radon Transform (FRT) is a powerful tool for the estimation of fiber populations with High Angular Resolution Diffusion Imaging (HARDI). It is used in Q-Ball imaging (QBI), and other HARDI techniques such as the recent Orientation Probability Density Transform (OPDT), to estimate fiber populations with very few restrictions on the diffusion model. The FRT consists in the integration of the attenuation signal, sampled by the MRI scanner on the unit sphere, along equators orthogonal to the directions of interest. It is easily proved that this calculation is equivalent to the integration of the diffusion propagator along such directions, although a characteristic blurring with a Bessel kernel is introduced. Under a different point of view, the FRT can be seen as an efficient way to compute the angular part of the integral of the attenuation signal in the plane orthogonal to each direction of the diffusion propagator. In this paper, Stoke’s theorem is used to prove that the FRT can in fact be used to compute accurate estimates of the true integrals defining the functions of interest in HARDI, keeping the diffusion model as little restrictive as possible. Varying the assumptions on the attenuation signal, we derive new estimators of fiber orientations, generalizing both Q-Balls and the OPDT. Extensive experiments with both synthetic and real data have been intended to show that the new techniques improve existing ones in many situations.
Publications by Year: 2010
Rathi Y, Malcolm J, Michailovich O, Goldstein J, Seidman L, McCarley RW, Westin CF, Shenton ME. Biomarkers for Identifying First Episode Schizophrenia Patients using Diffusion Weighted Imaging. Med Image Comput Comput Assist Interv. 2010;13(Pt 1):657–65.
Recent advances in diffusion weighted MR imaging (dMRI) has made it a tool of choice for investigating white matter abnormalities of the brain and central nervous system. In this work, we design a system that detects abnormal features (biomarkers) of first-episode schizophrenia patients and then classifies them using these features. We use two different models of the dMRI data, namely, spherical harmonics and the two-tensor model. The algorithm works by first computing several diffusion measures from each model. An affine-invariant representation of each subject is then computed, thus avoiding the need for registration. This representation is used within a kernel based feature selection algorithm to determine the biomarkers that are statistically different between the two populations. Confirmation of how well these biomarkers identify each population is obtained by using several classifiers such as, k-nearest neighbors, Parzen window classifier, and support vector machines to separate 21 first-episode patients from 20 age-matched normal controls. Classification results using leave-many-out cross-validation scheme are given for each representation. This algorithm is a first step towards early detection of schizophrenia.
We introduce a fibre tractography framework based on a particle filter which estimates a local geometrical model of the underlying white matter tract, formulated as a ’streamline flow’ using generalized helicoids. The method is not dependent on the diffusion model, and is applicable to diffusion tensor (DT) data as well as to high angular resolution reconstructions. The geometrical model allows for a robust inference of local tract geometry, which, in the context of the causal filter estimation, guides tractography through regions with partial volume effects. We validate the method on synthetic data and present results on two types in vivo data: diffusion tensors and a spherical harmonic reconstruction of the fibre orientation distribution function (fODF).
We describe a neuroimaging protocol that utilizes an anatomical atlas of the human head to guide diffuse optical tomography of human brain activation. The protocol is demonstrated by imaging the hemodynamic response to median-nerve stimulation in three healthy subjects, and comparing the images obtained using a head atlas with the images obtained using the subject-specific head anatomy. The results indicate that using the head atlas anatomy it is possible to reconstruct the location of the brain activation to the expected gyrus of the brain, in agreement with the results obtained with the subject-specific head anatomy. The benefits of this novel method derive from eliminating the need for subject-specific head anatomy and thus obviating the need for a subject-specific MRI to improve the anatomical interpretation of diffuse optical tomography images of brain activation.
This work provides a model for tubular structures, and devises an algorithm to automatically extract tubular anatomical structures from medical imagery. Our model fits many anatomical structures in medical imagery, in particular, various fiber bundles in the brain (imaged through diffusion-weighted magnetic resonance (DW-MRI)) such as the cingulum bundle, and blood vessel trees in computed tomography angiograms (CTAs). Extraction of the cingulum bundle is of interest because of possible ties to schizophrenia, and extracting blood vessels is helpful in the diagnosis of cardiovascular diseases. The tubular model we propose has advantages over many existing approaches in literature: fewer degrees-of-freedom over a general deformable surface hence energies defined on such tubes are less sensitive to undesirable local minima, and the tube (in 3-D) can be naturally represented by a 4-D curve (a radius function and centerline), which leads to computationally less costly algorithms and has the advantage that the centerline of the tube is obtained without additional effort. Our model also generalizes to tubular trees, and the extraction algorithm that we design automatically detects and evolves branches of the tree. We demonstrate the performance of our algorithm on 20 datasets of DW-MRI data and 32 datasets of CTA, and quantify the results of our algorithm when expert segmentations are available.
In this paper we present a new computationally efficient numerical scheme for the minimizing flow approach for the computation of the optimal L(2) mass transport mapping. In contrast to the integration of a time dependent partial differential equation proposed in [S. Angenent, S. Haker, and A. Tannenbaum, SIAM J. Math. Anal., 35 (2003), pp. 61-97], we employ in the present work a direct variational method. The efficacy of the approach is demonstrated on both real and synthetic data.
Registration uncertainty may be important information to convey to a surgeon when surgical decisions are taken based on registered image data. However, conventional non-rigid registration methods only provide the most likely deformation. In this paper we show how to determine the registration uncertainty, as well as the most likely deformation, by using an elastic Bayesian registration framework that generates a dense posterior distribution on deformations. We model both the likelihood and the elastic prior on deformations with Boltzmann distributions and characterize the posterior with a Markov Chain Monte Carlo algorithm. We introduce methods that summarize the high-dimensional uncertainty information and show how these summaries can be visualized in a meaningful way. Based on a clinical neurosurgical dataset, we demonstrate the importance that uncertainty information could have on neurosurgical decision making.
This article presents a summary of the key-note lecture delivered at Biomechanics 10 Conference held in August 2010 in Warsaw. We present selected topics in the area of mathematical and numerical modelling of the brain biomechanics for neurosurgical simulation and brain image registration. These processes can reasonably be described in purely mechanical terms, such as displacements, strains and stresses and therefore can be analysed using established methods of continuum mechanics. We advocate the use of fully non-linear theory of continuum mechanics. We discuss in some detail modelling geometry, boundary conditions, loading and material properties. We consider numerical problems such as the use of hexahedral and mixed hexahedral-tetrahedral meshes as well as meshless spatial discretisation schemes. We advocate the use of Total Lagrangian Formulation of both finite element and meshless methods together with explicit time-stepping procedures. We support our recommendations and conclusions with an example of brain shift computation for intraoperative image registration.
Chen K, Zhang Y, Pohl K, Syeda-Mahmood T, Song Z, Wong STC. Coronary artery segmentation using geometric moments based tracking and snake-driven refinement. Conf Proc IEEE Eng Med Biol Soc. 2010;2010:3133–7.
Automatic or semi-automatic segmentation and tracking of artery trees from computed tomography angiography (CTA) is an important step to improve the diagnosis and treatment of artery diseases, but it still remains a significant challenging problem. In this paper, we present an artery extraction method to address the challenge. The proposed method consists of two steps: (1) a geometric moments based tracking to secure a rough centerline, and (2) a fully automatic generalized cylinder structure-based snake method to refine the centerlines and estimate the radii of the arteries. In this method, a new line direction based on first and second order geometric moments is adopted while both gradient and intensity information are used in the snake model to improve the accuracy. The approach has been evaluated on synthetic images as well as 8 clinical coronary CTA images with 32 coronary arteries. Our method achieves 94.7% overlap tracking ability within an average distance inside the vessel of 0.36 mm.
Levitt JJ, Kubicki M, Nestor PG, Ersner-Hershfield H, Westin CF, Alvarado JL, Kikinis R, Jolesz FA, McCarley RW, Shenton ME. A Diffusion Tensor Imaging Study of the Anterior Limb of the Internal Capsule in Schizophrenia. Psychiatry Res. 2010;184(3):143–50.
Frontal-subcortical cognitive and limbic feedback loops modulate higher cognitive functioning. The final step in these feedback loops is the thalamo-cortical projection through the anterior limb of the internal capsule (AL-IC). Using diffusion tensor imaging (DTI), we evaluated abnormalities in the AL-IC fiber tract in schizophrenia. Participants comprised 16 chronic schizophrenia patients and 19 male, normal controls, who were group matched for handedness, age, and parental socioeconomic status, and underwent DTI on a 1.5 Tesla GE system. We measured the diffusion indices, fractional anisotropy (FA), mean diffusivity (MD), radial diffusivity (RD), and axial diffusivity (AD), and manually segmented, based on FA maps, AL-IC volume, normalized for intracranial contents (ICC). The results showed a significant reduction in the ICC-corrected volume of the AL-IC in schizophrenia, but did not show diffusion measure group differences in the AL-IC in FA, MD, RD or AD. In addition, in the schizophrenia patients, AL-IC FA correlated positively with performance on measures of spatial and verbal declarative/episodic memory, and right AL-IC ICC-corrected volume correlated positively with more perseverative responses on the Wisconsin Card Sort Test (WCST). We found a reduction in AL-IC ICC-corrected volume in schizophrenia, without FA, MD, RD or AD group differences, implicating the presence of a structural abnormality in schizophrenia in this subcortical white matter region which contains important cognitive, and limbic feedback pathways that modulate prefrontal cortical function. Despite not demonstrating a group difference in FA, we found that AL-IC FA was a good predictor of spatial and verbal declarative/episodic memory performance in schizophrenia.