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. 2005 Mar 15;102(11):4158-63.
doi: 10.1073/pnas.0500291102. Epub 2005 Mar 3.

Physical limits to spatial resolution of optical recording: clarifying the spatial structure of cortical hypercolumns

Jonathan R Polimeni  1 , Domhnull Granquist-Fraser, Richard J Wood, Eric L Schwartz
Affiliations

Physical limits to spatial resolution of optical recording: clarifying the spatial structure of cortical hypercolumns

Jonathan R Polimeni et al. Proc Natl Acad Sci U S A. .

Abstract

Neurons in macaque primary visual cortex are spatially arranged by their global topographic position and in at least three overlapping local modular systems: ocular dominance columns, orientation pinwheels, and cytochrome oxidase (CO) blobs. Individual neurons in the blobs are not tuned to orientation, and populations of neurons in the pinwheel center regions show weak orientation tuning, suggesting a close relation between pinwheel centers and CO blobs. However, this hypothesis has been challenged by a series of optical recording experiments. In this report, we show that the statistical error associated with photon scatter and absorption in brain tissue combined with the blurring introduced by the optics of the imaging system has typically been in the range of 250 microm. These physical limitations cause a systematic error in the location of pinwheel centers because of the vectorial nature of these patterns, such that the apparent location of a pinwheel center measured by optical recording is never (on average) in the correct in vivo location. The systematic positional offset is approximately 116 microm, which is large enough to account for the claimed misalignment of CO blobs and pinwheel centers. Thus, optical recording, as it has been used to date, has insufficient spatial resolution to accurately locate pinwheel centers. The earlier hypothesis that CO blobs and pinwheel centers are coterminous remains the only hypothesis currently supported by reliable observation.

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Figures

Fig. 1.
Fig. 1.
Monte Carlo simulation. (a) Sample of 100 model photon paths in cortical tissue. Cortical gray matter, in this example, was taken to be 1,000 μm thick, and the gray matter/white matter interface is denoted by a dashed black line. The white star marks the model photon source 500 μm below the gray matter/air interface. Red dots mark points at which a photon was absorbed. Green dots mark points at which photons exit the tissue. The small 1-mm thickness of gray matter illustrated here demonstrates the qualitative difference as the model photon travels through gray matter versus white matter. However, in our simulations, cortical gray matter of 2.3-mm thickness was used, and each PSF was computed from 106 photons per reflectance source. (b) Resultant columnar PSF, averaged over sources at 200–500 μm cortical depth, with macroscope focus set at a depth of 300 μm. The FWHM is 234.3 μm. Also shown are a 280-μm FWHM Gaussian function, which is the result of Orbach and Cohen (21) (corrected by our Monte Carlo results for missing back-scatter), and a 50-μm FWHM Gaussian function, which is suggested as a possible value by Grinvald et al. (17).
Fig. 2.
Fig. 2.
Results of blurring orientation data. (a) Synthetic orientation tuning data generated by band-pass filtering random orientation values (30). The original average distance between pinwheel centers is set at 350 × 550 μm, and the number of pinwheels is 124. Positive chirality (i.e., right-handed) pinwheels are indicated by white circles and negative chirality is indicated by black squares. The solid and dashed black lines trace out zero-crossings of the orientation map, whose intersections mark the pinwheel center locations for a continuous orientation map, a result known as the sign theorem (36). (b) Blurring the data of a with a Cauchy filter whose FWHM is 240 μm results in an average pinwheel distance of 499.1 μm and 93 pinwheels. If the pattern in a is taken as the true in vivo orientation map, the pattern in b is that one that would be produced by imaging with the blur that we have estimated from our joint photon-scatter simulations and optics model. The pseudocolor map of orientation is provided below. (Scale bars, 1 mm.)
Fig. 3.
Fig. 3.
Effects of blur on pinwheel center position. (a) Simulation of pinwheel movement and annihilation due to low-pass filtering with increasing FWHM to 1,000 in vivo pinwheel patterns with 350 × 550-μm spacing. As the Cauchy blurring kernel broadens, the average pinwheel movement increases nearly linearly, resulting in a bias in the observed singularity location relative to the true in vivo location of the singularity. At 240 μm FWHM, the orientation singularity position error is 116 μm on average. (b) Simulation of the experiment of Maldonado et al. (15). The offset of the tetrode recording site from the true orientation singularity location is demonstrated on a synthetic orientation tuning preference map. Here, the tetrode is illustrated by a spotlight of radius 65 μm offset from a orientation singularity by 116 μm. In this example, the tetrode observes an orientation range of ≈40°. The black ring marks the area of a CO blob with a 100-μm radius centered at the chosen orientation singularity, and the areas of the tetrode recording and the CO blob exhibit little overlap. (Scale bar, 500 μm.)
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