Computer generation and quantitative morphometric analysis of virtual neurons.

An important goal in computational neuroanatomy is the complete and accurate simulation of neuronal morphology. We are developing computational tools to model three-dimensional dendritic structures based on sets of stochastic rules. This paper reports an extensive, quantitative anatomical characterization of simulated motoneurons and Purkinje cells. We used several local and global algorithms implemented in the L-Neuron and ArborVitae programs to generate sets of virtual neurons. Parameters statistics for all algorithms were measured from experimental data, thus providing a compact and consistent description of these morphological classes. We compared the emergent anatomical features of each group of virtual neurons with those of the experimental database in order to gain insights on the plausibility of the model assumptions, potential improvements to the algorithms, and non-trivial relations among morphological parameters. Algorithms mainly based on local constraints (e.g., branch diameter) were successful in reproducing many morphological properties of both motoneurons and Purkinje cells (e.g. total length, asymmetry, number of bifurcations). The addition of global constraints (e.g., trophic factors) improved the angle-dependent emergent characteristics (average Euclidean distance from the soma to the dendritic terminations, dendritic spread). Virtual neurons systematically displayed greater anatomical variability than real cells, suggesting the need for additional constraints in the models. For several emergent anatomical properties, a specific algorithm reproduced the experimental statistics better than the others did. However, relative performances were often reversed for different anatomical properties and/or morphological classes. Thus, combining the strengths of alternative generative models could lead to comprehensive algorithms for the complete and accurate simulation of dendritic morphology.

Generation, description and storage of dendritic morphology data.

It is generally assumed that the variability of neuronal morphology has an important effect on both the connectivity and the activity of the nervous system, but this effect has not been thoroughly investigated. Neuroanatomical archives represent a crucial tool to explore structure-function relationships in the brain. We are developing computational tools to describe, generate, store and render large sets of three-dimensional neuronal structures in a format that is compact, quantitative, accurate and readily accessible to the neuroscientist. Single-cell neuroanatomy can be characterized quantitatively at several levels. In computer-aided neuronal tracing files, a dendritic tree is described as a series of cylinders, each represented by diameter, spatial coordinates and the connectivity to other cylinders in the tree. This 'Cartesian' description constitutes a completely accurate mapping of dendritic morphology but it bears little intuitive information for the neuroscientist. In contrast, a classical neuroanatomical analysis characterizes neuronal dendrites on the basis of the statistical distributions of morphological parameters, e.g. maximum branching order or bifurcation asymmetry. This description is intuitively more accessible, but it only yields information on the collective anatomy of a group of dendrites, i.e. it is not complete enough to provide a precise 'blueprint' of the original data. We are adopting a third, intermediate level of description, which consists of the algorithmic generation of neuronal structures within a certain morphological class based on a set of 'fundamental', measured parameters. This description is as intuitive as a classical neuroanatomical analysis (parameters have an intuitive interpretation), and as complete as a Cartesian file (the algorithms generate and display complete neurons). The advantages of the algorithmic description of neuronal structure are immense. If an algorithm can measure the values of a handful of parameters from an experimental database and generate virtual neurons whose anatomy is statistically indistinguishable from that of their real counterparts, a great deal of data compression and amplification can be achieved. Data compression results from the quantitative and complete description of thousands of neurons with a handful of statistical distributions of parameters. Data amplification is possible because, from a set of experimental neurons, many more virtual analogues can be generated. This approach could allow one, in principle, to create and store a neuroanatomical database containing data for an entire human brain in a personal computer. We are using two programs, L-NEURON and ARBORVITAE, to investigate systematically the potential of several different algorithms for the generation of virtual neurons. Using these programs, we have generated anatomically plausible virtual neurons for several morphological classes, including guinea pig cerebellar Purkinje cells and cat spinal cord motor neurons. These virtual neurons are stored in an online electronic archive of dendritic morphology. This process highlights the potential and the limitations of the 'computational neuroanatomy' strategy for neuroscience databases.

Transformation of a set of slices rotated on a common axis to a set of Z-slices: application to three-dimensional visualization of the in vivo human lens.

A technique that transforms a set of images acquired as a rotating frame about an axis (Z axis) into a set of images along the Z axis in presented. This technique is applied to the three-dimensional visualization of the in vivo human lens. A Scheimpfling slit camera acquired 60 optical images through the in vivo human lens. Between each image acquisition the plane containing the slit beam of light was sequentially rotated. This set of 60 images was transformed into a new stack of images on the Z axis. The transformed stack of Z images was visualized with volume rendering software.

Three-dimensional volume visualization of the in vivo human ocular lens showing localization of the cataract.

An in vivo human lens containing a cataract has been visualized by volume rendering a transformed series of 60 rotated Scheimpflug digital images. The data set was obtained by rotating the Scheimpflug camera about the optic axis of the lens in 3-degree increments. The set of 60 Scheimpflug digital images were mathematically transformed into a new data set in which the images are oriented perpendicular to the optic axis of the eye. The transformed set of optical sections were first aligned to correct for eye movements during the data collection process, then rendered into a three-dimensional volume reconstruction with volume-rendering computer graphics techniques. The viewpoint and the transparency of the volume rendered in vivo human lens were varied in order to observe volume opacities in various regions of the lens. To help visualize lens opacities, the intensity of light scattering was pseudocolor-coded as an integral part of the three-dimensional volume rendering. Three-dimensional, pseudocolored volume rendering of the in vivo human ocular lens represents a new technique to visualize in vivo human cataracts.

Growth of thalamic afferents into mouse barrel cortex.

We studied thalamocortical afferent (TCA) growth into somatosensory cortex as the whisker barrels emerge in postnatal mice. Ingrowing fibers from the ventrobasal (VB) thalamus were selectively labeled by two means. Under direct vision, individual axons and populations of axons were labeled in vitro with HRP, or in fixed tissue with Dil (1,1'-dioctodecyl-3,3,3',3'-tetramethylindocarbocyanine perchlorate), in pieces of brain containing both the source nucleus in the thalamus and its cortical target. Many simple thalamocortical afferents are already within the upper cortical plate at birth [postnatal day one (PND1)]. Initially, TCAs from each point in the thalamus distribute in the cortex as two-dimensional "Gaussians," which overlap laterally to constitute a uniform projection pattern. The projection is topographic, because adjacent focal injections within VB label adjacent cortical loci. Subsequent development of barreloids (thalamic representations of the whiskers) partitions the TCA projection into a set of whisker-related Gaussians, centered on cortical targets whose collective topography reflects that of the source pattern. After barreloids form on about PND3, but before barrels appear in cytoarchitecture on about PND5, the overlapping TCAs segregate into dense terminal clusters in layer IV, around which barrels later mature. Time series of single fibers traced with camera lucida explain this transformation that is so noticeable at the population level. As early as PND1, individual TCAs emit multiple ascending collaterals on their horizontal run through white matter and oblique ascent into upper cortex. Subsequently, by PND4, and proceeding at least through PND7, there is accelerated terminal arborization of selected appropriate collateral branches and pruning back of other inappropriate ones. The selection mechanism appears to result from within-group reinforcement events that are stronger for branches toward the center of each whisker-related Gaussian distribution.

Computer-aided analyses of thalamocortical afferent ingrowth.

Segregation of thalamocortical afferent (TCA) fibers precedes barrel formation in rodent somatosensory cortex (Killackey and Leshin, 1975; Jeanmonod et al., 1981; Jensen and Killackey, 1987b; Senft, 1989; Erzurumlu and Jhaveri, 1990). Hypotheses about the arborization strategies followed by these ingrowing fibers have been generated from evaluation of labeled terminal fragments of mouse TCAs (Senft and Woolsey, 1991a). Those TCAs were of necessity truncated by the histological processing needed to observe them at high resolution. This fragmentation, along with biological variability, forces conclusions about single intact axons to be derived from populations of parts of arbors. To evaluate the hypotheses critically, we designed a computer program to quantify morphological aspects of labeled TCAs drawn with a camera lucida. We constructed algorithms to abstract, from fiber populations, properties minimally affected by truncation. Our program analyzes, and displays as histograms, fiber and branch densities and orientations. To represent these features by additional graphical means, "average" ingrowing TCAs were generated, based on the accumulated statistics of the traced fiber fragments. Quantitative descriptions of TCA populations from postnatal day 1 (PND1) through PND7 are presented. These analyses show that fibers and their branches accumulate with age within the cortical plate (emergent layer IV), and to a lesser extent within developing layer VI. Simultaneously, the distributions of these afferents within cortical laminae transform from uniform to patchy in the plane of the cortex. Peaks exhibit the periodicity typical of mature barrels. Branches become more numerous focally as and where layer IV barrels emerge. Individually traced arbors show reduced total widths consistent with progressive pruning of branches extending into territories of inappropriate barrels, both in layer IV and deeper in the cortex.

Mouse barrel cortex viewed as Dirichlet domains.

Barrels are patterned groups of neurons in rodent somatosensory cortex that correspond one to one with the animal's facial whiskers. Dirichlet domains are a class of convex polygon found frequently in nature, often arising by nucleation from center points. Analytic and graphical methods were devised to verify the hypothesis that Dirichlet domains accurately describe the adult barrel fields of normal mice. We found that normal barrel fields and abnormal barrel fields caused by supernumerary whiskers or lesions to the whisker pad are closely approximated by this mathematical formalism. This implies that each developing cortical barrel organizes about a center point. Experiments in neonatal animals (Senft and Woolsey, 1991a) demonstrate foci in the thalamocortical afferent (TCA) distributions. These results support an hypothesis in which TCAs are the nucleating agents causing barrels to organize as Dirichlet domains. This is made possible because TCA terminals from each barreloid (a whisker-related group of cells in the ventrobasal complex of the thalamus) initially colonize somatosensory cortex with an approximately "Gaussian" distribution. These peaked groups of related TCAs behave as Dirichlet domain centers. They generate barrel structures competitively, in animals with normal or with perturbed whisker patterns, via statistical epigenetic interactions within and between distinct TCA Gaussians associated with separate whiskers. This leads to selective axon outgrowth and pruning of single TCA branches, regulated by the TCA population, and creates beneath each Gaussian the dense knot of related TCA arbors typical of the barrel cortex. Similar parcellation of neuronal processes into contending subgroups having spatially coherent actions could lead to nucleation of other geometric patterns as Dirichlet domains elsewhere in the brain.

Optical sectioning of HRP-stained molluscan neurons.

The use of high-resolution differential interference contrast(DIC) microscopy on cleared whole-mounts of the circumesophageal nervous system from Hermissenda crassicornis permits visualization of neuronal morphology in detail without the need for physical sectioning. Such optical sectioning, when preceded by intracellular iontophoresis of horseradish peroxidase (HRP) permits rapid and accurate examination of the arborization of electrically characterized neurons. Details such as varicosities and terminal swellings can readily be resolved. This method has revealed new morphological features of neurons implicated in training-specific behavioral modification in Hermissenda, and promises to be of further general use for the quantitative morphometry of electrically identified neurons.