On variational solutions for whole brain serial-section histology using a Sobolev prior in the computational anatomy random orbit model.

This paper presents a variational framework for dense diffeomorphic atlas-mapping onto high-throughput histology stacks at the 20 µm meso-scale. The observed sections are modelled as Gaussian random fields conditioned on a sequence of unknown section by section rigid motions and unknown diffeomorphic transformation of a three-dimensional atlas. To regularize over the high-dimensionality of our parameter space (which is a product space of the rigid motion dimensions and the diffeomorphism dimensions), the histology stacks are modelled as arising from a first order Sobolev space smoothness prior. We show that the joint maximum a-posteriori, penalized-likelihood estimator of our high dimensional parameter space emerges as a joint optimization interleaving rigid motion estimation for histology restacking and large deformation diffeomorphic metric mapping to atlas coordinates. We show that joint optimization in this parameter space solves the classical curvature non-identifiability of the histology stacking problem. The algorithms are demonstrated on a collection of whole-brain histological image stacks from the Mouse Brain Architecture Project.

ESTIMATING DIFFEOMORPHIC MAPPINGS BETWEEN TEMPLATES AND NOISY DATA: VARIANCE BOUNDS ON THE ESTIMATED CANONICAL VOLUME FORM.

Anatomy is undergoing a renaissance driven by the availability of large digital data sets generated by light microscopy. A central computational task is to map individual data volumes to standardized templates. This is accomplished by regularized estimation of a diffeomorphic transformation between the coordinate systems of the individual data and the template, building the transformation incrementally by integrating a smooth flow field. The canonical volume form of this transformation is used to quantify local growth, atrophy, or cell density. While multiple implementations exist for this estimation, less attention has been paid to the variance of the estimated diffeomorphism for noisy data. Notably, there is an infinite dimensional unobservable space defined by those diffeomorphisms which leave the template invariant. These form the stabilizer subgroup of the diffeomorphic group acting on the template. The corresponding flat directions in the energy landscape are expected to lead to increased estimation variance. Here we show that a least-action principle used to generate geodesics in the space of diffeomor-phisms connecting the subject brain to the template removes the stabilizer. This provides reduced-variance estimates of the volume form. Using simulations we demonstrate that the asymmetric large deformation diffeomorphic mapping methods (LDDMM), which explicitly incorporate the asymmetry between idealized template images and noisy empirical images, provide lower variance estimators than their symmetrized counterparts (cf. ANTs). We derive Cramer-Rao bounds for the variances in the limit of small deformations. Analytical results are shown for the Jacobian in terms of perturbations of the vector fields and divergence of the vector field.

Preserving Derivative Information while Transforming Neuronal Curves.

The international neuroscience community is building the first comprehensive atlases of brain cell types to understand how the brain functions from a higher resolution, and more integrated perspective than ever before. In order to build these atlases, subsets of neurons (e.g. serotonergic neurons, prefrontal cortical neurons etc.) are traced in individual brain samples by placing points along dendrites and axons. Then, the traces are mapped to common coordinate systems by transforming the positions of their points, which neglects how the transformation bends the line segments in between. In this work, we apply the theory of jets to describe how to preserve derivatives of neuron traces up to any order. We provide a framework to compute possible error introduced by standard mapping methods, which involves the Jacobian of the mapping transformation. We show how our first order method improves mapping accuracy in both simulated and real neuron traces under random diffeomorphisms. Our method is freely available in our open-source Python package brainlit.

Preserving Derivative Information while Transforming Neuronal Curves.

The international neuroscience community is building the first comprehensive atlases of brain cell types to understand how the brain functions from a higher resolution, and more integrated perspective than ever before. In order to build these atlases, subsets of neurons (e.g. serotonergic neurons, prefrontal cortical neurons etc.) are traced in individual brain samples by placing points along dendrites and axons. Then, the traces are mapped to common coordinate systems by transforming the positions of their points, which neglects how the transformation bends the line segments in between. In this work, we apply the theory of jets to describe how to preserve derivatives of neuron traces up to any order. We provide a framework to compute possible error introduced by standard mapping methods, which involves the Jacobian of the mapping transformation. We show how our first order method improves mapping accuracy in both simulated and real neuron traces under random diffeomorphisms. Our method is freely available in our open-source Python package brainlit.

Preserving Derivative Information while Transforming Neuronal Curves.

The international neuroscience community is building the first comprehensive atlases of brain cell types to understand how the brain functions from a higher resolution, and more integrated perspective than ever before. In order to build these atlases, subsets of neurons (e.g. serotonergic neurons, prefrontal cortical neurons etc.) are traced in individual brain samples by placing points along dendrites and axons. Then, the traces are mapped to common coordinate systems by transforming the positions of their points, which neglects how the transformation bends the line segments in between. In this work, we apply the theory of jets to describe how to preserve derivatives of neuron traces up to any order. We provide a framework to compute possible error introduced by standard mapping methods, which involves the Jacobian of the mapping transformation. We show how our first order method improves mapping accuracy in both simulated and real neuron traces, though zeroth order mapping is generally adequate in our real data setting. Our method is freely available in our open-source Python package brainlit.

Early amygdala and ERC atrophy linked to 3D reconstruction of rostral neurofibrillary tau tangle pathology in Alzheimer's disease.

Previous research has emphasized the unique impact of Alzheimer's Disease (AD) pathology on the medial temporal lobe (MTL), a reflection that tau pathology is particularly striking in the entorhinal and transentorhinal cortex (ERC, TEC) early in the course of disease. However, other brain regions are affected by AD pathology during its early phases. Here, we use longitudinal diffeomorphometry to measure the atrophy rate from MRI of the amygdala compared with that in the ERC and TEC in cognitively unimpaired (CU) controls, CU individuals who progressed to mild cognitive impairment (MCI), and individuals with MCI who progressed to dementia of the AD type (DAT), using a dataset from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Our results show significantly higher atrophy rates of the amygdala in both groups of 'converters' (CU→MCI, MCI→DAT) compared to controls, with rates of volume loss comparable to rates of thickness loss in the ERC and TEC. We localize atrophy within the amygdala within each of these groups using fixed effects modeling. Controlling for the familywise error rate highlights the medial regions of the amygdala as those with significantly higher atrophy in both groups of converters than in controls. Using our recently developed method, referred to as Projective LDDMM, we map measures of neurofibrillary tau tangles (NFTs) from digital pathology to MRI atlases and reconstruct dense 3D spatial distributions of NFT density within regions of the MTL. The distribution of NFTs is consistent with the spatial distribution of MR measured atrophy rates, revealing high densities (and atrophy) in the amygdala (particularly medial), ERC, and rostral third of the MTL. The similarity of the location of NFTs in AD and shape changes in a well-defined clinical population suggests that amygdalar atrophy rate, as measured through MRI may be a viable biomarker for AD.

Beyond noise power in 3D computed tomography: the local NPS and off-diagonal elements of the Fourier domain covariance matrix.

PURPOSE: To investigate the correlation and stationarity of noise in volumetric computed tomography (CT) using the local discrete noise-power spectrum (NPS) and off-diagonal elements of the covariance matrix of the discrete Fourier transform of noise-only images (denoted Σ(DFT)). Experimental conditions were varied to affect noise correlation and stationarity, the effects were quantified in terms of the NPS and Σ(DFT), and practical considerations in CT performance characterization were identified. METHODS: Cone-beam CT (CBCT) images were acquired using a benchtop system comprising an x-ray tube and flat-panel detector for a range of acquisition techniques (e.g., dose and x-ray scatter) and three phantom configurations hypothesized to impart distinct effects on the NPS and Σ(DFT): (A) air, (B) a 20-cm-diameter water cylinder with a bowtie filter, and (C) the cylinder without a bowtie filter. The NPS and off-diagonal elements of the Σ(DFT) were analyzed as a function of position within the reconstructions. RESULTS: The local NPS varied systematically throughout the axial plane in a manner consistent with changes in fluence transmitted to the detector and view sampling effects. Variability in fluence was manifest in the NPS magnitude-e.g., a factor of ~2 variation in NPS magnitude within the axial plane for case C (cylinder without bowtie), compared to nearly constant NPS magnitude for case B (bowtie filter matched to the cylinder). View sampling effects were most prominent in case A (air) where the variance increased at greater distance from the center of reconstruction and in case C (cylinder) where the NPS exhibited correlations in the radial direction. The effects of detector lag were observed as azimuthal correlation. The cylinder (without bowtie) had the strongest nonstationarity because of the larger variability in fluence transmitted to the detector. The diagonal elements of the Σ(DFT) were equivalent to the NPS estimated from the periodogram, and the average off-diagonal elements of the Σ(DFT) exhibited amplitude of ~1% of the NPS for the experimental conditions investigated. Furthermore, the off-diagonal elements demonstrated fairly long tails of nearly constant amplitude, with magnitude somewhat reduced for experimental conditions associated with greater stationarity (viz., lower Σ(DFT) tails for cases A and B in comparison to case C). CONCLUSIONS: Volumetric CT exhibits nonstationarity in the NPS as hypothesized in relation to fluence uniformity and view sampling. Measurement of the NPS should seek to minimize such changes in noise correlations and include careful reporting of experimental conditions (e.g., phantom design and use of a bowtie filter) and spatial dependence (e.g., analysis at fixed radius within a phantom). Off-diagonal elements of the Σ(DFT) similarly depend on experimental conditions and can be readily computed from the same data as the NPS. This work begins to check assumptions in NPS analysis examine the extent to which NPS is an appropriate descriptor of noise correlations, and investigate the magnitude of off-diagonal elements of the Σ(DFT). While the magnitude of such off-diagonal elements appears to be low, their cumulative effect on space-variant detectability remains to be investigated-e.g., using task-specific figures of merit.

Effects of protocol and obesity on dose conversion factors in adult body CT.

PURPOSE: In computed tomography (CT), organ dose, effective dose, and risk index can be estimated from volume-weighted CT dose index (CTDI(vol)) or dose-length product (DLP) using conversion coefficients. Studies have investigated how these coefficients vary across scanner models, scan parameters, and patient size. However, their variability across CT protocols has not been systematically studied. Furthermore, earlier studies of the effect of patient size have not included obese individuals, which currently represent more than one-third of U.S. adults. The purpose of this study was to assess the effects of protocol and obesity on dose and risk conversion coefficients in adult body CT. METHODS: Whole-body computational phantoms were created from clinical CT images of six adult patients (three males, three females), representing normal-weight patients and patients of three obesity classes. Body CT protocols at our institution were selected and categorized into ten examination categories based on anatomical region examined. A validated Monte Carlo program was used to estimate organ dose. Organ dose estimates were normalized by CTDI(vol) and size-specific dose estimate (SSDE) to obtain organ dose conversion coefficients (denoted as h and h(ss) factors, respectively). Assuming each phantom to be 20, 40, and 60 years old, effective dose and risk index were calculated and normalized by DLP to obtain effective dose and risk index conversion coefficients (denoted as k and q factors, respectively). Coefficient of variation was used to quantify the variability of each conversion coefficient across examination categories. The effect of obesity was assessed by comparing each obese phantom with the normal-weight phantom of the same gender. RESULTS: For a given organ, the variability of h factor across examination categories that encompassed the entire organ volume was generally within 15%. However, k factor varied more across examination categories (15%-27%). For all three ages, the variability of q factor was small for male (<10%), but large for female phantoms (21%-43%). Relative to the normal-weight phantoms, the reduction in h factor (an average across fully encompassed organs) was 17%-42%, 17%-40%, and 51%-63% for obese-class-I, obese-class-II, and obese-class-III phantoms, respectively. h(ss) factor was not independent of patient diameter and generally decreased with increasing obesity. Relative to the normal-weight phantoms, the reduction in k factor was 12%-40%, 14%-46%, and 44%-59% for obese-class-I, obese-class-II, and obese-class-III phantoms, respectively. The respective reduction in q factor was 11%-36%, 17%-42%, and 48%-59% at 20 years of age and similar at other ages. CONCLUSIONS: In adult body CT, dose to an organ fully encompassed by the primary radiation beam can be estimated from CTDI(vol) using a protocol-independent conversion coefficient. However, fully encompassed organs only account for 50% ± 19% of k factor and 46% ± 24% of q factor. Dose received by partially encompassed organs is also substantial. To estimate effective dose and risk index from DLP, it is necessary to use conversion coefficients specific to the anatomical region examined. Obesity has a significant effect on dose and risk conversion coefficients, which cannot be predicted using body diameter alone. SSDE-normalized organ dose is not independent of diameter. SSDE itself generally overestimates organ dose for obese patients.

Hidden Markov modeling for maximum probability neuron reconstruction.

Recent advances in brain clearing and imaging have made it possible to image entire mammalian brains at sub-micron resolution. These images offer the potential to assemble brain-wide atlases of neuron morphology, but manual neuron reconstruction remains a bottleneck. Several automatic reconstruction algorithms exist, but most focus on single neuron images. In this paper, we present a probabilistic reconstruction method, ViterBrain, which combines a hidden Markov state process that encodes neuron geometry with a random field appearance model of neuron fluorescence. ViterBrain utilizes dynamic programming to compute the global maximizer of what we call the most probable neuron path. We applied our algorithm to imperfect image segmentations, and showed that it can follow axons in the presence of noise or nearby neurons. We also provide an interactive framework where users can trace neurons by fixing start and endpoints. ViterBrain is available in our open-source Python package brainlit.

Projective Diffeomorphic Mapping of Molecular Digital Pathology with Tissue MRI.

Reconstructing dense 3D anatomical coordinates from 2D projective measurements has become a central problem in digital pathology for both animal models and human studies. Here we describe Projective Large Deformation Diffeomorphic Metric Mapping (LDDMM), a technique which projects diffeomorphic mappings of dense human magnetic resonance imaging (MRI) atlases at tissue scales onto sparse measurements at micrometre scales associated with histological and more general optical imaging modalities. We solve the problem of dense mapping surjectively onto histological sections by incorporating technologies for crossing modalities that use nonlinear scattering transforms to represent multiple radiomic-like textures at micron scales, together with a Gaussian mixture-model framework for modelling tears and distortions associated to each section. We highlight the significance of our method through incorporation of neuropathological measures and MRI, of relevance to the development of biomarkers for Alzheimer's disease and one instance of the integration of imaging data across the scales of clinical imaging and digital pathology.

Analysis of Fourier-domain task-based detectability index in tomosynthesis and cone-beam CT in relation to human observer performance.

PURPOSE: Design and optimization of medical imaging systems benefit from accurate theoretical modeling that identifies the physical factors governing image quality, particularly in the early stages of system development. This work extends Fourier metrics of imaging performance and detectability index (d') to tomosynthesis and cone-beam CT (CBCT) and investigates the extent to which d' is a valid descriptor of task-based imaging performance as assessed by human observers, METHODS: The detectability index for tasks presented in 2D slices (d'(slice)) was derived from 3D cascaded systems analysis of tomosynthesis and CBCT. Anatomical background noise measured in a physical phantom presenting power-law spectral density was incorporated in the "generalized" noise-equivalent quanta. Theoretical calculations of d'(slice) were performed as a function of total angular extent (theta(tot)) of source-detector orbit ranging 10 degrees - 360 degrees under two acquisition schemes: (i) Constant angular separation between projections (constant-delta theta), giving variable number of projections (N(proj)) and dose vs theta(tot) and (ii) constant number of projections (constant-N(proj)), giving constant dose (but variable angular sampling) with theta(tot). Five simple observer models were investigated: Prewhitening (PW), prewhitening with eye filter and internal noise (PWEi), nonprewhitening (NPW), nonprewhitening with eye filter (NPWE), and nonprewhitening with eye filter and internal noise (NPWEi). Human observer performance was measured in 9AFC tests for five simple imaging tasks presented within uniform and power-law clutter backgrounds. Measurements (from 9AFC tests) and theoretical calculations (from cascaded systems analysis of d'(slice)) were compared in terms of area under the ROC curve (A(z)) RESULTS: Reasonable correspondence between theoretical calculations and human observer performance was achieved for all imaging tasks over the broad range of experimental conditions and acquisition schemes. The PW and PWEi observer models tended to overestimate detectability, while the various NPW models predicted observer performance fairly well, with NPWEi giving the best overall agreement. Detectability was shown to increase with theta(tot) due to the reduction of out-of-plane clutter, reaching a plateau after a particular theta(tot) that depended on the imaging task. Depending on the acquisition scheme, however (i.e., constant-N(proj) or delta theta), detectability was seen in some cases to decline at higher theta(tot) due to tradeoffs among quantum noise, background clutter, and view sampling. CONCLUSIONS: Generalized detectability index derived from a 3D cascaded systems model shows reasonable correspondence with human observer performance over a fairly broad range of imaging tasks and conditions, although discrepancies were observed in cases relating to orbits intermediate to 180 degrees and 360 degrees. The basic correspondence of theoretical and measured performance supports the application of such a theoretical framework for system design and optimization of tomosynthesis and CBCT.

Corrigendum to "Robust Diffeomorphic Mapping via Geodesically Controlled Active Shapes".

[This corrects the article DOI: 10.1155/2013/205494.].

Fitting Splines to Axonal Arbors Quantifies Relationship Between Branch Order and Geometry.

Neuromorphology is crucial to identifying neuronal subtypes and understanding learning. It is also implicated in neurological disease. However, standard morphological analysis focuses on macroscopic features such as branching frequency and connectivity between regions, and often neglects the internal geometry of neurons. In this work, we treat neuron trace points as a sampling of differentiable curves and fit them with a set of branching B-splines. We designed our representation with the Frenet-Serret formulas from differential geometry in mind. The Frenet-Serret formulas completely characterize smooth curves, and involve two parameters, curvature and torsion. Our representation makes it possible to compute these parameters from neuron traces in closed form. These parameters are defined continuously along the curve, in contrast to other parameters like tortuosity which depend on start and end points. We applied our method to a dataset of cortical projection neurons traced in two mouse brains, and found that the parameters are distributed differently between primary, collateral, and terminal axon branches, thus quantifying geometric differences between different components of an axonal arbor. The results agreed in both brains, further validating our representation. The code used in this work can be readily applied to neuron traces in SWC format and is available in our open-source Python package brainlit: http://brainlit.neurodata.io/.

Visualization of Speech Perception Analysis via Phoneme Alignment: A Pilot Study.

Objective: Speech tests assess the ability of people with hearing loss to comprehend speech with a hearing aid or cochlear implant. The tests are usually at the word or sentence level. However, few tests analyze errors at the phoneme level. So, there is a need for an automated program to visualize in real time the accuracy of phonemes in these tests. Method: The program reads in stimulus-response pairs and obtains their phonemic representations from an open-source digital pronouncing dictionary. The stimulus phonemes are aligned with the response phonemes via a modification of the Levenshtein Minimum Edit Distance algorithm. Alignment is achieved via dynamic programming with modified costs based on phonological features for insertion, deletions and substitutions. The accuracy for each phoneme is based on the F1-score. Accuracy is visualized with respect to place and manner (consonants) or height (vowels). Confusion matrices for the phonemes are used in an information transfer analysis of ten phonological features. A histogram of the information transfer for the features over a frequency-like range is presented as a phonemegram. Results: The program was applied to two datasets. One consisted of test data at the sentence and word levels. Stimulus-response sentence pairs from six volunteers with different degrees of hearing loss and modes of amplification were analyzed. Four volunteers listened to sentences from a mobile auditory training app while two listened to sentences from a clinical speech test. Stimulus-response word pairs from three lists were also analyzed. The other dataset consisted of published stimulus-response pairs from experiments of 31 participants with cochlear implants listening to 400 Basic English Lexicon sentences via different talkers at four different SNR levels. In all cases, visualization was obtained in real time. Analysis of 12,400 actual and random pairs showed that the program was robust to the nature of the pairs. Conclusion: It is possible to automate the alignment of phonemes extracted from stimulus-response pairs from speech tests in real time. The alignment then makes it possible to visualize the accuracy of responses via phonological features in two ways. Such visualization of phoneme alignment and accuracy could aid clinicians and scientists.

From Picoscale Pathology to Decascale Disease: Image Registration with a Scattering Transform and Varifolds for Manipulating Multiscale Data.

Advances in neuroimaging have yielded extensive variety in the scale and type of data available. Effective integration of such data promises deeper understanding of anatomy and disease-with consequences for both diagnosis and treatment. Often catered to particular datatypes or scales, current computational tools and mathematical frameworks remain inadequate for simultaneously registering these multiple modes of "images" and statistically analyzing the ensuing menagerie of data. Here, we present (1) a registration algorithm using a "scattering transform" to align high and low resolution images and (2) a varifold-based modeling framework to compute 3D spatial statistics of multiscale data. We use our methods to quantify microscopic tau pathology across macroscopic 3D regions of the medial temporal lobe to address a major challenge in the diagnosis of Alzheimer's Disease-the reliance on invasive methods to detect microscopic pathology.

Visualizing synaptic plasticity in vivo by large-scale imaging of endogenous AMPA receptors.

Elucidating how synaptic molecules such as AMPA receptors mediate neuronal communication and tracking their dynamic expression during behavior is crucial to understand cognition and disease, but current technological barriers preclude large-scale exploration of molecular dynamics in vivo. We have developed a suite of innovative methodologies that break through these barriers: a new knockin mouse line with fluorescently tagged endogenous AMPA receptors, two-photon imaging of hundreds of thousands of labeled synapses in behaving mice, and computer vision-based automatic synapse detection. Using these tools, we can longitudinally track how the strength of populations of synapses changes during behavior. We used this approach to generate an unprecedentedly detailed spatiotemporal map of synapses undergoing changes in strength following sensory experience. More generally, these tools can be used as an optical probe capable of measuring functional synapse strength across entire brain areas during any behavioral paradigm, describing complex system-wide changes with molecular precision.

A 7 Tesla Amygdalar-Hippocampal Shape Analysis of Lithium Response in Bipolar Disorder.

Research to discover clinically useful predictors of lithium response in patients with bipolar disorder has largely found them to be elusive. We demonstrate here that detailed neuroimaging may have the potential to fill this important gap in mood disorder therapeutics. Lithium treatment and bipolar disorder have both been shown to affect anatomy of the hippocampi and amygdalae but there is no consensus on the nature of their effects. We aimed to investigate structural surface anatomy changes in amygdala and hippocampus correlated with treatment response in bipolar disorder. Patients with bipolar disorder (N = 14) underwent lithium treatment, were classified by response status at acute and long-term time points, and scanned with 7 Tesla structural MRI. Large Deformation Diffeomorphic Metric Mapping was applied to detect local differences in hippocampal and amygdalar anatomy between lithium responders and non-responders. Anatomy was also compared to 21 healthy comparison participants. A patch of the ventral surface of the left hippocampus was found to be significantly atrophied in non-responders as compared to responders at the acute time point and was associated at a trend-level with long-term response status. We did not detect an association between response status and surface anatomy of the right hippocampus or amygdala. To the best of our knowledge, this is the first shape analysis of hippocampus and amygdala in bipolar disorder using 7 Tesla MRI. These results can inform future work investigating possible neuroimaging predictors of lithium response in bipolar disorder.

Entorhinal and Transentorhinal Atrophy in Preclinical Alzheimer's Disease.

This study examines the atrophy patterns in the entorhinal and transentorhinal cortices of subjects that converted from normal cognition to mild cognitive impairment. The regions were manually segmented from 3T MRI, then corrected for variability in boundary definition over time using an automated approach called longitudinal diffeomorphometry. Cortical thickness was calculated by deforming the gray matter-white matter boundary surface to the pial surface using an approach called normal geodesic flow. The surface was parcellated based on four atlases using large deformation diffeomorphic metric mapping. Average cortical thickness was calculated for (1) manually-defined entorhinal cortex, and (2) manually-defined transentorhinal cortex. Group-wise difference analysis was applied to determine where atrophy occurred, and change point analysis was applied to determine when atrophy started to occur. The results showed that by the time a diagnosis of mild cognitive impairment is made, the transentorhinal cortex and entorhinal cortex was up to 0.6 mm thinner than a control with normal cognition. A change point in atrophy rate was detected in the transentorhinal cortex 9-14 years prior to a diagnosis of mild cognitive impairment, and in the entorhinal cortex 8-11 years prior. The findings are consistent with autopsy findings that demonstrate neuronal changes in the transentorhinal cortex before the entorhinal cortex.