Rapid Radial T1 and T2 Mapping of the Hip Articular Cartilage With Magnetic Resonance Fingerprinting.

BACKGROUND: Quantitative MRI can detect early changes in cartilage biochemical components, but its routine clinical implementation is challenging. PURPOSE: To introduce a novel technique to measure T1 and T2 along radial sections of the hip for accurate and reproducible multiparametric quantitative cartilage assessment in a clinically feasible scan time. STUDY TYPE: Reproducibility, technical validation. SUBJECTS/PHANTOM: A seven-compartment phantom and three healthy volunteers. FIELD STRENGTH/SEQUENCE: A novel MR pulse sequence that simultaneously measures proton density (PD), T1 , and T2 at 3 T was developed. Automatic positioning and semiautomatic cartilage segmentation were implemented to improve consistency and simplify workflow. ASSESSMENT: Intra- and interscanner variability of our technique was assessed over multiple scans on three different MR scanners. STATISTICAL TESTS: For each scan, the median of cartilage T1 and T2 over six radial slices was calculated. Restricted maximum likelihood estimation of variance components was used to estimate intrasubject variances reflecting variation between results from the two scans using the same scanner (intrascanner variance) and variation among results from the three scanners (interscanner variance). RESULTS: The estimation error for T1 and T2 with respect to reference standard measurements was less than 3% on average for the phantom. The average interscanner coefficient of variation was 1.5% (1.2-1.9%) and 0.9% (0.0-3.7%) for T1 and T2 , respectively, in the seven compartments of the phantom. Total scan time in vivo was 7:13 minutes to obtain PD, T1 , and T2 maps along six radial hip sections at 0.6 × 0.6 × 4.0 mm3 voxel resolution. Interscanner variability for the in vivo study was 1.99% and 5.46% for T1 and T2 , respectively. in vivo intrascanner variability was 1.15% for T1 and 3.24% for T2 . DATA CONCLUSION: Our method, which includes slice positioning, model-based parameter estimation, and cartilage segmentation, is highly reproducible. It could enable employing quantitative hip cartilage evaluation for longitudinal and multicenter studies. LEVEL OF EVIDENCE: 1 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2019;50:810-815.

Modeling Longitudinal Optical Coherence Tomography Images for Monitoring and Analysis of Glaucoma Progression.

Glaucoma causes progressive visual field deterioration and is the leading cause of blindness worldwide. Glaucomatous damage is irreversible and greatly impacts quality of life. Therefore, it is critically important to detect glaucoma early and closely monitor progression to preserve functional vision. Glaucoma is routinely monitored in the clinical setting using optical coherence tomography (OCT) for derived measures such as the thickness of important visual structures. There is not a consensus of what measures represent the most relevant biomarkers of glaucoma progression. Further, despite the increasing availability of longitudinal OCT data, a quantitative model of 3D structural change over time associated with glaucoma does not exist. In this paper we present an algorithm that will perform hierarchical geodesic modeling at the imaging level, considering 3D OCT images as observations of structural change over time. Hierarchical modeling includes subject-wise trajectories as geodesics in the space of diffeomorphisms and population level (glaucoma vs control) trajectories are also geodesics which explain subject-wise trajectories as deviations from the mean. Our preliminary experiments demonstrate a greater magnitude of structural change associated with glaucoma compared to normal aging. Our algorithm has the potential application in patient-specific monitoring and analysis of glaucoma progression as well as a statistical model of population trends and population variability.

Hierarchical Geodesic Polynomial Model for Multilevel Analysis of Longitudinal Shape.

Longitudinal analysis is a core aspect of many medical applications for understanding the relationship between an anatomical subject's function and its trajectory of shape change over time. Whereas mixed-effects (or hierarchical) modeling is the statistical method of choice for analysis of longitudinal data, we here propose its extension as hierarchical geodesic polynomial model (HGPM) for multilevel analyses of longitudinal shape data. 3D shapes are transformed to a non-Euclidean shape space for regression analysis using geodesics on a high dimensional Riemannian manifold. At the subject-wise level, each individual trajectory of shape change is represented by a univariate geodesic polynomial model on timestamps. At the population level, multivariate polynomial expansion is applied to uni/multivariate geodesic polynomial models for both anchor points and tangent vectors. As such, the trajectory of an individual subject's shape changes over time can be modeled accurately with a reduced number of parameters, and population-level effects from multiple covariates on trajectories can be well captured. The implemented HGPM is validated on synthetic examples of points on a unit 3D sphere. Further tests on clinical 4D right ventricular data show that HGPM is capable of capturing observable effects on shapes attributed to changes in covariates, which are consistent with qualitative clinical evaluations. HGPM demonstrates its effectiveness in modeling shape changes at both subject-wise and population levels, which is promising for future studies of the relationship between shape changes over time and the level of dysfunction severity on anatomical objects associated with disease.

Geodesic Logistic Analysis of Lumbar Spine Intervertebral Disc Shapes in Supine and Standing Positions.

Non-specific lower back pain (LBP) is a world-wide public health problem that affects people of all ages. Despite the high prevalence of non-specific LBP and the associated economic burdens, the pathoanatomical mechanisms for the development and course of the condition remain unclear. While intervertebral disc degeneration (IDD) is associated with LBP, there is overlapping occurrence of IDD in symptomatic and asymptomatic individuals, suggesting that degeneration alone cannot identify LBP populations. Previous work has been done trying to relate linear measurements of compression obtained from Magnetic Resonance Imaging (MRI) to pain unsuccessfully. To bridge this gap, we propose to use advanced non-Euclidean statistical shape analysis methods to develop biomarkers that can help identify symptomatic and asymptomatic adults who might be susceptible to standing-induced LBP. We scanned 4 male and 7 female participants who exhibited lower back pain after prolonged standing using an Open Upright MRI. Supine and standing MRIs were obtained for each participant. Patients reported their pain intensity every fifteen minutes within a period of 2 h. Using our proposed geodesic logistic regression, we related the structure of their lower spine to pain and computed a regression model that can delineate lower spine structures using reported pain intensities. These results indicate the feasibility of identifying individuals who may suffer from lower back pain solely based on their spinal anatomy. Our proposed spinal shape analysis methodology have the potential to provide powerful information to the clinicians so they can make better treatment decisions.

SlicerSALT: From Medical Images to Quantitative Insights of Anatomy.

Three-dimensional (3D) shape lies at the core of understanding the physical objects that surround us. In the biomedical field, shape analysis has been shown to be powerful in quantifying how anatomy changes with time and disease. The Shape AnaLysis Toolbox (SALT) was created as a vehicle for disseminating advanced shape methodology as an open source, free, and comprehensive software tool. We present new developments in our shape analysis software package, including easy-to-interpret statistical methods to better leverage the quantitative information contained in SALT's shape representations. We also show SlicerPipelines, a module to improve the usability of SALT by facilitating the analysis of large-scale data sets, automating workflows for non-expert users, and allowing the distribution of reproducible workflows.

Segmentation-Renormalized Deep Feature Modulation for Unpaired Image Harmonization.

Deep networks are now ubiquitous in large-scale multi-center imaging studies. However, the direct aggregation of images across sites is contraindicated for downstream statistical and deep learning-based image analysis due to inconsistent contrast, resolution, and noise. To this end, in the absence of paired data, variations of Cycle-consistent Generative Adversarial Networks have been used to harmonize image sets between a source and target domain. Importantly, these methods are prone to instability, contrast inversion, intractable manipulation of pathology, and steganographic mappings which limit their reliable adoption in real-world medical imaging. In this work, based on an underlying assumption that morphological shape is consistent across imaging sites, we propose a segmentation-renormalized image translation framework to reduce inter-scanner heterogeneity while preserving anatomical layout. We replace the affine transformations used in the normalization layers within generative networks with trainable scale and shift parameters conditioned on jointly learned anatomical segmentation embeddings to modulate features at every level of translation. We evaluate our methodologies against recent baselines across several imaging modalities (T1w MRI, FLAIR MRI, and OCT) on datasets with and without lesions. Segmentation-renormalization for translation GANs yields superior image harmonization as quantified by Inception distances, demonstrates improved downstream utility via post-hoc segmentation accuracy, and improved robustness to translation perturbation and self-adversarial attacks.

ACCELERATION CONTROLLED DIFFEOMORPHISMS FOR NONPARAMETRIC IMAGE REGRESSION.

The analysis of medical image time-series is becoming increasingly important as longitudinal imaging studies are maturing and large scale open imaging databases are becoming available. Image regression is widely used for several purposes: as a statistical representation for hypothesis testing, to bring clinical scores and images not acquired at the same time into temporal correspondence, or as a consistency filter to enforce temporal correlation. Geodesic image regression is the most prominent method, but the geodesic constraint limits the flexibility and therefore the application of the model, particularly when the observation time window is large or the anatomical changes are non-monotonic. In this paper, we propose to parameterize diffeomorphic flow by acceleration rather than velocity, as in the geodesic model. This results in a nonparametric image regression model which is completely flexible to capture complex change trajectories, while still constrained to be diffeomorphic and with a guarantee of temporal smoothness. We demonstrate the application of our model on synthetic 2D images as well as real 3D images of the cardiac cycle.

Hierarchical Multi-Geodesic Model for Longitudinal Analysis of Temporal Trajectories of Anatomical Shape and Covariates.

Longitudinal regression analysis for clinical imaging studies is essential to investigate unknown relationships between subject-wise changes over time and subject-specific characteristics, represented by covariates such as disease severity or a level of genetic risk. Image-derived data in medical image analysis, e.g. diffusion tensors or geometric shapes, are often represented on nonlinear Riemannian manifolds. Hierarchical geodesic models were suggested to characterize subject-specific changes of nonlinear data on Riemannian manifolds as extensions of a linear mixed effects model. We propose a new hierarchical multi-geodesic model to enable analysis of the relationship between subject-wise anatomical shape changes on a Riemannian manifold and multiple subject-specific characteristics. Each individual subject-wise shape change is represented by a univariate geodesic model. The effects of subject-specific covariates on the estimated subject-wise trajectories are then modeled by multivariate intercept and slope models which together form a multi-geodesic model. Validation was performed with a synthetic example on a S 2 manifold. The proposed method was applied to a longitudinal set of 72 corpus callosum shapes from 24 autism spectrum disorder subjects to study the relationship between anatomical shape changes and the autism severity score, resulting in statistics for the population but also for each subject. To our knowledge, this is the first longitudinal framework to model anatomical developments over time as functions of both continuous and categorical covariates on a nonlinear shape space.

Model selection for spatiotemporal modeling of early childhood sub-cortical development.

Spatiotemporal shape models capture the dynamics of shape change over time and are an essential tool for monitoring and measuring anatomical growth or degeneration. In this paper we evaluate non-parametric shape regression on the challenging problem of modeling early childhood sub-cortical development starting from birth. Due to the flexibility of the model, it can be challenging to choose parameters which lead to a good model fit yet does not over fit. We systematically test a variety of parameter settings to evaluate model fit as well as the sensitivity of the method to specific parameters, and we explore the impact of missing data on model estimation.

4D CONTINUOUS MEDIAL REPRESENTATION BY GEODESIC SHAPE REGRESSION.

Longitudinal shape analysis has shown great potential to model anatomical processes from baseline to follow-up observations. Shape regression estimates a continuous trajectory of time-discrete anatomical shapes to quantify temporal changes. The need for shape alignment and point-to-point correspondences represent limitations of current shape analysis methodologies, and present significant challenges in shape evaluation. We propose a method that estimates a continuous trajectory of continuous medial representations (CM-Rep) from a set of time-discrete observed shapes. To avoid the traditional step of aligning individual objects, shape changes are modeled via diffeomorphic ambient space deformations. Using a medial shape representation, we separately capture object pose changes and intrinsic geometry changes. Tests and validation with synthetic and real anatomical shapes demonstrate that the new method captures extrinsic shape changes as well as intrinsic shape changes encoded with CM-Reps, a highly relevant property for studying growth and disease processes.

ESTIMATING SHAPE CORRESPONDENCE FOR POPULATIONS OF OBJECTS WITH COMPLEX TOPOLOGY.

Statistical shape analysis captures the geometric properties of a given set of shapes, obtained from medical images, by means of statistical methods. Orthognathic surgery is a type of craniofacial surgery that is aimed at correcting severe skeletal deformities in the mandible and maxilla. Methods assuming spherical topology cannot represent the class of anatomical structures exhibiting complex geometries and topologies, including the mandible. In this paper we propose methodology based on non-rigid deformations of 3D geometries to be applied to objects with thin, complex structures. We are able to accurately and quantitatively characterize bone healing at the osteotomy site as well as condylar remodeling for three orthognathic surgery cases, demonstrating the effectiveness of the proposed methodology.

Analysis of Morphological Changes of Lamina Cribrosa Under Acute Intraocular Pressure Change.

Glaucoma is the second leading cause of blindness world-wide. Despite active research efforts driven by the importance of diagnosis and treatment of the optic degenerative neuropathy, the relationship between structural and functional changes along the glaucomateous evolution are still not clearly understood. Dynamic changes of the lamina cribrosa (LC) in the presence of intraocular pressure (IOP) were suggested to play a significant role in optic nerve damage, which motivates the proposed research to explore the relationship of changes of the 3D structure of the LC collagen meshwork to clinical diagnosis. We introduce a framework to quantify 3D dynamic morphological changes of the LC under acute IOP changes in a series of swept-source optical coherence tomography (SS-OCT) scans taken under different pressure states. Analysis of SS-OCT images faces challenges due to low signal-to-noise ratio, anisotropic resolution, and observation variability caused by subject and ocular motions. We adapt unbiased diffeomorphic atlas building which serves multiple purposes critical for this analysis. Analysis of deformation fields yields desired global and local information on pressure-induced geometric changes. Deformation variability, estimated with repeated images of a healthy volunteer without IOP elevation, is found to be a magnitude smaller than pressure-induced changes and thus illustrates feasibility of the proposed framework. Results in a clinical study with healthy, glaucoma suspect, and glaucoma subjects demonstrate the potential of the proposed method for non-invasive in vivo analysis of LC dynamics, potentially leading to early prediction and diagnosis of glaucoma.

SlicerSALT: Shape AnaLysis Toolbox.

SlicerSALT is an open-source platform for disseminating state-of-the-art methods for performing statistical shape analysis. These methods are developed as 3D Slicer extensions to take advantage of its powerful underlying libraries. SlicerSALT itself is a heavily customized 3D Slicer package that is designed to be easy to use for shape analysis researchers. The packaged methods include powerful techniques for creating and visualizing shape representations as well as performing various types of analysis.

Geodesic shape regression with multiple geometries and sparse parameters.

Many problems in medicine are inherently dynamic processes which include the aspect of change over time, such as childhood development, aging, and disease progression. From medical images, numerous geometric structures can be extracted with various representations, such as landmarks, point clouds, curves, and surfaces. Different sources of geometry may characterize different aspects of the anatomy, such as fiber tracts from DTI and subcortical shapes from structural MRI, and therefore require a modeling scheme which can include various shape representations in any combination. In this paper, we present a geodesic regression model in the large deformation (LDDMM) framework applicable to multi-object complexes in a variety of shape representations. Our model decouples the deformation parameters from the specific shape representations, allowing the complexity of the model to reflect the nature of the shape changes, rather than the sampling of the data. As a consequence, the sparse representation of diffeomorphic flow allows for the straightforward embedding of a variety of geometry in different combinations, which all contribute towards the estimation of a single deformation of the ambient space. Additionally, the sparse representation along with the geodesic constraint results in a compact statistical model of shape change by a small number of parameters defined by the user. Experimental validation on multi-object complexes demonstrate robust model estimation across a variety of parameter settings. We further demonstrate the utility of our method to support the analysis of derived shape features, such as volume, and explore shape model extrapolation. Our method is freely available in the software package deformetrica which can be downloaded at www.deformetrica.org.

Subject-Specific Longitudinal Shape Analysis by Coupling Spatiotemporal Shape Modeling with Medial Analysis.

Modeling subject-specific shape change is one of the most important challenges in longitudinal shape analysis of disease progression. Whereas anatomical change over time can be a function of normal aging; anatomy can also be impacted by disease related degeneration. Shape changes to anatomy may also be affected by external structural changes from neighboring structures, which may cause non-linear pose variations. In this paper, we propose a framework to analyze disease related shape changes by coupling extrinsic modeling of the ambient anatomical space via spatiotemporal deformations with intrinsic shape properties from medial surface analysis. We compare intrinsic shape properties of a subject-specific shape trajectory to a normative 4D shape atlas representing normal aging to separately quantify shape changes related to disease. The spatiotemporal shape modeling establishes inter/intra subject anatomical correspondence, which in turn enables comparisons between subjects and the 4D shape atlas, and also quantitative analysis of disease related shape change. The medial surface analysis captures intrinsic shape properties related to local patterns of deformation. The proposed framework simultaneously models extrinsic longitudinal shape changes in the ambient anatomical space, as well as intrinsic shape properties to give localized measurements of degeneration. Six high risk subjects and six controls are randomly sampled from a Huntington's disease image database for quantitative and qualitative comparison.

Longitudinal modeling of appearance and shape and its potential for clinical use.

Clinical assessment routinely uses terms such as development, growth trajectory, degeneration, disease progression, recovery or prediction. This terminology inherently carries the aspect of dynamic processes, suggesting that single measurements in time and cross-sectional comparison may not sufficiently describe spatiotemporal changes. In view of medical imaging, such tasks encourage subject-specific longitudinal imaging. Whereas follow-up, monitoring and prediction are natural tasks in clinical diagnosis of disease progression and of assessment of therapeutic intervention, translation of methodologies for calculation of temporal profiles from longitudinal data to clinical routine still requires significant research and development efforts. Rapid advances in image acquisition technology with significantly reduced acquisition times and with increase of patient comfort favor repeated imaging over the observation period. In view of serial imaging ranging over multiple years, image acquisition faces the challenging issue of scanner standardization and calibration which is crucial for successful spatiotemporal analysis. Longitudinal 3D data, represented as 4D images, capture time-varying anatomy and function. Such data benefits from dedicated analysis methods and tools that make use of the inherent correlation and causality of repeated acquisitions of the same subject. Availability of such data spawned progress in the development of advanced 4D image analysis methodologies that carry the notion of linear and nonlinear regression, now applied to complex, high-dimensional data such as images, image-derived shapes and structures, or a combination thereof. This paper provides examples of recently developed analysis methodologies for 4D image data, primarily focusing on progress in areas of core expertise of the authors. These include spatiotemporal shape modeling and growth trajectories of white matter fiber tracts demonstrated with examples from ongoing longitudinal clinical neuroimaging studies such as analysis of early brain growth in subjects at risk for mental illness and neurodegeneration in Huntington's disease (HD). We will discuss broader aspects of current limitations and need for future research in view of data consistency and analysis methodologies.

Bayesian Covariate Selection in Mixed-Effects Models For Longitudinal Shape Analysis.

The goal of longitudinal shape analysis is to understand how anatomical shape changes over time, in response to biological processes, including growth, aging, or disease. In many imaging studies, it is also critical to understand how these shape changes are affected by other factors, such as sex, disease diagnosis, IQ, etc. Current approaches to longitudinal shape analysis have focused on modeling age-related shape changes, but have not included the ability to handle covariates. In this paper, we present a novel Bayesian mixed-effects shape model that incorporates simultaneous relationships between longitudinal shape data and multiple predictors or covariates to the model. Moreover, we place an Automatic Relevance Determination (ARD) prior on the parameters, that lets us automatically select which covariates are most relevant to the model based on observed data. We evaluate our proposed model and inference procedure on a longitudinal study of Huntington's disease from PREDICT-HD. We first show the utility of the ARD prior for model selection in a univariate modeling of striatal volume, and next we apply the full high-dimensional longitudinal shape model to putamen shapes.

GEODESIC REGRESSION OF IMAGE AND SHAPE DATA FOR IMPROVED MODELING OF 4D TRAJECTORIES.

A variety of regression schemes have been proposed on images or shapes, although available methods do not handle them jointly. In this paper, we present a framework for joint image and shape regression which incorporates images as well as anatomical shape information in a consistent manner. Evolution is described by a generative model that is the analog of linear regression, which is fully characterized by baseline images and shapes (intercept) and initial momenta vectors (slope). Further, our framework adopts a control point parameterization of deformations, where the dimensionality of the deformation is determined by the complexity of anatomical changes in time rather than the sampling of the image and/or the geometric data. We derive a gradient descent algorithm which simultaneously estimates baseline images and shapes, location of control points, and momenta. Experiments on real medical data demonstrate that our framework effectively combines image and shape information, resulting in improved modeling of 4D (3D space + time) trajectories.

Diffeomorphic shape trajectories for improved longitudinal segmentation and statistics.

Longitudinal imaging studies involve tracking changes in individuals by repeated image acquisition over time. The goal of these studies is to quantify biological shape variability within and across individuals, and also to distinguish between normal and disease populations. However, data variability is influenced by outside sources such as image acquisition, image calibration, human expert judgment, and limited robustness of segmentation and registration algorithms. In this paper, we propose a two-stage method for the statistical analysis of longitudinal shape. In the first stage, we estimate diffeomorphic shape trajectories for each individual that minimize inconsistencies in segmented shapes across time. This is followed by a longitudinal mixed-effects statistical model in the second stage for testing differences in shape trajectories between groups. We apply our method to a longitudinal database from PREDICT-HD and demonstrate our approach reduces unwanted variability for both shape and derived measures, such as volume. This leads to greater statistical power to distinguish differences in shape trajectory between healthy subjects and subjects with a genetic biomarker for Huntington's disease (HD).

Geodesic shape regression in the framework of currents.

Shape regression is emerging as an important tool for the statistical analysis of time dependent shapes. In this paper, we develop a new generative model which describes shape change over time, by extending simple linear regression to the space of shapes represented as currents in the large deformation diffeomorphic metric mapping (LDDMM) framework. By analogy with linear regression, we estimate a baseline shape (intercept) and initial momenta (slope) which fully parameterize the geodesic shape evolution. This is in contrast to previous shape regression methods which assume the baseline shape is fixed. We further leverage a control point formulation, which provides a discrete and low dimensional parameterization of large diffeomorphic transformations. This flexible system decouples the parameterization of deformations from the specific shape representation, allowing the user to define the dimensionality of the deformation parameters. We present an optimization scheme that estimates the baseline shape, location of the control points, and initial momenta simultaneously via a single gradient descent algorithm. Finally, we demonstrate our proposed method on synthetic data as well as real anatomical shape complexes.