Development and validation of the automated imaging differentiation in parkinsonism (AID-P): a multicentre machine learning study.

BACKGROUND: Development of valid, non-invasive biomarkers for parkinsonian syndromes is crucially needed. We aimed to assess whether non-invasive diffusion-weighted MRI can distinguish between parkinsonian syndromes using an automated imaging approach. METHODS: We did an international study at 17 MRI centres in Austria, Germany, and the USA. We used diffusion-weighted MRI from 1002 patients and the Movement Disorders Society Unified Parkinson's Disease Rating Scale part III (MDS-UPDRS III) to develop and validate disease-specific machine learning comparisons using 60 template regions and tracts of interest in Montreal Neurological Institute space between Parkinson's disease and atypical parkinsonism (multiple system atrophy and progressive supranuclear palsy) and between multiple system atrophy and progressive supranuclear palsy. For each comparison, models were developed on a training and validation cohort and evaluated in an independent test cohort by quantifying the area under the curve (AUC) of receiving operating characteristic curves. The primary outcomes were free water and free-water-corrected fractional anisotropy across 60 different template regions. FINDINGS: In the test cohort for disease-specific comparisons, the diffusion-weighted MRI plus MDS-UPDRS III model (Parkinson's disease vs atypical parkinsonism had an AUC 0·962; multiple system atrophy vs progressive supranuclear palsy AUC 0·897) and diffusion-weighted MRI only model had high AUCs (Parkinson's disease vs atypical parkinsonism AUC 0·955; multiple system atrophy vs progressive supranuclear palsy AUC 0·926), whereas the MDS-UPDRS III only models had significantly lower AUCs (Parkinson's disease vs atypical parkinsonism 0·775; multiple system atrophy vs progressive supranuclear palsy 0·582). These results indicate that a non-invasive imaging approach is capable of differentiating forms of parkinsonism comparable to current gold standard methods. INTERPRETATIONS: This study provides an objective, validated, and generalisable imaging approach to distinguish different forms of parkinsonian syndromes using multisite diffusion-weighted MRI cohorts. The diffusion-weighted MRI method does not involve radioactive tracers, is completely automated, and can be collected in less than 12 min across 3T scanners worldwide. The use of this test could positively affect the clinical care of patients with Parkinson's disease and parkinsonism and reduce the number of misdiagnosed cases in clinical trials. FUNDING: National Institutes of Health and Parkinson's Foundation.

Development and Validation of the Automated Imaging Differentiation in Parkinsonism (AID-P): A Multi-Site Machine Learning Study.

Background: There is a critical need to develop valid, non-invasive biomarkers for Parkinsonian syndromes. The current 17-site, international study assesses whether non-invasive diffusion MRI (dMRI) can distinguish between Parkinsonian syndromes. Methods: We used dMRI from 1002 subjects, along with the Movement Disorders Society Unified Parkinson's Disease Rating Scale part III (MDS-UPDRS III), to develop and validate disease-specific machine learning comparisons using 60 template regions and tracts of interest in Montreal Neurological Institute (MNI) space between Parkinson's disease (PD) and Atypical Parkinsonism (multiple system atrophy - MSA, progressive supranuclear palsy - PSP), as well as between MSA and PSP. For each comparison, models were developed on a training/validation cohort and evaluated in a test cohort by quantifying the area under the curve (AUC) of receiving operating characteristic (ROC) curves. Findings: In the test cohort for both disease-specific comparisons, AUCs were high in the dMRI + MDS-UPDRS (PD vs. Atypical Parkinsonism: 0·962; MSA vs. PSP: 0·897) and dMRI Only (PD vs. Atypical Parkinsonism: 0·955; MSA vs. PSP: 0·926) models, whereas the MDS-UPDRS III Only models had significantly lower AUCs (PD vs. Atypical Parkinsonism: 0·775; MSA vs. PSP: 0·582). Interpretations: This study provides an objective, validated, and generalizable imaging approach to distinguish different forms of Parkinsonian syndromes using multi-site dMRI cohorts. The dMRI method does not involve radioactive tracers, is completely automated, and can be collected in less than 12 minutes across 3T scanners worldwide. The use of this test could thus positively impact the clinical care of patients with Parkinson's disease and Parkinsonism as well as reduce the number of misdiagnosed cases in clinical trials.

Assessment of Haptic Interaction for Home-Based Physical Tele-Therapy using Wearable Devices and Depth Sensors.

In this paper a prototype system is presented for home-based physical tele-therapy using a wearable device for haptic feedback. The haptic feedback is generated as a sequence of vibratory cues from 8 vibrator motors equally spaced along an elastic wearable band. The motors guide the patients' movement as they perform a prescribed exercise routine in a way that replaces the physical therapists' haptic guidance in an unsupervised or remotely supervised home-based therapy session. A pilot study of 25 human subjects was performed that focused on: a) testing the capability of the system to guide the users in arbitrary motion paths in the space and b) comparing the motion of the users during typical physical therapy exercises with and without haptic-based guidance. The results demonstrate the efficacy of the proposed system.

Perpendicular fibre tracking for neural fibre bundle analysis using diffusion MRI.

Information on the directionality and structure of axonal fibres in neural tissue can be obtained by analysing diffusion-weighted MRI data sets. Several fibre tracking algorithms have been presented in the literature that trace the underlying field of principal orientations of water diffusion, which correspond to the local primary eigenvectors of the diffusion tensor field. However, the majority of the existing techniques ignore the secondary and tertiary orientations of diffusion, which contain significant information on the local patterns of diffusion. In this paper, we introduce the idea of perpendicular fibre tracking and present a novel dynamic programming method that traces surfaces, which are locally perpendicular to the axonal fibres. This is achieved by using a cost function, with geometric and fibre orientation constraints, that is evaluated dynamically for every voxel in the image domain starting from a given seed point. The proposed method is tested using synthetic and real DW-MRI data sets. The results conclusively demonstrate the accuracy and effectiveness of our method.

Tensor body: real-time reconstruction of the human body and avatar synthesis from RGB-D.

Real-time 3-D reconstruction of the human body has many applications in anthropometry, telecommunications, gaming, fashion, and other areas of human-computer interaction. In this paper, a novel framework is presented for reconstructing the 3-D model of the human body from a sequence of RGB-D frames. The reconstruction is performed in real time while the human subject moves arbitrarily in front of the camera. The method employs a novel parameterization of cylindrical-type objects using Cartesian tensor and b-spline bases along the radial and longitudinal dimension respectively. The proposed model, dubbed tensor body, is fitted to the input data using a multistep framework that involves segmentation of the different body regions, robust filtering of the data via a dynamic histogram, and energy-based optimization with positive-definite constraints. A Riemannian metric on the space of positive-definite tensor splines is analytically defined and employed in this framework. The efficacy of the presented methods is demonstrated in several real-data experiments using the Microsoft Kinect sensor.

Automated human avatar synthesis for obesity control using low-cost depth cameras.

In this paper a framework is presented for monitoring shape changes on the human body with applications to obesity control. This framework uses a low-cost infrared depth camera in order to capture the 3D shape of the human body and approximate it as a set of spherical functions.

Symmetric positive semi-definite Cartesian Tensor fiber orientation distributions (CT-FOD).

A novel method for estimating a field of fiber orientation distribution (FOD) based on signal de-convolution from a given set of diffusion weighted magnetic resonance (DW-MR) images is presented. We model the FOD by higher order Cartesian tensor basis using a parametrization that explicitly enforces the positive semi-definite property to the computed FOD. The computed Cartesian tensors, dubbed Cartesian Tensor-FOD (CT-FOD), are symmetric positive semi-definite tensors whose coefficients can be efficiently estimated by solving a linear system with non-negative constraints. Next, we show how to use our method for converting higher-order diffusion tensors to CT-FODs, which is an essential task since the maxima of higher-order tensors do not correspond to the underlying fiber orientations. Finally, we propose a diffusion anisotropy index computed directly from CT-FODs using higher order tensor distance measures thus consolidating the whole analysis pipeline of diffusion imaging solely using CT-FODs. We evaluate our method qualitatively and quantitatively using simulated DW-MR images, phantom images, and human brain real dataset. The results conclusively demonstrate the superiority of the proposed technique over several existing multi-fiber reconstruction methods.

APPROXIMATING SYMMETRIC POSITIVE SEMIDEFINITE TENSORS OF EVEN ORDER().

Tensors of various orders can be used for modeling physical quantities such as strain and diffusion as well as curvature and other quantities of geometric origin. Depending on the physical properties of the modeled quantity, the estimated tensors are often required to satisfy the positivity constraint, which can be satisfied only with tensors of even order. Although the space [Formula: see text] of 2m(th)-order symmetric positive semi-definite tensors is known to be a convex cone, enforcing positivity constraint directly on [Formula: see text] is usually not straightforward computationally because there is no known analytic description of [Formula: see text] for m > 1. In this paper, we propose a novel approach for enforcing the positivity constraint on even-order tensors by approximating the cone [Formula: see text] for the cases 0 < m < 3, and presenting an explicit characterization of the approximation Σ(2) (m) ⊂ Ω(2) (m) for m ≥ 1, using the subset [Formula: see text] of semi-definite tensors that can be written as a sum of squares of tensors of order m. Furthermore, we show that this approximation leads to a non-negative linear least-squares (NNLS) optimization problem with the complexity that equals the number of generators in Σ(2) (m). Finally, we experimentally validate the proposed approach and we present an application for computing 2m(th)-order diffusion tensors from Diffusion Weighted Magnetic Resonance Images.

Non-lambertian reflectance modeling and shape recovery of faces using tensor splines.

Modeling illumination effects and pose variations of a face is of fundamental importance in the field of facial image analysis. Most of the conventional techniques that simultaneously address both of these problems work with the Lambertian assumption and thus fall short of accurately capturing the complex intensity variation that the facial images exhibit or recovering their 3D shape in the presence of specularities and cast shadows. In this paper, we present a novel Tensor-Spline-based framework for facial image analysis. We show that, using this framework, the facial apparent BRDF field can be accurately estimated while seamlessly accounting for cast shadows and specularities. Further, using local neighborhood information, the same framework can be exploited to recover the 3D shape of the face (to handle pose variation). We quantitatively validate the accuracy of the Tensor Spline model using a more general model based on the mixture of single-lobed spherical functions. We demonstrate the effectiveness of our technique by presenting extensive experimental results for face relighting, 3D shape recovery, and face recognition using the Extended Yale B and CMU PIE benchmark data sets.

Symmetric positive-definite Cartesian tensor orientation distribution functions (CT-ODF).

A novel method for estimating a field of orientation distribution functions (ODF) from a given set of DW-MR images is presented. We model the ODF by Cartesian tensor basis using a parametrization that explicitly enforces the positive definite property to the computed ODF. The computed Cartesian tensors, dubbed Cartesian Tensor-ODF (CT-ODF), are symmetric positive definite tensors whose coefficients can be efficiently estimated by solving a linear system with non-negative constraints. Furthermore, we show how to use our method for converting higher-order diffusion tensors to CT-ODFs, which is an essential task since the maxima of higher-order tensors do not correspond to the underlying fiber orientations. We quantitatively evaluate our method using simulated DW-MR images as well as a real brain dataset from a post-mortem porcine brain. The results conclusively demonstrate the superiority of the proposed technique over several existing multi-fiber reconstruction methods.

A UNIFIED FRAMEWORK FOR ESTIMATING DIFFUSION TENSORS OF ANY ORDER WITH SYMMETRIC POSITIVE-DEFINITE CONSTRAINTS.

Cartesian tensors of various orders have been employed for either modeling the diffusivity or the orientation distribution function in Diffusion-Weighted MRI datasets. In both cases, the estimated tensors have to be positive-definite since they model positive-valued functions. In this paper we present a novel unified framework for estimating positive-definite tensors of any order, in contrast to the existing methods in literature, which are either order-specific or fail to handle the positive-definite property. The proposed framework employs a homogeneous polynomial parametrization that covers the full space of any order positive-definite tensors and explicitly imposes the positive-definite constraint on the estimated tensors. We show that this parametrization leads to a linear system that is solved using the non-negative least squares technique. The framework is demonstrated using synthetic and real data from an excised rat hippocampus.

Adaptive kernels for multi-fiber reconstruction.

In this paper we present a novel method for multi-fiber reconstruction given a diffusion-weighted MRI dataset. There are several existing methods that employ various spherical deconvolution kernels for achieving this task. However the kernels in all of the existing methods rely on certain assumptions regarding the properties of the underlying fibers, which introduce inaccuracies and unnatural limitations in them. Our model is a non trivial generalization of the spherical deconvolution model, which unlike the existing methods does not make use of a fix-shaped kernel. Instead, the shape of the kernel is estimated simultaneously with the rest of the unknown parameters by employing a general adaptive model that can theoretically approximate any spherical deconvolution kernel. The performance of our model is demonstrated using simulated and real diffusion-weighed MR datasets and compared quantitatively with several existing techniques in literature. The results obtained indicate that our model has superior performance that is close to the theoretic limit of the best possible achievable result.

Regularized positive-definite fourth order tensor field estimation from DW-MRI.

In Diffusion Weighted Magnetic Resonance Image (DW-MRI) processing, a 2nd order tensor has been commonly used to approximate the diffusivity function at each lattice point of the DW-MRI data. From this tensor approximation, one can compute useful scalar quantities (e.g. anisotropy, mean diffusivity) which have been clinically used for monitoring encephalopathy, sclerosis, ischemia and other brain disorders. It is now well known that this 2nd-order tensor approximation fails to capture complex local tissue structures, e.g. crossing fibers, and as a result, the scalar quantities derived from these tensors are grossly inaccurate at such locations. In this paper we employ a 4th order symmetric positive-definite (SPD) tensor approximation to represent the diffusivity function and present a novel technique to estimate these tensors from the DW-MRI data guaranteeing the SPD property. Several articles have been reported in literature on higher order tensor approximations of the diffusivity function but none of them guarantee the positivity of the estimates, which is a fundamental constraint since negative values of the diffusivity are not meaningful. In this paper we represent the 4th-order tensors as ternary quartics and then apply Hilbert's theorem on ternary quartics along with the Iwasawa parametrization to guarantee an SPD 4th-order tensor approximation from the DW-MRI data. The performance of this model is depicted on synthetic data as well as real DW-MRIs from a set of excised control and injured rat spinal cords, showing accurate estimation of scalar quantities such as generalized anisotropy and trace as well as fiber orientations.

Groupwise registration and atlas construction of 4th-order tensor fields using the R+ Riemannian metric.

Registration of Diffusion-Weighted MR Images (DW-MRI) can be achieved by registering the corresponding 2nd-order Diffusion Tensor Images (DTI). However, it has been shown that higher-order diffusion tensors (e.g. order-4) outperform the traditional DTI in approximating complex fiber structures such as fiber crossings. In this paper we present a novel method for unbiased group-wise non-rigid registration and atlas construction of 4th-order diffusion tensor fields. To the best of our knowledge there is no other existing method to achieve this task. First we define a metric on the space of positive-valued functions based on the Riemannian metric of real positive numbers (denoted by R+). Then, we use this metric in a novel functional minimization method for non-rigid 4th-order tensor field registration. We define a cost function that accounts for the 4th-order tensor re-orientation during the registration process and has analytic derivatives with respect to the transformation parameters. Finally, the tensor field atlas is computed as the minimizer of the variance defined using the Riemannian metric. We quantitatively compare the proposed method with other techniques that register scalar-valued or diffusion tensor (rank-2) representations of the DWMRI.

Groupwise Registration and Atlas Construction of 4th-Order Tensor Fields Using the ℝ Riemannian Metric.

Registration of Diffusion-Weighted MR Images (DW-MRI) can be achieved by registering the corresponding 2nd-order Diffusion Tensor Images (DTI). However, it has been shown that higher-order diffusion tensors (e.g. order-4) outperform the traditional DTI in approximating complex fiber structures such as fiber crossings. In this paper we present a novel method for unbiased group-wise non-rigid registration and atlas construction of 4th-order diffusion tensor fields. To the best of our knowledge there is no other existing method to achieve this task. First we define a metric on the space of positive-valued functions based on the Riemannian metric of real positive numbers (denoted by ℝ(+)). Then, we use this metric in a novel functional minimization method for non-rigid 4th-order tensor field registration. We define a cost function that accounts for the 4th-order tensor re-orientation during the registration process and has analytic derivatives with respect to the transformation parameters. Finally, the tensor field atlas is computed as the minimizer of the variance defined using the Riemannian metric. We quantitatively compare the proposed method with other techniques that register scalar-valued or diffusion tensor (rank-2) representations of the DWMRI.

Extracting tractosemas from a displacement probability field for tractography in DW-MRI.

In this paper we present a novel method for estimating a field of asymmetric spherical functions, dubbed tractosemas, given the intra-voxel displacement probability information. The peaks of tractosemas correspond to directions of distinct fibers, which can have either symmetric or asymmetric local fiber structure. This is in contrast to the existing methods that estimate fiber orientation distributions which are naturally symmetric and therefore cannot model asymmetries such as splaying fibers. We propose a method for extracting tractosemas from a given field of displacement probability iso-surfaces via a diffusion process. The diffusion is performed by minimizing a kernel convolution integral, which leads to an update formula expressed in the convenient form of a discrete kernel convolution. The kernel expresses the probability of diffusion between two neighboring spherical functions and we model it by the product of Gaussian and von Mises distributions. The model is validated via experiments on synthetic and real diffusion-weighted magnetic resonance (DW-MRI) datasets from a rat hippocampus and spinal cord.

FAST DISPLACEMENT PROBABILITY PROFILE APPROXIMATION FROM HARDI USING 4TH-ORDER TENSORS.

Cartesian tensor basis have been widely used to approximate spherical functions. In Medical Imaging, tensors of various orders have been used to model the diffusivity function in Diffusion-weighted MRI data sets. However, it is known that the peaks of the diffusivity do not correspond to orientations of the underlying fibers and hence the displacement probability profiles should be employed instead. In this paper, we present a novel representation of the probability profile by a 4(th) order tensor, which is a smooth spherical function that can approximate single-fibers as well as multiple-fiber structures. We also present a method for efficiently estimating the unknown tensor coefficients of the probability profile directly from a given high-angular resolution diffusion-weighted (HARDI) data set. The accuracy of our model is validated by experiments on synthetic and real HARDI datasets from a fixed rat spinal cord.

Registration of high angular resolution diffusion MRI images using 4th order tensors.

Registration of Diffusion Weighted (DW)-MRI datasets has been commonly achieved to date in literature by using either scalar or 2nd-order tensorial information. However, scalar or 2nd-order tensors fail to capture complex local tissue structures, such as fiber crossings, and therefore, datasets containing fiber-crossings cannot be registered accurately by using these techniques. In this paper we present a novel method for non-rigidly registering DW-MRI datasets that are represented by a field of 4th-order tensors. We use the Hellinger distance between the normalized 4th-order tensors represented as distributions, in order to achieve this registration. Hellinger distance is easy to compute, is scale and rotation invariant and hence allows for comparison of the true shape of distributions. Furthermore, we propose a novel 4th-order tensor re-transformation operator, which plays an essential role in the registration procedure and shows significantly better performance compared to the re-orientation operator used in literature for DTI registration. We validate and compare our technique with other existing scalar image and DTI registration methods using simulated diffusion MR data and real HARDI datasets.

Tensor splines for interpolation and approximation of DT-MRI with applications to segmentation of isolated rat hippocampi.

In this paper, we present novel algorithms for statistically robust interpolation and approximation of diffusion tensors-which are symmetric positive definite (SPD) matrices-and use them in developing a significant extension to an existing probabilistic algorithm for scalar field segmentation, in order to segment diffusion tensor magnetic resonance imaging (DT-MRI) datasets. Using the Riemannian metric on the space of SPD matrices, we present a novel and robust higher order (cubic) continuous tensor product of B-splines algorithm to approximate the SPD diffusion tensor fields. The resulting approximations are appropriately dubbed tensor splines. Next, we segment the diffusion tensor field by jointly estimating the label (assigned to each voxel) field, which is modeled by a Gauss Markov measure field (GMMF) and the parameters of each smooth tensor spline model representing the labeled regions. Results of interpolation, approximation, and segmentation are presented for synthetic data and real diffusion tensor fields from an isolated rat hippocampus, along with validation. We also present comparisons of our algorithms with existing methods and show significantly improved results in the presence of noise as well as outliers.

Symmetric positive 4th order tensors & their estimation from diffusion weighted MRI.

In Diffusion Weighted Magnetic Resonance Image (DW-MRI) processing a 2nd order tensor has been commonly used to approximate the diffusivity function at each lattice point of the DW-MRI data. It is now well known that this 2nd-order approximation fails to approximate complex local tissue structures, such as fibers crossings. In this paper we employ a 4th order symmetric positive semi-definite (PSD) tensor approximation to represent the diffusivity function and present a novel technique to estimate these tensors from the DW-MRI data guaranteeing the PSD property. There have been several published articles in literature on higher order tensor approximations of the diffusivity function but none of them guarantee the positive semi-definite constraint, which is a fundamental constraint since negative values of the diffusivity coefficients are not meaningful. In our methods, we parameterize the 4th order tensors as a sum of squares of quadratic forms by using the so called Gram matrix method from linear algebra and its relation to the Hilbert's theorem on ternary quartics. This parametric representation is then used in a nonlinear-least squares formulation to estimate the PSD tensors of order 4 from the data. We define a metric for the higher-order tensors and employ it for regularization across the lattice. Finally, performance of this model is depicted on synthetic data as well as real DW-MRI from an isolated rat hippocampus.