Statistical Inference for Imaging and Disease

Sandy Wells
Sandy Wells, PhD
Core PI

Our Publications

The Spatio-Temporal Modeling Core develops statistical methods for the analysis of functional MRI (fMRI) in populations and for the group-wise registration of large datasets. New lines of research include the analysis of multi-modal functional data and studies of the relationship between structure and function, which are used for neurosurgical intervention and other applications that require detailed maps of cortical areas that show these relationships. The work of this core is organized around the following specific aims.

1. State Space Modeling (SSM) Approach for fMRI Analysis
2. Feature-Based Analysis (FBA) of Structural MRI
3. Methodology for Quantitative Magnetic Susceptibility Mapping

The methods developed in the specific aims will be applied in a variety of clinical scenarios.

Under Aim 1, we are adapting current SSM methods to incorporate hierarchical state sequences. The latter technology will be applied in a clinical study of cognitive dysfunction in patients with HIV infection and/or histories of methamphetamine use with our clinical partner, TMARC, centered at the University of California, San Diego. Under Aim 2, we are continuing to refine our current algorithms for feature-based analysis of structural MRI in groups of subjects and the resulting FBA technology will be applied in a pilot project that analyzes historical multiple sclerosis (MS) data. Under Aim 3, we are extending current methods for QSM to analyze tissues from MRI phase data in healthy subjects. This data will then be applied in at least two clinical projects, Parkinson's Disease (3A) and Traumatic Brain Injury (3B). The scientific team is composed of experts in mathematics, statistical modeling, image analysis, and functional (fMRI) and structural magnetic resonance imaging (MRI).

Using state-space model (SSM) as a platform for aim 1, we are developing a framework that consists of statistical measures, software, experimental designs, and neuroscientific interpretations. This new framework will be used to study the spatial character of mental activity, its temporal structure, and its implications on the organization of the mental processes of an individual and their salient differences between populations. By using dynamic multivariate methods that study the spatio-temporal entirety of mental activity to further our understanding of the neurobiological underpinnings of complex psychological conditions, we will elucidate the temporal ordering of neural cascades, and in this way improve the possibility of detecting abnormal spatio-temporal pathways in mental processing due to biological and psychological pathologies, with implications on cognitive and preclinical studies in neurology and psychiatry pertaining to, e.g., disease, aging, and dementia. Moreover, identifying the salient layers of human cognition and the interactions between them will enable the neurobiological investigation of the complex cognitive, cultural, and social factors in neuroscientific experiments.

Developments in feature extraction (aim 2) will focus on identifying classes of image features most effective for feature-based analysis (FBA) of MS. Experiments will involve dual echo MR image data, consisting of proton density and T2-weighted brain images for each subject. How best to extract and combine features from multiple image modalities into an FBA framework remains an open research question. Research will compare the result of FBA from features extracted independently in different image modalities vs. extraction in joint representations. Furthermore, different feature classes developed for 2D images will be extended to volumetric data and assessed in terms of effectiveness in FBA. Different modalities such as PD and T2 offer complementary information regarding the underlying subject anatomy, and extracting features from a joint image representation combining modalities may prove more effective than independently in individual modalities.

Patients with Parkinson's disease (PD) suffer a 60% to 70% reduction of neurons in the substantia nigra (SN) by the time the first clinical symptoms of PD are noticed by the patient, precluding effective neuroprotective therapies. It is possible that neuroprotective medications would be effective if they could be initiated before there was substantial cell loss, which would require a noninvasive method to detect preclinical markers of disease. Hypoechogenicity on transcranial sonography has been identified as a potential biomarker of SN injury. The level of hypoechogenicity in PD patients, however, is highly variable (range 68% to 99%). A study of 20 post mortem PD brains found a positive correlation between iron concentration and echogenicity in the SN, suggesting imaging methods sensitive to iron concentration should allow robust identification of the SN. We are developing a new approach to QSM in aim 3, termed atlas-based susceptibility mapping (ASM), with the goal of classifying Parkinson's disease patients and controls based on mean susceptibility estimates in the SN.

Featured Technologies

1. State Space Modeling (SSM) Approach for fMRI Analysis

State space Modeling

In contrast to localization-based methods, we use a multivariate dynamical model to represent the brain transitioning through an abstract state-space as it performs a mental task. Here, for example, we demonstrate the presence of sequences of well-defined states in fMRI recordings, each corresponding to characteristic distributions of metabolic activity in the brain and highly correlated with the perceptual, cognitive, or affective mental state (i.e., “brain state”) of the subject [Janoos, 2013].

2. Feature-Based Analysis (FBA) of Structural MRI


Feature-based analysis (FBA) is a recent technique in which data are represented as a set of distinctive local features or patches rather than the more traditional image voxels. Here, we show feature-based alignment (FBA), a general method for efficient and robust model-to-image alignment. Volumetric images, e.g., CT scans of the human body, are modeled probabilistically as a collage of 3D scale-invariant image features within a normalized reference space. The example shows model-subject correspondences in CT volumes. Each image consists of upper (axial) and lower (sagittal) image slices. White circles illustrating the location and scale of features in the ACRIN model (left) and in the new subject (right). The arrows indicate corresponding features [Toews, 2012].

3. Methodology for Quantitative magnetic Susceptibility Mapping (QSM)


The image demonstrates the influence of age on iron accumulation in the brain, using a new approach to Quantitative magnetic Susceptibility Mapping (QSM), termed atlas-based susceptibility mapping (ASM). The ASM group averages for young (A) versus elderly (B) subjects show an age-dependent increase in estimated susceptibility values in subcortical regions known to accumulate iron in normal aging. Excessive iron accumulation occurs in a range of neurodegenerative disorders, for example, Parkinson’s disease (PD), Alzheimer’s disease (AD), Multiple sclerosis (MS), and Huntington’s disease (HD), as well as in traumatic brain injury. These iron deposits cause spatial variations in the magnetic susceptibility of tissue, which result in magnetic field perturbations that alter the phase of the MRI signal. Reconstructing magnetic susceptibility maps from MRI phase data can provide valuable insights into iron distribution in vivo.

In contrast to localization-based methods, we use a multivariate dynamical model to represent the brain transitioning through an abstract state-space as it performs a mental task. Here, for example, we demonstrate the presence of sequences of well-defined states in fMRI recordings, each corresponding to characteristic distributions of metabolic activity in the brain and highly correlated with the perceptual, cognitive, or affective mental state (i.e., “brain state”) of the subject [Janoos, 2013].

Feature-based analysis (FBA) is a recent technique in which data are represented as a set of distinctive local features or patches rather than the more traditional image voxels. Here, we show feature-based alignment (FBA), a general method for efficient and robust model-to-image alignment. Volumetric images, e.g., CT scans of the human body, are modeled probabilistically as a collage of 3D scale-invariant image features within a normalized reference space. The example shows model-subject correspondences in CT volumes. Each image consists of upper (axial) and lower (sagittal) image slices. White circles illustrating the location and scale of features in the ACRIN model (left) and in the new subject (right). The arrows indicate corresponding features [Toews, 2012].

Research Highlights

Toews FBA   

Invariant Feature-Based Analysis (FBA) of Medical Images During this year Toews and Wells presented their overview of an inference method that is well-suited to large sets of medical images based upon a framework where distinctive 3D scale-invariant features are indexed efficiently to identify approximate nearest-neighbor (NN) feature matches in O(log N) computational complexity in the number of images N. Shown here are Lung CT visualizations of the 20 disease-informative features of COPD corresponding to Gold 0 (a) and Gold 4 (b) disease severity [Toews, 2016].


Keypoint Transfer Segmentation An image segmentation method is presented that transfers label maps of entire organs from the training images to the novel image to be segmented. Coronal views of example segmentation results for contrast-enhanced CT (left) and whole body CT (right) are overlaid on intensity images. Each series reports segmentations in the following order: manual, key point transfer, and locally weighted multi-atlas [Wachinger, 2015].

Developments in State Space Modeling (SSM) of fMRI under Aim 1

The Wells science team reported the following progress in reference to aim 1. State Space Modeling Wells and Toews visited colleagues at the University Hospital Geneva and gave a talk summarizing their state space analysis methodology [Wells 2015]. The Geneva group is prominent in the state-space analysis of EEG, and they are currently collecting simultaneous EEG and fMRI of epilepsy patients. They discussed potential approaches to state-space analysis of such joint data. The other progress under this aim applies to the application of SSM of fMRI in a collaboration with Prof. Greg Brown and the NIH-Funded Translational Methamphetamine Research Center (TMARC) at UCSD. For progress related to this collaboration (see TMARC CP, below).

Developments in Feature Based Analysis (FBA) of medical Images under Aim 2

The Feature Based Analysis (FBA) project has made significant progress and is producing outstanding results. FBA generates hundreds to thousands of features per scan for MRI and CT data. To date, the application of the technology includes segmentation, registration, neuroimage analysis, and disease analysis. In this year, two publications appeared related to progress noted in the last report, one on COPD disease classification [Toews, 2015] and a second on a segmentation method called Keypoint Transfer Segmentation [Wachinger, 2015]. In yet another collaborative effort, the FBA methodology was used to register 3D cine ultrasound images of the heart, leading to a manuscript submission [Bersvendsen, 2016]. The team also used feature correspondence counts to define a Jaccard distance between subjects and showed reliable detection of twins in data from the human connectome project. By now, the FBA technology developed in NAC has been successfully applied in diverse applications; the emergent theme is that FBA combined with simple algorithms enables good performance in many areas. A summary of the activity was reported in several talks.

Development in Quantitative Susceptibility Mapping (QSM) under Aim 3

Quantitative Susceptibility Mapping QSM developments let to the appearance of a journal article describing the methodology and its application to analyzing age-related changes in the magnetic susceptibility of sub-cortical nuclei [Poynton, 2015]. While most of our research has been on the analysis of fMRI task data, we have recently collaborated on state space analysis of resting state EEG data (Custo 2017). 
At UCSF the technology has been applied to 7T imaging of Huntington’s Disease. (Poynton, C. B., et al. "Quantitative Susceptibility Mapping of Huntington’s Disease at 7 Tesla." Proceedings of the Joint Annual Meeting of the International Society for Magnetic Resonance in Medicine and the European Society for Magnetic Resonance in Medicine. 2014.)

Other Collaborative Projects

Tumor Associated Seizures in Glioblastoma In our service collaboration with the National Center for Image-Guided Therapy (NCIGT), we guided the development of a methodology, based on tolerance limits, for validating image registration methods in specific applications [Fedorov, 2014]. We also provided analysis advice in a local project on the relationships among tumor region, seizures, and genetics (FIGURE 2). Tumor-associated seizures (TAS) are a common and significant cause of morbidity. Both imaging and gene expression features play significant roles in determining TAS, with strong interactions between them. We describe gene expression imaging tools which allow mapping of brain regions where gene expression has significant influence on TAS, and apply these methods to study 77 patients who underwent surgical evaluation for supratentorial glioblastomas. Tumor size and location were measured from MRI scans. A 9-set gene expression profile predicting long-term survivors was obtained from RNA derived from formalin-fixed paraffin embedded tissue. A total of 32 patients (42%) experienced preoperative TAS. Tumor volume was smaller (31.1 vs. 58.8 cubic cm, p<0.001) and there was a trend toward median survival being higher (48.4 vs. 32.7 months, p=0.055) in patients with TAS. Although the expression of only OLIG2 was significantly lower in patients with TAS in a groupwise analysis, gene expression imaging analysis revealed regions with significantly lower expression of OLIG2 and RTN1 in patients with TAS. Gene expression imaging is a powerful technique that demonstrates that the influence of gene expression on TAS is highly region specific. Regional variability should be evaluated with any genomic or molecular markers of solid brain lesions.

Gaussian Random Field Theory In collaboration with colleagues at MIT, in addition to (Wachinger 2015), we applied Gaussian Random Field theory to interpolating MRI images [Wachinger, 2014 MICCAI). We also contributed, with colleagues in the UK, on the development of probabilistic methods for segmenting the neocortex of a population of subjects, driven by diffusion MRI [Parisot, 2015].

Magneto Hydro Dynamics The TRDs collaboration with Children’s Hospital Boston on epilepsy image analysis saw the submission of an article on animal validation of direct MRI observations of tissue magnetic fields due to neural activity. We investigated an alternative mechanism, magneto hydro dynamics, that could explain the observations in humans [Balasubramanian, 2015]. 


Laurent Chauvin, Kuldeep Kumar, Christian Wachinger, Marc Vangel, Jacques de Guise, Christian Desrosiers, William Wells, and Matthew Toews. 1/2020. “Neuroimage Signature from Salient Keypoints is Highly Specific to Individuals and Shared by Close Relatives.” Neuroimage, 204, Pp. 116208.Abstract
Neuroimaging studies typically adopt a common feature space for all data, which may obscure aspects of neuroanatomy only observable in subsets of a population, e.g. cortical folding patterns unique to individuals or shared by close relatives. Here, we propose to model individual variability using a distinctive keypoint signature: a set of unique, localized patterns, detected automatically in each image by a generic saliency operator. The similarity of an image pair is then quantified by the proportion of keypoints they share using a novel Jaccard-like measure of set overlap. Experiments demonstrate the keypoint method to be highly efficient and accurate, using a set of 7536 T1-weighted MRIs pooled from four public neuroimaging repositories, including twins, non-twin siblings, and 3334 unique subjects. All same-subject image pairs are identified by a similarity threshold despite confounds including aging and neurodegenerative disease progression. Outliers reveal previously unknown data labeling inconsistencies, demonstrating the usefulness of the keypoint signature as a computational tool for curating large neuroimage datasets.
Christian Wachinger, Matthew Toews, Georg Langs, William Wells, and Polina Golland. 2/2020. “Keypoint Transfer for Fast Whole-Body Segmentation.” IEEE Trans Med Imaging, 39, 2, Pp. 273-82.Abstract
We introduce an approach for image segmentation based on sparse correspondences between keypoints in testing and training images. Keypoints represent automatically identified distinctive image locations, where each keypoint correspondence suggests a transformation between images. We use these correspondences to transfer label maps of entire organs from the training images to the test image. The keypoint transfer algorithm includes three steps: (i) keypoint matching, (ii) voting-based keypoint labeling, and (iii) keypoint-based probabilistic transfer of organ segmentations. We report segmentation results for abdominal organs in whole-body CT and MRI, as well as in contrast-enhanced CT and MRI. Our method offers a speed-up of about three orders of magnitude in comparison to common multi-atlas segmentation, while achieving an accuracy that compares favorably. Moreover, keypoint transfer does not require the registration to an atlas or a training phase. Finally, the method allows for the segmentation of scans with highly variable field-of-view.
Jian Wang, William M Wells, Polina Golland, and Miaomiao Zhang. 12/2019. “Registration Uncertainty Quantification via Low-dimensional Characterization of Geometric Deformations.” Magn Reson Imaging, 64, Pp. 122-31.Abstract
This paper presents an efficient approach to quantifying image registration uncertainty based on a low-dimensional representation of geometric deformations. In contrast to previous methods, we develop a Bayesian diffeomorphic registration framework in a bandlimited space, rather than a high-dimensional image space. We show that a dense posterior distribution on deformation fields can be fully characterized by much fewer parameters, which dramatically reduces the computational complexity of model inferences. To further avoid heavy computation loads introduced by random sampling algorithms, we approximate a marginal posterior by using Laplace's method at the optimal solution of log-posterior distribution. Experimental results on both 2D synthetic data and real 3D brain magnetic resonance imaging (MRI) scans demonstrate that our method is significantly faster than the state-of-the-art diffeomorphic registration uncertainty quantification algorithms, while producing comparable results.
Jie Luo, Alireza Sedghi, Karteek Popuri, Dana Cobzas, Miaomiao Zhang, Frank Preiswerk, Matthew Toews, Alexandra Golby, Masashi Sugiyama, William III M Wells, and Sarah Frisken. 10/2019. “On the Applicability of Registration Uncertainty.” In MICCAI 2019, LNCS 11765: Pp. 410-9. Shenzhen, China: Springer.Abstract
Estimating the uncertainty in (probabilistic) image registration enables, e.g., surgeons to assess the operative risk based on the trustworthiness of the registered image data. If surgeons receive inaccurately calculated registration uncertainty and misplace unwarranted confidence in the alignment solutions, severe consequences may result. For probabilistic image registration (PIR), the predominant way to quantify the registration uncertainty is using summary statistics of the distribution of transformation parameters. The majority of existing research focuses on trying out different summary statistics as well as means to exploit them. Distinctively, in this paper, we study two rarely examined topics: (1) whether those summary statistics of the transformation distribution most informatively represent the registration uncertainty; (2) Does utilizing the registration uncertainty always be beneficial. We show that there are two types of uncertainties: the transformation uncertainty, Ut, and label uncertainty Ul. The conventional way of using Ut to quantify Ul is inappropriate and can be misleading. By a real data experiment, we also share a potentially critical finding that making use of the registration uncertainty may not always be an improvement.
B Kocev, Horst K Hahn, L Linsend, William III M Wells, and Ron Kikinis. 3/2019. “Uncertainty-aware Asynchronous Scattered Motion Interpolation using Gaussian Process Regression.” Computerized Medical Imaging and Graphics, 72, Pp. 1-12.Abstract
We address the problem of interpolating randomly non-uniformly spatiotemporally scattered uncertain motion measurements, which arises in the context of soft tissue motion estimation. Soft tissue motion estimation is of great interest in the field of image-guided soft-tissue intervention and surgery navigation, because it enables the registration of pre-interventional/pre-operative navigation information on deformable soft-tissue organs. To formally define the measurements as spatiotemporally scattered motion signal samples, we propose a novel motion field representation. To perform the interpolation of the motion measurements in an uncertainty-aware optimal unbiased fashion, we devise a novel Gaussian process (GP) regression model with a non-constant-mean prior and an anisotropic covariance function and show through an extensive evaluation that it outperforms the state-of-the-art GP models that have been deployed previously for similar tasks. The employment of GP regression enables the quantification of uncertainty in the interpolation result, which would allow the amount of uncertainty present in the registered navigation information governing the decisions of the surgeon or intervention specialist to be conveyed.
Jie Luo, Matthew Toews, Inês Machado, Sarah Frisken, Miaomiao Zhang, Frank Preiswerk, Alireza Sedghi, Hongyi Ding, Steve Pieper, Polina Golland, Alexandra Golby, Masashi Sugiyama, and William III M Wells. 9/2018. “A Feature-Driven Active Framework for Ultrasound-Based Brain Shift Compensation.” In MICCAI 2018, LNCS 11073: Pp. 30-38. Granada, Spain: Springer.Abstract
A reliable Ultrasound (US)-to-US registration method to compensate for brain shift would substantially improve Image-Guided Neurological Surgery. Developing such a registration method is very challenging, due to factors such as the tumor resection, the complexity of brain pathology and the demand for fast computation. We propose a novel feature-driven active registration framework. Here, landmarks and their displacement are first estimated from a pair of US images using corresponding local image features. Subsequently, a Gaussian Process (GP) model is used to interpolate a dense deformation field from the sparse landmarks. Kernels of the GP are estimated by using variograms and a discrete grid search method. If necessary, the user can actively add new landmarks based on the image context and visualization of the uncertainty measure provided by the GP to further improve the result. We retrospectively demonstrate our registration framework as a robust and accurate brain shift compensation solution on clinical data.
Jie Luo, Sarah Frisken, Ines Machado, Miaomiao Zhang, Steve Pieper, Polina Golland, Matthew Toews, Prashin Unadkat, Alireza Sedghi, Haoyin Zhou, Alireza Mehrtash, Frank Preiswerk, Cheng-Chieh Cheng, Alexandra Golby, Masashi Sugiyama, and William M Wells. 12/2018. “Using the Variogram for Vector Outlier Screening: Application to Feature-based Image Registration.” Int J Comput Assist Radiol Surg, 13, 12, Pp. 1871-80.Abstract
PURPOSE: Matching points that are derived from features or landmarks in image data is a key step in some medical imaging applications. Since most robust point matching algorithms claim to be able to deal with outliers, users may place high confidence in the matching result and use it without further examination. However, for tasks such as feature-based registration in image-guided neurosurgery, even a few mismatches, in the form of invalid displacement vectors, could cause serious consequences. As a result, having an effective tool by which operators can manually screen all matches for outliers could substantially benefit the outcome of those applications. METHODS: We introduce a novel variogram-based outlier screening method for vectors. The variogram is a powerful geostatistical tool for characterizing the spatial dependence of stochastic processes. Since the spatial correlation of invalid displacement vectors, which are considered as vector outliers, tends to behave differently than normal displacement vectors, they can be efficiently identified on the variogram. RESULTS: We validate the proposed method on 9 sets of clinically acquired ultrasound data. In the experiment, potential outliers are flagged on the variogram by one operator and further evaluated by 8 experienced medical imaging researchers. The matching quality of those potential outliers is approximately 1.5 lower, on a scale from 1 (bad) to 5 (good), than valid displacement vectors. CONCLUSION: The variogram is a simple yet informative tool. While being used extensively in geostatistical analysis, it has not received enough attention in the medical imaging field. We believe there is a good deal of potential for clinically applying the proposed outlier screening method. By way of this paper, we also expect researchers to find variogram useful in other medical applications that involve motion vectors analyses.
Inês Machado, Matthew Toews, Jie Luo, Prashin Unadkat, Walid Essayed, Elizabeth George, Pedro Teodoro, Herculano Carvalho, Jorge Martins, Polina Golland, Steve Pieper, Sarah Frisken, Alexandra Golby, and William Wells. 10/2018. “Non-rigid Registration of 3D Ultrasound for Neurosurgery using Automatic Feature Detection and Matching.” Int J Comput Assist Radiol Surg, 13, 10, Pp. 1525-38.Abstract
PURPOSE: The brain undergoes significant structural change over the course of neurosurgery, including highly nonlinear deformation and resection. It can be informative to recover the spatial mapping between structures identified in preoperative surgical planning and the intraoperative state of the brain. We present a novel feature-based method for achieving robust, fully automatic deformable registration of intraoperative neurosurgical ultrasound images. METHODS: A sparse set of local image feature correspondences is first estimated between ultrasound image pairs, after which rigid, affine and thin-plate spline models are used to estimate dense mappings throughout the image. Correspondences are derived from 3D features, distinctive generic image patterns that are automatically extracted from 3D ultrasound images and characterized in terms of their geometry (i.e., location, scale, and orientation) and a descriptor of local image appearance. Feature correspondences between ultrasound images are achieved based on a nearest-neighbor descriptor matching and probabilistic voting model similar to the Hough transform. RESULTS: Experiments demonstrate our method on intraoperative ultrasound images acquired before and after opening of the dura mater, during resection and after resection in nine clinical cases. A total of 1620 automatically extracted 3D feature correspondences were manually validated by eleven experts and used to guide the registration. Then, using manually labeled corresponding landmarks in the pre- and post-resection ultrasound images, we show that our feature-based registration reduces the mean target registration error from an initial value of 3.3 to 1.5 mm. CONCLUSIONS: This result demonstrates that the 3D features promise to offer a robust and accurate solution for 3D ultrasound registration and to correct for brain shift in image-guided neurosurgery.
Matthew Toews and William M Wells. 1/2018. “Phantomless Auto-Calibration and Online Calibration Assessment for a Tracked Freehand 2-D Ultrasound Probe.” IEEE Trans Med Imaging, 37, 1, Pp. 262-72.Abstract
This paper presents a method for automatically calibrating and assessing the calibration quality of an externally tracked 2-D ultrasound (US) probe by scanning arbitrary, natural tissues, as opposed a specialized calibration phantom as is the typical practice. A generative topic model quantifies the posterior probability of calibration parameters conditioned on local 2-D image features arising from a generic underlying substrate. Auto-calibration is achieved by identifying the maximum a-posteriori image-to-probe transform, and calibration quality is assessed online in terms of the posterior probability of the current image-to-probe transform. Both are closely linked to the 3-D point reconstruction error (PRE) in aligning feature observations arising from the same underlying physical structure in different US images. The method is of practical importance in that it operates simply by scanning arbitrary textured echogenic structures, e.g., in-vivo tissues in the context of the US-guided procedures, without requiring specialized calibration procedures or equipment. Observed data take the form of local scale-invariant features that can be extracted and fit to the model in near real-time. Experiments demonstrate the method on a public data set of in vivo human brain scans of 14 unique subjects acquired in the context of neurosurgery. Online calibration assessment can be performed at approximately 3 Hz for the US images of pixels. Auto-calibration achieves an internal mean PRE of 1.2 mm and a discrepancy of [2 mm, 6 mm] in comparison to the calibration via a standard phantom-based method.
Guillermo Gallardo, William M Wells III, Rachid Deriche, and Demian Wassermann. 4/2018. “Groupwise Structural Parcellation of the Whole Cortex: A Logistic Random Effects Model Based Approach.” Neuroimage, 170, Pp. 307-20.Abstract

Current theories hold that brain function is highly related to long-range physical connections through axonal bundles, namely extrinsic connectivity. However, obtaining a groupwise cortical parcellation based on extrinsic connectivity remains challenging. Current parcellation methods are computationally expensive; need tuning of several parameters or rely on ad-hoc constraints. Furthermore, none of these methods present a model for the cortical extrinsic connectivity of the cortex. To tackle these problems, we propose a parsimonious model for the extrinsic connectivity and an efficient parceling technique based on clustering of tractograms. Our technique allows the creation of single subject and groupwise parcellations of the whole cortex. The parcellations obtained with our technique are in agreement with structural and functional parcellations in the literature. In particular, the motor and sensory cortex are subdivided in agreement with the human homunculus of Penfield. We illustrate this by comparing our resulting parcels with the motor strip mapping included in the Human Connectome Project data.

Anna Custo, Dimitri Van De Ville, William M Wells, Miralena I Tomescu, Denis Brunet, and Christoph M Michel. 12/2017. “Electroencephalographic Resting-State Networks: Source Localization of Microstates.” Brain Connect, 7, 10, Pp. 671-82.Abstract
Using electroencephalography (EEG) to elucidate the spontaneous activation of brain resting-state networks (RSNs) is nontrivial as the signal of interest is of low amplitude and it is difficult to distinguish the underlying neural sources. Using the principles of electric field topographical analysis, it is possible to estimate the meta-stable states of the brain (i.e., the resting-state topographies, so-called microstates). We estimated seven resting-state topographies explaining the EEG data set with k-means clustering (N = 164, 256 electrodes). Using a method specifically designed to localize the sources of broadband EEG scalp topographies by matching sensor and source space temporal patterns, we demonstrated that we can estimate the EEG RSNs reliably by measuring the reproducibility of our findings. After subtracting their mean from the seven EEG RSNs, we identified seven state-specific networks. The mean map includes regions known to be densely anatomically and functionally connected (superior frontal, superior parietal, insula, and anterior cingulate cortices). While the mean map can be interpreted as a "router," crosslinking multiple functional networks, the seven state-specific RSNs partly resemble and extend previous functional magnetic resonance imaging-based networks estimated as the hemodynamic correlates of four canonical EEG microstates.
Jenna Schabdach, William M Wells, Michael Cho, and Kayhan N Batmanghelich. 6/2017. “A Likelihood-Free Approach for Characterizing Heterogeneous Diseases in Large-Scale Studies.” Inf Process Med Imaging, 10265, Pp. 170-183.Abstract
We propose a non-parametric approach for characterizing heterogeneous diseases in large-scale studies. We target diseases where multiple types of pathology present simultaneously in each subject and a more severe disease manifests as a higher level of tissue destruction. For each subject, we model theof local image descriptors as samples generated by an unknown subject-specific probability density. Instead of approximating the probability density via a parametric family, we propose to side step the parametric inference by directly estimating the divergence between subject densities. Our method maps the collection of local image descriptors to a signaturethat is used to predict a clinical measurement. We are able to interpret the prediction of the clinical variable in the population and individual levels by carefully studying the divergences. We illustrate an application this method on simulated data as well as on a large-scale lung CT study of Chronic Obstructive Pulmonary Disease (COPD). Our approach outperforms classical methods on both simulated and COPD data and demonstrates the state-of-the-art prediction on an important physiologic measure of airflow (the forced respiratory volume in one second, FEV1).
Marc Niethammer, Kilian M Pohl, Firdaus Janoos, and William M Wells. 9/2017. “Active Mean Fields for Probabilistic Image Segmentation: Connections with Chan-Vese and Rudin-Osher-Fatemi Models.” SIAM J. Imaging Sci., 10, 3, Pp. 1069-1103.Abstract
Segmentation is a fundamental task for extracting semantically meaningful regions from an image. The goal of segmentation algorithms is to accurately assign object labels to each image location. However, image noise, shortcomings of algorithms, and image ambiguities cause uncertainty in label assignment. Estimating this uncertainty is important in multiple application domains, such as segmenting tumors from medical images for radiation treatment planning. One way to estimate these uncertainties is through the computation of posteriors of Bayesian models, which is computationally prohibitive for many practical applications. However, most computationally efficient methods fail to estimate label uncertainty. We therefore propose in this paper the active mean fields (AMF) approach, a technique based on Bayesian modeling that uses a mean-field approximation to efficiently compute a segmentation and its corresponding uncertainty. Based on a variational formulation, the resulting convex model combines any label-likelihood measure with a prior on the length of the segmentation boundary. A specific implementation of that model is the Chan-Vese segmentation model, in which the binary segmentation task is defined by a Gaussian likelihood and a prior regularizing the length of the segmentation boundary. Furthermore, the Euler-Lagrange equations derived from the AMF model are equivalent to those of the popular Rudin-Osher-Fatemi (ROF) model for image denoising. Solutions to the AMF model can thus be implemented by directly utilizing highly efficient ROF solvers on log-likelihood ratio fields. We qualitatively assess the approach on synthetic data as well as on real natural and medical images. For a quantitative evaluation, we apply our approach to the tt icgbench dataset.
Miaomiao Zhang, William M Wells, and Polina Golland. 10/2017. “Probabilistic Modeling of Anatomical Variability using a Low Dimensional Parameterization of Diffeomorphisms.” Med Image Anal, 41, Pp. 55-62.Abstract
We present an efficient probabilistic model of anatomical variability in a linear space of initial velocities of diffeomorphic transformations and demonstrate its benefits in clinical studies of brain anatomy. To overcome the computational challenges of the high dimensional deformation-based descriptors, we develop a latent variable model for principal geodesic analysis (PGA) based on a low dimensional shape descriptor that effectively captures the intrinsic variability in a population. We define a novel shape prior that explicitly represents principal modes as a multivariate complex Gaussian distribution on the initial velocities in a bandlimited space. 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 the state-of-the-art method such as tangent space PCA (TPCA) and probabilistic principal geodesic analysis (PPGA) that operate in the high dimensional image space.
Miaomiao Zhang, William M Wells, and Polina Golland. 10/2016. “Low-Dimensional Statistics of Anatomical Variability via Compact Representation of Image Deformations.” Med Image Comput Comput Assist Interv, 9902, Pp. 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).
Jørn Bersvendsen, Matthew Toews, Adriyana Danudibroto, William M Wells III, Stig Urheim, Raúl San José Estépar, and Eigil Samset. 2/2016. “Robust Spatio-Temporal Registration of 4D Cardiac Ultrasound Sequences.” Proc SPIE Int Soc Opt Eng, 9790.Abstract

Registration of multiple 3D ultrasound sectors in order to provide an extended field of view is important for the appreciation of larger anatomical structures at high spatial and temporal resolution. In this paper, we present a method for fully automatic spatio-temporal registration between two partially overlapping 3D ultrasound sequences. The temporal alignment is solved by aligning the normalized cross correlation-over-time curves of the sequences. For the spatial alignment, corresponding 3D Scale Invariant Feature Transform (SIFT) features are extracted from all frames of both sequences independently of the temporal alignment. A rigid transform is then calculated by least squares minimization in combination with random sample consensus. The method is applied to 16 echocardiographic sequences of the left and right ventricles and evaluated against manually annotated temporal events and spatial anatomical landmarks. The mean distances between manually identified landmarks in the left and right ventricles after automatic registration were (mean ± SD) 4.3 ± 1.2 mm compared to a reference error of 2.8 ± 0.6 mm with manual registration. For the temporal alignment, the absolute errors in valvular event times were 14.4 ± 11.6 ms for Aortic Valve (AV) opening, 18.6 ± 16.0 ms for AV closing, and 34.6 ± 26.4 ms for mitral valve opening, compared to a mean inter-frame time of 29 ms.

Padmavathi Sundaram, Aapo Nummenmaa, William M Wells III, Darren Orbach, Daniel Orringer, Robert Mulkern, and Yoshio Okada. 5/2016. “Direct Neural Current Imaging in an Intact Cerebellum with Magnetic Resonance Imaging.” Neuroimage, 132, Pp. 477-90.Abstract

The ability to detect neuronal currents with high spatiotemporal resolution using magnetic resonance imaging (MRI) is important for studying human brain function in both health and disease. While significant progress has been made, we still lack evidence showing that it is possible to measure an MR signal time-locked to neuronal currents with a temporal waveform matching concurrently recorded local field potentials (LFPs). Also lacking is evidence that such MR data can be used to image current distribution in active tissue. Since these two results are lacking even in vitro, we obtained these data in an intact isolated whole cerebellum of turtle during slow neuronal activity mediated by metabotropic glutamate receptors using a gradient-echo EPI sequence (TR=100ms) at 4.7T. Our results show that it is possible (1) to reliably detect an MR phase shift time course matching that of the concurrently measured LFP evoked by stimulation of a cerebellar peduncle, (2) to detect the signal in single voxels of 0.1mm3, (3) to determine the spatial phase map matching the magnetic field distribution predicted by the LFP map, (4) to estimate the distribution of neuronal current in the active tissue from a group-average phase map, and (5) to provide a quantitatively accurate theoretical account of the measured phase shifts. The peak values of the detected MR phase shifts were 0.27-0.37°, corresponding to local magnetic field changes of 0.67-0.93nT (for TE=26ms). Our work provides an empirical basis for future extensions to in vivo imaging of neuronal currents.

Lauren J O'Donnell, Yannick Suter, Laura Rigolo, Pegah Kahali, Fan Zhang, Isaiah Norton, Angela Albi, Olutayo Olubiyi, Antonio Meola, Walid I Essayed, Prashin Unadkat, Pelin Aksit Ciris, William M Wells III, Yogesh Rathi, Carl-Fredrik Westin, and Alexandra J Golby. 11/2016. “Automated White Matter Fiber Tract Identification in Patients with Brain Tumors.” Neuroimage Clin, 13, Pp. 138-53.Abstract

We propose a method for the automated identification of key white matter fiber tracts for neurosurgical planning, and we apply the method in a retrospective study of 18 consecutive neurosurgical patients with brain tumors. Our method is designed to be relatively robust to challenges in neurosurgical tractography, which include peritumoral edema, displacement, and mass effect caused by mass lesions. The proposed method has two parts. First, we learn a data-driven white matter parcellation or fiber cluster atlas using groupwise registration and spectral clustering of multi-fiber tractography from healthy controls. Key fiber tract clusters are identified in the atlas. Next, patient-specific fiber tracts are automatically identified using tractography-based registration to the atlas and spectral embedding of patient tractography. Results indicate good generalization of the data-driven atlas to patients: 80% of the 800 fiber clusters were identified in all 18 patients, and 94% of the 800 fiber clusters were found in 16 or more of the 18 patients. Automated subject-specific tract identification was evaluated by quantitative comparison to subject-specific motor and language functional MRI, focusing on the arcuate fasciculus (language) and corticospinal tracts (motor), which were identified in all patients. Results indicate good colocalization: 89 of 95, or 94%, of patient-specific language and motor activations were intersected by the corresponding identified tract. All patient-specific activations were within 3mm of the corresponding language or motor tract. Overall, our results indicate the potential of an automated method for identifying fiber tracts of interest for neurosurgical planning, even in patients with mass lesions.

Tassilo Klein and William M Wells III. 10/2015. “RF Ultrasound Distribution-Based Confidence Maps.” Int Conf Med Image Comput Comput Assist Interv. 18 (Pt2), Pp. 595-602.Abstract
Ultrasound is becoming an ever increasingly important modality in medical care. However, underlying physical acquisition principles are prone to image artifacts and result in overall quality variation. Therefore processing medical ultrasound data remains a challenging task. We propose a novel distribution-based measure of assessing the confidence in the signal, which emphasizes uncertainty in attenuated as well as shadow regions. In contrast to the similar recently proposed method that relies on image intensities, the new approach makes use of the enveloped-detected radio-frequency data, facilitating the use of Nakagami speckle statistics. Employing J-divergence as distance measure for the random-walk based algorithm, provides a natural measure of similarity, yielding a more reliable estimate of confidence. For evaluation of the model’s performance, tests are conducted on the application of shadow detection. Additionally, computed maps are presented for different organs such as neck, liver and prostate, showcasing the properties of the model. The probabilistic approach is shown to have beneficial features for image processing tasks.