Publications by Year: 2009

Sota Oguro, Junichi Tokuda, Haytham Elhawary, Steven Haker, Ron Kikinis, Clare M Tempany, and Nobuhiko Hata. 11/2009. “MRI Signal Intensity Based B-Spline Nonrigid Registration for Pre- and Intraoperative Imaging during Prostate Brachytherapy.” J Magn Reson Imaging, 30, 5, Pp. 1052-8.Abstract

PURPOSE: To apply an intensity-based nonrigid registration algorithm to MRI-guided prostate brachytherapy clinical data and to assess its accuracy. MATERIALS AND METHODS: A nonrigid registration of preoperative MRI to intraoperative MRI images was carried out in 16 cases using a Basis-Spline algorithm in a retrospective manner. The registration was assessed qualitatively by experts' visual inspection and quantitatively by measuring the Dice similarity coefficient (DSC) for total gland (TG), central gland (CG), and peripheral zone (PZ), the mutual information (MI) metric, and the fiducial registration error (FRE) between corresponding anatomical landmarks for both the nonrigid and a rigid registration method. RESULTS: All 16 cases were successfully registered in less than 5 min. After the nonrigid registration, DSC values for TG, CG, PZ were 0.91, 0.89, 0.79, respectively, the MI metric was -0.19 +/- 0.07 and FRE presented a value of 2.3 +/- 1.8 mm. All the metrics were significantly better than in the case of rigid registration, as determined by one-sided t-tests. CONCLUSION: The intensity-based nonrigid registration method using clinical data was demonstrated to be feasible and showed statistically improved metrics when compare to only rigid registration. The method is a valuable tool to integrate pre- and intraoperative images for brachytherapy.

Clare Poynton, Mark Jenkinson, and William M Wells III. 9/2009. “Atlas-based Improved Prediction of Magnetic Field Inhomogeneity for Distortion Correction of EPI Data.” Med Image Comput Comput Assist Interv, 12, Pt 2, Pp. 951-9.Abstract

We describe a method for atlas-based segmentation of structural MRI for calculation of magnetic fieldmaps. CT data sets are used to construct a probabilistic atlas of the head and corresponding MR is used to train a classifier that segments soft tissue, air, and bone. Subject-specific fieldmaps are computed from the segmentations using a perturbation field model. Previous work has shown that distortion in echo-planar images can be corrected using predicted fieldmaps. We obtain results that agree well with acquired fieldmaps: 90% of voxel shifts from predicted fieldmaps show subvoxel disagreement with those computed from acquired fieldmaps. In addition, our fieldmap predictions show statistically significant improvement following inclusion of the atlas.

Matthew Toews and William M Wells III. 7/2009. “Bayesian Registration via Local Image Regions: Information, Selection and Marginalization.” Inf Process Med Imaging, 21, Pp. 435-46.Abstract

We propose a novel Bayesian registration formulation in which image location is represented as a latent random variable. Location is marginalized to determine the maximum a priori (MAP) transform between images, which results in registration that is more robust than the alternatives of omitting locality (i.e. global registration) or jointly maximizing locality and transform (i.e. iconic registration). A mathematical link is established between the Bayesian registration formulation and the mutual information (MI) similarity measure. This leads to a novel technique for selecting informative image regions for registration, based on the MI of image intensity and spatial location. Experimental results demonstrate the effectiveness of the marginalization formulation and the MI-based region selection technique for ultrasound (US) to magnetic resonance (MR) registration in an image-guided neurosurgical application.

Petter Risholm, Eigil Samsett, Ion-Florin Talos, and William M Wells III. 7/2009. “A Non-rigid Registration Framework that Accommodates Resection and Retraction.” Inf Process Med Imaging, 21, Pp. 447-58.Abstract

Traditional non-rigid registration algorithms are incapable of accurately registering intra-operative with pre-operative images whenever tissue has been resected or retracted. In this work we present methods for detecting and handling retraction and resection. The registration framework is based on the bijective Demons algorithm using an anisotropic diffusion smoother. Retraction is detected at areas of the deformation field with high internal strain and the estimated retraction boundary is integrated as a diffusion boundary in the smoother to allow discontinuities to develop across the resection boundary. Resection is detected by a level set method evolving in the space where image intensities disagree. The estimated resection is integrated into the smoother as a diffusion sink to restrict image forces originating inside the resection from being diffused to surrounding areas. In addition, the deformation field is continuous across the diffusion sink boundary which allow us to move the boundary of the diffusion sink without changing values in the deformation field (no interpolation or extrapolation is needed). We present preliminary results on both synthetic and clinical data which clearly shows the added value of explicitly modeling these processes in a registration framework.

Aristotle N Voineskos, Lauren J O'Donnell, Nancy J Lobaugh, Doug Markant, Stephanie H Ameis, Marc Niethammer, Benoit H Mulsant, Bruce G Pollock, James L Kennedy, Carl-Fredrik Westin, and Martha E Shenton. 4/2009. “Quantitative Examination of a Novel Clustering Method using Magnetic Resonance Diffusion Tensor Tractography.” Neuroimage, 45, 2, Pp. 370-6.Abstract

MR diffusion tensor imaging (DTI) can measure and visualize organization of white matter fibre tracts in vivo. DTI is a relatively new imaging technique, and new tools developed for quantifying fibre tracts require evaluation. The purpose of this study was to compare the reliability of a novel clustering approach with a multiple region of interest (MROI) approach in both healthy and disease (schizophrenia) populations. DTI images were acquired in 20 participants (n=10 patients with schizophrenia: 56+/-15 years; n=10 controls: 51+/-20 years) (1.5 T GE system) with diffusion gradients applied in 23 non-collinear directions, repeated three times. Whole brain seeding and creation of fibre tracts were then performed. Interrater reliability of the clustering approach, and the MROI approach, were each evaluated and the methods compared. There was high spatial (voxel-based) agreement within and between the clustering and MROI methods. Fractional anisotropy, trace, and radial and axial diffusivity values showed high intraclass correlation (p<0.001 for all tracts) for each approach. Differences in scalar indices of diffusion between the clustering and MROI approach were minimal. The excellent interrater reliability of the clustering method and high agreement with the MROI method, quantitatively and spatially, indicates that the clustering method can be used with confidence. The clustering method avoids biases of ROI drawing and placement, and, not limited by a priori predictions, may be a more robust and efficient way to identify and measure white matter tracts of interest.

Marcos Martin-Fernandez, Emma Muñoz-Moreno, L Cammoun, J-P Thiran, Carl-Fredrik Westin, and Carlos Alberola-López. 2/2009. “Sequential Anisotropic Multichannel Wiener Filtering with Rician Bias Correction Applied to 3D Regularization of DWI Data.” Med Image Anal, 13, 1, Pp. 19-35.Abstract

It has been shown that the tensor calculation is very sensitive to the presence of noise in the acquired images, yielding to very low quality Diffusion Tensor Images (DTI) data. Recent investigations have shown that the noise present in the Diffusion Weighted Images (DWI) causes bias effects on the DTI data which cannot be corrected if the noise characteristic is not taken into account. One possible solution is to increase the minimum number of acquired measurements (which is 7) to several tens (or even several hundreds). This has the disadvantage of increasing the acquisition time by one (or two) orders of magnitude, making the process inconvenient for a clinical setting. We here proposed a turn-around procedure for which the number of acquisitions is maintained but, the DWI data are filtered prior to determining the DTI. We show a significant reduction on the DTI bias by means of a simple and fast procedure which is based on linear filtering; well-known drawbacks of such filters are circumvented by means of anisotropic neighborhoods and sequential application of the filter itself. Information of the first order probability density function of the raw data, namely, the Rice distribution, is also included. Results are shown both for synthetic and real datasets. Some error measurements are determined in the synthetic experiments, showing how the proposed scheme is able to reduce them. It is worth noting a 50% increase in the linear component for real DTI data, meaning that the bias in the DTI is considerably reduced. A novel fiber smoothness measure is defined to evaluate the resulting tractography for real DWI data. Our findings show that after filtering, fibers are considerably smoother on the average. Execution times are very low as compared to other reported approaches which allows for a real-time implementation.

Jennifer Fitzsimmons, Marek Kubicki, Smith A.K., Georgia B Bushell, Raul San Jose Estépar, Carl-Fredrik Westin, Paul G Nestor, Margaret Niznikiewicz, Ron Kikinis, Robert W McCarley, and Martha E Shenton. 1/2009. “Diffusion Tractography of the Fornix in Schizophrenia.” Schizophr Res, 107, 1, Pp. 39-46.Abstract

BACKGROUND: White matter fiber tracts, especially those interconnecting the frontal and temporal lobes, are likely implicated in pathophysiology of schizophrenia. Very few studies, however, have focused on the fornix, a compact bundle of white matter fibers, projecting from the hippocampus to the septum, anterior nucleus of the thalamus and the mamillary bodies. Diffusion Tensor Imaging (DTI), and a new post-processing method, fiber tractography, provides a unique opportunity to visualize and to quantify entire trajectories of fiber bundles, such as the fornix, in vivo. We applied these techniques to quantify fornix diffusion anisotropy in schizophrenia. METHODS: DTI images were used to evaluate the left and the right fornix in 36 male patients diagnosed with chronic schizophrenia and 35 male healthy individuals, group matched on age, parental socioeconomic status, and handedness. Regions of interest were drawn manually, blind to group membership, to guide tractography, and fractional anisotropy (FA), a measure of fiber integrity, was calculated and averaged over the entire tract for each subject. The Doors and People test (DPT) was used to evaluate visual and verbal memory, combined recall and combined recognition. RESULTS: Analysis of variance was performed and findings demonstrated a difference between patients with schizophrenia and controls for fornix FA (p=0.006). Protected post-hoc independent sample t-tests demonstrated a bilateral FA decrease in schizophrenia, compared with control subjects (left side: p=0.048; right side p=0.006). Higher fornix FA was statistically significantly correlated with DPT and measures of combined visual memory (r=0.554, p=0.026), combined verbal memory (r=0.647, p=0.007), combined recall (r=0.516, p=0.041), and combined recognition (r=0.710, p=0.002) for the control group. No such statistically significant correlations were found in the patient group. CONCLUSIONS: Our findings show the utility of applying DTI and tractography to study white matter fiber tracts in vivo in schizophrenia. Specifically, we observed a bilateral disruption in fornix integrity in schizophrenia, thus broadening our understanding of the pathophysiology of this disease.

Tauseef Ur Rehman, Eldad Haber, Gallagher Pryor, John Melonakos, and Allen Tannenbaum. 2009. “3D nonrigid registration via optimal mass transport on the GPU.” Med Image Anal, 13, 6, Pp. 931-40.Abstract
In this paper, we present a new computationally efficient numerical scheme for the minimizing flow approach for optimal mass transport (OMT) with applications to non-rigid 3D image registration. The approach utilizes all of the gray-scale data in both images, and the optimal mapping from image A to image B is the inverse of the optimal mapping from B to A. Further, no landmarks need to be specified, and the minimizer of the distance functional involved is unique. Our implementation also employs multigrid, and parallel methodologies on a consumer graphics processing unit (GPU) for fast computation. Although computing the optimal map has been shown to be computationally expensive in the past, we show that our approach is orders of magnitude faster then previous work and is capable of finding transport maps with optimality measures (mean curl) previously unattainable by other works (which directly influences the accuracy of registration). We give results where the algorithm was used to compute non-rigid registrations of 3D synthetic data as well as intra-patient pre-operative and post-operative 3D brain MRI datasets.
Grady Nunnery, Eli Hershkovits, Allen Tannenbaum, and Rina Tannenbaum. 2009. “Adsorption of poly(methyl methacrylate) on concave Al2O3 surfaces in nanoporous membranes.” Langmuir, 25, 16, Pp. 9157-63.Abstract
The objective of this study was to determine the influence of polymer molecular weight and surface curvature on the adsorption of polymers onto concave surfaces. Poly(methyl methacrylate) (PMMA) of various molecular weights was adsorbed onto porous aluminum oxide membranes having various pore sizes, ranging from 32 to 220 nm. The surface coverage, expressed as repeat units per unit surface area, was observed to vary linearly with molecular weight for molecular weights below approximately 120,000 g/mol. The coverage was independent of molecular weight above this critical molar mass, as was previously reported for the adsorption of PMMA on convex surfaces. Furthermore, the coverage varied linearly with pore size. A theoretical model was developed to describe curvature-dependent adsorption by considering the density gradient that exists between the surface and the edge of the adsorption layer. According to this model, the density gradient of the adsorbed polymer segments scales inversely with particle size, while the total coverage scales linearly with particle size, in good agreement with experiment. These results show that the details of the adsorption of polymers onto concave surfaces with cylindrical geometries can be used to calculate molecular weight (below a critical molecular weight) if pore size is known. Conversely, pore size can also be determined with similar adsorption experiments. Most significantly, for polymers above a critical molecular weight, the precise molecular weight need not be known in order to determine pore size. Moreover, the adsorption developed and validated in this work can be used to predict coverage also onto surfaces with different geometries.
Behnood Gholami, Wassim M Haddad, and Allen R Tannenbaum. 2009. “Agitation and pain assessment using digital imaging.” Conf Proc IEEE Eng Med Biol Soc, 2009, Pp. 2176-9.Abstract
Pain assessment in patients who are unable to verbally communicate with medical staff is a challenging problem in patient critical care. The fundamental limitations in sedation and pain assessment in the intensive care unit (ICU) stem from subjective assessment criteria, rather than quantifiable, measurable data for ICU sedation and analgesia. This often results in poor quality and inconsistent treatment of patient agitation and pain from nurse to nurse. Recent advancements in pattern recognition techniques using a relevance vector machine algorithm can assist medical staff in assessing sedation and pain by constantly monitoring the patient and providing the clinician with quantifiable data for ICU sedation. In this paper, we show that the pain intensity assessment given by a computer classifier has a strong correlation with the pain intensity assessed by expert and non-expert human examiners.
Mert R Sabuncu, Thomas BT Yeo, Koen Van Leemput, Tom Vercauteren, and Polina Golland. 2009. “Asymmetric image-template registration.” Med Image Comput Comput Assist Interv, 12, Pt 1, Pp. 565-73.Abstract
A natural requirement in pairwise image registration is that the resulting deformation is independent of the order of the images. This constraint is typically achieved via a symmetric cost function and has been shown to reduce the effects of local optima. Consequently, symmetric registration has been successfully applied to pairwise image registration as well as the spatial alignment of individual images with a template. However, recent work has shown that the relationship between an image and a template is fundamentally asymmetric. In this paper, we develop a method that reconciles the practical advantages of symmetric registration with the asymmetric nature of image-template registration by adding a simple correction factor to the symmetric cost function. We instantiate our model within a log-domain diffeomorphic registration framework. Our experiments show exploiting the asymmetry in image-template registration improves alignment in the image coordinates.
Koen Van Leemput, Akram Bakkour, Thomas Benner, Graham Wiggins, Lawrence L Wald, Jean Augustinack, Bradford C Dickerson, Polina Golland, and Bruce Fischl. 2009. “Automated segmentation of hippocampal subfields from ultra-high resolution in vivo MRI.” Hippocampus, 19, 6, Pp. 549-57.Abstract
Recent developments in MRI data acquisition technology are starting to yield images that show anatomical features of the hippocampal formation at an unprecedented level of detail, providing the basis for hippocampal subfield measurement. However, a fundamental bottleneck in MRI studies of the hippocampus at the subfield level is that they currently depend on manual segmentation, a laborious process that severely limits the amount of data that can be analyzed. In this article, we present a computational method for segmenting the hippocampal subfields in ultra-high resolution MRI data in a fully automated fashion. Using Bayesian inference, we use a statistical model of image formation around the hippocampal area to obtain automated segmentations. We validate the proposed technique by comparing its segmentations to corresponding manual delineations in ultra-high resolution MRI scans of 10 individuals, and show that automated volume measurements of the larger subfields correlate well with manual volume estimates. Unlike manual segmentations, our automated technique is fully reproducible, and fast enough to enable routine analysis of the hippocampal subfields in large imaging studies.
Antonio Tristán-Vega, Carl-Fredrik Westin, and Santiago Aja-Fernández. 2009. “Bias of least squares approaches for diffusion tensor estimation from array coils in DT-MRI.” Med Image Comput Comput Assist Interv, 12, Pt 1, Pp. 919-26.Abstract
Least Squares (LS) and its weighted version are standard techniques to estimate the Diffusion Tensor (DT) from Diffusion Weighted Images (DWI). They require to linearize the problem by computing the logarithm of the DWI. For the single-coil Rician noise model it has been shown that this model does not introduce a significant bias, but for multiple array coils and parallel imaging, the noise cannot longer be modeled as Rician. As a result the validity of LS approaches is not assured. An analytical study of noise statistics for a multiple coil system is carried out, together with the Weighted LS formulation and noise analysis for this model. Results show that the bias in the computation of the components of the DT may be comparable to their variance in many cases, stressing the importance of unbiased filtering previous to DT estimation.
Amanda K Wake, John N Oshinski, Allen R Tannenbaum, and Don P Giddens. 2009. “Choice of in vivo versus idealized velocity boundary conditions influences physiologically relevant flow patterns in a subject-specific simulation of flow in the human carotid bifurcation.” J Biomech Eng, 131, 2, Pp. 021013.Abstract
Accurate fluid mechanics models are important tools for predicting the flow field in the carotid artery bifurcation and for understanding the relationship between hemodynamics and the initiation and progression of atherosclerosis. Clinical imaging modalities can be used to obtain geometry and blood flow data for developing subject-specific human carotid artery bifurcation models. We developed subject-specific computational fluid dynamics models of the human carotid bifurcation from magnetic resonance (MR) geometry data and phase contrast MR velocity data measured in vivo. Two simulations were conducted with identical geometry, flow rates, and fluid parameters: (1) Simulation 1 used in vivo measured velocity distributions as time-varying boundary conditions and (2) Simulation 2 used idealized fully-developed velocity profiles as boundary conditions. The position and extent of negative axial velocity regions (NAVRs) vary between the two simulations at any given point in time, and these regions vary temporally within each simulation. The combination of inlet velocity boundary conditions, geometry, and flow waveforms influences NAVRs. In particular, the combination of flow division and the location of the velocity peak with respect to individual carotid geometry landmarks (bifurcation apex position and the departure angle of the internal carotid) influences the size and location of these reversed flow zones. Average axial wall shear stress (WSS) distributions are qualitatively similar for the two simulations; however, instantaneous WSS values vary with the choice of velocity boundary conditions. By developing subject-specific simulations from in vivo measured geometry and flow data and varying the velocity boundary conditions in otherwise identical models, we isolated the effects of measured versus idealized velocity distributions on blood flow patterns. Choice of velocity distributions at boundary conditions is shown to influence pathophysiologically relevant flow patterns in the human carotid bifurcation. Although mean WSS distributions are qualitatively similar for measured and idealized inlet boundary conditions, instantaneous NAVRs differ and warrant imposing in vivo velocity boundary conditions in computational simulations. A simulation based on in vivo measured velocity distributions is preferred for modeling hemodynamics in subject-specific carotid artery bifurcation models when studying atherosclerosis initiation and development.
Leonard B Kaban, Edward B Seldin, Ron Kikinis, Krishna Yeshwant, Bonnie L Padwa, and Maria J Troulis. 2009. “Clinical application of curvilinear distraction osteogenesis for correction of mandibular deformities.” J Oral Maxillofac Surg, 67, 5, Pp. 996-1008.Abstract
PURPOSE: To report the use of a semiburied curvilinear distraction device, with a 3-dimensional (3D) computed tomography treatment planning system, for correction of mandibular deformities. MATERIALS AND METHODS: This was a retrospective evaluation of 13 consecutive patients, with syndromic and nonsyndromic micrognathia, who underwent correction by curvilinear distraction osteogenesis. A 3D computed tomography scan was obtained for each patient and imported into a 3D treatment planning system (Slicer/Osteoplan). Surgical guides were constructed to localize the osteotomy and to drill holes to secure the distractor's proximal and distal footplates to the mandible. Postoperatively, patients were followed by clinical examination and plain radiographs to ensure the desired vector of movement. At end distraction, when possible, a 3D computed tomography scan was obtained to document the final mandibular position. RESULTS: Of the 13 patients, 8 were females and 5 were males, with a mean age of 11.9 years (range 15 months to 39 years). All 13 underwent bilateral mandibular curvilinear distraction. Of the 13 patients, 8 were 16 years old or younger and 5 were younger than 6 years of age. The diagnoses included Treacher Collins syndrome (n = 3), Nager syndrome (n = 3), craniofacial microsomia (n = 2), post-traumatic ankylosis (n = 1), and micrognathia (syndromic, n = 3; nonsyndromic, n = 1). The correct distractor placement, vector of movement, and final mandibular position were achieved in 10 of 13 patients. In the other 3 patients, the desired jaw position was achieved by "molding" the regenerate. CONCLUSIONS: The use of a semiburied curvilinear distraction device, with 3D treatment planning, is a potentially powerful tool to correct complex mandibular deformities.
Daniel L Rubin, Ion-Florin Talos, Michael Halle, Mark A Musen, and Ron Kikinis. 2009. “Computational neuroanatomy: ontology-based representation of neural components and connectivity.” BMC Bioinformatics, 10 Suppl 2, Pp. S3.Abstract
BACKGROUND: A critical challenge in neuroscience is organizing, managing, and accessing the explosion in neuroscientific knowledge, particularly anatomic knowledge. We believe that explicit knowledge-based approaches to make neuroscientific knowledge computationally accessible will be helpful in tackling this challenge and will enable a variety of applications exploiting this knowledge, such as surgical planning. RESULTS: We developed ontology-based models of neuroanatomy to enable symbolic lookup, logical inference and mathematical modeling of neural systems. We built a prototype model of the motor system that integrates descriptive anatomic and qualitative functional neuroanatomical knowledge. In addition to modeling normal neuroanatomy, our approach provides an explicit representation of abnormal neural connectivity in disease states, such as common movement disorders. The ontology-based representation encodes both structural and functional aspects of neuroanatomy. The ontology-based models can be evaluated computationally, enabling development of automated computer reasoning applications. CONCLUSION: Neuroanatomical knowledge can be represented in machine-accessible format using ontologies. Computational neuroanatomical approaches such as described in this work could become a key tool in translational informatics, leading to decision support applications that inform and guide surgical planning and personalized care for neurological disease in the future.
Ulas Ziyan, Mert R Sabuncu, Eric WL Grimson, and Carl-Fredrik Westin. 2009. “Consistency Clustering: A Robust Algorithm for Group-wise Registration, Segmentation and Automatic Atlas Construction in Diffusion MRI.” Int J Comput Vis, 85, 3, Pp. 279-290.Abstract
We propose an integrated registration and clustering algorithm, called "consistency clustering", that automatically constructs a probabilistic white-matter atlas from a set of multi-subject diffusion weighted MR images. We formulate the atlas creation as a maximum likelihood problem which the proposed method solves using a generalized Expectation Maximization (EM) framework. Additionally, the algorithm employs an outlier rejection and denoising strategy to produce sharp probabilistic maps of certain bundles of interest. We test this algorithm on synthetic and real data, and evaluate its stability against initialization. We demonstrate labeling a novel subject using the resulting spatial atlas and evaluate the accuracy of this labeling. Consistency clustering is a viable tool for completely automatic white-matter atlas construction for sub-populations and the resulting atlas is potentially useful for making diffusion measurements in a common coordinate system to identify pathology related changes or developmental trends.
David C Banks and Kevin M Beason. 2009. “Decoupling illumination from isosurface generation using 4D light transport.” IEEE Trans Vis Comput Graph, 15, 6, Pp. 1595-602.Abstract
One way to provide global illumination for the scientist who performs an interactive sweep through a 3D scalar dataset is to pre-compute global illumination, resample the radiance onto a 3D grid, then use it as a 3D texture. The basic approach of repeatedly extracting isosurfaces, illuminating them, and then building a 3D illumination grid suffers from the non-uniform sampling that arises from coupling the sampling of radiance with the sampling of isosurfaces. We demonstrate how the illumination step can be decoupled from the isosurface extraction step by illuminating the entire 3D scalar function as a 3-manifold in 4-dimensional space. By reformulating light transport in a higher dimension, one can sample a 3D volume without requiring the radiance samples to aggregate along individual isosurfaces in the pre-computed illumination grid.
Yogesh Rathi, Oleg Michailovich, Martha E Shenton, and Sylvain Bouix. 2009. “Directional functions for orientation distribution estimation.” Med Image Anal, 13, 3, Pp. 432-44.Abstract
Computing the orientation distribution function (ODF) from high angular resolution diffusion imaging (HARDI) signals makes it possible to determine the orientation of fiber bundles of the brain. The HARDI signals are samples measured from a spherical shell and thus require processing on the sphere. Past work on ODF estimation involved using the spherical harmonics or spherical radial basis functions. In this work, we propose three novel directional functions able to represent the measured signals in a very compact manner, i.e., they require very few parameters to completely describe the measured signal. Analytical expressions are derived for computing the corresponding ODF. The directional functions can represent diffusion in a particular direction and mixture models can be used to represent multi-fiber orientations. We show how to estimate the parameters of this mixture model and elaborate on the differences between these functions. We also compare this general framework with estimation of ODF using spherical harmonics on some real and synthetic data. The proposed method could be particularly useful in applications such as tractography and segmentation. Details are also given on different ways in which interpolation can be performed using directional functions. In particular, we discuss a complete Euclidean as well as a "hybrid" framework, comprising of the Riemannian as well as Euclidean spaces, to perform interpolation and compute geodesic distances between two ODF's.
Wanmei Ou, Matti S Hämäläinen, and Polina Golland. 2009. “A distributed spatio-temporal EEG/MEG inverse solver.” Neuroimage, 44, 3, Pp. 932-46.Abstract
We propose a novel l(1)l(2)-norm inverse solver for estimating the sources of EEG/MEG signals. Based on the standard l(1)-norm inverse solvers, this sparse distributed inverse solver integrates the l(1)-norm spatial model with a temporal model of the source signals in order to avoid unstable activation patterns and "spiky" reconstructed signals often produced by the currently used sparse solvers. The joint spatio-temporal model leads to a cost function with an l(1)l(2)-norm regularizer whose minimization can be reduced to a convex second-order cone programming (SOCP) problem and efficiently solved using the interior-point method. The efficient computation of the SOCP problem allows us to implement permutation tests for estimating statistical significance of the inverse solution. Validation with simulated and human MEG data shows that the proposed solver yields source time course estimates qualitatively similar to those obtained through dipole fitting, but without the need to specify the number of dipole sources in advance. Furthermore, the l(1)l(2)-norm solver achieves fewer false positives and a better representation of the source locations than the conventional l(2) minimum-norm estimates.