Automated synaptic connectivity inference for volume electron microscopy.

Teravoxel volume electron microscopy data sets from neural tissue can now be acquired in weeks, but data analysis requires years of manual labor. We developed the SyConn framework, which uses deep convolutional neural networks and random forest classifiers to infer a richly annotated synaptic connectivity matrix from manual neurite skeleton reconstructions by automatically identifying mitochondria, synapses and their types, axons, dendrites, spines, myelin, somata and cell types. We tested our approach on serial block-face electron microscopy data sets from zebrafish, mouse and zebra finch, and computed the synaptic wiring of songbird basal ganglia. We found that, for example, basal-ganglia cell types with high firing rates in vivo had higher densities of mitochondria and vesicles and that synapse sizes and quantities scaled systematically, depending on the innervated postsynaptic cell types.

High-resolution whole-brain staining for electron microscopic circuit reconstruction.

Currently only electron microscopy provides the resolution necessary to reconstruct neuronal circuits completely and with single-synapse resolution. Because almost all behaviors rely on neural computations widely distributed throughout the brain, a reconstruction of brain-wide circuits-and, ultimately, the entire brain-is highly desirable. However, these reconstructions require the undivided brain to be prepared for electron microscopic observation. Here we describe a preparation, BROPA (brain-wide reduced-osmium staining with pyrogallol-mediated amplification), that results in the preservation and staining of ultrastructural details throughout the brain at a resolution necessary for tracing neuronal processes and identifying synaptic contacts between them. Using serial block-face electron microscopy (SBEM), we tested human annotator ability to follow neural 'wires' reliably and over long distances as well as the ability to detect synaptic contacts. Our results suggest that the BROPA method can produce a preparation suitable for the reconstruction of neural circuits spanning an entire mouse brain.

Staining and embedding the whole mouse brain for electron microscopy.

The development of methods for imaging large contiguous volumes with the electron microscope could allow the complete mapping of a whole mouse brain at the single-axon level. We developed a method based on prolonged immersion that enables staining and embedding of the entire mouse brain with uniform myelin staining and a moderate preservation of the tissue's ultrastructure. We tested the ability to follow myelinated axons using serial block-face electron microscopy.

Low-dosage Maximum-A-Posteriori Focusing and Stigmation.

Radiation damage is often an issue during high-resolution imaging, making low-dose focusing and stigmation essential, in particular when no part of the sample can be "sacrificed" for this. An example is serial block-face electron microscopy, where the imaging resolution must be kept optimal during automated acquisition that can last months. Here, we present an algorithm, which we call "Maximum-A-Posteriori Focusing and Stigmation (MAPFoSt)," that was designed to make optimal use of the available signal. We show that MAPFoSt outperforms the built-in focusing algorithm of a commercial scanning electron microscope even at a tenfold reduced total dose. MAPFoSt estimates multiple aberration modes (focus and the two astigmatism coefficients) using just two test images taken at different focus settings. Using an incident electron dose density of 2,500 electrons/pixel and a signal-to-noise ratio of about one, all three coefficients could be estimated to within <7% of the depth of focus, using 19 detected secondary electrons per pixel. A generalization to higher-order aberrations and to other forms of imaging in both two and three dimensions appears possible.

A proposal for a coordinated effort for the determination of brainwide neuroanatomical connectivity in model organisms at a mesoscopic scale.

In this era of complete genomes, our knowledge of neuroanatomical circuitry remains surprisingly sparse. Such knowledge is critical, however, for both basic and clinical research into brain function. Here we advocate for a concerted effort to fill this gap, through systematic, experimental mapping of neural circuits at a mesoscopic scale of resolution suitable for comprehensive, brainwide coverage, using injections of tracers or viral vectors. We detail the scientific and medical rationale and briefly review existing knowledge and experimental techniques. We define a set of desiderata, including brainwide coverage; validated and extensible experimental techniques suitable for standardization and automation; centralized, open-access data repository; compatibility with existing resources; and tractability with current informatics technology. We discuss a hypothetical but tractable plan for mouse, additional efforts for the macaque, and technique development for human. We estimate that the mouse connectivity project could be completed within five years with a comparatively modest budget.

A carbon nanotube tape for serial-section electron microscopy of brain ultrastructure.

Automated tape-collecting ultramicrotomy in conjunction with scanning electron microscopy (SEM) is a powerful approach for volume electron microscopy and three-dimensional neuronal circuit analysis. Current tapes are limited by section wrinkle formation, surface scratches and sample charging during imaging. Here we show that a plasma-hydrophilized carbon nanotube (CNT)-coated polyethylene terephthalate (PET) tape effectively resolves these issues and produces SEM images of comparable quality to those from transmission electron microscopy. CNT tape can withstand multiple rounds of imaging, offer low surface resistance across the entire tape length and generate no wrinkles during the collection of ultrathin sections. When combined with an enhanced en bloc staining protocol, CNT tape-processed brain sections reveal detailed synaptic ultrastructure. In addition, CNT tape is compatible with post-embedding immunostaining for light and electron microscopy. We conclude that CNT tape can enable high-resolution volume electron microscopy for brain ultrastructure analysis.

Progress Towards Mammalian Whole-Brain Cellular Connectomics.

Neurons are the fundamental structural units of the nervous system-i.e., the Neuron Doctrine-as the pioneering work of Santiago Ramón y Cajal in the 1880's clearly demonstrated through careful observation of Golgi-stained neuronal morphologies. However, at that time sample preparation, imaging methods and computational tools were either nonexistent or insufficiently developed to permit the precise mapping of an entire brain with all of its neurons and their connections. Some measure of the "mesoscopic" connectional organization of the mammalian brain has been obtained over the past decade by alignment of sparse subsets of labeled neurons onto a reference atlas or via MRI-based diffusion tensor imaging. Neither method, however, provides data on the complete connectivity of all neurons comprising an individual brain. Fortunately, whole-brain cellular connectomics now appears within reach due to recent advances in whole-brain sample preparation and high-throughput electron microscopy (EM), though substantial obstacles remain with respect to large volume electron microscopic acquisitions and automated neurite reconstructions. This perspective examines the current status and problems associated with generating a mammalian whole-brain cellular connectome and argues that the time is right to launch a concerted connectomic attack on a small mammalian whole-brain.

Correlated inhibitory and excitatory inputs to the coincidence detector: analytical solution.

We present a solution for the steady-state output rate of an ideal coincidence detector receiving an arbitrary number of excitatory and inhibitory inputspike trains. All excitatory spike trains have identical binomial count distributions (which includes Poisson statistics as a special case) and arbitrary pairwise cross correlations between them. The same applies to the inhibitory inputs, and the rates and correlation functions of excitatory and inhibitory populations may be the same or different from each other. Thus, for each population independently, the correlation may range from complete independence to perfect correlation (identical processes). We find that inhibition, if made sufficiently strong, will result in an inverted U-shaped curve for the output rate of a coincidence detector as a function of input rates for the case of identical inhibitory and excitory input rates. This leads to the prediction that higher presynaptic (input) rates may lead to lower postsynaptic (output) rates where the output rate may fall faster than the inverse of the input rate, and shows some qualitative similarities to the case of purely excitatory inputs with synaptic depression. In general, we find that including inhibition invariably and significantly increases the behavioral repertoire of the coincidence detector over the case of pure excitatory input.

Learning to segment neurons with non-local quality measures.

Segmentation schemes such as hierarchical region merging or correllation clustering rely on edge weights between adjacent (super-)voxels. The quality of these edge weights directly affects the quality of the resulting segmentations. Unstructured learning methods seek to minimize the classification error on individual edges. This ignores that a few local mistakes (tiny boundary gaps) can cause catastrophic global segmentation errors. Boundary evidence learning should therefore optimize structured quality criteria such as Rand Error or Variation of Information. We present the first structured learning scheme using a structured loss function; and we introduce a new hierarchical scheme that allows to approximately solve the NP hard prediction problem even for huge volume images. The value of these contributions is demonstrated on two challenging neural circuit reconstruction problems in serial sectioning electron microscopic images with billions of voxels. Our contributions lead to a partitioning quality that improves over the current state of the art.

The developmental remodeling of eye-specific afferents in the ferret dorsal lateral geniculate nucleus.

Eye-specific projections to the dorsal lateral geniculate nucleus (dLGN) serve as a model for exploring how precise patterns of circuitry form during development in the mammalian central nervous system. Using a combination of dual-label anterograde retinogeniculate tracing and Nissl-staining, we studied the patterns of eye-specific afferents and cellular laminae in the dLGN of the pigmented sable ferret at eight developmental timepoints between birth and adulthood. Each time point was investigated in the three standard orthogonal planes of section, allowing us to generate a complete anatomical map of eye-specific development in this species. We find that eye-specific retinal ganglion cell axon segregation varies according to location in the dLGN, with the principle contralateral (A) and ipsilateral layers (A1) maturing first, followed by the contralateral and ipsilateral C laminae. Cytoarchitectural lamination lags behind eye-specific segregation, except in the C laminae where underlying cellular layers never develop to accompany eye-specific afferent domains. The emergence of On/Off sublaminae occurs following eye-specific segregation in this species. On the basis of these findings, we constructed a three-dimensional map of eye-specific channels in the developing and mature ferret dLGN.

Complete 3D visualization of primate striosomes by KChIP1 immunostaining.

High-resolution 3D reconstruction and morphometric analysis of striosomes was carried out in macaque monkeys by using immunocytochemistry for the Kv4 potassium channel subunit potassium channel interacting protein 1 (KChIP1), a novel marker. The striosomes form a connected reticulum made up of two distinct planar sheets spanning several millimeters in the putamen, and long finger-like branches in the caudate nucleus and putamen. Although their spatial organization is variable, morphometric analysis of the striosomes, utilizing skeletonizations, reveals several quantitative invariant measures of striosome organization, including the following findings: 1) individual bifurcation-free striosome branches are 355 +/- 108.5 microm in diameter and 1,013 +/- 751 microm in length, and are both lognormally distributed; and 2) striosome branches exhibit three pronounced orientation preferences that are approximately orthogonal. The former finding suggests a fundamental anatomical and functional component of the striatum, whereas the latter indicates that striosomes are more lattice-like than their spatial variability suggests. The perceived variable spatial organization of the striosomes in primates belies many invariant features that may reflect striatal function, development, and pathophysiology.

Exact solutions for rate and synchrony in recurrent networks of coincidence detectors.

We provide analytical solutions for mean firing rates and cross-correlations of coincidence detector neurons in recurrent networks with excitatory or inhibitory connectivity, with rate-modulated steady-state spiking inputs. We use discrete-time finite-state Markov chains to represent network state transition probabilities, which are subsequently used to derive exact analytical solutions for mean firing rates and cross-correlations. As illustrated in several examples, the method can be used for modeling cortical microcircuits and clarifying single-neuron and population coding mechanisms. We also demonstrate that increasing firing rates do not necessarily translate into increasing cross-correlations, though our results do support the contention that firing rates and cross-correlations are likely to be coupled. Our analytical solutions underscore the complexity of the relationship between firing rates and cross-correlations.

BrainMaps.org - Interactive High-Resolution Digital Brain Atlases and Virtual Microscopy.

BrainMaps.org is an interactive high-resolution digital brain atlas and virtual microscope that is based on over 20 million megapixels of scanned images of serial sections of both primate and non-primate brains and that is integrated with a high-speed database for querying and retrieving data about brain structure and function over the internet. Complete brain datasets for various species, including Homo sapiens, Macaca mulatta, Chlorocebus aethiops, Felis catus, Mus musculus, Rattus norvegicus, and Tyto alba, are accessible online. The methods and tools we describe are useful for both research and teaching, and can be replicated by labs seeking to increase accessibility and sharing of neuroanatomical data. These tools offer the possibility of visualizing and exploring completely digitized sections of brains at a sub-neuronal level, and can facilitate large-scale connectional tracing, histochemical and stereological analyses.

The thalamus of the monotremes: cyto- and myeloarchitecture and chemical neuroanatomy.

Echidna and platypus brains were sectioned and stained by Nissl or myelin stains or immunocytochemically for calcium-binding proteins, gamma aminobutyric acid (GABA) or other antigens. Cyto- and myeloarchitecture revealed thalami that are fundamentally mammalian in organization, with the three principal divisions of the thalamus (epithalamus, dorsal thalamus and ventral thalamus) identifiable as in marsupials and eutherian mammals. The dorsal thalamus exhibits more nuclear parcellation than hitherto described, but lack of an internal medullary lamina, caused by splaying out of afferent fibre tracts that contribute to it in other mammals, makes identification of anterior, medial and intralaminar nuclear groups difficult. Differentiation of the ventral nuclei is evident with the ventral posterior nucleus of the platypus enormously expanded into the interior of the cerebral hemisphere, where it adopts a relationship to the striatum not seen in other mammals. Other nuclei such as the lateral dorsal become identifiable by expression of patterns of calcium-binding proteins identical to those found in other mammals. GABA cells are present in the ventral and dorsal thalamic nuclei, and in the ventral thalamus form a remarkable continuum with GABA cells of the two segments of the globus pallidus and pars reticulata of the substantia nigra.

Interactive visualization of multiresolution image stacks in 3D.

Conventional microscopy, electron microscopy, and imaging techniques such as MRI and PET commonly generate large stacks of images of the sectioned brain. In other domains, such as neurophysiology, variables such as space or time are also varied along a stack axis. Digital image sizes have been progressively increasing and in virtual microscopy, it is now common to work with individual image sizes that are several hundred megapixels and several gigabytes in size. The interactive visualization of these high-resolution, multiresolution images in 2D has been addressed previously [Sullivan, G., and Baker, R., 1994. Efficient quad-tree coding of images and video. IEEE Trans. Image Process. 3 (3), 327-331]. Here, we describe a method for interactive visualization of multiresolution image stacks in 3D. The method, characterized as quad-tree based multiresolution image stack interactive visualization using a texel projection based criterion, relies on accessing and projecting image tiles from multiresolution image stacks in such a way that, from the observer's perspective, image tiles all appear approximately the same size even though they are accessed from different tiers within the images comprising the stack. This method enables efficient navigation of high-resolution image stacks. We implement this method in a program called StackVis, which is a Windows-based, interactive 3D multiresolution image stack visualization system written in C++ and using OpenGL. It is freely available at http://brainmaps.org.

Internet-enabled high-resolution brain mapping and virtual microscopy.

Virtual microscopy involves the conversion of histological sections mounted on glass microscope slides to high-resolution digital images. Virtual microscopy offers several advantages over traditional microscopy, including remote viewing and data sharing, annotation, and various forms of data mining. We describe a method utilizing virtual microscopy for generation of internet-enabled, high-resolution brain maps and atlases. Virtual microscopy-based digital brain atlases have resolutions approaching 100,000 dpi, which exceeds by three or more orders of magnitude resolutions obtainable in conventional print atlases, MRI, and flat-bed scanning. Virtual microscopy-based digital brain atlases are superior to conventional print atlases in five respects: (1) resolution, (2) annotation, (3) interaction, (4) data integration, and (5) data mining. Implementation of virtual microscopy-based digital brain atlases is located at BrainMaps.org, which is based on more than 10 million megapixels (35 terabytes) of scanned images of serial sections of primate and non-primate brains with a resolution of 0.46 microm/pixel (55,000 dpi). The method can be replicated by labs seeking to increase accessibility and sharing of neuroanatomical data. Online tools offer the possibility of visualizing and exploring completely digitized sections of brains at a sub-neuronal level and can facilitate large-scale connectional tracing, histochemical, and stereological analyses.

A novel method for visualizing functional connectivity using principal component analysis.

Functional connectivity is a useful measure of voxel-wise functional magnetic resonance imaging signals that allows for the identification of functionally related brain areas and distributed networks. However, the high dimensionality of functional connectivity makes it difficult to visualize. In most studies, a small percentage of the total functional connectivity is visualized through diagrams that are constructed using individual seed voxels. In the present study describes a new method for visualizing most of the functional connectivity through a single diagram. This method does not rely on seed voxels, but rather employs a reduction of the high-dimensionality of the functional connectivity via a projection onto a three-dimensional color space using principal components analysis. With this new method, most of the information contained in a functional connectivity matrix can be represented through a single color-coded functional connectivity map, thereby facilitating a greater visual appreciation of functional connectivity.

Rate and synchrony in feedforward networks of coincidence detectors: analytical solution.

We provide an analytical recurrent solution for the firing rates and cross-correlations of feedforward networks with arbitrary connectivity, excitatory or inhibitory, in response to steady-state spiking input to all neurons in the first network layer. Connections can go between any two layers as long as no loops are produced. Mean firing rates and pairwise cross-correlations of all input neurons can be chosen individually. We apply this method to study the propagation of rate and synchrony information through sample networks to address the current debate regarding the efficacy of rate codes versus temporal codes. Our results from applying the network solution to several examples support the following conclusions: (1) differential propagation efficacy of rate and synchrony to higher layers of a feedforward network is dependent on both network and input parameters, and (2) previous modeling and simulation studies exclusively supporting either rate or temporal coding must be reconsidered within the limited range of network and input parameters used. Our exact, analytical solution for feedforward networks of coincidence detectors should prove useful for further elucidating the efficacy and differential roles of rate and temporal codes in terms of different network and input parameter ranges.

Synaptic depression leads to nonmonotonic frequency dependence in the coincidence detector.

In this letter, we extend our previous analytical results (Mikula & Niebur, 2003) for the coincidence detector by taking into account probabilistic frequency-dependent synaptic depression. We present a solution for the steady-state output rate of an ideal coincidence detector receiving an arbitrary number of input spike trains with identical binomial count distributions (which includes Poisson statistics as a special case) and identical arbitrary pairwise cross-correlations, from zero correlation (independent processes) to perfect correlation (identical processes). Synapses vary their efficacy probabilistically according to the observed depression mechanisms. Our results show that synaptic depression, if made sufficiently strong, will result in an inverted U-shaped curve for the output rate of a coincidence detector as a function of input rate. This leads to the counterintuitive prediction that higher presynaptic (input) rates may lead to lower postsynaptic (output) rates where the output rate may fall faster than the inverse of the input rate.

The effects of input rate and synchrony on a coincidence detector: analytical solution.

We derive analytically the solution for the output rate of the ideal coincidence detector. The solution is for an arbitrary number of input spike trains with identical binomial count distributions (which includes Poisson statistics as a special case) and identical arbitrary pairwise cross-correlations, from zero correlation (independent processes) to complete correlation (identical processes).