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1.
Life (Basel) ; 13(2)2023 Feb 04.
Article in English | MEDLINE | ID: mdl-36836797

ABSTRACT

We propose a methodology for monitoring an artificial intelligence (AI) tool for breast cancer screening when deployed in clinical centers. An AI trained to detect suspicious regions of interest in the four views of a mammogram and to characterize their level of suspicion with a score ranging from one (low suspicion) to ten (high suspicion of malignancy) was deployed in four radiological centers across the US. Results were collected between April 2021 and December 2022, resulting in a dataset of 36,581 AI records. To assess the behavior of the AI, its score distribution in each center was compared to a reference distribution obtained in silico using the Pearson correlation coefficient (PCC) between each center AI score distribution and the reference. The estimated PCCs were 0.998 [min: 0.993, max: 0.999] for center US-1, 0.975 [min: 0.923, max: 0.986] for US-2, 0.995 [min: 0.972, max: 0.998] for US-3 and 0.994 [min: 0.962, max: 0.982] for US-4. These values show that the AI behaved as expected. Low PCC values could be used to trigger an alert, which would facilitate the detection of software malfunctions. This methodology can help create new indicators to improve monitoring of software deployed in hospitals.

2.
Radiol Artif Intell ; 2(6): e190208, 2020 Nov.
Article in English | MEDLINE | ID: mdl-33937844

ABSTRACT

PURPOSE: To evaluate the benefits of an artificial intelligence (AI)-based tool for two-dimensional mammography in the breast cancer detection process. MATERIALS AND METHODS: In this multireader, multicase retrospective study, 14 radiologists assessed a dataset of 240 digital mammography images, acquired between 2013 and 2016, using a counterbalance design in which half of the dataset was read without AI and the other half with the help of AI during a first session and vice versa during a second session, which was separated from the first by a washout period. Area under the receiver operating characteristic curve (AUC), sensitivity, specificity, and reading time were assessed as endpoints. RESULTS: The average AUC across readers was 0.769 (95% CI: 0.724, 0.814) without AI and 0.797 (95% CI: 0.754, 0.840) with AI. The average difference in AUC was 0.028 (95% CI: 0.002, 0.055, P = .035). Average sensitivity was increased by 0.033 when using AI support (P = .021). Reading time changed dependently to the AI-tool score. For low likelihood of malignancy (< 2.5%), the time was about the same in the first reading session and slightly decreased in the second reading session. For higher likelihood of malignancy, the reading time was on average increased with the use of AI. CONCLUSION: This clinical investigation demonstrated that the concurrent use of this AI tool improved the diagnostic performance of radiologists in the detection of breast cancer without prolonging their workflow.Supplemental material is available for this article.© RSNA, 2020.

3.
Neuroimage Clin ; 14: 629-640, 2017.
Article in English | MEDLINE | ID: mdl-28348954

ABSTRACT

In imaging studies of neonates, particularly in the clinical setting, diffusion tensor imaging-based tractography is typically unreliable due to the use of fast acquisition protocols that yield low resolution and signal-to-noise ratio (SNR). These image acquisition protocols are implemented with the aim of reducing motion artifacts that may be produced by the movement of the neonate's head during the scanning session. Furthermore, axons are not yet fully myelinated in these subjects. As a result, the water molecules' movements are not as constrained as in older brains, making it even harder to define structure using diffusion profiles. Here, we introduce a post-processing method that overcomes the difficulties described above, allowing the determination of reliable tracts in newborns. We tested our method using neonatal data and successfully extracted some of the limbic, association and commissural fibers, all of which are typically difficult to obtain by direct tractography. Geometrical and diffusion based features of the tracts are then utilized to compare premature babies to term babies. Our results quantify the maturation of white matter fiber tracts in neonates.


Subject(s)
Brain Mapping , Brain/diagnostic imaging , Brain/growth & development , Neural Pathways/diagnostic imaging , Anisotropy , Diffusion Magnetic Resonance Imaging , Female , Humans , Image Processing, Computer-Assisted , Infant , Male , Neural Pathways/growth & development , Regression Analysis
5.
Article in English | MEDLINE | ID: mdl-23286032

ABSTRACT

We present an extension of the diffeomorphic Geometric Demons algorithm which combines the iconic registration with geometric constraints. Our algorithm works in the log-domain space, so that one can efficiently compute the deformation field of the geometry. We represent the shape of objects of interest in the space of currents which is sensitive to both location and geometric structure of objects. Currents provides a distance between geometric structures that can be defined without specifying explicit point-to-point correspondences. We demonstrate this framework by registering simultaneously T1 images and 65 fiber bundles consistently extracted in 12 subjects and compare it against non-linear T1, tensor, and multi-modal T1 + Fractional Anisotropy (FA) registration algorithms. Results show the superiority of the Log-domain Geometric Demons over their purely iconic counterparts.


Subject(s)
Algorithms , Brain/cytology , Diffusion Tensor Imaging/methods , Image Interpretation, Computer-Assisted/methods , Nerve Fibers, Myelinated/ultrastructure , Subtraction Technique , Humans , Image Enhancement/methods , Reproducibility of Results , Sensitivity and Specificity
6.
Article in English | MEDLINE | ID: mdl-21995007

ABSTRACT

In this paper, we propose to use the full diffusion tensor to perform brain-wide score prediction on diffusion tensor imaging (DTI) using the log-Euclidean framework., rather than the commonly used fractional anisotropy (FA). Indeed, scalar values such as the FA do not capture all the information contained in the diffusion tensor. Additionally, full tensor information is included in every step of the pre-processing pipeline: registration, smoothing and feature selection using voxelwise multivariate regression analysis. This approach was tested on data obtained from 30 children and adolescents with autism spectrum disorder and showed some improvement over the FA-only analysis.


Subject(s)
Brain/pathology , Child Development Disorders, Pervasive/pathology , Diffusion Tensor Imaging/methods , Image Processing, Computer-Assisted/methods , Magnetic Resonance Imaging/methods , Algorithms , Artificial Intelligence , Brain Mapping/methods , Child , Humans , Models, Statistical , Multivariate Analysis , Software
7.
Neuroimage ; 56(1): 220-34, 2011 May 01.
Article in English | MEDLINE | ID: mdl-21256221

ABSTRACT

As it provides the only method for mapping white matter fibers in vivo, diffusion MRI tractography is gaining importance in clinical and neuroscience research. However, despite the increasing availability of different diffusion models and tractography algorithms, it remains unclear how to select the optimal fiber reconstruction method, given certain imaging parameters. Consequently, it is of utmost importance to have a quantitative comparison of these models and algorithms and a deeper understanding of the corresponding strengths and weaknesses. In this work, we use a common dataset with known ground truth and a reproducible methodology to quantitatively evaluate the performance of various diffusion models and tractography algorithms. To examine a wide range of methods, the dataset, but not the ground truth, was released to the public for evaluation in a contest, the "Fiber Cup". 10 fiber reconstruction methods were evaluated. The results provide evidence that: 1. For high SNR datasets, diffusion models such as (fiber) orientation distribution functions correctly model the underlying fiber distribution and can be used in conjunction with streamline tractography, and 2. For medium or low SNR datasets, a prior on the spatial smoothness of either the diffusion model or the fibers is recommended for correct modelling of the fiber distribution and proper tractography results. The phantom dataset, the ground truth fibers, the evaluation methodology and the results obtained so far will remain publicly available on: http://www.lnao.fr/spip.php?rubrique79 to serve as a comparison basis for existing or new tractography methods. New results can be submitted to fibercup09@gmail.com and updates will be published on the webpage.


Subject(s)
Algorithms , Brain Mapping/instrumentation , Brain/anatomy & histology , Diffusion Tensor Imaging/instrumentation , Neural Pathways/anatomy & histology , Phantoms, Imaging , Brain Mapping/methods , Humans
8.
Neuroimage ; 55(4): 1577-86, 2011 Apr 15.
Article in English | MEDLINE | ID: mdl-21256236

ABSTRACT

In recent years, diffusion tensor imaging (DTI) has become the modality of choice to investigate white matter pathology in the developing brain. To study neonate Krabbe disease with DTI, we evaluate the performance of linear and non-linear DTI registration algorithms for atlas based fiber tract analysis. The DTI scans of 10 age-matched neonates with infantile Krabbe disease are mapped into an atlas for the analysis of major fiber tracts - the genu and splenium of the corpus callosum, the internal capsules tracts and the uncinate fasciculi. The neonate atlas is based on 377 healthy control subjects, generated using an unbiased diffeomorphic atlas building method. To evaluate the performance of one linear and seven nonlinear commonly used registration algorithms for DTI we propose the use of two novel evaluation metrics: a regional matching quality criterion incorporating the local tensor orientation similarity, and a fiber property profile based metric using normative correlation. Our experimental results indicate that the whole tensor based registration method within the DTI-ToolKit (DTI-TK) shows the best performance for our application.


Subject(s)
Algorithms , Diffusion Tensor Imaging/methods , Image Interpretation, Computer-Assisted/methods , Leukodystrophy, Globoid Cell/pathology , Nerve Fibers, Myelinated/pathology , Pattern Recognition, Automated/methods , Subtraction Technique , Computer Simulation , Female , Humans , Image Enhancement/methods , Infant , Infant, Newborn , Male , Models, Anatomic , Reproducibility of Results , Sensitivity and Specificity
9.
Neuroimage ; 55(3): 1073-90, 2011 Apr 01.
Article in English | MEDLINE | ID: mdl-21126594

ABSTRACT

This paper proposes a generic framework for the registration, the template estimation and the variability analysis of white matter fiber bundles extracted from diffusion images. This framework is based on the metric on currents for the comparison of fiber bundles. This metric measures anatomical differences between fiber bundles, seen as global homologous structures across subjects. It avoids the need to establish correspondences between points or between individual fibers of different bundles. It can measure differences both in terms of the geometry of the bundles (like its boundaries) and in terms of the density of fibers within the bundle. It is robust to fiber interruptions and reconnections. In addition, a recently introduced sparse approximation algorithm allows us to give an interpretable representation of the fiber bundles and their variations in the framework of currents. First, we used this metric to drive the registration between two sets of homologous fiber bundles of two different subjects. A dense deformation of the underlying white matter is estimated, which is constrained by the bundles seen as global anatomical landmarks. By contrast, the alignment obtained from image registration is driven only by the local gradient of the image. Second, we propose a generative statistical model for the analysis of a collection of homologous bundles. This model consistently estimates prototype fiber bundles (called template), which capture the anatomical invariants in the population, a set of deformations, which align the geometry of the template to that of each subject and a set of residual perturbations. The statistical analysis of both the deformations and the residuals describe the anatomical variability in terms of geometry (stretching, torque, etc.) and "texture" (fiber density, etc.). Third, this statistical modeling allows us to simulate new synthetic bundles according to the estimated variability. This gives a way to interpret the anatomical features that the model detects consistently across the subjects. This may be used to better understand the bias introduced by the fiber extraction methods and eventually to give anatomical characterization of the normal or pathological variability of fiber bundles.


Subject(s)
Atlases as Topic , Brain/anatomy & histology , Image Processing, Computer-Assisted/methods , Nerve Fibers, Myelinated/physiology , Algorithms , Brain/cytology , Brain Mapping , Data Interpretation, Statistical , Humans , Image Enhancement/methods , Imaging, Three-Dimensional/methods , Linear Models , Models, Neurological , Pyramidal Tracts/anatomy & histology , Pyramidal Tracts/cytology
10.
Article in English | MEDLINE | ID: mdl-20879232

ABSTRACT

Functional brain connectivity, as revealed through distant correlations in the signals measured by functional Magnetic Resonance Imaging (fMRI), is a promising source of biomarkers of brain pathologies. However, establishing and using diagnostic markers requires probabilistic inter-subject comparisons. Principled comparison of functional-connectivity structures is still a challenging issue. We give a new matrix-variate probabilistic model suitable for inter-subject comparison of functional connectivity matrices on the manifold of Symmetric Positive Definite (SPD) matrices. We show that this model leads to a new algorithm for principled comparison of connectivity coefficients between pairs of regions. We apply this model to comparing separately post-stroke patients to a group of healthy controls. We find neurologically-relevant connection differences and show that our model is more sensitive that the standard procedure. To the best of our knowledge, these results are the first report of functional connectivity differences between a single-patient and a group and thus establish an important step toward using functional connectivity as a diagnostic tool.


Subject(s)
Algorithms , Brain/physiopathology , Image Interpretation, Computer-Assisted/methods , Magnetic Resonance Imaging/methods , Stroke/diagnosis , Stroke/physiopathology , Analysis of Variance , Computer Simulation , Data Interpretation, Statistical , Humans , Image Enhancement/methods , Models, Neurological , Models, Statistical , Reproducibility of Results , Sensitivity and Specificity
11.
Article in English | MEDLINE | ID: mdl-20879274

ABSTRACT

This paper presents a method inferring a model of the brain white matter organisation from HARDI tractography results computed for a group of subjects. This model is made up of a set of generic fiber bundles that can be detected in most of the population. Our approach is based on a two-level clustering strategy. The first level is a multiresolution intra-subject clustering of the million tracts that are computed for each brain. This analysis reduces the complexity of the data to a few thousands fiber bundles for each subject. The second level is an intersubject clustering over fiber bundle centroids from all the subjects using a pairwise distance computed after spatial normalization. The resulting model includes the large bundles of anatomical literature and about 20 U-fiber bundles in each hemisphere.


Subject(s)
Algorithms , Brain/anatomy & histology , Diffusion Magnetic Resonance Imaging/methods , Image Interpretation, Computer-Assisted/methods , Nerve Fibers, Myelinated/ultrastructure , Pattern Recognition, Automated/methods , Computer Simulation , Humans , Image Enhancement/methods , Models, Anatomic , Models, Neurological , Reproducibility of Results , Sensitivity and Specificity
12.
Inf Process Med Imaging ; 21: 114-25, 2009.
Article in English | MEDLINE | ID: mdl-19694257

ABSTRACT

The purpose of this paper is to measure the variability of a population of white matter fiber bundles without imposing unrealistic geometrical priors. In this respect, modeling fiber bundles as currents seems particularly relevant, as it gives a metric between bundles which relies neither on point nor on fiber correspondences and which is robust to fiber interruption. First, this metric is included in a diffeomorphic registration scheme which consistently aligns sets of fiber bundles. In particular, we show that aligning directly fiber bundles may solve the aperture problem which appears when fiber mappings are constrained by tensors only. Second, the measure of variability of a population of fiber bundles is based on a statistical model which considers every bundle as a random diffeomorphic deformation of a common template plus a random non-diffeomorphic perturbation. Thus, the variability is decomposed into a geometrical part and a "texture" part. Our results on real data show that both parts may contain interesting anatomical features.


Subject(s)
Algorithms , Brain/anatomy & histology , Diffusion Magnetic Resonance Imaging/methods , Image Interpretation, Computer-Assisted/methods , Imaging, Three-Dimensional/methods , Nerve Fibers, Myelinated/ultrastructure , Pattern Recognition, Automated/methods , Artificial Intelligence , Cluster Analysis , Computer Simulation , Humans , Image Enhancement/methods , Models, Neurological , Models, Statistical , Reproducibility of Results , Sensitivity and Specificity
13.
IEEE Trans Med Imaging ; 28(12): 1914-28, 2009 Dec.
Article in English | MEDLINE | ID: mdl-19556193

ABSTRACT

In this paper, we propose the DT-REFinD algorithm for the diffeomorphic nonlinear registration of diffusion tensor images. Unlike scalar images, deforming tensor images requires choosing both a reorientation strategy and an interpolation scheme. Current diffusion tensor registration algorithms that use full tensor information face difficulties in computing the differential of the tensor reorientation strategy and consequently, these methods often approximate the gradient of the objective function. In the case of the finite-strain (FS) reorientation strategy, we borrow results from the pose estimation literature in computer vision to derive an analytical gradient of the registration objective function. By utilizing the closed-form gradient and the velocity field representation of one parameter subgroups of diffeomorphisms, the resulting registration algorithm is diffeomorphic and fast. We contrast the algorithm with a traditional FS alternative that ignores the reorientation in the gradient computation. We show that the exact gradient leads to significantly better registration at the cost of computation time. Independently of the choice of Euclidean or Log-Euclidean interpolation and sum of squared differences dissimilarity measure, the exact gradient achieves better alignment over an entire spectrum of deformation penalties. Alignment quality is assessed with a battery of metrics including tensor overlap, fractional anisotropy, inverse consistency and closeness to synthetic warps. The improvements persist even when a different reorientation scheme, preservation of principal directions, is used to apply the final deformations.


Subject(s)
Algorithms , Elasticity Imaging Techniques/methods , Image Enhancement/methods , Image Interpretation, Computer-Assisted/methods , Pattern Recognition, Automated/methods , Subtraction Technique , Artificial Intelligence , Computer Simulation , Humans , Models, Biological , Reproducibility of Results , Sensitivity and Specificity
14.
Med Image Comput Comput Assist Interv ; 12(Pt 1): 886-93, 2009.
Article in English | MEDLINE | ID: mdl-20426072

ABSTRACT

In this paper, we compare a representative selection of current state-of-the-art algorithms in diffusion-weighted magnetic resonance imaging (dwMRI) tractography, and propose a novel way to quantitatively define the connectivity between brain regions. As criterion for the comparison, we quantify the connectivity computed with the different methods. We provide initial results using diffusion tensor, spherical deconvolution, ball-and-stick model, and persistent angular structure (PAS) along with deterministic and probabilistic tractography algorithms on a human DWI dataset. The connectivity is presented for a representative selection of regions in the brain in matrices and connectograms. Our results show that fiber crossing models are able to reveal connections between more brain areas than the simple tensor model. Probabilistic approaches show in average more connected regions but lower connectivity values than deterministic methods.


Subject(s)
Brain/cytology , Diffusion Tensor Imaging/methods , Image Interpretation, Computer-Assisted/methods , Imaging, Three-Dimensional/methods , Nerve Fibers, Myelinated/ultrastructure , Pattern Recognition, Automated/methods , Subtraction Technique , Algorithms , Artificial Intelligence , Humans , Image Enhancement/methods , Reproducibility of Results , Sensitivity and Specificity
15.
Med Image Comput Comput Assist Interv ; 12(Pt 1): 927-34, 2009.
Article in English | MEDLINE | ID: mdl-20426077

ABSTRACT

This paper introduces a novel framework for global diffusion MRI tractography inspired from a spin glass model. The entire white matter fascicle map is parameterized by pieces of fibers called spins. Spins are encouraged to move and rotate to align with the main fiber directions, and to assemble into longer chains of low curvature. Moreover, they have the ability to adapt their quantity in regions where the spin concentration is not sufficient to correctly model the data. The optimal spin glass configuration is retrieved by an iterative minimization procedure, where chains are finally assimilated to fibers. As a result, all brain fibers appear as growing simultaneously until they merge with other fibers or reach the domain boundaries. In case of an ambiguity within a region like a crossing, the contribution of all neighboring fibers is used determine the correct neural pathway. This framework is tested on a MR phantom representing a 45 degrees crossing and a real brain dataset. Notably, the framework was able to retrieve the triple crossing between the callosal fibers, the corticospinal tract and the arcuate fasciculus.


Subject(s)
Algorithms , Brain/cytology , Diffusion Tensor Imaging/methods , Image Interpretation, Computer-Assisted/methods , Imaging, Three-Dimensional/methods , Nerve Fibers, Myelinated/ultrastructure , Pattern Recognition, Automated/methods , Artificial Intelligence , Humans , Image Enhancement/methods , Reproducibility of Results , Sensitivity and Specificity , Subtraction Technique
16.
Med Image Comput Comput Assist Interv ; 11(Pt 1): 975-82, 2008.
Article in English | MEDLINE | ID: mdl-18979840

ABSTRACT

The emergence of new modalities such as Diffusion Tensor Imaging (DTI) is of great interest for the characterization and the temporal study of Multiple Sclerosis (MS). DTI indeed gives information on water diffusion within tissues and could therefore reveal alterations in white matter fibers before being visible in conventional MRI. However, recent studies generally rely on scalar measures derived from the tensors such as FA or MD instead of using the full tensor itself. Therefore, a certain amount of information is left unused. In this article, we present a framework to study the benefits of using the whole diffusion tensor information to detect statistically significant differences between each individual MS patient and a database of control subjects. This framework, based on the comparison of the MS patient DTI and a mean DTI atlas built from the control subjects, allows us to look for differences both in normally appearing white matter but also in and around the lesions of each patient. We present a study on a database of 11 MS patients, showing the ability of the DTI to detect not only significant differences on the lesions but also in regions around them, enabling an early detection of an extension of the MS disease.


Subject(s)
Algorithms , Artificial Intelligence , Brain/pathology , Diffusion Magnetic Resonance Imaging/methods , Image Interpretation, Computer-Assisted/methods , Multiple Sclerosis/pathology , Nerve Fibers, Myelinated/pathology , Pattern Recognition, Automated/methods , Humans , Image Enhancement/methods , Reproducibility of Results , Sensitivity and Specificity
17.
IEEE Trans Med Imaging ; 26(11): 1472-82, 2007 Nov.
Article in English | MEDLINE | ID: mdl-18041263

ABSTRACT

Diffusion tensor magnetic resonance imaging (DT-MRI or DTI) is an imaging modality that is gaining importance in clinical applications. However, in a clinical environment, data have to be acquired rapidly, often at the expense of the image quality. This often results in DTI datasets that are not suitable for complex postprocessing like fiber tracking. We propose a new variational framework to improve the estimation of DT-MRI in this clinical context. Most of the existing estimation methods rely on a log-Gaussian noise (Gaussian noise on the image logarithms), or a Gaussian noise, that do not reflect the Rician nature of the noise in MR images with a low signal-to-noise ratio (SNR). With these methods, the Rician noise induces a shrinking effect: the tensor volume is underestimated when other noise models are used for the estimation. In this paper, we propose a maximum likelihood strategy that fully exploits the assumption of a Rician noise. To further reduce the influence of the noise, we optimally exploit the spatial correlation by coupling the estimation with an anisotropic prior previously proposed on the spatial regularity of the tensor field itself, which results in a maximum a posteriori estimation. Optimizing such a nonlinear criterion requires adapted tools for tensor computing. We show that Riemannian metrics for tensors, and more specifically the log-Euclidean metrics, are a good candidate and that this criterion can be efficiently optimized. Experiments on synthetic data show that our method correctly handles the shrinking effect even with very low SNR, and that the positive definiteness of tensors is always ensured. Results on real clinical data demonstrate the truthfulness of the proposed approach and show promising improvements of fiber tracking in the brain and the spinal cord.


Subject(s)
Algorithms , Diffusion Magnetic Resonance Imaging/methods , Image Enhancement/methods , Image Interpretation, Computer-Assisted/methods , Imaging, Three-Dimensional/methods , Nerve Fibers, Myelinated/ultrastructure , Pattern Recognition, Automated/methods , Artificial Intelligence , Computer Simulation , Humans , Models, Neurological , Models, Statistical , Reproducibility of Results , Sensitivity and Specificity
18.
Neuroimaging Clin N Am ; 17(1): 137-47, 2007 Feb.
Article in English | MEDLINE | ID: mdl-17493544

ABSTRACT

Diffusion-weighted imaging and fractional anisotropy may be more sensitive than other conventional magnetic resonance imaging techniques to detect, characterize, and map the extent of spinal cord lesions. Fiber tracking offers the possibility of visualizing the integrity of white matter tracts surrounding some lesions, and this information may help in formulating a differential diagnosis and in planning biopsies or resection. Fractional anisotropy measurements may also play a role in predicting the outcome of patients who have spinal cord lesions. In this article, we address several conditions in which diffusion-weighted imaging and fiber tracking is known to be useful and speculate on others in which we believe these techniques will be useful in the near future.


Subject(s)
Diffusion Magnetic Resonance Imaging/methods , Diffusion Magnetic Resonance Imaging/trends , Nerve Fibers, Myelinated/pathology , Spinal Cord Diseases/diagnosis , Spinal Cord Neoplasms/diagnosis , Spinal Cord/pathology , Humans , Imaging, Three-Dimensional/methods
19.
Neuroimage ; 34(2): 639-50, 2007 Jan 15.
Article in English | MEDLINE | ID: mdl-17113311

ABSTRACT

Modeling and understanding the variability of brain structures is a fundamental problem in neurosciences. Improved mathematical representations of structural brain variation are needed to help detect and understand genetic or disease related sources of abnormality, as well as to improve statistical power when integrating functional brain mapping data across subjects. In this paper, we develop a new mathematical model of normal brain variation based on a large set of cortical sulcal landmarks (72 per brain) delineated in each of 98 healthy human subjects scanned with 3D MRI (age: 51.8+/-6.2 years). We propose an original method to compute an average representation of the sulcal curves, which constitutes the mean anatomy. After affine alignment of the individual data across subjects, the second order moment distribution of the sulcal position is modeled as a sparse field of covariance tensors (symmetric, positive definite matrices). To extrapolate this information to the full brain, one has to overcome the limitations of the standard Euclidean matrix calculus. We propose an affine-invariant Riemannian framework to perform computations with tensors. In particular, we generalize radial basis function (RBF) interpolation and harmonic diffusion partial differential equations (PDEs) to tensor fields. As a result, we obtain a dense 3D variability map that agrees well with prior results on smaller subject samples. Moreover, "leave one (sulcus) out" tests show that our model is globally able to recover the missing information on brain variation when there is a consistent neighboring pattern of variability. Finally, we propose an innovative method to analyze the asymmetry of brain variability. As expected, the greatest asymmetries are found in regions that includes the primary language areas. Interestingly, any such asymmetries in anatomical variance, if it remains after anatomical normalization, could explain why there may be greater power to detect group activation in one hemisphere versus the other in fMRI studies.


Subject(s)
Brain/anatomy & histology , Imaging, Three-Dimensional , Models, Theoretical , Algorithms , Humans , Magnetic Resonance Imaging
20.
Magn Reson Med ; 56(2): 411-21, 2006 Aug.
Article in English | MEDLINE | ID: mdl-16788917

ABSTRACT

Diffusion tensor imaging (DT-MRI or DTI) is an emerging imaging modality whose importance has been growing considerably. However, the processing of this type of data (i.e., symmetric positive-definite matrices), called "tensors" here, has proved difficult in recent years. Usual Euclidean operations on matrices suffer from many defects on tensors, which have led to the use of many ad hoc methods. Recently, affine-invariant Riemannian metrics have been proposed as a rigorous and general framework in which these defects are corrected. These metrics have excellent theoretical properties and provide powerful processing tools, but also lead in practice to complex and slow algorithms. To remedy this limitation, a new family of Riemannian metrics called Log-Euclidean is proposed in this article. They also have excellent theoretical properties and yield similar results in practice, but with much simpler and faster computations. This new approach is based on a novel vector space structure for tensors. In this framework, Riemannian computations can be converted into Euclidean ones once tensors have been transformed into their matrix logarithms. Theoretical aspects are presented and the Euclidean, affine-invariant, and Log-Euclidean frameworks are compared experimentally. The comparison is carried out on interpolation and regularization tasks on synthetic and clinical 3D DTI data.


Subject(s)
Algorithms , Brain Mapping/methods , Diffusion Magnetic Resonance Imaging , Image Processing, Computer-Assisted/methods , Humans , Mathematics
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