Nicholas V. Swindale

Diffusion tensor fiber tracking shows distinct corticostriatal circuits in humans

A landmark of corticostriatal connectivity in nonhuman primates is that cortical connections are organized into a set of discrete circuits. Each circuit is assumed to perform distinct behavioral functions. In animals, most connectivity studies are performed using invasive tracing methods, which are nonapplicable in humans. To test the proposal that corticostriatal connections are organized as multiple circuits in humans, we used diffusion tensor imaging axonal tracking, a new magnetic resonance technique that allows demonstration of fiber tracts in a noninvasive manner. Diffusion tensor imaging–based fiber tracking showed that the posterior (sensorimotor), anterior (associative), and ventral (limbic) compartments of the human striatum have specific connections with the cortex, and particularly the frontal lobes. These results provide the first direct demonstration of distinct corticostriatal connections in humans.

Ability of the heidelberg retina tomograph to detect early glaucomatous visual field loss.

PurposeThe Heidleberg Retina Tomograph provides rapid, reproducible measurements of optic disc topography as well as calculations of disc parameters. We used a stepwise discriminant analysis to determine which parameters were most useful in detecting individuals with early glaucomatous visual field loss. MethodsWe studied one eye in each of 45 normal individuals and one eye in each of 46 individuals with early glaucomatous visual field loss. The appearance of the optic disc was not used for classification purposes so as not to bias the diagnostic determination obtained by the instrument. The data were analyzed using the reference plane of the software version 1.10 and using a method incorporating the height of the papillomacular bundle as reference level with and without age correction. ResultsWe obtained an 89% sensitivity and 78% specificity for the detection of early visual field loss using the standard reference level. The jackknife classification revealed lower sensitivity of 87% and an unchanged specificity of 78%. With the method incorporating the height of the papillomacular bundle as reference level, the sensitivity was 87% and the specificity was 84% for detecting early visual field loss. The jackknife classification revealed a sensitivity of 87% and a specificity of 82%. With the age correction, the sensitivity was 87%, specificity 84% with regular and jackknife classification. With the standard reference level, the important parameters were the third moment and the maximum depth, with the papillomacular bundle reference level volume above reference level added as important, and with age correction, height variation in contour replaced maximum depth in the analysis. ConclusionThree significant shape parameters of the optic disc can be used to detect early glaucomatous visual field loss.

Orientation tuning curves: empirical description and estimation of parameters

Abstract. This paper compares the ability of some simple model functions to describe orientation tuning curves obtained in extracellular single-unit recordings from area 17 of the cat visual cortex. It also investigates the relationships between three methods currently used to estimate preferred orientation from tuning curve data: (a) least-squares curve fitting, (b) the vector sum method and (c) the Fourier transform method (Wörgötter and Eysel 1987). The results show that the best fitting model function for single-unit orientation tuning curves is a von Mises circular function with a variable degree of skewness. However, other functions, such as a wrapped Gaussian, fit the data nearly as well. A cosine function provides a poor description of tuning curves in almost all instances. It is demonstrated that the vector sum and Fourier methods of determining preferred orientation are equivalent, and identical to calculating a least-square fit of a cosine function to the data. Least-squares fitting of a better model function, such as a von Mises function or a wrapped Gaussian, is therefore likely to be a better method for estimating preferred orientation. Monte-Carlo simulations confirmed this, although for broad orientation tuning curves sampled at 45° intervals, as is typical in optical recording experiments, all the methods gave similarly accurate estimates of preferred orientation. The sampling interval, the estimated error in the response measurements and the probable shape of the underlying response function all need to be taken into account in deciding on the best method of estimating preferred orientation from physiological measurements of orientation tuning data.

A Model for the Formation of Ocular Dominance Stripes

The paper describes a model of competition that explains the formation of the ocular dominance stripes found in layer IVc of cat and monkey visual cortex. The main proposal is that synapses exert effects on the growth of other synapses, and that these effects extend over distances of at least 600 μm and vary in magnitude and sign within this distance. Interactions between like type synapses are assumed to be stimulating for distances up to about 200 μm, and inhibitory for distances of 200-600 μm. The reverse is true of interactions between synapses of opposite eye type, where the effects are inhibitory for distances up to about 200 μm and stimulating for longer ones. The interactions are assumed to be circularly symmetric. Growth of, for example, right eye synapses at one point will therefore (a) encourage local growth of right eye synapses and inhibit local growth of left eye synapses and (b) encourage growth of left eye synapses and inhibit growth of right eye synapses in an annular ring surrounding the point of initial increase. At the start of development, right and left eye synapses are assumed to be intermixed randomly within layer IVc. Computer simulations show that a wide variety of conditions incorporating these assumptions will lead to the formation of stripe patterns. These reproduce many of the morphological features of monkey ocular dominance stripes, including Y- and Н-type branches and terminations, the tendency for stripes to run at right angles into the boundaries of the pattern, and to narrow at branch points. The model can explain the effects of monocular deprivation on stripe morphology if it is assumed that the effectiveness of deprived eye synapses in determining rates of growth locally is reduced. The existence of a critical period for these effects can be explained if it is assumed that lateral growth of terminals does not occur, and that some factor such as a limited availability of postsynaptic sites decreases the rate of growth of synapses as their density approaches a maximum. The model can be generalized to account for pattern formation in other systems, such as zebra or mackerel skin, where similar striped patterns occur. In this context, the simplest model based on diffusion that will produce a pattern of stripes requires that one cell type should secrete two substances, one of which stimulates growth or differentiation of its parent cell type and has a low rate of diffusion or is rapidly inactivated, and another that inhibits growth or differentiation and either has a higher rate of diffusion or is less rapidly inactivated. A preliminary account of some of these results has appeared elsewhere (Swindale 1979).

Visual cortex maps are optimized for uniform coverage

Cat visual cortex contains a topographic map of visual space, plus superimposed, spatially periodic maps of ocular dominance, spatial frequency and orientation. It is hypothesized that the layout of these maps is determined by two constraints: continuity or smooth mapping of stimulus properties across the cortical surface, and coverage uniformity or uniform representation of combinations of map features over visual space. Here we use a quantitative measure of coverage uniformity (c′) to test the hypothesis that cortical maps are optimized for coverage. When we perturbed the spatial relationships between ocular dominance, spatial frequency and orientation maps obtained in single regions of cortex, we found that cortical maps are at a local minimum for c′. This suggests that coverage optimization is an important organizing principle governing cortical map development.

A Model for the Formation of Orientation Columns

A mathematical model is proposed to describe the formation of orientation columns in mammalian visual cortex. The model is similar in concept to that proposed for ocular dominance column formation (Swindale 1980), the essential difference being that orientation is a vector rather than a scalar variable. It is assumed that initially orientation selectivity is weak and randomly distributed, and that selectivity develops in such a way that the orientation preferences of neurons less than about 200 μm apart tend to change in a similar direction, whereas the preferences of cells further apart tend to develop in opposite directions. No hypotheses are made about the anatomical or physiological basis of these interactions, and it is not necessary to assume that they are the result of environmental stimulation, as with existing models for the the development of orientation selectivity (see, for example, von der Malsburg, 1973). The model reproduces the experimental data on orientation columns: roughly linear sequences of orientation change are produced, and these alternate unpredictably between clockwise and anticlockwise directions of change. Continuous sequences may span several 180° cycles of rotation. The sequences are generally smooth, but abrupt discontinuities of up to 90° also occur. The iso-orientation domains for large orientation ranges (60–90°) are periodically spaced branching stripes that resemble those demonstrated in animals by the 2-deoxyglucose technique. The domains for narrower orientation ranges are periodically spaced but are more irregular in shape, though sometimes thin and elongated. The model makes a number of predictions that can be tested experimentally. Of particular interest are the discontinuities in the orientation sequences: these should be distributed with a spacing roughly equal to, or half, that of the iso-orientation domains. Each should be surrounded by one or two complete sets of iso-orientation domains, and each may be associated with regions where cells are not orientation selective. These regions may be more extensive in younger animals, when the columns are at an intermediate stage of formation, and less numerous where the columns run parallel and unbranched over large areas.

Is the cerebral cortex modular

Two types of modular subunit, differing in size, have been hypothesized to exist in the cerebral cortex. The first, known as a mini-column, consists of a group of 110 +/- 10 cells which form a fascicle about 30 micrograms in diameter oriented perpendicular to the cortical surface. Mini-columns are believed to be organized into larger modular groupings, referred to here as macro-columns, with a diameter of about a millimetre or less. Nicholas Swindale argues in this article that there is very little real evidence in favour of either type of module. As an alternative, he suggests that the diversity of types of columnar organization, both within and between different cortical areas, may reflect the diversity of types of information stored in the cortex. Consequently, columnar organization can be expected to vary within and between species, and even between different individuals of the same species. This new interpretation is in line with current neural network theories, which do not demand the existence of structural modularity, but show how complex forms of organization can result from the existence of simple processing rules between the elements of a structure given complex structured inputs.

Sector-based analysis of optic nerve head shape parameters and visual field indices in healthy and glaucomatous eyes.

PurposeTo evaluate the correlations between the sector optic nerve head parameters measured by Heidelberg Retina Tomograph (HRT, Heidelberg Engineering, Heidelberg, Germany), version 1.1 IS, and the visual field. MethodsOne eye was randomly chosen from 55 individuals with glaucoma and 50 healthy individuals. Each participant had at least one Humphrey visual field, program 30–2 (Humphrey Instruments. San Leandro, CA. U.S.A.), and three 10° HRT pictures. From the mean of the three HRT pictures, global measurements, superior (45°-135°). nasal (135°-225°), inferior (225°-315°), and temporal (315°-45°) sector measurements were calculated for the following parameters: disc area, effective area, area below reference, mean height of contour, volume below surface, volume above surface, volume below reference, volume above reference, and third moment. From the visual field results, mean deviation (MD). superior MD. and inferior MD were calculated. For each HRT parameter we calculated the “r” Pearson correlation with the corresponding visual field measures. ResultsWithin the combined healthy and glaucomatous groups we found highly significant (p < 0.001) correlations between the following HRT parameters and the visual field MD: inferior and mean hight of contour (r = −0.53), inferior and third moment (r = −0.52). global and third moment (r = −0.49). inferior and volume above reference (r = 0.47). superior and third moment (r = −0.46), and superior and area below reference (r = −0.44). Correlations between global mean deviation and nasal or temporal sector parameters were generally smaller and less significant. ConclusionsInterior and superior HRT sector parameters were correlated with the respective visual field indices. In many cases these correlations were as strong or stronger than with the global equivalent shape measures.

A model for the coordinated development of columnar systems in primate striate cortex

The existence of patchy regions in primate striate cortex in which orientation selectivity is reduced, and which lie in the centers of ocular dominance stripes is well established (Hubel and Livingstone 1981). Analysis of functional maps obtained with voltage sensitive dyes (Blasdel and Salama 1986) has suggested that regions where the spatial rate of change of orientation preference is high, tend to be aligned either along the centers of ocular dominance stripes, or to intersect stripe borders at right angles. In this paper I present results from a developmental model which show that a tendency for orientation selectivity to develop more slowly in the centers of ocular dominance stripes would lead to the observed relationships between the layout of ocular dominance and the map of orientation gradient. This occurs despite the fact that there is no direct connection between the measures of preferred orientation (from which the gradient map is derived) and orientation selectivity (which is independent of preferred orientation). I also show that in both the monkey and the model, orientation singularities have an irregular distribution, but tend to be concentrated in the centers of the ocular dominance stripes. The average density of singularities is about 3/λθ2, where λθ is the period of the orientation columns. The results are based on an elaboration of previous models (Swindale 1980, 1982) which show how, given initially disordered starting conditions, lateral interactions that are short-range excitatory and long-range inhibitory can lead to the development of patterns of orientation or ocular dominance that resemble those found in monkey striate cortex. To explain the coordinated development of the two kinds of column, it is proposed that there is an additional tendency in development for the rate of increase in orientation selectivity to be reduced in the centers of emerging ocular dominance stripes. This might come about if a single factor modulates plasticity in each cell, or column of cells. Thus plasticity may be turned off first in regions in the centers of ocular dominance stripes where relatively extreme and therefore stable ocular dominance values are achieved early in development. Consequently it will be hard for cells in these columns to modify other properties such as orientation preference or selectivity.

Coverage and the design of striate cortex

Hubel and Wiesel (1977) suggested that ocular dominance and orientation columns in the macaque monkey striate cortex might be bands of uniform width that intersected orthogonally. They pointed out that if this were the case, there would be an equal allocation of cells of different orientation preference to each eye and to each point in visual space. However, orientation and ocular dominance columns have a more complex structural organization than is implied by this model: for example, iso-orientation domains do not intersect ocular dominance stripes at right angles and the two columnar systems have different periodicities. This raises the question as to how well the striate cortex manages to allocate equal numbers of neurons of different orientation preference to each eye and to each region of visual space, a factor referred to here as coverage. This paper defines a measure of uniformity of coverage, c′, and investigates its dependence on several different parameters of columnar organisation. Calculations were done first using a simplified one-dimensional model of orientation and ocular dominance columns and were then repeated using more realistic two-dimensional models, generated with the algorithms described in the preceding paper (Swindale 1991). Factors investigated include the relative periodicities of the two columnar systems, the size of the cortical point image, the width of orientation tuning curves, whether columns are spatially anisotropic or not, and the role of the structural relationships between columns described by Blasdel and Salama (1986). The results demonstrate that coverage is most uniform when orientation hypercolumns are about half the size of ocular dominance hypercolumns. Coverage is most uneven when the hypercolumns are the same size, unless they are related in the way described by Blasdel and Salama, in which case coverage gets only slightly worse as the size ratio (ori/od) increases above 0.5. The minimum diameter of cortical point image that ensures reasonably uniform coverage is about twice the size of an ocular dominance hypercolumn i.e. about 1.5–2.0 mm.