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Diffusion tensor smoothing through weighted Karcher means.

ABSTRACT: Diffusion tensor magnetic resonance imaging (MRI) quantifies the spatial distribution of water Diffusion at each voxel on a regular grid of locations in a biological specimen by Diffusion tensors- 3 × 3 positive definite matrices. Removal of noise from DTI is an important problem due to the high scientific relevance of DTI and relatively low signal to noise ratio it provides. Leading approaches to this problem amount to estimation of weighted Karcher means of Diffusion tensors within spatial neighborhoods, under various metrics imposed on the space of tensors. However, it is unclear how the behavior of these estimators varies with the magnitude of DTI sensor noise (the noise resulting from the thermal e!ects of MRI scanning) as well as the geometric structure of the underlying Diffusion tensor neighborhoods. In this paper, we combine theoretical analysis, empirical analysis of simulated DTI data, and empirical analysis of real DTI scans to compare the noise removal performance of three kernel-based DTI smoothers that are based on Euclidean, log-Euclidean, and affine-invariant metrics. The results suggest, contrary to conventional wisdom, that imposing a simplistic Euclidean metric may in fact provide comparable or superior noise removal, especially in relatively unstructured regions and/or in the presence of moderate to high levels of sensor noise. On the contrary, log-Euclidean and affine-invariant metrics may lead to better noise removal in highly structured anatomical regions, especially when the sensor noise is of low magnitude. These findings emphasize the importance of considering the interplay of sensor noise magnitude and tensor field geometric structure when assessing Diffusion tensor smoothing options. They also point to the necessity for continued development of smoothing methods that perform well across a large range of scenarios.

SUBMITTER: Carmichael O

PROVIDER: S-EPMC4239671 | biostudies-literature | 2013

REPOSITORIES: biostudies-literature

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Diffusion tensor smoothing through weighted Karcher means.

Carmichael Owen O Chen Jun J Paul Debashis D Peng Jie J

Electronic journal of statistics 20130101

Diffusion tensor magnetic resonance imaging (MRI) quantifies the spatial distribution of water Diffusion at each voxel on a regular grid of locations in a biological specimen by Diffusion tensors- 3 × 3 positive definite matrices. Removal of noise from DTI is an important problem due to the high scientific relevance of DTI and relatively low signal to noise ratio it provides. Leading approaches to this problem amount to estimation of weighted Karcher means of Diffusion tensors within spatial nei ...[more]

PMID: 25419264

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Project description:BackgroundTo investigate the effect of using a Rician nonlocal means (NLM) filter on quantification of diffusion tensor (DT)- and diffusion kurtosis (DK)-derived metrics in various anatomical regions of the human brain and the spinal cord, when combined with a constrained linear least squares (CLLS) approach.MethodsProspective brain data from 9 healthy subjects and retrospective spinal cord data from 5 healthy subjects from a 3 T MRI scanner were included in the study. Prior to tensor estimation, registered diffusion weighted images were denoised by an optimized blockwise NLM filter with CLLS. Mean kurtosis (MK), radial kurtosis (RK), axial kurtosis (AK), mean diffusivity (MD), radial diffusivity (RD), axial diffusivity (AD) and fractional anisotropy (FA), were determined in anatomical structures of the brain and the spinal cord. DTI and DKI metrics, signal-to-noise ratio (SNR) and Chi-square values were quantified in distinct anatomical regions for all subjects, with and without Rician denoising.ResultsThe averaged SNR significantly increased with Rician denoising by a factor of 2 while the averaged Chi-square values significantly decreased up to 61% in the brain and up to 43% in the spinal cord after Rician NLM filtering. In the brain, the mean MK varied from 0.70 (putamen) to 1.27 (internal capsule) while AK and RK varied from 0.58 (corpus callosum) to 0.92 (cingulum) and from 0.70 (putamen) to 1.98 (corpus callosum), respectively. In the spinal cord, FA varied from 0.78 in lateral column to 0.81 in dorsal column while MD varied from 0.91 × 10-3 mm2/s (lateral) to 0.93 × 10-3 mm2/s (dorsal). RD varied from 0.34 × 10-3 mm2/s (dorsal) to 0.38 × 10-3 mm2/s (lateral) and AD varied from 1.96 × 10-3 mm2/s (lateral) to 2.11 × 10-3 mm2/s (dorsal).ConclusionsOur results show a Rician denoising NLM filter incorporated with CLLS significantly increases SNR and reduces estimation errors of DT- and KT-derived metrics, providing the reliable metrics estimation with adequate SNR levels.

Project description:BackgroundDynamic diffusion magnetic resonance imaging (ddMRI) metrics can assess transient microstructural alterations in tissue diffusivity but requires additional scan time hindering its clinical application.PurposeTo determine whether a diffusion gradient table can simultaneously acquire data to estimate dynamic and diffusion tensor imaging (DTI) metrics.Study typeProspective.SubjectsSeven healthy subjects, 39 epilepsy patients (15 female, 31 male, age ± 15).Field strength/sequenceTwo-dimensional diffusion MRI (b = 1000 s/mm2 ) at a field strength of 3 T. Sessions in healthy subjects-standard ddMRI (30 directions), standard DTI (15 and 30 directions), and nested cubes scans (15 and 30 directions). Sessions in epilepsy patients-two 30 direction (standard ddMRI, 10 nested cubes) or two 15 direction scans (standard DTI, 5 nested cubes).AssessmentFifteen direction DTI was repeated twice for within-session test-retest measurements in healthy subjects. Bland-Altman analysis computed bias and limits of agreement for DTI metrics using test-retest scans and standard 15 direction vs. 5 nested cubes scans. Intraclass correlation (ICC) analysis compared tensor metrics between 15 direction DTI scans (standard vs. 5 nested cubes) and the coefficients of variation (CoV) of trace and apparent diffusion coefficient (ADC) between 30 direction ddMRI scans (standard vs. 10 nested cubes).Statistical testsBland-Altman and ICC analysis using a P-value of 0.05 for statistical significance.ResultsCorrelations of mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD) were strong and significant in gray (ICC > 0.95) and white matter (ICC > 0.95) between standard vs. nested cubes DTI acquisitions. Correlation of white matter fractional anisotropy was also strong (ICC > 0.95) and significant. ICCs of the CoV of dynamic ADC measured using repeated cubes and nested cubes acquisitions were modest (ICC >0.60), but significant in gray matter.ConclusionA nested cubes diffusion gradient table produces tensor-based and dynamic diffusion measurements in a single acquisition.Level of evidence2 TECHNICAL EFFICACY: Stage 1.

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Diffusion tensor smoothing through weighted Karcher means.

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Diffusion tensor smoothing through weighted Karcher means.

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