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Standard anatomical and visual space for the mouse retina: computational reconstruction and transformation of flattened retinae with the Retistruct package.

Sterratt DC, Lyngholm D, Willshaw DJ, Thompson ID - PLoS Comput. Biol. (2013)

Bottom Line: The variable nature of relaxing cuts and associated tears limits quantitative cross-animal comparisons.Projecting anatomically defined uncrossed retinal projections into visual space gives binocular congruence if the optical axis of the mouse eye is oriented at 64° azimuth and 22° elevation, in concordance with previous results.Moreover, using these coordinates, the dorsoventral boundary for S-opsin expressing cones closely matches the horizontal meridian.

View Article: PubMed Central - PubMed

Affiliation: Institute for Adaptive and Neural Computation, School of Informatics, University of Edinburgh, Edinburgh, Scotland, United Kingdom. david.c.sterratt@ed.ac.uk

ABSTRACT
The concept of topographic mapping is central to the understanding of the visual system at many levels, from the developmental to the computational. It is important to be able to relate different coordinate systems, e.g. maps of the visual field and maps of the retina. Retinal maps are frequently based on flat-mount preparations. These use dissection and relaxing cuts to render the quasi-spherical retina into a 2D preparation. The variable nature of relaxing cuts and associated tears limits quantitative cross-animal comparisons. We present an algorithm, "Retistruct," that reconstructs retinal flat-mounts by mapping them into a standard, spherical retinal space. This is achieved by: stitching the marked-up cuts of the flat-mount outline; dividing the stitched outline into a mesh whose vertices then are mapped onto a curtailed sphere; and finally moving the vertices so as to minimise a physically-inspired deformation energy function. Our validation studies indicate that the algorithm can estimate the position of a point on the intact adult retina to within 8° of arc (3.6% of nasotemporal axis). The coordinates in reconstructed retinae can be transformed to visuotopic coordinates. Retistruct is used to investigate the organisation of the adult mouse visual system. We orient the retina relative to the nictitating membrane and compare this to eye muscle insertions. To align the retinotopic and visuotopic coordinate systems in the mouse, we utilised the geometry of binocular vision. In standard retinal space, the composite decussation line for the uncrossed retinal projection is located 64° away from the retinal pole. Projecting anatomically defined uncrossed retinal projections into visual space gives binocular congruence if the optical axis of the mouse eye is oriented at 64° azimuth and 22° elevation, in concordance with previous results. Moreover, using these coordinates, the dorsoventral boundary for S-opsin expressing cones closely matches the horizontal meridian.

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Estimation of reconstruction error using optic disc location. A,Inferred positions of optic discs from 72 adult reconstructed retinae plotted on the same polar projection. The colatitude and longitude of the Karcher mean is (3.7°, 95.4°). The standard deviation in the angular displacement from the mean is 7.4°. B, The same data plotted on a larger scale. C, The relationship between the deformation of the reconstruction and distance  of the inferred optic disc from the population mean. There was a significant correlation between the two ().
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pcbi-1002921-g004: Estimation of reconstruction error using optic disc location. A,Inferred positions of optic discs from 72 adult reconstructed retinae plotted on the same polar projection. The colatitude and longitude of the Karcher mean is (3.7°, 95.4°). The standard deviation in the angular displacement from the mean is 7.4°. B, The same data plotted on a larger scale. C, The relationship between the deformation of the reconstruction and distance of the inferred optic disc from the population mean. There was a significant correlation between the two ().

Mentions: The deformation measure gives an indication of how easy it is to morph any particular flattened retina onto a partial sphere, but it does not indicate the error involved in the reconstruction, i.e. the difference between the inferred position on the spherical retina and the original position on the spherical retina. The ideal method for estimating the error would be to flatten a retina marked in known locations, and then compare the inferred with the known locations. However, this proved to be technically very difficult and so we tried another method of estimating the error that uses the inferred locations of the optic discs across a number of retinae. In mice, the optic disc is located “rather precisely in the geometric center of the retina” [18], though this has not, as far as we are aware, been measured. We marked the optic disc in 72 flat-mounted adult retinae, and the distribution of the centres of the inferred locations of these optic discs is shown in Figure 4A,B. The mean colatitude and longitude of these optic discs is (3.7°, 95.4°) with a standard deviation of 7.4°. The mean is therefore 3.7° away from the geometrical centre of the retina, in good agreement with the qualitative observation that the optic disc is at the geometric centre of the retina. Under the, questionable, assumption that none of the variability is biological, this suggests that an upper bound on the accuracy of the reconstruction algorithm is 7.4°. There is a significant relationship between the deformation error and the inferred distance of the optic disc from the mean optic disc location (Figure 4C). If reconstructions require accuracy to less than 7.4°, this could be achieved by increasing the stringency of values used to reject reconstructions. Rounding up this error gives a value of 8°, which is 3.6% of the 223° along the nasotemporal axis of the adult eye. It is worth noting that the error of reconstruction depends not only on the algorithm, but also the data presented to it, which is intrinsically variable.


Standard anatomical and visual space for the mouse retina: computational reconstruction and transformation of flattened retinae with the Retistruct package.

Sterratt DC, Lyngholm D, Willshaw DJ, Thompson ID - PLoS Comput. Biol. (2013)

Estimation of reconstruction error using optic disc location. A,Inferred positions of optic discs from 72 adult reconstructed retinae plotted on the same polar projection. The colatitude and longitude of the Karcher mean is (3.7°, 95.4°). The standard deviation in the angular displacement from the mean is 7.4°. B, The same data plotted on a larger scale. C, The relationship between the deformation of the reconstruction and distance  of the inferred optic disc from the population mean. There was a significant correlation between the two ().
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3585388&req=5

pcbi-1002921-g004: Estimation of reconstruction error using optic disc location. A,Inferred positions of optic discs from 72 adult reconstructed retinae plotted on the same polar projection. The colatitude and longitude of the Karcher mean is (3.7°, 95.4°). The standard deviation in the angular displacement from the mean is 7.4°. B, The same data plotted on a larger scale. C, The relationship between the deformation of the reconstruction and distance of the inferred optic disc from the population mean. There was a significant correlation between the two ().
Mentions: The deformation measure gives an indication of how easy it is to morph any particular flattened retina onto a partial sphere, but it does not indicate the error involved in the reconstruction, i.e. the difference between the inferred position on the spherical retina and the original position on the spherical retina. The ideal method for estimating the error would be to flatten a retina marked in known locations, and then compare the inferred with the known locations. However, this proved to be technically very difficult and so we tried another method of estimating the error that uses the inferred locations of the optic discs across a number of retinae. In mice, the optic disc is located “rather precisely in the geometric center of the retina” [18], though this has not, as far as we are aware, been measured. We marked the optic disc in 72 flat-mounted adult retinae, and the distribution of the centres of the inferred locations of these optic discs is shown in Figure 4A,B. The mean colatitude and longitude of these optic discs is (3.7°, 95.4°) with a standard deviation of 7.4°. The mean is therefore 3.7° away from the geometrical centre of the retina, in good agreement with the qualitative observation that the optic disc is at the geometric centre of the retina. Under the, questionable, assumption that none of the variability is biological, this suggests that an upper bound on the accuracy of the reconstruction algorithm is 7.4°. There is a significant relationship between the deformation error and the inferred distance of the optic disc from the mean optic disc location (Figure 4C). If reconstructions require accuracy to less than 7.4°, this could be achieved by increasing the stringency of values used to reject reconstructions. Rounding up this error gives a value of 8°, which is 3.6% of the 223° along the nasotemporal axis of the adult eye. It is worth noting that the error of reconstruction depends not only on the algorithm, but also the data presented to it, which is intrinsically variable.

Bottom Line: The variable nature of relaxing cuts and associated tears limits quantitative cross-animal comparisons.Projecting anatomically defined uncrossed retinal projections into visual space gives binocular congruence if the optical axis of the mouse eye is oriented at 64° azimuth and 22° elevation, in concordance with previous results.Moreover, using these coordinates, the dorsoventral boundary for S-opsin expressing cones closely matches the horizontal meridian.

View Article: PubMed Central - PubMed

Affiliation: Institute for Adaptive and Neural Computation, School of Informatics, University of Edinburgh, Edinburgh, Scotland, United Kingdom. david.c.sterratt@ed.ac.uk

ABSTRACT
The concept of topographic mapping is central to the understanding of the visual system at many levels, from the developmental to the computational. It is important to be able to relate different coordinate systems, e.g. maps of the visual field and maps of the retina. Retinal maps are frequently based on flat-mount preparations. These use dissection and relaxing cuts to render the quasi-spherical retina into a 2D preparation. The variable nature of relaxing cuts and associated tears limits quantitative cross-animal comparisons. We present an algorithm, "Retistruct," that reconstructs retinal flat-mounts by mapping them into a standard, spherical retinal space. This is achieved by: stitching the marked-up cuts of the flat-mount outline; dividing the stitched outline into a mesh whose vertices then are mapped onto a curtailed sphere; and finally moving the vertices so as to minimise a physically-inspired deformation energy function. Our validation studies indicate that the algorithm can estimate the position of a point on the intact adult retina to within 8° of arc (3.6% of nasotemporal axis). The coordinates in reconstructed retinae can be transformed to visuotopic coordinates. Retistruct is used to investigate the organisation of the adult mouse visual system. We orient the retina relative to the nictitating membrane and compare this to eye muscle insertions. To align the retinotopic and visuotopic coordinate systems in the mouse, we utilised the geometry of binocular vision. In standard retinal space, the composite decussation line for the uncrossed retinal projection is located 64° away from the retinal pole. Projecting anatomically defined uncrossed retinal projections into visual space gives binocular congruence if the optical axis of the mouse eye is oriented at 64° azimuth and 22° elevation, in concordance with previous results. Moreover, using these coordinates, the dorsoventral boundary for S-opsin expressing cones closely matches the horizontal meridian.

Show MeSH
Related in: MedlinePlus