Large-scale automated histology in the pursuit of connectomes.

How does the brain compute? Answering this question necessitates neuronal connectomes, annotated graphs of all synaptic connections within defined brain areas. Further, understanding the energetics of the brain's computations requires vascular graphs. The assembly of a connectome requires sensitive hardware tools to measure neuronal and neurovascular features in all three dimensions, as well as software and machine learning for data analysis and visualization. We present the state of the art on the reconstruction of circuits and vasculature that link brain anatomy and function. Analysis at the scale of tens of nanometers yields connections between identified neurons, while analysis at the micrometer scale yields probabilistic rules of connection between neurons and exact vascular connectivity.

Correlations of neuronal and microvascular densities in murine cortex revealed by direct counting and colocalization of nuclei and vessels.

It is well known that the density of neurons varies within the adult brain. In neocortex, this includes variations in neuronal density between different lamina as well as between different regions. Yet the concomitant variation of the microvessels is largely uncharted. Here, we present automated histological, imaging, and analysis tools to simultaneously map the locations of all neuronal and non-neuronal nuclei and the centerlines and diameters of all blood vessels within thick slabs of neocortex from mice. Based on total inventory measurements of different cortical regions ( approximately 10(7) cells vectorized across brains), these methods revealed: (1) In three dimensions, the mean distance of the center of neuronal somata to the closest microvessel was 15 mum. (2) Volume samples within lamina of a given region show that the density of microvessels does not match the strong laminar variation in neuronal density. This holds for both agranular and granular cortex. (3) Volume samples in successive radii from the midline to the ventral-lateral edge, where each volume summed the number of cells and microvessels from the pia to the white matter, show a significant correlation between neuronal and microvessel densities. These data show that while neuronal and vascular densities do not track each other on the 100 mum scale of cortical lamina, they do track each other on the 1-10 mm scale of the cortical mantle. The absence of a disproportionate density of blood vessels in granular lamina is argued to be consistent with the initial locus of functional brain imaging signals.

The cortical angiome: an interconnected vascular network with noncolumnar patterns of blood flow.

What is the nature of the vascular architecture in the cortex that allows the brain to meet the energy demands of neuronal computations? We used high-throughput histology to reconstruct the complete angioarchitecture and the positions of all neuronal somata of multiple cubic millimeter regions of vibrissa primary sensory cortex in mouse. Vascular networks were derived from the reconstruction. In contrast with the standard model of cortical columns that are tightly linked with the vascular network, graph-theoretical analyses revealed that the subsurface microvasculature formed interconnected loops with a topology that was invariant to the position and boundary of columns. Furthermore, the calculated patterns of blood flow in the networks were unrelated to location of columns. Rather, blood sourced by penetrating arterioles was effectively drained by the penetrating venules to limit lateral perfusion. This analysis provides the underpinning to understand functional imaging and the effect of penetrating vessels strokes on brain viability.

Vectorization of optically sectioned brain microvasculature: learning aids completion of vascular graphs by connecting gaps and deleting open-ended segments.

A graph of tissue vasculature is an essential requirement to model the exchange of gasses and nutriments between the blood and cells in the brain. Such a graph is derived from a vectorized representation of anatomical data, provides a map of all vessels as vertices and segments, and may include the location of nonvascular components, such as neuronal and glial somata. Yet vectorized data sets typically contain erroneous gaps, spurious endpoints, and spuriously merged strands. Current methods to correct such defects only address the issue of connecting gaps and further require manual tuning of parameters in a high dimensional algorithm. To address these shortcomings, we introduce a supervised machine learning method that (1) connects vessel gaps by "learned threshold relaxation"; (2) removes spurious segments by "learning to eliminate deletion candidate strands"; and (3) enforces consistency in the joint space of learned vascular graph corrections through "consistency learning." Human operators are only required to label individual objects they recognize in a training set and are not burdened with tuning parameters. The supervised learning procedure examines the geometry and topology of features in the neighborhood of each vessel segment under consideration. We demonstrate the effectiveness of these methods on four sets of microvascular data, each with >800(3) voxels, obtained with all optical histology of mouse tissue and vectorization by state-of-the-art techniques in image segmentation. Through statistically validated sampling and analysis in terms of precision recall curves, we find that learning with bagged boosted decision trees reduces equal-error error rates for threshold relaxation by 5-21% and strand elimination performance by 18-57%. We benchmark generalization performance across datasets; while improvements vary between data sets, learning always leads to a useful reduction in error rates. Overall, learning is shown to more than halve the total error rate, and therefore, human time spent manually correcting such vectorizations.