—Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of t... more —Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of the system. How to choose the right tuning parameter is a fundamental and difficult problem in learning the sparse system. In this paper, by treating the the tuning parameter as an additional dimension, persistent homological structures over the parameter space is introduced and explored. The structures are then further exploited in drastically speeding up the computation using the proposed soft-thresholding technique. The topological structures are further used as multivariate features in the tensor-based morphometry (TBM) in characterizing white matter alterations in children who have experienced severe early life stress and maltreatment. These analyses reveal that stress-exposed children exhibit more diffuse anatomical organization across the whole white matter region. Index Terms—GLASSO, maltreated children, persistent ho-mology, sparse brain networks, sparse correlations, tensor-based morphometry.
The growth patterns of different anatomic structures in the human body vary in terms of growth am... more The growth patterns of different anatomic structures in the human body vary in terms of growth amount over time, growth rate and growth periods. The oral and pharyngeal structures, also known as vocal tract structures, are housed in the craniofacial complex where the cranium/brain follows a distinct neural growth pattern, and the face follows a distinct somatic or skeletal growth pattern. Thus, it is reasonable to expect the oral and pharyngeal structures to follow a combined or mixed growth pattern. Existing parametric growth models are limited in that they are mainly focused on modeling one particular type of growth pattern. In this paper, we propose a novel composite growth model using neural and somatic baseline curves to fit the combined growth pattern of select vocal tract structures. The method can also determine the overall percent contribution of each of the growth types.
The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecul... more The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecules, capturing both its radial and angular contents. The EAP can thus provide richer information about complex tissue microstructure properties than the orientation distribution function (ODF), an angular feature of the EAP. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed, such as diffusion propagator imaging (DPI) and spherical polar Fourier imaging (SPFI). In this study, a new analytical EAP reconstruction method is proposed, called Bessel Fourier Orientation Reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition, and is validated on both synthetic and real datasets. A significant portion of the paper is dedicated to comparing BFOR, SPFI, and DPI using hybrid, non-Cartesian sampling for multiple b-value acquisitions. Ways to mitigate the effects of Gibbs ringing on EAP reconstruction are also explored. In addition to analytical EAP reconstruction, the aforementioned modeling bases can be used to obtain rotationally invariant q-space indices of potential clinical value, an avenue which has not yet been thoroughly explored. Three such measures are computed: zero-displacement probability (Po), mean squared displacement (MSD), and generalized fractional anisotropy (GFA).
Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention, 2012
The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecul... more The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecules, capturing both its radial and angular contents, and hence providing rich information about complex tissue microstructure properties. Bessel Fourier orientation reconstruction (BFOR) is one of several analytical, non-Cartesian EAP reconstruction schemes employing multiple shell acquisitions that have recently been proposed. Such modeling bases have not yet been fully exploited in the extraction of rotationally invariant q-space indices that describe the degree of diffusion anisotropy/restrictivity. Such quantitative measures include the zero-displacement probability (P(o)), mean squared displacement (MSD), q-space inverse variance (QIV), and generalized fractional anisotropy (GFA), and all are simply scalar features of the EAP. In this study, a general relationship between MSD and q-space diffusion signal is derived and an EAP-based definition of GFA is introduced. A significant part ...
Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference, 2009
Diffusion Tensor Imaging (DTI) provides unique information about the underlying tissue structure ... more Diffusion Tensor Imaging (DTI) provides unique information about the underlying tissue structure of brain white matter in vivo, including both the geometry of fiber bundles as well as quantitative information about tissue properties as characterized by measures such as tensor orientation, anisotropy, and size. Our objective in this paper is to evaluate the utility of shape representations of white matter tracts extracted from DTI data for classification of clinically different population groups (here autistic vs control). As a first step, our algorithm extracts fiber bundles passing through approximately marked regions of interest on affinely aligned brain volumes. The subsequent analysis is entirely based on the geometric modeling of the extracted tracts. A key advantage of using such an abstraction is that it allows us to capture invariant features of brains allowing for efficient large sample size studies. We demonstrate that with the use of an appropriate representation of the t...
Proceedings - Society of Photo-Optical Instrumentation Engineers, Jan 21, 2014
The sparse regression framework has been widely used in medical image processing and analysis. Ho... more The sparse regression framework has been widely used in medical image processing and analysis. However, it has been rarely used in anatomical studies. We present a sparse shape modeling framework using the Laplace-Beltrami (LB) eigenfunctions of the underlying shape and show its improvement of statistical power. Traditionally, the LB-eigenfunctions are used as a basis for intrinsically representing surface shapes as a form of Fourier descriptors. To reduce high frequency noise, only the first few terms are used in the expansion and higher frequency terms are simply thrown away. However, some lower frequency terms may not necessarily contribute significantly in reconstructing the surfaces. Motivated by this idea, we present a LB-based method to filter out only the significant eigenfunctions by imposing a sparse penalty. For dense anatomical data such as deformation fields on a surface mesh, the sparse regression behaves like a smoothing process, which will reduce the error of incorre...
Structural and functional brain images are playing an important role in helping us understand the... more Structural and functional brain images are playing an important role in helping us understand the changes associated with neurological disorders such as Alzheimer's disease (AD). Recent efforts have now started investigating their utility for diagnosis purposes. This line of research has shown promising results where methods from machine learning (such as Support Vector Machines) have been used to identify AD-related patterns from images, for use in diagnosing new individual subjects. In this paper, we propose a new framework for AD classification which makes use of the Linear Program (LP) boosting with novel additional regularization based on spatial "smoothness" in 3D image coordinate spaces. The algorithm formalizes the expectation that since the examples for training the classifier are images, the voxels eventually selected for specifying the decision boundary must constitute spatially contiguous chunks, i.e., "regions" must be preferred over isolated vox...
There is significant interest, both from basic and applied research perspectives, in understandin... more There is significant interest, both from basic and applied research perspectives, in understanding how structural/functional connectivity changes can explain behavioral symptoms and predict decline in neurodegenerative diseases such as Alzheimer's disease (AD). The first step in most such analyses is to encode the connectivity information as a graph; then, one may perform statistical inference on various 'global' graph theoretic summary measures (e.g., modularity, graph diameter) and/or at the level of individual edges (or connections). For AD in particular, clear differences in connectivity at the dementia stage of the disease (relative to healthy controls) have been identified. Despite such findings, AD-related connectivity changes in preclinical disease remain poorly characterized. Such preclinical datasets are typically smaller and group differences are weaker. In this paper, we propose a new multi-resolution method for performing statistical analysis of connectivity...
Proceedings - Society of Photo-Optical Instrumentation Engineers, Jan 21, 2014
The sparse regression framework has been widely used in medical image processing and analysis. Ho... more The sparse regression framework has been widely used in medical image processing and analysis. However, it has been rarely used in anatomical studies. We present a sparse shape modeling framework using the Laplace-Beltrami (LB) eigenfunctions of the underlying shape and show its improvement of statistical power. Traditionally, the LB-eigenfunctions are used as a basis for intrinsically representing surface shapes as a form of Fourier descriptors. To reduce high frequency noise, only the first few terms are used in the expansion and higher frequency terms are simply thrown away. However, some lower frequency terms may not necessarily contribute significantly in reconstructing the surfaces. Motivated by this idea, we present a LB-based method to filter out only the significant eigenfunctions by imposing a sparse penalty. For dense anatomical data such as deformation fields on a surface mesh, the sparse regression behaves like a smoothing process, which will reduce the error of incorre...
We propose a new analysis framework to utilize the full information of brain functional networks ... more We propose a new analysis framework to utilize the full information of brain functional networks for computing the mean of a set of brain functional networks and embedding brain functional networks into a low-dimensional space in which traditional regression and classification analyses can be easily employed. For this, we first represent the brain functional network by a symmetric positive matrix computed using sparse inverse covariance estimation. We then impose a Log-Euclidean Riemannian manifold structure on brain functional networks whose norm gives a convenient and practical way to define a mean. Finally, based on the fact that the computation of linear operations can be done in the tangent space of this Riemannian manifold, we adopt Locally Linear Embedding (LLE) to the Log-Euclidean Riemannian manifold space in order to embed the brain functional networks into a low-dimensional space. We show that the integration of the Log-Euclidean manifold with LLE provides more efficient ...
One main obstacle in building a sophisticated parametric model along an arbitary anatomical manif... more One main obstacle in building a sophisticated parametric model along an arbitary anatomical manifold is the lack of an easily available orthonormal basis. Although there are at least two numerical techniques available for constructing an orhonormal basis such as the Laplacian eigenfunction approach and the Gram-Smidth orthogonaliza- tion, they are computationally not so trivial and costly. We present a relatively
We aimed to generate rigorous graphical and statistical reference data based on volumetric measur... more We aimed to generate rigorous graphical and statistical reference data based on volumetric measurements for assessing the relative severity of white matter hyperintensities (WMHs) in patients with stroke. We prospectively mapped WMHs from 2699 patients with first-ever ischemic stroke (mean age=66.8±13.0 years) enrolled consecutively from 11 nationwide stroke centers, from patient (fluid-attenuated-inversion-recovery) MRIs onto a standard brain template set. Using multivariable analyses, we assessed the impact of major (age/hypertension) and minor risk factors on WMH variability. We have produced a large reference data library showing the location and quantity of WMHs as topographical frequency-volume maps. This easy-to-use graphical reference data set allows the quantitative estimation of the severity of WMH as a percentile rank score. For all patients (median age=69 years), multivariable analysis showed that age, hypertension, atrial fibrillation, and left ventricular hypertrophy w...
Many brain diseases or disorders, such as depression, are known to be associated with abnormal fu... more Many brain diseases or disorders, such as depression, are known to be associated with abnormal functional connectivity in neural networks in the brain. Some bivariate measures of electroencephalography (EEG) for coupling analysis have been used widely in attempts to explain abnormalities related with depression. However, brain network evolution based on persistent functional connections in EEG signals could not be easily unveiled. For a geometrical exploration of brain network evolution, here, we used persistent brain network homology analysis with EEG signals from a corticosterone (CORT)-induced mouse model of depression. EEG signals were obtained from eight cortical regions (frontal, somatosensory, parietal, and visual cortices in each hemisphere). The persistent homology revealed a significantly different functional connectivity between the control and CORT model, but no differences in common coupling measures, such as cross correlation and coherence, were apparent. The CORT mode...
—Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of t... more —Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of the system. How to choose the right tuning parameter is a fundamental and difficult problem in learning the sparse system. In this paper, by treating the the tuning parameter as an additional dimension, persistent homological structures over the parameter space is introduced and explored. The structures are then further exploited in drastically speeding up the computation using the proposed soft-thresholding technique. The topological structures are further used as multivariate features in the tensor-based morphometry (TBM) in characterizing white matter alterations in children who have experienced severe early life stress and maltreatment. These analyses reveal that stress-exposed children exhibit more diffuse anatomical organization across the whole white matter region. Index Terms—GLASSO, maltreated children, persistent ho-mology, sparse brain networks, sparse correlations, tensor-based morphometry.
The growth patterns of different anatomic structures in the human body vary in terms of growth am... more The growth patterns of different anatomic structures in the human body vary in terms of growth amount over time, growth rate and growth periods. The oral and pharyngeal structures, also known as vocal tract structures, are housed in the craniofacial complex where the cranium/brain follows a distinct neural growth pattern, and the face follows a distinct somatic or skeletal growth pattern. Thus, it is reasonable to expect the oral and pharyngeal structures to follow a combined or mixed growth pattern. Existing parametric growth models are limited in that they are mainly focused on modeling one particular type of growth pattern. In this paper, we propose a novel composite growth model using neural and somatic baseline curves to fit the combined growth pattern of select vocal tract structures. The method can also determine the overall percent contribution of each of the growth types.
The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecul... more The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecules, capturing both its radial and angular contents. The EAP can thus provide richer information about complex tissue microstructure properties than the orientation distribution function (ODF), an angular feature of the EAP. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed, such as diffusion propagator imaging (DPI) and spherical polar Fourier imaging (SPFI). In this study, a new analytical EAP reconstruction method is proposed, called Bessel Fourier Orientation Reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition, and is validated on both synthetic and real datasets. A significant portion of the paper is dedicated to comparing BFOR, SPFI, and DPI using hybrid, non-Cartesian sampling for multiple b-value acquisitions. Ways to mitigate the effects of Gibbs ringing on EAP reconstruction are also explored. In addition to analytical EAP reconstruction, the aforementioned modeling bases can be used to obtain rotationally invariant q-space indices of potential clinical value, an avenue which has not yet been thoroughly explored. Three such measures are computed: zero-displacement probability (Po), mean squared displacement (MSD), and generalized fractional anisotropy (GFA).
Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention, 2012
The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecul... more The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecules, capturing both its radial and angular contents, and hence providing rich information about complex tissue microstructure properties. Bessel Fourier orientation reconstruction (BFOR) is one of several analytical, non-Cartesian EAP reconstruction schemes employing multiple shell acquisitions that have recently been proposed. Such modeling bases have not yet been fully exploited in the extraction of rotationally invariant q-space indices that describe the degree of diffusion anisotropy/restrictivity. Such quantitative measures include the zero-displacement probability (P(o)), mean squared displacement (MSD), q-space inverse variance (QIV), and generalized fractional anisotropy (GFA), and all are simply scalar features of the EAP. In this study, a general relationship between MSD and q-space diffusion signal is derived and an EAP-based definition of GFA is introduced. A significant part ...
Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference, 2009
Diffusion Tensor Imaging (DTI) provides unique information about the underlying tissue structure ... more Diffusion Tensor Imaging (DTI) provides unique information about the underlying tissue structure of brain white matter in vivo, including both the geometry of fiber bundles as well as quantitative information about tissue properties as characterized by measures such as tensor orientation, anisotropy, and size. Our objective in this paper is to evaluate the utility of shape representations of white matter tracts extracted from DTI data for classification of clinically different population groups (here autistic vs control). As a first step, our algorithm extracts fiber bundles passing through approximately marked regions of interest on affinely aligned brain volumes. The subsequent analysis is entirely based on the geometric modeling of the extracted tracts. A key advantage of using such an abstraction is that it allows us to capture invariant features of brains allowing for efficient large sample size studies. We demonstrate that with the use of an appropriate representation of the t...
Proceedings - Society of Photo-Optical Instrumentation Engineers, Jan 21, 2014
The sparse regression framework has been widely used in medical image processing and analysis. Ho... more The sparse regression framework has been widely used in medical image processing and analysis. However, it has been rarely used in anatomical studies. We present a sparse shape modeling framework using the Laplace-Beltrami (LB) eigenfunctions of the underlying shape and show its improvement of statistical power. Traditionally, the LB-eigenfunctions are used as a basis for intrinsically representing surface shapes as a form of Fourier descriptors. To reduce high frequency noise, only the first few terms are used in the expansion and higher frequency terms are simply thrown away. However, some lower frequency terms may not necessarily contribute significantly in reconstructing the surfaces. Motivated by this idea, we present a LB-based method to filter out only the significant eigenfunctions by imposing a sparse penalty. For dense anatomical data such as deformation fields on a surface mesh, the sparse regression behaves like a smoothing process, which will reduce the error of incorre...
Structural and functional brain images are playing an important role in helping us understand the... more Structural and functional brain images are playing an important role in helping us understand the changes associated with neurological disorders such as Alzheimer's disease (AD). Recent efforts have now started investigating their utility for diagnosis purposes. This line of research has shown promising results where methods from machine learning (such as Support Vector Machines) have been used to identify AD-related patterns from images, for use in diagnosing new individual subjects. In this paper, we propose a new framework for AD classification which makes use of the Linear Program (LP) boosting with novel additional regularization based on spatial "smoothness" in 3D image coordinate spaces. The algorithm formalizes the expectation that since the examples for training the classifier are images, the voxels eventually selected for specifying the decision boundary must constitute spatially contiguous chunks, i.e., "regions" must be preferred over isolated vox...
There is significant interest, both from basic and applied research perspectives, in understandin... more There is significant interest, both from basic and applied research perspectives, in understanding how structural/functional connectivity changes can explain behavioral symptoms and predict decline in neurodegenerative diseases such as Alzheimer's disease (AD). The first step in most such analyses is to encode the connectivity information as a graph; then, one may perform statistical inference on various 'global' graph theoretic summary measures (e.g., modularity, graph diameter) and/or at the level of individual edges (or connections). For AD in particular, clear differences in connectivity at the dementia stage of the disease (relative to healthy controls) have been identified. Despite such findings, AD-related connectivity changes in preclinical disease remain poorly characterized. Such preclinical datasets are typically smaller and group differences are weaker. In this paper, we propose a new multi-resolution method for performing statistical analysis of connectivity...
Proceedings - Society of Photo-Optical Instrumentation Engineers, Jan 21, 2014
The sparse regression framework has been widely used in medical image processing and analysis. Ho... more The sparse regression framework has been widely used in medical image processing and analysis. However, it has been rarely used in anatomical studies. We present a sparse shape modeling framework using the Laplace-Beltrami (LB) eigenfunctions of the underlying shape and show its improvement of statistical power. Traditionally, the LB-eigenfunctions are used as a basis for intrinsically representing surface shapes as a form of Fourier descriptors. To reduce high frequency noise, only the first few terms are used in the expansion and higher frequency terms are simply thrown away. However, some lower frequency terms may not necessarily contribute significantly in reconstructing the surfaces. Motivated by this idea, we present a LB-based method to filter out only the significant eigenfunctions by imposing a sparse penalty. For dense anatomical data such as deformation fields on a surface mesh, the sparse regression behaves like a smoothing process, which will reduce the error of incorre...
We propose a new analysis framework to utilize the full information of brain functional networks ... more We propose a new analysis framework to utilize the full information of brain functional networks for computing the mean of a set of brain functional networks and embedding brain functional networks into a low-dimensional space in which traditional regression and classification analyses can be easily employed. For this, we first represent the brain functional network by a symmetric positive matrix computed using sparse inverse covariance estimation. We then impose a Log-Euclidean Riemannian manifold structure on brain functional networks whose norm gives a convenient and practical way to define a mean. Finally, based on the fact that the computation of linear operations can be done in the tangent space of this Riemannian manifold, we adopt Locally Linear Embedding (LLE) to the Log-Euclidean Riemannian manifold space in order to embed the brain functional networks into a low-dimensional space. We show that the integration of the Log-Euclidean manifold with LLE provides more efficient ...
One main obstacle in building a sophisticated parametric model along an arbitary anatomical manif... more One main obstacle in building a sophisticated parametric model along an arbitary anatomical manifold is the lack of an easily available orthonormal basis. Although there are at least two numerical techniques available for constructing an orhonormal basis such as the Laplacian eigenfunction approach and the Gram-Smidth orthogonaliza- tion, they are computationally not so trivial and costly. We present a relatively
We aimed to generate rigorous graphical and statistical reference data based on volumetric measur... more We aimed to generate rigorous graphical and statistical reference data based on volumetric measurements for assessing the relative severity of white matter hyperintensities (WMHs) in patients with stroke. We prospectively mapped WMHs from 2699 patients with first-ever ischemic stroke (mean age=66.8±13.0 years) enrolled consecutively from 11 nationwide stroke centers, from patient (fluid-attenuated-inversion-recovery) MRIs onto a standard brain template set. Using multivariable analyses, we assessed the impact of major (age/hypertension) and minor risk factors on WMH variability. We have produced a large reference data library showing the location and quantity of WMHs as topographical frequency-volume maps. This easy-to-use graphical reference data set allows the quantitative estimation of the severity of WMH as a percentile rank score. For all patients (median age=69 years), multivariable analysis showed that age, hypertension, atrial fibrillation, and left ventricular hypertrophy w...
Many brain diseases or disorders, such as depression, are known to be associated with abnormal fu... more Many brain diseases or disorders, such as depression, are known to be associated with abnormal functional connectivity in neural networks in the brain. Some bivariate measures of electroencephalography (EEG) for coupling analysis have been used widely in attempts to explain abnormalities related with depression. However, brain network evolution based on persistent functional connections in EEG signals could not be easily unveiled. For a geometrical exploration of brain network evolution, here, we used persistent brain network homology analysis with EEG signals from a corticosterone (CORT)-induced mouse model of depression. EEG signals were obtained from eight cortical regions (frontal, somatosensory, parietal, and visual cortices in each hemisphere). The persistent homology revealed a significantly different functional connectivity between the control and CORT model, but no differences in common coupling measures, such as cross correlation and coherence, were apparent. The CORT mode...
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