Publications

2017
Bernal-Rusiel JL, Rannou N, Gollub RL, Pieper S, Murphy S, Robertson R, Grant PE, Pienaar R. Reusable Client-Side JavaScript Modules for Immersive Web-Based Real-Time Collaborative Neuroimage Visualization. Front Neuroinform. 2017;11 :32.Abstract
In this paper we present a web-based software solution to the problem of implementing real-time collaborative neuroimage visualization. In both clinical and research settings, simple and powerful access to imaging technologies across multiple devices is becoming increasingly useful. Prior technical solutions have used a server-side rendering and push-to-client model wherein only the server has the full image dataset. We propose a rich client solution in which each client has all the data and uses the Google Drive Realtime API for state synchronization. We have developed a small set of reusable client-side object-oriented JavaScript modules that make use of the XTK toolkit, a popular open-source JavaScript library also developed by our team, for the in-browser rendering and visualization of brain image volumes. Efficient realtime communication among the remote instances is achieved by using just a small JSON object, comprising a representation of the XTK image renderers' state, as the Google Drive Realtime collaborative data model. The developed open-source JavaScript modules have already been instantiated in a web-app called MedView, a distributed collaborative neuroimage visualization application that is delivered to the users over the web without requiring the installation of any extra software or browser plugin. This responsive application allows multiple physically distant physicians or researchers to cooperate in real time to reach a diagnosis or scientific conclusion. It also serves as a proof of concept for the capabilities of the presented technological solution.
Rydhög AS, Szczepankiewicz F, Wirestam R, Ahlgren A, Westin C-F, Knutsson L, Pasternak O. Separating Blood and Water: Perfusion and Free Water Elimination from Diffusion MRI in the Human Brain. Neuroimage. 2017;156 :423-34.Abstract
The assessment of the free water fraction in the brain provides important information about extracellular processes such as atrophy and neuroinflammation in various clinical conditions as well as in normal development and aging. Free water estimates from diffusion MRI are assumed to account for freely diffusing water molecules in the extracellular space, but may be biased by other pools of molecules in rapid random motion, such as the intravoxel incoherent motion (IVIM) of blood, where water molecules perfuse in the randomly oriented capillary network. The goal of this work was to separate the signal contribution of the perfusing blood from that of free-water and of other brain diffusivities. The influence of the vascular compartment on the estimation of the free water fraction and other diffusivities was investigated by simulating perfusion in diffusion MRI data. The perfusion effect in the simulations was significant, especially for the estimation of the free water fraction, and was maintained as long as low b-value data were included in the analysis. Two approaches to reduce the perfusion effect were explored in this study: (i) increasing the minimal b-value used in the fitting, and (ii) using a three-compartment model that explicitly accounts for water molecules in the capillary blood. Estimation of the model parameters while excluding low b-values reduced the perfusion effect but was highly sensitive to noise. The three-compartment model fit was more stable and additionally, provided an estimation of the volume fraction of the capillary blood compartment. The three-compartment model thus disentangles the effects of free water diffusion and perfusion, which is of major clinical importance since changes in these components in the brain may indicate different pathologies, i.e., those originating from the extracellular space, such as neuroinflammation and atrophy, and those related to the vascular space, such as vasodilation, vasoconstriction and capillary density. Diffusion MRI data acquired from a healthy volunteer, using multiple b-shells, demonstrated an expected non-zero contribution from the blood fraction, and indicated that not accounting for the perfusion effect may explain the overestimation of the free water fraction evinced in previous studies. Finally, the applicability of the method was demonstrated with a dataset acquired using a clinically feasible protocol with shorter acquisition time and fewer b-shells.
Ou Y, Zöllei L, Retzepi K, Castro V, Bates SV, Pieper S, Andriole KP, Murphy SN, Gollub RL, Grant PE. Using Clinically Acquired MRI to Construct Age-specific Atlases: Quantifying Spatiotemporal ADC Changes from Birth to 6-year Old. Hum Brain Mapp. 2017;38 (6) :3052-68.Abstract
Diffusion imaging is critical for detecting acute brain injury. However, normal apparent diffusion coefficient (ADC) maps change rapidly in early childhood, making abnormality detection difficult. In this article, we explored clinical PACS and electronic healthcare records (EHR) to create age-specific ADC atlases for clinical radiology reference. Using the EHR and three rounds of multiexpert reviews, we found ADC maps from 201 children 0-6 years of age scanned between 2006 and 2013 who had brain MRIs with no reported abnormalities and normal clinical evaluations 2+ years later. These images were grouped in 10 age bins, densely sampling the first 1 year of life (5 bins, including neonates and 4 quarters) and representing the 1-6 year age range (an age bin per year). Unbiased group-wise registration was used to construct ADC atlases for 10 age bins. We used the atlases to quantify (a) cross-sectional normative ADC variations; (b) spatiotemporal heterogeneous ADC changes; and (c) spatiotemporal heterogeneous volumetric changes. The quantified age-specific whole-brain and region-wise ADC values were compared to those from age-matched individual subjects in our study and in multiple existing independent studies. The significance of this study is that we have shown that clinically acquired images can be used to construct normative age-specific atlases. These first of their kind age-specific normative ADC atlases quantitatively characterize changes of myelination-related water diffusion in the first 6 years of life. The quantified voxel-wise spatiotemporal ADC variations provide standard references to assist radiologists toward more objective interpretation of abnormalities in clinical images. Our atlases are available at https://www.nitrc.org/projects/mgh_adcatlases.
Halle M, Demeusy V, Kikinis R. The Open Anatomy Browser: A Collaborative Web-Based Viewer for Interoperable Anatomy Atlases. Front Neuroinform. 2017;11 :22.Abstract

The Open Anatomy Browser (OABrowser) is an open source, web-based, zero-installation anatomy atlas viewer based on current web browser technologies and evolving anatomy atlas interoperability standards. OABrowser displays three-dimensional anatomical models, image cross-sections of labeled structures and source radiological imaging, and a text-based hierarchy of structures. The viewer includes novel collaborative tools: users can save bookmarks of atlas views for later access and exchange those bookmarks with other users, and dynamic shared views allow groups of users can participate in a collaborative interactive atlas viewing session. We have published several anatomy atlases (an MRI-derived brain atlas and atlases of other parts of the anatomy) to demonstrate OABrowser's functionality. The atlas source data, processing tools, and the source for OABrowser are freely available through GitHub and are distributed under a liberal open source license.

Black D, Hettig J, Luz M, Hansen C, Kikinis R, Hahn H. Auditory Feedback to Support Image-Guided Medical Needle Placement. Int J Comput Assist Radiol Surg. 2017;12 (9) :1655-63.Abstract
PURPOSE: During medical needle placement using image-guided navigation systems, the clinician must concentrate on a screen. To reduce the clinician's visual reliance on the screen, this work proposes an auditory feedback method as a stand-alone method or to support visual feedback for placing the navigated medical instrument, in this case a needle. METHODS: An auditory synthesis model using pitch comparison and stereo panning parameter mapping was developed to augment or replace visual feedback for navigated needle placement. In contrast to existing approaches which augment but still require a visual display, this method allows view-free needle placement. An evaluation with 12 novice participants compared both auditory and combined audiovisual feedback against existing visual methods. RESULTS: Using combined audiovisual display, participants show similar task completion times and report similar subjective workload and accuracy while viewing the screen less compared to using the conventional visual method. The auditory feedback leads to higher task completion times and subjective workload compared to both combined and visual feedback. CONCLUSION: Audiovisual feedback shows promising results and establishes a basis for applying auditory feedback as a supplement to visual information to other navigated interventions, especially those for which viewing a patient is beneficial or necessary.
Chen X, Xu L, Wang H, Wang F, Wang Q, Kikinis R. Development of a Surgical Navigation System Based on 3D Slicer for Intraoperative Implant Placement Surgery. Med Eng Phys. 2017;41 :81-9.Abstract

Implant placement has been widely used in various kinds of surgery. However, accurate intraoperative drilling performance is essential to avoid injury to adjacent structures. Although some commercially-available surgical navigation systems have been approved for clinical applications, these systems are expensive and the source code is not available to researchers. 3D Slicer is a free, open source software platform for the research community of computer-aided surgery. In this study, a loadable module based on Slicer has been developed and validated to support surgical navigation. This research module allows reliable calibration of the surgical drill, point-based registration and surface matching registration, so that the position and orientation of the surgical drill can be tracked and displayed on the computer screen in real time, aiming at reducing risks. In accuracy verification experiments, the mean target registration error (TRE) for point-based and surface-based registration were 0.31±0.06mm and 1.01±0.06mm respectively, which should meet clinical requirements. Both phantom and cadaver experiments demonstrated the feasibility of our surgical navigation software module.

Herberthson M, Özarslan E, Knutsson H, Westin C-F. Dynamics of Local Magnetization in the Eigenbasis of the Bloch-Torrey Operator. J Chem Phys. 2017;146 (12) :124201.Abstract

We consider diffusion within pores with general shapes in the presence of spatially linear magnetic field profiles. The evolution of local magnetization of the spin bearing particles can be described by the Bloch-Torrey equation. We study the diffusive process in the eigenbasis of the non-Hermitian Bloch-Torrey operator. It is possible to find expressions for some special temporal gradient waveforms employed to sensitize the nuclear magnetic resonance (NMR) signal to diffusion. For more general gradient waveforms, we derive an efficient numerical solution by introducing a novel matrix formalism. Compared to previous methods, this new approach requires a fewer number of eigenfunctions to achieve the same accuracy. This shows that these basis functions are better suited to the problem studied. The new framework could provide new important insights into the fundamentals of diffusion sensitization, which could further the development of the field of NMR.

Albi A, Pasternak O, Minati L, Marizzoni M, Bartrés-Faz D, Bargalló N, Bosch B, Rossini PM, Marra C, Müller B, et al. Free Water Elimination Improves Test-Retest Reproducibility of Diffusion Tensor Imaging Indices in the Brain: A Longitudinal Multisite Study of Healthy Elderly Subjects. Hum Brain Mapp. 2017;38 (1) :12-26.Abstract

Free water elimination (FWE) in brain diffusion MRI has been shown to improve tissue specificity in human white matter characterization both in health and in disease. Relative to the classical diffusion tensor imaging (DTI) model, FWE is also expected to increase sensitivity to microstructural changes in longitudinal studies. However, it is not clear if these two models differ in their test-retest reproducibility. This study compares a bi-tensor model for FWE with DTI by extending a previous longitudinal-reproducibility 3T multisite study (10 sites, 7 different scanner models) of 50 healthy elderly participants (55-80 years old) scanned in two sessions at least 1 week apart. We computed the reproducibility of commonly used DTI metrics (FA: fractional anisotropy, MD: mean diffusivity, RD: radial diffusivity, and AXD: axial diffusivity), derived either using a DTI model or a FWE model. The DTI metrics were evaluated over 48 white-matter regions of the JHU-ICBM-DTI-81 white-matter labels atlas, and reproducibility errors were assessed. We found that relative to the DTI model, FWE significantly reduced reproducibility errors in most areas tested. In particular, for the FA and MD metrics, there was an average reduction of approximately 1% in the reproducibility error. The reproducibility scores did not significantly differ across sites. This study shows that FWE improves sensitivity and is thus promising for clinical applications, with the potential to identify more subtle changes. The increased reproducibility allows for smaller sample size or shorter trials in studies evaluating biomarkers of disease progression or treatment effects. Hum Brain Mapp 38:12-26, 2017. © 2016 Wiley Periodicals, Inc.

Shaffer JJ, Ghayoor A, Long JD, Kim RE-Y, Lourens S, O'Donnell LJ, Westin C-F, Rathi Y, Magnotta V, Paulsen JS, et al. Longitudinal Diffusion Changes in Prodromal and Early HD: Evidence of White-matter Tract Deterioration. Hum Brain Mapp. 2017;38 (3) :1460-77.Abstract

INTRODUCTION: Huntington's disease (HD) is a genetic neurodegenerative disorder that primarily affects striatal neurons. Striatal volume loss is present years before clinical diagnosis; however, white matter degradation may also occur prior to diagnosis. Diffusion-weighted imaging (DWI) can measure microstructural changes associated with degeneration that precede macrostructural changes. DWI derived measures enhance understanding of degeneration in prodromal HD (pre-HD). METHODS: As part of the PREDICT-HD study, N = 191 pre-HD individuals and 70 healthy controls underwent two or more (baseline and 1-5 year follow-up) DWI, with n = 649 total sessions. Images were processed using cutting-edge DWI analysis methods for large multicenter studies. Diffusion tensor imaging (DTI) metrics were computed in selected tracts connecting the primary motor, primary somato-sensory, and premotor areas of the cortex with the subcortical caudate and putamen. Pre-HD participants were divided into three CAG-Age Product (CAP) score groups reflecting clinical diagnosis probability (low, medium, or high probabilities). Baseline and longitudinal group differences were examined using linear mixed models. RESULTS: Cross-sectional and longitudinal differences in DTI measures were present in all three CAP groups compared with controls. The high CAP group was most affected. CONCLUSIONS: This is the largest longitudinal DWI study of pre-HD to date. Findings showed DTI differences, consistent with white matter degeneration, were present up to a decade before predicted HD diagnosis. Our findings indicate a unique role for disrupted connectivity between the premotor area and the putamen, which may be closely tied to the onset of motor symptoms in HD. 

Ning L, Setsompop K, Westin C-F, Rathi Y. New Insights about Time-varying Diffusivity and its Estimation from Diffusion MRI. Magn Reson Med. 2017;78 (2) :763-74.Abstract

PURPOSE: Characterizing the relation between the applied gradient sequences and the measured diffusion MRI signal is important for estimating the time-dependent diffusivity, which provides important information about the microscopic tissue structure. THEORY AND METHODS: In this article, we extend the classical theory of Stepišnik for measuring time-dependent diffusivity under the Gaussian phase approximation. In particular, we derive three novel expressions which represent the diffusion MRI signal in terms of the mean-squared displacement, the instantaneous diffusivity, and the velocity autocorrelation function. We present the explicit signal expressions for the case of single diffusion encoding and oscillating gradient spin-echo sequences. Additionally, we also propose three different models to represent time-varying diffusivity and test them using Monte-Carlo simulations and in vivo human brain data. RESULTS: The time-varying diffusivities are able to distinguish the synthetic structures in the Monte-Carlo simulations. There is also strong statistical evidence about time-varying diffusivity from the in vivo human data set. CONCLUSION: The proposed theory provides new insights into our understanding of the time-varying diffusivity using different gradient sequences. The proposed models for representing time-varying diffusivity can be utilized to study time-varying diffusivity using in vivo human brain diffusion MRI data. 

Ning L, Özarslan E, Westin C-F, Rathi Y. Precise Inference and Characterization of Structural Organization (PICASO) of Tissue from Molecular Diffusion. Neuroimage. 2017;146 :452-73.Abstract

Inferring the microstructure of complex media from the diffusive motion of molecules is a challenging problem in diffusion physics. In this paper, we introduce a novel representation of diffusion MRI (dMRI) signal from tissue with spatially-varying diffusivity using a diffusion disturbance function. This disturbance function contains information about the (intra-voxel) spatial fluctuations in diffusivity due to restrictions, hindrances and tissue heterogeneity of the underlying tissue substrate. We derive the short- and long-range disturbance coefficients from this disturbance function to characterize the tissue structure and organization. Moreover, we provide an exact relation between the disturbance coefficients and the time-varying moments of the diffusion propagator, as well as their relation to specific tissue microstructural information such as the intra-axonal volume fraction and the apparent axon radius. The proposed approach is quite general and can model dMRI signal for any type of gradient sequence (rectangular, oscillating, etc.) without using the Gaussian phase approximation. The relevance of the proposed PICASO model is explored using Monte-Carlo simulations and in-vivo dMRI data. The results show that the estimated disturbance coefficients can distinguish different types of microstructural organization of axons.

Pujol S, Cabeen R, Sébille SB, Yelnik J, François C, Fernandez Vidal S, Karachi C, Zhao Y, Cosgrove RG, Jannin P, et al. In vivo Exploration of the Connectivity between the Subthalamic Nucleus and the Globus Pallidus in the Human Brain using Multi-Fiber Tractography. Front Neuroanat. 2017;10 :119.Abstract

The basal ganglia is part of a complex system of neuronal circuits that play a key role in the integration and execution of motor, cognitive and emotional function in the human brain. Parkinson's disease is a progressive neurological disorder of the motor circuit characterized by tremor, rigidity, and slowness of movement. Deep brain stimulation (DBS) of the subthalamic nucleus and the globus pallidus pars interna provides an efficient treatment to reduce symptoms and levodopa-induced side effects in Parkinson's disease patients. While the underlying mechanism of action of DBS is still unknown, the potential modulation of white matter tracts connecting the surgical targets has become an active area of research. With the introduction of advanced diffusion MRI acquisition sequences and sophisticated post-processing techniques, the architecture of the human brain white matter can be explored in vivo. The goal of this study is to investigate the white matter connectivity between the subthalamic nucleus and the globus pallidus. Two multi-fiber tractography methods were used to reconstruct pallido-subthalamic, subthalamo-pallidal and pyramidal fibers in five healthy subjects datasets of the Human Connectome Project. The anatomical accuracy of the tracts was assessed by four judges with expertise in neuroanatomy, functional neurosurgery, and diffusion MRI. The variability among subjects was evaluated based on the fractional anisotropy and mean diffusivity of the tracts. Both multi-fiber approaches enabled the detection of complex fiber architecture in the basal ganglia. The qualitative evaluation by experts showed that the identified tracts were in agreement with the expected anatomy. Tract-derived measurements demonstrated relatively low variability among subjects. False-negative tracts demonstrated the current limitations of both methods for clinical decision-making. Multi-fiber tractography methods combined with state-of-the-art diffusion MRI data have the potential to help identify white matter tracts connecting DBS targets in functional neurosurgery intervention.

Sastry R, Bi WL, Pieper S, Frisken S, Kapur T, Wells III WM, Golby AJ. Applications of Ultrasound in the Resection of Brain Tumors. J Neuroimaging. 2017;27 (1) :5-15.Abstract

Neurosurgery makes use of preoperative imaging to visualize pathology, inform surgical planning, and evaluate the safety of selected approaches. The utility of preoperative imaging for neuronavigation, however, is diminished by the well-characterized phenomenon of brain shift, in which the brain deforms intraoperatively as a result of craniotomy, swelling, gravity, tumor resection, cerebrospinal fluid (CSF) drainage, and many other factors. As such, there is a need for updated intraoperative information that accurately reflects intraoperative conditions. Since 1982, intraoperative ultrasound has allowed neurosurgeons to craft and update operative plans without ionizing radiation exposure or major workflow interruption. Continued evolution of ultrasound technology since its introduction has resulted in superior imaging quality, smaller probes, and more seamless integration with neuronavigation systems. Furthermore, the introduction of related imaging modalities, such as 3-dimensional ultrasound, contrast-enhanced ultrasound, high-frequency ultrasound, and ultrasound elastography, has dramatically expanded the options available to the neurosurgeon intraoperatively. In the context of these advances, we review the current state, potential, and challenges of intraoperative ultrasound for brain tumor resection. We begin by evaluating these ultrasound technologies and their relative advantages and disadvantages. We then review three specific applications of these ultrasound technologies to brain tumor resection: (1) intraoperative navigation, (2) assessment of extent of resection, and (3) brain shift monitoring and compensation. We conclude by identifying opportunities for future directions in the development of ultrasound technologies.

2016
Peters TM, Linte CA. Image-guided Interventions and Computer-integrated Therapy: Quo Vadis?. Med Image Anal. 2016;33 :56-63.Abstract
Significant efforts have been dedicated to minimizing invasiveness associated with surgical interventions, most of which have been possible thanks to the developments in medical imaging, surgical navigation, visualization and display technologies. Image-guided interventions have promised to dramatically change the way therapies are delivered to many organs. However, in spite of the development of many sophisticated technologies over the past two decades, other than some isolated examples of successful implementations, minimally invasive therapy is far from enjoying the wide acceptance once envisioned. This paper provides a large-scale overview of the state-of-the-art developments, identifies several barriers thought to have hampered the wider adoption of image-guided navigation, and suggests areas of research that may potentially advance the field.
Binder P, Batmanghelich KN, Estepar RSJ, Golland P. Unsupervised Discovery of Emphysema Subtypes in a Large Clinical Cohort. Int Conf Med Image Comput Comput Assist Interv. Workshop on Machine Learning in Medical Imaging. 2016;19 (WS) :180-7.
Fan Z, Peter S, Cai W, Song Y, Verma R, Carl-Fredrik W, O'Donnell LJ. Fiber Clustering Based White Matter Connectivity Analysis for Prediction of Autism Spectrum Disorder using Diffusion Tensor Imaging. IEEE Int Symp Biomed Imaging. 2016.Abstract
Autism Spectrum Disorder (ASD) has been suggested to associate with alterations in brain connectivity. In this study, we focus on a fiber clustering tractography segmentation strategy to observe white matter connectivity alterations in ASD. Compared to another popular parcellation-based approach for tractography segmentation based on cortical regions, we hypothesized that the clustering-based method could provide a more anatomically correspondent division of white matter. We applied this strategy to conduct a population-based group statistical analysis for the automated prediction of ASD. We obtained a maximum classification accuracy of 81.33% be- tween ASDs and controls, compared to the results of 78.00% from the parcellation-based method.
 
Zhang ISBI 2016
Bartling S, Jakab M, Kikinis R. CT-based Atlas of the Ear. Surgical Planning Laboratory, Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA.; 2016. Publisher's VersionAbstract
The Surgical Planning Laboratory at Brigham and Women's Hospital, Harvard Medical School, developed the SPL Ear Atlas. The atlas was derived from a high-resolution flat-panel computed tomography (CT) scan (aprox 140 µm high contrast resultion), using semi-automated image segmentation and three-dimensional reconstruction techniques [Gupta, Bartling, et al. AJNR Am J Neuroradiol. 2004.]. The current version consists of: 1. the original CT scan; 2. a set of detailed label maps; 3. a set of three-dimensional models of the labeled anatomical structures; 4. mrb (Medical Reality Bundle) file archive that contains the mrml scene file and all data for loading into Slicer 4 for displaying the volumes in 3D Slicer version 4.0 or greater; 5. several pre-defined 3D-views (“anatomy teaching files”). The SPL Ear Atlas provides important reference information for surgical planning, anatomy teaching, and template driven segmentation. Visualization of the data requires 3D Slicer. This software package can be downloaded from here. We are pleased to make this atlas available to our colleagues for free download. Please note that the data is being distributed under the Slicer license. By downloading these data, you agree to acknowledge our contribution in any of your publications that result form the use of this atlas. This work is funded as part of the Neuroimaging Analysis Center, grant number P41 RR013218, by the NIH's National Center for Research Resources (NCRR) and grant number P41 EB015902, by the NIH's National Institute of Biomedical Imaging and Bioengineering (NIBIB) and the Google Faculty Research Award.
Kapur T, Tempany CM. Proceedings of the 8th Image Guided Therapy Workshop. 2016;8 :1-68. 2016 IGT Workshop Proceedings
Langs G, Wang D, Golland P, Mueller S, Pan R, Sabuncu MR, Sun W, Li K, Liu H. Identifying Shared Brain Networks in Individuals by Decoupling Functional and Anatomical Variability. Cereb Cortex. 2016;26 (10) :4004-14.Abstract
The connectivity architecture of the human brain varies across individuals. Mapping functional anatomy at the individual level is challenging, but critical for basic neuroscience research and clinical intervention. Using resting-state functional connectivity, we parcellated functional systems in an "embedding space" based on functional characteristics common across the population, while simultaneously accounting for individual variability in the cortical distribution of functional units. The functional connectivity patterns observed in resting-state data were mapped in the embedding space and the maps were aligned across individuals. A clustering algorithm was performed on the aligned embedding maps and the resulting clusters were transformed back to the unique anatomical space of each individual. This novel approach identified functional systems that were reproducible within subjects, but were distributed across different anatomical locations in different subjects. Using this approach for intersubject alignment improved the predictability of individual differences in language laterality when compared with anatomical alignment alone. Our results further revealed that the strength of association between function and macroanatomy varied across the cortex, which was strong in unimodal sensorimotor networks, but weak in association networks.
Zhang M, Wells WM, Golland P. Low-Dimensional Statistics of Anatomical Variability via Compact Representation of Image Deformations. Med Image Comput Comput Assist Interv. 2016;9902 :166-73.Abstract
Using image-based descriptors to investigate clinical hypotheses and therapeutic implications is challenging due to the notorious "curse of dimensionality" coupled with a small sample size. In this paper, we present a low-dimensional analysis of anatomical shape variability in the space of diffeomorphisms and demonstrate its benefits for clinical studies. To combat the high dimensionality of the deformation descriptors, we develop a probabilistic model of principal geodesic analysis in a bandlimited low-dimensional space that still captures the underlying variability of image data. We demonstrate the performance of our model on a set of 3D brain MRI scans from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Our model yields a more compact representation of group variation at substantially lower computational cost than models based on the high-dimensional state-of-the-art approaches such as tangent space PCA (TPCA) and probabilistic principal geodesic analysis (PPGA).

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