We consider transportation over a strongly connected, directed graph. The scheduling amounts to selecting transition probabilities for a discrete-time Markov evolution which is designed to be consistent with initial and final marginal constraints on mass transport. We address the situation where initially the mass is concentrated on certain nodes and needs to be transported in a certain time period to another set of nodes, possibly disjoint from the first. The random evolution is selected to be closest to a prior measure on paths in the relative entropy sense-such a construction is known as a Schrödinger bridge between the two given marginals. It may be viewed as an atypical stochastic control problem where the control consists in suitably modifying the prior transition mechanism. The prior can be chosen to incorporate constraints and costs for traversing specific edges of the graph, but it can also be selected to allocate equal probability to all paths of equal length connecting any two nodes (i.e., a uniform distribution on paths). This latter choice for prior transitions relies on the so-called Ruelle-Bowen random walker and gives rise to scheduling that tends to utilize all paths as uniformly as the topology allows. Thus, this Ruelle-Bowen law () taken as prior, leads to a transportation plan that tends to lessen congestion and ensures a level of robustness. We also show that the distribution on paths, which attains the maximum entropy rate for the random walker given by the topological entropy, can itself be obtained as the time-homogeneous solution of a maximum entropy problem for measures on paths (also a Schrödinger bridge problem, albeit with prior that is not a probability measure). Finally we show that the paradigm of Schrödinger bridges as a mechanism for scheduling transport on networks can be adapted to graphs that are not strongly connected, as well as to weighted graphs. In the latter case, our approach may be used to design a transportation plan which effectively compromises between robustness and other criteria such as cost. Indeed, we explicitly provide a robust transportation plan which assigns maximum probability to minimum cost paths and therefore compares favourably with Optimal Mass Transportation strategies.
We propose an optimization method for estimating patient- specific muscle fiber arrangement from clinical CT. Our approach first computes the structure tensor field to estimate local orientation, then a geometric template representing fiber arrangement is fitted using a B- spline deformation by maximizing fitness of the local orientation using a smoothness penalty. The initialization is computed with a previously proposed algorithm that takes account of only the muscle’s surface shape. Evaluation was performed using a CT volume (1.0mm3/voxel) and high resolution optical images of a serial cryosection (0.1mm3/voxel). The mean fiber distance error at the initialization of 6.00 mm was decreased to 2.78mm after the proposed optimization for the gluteus maximus muscle, and from 5.28 mm to 3.09 mm for the gluteus medius muscle. The result from 20 patient CT images suggested that the proposed algorithm reconstructed an anatomically more plausible fiber arrangement than the previous method.
Geodesic regression on images enables studies of brain development and degeneration, disease progression, and tumor growth. The high-dimensional nature of image data presents significant computational challenges for the current regression approaches and prohibits large scale studies. In this paper, we present a fast geodesic regression method that dramatically decreases the computational cost of the inference procedure while maintaining prediction accuracy. We employ an efficient low dimensional representation of diffeomorphic transformations derived from the image data and characterize the regressed trajectory in the space of diffeomorphisms by its initial conditions, i.e., an initial image template and an initial velocity field computed as a weighted average of pairwise diffeomorphic image registration results. This construction is achieved by using a first-order approximation of pairwise distances between images. We demonstrate the efficiency of our model on a set of 3D brain MRI scans from the OASIS dataset and show that it is dramatically faster than the state-of-the-art regression methods while producing equally good regression results on the large subject cohort.
We propose a general dynamic regression framework for partial correlation and causality analysis of functional brain networks. Using the optimal prediction theory, we present the solution of the dynamic regression problem by minimizing the entropy of the associated stochastic process. We also provide the relation between the solutions and the linear dependence models of Geweke and Granger and derive novel expressions for computing partial correlation and causality using an optimal prediction filter with minimum error variance. We use the proposed dynamic framework to study the intrinsic partial correlation and causal- ity between seven different brain networks using resting state functional MRI (rsfMRI) data from the Human Connectome Project (HCP) and compare our results with those obtained from standard correlation and causality measures. The results show that our optimal prediction filter explains a significant portion of the variance in the rsfMRI data at low frequencies, unlike standard partial correlation analysis.
This work presents a supra-threshold fiber cluster (STFC) analysis that leverages the whole brain fiber geometry to enhance sta- tistical group difference analysis. The proposed method consists of (1) a study-specific data-driven tractography parcellation to obtain white matter (WM) tract parcels according to the WM anatomy and (2) a nonparametric permutation-based STFC test to identify significant dif- ferences between study populations (e.g. disease and healthy). The basic idea of our method is that a WM parcel’s neighborhood (parcels with similar WM anatomy) can support the parcel’s statistical significance when correcting for multiple comparisons. The method is demonstrated by application to a multi-shell diffusion MRI dataset from 59 individuals, including 30 attention deficit hyperactivity disorder (ADHD) patients and 29 healthy controls (HCs). Evaluations are conducted using both synthetic and real data. The results indicate that our STFC method gives greater sensitivity in finding group differences in WM tract parcels compared to several traditional multiple comparison correction methods.
PURPOSE: Accurate segmentation of lung nodules is crucial in the development of imaging biomarkers for predicting malignancy of the nodules. Manual segmentation is time consuming and affected by inter-observer variability. We evaluated the robustness and accuracy of a publically available semiautomatic segmentation algorithm that is implemented in the 3D Slicer Chest Imaging Platform (CIP) and compared it with the performance of manual segmentation. METHODS: CT images of 354 manually segmented nodules were downloaded from the LIDC database. Four radiologists performed the manual segmentation and assessed various nodule characteristics. The semiautomatic CIP segmentation was initialized using the centroid of the manual segmentations, thereby generating four contours for each nodule. The robustness of both segmentation methods was assessed using the region of uncertainty (δ) and Dice similarity index (DSI). The robustness of the segmentation methods was compared using the Wilcoxon-signed rank test (pWilcoxon<0.05). The Dice similarity index (DSIAgree) between the manual and CIP segmentations was computed to estimate the accuracy of the semiautomatic contours. RESULTS: The median computational time of the CIP segmentation was 10 s. The median CIP and manually segmented volumes were 477 ml and 309 ml, respectively. CIP segmentations were significantly more robust than manual segmentations (median δCIP = 14ml, median dsiCIP = 99% vs. median δmanual = 222ml, median dsimanual = 82%) with pWilcoxon~10-16. The agreement between CIP and manual segmentations had a median DSIAgree of 60%. While 13% (47/354) of the nodules did not require any manual adjustment, minor to substantial manual adjustments were needed for 87% (305/354) of the nodules. CIP segmentations were observed to perform poorly (median DSIAgree≈50%) for non-/sub-solid nodules with subtle appearances and poorly defined boundaries. CONCLUSION: Semi-automatic CIP segmentation can potentially reduce the physician workload for 13% of nodules owing to its computational efficiency and superior stability compared to manual segmentation. Although manual adjustment is needed for many cases, CIP segmentation provides a preliminary contour for physicians as a starting point.
PRIMARY OBJECTIVE: There is a need to understand pathologic processes of the brain following mild traumatic brain injury (mTBI). Previous studies report axonal injury and oedema in the first week after injury in a rodent model. This study aims to investigate the processes occurring 1 week after injury at the time of regeneration and degeneration using diffusion tensor imaging (DTI) in the impact acceleration rat mTBI model. RESEARCH DESIGN: Eighteen rats were subjected to impact acceleration injury, and three rats served as sham controls. Seven days post injury, DTI was acquired from fixed rat brains using a 7T scanner. Group comparison of Fractional Anisotropy (FA) values between traumatized and sham animals was performed using Tract-Based Spatial Statistics (TBSS), a method that we adapted for rats. MAIN OUTCOMES AND RESULTS: TBSS revealed white matter regions of the brain with increased FA values in the traumatized versus sham rats, localized mainly to the contrecoup region. Regions of increased FA included the pyramidal tract, the cerebral peduncle, the superior cerebellar peduncle and to a lesser extent the fibre tracts of the corpus callosum, the anterior commissure, the fimbria of the hippocampus, the fornix, the medial forebrain bundle and the optic chiasm. CONCLUSION: Seven days post injury, during the period of tissue reparation in the impact acceleration rat model of mTBI, microstructural changes to white matter can be detected using DTI.
BACKGROUND: Mixed vascular and neurodegenerative dementia, such as Alzheimer's disease (AD) with concomitant cerebrovascular disease, has emerged as the leading cause of age-related cognitive impairment. The brain white matter (WM) microstructural changes in neurodegeneration well-documented by diffusion tensor imaging (DTI) can originate from brain tissue or extracellular free water changes. The differential microstructural and free water changes in AD with and without cerebrovascular disease, especially in normal-appearing WM, remain largely unknown. To cover these gaps, we aimed to characterize the WM free water and tissue microstructural changes in AD and mixed dementia as well as their associations with cognition using a novel free water imaging method. METHODS: We compared WM free water and free water-corrected DTI measures as well as white matter hyperintensity (WMH) in patients with AD with and without cerebrovascular disease, patients with vascular dementia, and age-matched healthy control subjects. RESULTS: The cerebrovascular disease groups had higher free water than the non-cerebrovascular disease groups. Importantly, besides the cerebrovascular disease groups, patients with AD without cerebrovascular disease also had increased free water in normal-appearing WM compared with healthy control subjects, reflecting mild vascular damage. Such free water increases in WM or normal-appearing WM (but not WMH) contributed to dementia severity. Whole-brain voxel-wise analysis revealed a close association between widespread free water increases and poorer attention, executive functioning, visual construction, and motor performance, whereas only left hemispheric free water increases were related to language deficits. Moreover, compared with the original DTI metrics, the free water-corrected DTI metric revealed tissue damage-specific (frontal and occipital) microstructural differences between the cerebrovascular disease and non-cerebrovascular disease groups. In contrast to both lobar and subcortical/brainstem free water increases, only focal lobar microstructural damage was associated with poorer cognitive performance. CONCLUSIONS: Our findings suggest that free water analysis isolates probable mild vascular damage from WM microstructural alterations and underscore the importance of normal-appearing WM changes underlying cognitive and functional impairment in AD with and without cerebrovascular disease. Further developed, the combined free water and tissue neuroimaging assays could help in differential diagnosis, treatment planning, and disease monitoring of patients with mixed dementia.
OBJECTIVE: To describe the design and rationale for the genetic analysis of acute and chronic cerebrovascular neuroimaging phenotypes detected on clinical MRI in patients with acute ischemic stroke (AIS) within the scope of the MRI-GENetics Interface Exploration (MRI-GENIE) study. METHODS: MRI-GENIE capitalizes on the existing infrastructure of the Stroke Genetics Network (SiGN). In total, 12 international SiGN sites contributed MRIs of 3,301 patients with AIS. Detailed clinical phenotyping with the web-based Causative Classification of Stroke (CCS) system and genome-wide genotyping data were available for all participants. Neuroimaging analyses include the manual and automated assessments of established MRI markers. A high-throughput MRI analysis pipeline for the automated assessment of cerebrovascular lesions on clinical scans will be developed in a subset of scans for both acute and chronic lesions, validated against gold standard, and applied to all available scans. The extracted neuroimaging phenotypes will improve characterization of acute and chronic cerebrovascular lesions in ischemic stroke, including CCS subtypes, and their effect on functional outcomes after stroke. Moreover, genetic testing will uncover variants associated with acute and chronic MRI manifestations of cerebrovascular disease. CONCLUSIONS: The MRI-GENIE study aims to develop, validate, and distribute the MRI analysis platform for scans acquired as part of clinical care for patients with AIS, which will lead to (1) novel genetic discoveries in ischemic stroke, (2) strategies for personalized stroke risk assessment, and (3) personalized stroke outcome assessment.
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.
In this note, we combined pediatric sarcoma data from Columbia University with adult sarcoma data collected from TCGA, in order to see if one can automatically discern a unique pediatric cluster in the combined data set. Using a novel clustering pipeline based on optimal transport theory, this turned out to be the case. The overall methodology may find uses for the classification of data from other biological networking problems.
Diffusion MRI tractography is increasingly used in pre-operative neurosurgical planning to visualize critical fiber tracts. However, a major challenge for conventional tractography, especially in patients with brain tumors, is tracing fiber tracts that are affected by vasogenic edema, which increases water content in the tissue and lowers diffusion anisotropy. One strategy for improving fiber tracking is to use a tractography method that is more sensitive than the traditional single-tensor streamline tractography. We performed experiments to assess the performance of two-tensor unscented Kalman filter (UKF) tractography in edema. UKF tractography fits a diffusion model to the data during fiber tracking, taking advantage of prior information from the previous step along the fiber. We studied UKF performance in a synthetic diffusion MRI digital phantom with simulated edema and in retrospective data from two neurosurgical patients with edema affecting the arcuate fasciculus and corticospinal tracts. We compared the performance of several tractography methods including traditional streamline, UKF single-tensor, and UKF two-tensor. To provide practical guidance on how the UKF method could be employed, we evaluated the impact of using various seed regions both inside and outside the edematous regions, as well as the impact of parameter settings on the tractography sensitivity. We quantified the sensitivity of different methods by measuring the percentage of the patient-specific fMRI activation that was reached by the tractography. We expected that diffusion anisotropy threshold parameters, as well as the inclusion of a free water model, would significantly influence the reconstruction of edematous WM fiber tracts, because edema increases water content in the tissue and lowers anisotropy. Contrary to our initial expectations, varying the fractional anisotropy threshold and including a free water model did not affect the UKF two-tensor tractography output appreciably in these two patient datasets. The most effective parameter for increasing tracking sensitivity was the generalized anisotropy (GA) threshold, which increased the length of tracked fibers when reduced to 0.075. In addition, the most effective seeding strategy was seeding in the whole brain or in a large region outside of the edema. Overall, the main contribution of this study is to provide insight into how UKF tractography can work, using a two-tensor model, to begin to address the challenge of fiber tract reconstruction in edematous regions near brain tumors.
In order to bridge microscopic molecular motion with macroscopic diffusion MR signal in complex structures, we propose a general stochastic model for molecular motion in a magnetic field. The Fokker-Planck equation of this model governs the probability density function describing the diffusion-magnetization propagator. From the propagator we derive a generalized version of the Bloch-Torrey equation and the relation to the random phase approach. This derivation does not require assumptions such as a spatially constant diffusion coefficient, or ad hoc selection of a propagator. In particular, the boundary conditions that implicitly incorporate the microstructure into the diffusion MR signal can now be included explicitly through a spatially varying diffusion coefficient. While our generalization is reduced to the conventional Bloch-Torrey equation for piecewise constant diffusion coefficients, it also predicts scenarios in which an additional term to the equation is required to fully describe the MR signal.
The glymphatic pathway is a system which facilitates continuous cerebrospinal fluid (CSF) and interstitial fluid (ISF) exchange and plays a key role in removing waste products from the rodent brain. Dysfunction of the glymphatic pathway may be implicated in the pathophysiology of Alzheimer's disease. Intriguingly, the glymphatic system is most active during deep wave sleep general anesthesia. By using paramagnetic tracers administered into CSF of rodents, we previously showed the utility of MRI in characterizing a macroscopic whole brain view of glymphatic transport but we have yet to define and visualize the specific flow patterns. Here we have applied an alternative mathematical analysis approach to a dynamic time series of MRI images acquired every 4min over ∼3h in anesthetized rats, following administration of a small molecular weight paramagnetic tracer into the CSF reservoir of the cisterna magna. We use Optimal Mass Transport (OMT) to model the glymphatic flow vector field, and then analyze the flow to find the network of CSF-ISF flow channels. We use 3D visualization computational tools to visualize the OMT defined network of CSF-ISF flow channels in relation to anatomical and vascular key landmarks from the live rodent brain. The resulting OMT model of the glymphatic transport network agrees largely with the current understanding of the glymphatic transport patterns defined by dynamic contrast-enhanced MRI revealing key CSF transport pathways along the ventral surface of the brain with a trajectory towards the pineal gland, cerebellum, hypothalamus and olfactory bulb. In addition, the OMT analysis also revealed some interesting previously unnoticed behaviors regarding CSF transport involving parenchymal streamlines moving from ventral reservoirs towards the surface of the brain, olfactory bulb and large central veins.
We perform a review of the literature in the field of white matter tractography for neurosurgical planning, focusing on those works where tractography was correlated with clinical information such as patient outcome, clinical functional testing, or electro-cortical stimulation. We organize the review by anatomical location in the brain and by surgical procedure, including both supratentorial and infratentorial pathologies, and excluding spinal cord applications. Where possible, we discuss implications of tractography for clinical care, as well as clinically relevant technical considerations regarding the tractography methods. We find that tractography is a valuable tool in variable situations in modern neurosurgery. Our survey of recent reports demonstrates multiple potentially successful applications of white matter tractography in neurosurgery, with progress towards overcoming clinical challenges of standardization and interpretation.
PURPOSE: Surgical navigation systems rely on a monitor placed in the operating room to relay information. Optimal monitor placement can be challenging in crowded rooms, and it is often not possible to place the monitor directly beside the situs. The operator must split attention between the navigation system and the situs. We present an approach for needle-based interventions to provide navigational feedback directly on the instrument and close to the situs by mounting a small display onto the needle. METHODS: By mounting a small and lightweight smartwatch display directly onto the instrument, we are able to provide navigational guidance close to the situs and directly in the operator's field of view, thereby reducing the need to switch the focus of view between the situs and the navigation system. We devise a specific variant of the established crosshair metaphor suitable for the very limited screen space. We conduct an empirical user study comparing our approach to using a monitor and a combination of both. RESULTS: Results from the empirical user study show significant benefits for cognitive load, user preference, and general usability for the instrument-mounted display, while achieving the same level of performance in terms of time and accuracy compared to using a monitor. CONCLUSION: We successfully demonstrate the feasibility of our approach and potential benefits. With ongoing technological advancements, instrument-mounted displays might complement standard monitor setups for surgical navigation in order to lower cognitive demands and for improved usability of such systems.
The neural correlates of spaceflight-induced sensorimotor impairments are unknown. Head down-tilt bed rest (HDBR) serves as a microgravity analog because it mimics the headward fluid shift and axial body unloading of spaceflight. We investigated focal brain white matter (WM) changes and fluid shifts during 70 days of 6° HDBR in 16 subjects who were assessed pre (2x), during (3x), and post-HDBR (2x). Changes over time were compared to those in control subjects (n = 12) assessed four times over 90 days. Diffusion MRI was used to assess WM microstructure and fluid shifts. Free-Water Imaging was used to quantify distribution of intracranial extracellular free water (FW). Additionally, we tested whether WM and FW changes correlated with changes in functional mobility and balance measures. HDBR resulted in FW increases in fronto-temporal regions and decreases in posterior-parietal regions that largely recovered by two weeks post-HDBR. WM microstructure was unaffected by HDBR. FW decreases in the post-central gyrus and precuneus correlated negatively with balance changes. We previously reported that gray matter increases in these regions were associated with less HDBR-induced balance impairment, suggesting adaptive structural neuroplasticity. Future studies are warranted to determine causality and underlying mechanisms.
Diffusion MRI has been proposed as a non-invasive technique for axonal diameter mapping. However, accurate estimation of small diameters requires strong gradients, which is a challenge for the transition of the technique from preclinical to clinical MRI scanners, since these have weaker gradients. In this work, we develop a framework to estimate the lower bound for accurate diameter estimation, which we refer to as the resolution limit. We analyse only the contribution from the intra-axonal space and assume that axons can be represented by impermeable cylinders. To address the growing interest in using techniques for diffusion encoding that go beyond the conventional single diffusion encoding (SDE) sequence, we present a generalised analysis capable of predicting the resolution limit regardless of the gradient waveform. Using this framework, waveforms were optimised to minimise the resolution limit. The results show that, for parallel cylinders, the SDE experiment is optimal in terms of yielding the lowest possible resolution limit. In the presence of orientation dispersion, diffusion encoding sequences with square-wave oscillating gradients were optimal. The resolution limit for standard clinical MRI scanners (maximum gradient strength 60-80 mT/m) was found to be between 4 and 8 μm, depending on the noise levels and the level of orientation dispersion. For scanners with a maximum gradient strength of 300 mT/m, the limit was reduced to between 2 and 5 μm.
PURPOSE: To investigate the heating of EEG electrodes during magnetic resonance imaging (MRI) scans and to better understand the underlying physical mechanisms with a focus on the antenna effect. MATERIALS AND METHODS: Gold cup and conductive plastic electrodes were placed on small watermelons with fiberoptic probes used to measure electrode temperature changes during a variety of 1.5T and 3T MRI scans. A subset of these experiments was repeated on a healthy human volunteer. RESULTS: The differences between gold and plastic electrodes did not appear to be practically significant. For both electrode types, we observed heating below 4°C for straight wires whose lengths were multiples of ½ the radiofrequency (RF) wavelength and stronger heating (over 15°C) for wire lengths that were odd multiples of ¼ RF wavelength, consistent with the antenna effect. CONCLUSIONS: The antenna effect, which has received little attention so far in the context of EEG-MRI safety, can play as significant a role as the loop effect (from electromagnetic induction) in the heating of EEG electrodes, and therefore wire lengths that are odd multiples of ¼ RF wavelength should be avoided. These results have important implications for the design of EEG electrodes and MRI studies as they help to minimize the risk to patients undergoing MRI with EEG electrodes in place.
PURPOSE: This article investigates the current state of the art of the use of auditory display in image-guided medical interventions. Auditory display is a means of conveying information using sound, and we review the use of this approach to support navigated interventions. We discuss the benefits and drawbacks of published systems and outline directions for future investigation. METHODS: We undertook a review of scientific articles on the topic of auditory rendering in image-guided intervention. This includes methods for avoidance of risk structures and instrument placement and manipulation. The review did not include auditory display for status monitoring, for instance in anesthesia. RESULTS: We identified 15 publications in the course of the search. Most of the literature (60%) investigates the use of auditory display to convey distance of a tracked instrument to an object using proximity or safety margins. The remainder discuss continuous guidance for navigated instrument placement. Four of the articles present clinical evaluations, 11 present laboratory evaluations, and 3 present informal evaluation (2 present both laboratory and clinical evaluations). CONCLUSION: Auditory display is a growing field that has been largely neglected in research in image-guided intervention. Despite benefits of auditory displays reported in both the reviewed literature and non-medical fields, adoption in medicine has been slow. Future challenges include increasing interdisciplinary cooperation with auditory display investigators to develop more meaningful auditory display designs and comprehensive evaluations which target the benefits and drawbacks of auditory display in image guidance.