Publications by Year: 2011

2011
Haytham Elhawary, Haiying Liu, Pratik Patel, Isaiah Norton, Laura Rigolo, Xenophon Papademetris, Nobuhiko Hata, and Alexandra J Golby. 2011. “Intraoperative real-time querying of white matter tracts during frameless stereotactic neuronavigation.” Neurosurgery, 68, 2, Pp. 506-16; discussion 516.Abstract
BACKGROUND: Brain surgery faces important challenges when trying to achieve maximum tumor resection while avoiding postoperative neurological deficits. OBJECTIVE: For surgeons to have optimal intraoperative information concerning white matter (WM) anatomy, we developed a platform that allows the intraoperative real-time querying of tractography data sets during frameless stereotactic neuronavigation. METHODS: Structural magnetic resonance imaging, functional magnetic resonance imaging, and diffusion tensor imaging were performed on 5 patients before they underwent lesion resection using neuronavigation. During the procedure, the tracked surgical tool tip position was transferred from the navigation system to the 3-dimensional Slicer software package, which used this position to seed the WM tracts around the tool tip location, rendering a geometric visualization of these tracts on the preoperative images previously loaded onto the navigation system. The clinical feasibility of this approach was evaluated in 5 cases of lesion resection. In addition, system performance was evaluated by measuring the latency between surgical tool tracking and visualization of the seeded WM tracts. RESULTS: Lesion resection was performed successfully in all 5 patients. The seeded WM tracts close to the lesion and other critical structures, as defined by the functional and structural images, were interactively visualized during the intervention to determine their spatial relationships relative to the lesion and critical cortical areas. Latency between tracking and visualization of tracts was less than a second for a fiducial radius size of 4 to 5 mm. CONCLUSION: Interactive tractography can provide an intuitive way to inspect critical WM tracts in the vicinity of the surgical region, allowing the surgeon to have increased intraoperative WM information to execute the planned surgical resection.
Lauren J O'Donnell and Carl-Fredrik Westin. 2011. “An Introduction to Diffusion Tensor Image Analysis.” Neurosurg Clin N Am, 22, 2, Pp. 185-96.Abstract

Diffusion tensor magnetic resonance imaging (DTI) is a relatively new technology that is popular for imaging the white matter of the brain. This article provides a basic and broad overview of DTI to enable the reader to develop an intuitive understanding of these types of data, and an awareness of their strengths and weaknesses.

Georg Langs, Danial Lashkari, Andrew Sweet, Yanmei Tie, Laura Rigolo, Alexandra J Golby, and Polina Golland. 2011. “Learning an atlas of a cognitive process in its functional geometry.” Inf Process Med Imaging, 22, Pp. 135-46.Abstract
In this paper we construct an atlas that captures functional characteristics of a cognitive process from a population of individuals. The functional connectivity is encoded in a low-dimensional embedding space derived from a diffusion process on a graph that represents correlations of fMRI time courses. The atlas is represented by a common prior distribution for the embedded fMRI signals of all subjects. The atlas is not directly coupled to the anatomical space, and can represent functional networks that are variable in their spatial distribution. We derive an algorithm for fitting this generative model to the observed data in a population. Our results in a language fMRI study demonstrate that the method identifies coherent and functionally equivalent regions across subjects.
Petter Risholm, Alexandra J Golby, and William M Wells III. 2011. “Multimodal image registration for preoperative planning and image-guided neurosurgical procedures.” Neurosurg Clin N Am, 22, 2, Pp. 197-206.Abstract

Image registration is the process of transforming images acquired at different time points, or with different imaging modalities, into the same coordinate system. It is an essential part of any neurosurgical planning and navigation system because it facilitates combining images with important complementary, structural, and functional information to improve the information based on which a surgeon makes critical decisions. Brigham and Women's Hospital (BWH) has been one of the pioneers in developing intraoperative registration methods for aligning preoperative and intraoperative images of the brain. This article presents an overview of intraoperative registration and highlights some recent developments at BWH.

Bruno Madore, Lawrence P. Panych, Chang-Sheng Mei, Jing Yuan, and Renxin Chu. 2011. “Multipathway Sequences for MR Thermometry.” Magn Reson Med, 66, 3, Pp. 658-68.Abstract

MR-based thermometry is a valuable adjunct to thermal ablation therapies as it helps to determine when lethal doses are reached at the target and whether surrounding tissues are safe from damage. When the targeted lesion is mobile, MR data can further be used for motion-tracking purposes. The present work introduces pulse sequence modifications that enable significant improvements in terms of both temperature-to-noise-ratio properties and target-tracking abilities. Instead of sampling a single magnetization pathway as in typical MR thermometry sequences, the pulse-sequence design introduced here involves sampling at least one additional pathway. Image reconstruction changes associated with the proposed sampling scheme are also described. The method was implemented on two commonly used MR thermometry sequences: the gradient-echo and the interleaved echo-planar imaging sequences. Data from the extra pathway enabled temperature-to-noise-ratio improvements by up to 35%, without increasing scan time. Potentially of greater significance is that the sampled pathways featured very different contrast for blood vessels, facilitating their detection and use as internal landmarks for tracking purposes. Through improved temperature-to-noise-ratio and lesion-tracking abilities, the proposed pulse-sequence design may facilitate the use of MR-monitored thermal ablations as an effective treatment option even in mobile organs such as the liver and kidneys.

Mohammed H Aljallad, Jing Yuan, Magdalini C Pilatou, Nathan J McDannold, and Lawrence P. Panych. 2011. “Multi-resolution MRI Temperature Monitoring in a Reduced Field of View.” Magn Reson Imaging, 29, 9, Pp. 1205-14.Abstract

PURPOSE: The purpose was to develop a new magnetic resonance imaging technique for fast temperature monitoring with extended volume coverage. MATERIALS AND METHODS: The Multiple Resolutions Along Phase-Encode and Slice-Select Dimensions (MURPS) method was implemented in both a two-dimensional (2D) spoiled gradient echo (SPGR) sequence and a multishot echo-planar imaging (EPI) sequence. Both modified sequences were used to acquire image data from three slices with variable phase-encode resolution and slice thickness. In the SPGR sequence, a 2D resonant frequency pulse was also implemented to enable imaging within a reduced field of view, and this was used to monitor (at 1.5 T) the temperature changes in a live rabbit and in gel phantoms heated by focused ultrasound. A modified EPI sequence was tested during heating of a phantom undergoing motion. RESULTS: The in vivo experiments demonstrated that temperature changes in unexpected locations away from the focal plane, such as near bone structures, could be detected due to the extra volume coverage afforded by the MURPS method. Temperature changes in a moving phantom were resolved using the MURPS EPI sequence with an acquisition rate of three slices every 300 ms. CONCLUSION: The MURPS method enables temperature monitoring over multiple slices without loss of temporal resolution compared with single-slice imaging and, if combined with multishot EPI, enables volume temperature monitoring in moving organs.

Gabriel Zada, Pankaj K Agarwalla, Srinivasan Mukundan, Ian F Dunn, Alexandra J Golby, and Edward R Laws. 2011. “The neurosurgical anatomy of the sphenoid sinus and sellar floor in endoscopic transsphenoidal surgery.” J Neurosurg, 114, 5, Pp. 1319-30.Abstract

OBJECT: A considerable degree of variability exists in the anatomy of the sphenoid sinus, sella turcica, and surrounding skull base structures. The authors aimed to characterize neuroimaging and intraoperative variations in the sagittal and coronal surgical anatomy of healthy controls and patients with sellar lesions. METHODS: Magnetic resonance imaging studies obtained in 100 healthy adults and 78 patients with sellar lesions were reviewed. The following measurements were made on midline sagittal images: sellar face, sellar prominence, sellar angle, tuberculum sellae angle, sellar-clival angle, length of planum sphenoidale, and length of clivus. The septal configuration of the sphenoid sinus was classified as either simple or complex, according to the number of septa, their symmetry, and their morphological features. The following measurements were made on coronal images: maximum width of the sphenoid sinus and sellar face, and the distance between the parasellar and midclivus internal carotid arteries. Neuroimaging results were correlated with intraoperative findings during endoscopic transsphenoidal surgery. RESULTS: Three sellar floor morphologies were defined in normal adults: prominent (sellar angle of < 90°) in 25%, curved (sellar angle 90-150°) in 63%, flat (sellar angle > 150°) in 11%, and no floor (conchal sphenoid) in 1%. In healthy adults, the following mean measurements were obtained: sellar face, 13.4 mm; sellar prominence, 3.0 mm; sellar angle, 112°; angle of tuberculum sellae, 112°; and sellar-clival angle, 117°. Compared with healthy adults, patients with sellar lesions were more likely to have prominent sellar types (43% vs 25%, p = 0.01), a more acute sellar angle (102° vs 112°, p = 0.03), a more prominent sellar floor (3.8 vs 3.0 mm, p < 0.005), and more acute tuberculum (105° vs 112°, p < 0.01) and sellar-clival (105° vs 117°, p < 0.003) angles. A flat sellar floor was more difficult to identify intraoperatively and more likely to require the use of a chisel or drill to expose (75% vs 25%, p = 0.01). A simple sphenoid sinus configuration (no septa, 1 vertical septum, or 2 symmetric vertical septa) was noted in 71% of studies, and the other 29% showed a complex configuration (2 or more asymmetrical septa, 3 or more septa of any kind, or the presence of a horizontal septum). Intraoperative correlation was more challenging in cases with complex sinus anatomy; the most reliable intraoperative midline markers were the vomer, superior sphenoid rostrum, and bilateral parasellar and clival carotid protuberances. CONCLUSIONS: Preoperative assessment of neuroimaging studies is critical for characterizing the morphological characteristics of the sphenoid sinus, sellar floor, tuberculum sellae, and clivus. The flat sellar type identified in 11% of people) or a complex sphenoid sinus configuration (in 29% of people) may make intraoperative correlation substantially more challenging. An understanding of the regional anatomy and its variability can improve the safety and accuracy of transsphenoidal and extended endoscopic skull base approaches.

Kilian M Pohl, Ender Konukoglu, Sebastian Novellas, Nicholas Ayache, Andriy Fedorov, Ion-Florin Talos, Alexandra J Golby, William M Wells III, Ron Kikinis, and Peter M Black. 2011. “A new metric for detecting change in slowly evolving brain tumors: validation in meningioma patients.” Neurosurgery, 68, 1 Suppl Operative, Pp. 225-33.Abstract

BACKGROUND: Change detection is a critical component in the diagnosis and monitoring of many slowly evolving pathologies. OBJECTIVE: This article describes a semiautomatic monitoring approach using longitudinal medical images. We test the method on brain scans of patients with meningioma, which experts have found difficult to monitor because the tumor evolution is very slow and may be obscured by artifacts related to image acquisition. METHODS: We describe a semiautomatic procedure targeted toward identifying difficult-to-detect changes in brain tumor imaging. The tool combines input from a medical expert with state-of-the-art technology. The software is easy to calibrate and, in less than 5 minutes, returns the total volume of tumor change in mm. We test the method on postgadolinium, T1-weighted magnetic resonance images of 10 patients with meningioma and compare our results with experts' findings. We also perform benchmark testing with synthetic data. RESULTS: Our experiments indicated that experts' visual inspections are not sensitive enough to detect subtle growth. Measurements based on experts' manual segmentations were highly accurate but also labor intensive. The accuracy of our approach was comparable to the experts' results. However, our approach required far less user input and generated more consistent measurements. CONCLUSION: The sensitivity of experts' visual inspection is often too low to detect subtle growth of meningiomas from longitudinal scans. Measurements based on experts' segmentation are highly accurate but generally too labor intensive for standard clinical settings. We described an alternative metric that provides accurate and robust measurements of subtle tumor changes while requiring a minimal amount of user input.

Romeil Sandhu, Samuel Dambreville, Anthony Yezzi, and Allen Tannenbaum. 2011. “A nonrigid kernel-based framework for 2D-3D pose estimation and 2D image segmentation.” IEEE Trans Pattern Anal Mach Intell, 33, 6, Pp. 1098-115.Abstract
In this work, we present a nonrigid approach to jointly solving the tasks of 2D-3D pose estimation and 2D image segmentation. In general, most frameworks that couple both pose estimation and segmentation assume that one has exact knowledge of the 3D object. However, under nonideal conditions, this assumption may be violated if only a general class to which a given shape belongs is given (e.g., cars, boats, or planes). Thus, we propose to solve the 2D-3D pose estimation and 2D image segmentation via nonlinear manifold learning of 3D embedded shapes for a general class of objects or deformations for which one may not be able to associate a skeleton model. Thus, the novelty of our method is threefold: first, we present and derive a gradient flow for the task of nonrigid pose estimation and segmentation. Second, due to the possible nonlinear structures of one's training set, we evolve the pre-image obtained through kernel PCA for the task of shape analysis. Third, we show that the derivation for shape weights is general. This allows us to use various kernels, as well as other statistical learning methodologies, with only minimal changes needing to be made to the overall shape evolution scheme. In contrast with other techniques, we approach the nonrigid problem, which is an infinite-dimensional task, with a finite-dimensional optimization scheme. More importantly, we do not explicitly need to know the interaction between various shapes such as that needed for skeleton models as this is done implicitly through shape learning. We provide experimental results on several challenging pose estimation and segmentation scenarios.
Petter Risholm, James Ross, George R Washko, and William M Wells III. 2011. “Probabilistic elastography: estimating lung elasticity.” Inf Process Med Imaging, 22, Pp. 699-710.Abstract

We formulate registration-based elastography in a probabilistic framework and apply it to study lung elasticity in the presence of emphysematous and fibrotic tissue. The elasticity calculations are based on a Finite Element discretization of a linear elastic biomechanical model. We marginalize over the boundary conditions (deformation) of the biomechanical model to determine the posterior distribution over elasticity parameters. Image similarity is included in the likelihood, an elastic prior is included to constrain the boundary conditions, while a Markov model is used to spatially smooth the inhomogeneous elasticity. We use a Markov Chain Monte Carlo (MCMC) technique to characterize the posterior distribution over elasticity from which we extract the most probable elasticity as well as the uncertainty of this estimate. Even though registration-based lung elastography with inhomogeneous elasticity is challenging due the problem's highly underdetermined nature and the sparse image information available in lung CT, we show promising preliminary results on estimating lung elasticity contrast in the presence of emphysematous and fibrotic tissue.

Petter Risholm, Andriy Fedorov, Jennifer Pursley, Kemal Tuncali, Robert Cormack, and William M Wells III. 2011. “Probabilistic Non-rigid Registration of Prostate Images: Modeling and Quantifying Uncertainty.” Proc IEEE Int Symp Biomed Imaging, 2011, Pp. 553-556.Abstract

Registration of pre- to intra-procedural prostate images needs to handle the large changes in position and shape of the prostate caused by varying rectal filling and patient positioning. We describe a probabilistic method for non-rigid registration of prostate images which can quantify the most probable deformation as well as the uncertainty of the estimated deformation. The method is based on a biomechanical Finite Element model which treats the prostate as an elastic material. We use a Markov Chain Monte Carlo sampler to draw deformation configurations from the posterior distribution. In practice, we simultaneously estimate the boundary conditions (surface displacements) and the internal deformations of our biomechanical model. The proposed method was validated on a clinical MRI dataset with registration results comparable to previously published methods, but with the added benefit of also providing uncertainty estimates which may be important to take into account during prostate biopsy and brachytherapy procedures.

Fiona M Fennessy, Chung Yin Kong, Clare M Tempany, and Shannon J Swan. 2011. “Quality-of-life assessment of fibroid treatment options and outcomes.” Radiology, 259, 3, Pp. 785-92.Abstract
PURPOSE: To obtain utilities (a unit of measure of a person's relative preferences for different health states compared with death or worst possible outcome) for uterine fibroids before and after treatment and to measure short-term utilities for the following uterine fibroid treatments: abdominal hysterectomy, magnetic resonance (MR) imaging-guided focused ultrasound surgery, and uterine artery embolization (UAE). MATERIALS AND METHODS: This retrospective study was approved by the institutional review board and was HIPAA compliant. The waiting trade-off (WTO) method, a variation on the time trade-off (TTO) method, is used to obtain utilities for diagnostic procedures on the basis of the fact that people wait longer to avoid noxious tests and/or procedures. The WTO method provides short-term quality of life tolls in terms of quality-adjusted life-weeks by scaling wait times with pre- and posttreatment utilities. Utilities for uterine fibroids before and after treatment were obtained with the TTO method and a visual analog scale (VAS) by using a questionnaire administered by means of a phone interview. WTO wait times were adjusted for quality of life with VAS and TTO utilities and a transformation of VAS. Wait times were compared by using nonparametric tests. The study participants included 62 patients who had undergone abdominal hysterectomy, 74 who had undergone UAE, and 61 who had undergone MR imaging-guided focused ultrasound surgery. RESULTS: Quality of life increased with all treatments. The median WTO wait time was higher for hysterectomy (21.6 weeks) than for UAE or MR imaging-guided focused ultrasound surgery (14.1 weeks for both) (P < .05). Quality-adjusted life-week tolls were smaller when scaled according to TTO than when scaled according to VAS or transformation of VAS. CONCLUSION: Quality of life increased after all fibroid treatments. WTO is feasible for assessing the quality-adjusted morbidity of treatment procedures. SUPPLEMENTAL MATERIAL: http://radiology.rsna.org/lookup/suppl/doi:10.1148/radiol.11100704/-/DC1.
Pascal O Zinn, Bhanu Mahajan, Bhanu Majadan, Pratheesh Sathyan, Sanjay K Singh, Sadhan Majumder, Ferenc A Jolesz, and Rivka R Colen. 2011. “Radiogenomic mapping of edema/cellular invasion MRI-phenotypes in glioblastoma multiforme.” PLoS One, 6, 10, Pp. e25451.Abstract
BACKGROUND: Despite recent discoveries of new molecular targets and pathways, the search for an effective therapy for Glioblastoma Multiforme (GBM) continues. A newly emerged field, radiogenomics, links gene expression profiles with MRI phenotypes. MRI-FLAIR is a noninvasive diagnostic modality and was previously found to correlate with cellular invasion in GBM. Thus, our radiogenomic screen has the potential to reveal novel molecular determinants of invasion. Here, we present the first comprehensive radiogenomic analysis using quantitative MRI volumetrics and large-scale gene- and microRNA expression profiling in GBM. METHODS: Based on The Cancer Genome Atlas (TCGA), discovery and validation sets with gene, microRNA, and quantitative MR-imaging data were created. Top concordant genes and microRNAs correlated with high FLAIR volumes from both sets were further characterized by Kaplan Meier survival statistics, microRNA-gene correlation analyses, and GBM molecular subtype-specific distribution. RESULTS: The top upregulated gene in both the discovery (4 fold) and validation (11 fold) sets was PERIOSTIN (POSTN). The top downregulated microRNA in both sets was miR-219, which is predicted to bind to POSTN. Kaplan Meier analysis demonstrated that above median expression of POSTN resulted in significantly decreased survival and shorter time to disease progression (P<0.001). High POSTN and low miR-219 expression were significantly associated with the mesenchymal GBM subtype (P<0.0001). CONCLUSION: Here, we propose a novel diagnostic method to screen for molecular cancer subtypes and genomic correlates of cellular invasion. Our findings also have potential therapeutic significance since successful molecular inhibition of invasion will improve therapy and patient survival in GBM.
Bruno Madore, W. Scott Hoge, Tzu-Cheng Chao, Gary P. Zientara, and Renxin Chu. 2011. “Retrospectively Gated Cardiac Cine Imaging with Temporal and Spatial Acceleration.” Magn Reson Imaging, 29, 4, Pp. 457-69.Abstract

Parallel imaging methods are routinely used to accelerate the image acquisition process in cardiac cine imaging. The addition of a temporal acceleration method, whereby k-space is sampled differently for different time frames, has been shown in prior work to improve image quality as compared to parallel imaging by itself. However, such temporal acceleration strategies prove difficult to combine with retrospectively gated cine imaging. The only currently published method to feature such combination, by Hansen et al. [Magn Reson Med 55 (2006) 85-91] tends to be associated with prohibitively long reconstruction times. The goal of the present work was to develop a retrospectively gated cardiac cine method that features both parallel imaging and temporal acceleration, capable of achieving significant acceleration factors on commonly available hardware and associated with reconstruction times short enough for practical use in a clinical context. Seven cardiac patients and a healthy volunteer were recruited and imaged, with acceleration factors of 3.5 or 4.5, using an eight-channel product cardiac array on a 1.5-T system. The prescribed FOV value proved slightly too small in three patients, and one of the patients had a bigemini condition. Despite these additional challenges, good-quality results were obtained for all slices and all patients, with a reconstruction time of 0.98±0.07 s per frame, or about 20 s for a 20-frame slice, using a single processor on a single PC. As compared to using parallel imaging by itself, the addition of a temporal acceleration strategy provided much resistance to artifacts.

Hussein Kekhia, Laura Rigolo, Isaiah Norton, and Alexandra J Golby. 2011. “Special surgical considerations for functional brain mapping.” Neurosurg Clin N Am, 22, 2, Pp. 111-32.Abstract

The development of functional mapping techniques gives neurosurgeons many options for preoperative planning. Integrating functional and anatomic data can inform patient selection and surgical planning and makes functional mapping more accessible than when only invasive studies were available. However, the applications of functional mapping to neurosurgical patients are still evolving. Functional imaging remains complex and requires an understanding of the underlying physiologic and imaging characteristics. Neurosurgeons must be accustomed to interpreting highly processed data. Successful implementation of functional image-guided procedures requires efficient interactions between neurosurgeon, neurologist, radiologist, neuropsychologist, and others, but promises to enhance the care of patients.

Santiago Aja-Fernández, Antonio Tristán-Vega, and W. Scott Hoge. 2011. “Statistical Noise Analysis in GRAPPA using a Parametrized Noncentral Chi Approximation Model.” Magn Reson Med, 65, 4, Pp. 1195-206.Abstract

The characterization of the distribution of noise in the magnitude MR image is a very important problem within image processing algorithms. The Rician noise assumed in single-coil acquisitions has been the keystone for signal-to-noise ratio estimation, image filtering, or diffusion tensor estimation for years. With the advent of parallel protocols such as sensitivity encoding or Generalized Autocalibrated Partially Parallel Acquisitions that allow accelerated acquisitions, this noise model no longer holds. Since Generalized Autocalibrated Partially Parallel Acquisitions reconstructions yield the combination of the squared signals recovered at each receiving coil, noncentral Chi statistics have been previously proposed to model the distribution of noise. However, we prove in this article that this is a weak model due to several artifacts in the acquisition scheme, mainly the correlation existing between the signals obtained at each coil. Alternatively, we propose to model such correlations with a reduction in the number of degrees of freedom of the signal, which translates in an equivalent nonaccelerated system with a minor number of independent receiving coils and, consequently, a lower signal-to-noise ratio. With this model, a noncentral Chi distribution can be assumed for all pixels in the image, whose effective number of coils and effective variance of noise can be explicitly computed in a closed form from the Generalized Autocalibrated Partially Parallel Acquisitions interpolation coefficients. Extensive experiments over both synthetic and in vivo data sets have been performed to show the goodness of fit of out model.

Xiaogang Wang, Eric WL Grimson, and Carl-Fredrik Westin. 2011. “Tractography segmentation using a hierarchical Dirichlet processes mixture model.” Neuroimage, 54, 1, Pp. 290-302.Abstract
In this paper, we propose a new nonparametric Bayesian framework to cluster white matter fiber tracts into bundles using a hierarchical Dirichlet processes mixture (HDPM) model. The number of clusters is automatically learned driven by data with a Dirichlet process (DP) prior instead of being manually specified. After the models of bundles have been learned from training data without supervision, they can be used as priors to cluster/classify fibers of new subjects for comparison across subjects. When clustering fibers of new subjects, new clusters can be created for structures not observed in the training data. Our approach does not require computing pairwise distances between fibers and can cluster a huge set of fibers across multiple subjects. We present results on several data sets, the largest of which has more than 120,000 fibers.
Yun Jing and Greg T Clement. 2011. “On the Use of Gegenbauer Reconstructions for Shock Wave Propagation Modeling.” J Acoust Soc Am, 130, 3, Pp. 1115-24.Abstract

In therapeutic ultrasound, the presence of shock waves can be significant due to the use of high intensity beams, as well as due to shock formation during inertial cavitation. Although modeling of such strongly nonlinear waves can be carried out using spectral methods, such calculations are typically considered impractical, since accurate calculations often require hundreds or even thousands of harmonics to be considered, leading to prohibitive computational times. Instead, time-domain algorithms which generally utilize Godunov-type finite-difference schemes are commonly used. Although these time domain methods can accurately model steep shock wave fronts, unlike spectral methods they are inherently unsuitable for modeling realistic tissue dispersion relations. Motivated by the need for a more general model, the use of Gegenbauer reconstructions as a postprocess tool to resolve the band-limitations of the spectral methods are investigated. The present work focuses on eliminating the Gibbs phenomenon when representing a steep wave front using a limited number of harmonics. Both plane wave and axisymmetric 2D transducer problems will be presented to characterize the proposed method.

Demian Wassermann, Yogesh Rathi, Sylvain Bouix, Marek Kubicki, Ron Kikinis, Martha Shenton, and Carl-Fredrik Westin. 2011. “White matter bundle registration and population analysis based on Gaussian processes.” Inf Process Med Imaging, 22, Pp. 320-32.Abstract
This paper proposes a method for the registration of white matter tract bundles traced from diffusion images and its extension to atlas generation, Our framework is based on a Gaussian process representation of tract density maps. Such a representation avoids the need for point-to-point correspondences, is robust to tract interruptions and reconnections and seamlessly handles the comparison and combination of white matter tract bundles. Moreover, being a parametric model, this approach has the potential to be defined in the Gaussian processes' parameter space, without the need for resampling the fiber bundles during the registration process. We use the similarity measure of our Gaussian process framework, which is in fact an inner product, to drive a diffeomorphic registration algorithm between two sets of homologous bundles which is not biased by point-to-point correspondences or the parametrization of the tracts. We estimate a dense deformation of the underlying white matter using the bundles as anatomical landmarks and obtain a population atlas of those fiber bundles. Finally we test our results in several different bundles obtained from in-vivo data.

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