Jacobian Determinant

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Paul M Thompson - One of the best experts on this subject based on the ideXlab platform.

  • mapping abnormal subcortical brain morphometry in an elderly hiv cohort
    NeuroImage: Clinical, 2015
    Co-Authors: Benjamin S C Wade, Boris A Gutman, Victor Valcour, Lauren Wendelkenriegelhaupt, Pardis Esmaeilifiridouni, Shantanu H Joshi, Paul M Thompson
    Abstract:

    Over 50% of HIV + individuals exhibit neurocognitive impairment and subcortical atrophy, but the profile of brain abnormalities associated with HIV is still poorly understood. Using surface-based shape analyses, we mapped the 3D profile of subcortical morphometry in 63 elderly HIV + participants and 31 uninfected controls. The thalamus, caudate, putamen, pallidum, hippocampus, amygdala, brainstem, accumbens, callosum and ventricles were segmented from high-resolution MRIs. To investigate shape-based morphometry, we analyzed the Jacobian Determinant (JD) and radial distances (RD) defined on each region's surfaces. We also investigated effects of nadir CD4 + T-cell counts, viral load, time since diagnosis (TSD) and cognition on subcortical morphology. Lastly, we explored whether HIV + participants were distinguishable from unaffected controls in a machine learning context. All shape and volume features were included in a random forest (RF) model. The model was validated with 2-fold cross-validation. Volumes of HIV + participants' bilateral thalamus, left pallidum, left putamen and callosum were significantly reduced while ventricular spaces were enlarged. Significant shape variation was associated with HIV status, TSD and the Wechsler adult intelligence scale. HIV + people had diffuse atrophy, particularly in the caudate, putamen, hippocampus and thalamus. Unexpectedly, extended TSD was associated with increased thickness of the anterior right pallidum. In the classification of HIV + participants vs. controls, our RF model attained an area under the curve of 72%.

  • initial results on development and application of statistical atlas of femoral cartilage in osteoarthritis to determine sex differences in structure data from the osteoarthritis initiative
    Journal of Magnetic Resonance Imaging, 2011
    Co-Authors: Hussain Z Tameem, Paul M Thompson, Siamak Ardekani, Leanne L Seeger, Usha Sinha
    Abstract:

    Purpose: To create an average atlas of knee femoral cartilage morphology, to apply the atlas for quantitative assessment of osteoarthritis (OA), and to study localized sex differences. Materials and Methods: High-resolution 3D magnetic resonance imaging (MRI) data of the knee cartilage collected at 3 T as part of the Osteoarthritis Initiative (OAI) were used. An atlas was created based on images from 30 male Caucasian high-risk subjects with no symptomatic OA at baseline. A female cohort of age- and disease-matched Caucasian subjects was also selected from the OAI database. The Jacobian Determinant was calculated from the deformation vector fields that nonlinearly registered each subject to the atlas. Statistical analysis based on the general linear model was used to test for regions of significant differences in the Jacobian values between the two cohorts. Results: The average Jacobian was larger in women (1.2 ± 0.078) than in men (1.08 ± 0.097), showing that after global scaling to the male template, the female cartilage was thicker in most regions. Regions showing significant structural differences include the medial weight bearing region, the trochlear (femoral) side of the patellofemoral compartment, and the lateral posterior condyle. Conclusion: Sex-based differences in cartilage structure were localized using tensor based morphometry in a cohort of high-risk subjects. J. Magn. Reson. Imaging 2011;. © 2011 Wiley-Liss, Inc.

  • multivariate tensor based morphometry on surfaces application to mapping ventricular abnormalities in hiv aids
    NeuroImage, 2010
    Co-Authors: Yalin Wang, Tony F Chan, Arthur W Toga, Oscar L. Lopez, Howard J. Aizenstein, Jie Zhang, Boris A Gutman, James T Becker, Robert Tamburo, Paul M Thompson
    Abstract:

    Here we developed a new method, called multivariate tensor-based surface morphometry (TBM), and applied it to study lateral ventricular surface differences associated with HIV/AIDS. Using concepts from differential geometry and the theory of differential forms, we created mathematical structures known as holomorphic one-forms, to obtain an efficient and accurate conformal parameterization of the lateral ventricular surfaces in the brain. The new meshing approach also provides a natural way to register anatomical surfaces across subjects, and improves on prior methods as it handles surfaces that branch and join at complex 3D junctions. To analyze anatomical differences, we computed new statistics from the Riemannian surface metrics-these retain multivariate information on local surface geometry. We applied this framework to analyze lateral ventricular surface morphometry in 3D MRI data from 11 subjects with HIV/AIDS and 8 healthy controls. Our method detected a 3D profile of surface abnormalities even in this small sample. Multivariate statistics on the local tensors gave better effect sizes for detecting group differences, relative to other TBM-based methods including analysis of the Jacobian Determinant, the largest and smallest eigenvalues of the surface metric, and the pair of eigenvalues of the Jacobian matrix. The resulting analysis pipeline may improve the power of surface-based morphometry studies of the brain.

  • multivariate tensor based brain anatomical surface morphometry via holomorphic one forms
    Medical Image Computing and Computer-Assisted Intervention, 2009
    Co-Authors: Yalin Wang, Tony F Chan, Arthur W Toga, Paul M Thompson
    Abstract:

    Here we introduce multivariate tensor-based surface morphometry using holomorphic one-forms to study brain anatomy. We computed new statistics from the Riemannian metric tensors that retain the full information in the deformation tensor fields. We introduce two different holomorphic one-forms that induce different surface conformal parameterizations. We applied this framework to 3D MRI data to analyze hippocampal surface morphometry in Alzheimer's Disease (AD; 26 subjects), lateral ventricular surface morphometry in HIV/AIDS (19 subjects) and cortical surface morphometry in Williams Syndrome (WS; 80 subjects). Experimental results demonstrated that our method powerfully detected brain surface abnormalities. Multivariate statistics on the local tensors outperformed other TBM methods including analysis of the Jacobian Determinant, the largest eigenvalue, or the pair of eigenvalues, of the surface Jacobian matrix.

Arthur W Toga - One of the best experts on this subject based on the ideXlab platform.

  • multivariate tensor based morphometry on surfaces application to mapping ventricular abnormalities in hiv aids
    NeuroImage, 2010
    Co-Authors: Yalin Wang, Tony F Chan, Arthur W Toga, Oscar L. Lopez, Howard J. Aizenstein, Jie Zhang, Boris A Gutman, James T Becker, Robert Tamburo, Paul M Thompson
    Abstract:

    Here we developed a new method, called multivariate tensor-based surface morphometry (TBM), and applied it to study lateral ventricular surface differences associated with HIV/AIDS. Using concepts from differential geometry and the theory of differential forms, we created mathematical structures known as holomorphic one-forms, to obtain an efficient and accurate conformal parameterization of the lateral ventricular surfaces in the brain. The new meshing approach also provides a natural way to register anatomical surfaces across subjects, and improves on prior methods as it handles surfaces that branch and join at complex 3D junctions. To analyze anatomical differences, we computed new statistics from the Riemannian surface metrics-these retain multivariate information on local surface geometry. We applied this framework to analyze lateral ventricular surface morphometry in 3D MRI data from 11 subjects with HIV/AIDS and 8 healthy controls. Our method detected a 3D profile of surface abnormalities even in this small sample. Multivariate statistics on the local tensors gave better effect sizes for detecting group differences, relative to other TBM-based methods including analysis of the Jacobian Determinant, the largest and smallest eigenvalues of the surface metric, and the pair of eigenvalues of the Jacobian matrix. The resulting analysis pipeline may improve the power of surface-based morphometry studies of the brain.

  • multivariate tensor based brain anatomical surface morphometry via holomorphic one forms
    Medical Image Computing and Computer-Assisted Intervention, 2009
    Co-Authors: Yalin Wang, Tony F Chan, Arthur W Toga, Paul M Thompson
    Abstract:

    Here we introduce multivariate tensor-based surface morphometry using holomorphic one-forms to study brain anatomy. We computed new statistics from the Riemannian metric tensors that retain the full information in the deformation tensor fields. We introduce two different holomorphic one-forms that induce different surface conformal parameterizations. We applied this framework to 3D MRI data to analyze hippocampal surface morphometry in Alzheimer's Disease (AD; 26 subjects), lateral ventricular surface morphometry in HIV/AIDS (19 subjects) and cortical surface morphometry in Williams Syndrome (WS; 80 subjects). Experimental results demonstrated that our method powerfully detected brain surface abnormalities. Multivariate statistics on the local tensors outperformed other TBM methods including analysis of the Jacobian Determinant, the largest eigenvalue, or the pair of eigenvalues, of the surface Jacobian matrix.

  • generalized tensor based morphometry of hiv aids using multivariate statistics on deformation tensors
    IEEE Transactions on Medical Imaging, 2008
    Co-Authors: Natasha Lepore, C. Brun, Yi-yu Chou, Ming-chang Chiang, Rebecca A. Dutton, Kiralee M. Hayashi, Eileen Luders, Oscar L. Lopez, Howard J. Aizenstein, Arthur W Toga
    Abstract:

    This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian Determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling's test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian Determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry.

David J Sharp - One of the best experts on this subject based on the ideXlab platform.

  • spatial patterns of progressive brain volume loss after moderate severe traumatic brain injury
    Brain, 2018
    Co-Authors: James H Cole, Amy Jolly, Sara De Simoni, Niall J Bourke, Maneesh C Patel, Gregory Scott, David J Sharp
    Abstract:

    Traumatic brain injury leads to significant loss of brain volume, which continues into the chronic stage. This can be sensitively measured using volumetric analysis of MRI. Here we: (i) investigated longitudinal patterns of brain atrophy; (ii) tested whether atrophy is greatest in sulcal cortical regions; and (iii) showed how atrophy could be used to power intervention trials aimed at slowing neurodegeneration. In 61 patients with moderate-severe traumatic brain injury (mean age = 41.55 years ± 12.77) and 32 healthy controls (mean age = 34.22 years ± 10.29), cross-sectional and longitudinal (1-year follow-up) brain structure was assessed using voxel-based morphometry on T1-weighted scans. Longitudinal brain volume changes were characterized using a novel neuroimaging analysis pipeline that generates a Jacobian Determinant metric, reflecting spatial warping between baseline and follow-up scans. Jacobian Determinant values were summarized regionally and compared with clinical and neuropsychological measures. Patients with traumatic brain injury showed lower grey and white matter volume in multiple brain regions compared to controls at baseline. Atrophy over 1 year was pronounced following traumatic brain injury. Patients with traumatic brain injury lost a mean (± standard deviation) of 1.55% ± 2.19 of grey matter volume per year, 1.49% ± 2.20 of white matter volume or 1.51% ± 1.60 of whole brain volume. Healthy controls lost 0.55% ± 1.13 of grey matter volume and gained 0.26% ± 1.11 of white matter volume; equating to a 0.22% ± 0.83 reduction in whole brain volume. Atrophy was greatest in white matter, where the majority (84%) of regions were affected. This effect was independent of and substantially greater than that of ageing. Increased atrophy was also seen in cortical sulci compared to gyri. There was no relationship between atrophy and time since injury or age at baseline. Atrophy rates were related to memory performance at the end of the follow-up period, as well as to changes in memory performance, prior to multiple comparison correction. In conclusion, traumatic brain injury results in progressive loss of brain tissue volume, which continues for many years post-injury. Atrophy is most prominent in the white matter, but is also more pronounced in cortical sulci compared to gyri. These findings suggest the Jacobian Determinant provides a method of quantifying brain atrophy following a traumatic brain injury and is informative in determining the long-term neurodegenerative effects after injury. Power calculations indicate that Jacobian Determinant images are an efficient surrogate marker in clinical trials of neuroprotective therapeutics.

Hermann Ney - One of the best experts on this subject based on the ideXlab platform.

  • Vocal tract normalization equals linear transformation in cepstral space
    IEEE Transactions on Speech and Audio Processing, 2005
    Co-Authors: Michael Pitz, Sirko Molau, Ralf Schlüter, Hermann Ney
    Abstract:

    Vocal tract normalization (VTN) is a widely used speaker normalization technique which reduces the effect of different lengths of the human vocal tract and results in an improved recognition accuracy of automatic speech recognition systems. We show that VTN results in a linear transformation in the cepstral domain, which so far have been considered as independent approaches of speaker normalization. We are now able to compute the Jacobian Determinant of the transformation matrix, which allows the normalization of the probability distributions used in speaker-normalization for automatic speech recognition. We show that VTN can be viewed as a special case of Maximum Likelihood Linear Regression (MLLR). Consequently, we can explain previous experimental results that improvements obtained by VTN and subsequent MLLR are not additive in some cases. For three typical warping functions the transformation matrix is calculated analytically and we show that the matrices are diagonal dominant and thus can be approximated by quindiagonal matrices.

  • vocal tract normalization as linear transformation of mfcc
    Conference of the International Speech Communication Association, 2003
    Co-Authors: Michael Pitz, Hermann Ney
    Abstract:

    We have shown previously that vocal tract normalization (VTN) results in a linear transformation in the cepstral domain. In this paper we show that Mel-frequency warping can equally well be integrated into the framework of VTN as linear transformation on the cepstrum. We show examples of transformation matrices to obtain VTN warped Mel-frequency cepstral coefficients (VTN-MFCC) as linear transformation of the original MFCC and discuss the effect of Mel-frequency warping on the Jacobian Determinant of the transformation matrix. Finally we show that there is a strong interdependence of VTN and Maximum Likelihood Linear Regression (MLLR) for the case of Gaussian emission probabilities.

Howard J. Aizenstein - One of the best experts on this subject based on the ideXlab platform.

  • multivariate tensor based morphometry on surfaces application to mapping ventricular abnormalities in hiv aids
    NeuroImage, 2010
    Co-Authors: Yalin Wang, Tony F Chan, Arthur W Toga, Oscar L. Lopez, Howard J. Aizenstein, Jie Zhang, Boris A Gutman, James T Becker, Robert Tamburo, Paul M Thompson
    Abstract:

    Here we developed a new method, called multivariate tensor-based surface morphometry (TBM), and applied it to study lateral ventricular surface differences associated with HIV/AIDS. Using concepts from differential geometry and the theory of differential forms, we created mathematical structures known as holomorphic one-forms, to obtain an efficient and accurate conformal parameterization of the lateral ventricular surfaces in the brain. The new meshing approach also provides a natural way to register anatomical surfaces across subjects, and improves on prior methods as it handles surfaces that branch and join at complex 3D junctions. To analyze anatomical differences, we computed new statistics from the Riemannian surface metrics-these retain multivariate information on local surface geometry. We applied this framework to analyze lateral ventricular surface morphometry in 3D MRI data from 11 subjects with HIV/AIDS and 8 healthy controls. Our method detected a 3D profile of surface abnormalities even in this small sample. Multivariate statistics on the local tensors gave better effect sizes for detecting group differences, relative to other TBM-based methods including analysis of the Jacobian Determinant, the largest and smallest eigenvalues of the surface metric, and the pair of eigenvalues of the Jacobian matrix. The resulting analysis pipeline may improve the power of surface-based morphometry studies of the brain.

  • generalized tensor based morphometry of hiv aids using multivariate statistics on deformation tensors
    IEEE Transactions on Medical Imaging, 2008
    Co-Authors: Natasha Lepore, C. Brun, Yi-yu Chou, Ming-chang Chiang, Rebecca A. Dutton, Kiralee M. Hayashi, Eileen Luders, Oscar L. Lopez, Howard J. Aizenstein, Arthur W Toga
    Abstract:

    This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian Determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling's test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian Determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry.