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.

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.

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.

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.

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.

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/.

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

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

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.

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.

Vestibular function and cortical and sub-cortical alterations in an aging population.

While it is well known that the vestibular system is responsible for maintaining balance, posture and coordination, there is increasing evidence that it also plays an important role in cognition. Moreover, a growing number of epidemiological studies are demonstrating a link between vestibular dysfunction and cognitive deficits in older adults; however, the exact pathways through which vestibular loss may affect cognition are unknown. In this cross-sectional study, we sought to identify relationships between vestibular function and variation in morphometry in brain structures from structural neuroimaging. We used a subset of 80 participants from the Baltimore Longitudinal Study of Aging, who had both brain MRI and vestibular physiological data acquired during the same visit. Vestibular function was evaluated through the cervical vestibular-evoked myogenic potential (cVEMP). The brain structures of interest that we analyzed were the hippocampus, amygdala, thalamus, caudate nucleus, putamen, insula, entorhinal cortex (ERC), trans-entorhinal cortex (TEC) and perirhinal cortex, as these structures comprise or are connected with the putative "vestibular cortex." We modeled the volume and shape of these structures as a function of the presence/absence of cVEMP and the cVEMP amplitude, adjusting for age and sex. We observed reduced overall volumes of the hippocampus and the ERC associated with poorer vestibular function. In addition, we also found significant relationships between the shape of the hippocampus (p = 0.0008), amygdala (p = 0.01), thalamus (p = 0.008), caudate nucleus (p = 0.002), putamen (p = 0.02), and ERC-TEC complex (p = 0.008) and vestibular function. These findings provide novel insight into the multiple pathways through which vestibular loss may impact brain structures that are critically involved in spatial memory, navigation and orientation.

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.

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.

Cortical thickness atrophy in the transentorhinal cortex in mild cognitive impairment.

This study examines the atrophy rates of subjects with mild cognitive impairment (MCI) compared to controls in four regions within the medial temporal lobe: the transentorhinal cortex (TEC), entorhinal cortex (ERC), hippocampus, and amygdala. These regions were manually segmented and then corrected for undesirable longitudinal variability via Large Deformation Diffeomorphic Metric Mapping (LDDMM) based longitudinal diffeomorphometry. Diffeomorphometry techniques were used to compare thickness measurements in the TEC with the ERC. There were more significant changes in thickness atrophy rate in the TEC than medial regions of the entorhinal cortex. Volume measures were also calculated for all four regions. Classifiers were constructed using linear discriminant analysis to demonstrate that average thickness and atrophy rate of TEC together was the most discriminating measure compared to the thickness and volume measures in the areas examined, in differentiating MCI from controls. These findings are consistent with autopsy findings demonstrating that initial neuronal changes are found in TEC before spreading more medially in the ERC and to other regions in the medial temporal lobe. These findings suggest that the TEC thickness could serve as a biomarker for Alzheimer's disease in the prodromal phase of the disease.

Diffeomorphic Upsampling of Serially Acquired Sparse 2D Cross-Sections in Cardiac MRI.

In this paper, we propose a new technique for interpolating shapes in order to upsample a sparsely acquired serial-section image stack. The method is based on a maximum a posteriori estimation strategy which models neighboring sections as observations of random deformations of an image to be estimated. We show the computation of diffeomorphic trajectories between observed sections and define estimated upsampled image sections as a Jacobian-weighted sum of flowing images at corresponding distances along those trajectories. We apply this methodology to upsample stacks of sparse 2D magnetic resonance cross-sections through live mouse hearts. We show that the proposed method results in smoother and more accurate reconstructions over linear interpolation, and report a Dice coefficient of 0.8727 against ground truth segmentations in our dataset and statistically significant improvements in both left ventricular segmentation accuracy and image intensity estimates.

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.