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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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Measurement of muscle insertion angles. A,Flat-mounted retina showing stitching and insertions for superior rectus (red), lateral rectus (green) and inferior rectus (blue). N indicates nasal cut. Plots on right represent the distortions introduced by reconstructing retina (see Figure 2 for explanation). B, Azimuthal equilateral projection of reconstructed retina in A. Dashed lines represent vectors connecting muscle insertion point to the optic disc. C, Muscle insertion points from 17 retinae. Solid black circles represent the optic discs for individual retinae. Dashed lines represent the line from each individual insertion point to its respective optic disc. Solid lines are from the Karcher mean insertion to the Karcher mean location of the optic disc. Grid Spacing is 15°. D, Plot of the angles of the angles of vectors connecting muscle insertions of Superior Rectus (SR), Lateral Rectus (LR) and Inferior Rectus (IR) to the individual optic discs. Bar represents the mean and error-bars are standard deviation.
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pcbi-1002921-g007: Measurement of muscle insertion angles. A,Flat-mounted retina showing stitching and insertions for superior rectus (red), lateral rectus (green) and inferior rectus (blue). N indicates nasal cut. Plots on right represent the distortions introduced by reconstructing retina (see Figure 2 for explanation). B, Azimuthal equilateral projection of reconstructed retina in A. Dashed lines represent vectors connecting muscle insertion point to the optic disc. C, Muscle insertion points from 17 retinae. Solid black circles represent the optic discs for individual retinae. Dashed lines represent the line from each individual insertion point to its respective optic disc. Solid lines are from the Karcher mean insertion to the Karcher mean location of the optic disc. Grid Spacing is 15°. D, Plot of the angles of the angles of vectors connecting muscle insertions of Superior Rectus (SR), Lateral Rectus (LR) and Inferior Rectus (IR) to the individual optic discs. Bar represents the mean and error-bars are standard deviation.

Mentions: To examine the orientation of the eye, the locations of the insertions of superior, lateral and inferior rectus into the globe of the eye were marked onto the retina (Figure 7A; see Supplemental Materials and Methods, Text S1, for procedure). The nasal pole of the retinae is determined with reference to the nictitating membrane. The retinae were reconstructed and plotted in an azimuthal equidistant polar projection and the vectors connecting the insertion points and the optic disc were plotted (Figure 7B). Once in a standard space, the muscle insertion points () from all the retinae () were plotted in the same plot and the vectors connecting the Karcher mean of each muscle insertion and the Karcher mean for the optic disc location were plotted (Figure 7C). Figure 7D shows the mean vector angles: lateral rectus, at 184.9±3.6°, is directly opposite the nasal cut, superior rectus is at 91.3±5.9° and inferior rectus is at 284.2±4.1°,where nasal is 0°. It is noticeable that there is considerable variability in the locations of the muscle insertions, certainly when compared to the variability of the optic discs. A considerable contributory factor in this is the large extent of the muscle and the relative difficulty in determining the centre of the muscle.


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)

Measurement of muscle insertion angles. A,Flat-mounted retina showing stitching and insertions for superior rectus (red), lateral rectus (green) and inferior rectus (blue). N indicates nasal cut. Plots on right represent the distortions introduced by reconstructing retina (see Figure 2 for explanation). B, Azimuthal equilateral projection of reconstructed retina in A. Dashed lines represent vectors connecting muscle insertion point to the optic disc. C, Muscle insertion points from 17 retinae. Solid black circles represent the optic discs for individual retinae. Dashed lines represent the line from each individual insertion point to its respective optic disc. Solid lines are from the Karcher mean insertion to the Karcher mean location of the optic disc. Grid Spacing is 15°. D, Plot of the angles of the angles of vectors connecting muscle insertions of Superior Rectus (SR), Lateral Rectus (LR) and Inferior Rectus (IR) to the individual optic discs. Bar represents the mean and error-bars are standard deviation.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002921-g007: Measurement of muscle insertion angles. A,Flat-mounted retina showing stitching and insertions for superior rectus (red), lateral rectus (green) and inferior rectus (blue). N indicates nasal cut. Plots on right represent the distortions introduced by reconstructing retina (see Figure 2 for explanation). B, Azimuthal equilateral projection of reconstructed retina in A. Dashed lines represent vectors connecting muscle insertion point to the optic disc. C, Muscle insertion points from 17 retinae. Solid black circles represent the optic discs for individual retinae. Dashed lines represent the line from each individual insertion point to its respective optic disc. Solid lines are from the Karcher mean insertion to the Karcher mean location of the optic disc. Grid Spacing is 15°. D, Plot of the angles of the angles of vectors connecting muscle insertions of Superior Rectus (SR), Lateral Rectus (LR) and Inferior Rectus (IR) to the individual optic discs. Bar represents the mean and error-bars are standard deviation.
Mentions: To examine the orientation of the eye, the locations of the insertions of superior, lateral and inferior rectus into the globe of the eye were marked onto the retina (Figure 7A; see Supplemental Materials and Methods, Text S1, for procedure). The nasal pole of the retinae is determined with reference to the nictitating membrane. The retinae were reconstructed and plotted in an azimuthal equidistant polar projection and the vectors connecting the insertion points and the optic disc were plotted (Figure 7B). Once in a standard space, the muscle insertion points () from all the retinae () were plotted in the same plot and the vectors connecting the Karcher mean of each muscle insertion and the Karcher mean for the optic disc location were plotted (Figure 7C). Figure 7D shows the mean vector angles: lateral rectus, at 184.9±3.6°, is directly opposite the nasal cut, superior rectus is at 91.3±5.9° and inferior rectus is at 284.2±4.1°,where nasal is 0°. It is noticeable that there is considerable variability in the locations of the muscle insertions, certainly when compared to the variability of the optic discs. A considerable contributory factor in this is the large extent of the muscle and the relative difficulty in determining the centre of the muscle.

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