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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 the ipsilateral projection. A,Schematic illustrating the retinal label resulting from bilateral injections of Fluoro-Ruby (magenta) and Fluoro-Emerald (cyan) dye into the dLGN. B, Flat-mounted retina with label resulting from bilateral injections of Fluoro-Ruby (magenta) and Fluoro-Emerald (cyan) into left and right dLGN, respectively. C–D, Azimuthal equilateral projection of reconstructed retina in B. Isodensity contours for 5%, 25%, 50%, 75% & 95% are plotted using the kernel density estimates (KDEs) for fully sampled retinae (C) or kernel regression (KR) estimates for partially sampled retinae (D). Blue diamond is the peak density and magenta (C) or cyan (D) diamond is the Karcher mean. Yellow circle is the optic disc. E, Composite plot with ipsilateral label from unilateral injections (). Black dashed lines represent the median angle from the optic axis to the peripheral edges of the 5% isodensity contour. Coloured diamonds represent the Karcher means of the label in the individual retinae and large coloured circles are the optic discs for the individual retinae. White square and circle represent the average Karcher mean. The central dashed angle represents the median central edge of the 5% isodensity contour. F, Mean distances from either optic disc or optic axis of reconstructed retinae to the central edge of the 5% isodensity contour along a line passing through the Karcher mean of the label. G, The extent of the ipsilateral label and the distance beyond the horizontal and vertical axes. Grid spacing is 20°. In F–G, line represents the mean and error bars are standard error of the mean. Scale bar in C & D is 1 mm.
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pcbi-1002921-g005: Measurement of the ipsilateral projection. A,Schematic illustrating the retinal label resulting from bilateral injections of Fluoro-Ruby (magenta) and Fluoro-Emerald (cyan) dye into the dLGN. B, Flat-mounted retina with label resulting from bilateral injections of Fluoro-Ruby (magenta) and Fluoro-Emerald (cyan) into left and right dLGN, respectively. C–D, Azimuthal equilateral projection of reconstructed retina in B. Isodensity contours for 5%, 25%, 50%, 75% & 95% are plotted using the kernel density estimates (KDEs) for fully sampled retinae (C) or kernel regression (KR) estimates for partially sampled retinae (D). Blue diamond is the peak density and magenta (C) or cyan (D) diamond is the Karcher mean. Yellow circle is the optic disc. E, Composite plot with ipsilateral label from unilateral injections (). Black dashed lines represent the median angle from the optic axis to the peripheral edges of the 5% isodensity contour. Coloured diamonds represent the Karcher means of the label in the individual retinae and large coloured circles are the optic discs for the individual retinae. White square and circle represent the average Karcher mean. The central dashed angle represents the median central edge of the 5% isodensity contour. F, Mean distances from either optic disc or optic axis of reconstructed retinae to the central edge of the 5% isodensity contour along a line passing through the Karcher mean of the label. G, The extent of the ipsilateral label and the distance beyond the horizontal and vertical axes. Grid spacing is 20°. In F–G, line represents the mean and error bars are standard error of the mean. Scale bar in C & D is 1 mm.

Mentions: The reconstruction method has enabled the quantification of the binocular projection from the retina to the dLGN across multiple animals. To label the projection, the dLGN in adult mice was injected either with Fluoro-Ruby or Fluoro-Emerald. Further, in some animals, the injections were bilateral (see Figure 5A and Supplemental Materials and Methods, Text S1, for details). The Retistruct program was used to reconstruct the retinae. The plots in Figures 5B–D show the label in one retina from an animal that had received bilateral injections into the dLGN (Figure 5A). These plots were done using an in-house camera-lucida set-up, sampling the entire ventrotemporal crescent for the ipsilateral retina and one in nine 150 m square boxes for the contralateral label (Figure 5B). The ipsilateral projection (Figure 5C) is restricted to the ventrotemporal crescent whereas label from the contralateral projection (Figure 5D) is distributed widely. The nature of the overlap between the uncrossed and crossed projections is evident in Figure 5B. Having reconstructed the retinae into a standard space, we quantified the projection patterns by deriving kernel density estimates (KDEs) of the underlying probability of data points appearing at any point in the retina and represented these estimates using contours that exclude 5%, 25%, 50% and 95% of the points (Figure 5C). In the case of the contralateral label, the data consisted of cell counts within defined boxes on the flattened retina. Here we used kernel regression (KR) as the source for the contouring algorithm (Figure 5D; see Supplemental Materials and Methods, Text S1, for details). The Karcher mean of the data points is represented by the magenta and cyan diamonds in either plot and the peak density for the kernel is represented by the blue diamond. It is worth noting that these two measures often give different locations, as would be expected from skewed distributions.


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 the ipsilateral projection. A,Schematic illustrating the retinal label resulting from bilateral injections of Fluoro-Ruby (magenta) and Fluoro-Emerald (cyan) dye into the dLGN. B, Flat-mounted retina with label resulting from bilateral injections of Fluoro-Ruby (magenta) and Fluoro-Emerald (cyan) into left and right dLGN, respectively. C–D, Azimuthal equilateral projection of reconstructed retina in B. Isodensity contours for 5%, 25%, 50%, 75% & 95% are plotted using the kernel density estimates (KDEs) for fully sampled retinae (C) or kernel regression (KR) estimates for partially sampled retinae (D). Blue diamond is the peak density and magenta (C) or cyan (D) diamond is the Karcher mean. Yellow circle is the optic disc. E, Composite plot with ipsilateral label from unilateral injections (). Black dashed lines represent the median angle from the optic axis to the peripheral edges of the 5% isodensity contour. Coloured diamonds represent the Karcher means of the label in the individual retinae and large coloured circles are the optic discs for the individual retinae. White square and circle represent the average Karcher mean. The central dashed angle represents the median central edge of the 5% isodensity contour. F, Mean distances from either optic disc or optic axis of reconstructed retinae to the central edge of the 5% isodensity contour along a line passing through the Karcher mean of the label. G, The extent of the ipsilateral label and the distance beyond the horizontal and vertical axes. Grid spacing is 20°. In F–G, line represents the mean and error bars are standard error of the mean. Scale bar in C & D is 1 mm.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002921-g005: Measurement of the ipsilateral projection. A,Schematic illustrating the retinal label resulting from bilateral injections of Fluoro-Ruby (magenta) and Fluoro-Emerald (cyan) dye into the dLGN. B, Flat-mounted retina with label resulting from bilateral injections of Fluoro-Ruby (magenta) and Fluoro-Emerald (cyan) into left and right dLGN, respectively. C–D, Azimuthal equilateral projection of reconstructed retina in B. Isodensity contours for 5%, 25%, 50%, 75% & 95% are plotted using the kernel density estimates (KDEs) for fully sampled retinae (C) or kernel regression (KR) estimates for partially sampled retinae (D). Blue diamond is the peak density and magenta (C) or cyan (D) diamond is the Karcher mean. Yellow circle is the optic disc. E, Composite plot with ipsilateral label from unilateral injections (). Black dashed lines represent the median angle from the optic axis to the peripheral edges of the 5% isodensity contour. Coloured diamonds represent the Karcher means of the label in the individual retinae and large coloured circles are the optic discs for the individual retinae. White square and circle represent the average Karcher mean. The central dashed angle represents the median central edge of the 5% isodensity contour. F, Mean distances from either optic disc or optic axis of reconstructed retinae to the central edge of the 5% isodensity contour along a line passing through the Karcher mean of the label. G, The extent of the ipsilateral label and the distance beyond the horizontal and vertical axes. Grid spacing is 20°. In F–G, line represents the mean and error bars are standard error of the mean. Scale bar in C & D is 1 mm.
Mentions: The reconstruction method has enabled the quantification of the binocular projection from the retina to the dLGN across multiple animals. To label the projection, the dLGN in adult mice was injected either with Fluoro-Ruby or Fluoro-Emerald. Further, in some animals, the injections were bilateral (see Figure 5A and Supplemental Materials and Methods, Text S1, for details). The Retistruct program was used to reconstruct the retinae. The plots in Figures 5B–D show the label in one retina from an animal that had received bilateral injections into the dLGN (Figure 5A). These plots were done using an in-house camera-lucida set-up, sampling the entire ventrotemporal crescent for the ipsilateral retina and one in nine 150 m square boxes for the contralateral label (Figure 5B). The ipsilateral projection (Figure 5C) is restricted to the ventrotemporal crescent whereas label from the contralateral projection (Figure 5D) is distributed widely. The nature of the overlap between the uncrossed and crossed projections is evident in Figure 5B. Having reconstructed the retinae into a standard space, we quantified the projection patterns by deriving kernel density estimates (KDEs) of the underlying probability of data points appearing at any point in the retina and represented these estimates using contours that exclude 5%, 25%, 50% and 95% of the points (Figure 5C). In the case of the contralateral label, the data consisted of cell counts within defined boxes on the flattened retina. Here we used kernel regression (KR) as the source for the contouring algorithm (Figure 5D; see Supplemental Materials and Methods, Text S1, for details). The Karcher mean of the data points is represented by the magenta and cyan diamonds in either plot and the peak density for the kernel is represented by the blue diamond. It is worth noting that these two measures often give different locations, as would be expected from skewed distributions.

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