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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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Examples of reconstructed retinae. A–D,An example of a reconstruction of an adult retina with low deformation measure . A, Plot of length of edge on the sphere versus length of edge on the flat retina. Red indicates an edge that has expanded and blue a edge that has been compressed. B, The log strain  indicated using the same colour scheme on the flat retina. C, The flat representation of lines of latitude and longitude with the optic disc (blue). D, The azimuthal equidistant (polar) representation showing the locations of the cuts and tears (cyan) and the location of the optic disc (blue). E–H, An example of a reconstruction of a P0 retina with high deformation energy . Meaning of E–H same as for corresponding panel in A–D. All scale bars are 1 mm.
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pcbi-1002921-g002: Examples of reconstructed retinae. A–D,An example of a reconstruction of an adult retina with low deformation measure . A, Plot of length of edge on the sphere versus length of edge on the flat retina. Red indicates an edge that has expanded and blue a edge that has been compressed. B, The log strain indicated using the same colour scheme on the flat retina. C, The flat representation of lines of latitude and longitude with the optic disc (blue). D, The azimuthal equidistant (polar) representation showing the locations of the cuts and tears (cyan) and the location of the optic disc (blue). E–H, An example of a reconstruction of a P0 retina with high deformation energy . Meaning of E–H same as for corresponding panel in A–D. All scale bars are 1 mm.

Mentions: To assess the amount of residual deformation at the end of the energy minimisation procedure, we plotted the length of each edge in the spherical mesh versus the length of the corresponding edge in the flat mesh (Figure 2A), using the same colour scale as in Figure 1D,E. A measure of the overall deformation of reconstruction is:(1)where the summation is over , the set of edges, the mean length of an edge in the flat mesh is , and the number of edges is . Physically, this measure is the square root of the elastic energy contained in the notional springs. It is constructed so as to be of a similar order to the mean fractional deformation.


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)

Examples of reconstructed retinae. A–D,An example of a reconstruction of an adult retina with low deformation measure . A, Plot of length of edge on the sphere versus length of edge on the flat retina. Red indicates an edge that has expanded and blue a edge that has been compressed. B, The log strain  indicated using the same colour scheme on the flat retina. C, The flat representation of lines of latitude and longitude with the optic disc (blue). D, The azimuthal equidistant (polar) representation showing the locations of the cuts and tears (cyan) and the location of the optic disc (blue). E–H, An example of a reconstruction of a P0 retina with high deformation energy . Meaning of E–H same as for corresponding panel in A–D. All scale bars are 1 mm.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002921-g002: Examples of reconstructed retinae. A–D,An example of a reconstruction of an adult retina with low deformation measure . A, Plot of length of edge on the sphere versus length of edge on the flat retina. Red indicates an edge that has expanded and blue a edge that has been compressed. B, The log strain indicated using the same colour scheme on the flat retina. C, The flat representation of lines of latitude and longitude with the optic disc (blue). D, The azimuthal equidistant (polar) representation showing the locations of the cuts and tears (cyan) and the location of the optic disc (blue). E–H, An example of a reconstruction of a P0 retina with high deformation energy . Meaning of E–H same as for corresponding panel in A–D. All scale bars are 1 mm.
Mentions: To assess the amount of residual deformation at the end of the energy minimisation procedure, we plotted the length of each edge in the spherical mesh versus the length of the corresponding edge in the flat mesh (Figure 2A), using the same colour scale as in Figure 1D,E. A measure of the overall deformation of reconstruction is:(1)where the summation is over , the set of edges, the mean length of an edge in the flat mesh is , and the number of edges is . Physically, this measure is the square root of the elastic energy contained in the notional springs. It is constructed so as to be of a similar order to the mean fractional deformation.

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