In the broadest sense, computational neuroanatomy is the application of computational techniques (e.g. analysis, visualization, modeling, and simulation) to the investigation of neural structure. Within the field of computational neuroscience, computational neuroanatomy is principally considered to aim at creating anatomically accurate models of the nervous system. At the cellular level, computational neuroanatomy is based on the quantitative description of the structure of individual neurons, the density of neuronal elements within specific brain areas, and their interconnectivity. An important goal in computational neuroanatomy is to relate the structure to the function, at both the single cell and network levels. Combining precise morphology and detailed biophysics of single cells within large-scale realistic and data-driven network models allows simulation of emergent properties of neural circuits. Development of databases of neuronal structures (e.g.NeuroMorpho.Org ) and biophysical models (e.g. SenseLab ModelDB) enables quantitative data transfer between laboratories and constitutes an essential area of scientific emphasis in contemporary computational neuroanatomy research.
Staining and imaging techniques for morphology and connectivity
For about a century the Golgi technique has been very successful in staining neurons enabling the semi-automatic reconstruction and the quantitative analysis of their neuronal branching patterns (e.g., Glaser and van der Loos, 65; Overdijk et al., 78). In combination with other classical staining methods it has been used to achieve a quantitative statistical description of brain tissue in terms of the density of neurons, synapses, and total length of axonal and dendritic arborizations (per cubic millimeter). For more details see the section on stereology and the book by Braitenberg and Schuez (1991). Further progress in computational neuroanatomy was enabled by the spread of modern imaging techniques that allow digital reconstructions of dendritic and axonal morpohology. In the last few decades, the development of intracellular labeling (Cullheim and Kellerth, 78, Snow et al., 76) using biocytin/HRP injections and various visualization methods, including HRP-DAB or fluorescent avidin reaction (Morozov et al., 02), has led to a large output of high resolution data about dendritic morphology. Tracer injections are typically performed in single neurons in vivo (anesthetized animal) or in vitro (slice conditions), and microscopy rendering often involves fixing and reslicing the tissue. New visualization approaches, such as GFP expression in specific cell types, allow direct morphology observation in vivo, both at the whole cell and subcellular levels (Oliva et al., 02, Trachtenberg et al., 02). In addition, cell-class specific GFP expression in conjunction with traditional in vitro microscopy reduces the sampling bias due to limited access to certain neuron types in vivo and variable cell survival during slice preparation. Finally, in vivo visualization enables observation of developmental and activity-dependent morphological changes, such as individual spine plasticity (Majewska et al., 06). McCormick (99) reconstructs neurons and their connections directly from stacks of thin sections, milled off from a block of tissue. Methods of automatic slice production, image capture and digitization play an important role in high-volume reconstructions (see Cryoplane Fluorescence Microscopy, Scope Controller and Neurolucida).
Quantitative analysis of dendritic and axonal morphology
A fundamental step for computational neuroanatomy is the tracing of the acquired neuronal images into a three-dimensional (3D) digital representation of the branching dendrites and/or axons (Figure 1). Traditionally performed manually, this process is very labor intensive severely limiting the number of available reconstructions. Both commercial (Neurolucida, MicroBrightField) and freeware software systems (Neuromantic,NeuroMorpho, or NeuronStudio) offer some level of automatization of the reconstruction process. These tools considerably simplify data acquisition thus contributing to the increase of the neuron morphology databases. In computer-aided neuromorphological reconstructions, the digital tracing files describe neuronal trees as a series of interconnected cylinders, each represented by diameter, spatial coordinates, and links to other cylinders in the arbor (Overdijk et al., 78, Uylings et al., 89, Ascoli et al., 01). The number of data points representing a single neuron can be quite large (see examples e.g. at NeuroMorpho.Org ).
Digital reconstructions enable quantitative analysis of neuronal shapes by means of morphometric parameters describing the metrical and topological properties and the spatial embedding of the three-dimensional structures (Uylings et al., 86, Hillman, 88, Burke et al, 92, Ascoli et al, 01, Uylings and Van Pelt, 02). These morphometric parameters make it possible to statistically describe the variability in neuronal morphologies. In more advanced approaches investigators have designed procedures for the computational generation of neuronal morphologies with realistic variabilities in their shapes based on intrinsic correlations between morphometric parameters (Hillman, 88, Burke et al., 92, Ascoli et al., 01) or based on neuronal growth principles (Van Pelt and Uylings, 07). Both the reconstruction and the growth-model approach are algorithmic procedures, using a limited set of statistical descriptors (basic parameters) or growth rules, respectively, to generate stochastic neuronal structures that are statistically indistinguishable from the real neurons of the same morphological class (e.g. Samsonovich and Ascoli, 05, Van Pelt and Schierwagen, 04). Freeware tools for the reconstruction approach are available to measure nearly unlimited structural features from digital reconstruction files (e.g., the L-Measure software program). The ability to characterize neurons with a compact code consisting of a few statistical descriptors represents a valuable compression tool of vast neuroanatomical data.
Potential synaptic connectivity between individual cells
The number of synapses between two given cells in a brain depends on multiple factors, including partitioning of 3D space by the dendrites of multiple neurons that share it, trajectories of the axons that navigate this 3D neuropil forest, and spatial distribution of chemical factors during axonal growth and neuronal activity. While the reconstruction of dendritic and axonal trees of selected pre- and postsynaptic cells is possible, in fixed adult tissue the neuronal activity pattern and the chemical makeup of the environment during development are obviously unknown. Computational neuroanatomists have developed both theoretical and numerical approaches to tackle this issue. One study suggested that intricate branching of axonal and dendritic trees are optimized to provide a high degree of connectivity between neurons, given the existing geometrical restrictions (Chklovskii, 04). In a different attempt to predict individual axon pathways through well defined structural landmarks, a system was built for simulation of growth and branching of thalamocortical projections on the basis of a voxel-based mouse brain atlas (Senft, 02).
The critical underlying question remains: how does the number of synapses between two neurons depend on the overlap between their dendritic and axonal trees? According to "Peters rule", synaptic contacts occur where dendrites and axons happen to be in apposition. These "potential synapses" are required but not sufficient for an actual synapse formation; and the expected number of connections between two neurons is proportional to the product of their dendritic and axonal trees densities (e.g. Peters et al., 91). However, a recent study of connectivity between two neurons using glutamate uncaging and dendritic/axonal reconstruction shows that there may be fewer functional synapses than geometrical appositions (Shepherd et al., 05). Furthermore, the ratio of the number of functional synapses to that of total possible synapses specifically depends on the laminar source of axonal projection as well as dendritic target (Shepherd et al., 05). In particular, in the somatosensory cortex, this ratio for synapses between layer 5 and layers 2/3 is higher than the ratio for the layer 4 to layer 2/3 projection (but both are significantly less than 1). Therefore, notwithstanding a baseline correlation between potential synaptic connectivity and axo-dendritic overlap, the set of functional synapses effectively expressed at any one time represents only one of a combinatorial multitude of possibilities. On the one hand, this may subserve a greater network capacity for representation diversity. On the other, there is the additional possibility to increase total synaptic strength by recruiting new synapses (for example, as a result of learning).
Structure/activity relationship: dendritic trees, input processing and firing patterns
The computational simulation of detailed brain activity at the cellular level requires quantitative knowledge of neuronal class specific distribution of ionic channel and other membrane properties, as well as synaptic connectivity between neurons. Digital reconstructions of neuronal morphology represent a central node for both of these requirements. Furthermore, they have been proven useful to investigate another crucial facet of neuronal activity, namely the effect of dendritic structure on cell function. Numerous modeling reports demonstrated that the neuronal firing patterns simulated with anatomically realistic compartmental representations of the neurons with a specified channel distribution heavily depend on morphology. Several known “cortical spiking patterns” were obtained by distributing the same membrane properties on cell classes such as pyramidal and stellate cells (Mainen and Sejnowski, 96), or only changing the topological asymmetry of the model dendrites (Van Ooyen et al., 02). Even more specifically, the whole range of diverse firing observed in hippocampal CA3 pyramidal cells was reproduced when implementing an identical biophysical model on a set of morphologies which reflected the naturally occurring variability (Krichmar et al., 02). These findings are particularly striking because they were obtained with simple stimulation corresponding to the experimental protocol of somatic current injection. A more natural activation of synaptic inputs, which are distributed on the dendrites, would be expected to exacerbate the influence of morphology on output patterns. Following these results, extensive efforts are ongoing to correlate dendritic structure and neuronal activity in various cell classes. At the same time, multiple studies indicate that channel distribution can change dendritic processing and neuronal firing properties (e.g. Migliore et al., 05, Poirazi and Mel, 01).
While a detailed overview of biophysical models is beyond the scope of this article, it is clear that static anatomical information may be necessary but not sufficient to predict individual neuron properties. At the very least, the study of dynamic functional properties of neurons in vivo is required. Recent attempts to integrate vast and diverse information on the anatomical, physiological, and molecular characteristics of neurons into a comprehensive, practical, and useful classification system led to the emerging consensus that dendritic morphology is only one of the factors that can aid specific neuronal identification (Somogyi and Klausberger, 05). Axonal projections, laminar distribution of neuronal inputs and outputs, and immunohistochemical markers are other prominent features, especially for interneurons. Noticeably, computational neuroanatomy techniques (and particularly digital reconstructions among them) are contributing substantially to foster progress in many if not all of these aspects.
Stereology, cell densities, and brain region volumes
Quantification of network connectivity presupposes a robust estimate of cell count. It is important to recognize that the number of neurons in a given brain region is not constant over time, but can change during development, as a consequence of neurodegenerative disease, or in the process of learning, as was suggested in particular for hippocampal areas such as the dentate gyrus (DG). To compute the convergence and/or divergence ratios between cell populations in a normal brain, or to test hypotheses about changes in a specific cell group count associated with a particular neurological disorder, total cell numbers and densities have to be calculated. Earlier anatomical studies counted Nissl-stained cells in two-dimensional (2D) slices. A switch to the 3D volume is not trivial. Stereology techniques developed in the last decades (Gundersen, 86, Baddeley et al., 86, West et al., 91, Guillery and Herrup, 97) provide unbiased estimates of such quantitative 3D parameters as the number of cells, volumes of brain areas, and cell density. Development of specialized software such as Stereoinvestigator and Neurolucida (MicroBrightField) combines modern stereological tools with a precise control of microscope lateral (in the plane of each slide) and depth displacements. These programs automate data collection from 2D slices and significantly speed up and simplify acquiring 3D estimates.
Recent application of stereological techniques together with new cell-specific imaging labels has led to considerable scientific achievements. These include demonstrating a quantitative link between aging in human brain and number of neocortical neurons (Pakkenberg and Gundersen, 98), changes in Alzheimer’s disease (Stark et al., 07), link between the drop in the number of cells in hippocampal areas CA1 and DG and cognitive decline in Alzheimer patients (West et al., 04), discovering that a significant proportion (6%) of new DG cells develop each month (Cameron and McKay, 01), finding that decreased amygdala cell numbers but not volumes are associated with autism (Shuman and Amaral, 06), alterations in neuronal numbers in Schizophrenia (Dorph-Petersen et al., 07; Stark et al., 04; Pakkenberg, 90), and no further doubling of number of neurons in Broca’s area after birth (Uylings et al, 05). An important aspect of testing hypotheses associating changes in brain volume with specific neurological disorders involves parcellation of image stacks (e.g. from MRI scans), into specific areas as a prerequisite for the reliable measurement of corresponding volumes. Significant inter-subject variability, especially in the gyral and sulcal patterns of the human cortex, corroborated the idea of probabilistic brain atlases (Thompson et al., 00). Automated techniques have been developed to aid extraction of cortical thickness and boundaries of specific areas (Fischl et al., 00, Fischl and Dale, 04). Moreover, computational methods of cortical inflation and flattening exist to switch to a surface-based coordinate system for a more accurate representation of cortical topography (Fischl et al., 99). An important component of computational neuroanatomy develops tools for quantitative comparisons between different brain atlases (see "The Brain Architecture Project")
Connectivity between brain areas and network topology
Synaptic connectivity data between pairs of individual cells can be summarized into cell class-specific statistics that will generally be location dependent within a brain area. Another important aspect of computational neuroanatomy involves the analysis of connectivity between different brain regions. Structural connectivity can be assessed by tracer injections in a given area of interest and the subsequent study of fixed tissue (Van Essen, 85). In addition, the recently developed structural MRI technique, Diffusion Tensor Imaging (Shimony et al., 04, Mori and Zhang, 06), can be used in vivo. Computational analysis of cortico-cortical connections pointed out the similarities with the small-world network architecture (Watts and Strogatz, 98) which has a short average path length and relatively high clustering (Braitenberg and Schuez, 91, Hilgetag et al., 00, Sporns et al., 00). Network modeling studies demonstrated that changes in the fundamental pattern of network connectivity can contribute to the manifestation of pathological population activity such as epilepsy (Netoff et al., 04, Dyhrfjeld-Johnsen et al., 07). Structural connectivity between areas reflects the topological proximity of different areas, but not the total number and strength of the synaptic connections (which, in turn, can be modified during development or in a task-dependent manner). To address that, new modeling techniques estimate functional connectivity between different areas based on the correlation of activity as detected by fMRI, EEG or MEG activation (Lee et al., 06, David et al., 06).
Development and activity-dependent plasticity of neural connectivity
Neuroanatomical studies in fixed tissue produce a snapshot of neuronal structure and connectivity at a given moment in time. In the living brain, this architecture changes as it develops, or as a result of learning. A key challenge is to characterize the mechanisms contributing to these plastic changes. Sophisticated imaging techniques have been recently established to assess the dynamics of dendritic spine turnover in the mature sensory cortex in vivo (Majewska et al., 06). Meanwhile, methods for observing axonal extension, branching and maturation of synaptic contacts, as a consequence of or even during manipulation of the experimental environment, are still being developed (Alsina et al., 01, Mumm et al., 06). Biophysical models of molecular processes underlying axonal and dendritic elongation and branching (Janulevicius et al., 06, Graham and van Ooyen, 06) give an insight into intracellular and extracellular determinants of neuronal morphology. Computational techniques that relate developmental changes in neural architecture to the functionality of mature neural circuits provide a useful tool and allow testing hypothesized metabolic or activity-dependent constraints.
Numerous computational models explain how columnar structure and feature representation develops in the visual cortex (Swindale, 96) based on cross-correlation and Hebbian learning (Miller et al., 89, Nakagama et al., 06), elastic self-organizing nets (Goodhill and Willshaw, 90) or efficient information coding (Olshausen and Field, 96). These models typically use simplified neural elements, generalized cell populations with uniform properties, and connections with average weights from one cell class to another. The fate of an individual axon distributing synaptic contacts across a complex dendritic tree during development or experience-dependent plasticity remains to be fully explored. A separate class of models addresses effects of chemoattractors (Goodhill and Xu, 05), and homeostatic plasticity (Rabinovich and Segev, 06) on neural circuit organization and functionality.
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