Variational, geometric, and statistical methods for modeling brain anatomy and function

We survey the recent activities of the Odyssée Laboratory in the area of the application of mathematics to the design of models for studying brain anatomy and function. We start with the problem of reconstructing sources in MEG and EEG, and discuss the variational approach we have developed for solving these inverse problems. This motivates the need for geometric models of the head. We present a method for automatically and accurately extracting surface meshes of several tissues of the head from anatomical magnetic resonance (MR) images. Anatomical connectivity can be extracted from diffusion tensor magnetic resonance images but, in the current state of the technology, it must be preceded by a robust estimation and regularization stage. We discuss our work based on variational principles and show how the results can be used to track fibers in the white matter (WM) as geodesics in some Riemannian space. We then go to the statistical modeling of functional magnetic resonance imaging (fMRI) signals from the viewpoint of their decomposition in a pseudo-deterministic and stochastic part that we then use to perform clustering of voxels in a way that is inspired by the theory of support vector machines and in a way that is grounded in information theory. Multimodal image matching is discussed next in the framework of image statistics and partial differential equations (PDEs) with an eye on registering fMRI to the anatomy. The paper ends with a discussion of a new theory of random shapes that may prove useful in building anatomical and functional atlases.     

Mapping postnatal mouse brain development with diffusion tensor microimaging

While mouse brain development has been extensively studied using histology, quantitative characterization of morphological changes is still a challenging task. This paper presents how developing brain structures can be quantitatively characterized with magnetic resonance diffusion tensor microimaging coupled with techniques of computational anatomy. High resolution diffusion tensor images of ex vivo postnatal mouse brains provide excellent contrasts to reveal the evolutions of mouse forebrain structures. Using anatomical landmarks defined on diffusion tensor images, tissue level growth patterns of mouse brains were quantified. The results demonstrate the use of these techniques to three-dimensionally and quantitatively characterize brain growth.     

Magnetic Resonance Microscopy of the C57BL Mouse Brain

With the rapid progression in gene technologies, transgenic, targeted, and chemically induced mutations in mice are continually created. The major goal of these studies is to understand and characterize the effects of genotype on anatomy, physiology, and behavior and ultimately the role of genotype in development of disease. The demand for imaging techniques with high spatial resolution potential is rising because such imaging tools would expedite anatomical phenotyping in the genetically altered mice. Magnetic resonance microscopy (MRM) is a noninvasive, inherently three-dimensional (3D) imaging technique capable of visualizing several anatomical structures in the small mouse. The 3D nature of MRM also allows for interpretation of complex spatial relationships between substructures, which is important when phenotyping anatomically. The goal of this paper is to systematically describe three major brain regions in the C57BL/6J mouse at microanatomical spatial resolution ranges using in vitro MRM. We explore different MR contrast parameters, voxel sizes, and signal-to-noise ratios to best characterize C57BL/6J mouse brain microstructure by MRM. Further, we compare all MRM images with Nissl-stained brain sections. Major findings were as follows: T2* MR images visualized several gross anatomical regions in the mouse brain but not, for example, subregions within the hippocampus. Diffusion proton stains on the other hand were superior to T2* MR images and delineated many subregions within the hippocampus proper. Finally, contrast enhancement facilitated visualization of hippocampal anatomy on the T2* MR images. The results of this study are part of an ongoing initiative at our Center focused on creating a complete C57BL/6J mouse anatomical 3D image database by MRM.     

Hubless keypoint-based 3D deformable groupwise registration

We present a novel algorithm for Fast Registration Of image Groups (FROG), applied to large 3D image groups. Our approach extracts 3D SURF keypoints from images, computes matched pairs of keypoints and registers the group by minimizing pair distances in a hubless way i.e. without computing any central mean image. Using keypoints significantly reduces the problem complexity compared to voxel-based approaches, and enables us to provide an in-core global optimization, similar to the Bundle Adjustment for 3D reconstruction. As we aim to register images of different patients, the matching step yields many outliers. Then we propose a new EM-weighting algorithm which efficiently discards outliers. Global optimization is carried out with a fast gradient descent algorithm. This allows our approach to robustly register large datasets. The result is a set of diffeomorphic half transforms which link the volumes together and can be subsequently exploited for computational anatomy and landmark detection. We show experimental results on whole-body CT scans, with groups of up to 103 volumes. On a benchmark based on anatomical landmarks, our algorithm compares favorably with the star-groupwise voxel-based ANTs and NiftyReg approaches while being much faster. We also discuss the limitations of our approach for lower resolution images such as brain MRI.     

In vivo layer visualization of rat olfactory bulb by a swept source optical coherence tomography and its confirmation through electrocoagulation and anatomy

Here, we report in vivo 3-D visualization of the layered organization of a rat olfactory bulb (OB) by a swept source optical coherence tomography (SS-OCT). The SS-OCT operates at a wavelength of 1334 nm with respective theoretical depth and lateral resolutions of 6.7 μm and 15.4 μm in air and hence it is possible to get a 3D structural map of OB in vivo at the micron level resolution with millimeter-scale imaging depth. Up until now, with methods such as MRI, confocal microscopy, OB depth structure in vivo had not been clearly visualized as these do not satisfy the criterion of simultaneously providing micron-scale spatial resolution and imaging up to a few millimeter in depth. In order to confirm the OB's layered organization revealed by SS-OCT, we introduced the technique of electrocoagulation to make landmarks across the layered structure. To our knowledge this is such a first study that combines electrocoagulation and OCT in vivo of rat OB. Our results confirmed the layered organization of OB, and moreover the layers were clearly identified by electrocoagulation landmarks both in the OCT structural and anatomical slice images. We expect such a combined study is beneficial for both OCT and neuroscience fields.     

Quantifying atrial anatomy uncertainty from clinical data and its impact on electro-physiology simulation predictions

Patient-specific computational models of structure and function are increasingly being used to diagnose disease and predict how a patient will respond to therapy. Models of anatomy are often derived after segmentation of clinical images or from mapping systems which are affected by image artefacts, resolution and contrast. Quantifying the impact of uncertain anatomy on model predictions is important, as models are increasingly used in clinical practice where decisions need to be made regardless of image quality. We use a Bayesian probabilistic approach to estimate the anatomy and to quantify the uncertainty about the shape of the left atrium derived from Cardiac Magnetic Resonance images. We show that we can quantify uncertain shape, encode uncertainty about the left atrial shape due to imaging artefacts, and quantify the effect of uncertain shape on simulations of left atrial activation times.     

Anatomy of the cardiac conduction system

The specialized cardiomyocytes that constitute the conduction system in the human heart, initiate the electric impulse and result in rhythmic and synchronized contraction of the atria and ventricles. Although the atrioventricular (AV) conduction axis was described more than a century ago by Sunao Tawara, the anatomic pathway for propagation of impulse from atria to the ventricles has been a topic of debate for years. Over the past 2 decades, there has been a resurgence of conduction system pacing (CSP) by implanting pacing leads in the His bundle region in lieu of chronic right ventricular pacing that is associated with worse clinical outcomes. The inherent limitations of implanting the leads in the His bundle region has led to the emergence of left bundle branch area pacing in the past 3 years as an alternative strategy for CSP. The clinical experience from performing CSP has helped electrophysiologists gain deeper insight into the anatomy and physiology of cardiac conduction system. This review details the anatomy of the cardiac conduction system, and highlights some of the recently published articles that aid in better understanding of the AV conduction axis and its variations, the knowledge of which is critical for CSP. The remarkable evolution in technology has led to visualization of the cardiac conduction system using noninvasive, nondestructive high‐resolution contrast‐enhanced micro‐computed tomography imaging that may aid in future CSP. We also discuss from anatomical perspective, the differences seen clinically with His bundle pacing and left bundle branch area pacing.     

Functional and structural synergy for resolution recovery and partial volume correction in brain PET

Purpose: Positron Emission Tomography (PET) has the unique capability of measuring brain function but its clinical potential is affected by low resolution and lack of morphological detail. Here we propose and evaluate a wavelet synergistic approach that combines functional and structural information from a number of sources (CT, MRI and anatomical probabilistic atlases) for the accurate quantitative recovery of radioactivity concentration in PET images. When the method is combined with anatomical probabilistic atlases, the outcome is a functional volume corrected for partial volume effects.Methods: The proposed method is based on the multiresolution property of the wavelet transform. First, the target PET image and the corresponding anatomical image (CT/MRI/atlas-based segmented MRI) are decomposed into several resolution elements. Secondly, high-resolution components of the PET image are replaced, in part, with those of the anatomical image after appropriate scaling. The amount of structural input is weighted by the relative high frequency signal content of the two modalities. The method was validated on a digital Zubal phantom and clinical data to evaluate its quantitative potential.Results: Simulation studies showed the expected relationship between functional recovery and the amount of correct structural detail provided, with perfect recovery achieved when true images were used as anatomical reference. The use of T1-MRI images brought significant improvements in PET image resolution. However improvements were maximized when atlas-based segmented images as anatomical references were used; these results were replicated in clinical data sets.Conclusion: The synergistic use of functional and structural data, and the incorporation of anatomical probabilistic information in particular, generates morphologically corrected PET images of exquisite quality.     

Design and Construction of a Low-Frequency Ultrasound Acquisition Device for 2-D Brain Imaging Using Full-Waveform Inversion

The main techniques used to image the brain and obtain structural data are magnetic resonance imaging and X-ray computed tomography. These techniques produce images with high spatial resolution, but with the disadvantage of requiring very large equipment with special installation needs. In addition, X-ray tomography uses ionizing radiation, which limits their use. Ultrasound imaging is a safe technology that is delivered using compact and mobile devices. However, conventional ultrasound reconstruction techniques have failed to obtain images of the brain because of, fundamentally, the presence of the skull and the distortion that it produces on ultrasound. Recent studies have indicated that full-waveform inversion, a computational technique originally from Earth science, has the potential to generate accurate 3-D images of the brain. This technology can overcome the limitations of conventional ultrasound imaging, but a prototype for transcranial applications does not yet exist. Here, we investigate different designs of an annular array of ultrasound transducers to optimize the number of elements and rotations needed to conduct transcranial imaging with full-waveform inversion. This device uses small-diameter, low-frequency transducers that readily propagate ultrasound through the skull with good signal-to-noise ratios. It also incorporates the use of rotations to produce a high-density coverage of the target and acquire redundant traces that are beneficial for full-waveform inversion. We have built a ring of 40 transducers to illustrate that this design is capable of reconstructing images of the brain, retrieving its anatomy and acoustic properties with millimeter resolution. Laboratory results reveal the ability of this device to successfully image a 2.5-D brain- and skull-mimicking phantom using full-waveform inversion. To our knowledge, this is the first prototype ever used for transcranial-like imaging. The importance of these findings and their implications for the design of a 3-D reconstruction system with possible clinical applications are discussed.     

An optimized strategy for real-time hemorrhage monitoring with electrical impedance tomography

Delayed detection of an internal hemorrhage may result in serious disabilities and possibly death for a patient. Currently, there are no portable medical imaging instruments that are suitable for long-term monitoring of patients at risk of internal hemorrhage. Electrical impedance tomography (EIT) has the potential to monitor patients continuously as a novel functional image modality and instantly detect the occurrence of an internal hemorrhage. However, the low spatial resolution and high sensitivity to noise of this technique have limited its application in clinics. In addition, due to the circular boundary display mode used in current EIT images, it is difficult for clinicians to identify precisely which organ is bleeding using this technique. The aim of this study was to propose an optimized strategy for EIT reconstruction to promote the use of EIT for clinical studies, which mainly includes the use of anatomically accurate boundary shapes, rapid selection of optimal regularization parameters and image fusion of EIT and computed tomography images. The method was evaluated on retroperitoneal and intraperitoneal bleeding piglet data. Both traditional backprojection images and optimized images among different boundary shapes were reconstructed and compared. The experimental results demonstrated that EIT images with precise anatomical information can be reconstructed in which the image resolution and resistance to noise can be improved effectively.     

Computational anatomy: shape, growth, and atrophy comparison via diffeomorphisms

Computational anatomy (CA) is the mathematical study of anatomy I in I = I(alpha) o G, an orbit under groups of diffeomorphisms (i.e., smooth invertible mappings) g in G of anatomical exemplars I(alpha) in I. The observable images are the output of medical imaging devices. There are three components that CA examines: (i) constructions of the anatomical submanifolds, (ii) comparison of the anatomical manifolds via estimation of the underlying diffeomorphisms g in G defining the shape or geometry of the anatomical manifolds, and (iii) generation of probability laws of anatomical variation P(.) on the images I for inference and disease testing within anatomical models. This paper reviews recent advances in these three areas applied to shape, growth, and atrophy.     

Effects of network resolution on topological properties of human neocortex

Graph theoretical analyses applied to neuroimaging datasets have provided valuable insights into the large-scale anatomical organization of the human neocortex. Most of these studies were performed with different cortical scales leading to cortical networks with different levels of small-world organization. The present study investigates how resolution of thickness-based cortical scales impacts on topological properties of human anatomical cortical networks. To this end, we designed a novel approach aimed at determining the best trade-off between small-world attributes of anatomical cortical networks and the number of cortical regions included in the scale. Results revealed that schemes comprising 540-599 regions (surface areas spanning between 250 and 275 mm²) at sparsities below 10% showed a superior balance between small-world organization and the size of the cortical scale employed. Furthermore, we found that the cortical scale representing the best trade-off (599 regions) was more resilient to targeted attacks than atlas-based schemes (Desikan-Killiany atlas, 66 regions) and, most importantly, it did not differ that much from the finest cortical scale tested in the present study (1494 regions). In summary, our study confirms that topological organization of anatomical cortical networks varies with both sparsity and resolution of cortical scale, and it further provides a novel methodological framework aimed at identifying cortical schemes that maximize small-worldness with the lowest scale resolution possible.     

Angiography

The clinical usefulness of three dimensional images was widely recognized. The three dimensional digital subtraction angiography (3D-DSA) well demonstrated anatomical structures of cerebral arteries with high special resolution. This 3D observation allowed high quality planning for aneurysmal coil packing and neck clipping. Because of the bony structure and curvy arterial anatomy in the skull base region, 3D-CTA and MRA was sometimes distureved the demonstration of the anatomical relationship adjacent to the aneurysm. However, 3D-DSA not only demonstrated arterial anatomy, but also analyzed of vascular structure, quantifiably. And it was useful in radiation dose reduction by reduction of DSA exposure number. We believe that 3D-DSA should provided useful information for planning of surgical and endovascular treatment in the field of cerebro-vascular disease.     

Ultrasound of the normal kidney: A sonographic, anatomic and histologic correlation

Technical progress in sonographic equipment providing routinely high resolution images makes it appropriate that some criteria of normality have to be reviewed. In this paper normal sonographic images of the kidney are correlated with anatomy and histology. The effect of aging upon normal anatomical relations and histologic findings is analysed. Special attention is focussed on particular anatomical details as far as they can explain the particular topography or sonographic appearance of some pathologies.     

Reflections on ultrasound image analysis

Ultrasound (US) image analysis has advanced considerably in twenty years. Progress in ultrasound image analysis has always been fundamental to the advancement of image-guided interventions research due to the real-time acquisition capability of ultrasound and this has remained true over the two decades. But in quantitative ultrasound image analysis - which takes US images and turns them into more meaningful clinical information - thinking has perhaps more fundamentally changed. From roots as a poor cousin to Computed Tomography (CT) and Magnetic Resonance (MR) image analysis, both of which have richer anatomical definition and thus were better suited to the earlier eras of medical image analysis which were dominated by model-based methods, ultrasound image analysis has now entered an exciting new era, assisted by advances in machine learning and the growing clinical and commercial interest in employing low-cost portable ultrasound devices outside traditional hospital-based clinical settings. This short article provides a perspective on this change, and highlights some challenges ahead and potential opportunities in ultrasound image analysis which may both have high impact on healthcare delivery worldwide in the future but may also, perhaps, take the subject further away from CT and MR image analysis research with time.     

Patent foramen ovale closure: past, present and future

Patent foramen ovale (PFO) is a common congenital abnormality that has been implicated in a number of disease processes, including cryptogenic stroke and migraine headaches. Medical treatment for these processes is often considered inadequate and mechanical closure of the PFO is an attractive, albeit controversial, alternative. PFO closure has become common practice in many centers, although recent guidelines limit its indication to certain subsets of patients. This review first focuses on the anatomy, physiology and pathophysiology of PFO, and then reviews the currently available and experimental devices for PFO closure, as well as the present clinical data pertaining to them. Finally, we present our perspective of the PFO closure, with regard to its current use and future directions.     

Patent foramen ovale closure: past,present and future

Patent foramen ovale (PFO) is a common congenital abnormality that has been implicated in a number of disease processes, including cryptogenic stroke and migraine headaches. Medical treatment for these processes is often considered inadequate and mechanical closure of the PFO is an attractive, albeit controversial, alternative. PFO closure has become common practice in many centers, although recent guidelines limit its indication to certain subsets of patients. This review first focuses on the anatomy, physiology and pathophysiology of PFO, and then reviews the currently available and experimental devices for PFO closure, as well as the present clinical data pertaining to them. Finally, we present our perspective of the PFO closure, with regard to its current use and future directions.     

Low-field magnetic resonance image enhancement via stochastic image quality transfer

Low-field ($<1$T) magnetic resonance imaging (MRI) scanners remain in widespread use in low- and middle-income countries (LMICs) and are commonly used for some applications in higher income countries e.g. for small child patients with obesity, claustrophobia, implants, or tattoos. However, low-field MR images commonly have lower resolution and poorer contrast than images from high field (1.5T, 3T, and above). Here, we present Image Quality Transfer (IQT) to enhance low-field structural MRI by estimating from a low-field image the image we would have obtained from the same subject at high field. Our approach uses (i) a stochastic low-field image simulator as the forward model to capture uncertainty and variation in the contrast of low-field images corresponding to a particular high-field image, and (ii) an anisotropic U-Net variant specifically designed for the IQT inverse problem. We evaluate the proposed algorithm both in simulation and using multi-contrast (T1-weighted, T2-weighted, and fluid attenuated inversion recovery (FLAIR)) clinical low-field MRI data from an LMIC hospital. We show the efficacy of IQT in improving contrast and resolution of low-field MR images. We demonstrate that IQT-enhanced images have potential for enhancing visualisation of anatomical structures and pathological lesions of clinical relevance from the perspective of radiologists. IQT is proved to have capability of boosting the diagnostic value of low-field MRI, especially in low-resource settings.     

Benchmarking off-the-shelf statistical shape modeling tools in clinical applications

Statistical shape modeling (SSM) is widely used in biology and medicine as a new generation of morphometric approaches for the quantitative analysis of anatomical shapes. Technological advancements of in vivo imaging have led to the development of open-source computational tools that automate the modeling of anatomical shapes and their population-level variability. However, little work has been done on the evaluation and validation of such tools in clinical applications that rely on morphometric quantifications(e.g., implant design and lesion screening). Here, we systematically assess the outcome of widely used, state-of-the-art SSM tools, namely ShapeWorks, Deformetrica, and SPHARM-PDM. We use both quantitative and qualitative metrics to evaluate shape models from different tools. We propose validation frameworks for anatomical landmark/measurement inference and lesion screening. We also present a lesion screening method to objectively characterize subtle abnormal shape changes with respect to learned population-level statistics of controls. Results demonstrate that SSM tools display different levels of consistencies, where ShapeWorks and Deformetrica models are more consistent compared to models from SPHARM-PDM due to the groupwise approach of estimating surface correspondences. Furthermore, ShapeWorks and Deformetrica shape models are found to capture clinically relevant population-level variability compared to SPHARM-PDM models.