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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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Deformation of reconstructions and the effect of rim angle. A,Histogram of the reconstruction error measure  obtained from 288 successfully reconstructed retinae. B, Relationship between deformation measure and age. “A” indicates adult animals. C, Schematic diagram of eye, indicating the measurements  and  made on mouse eyes at different stages of development, and the rim angle  derived from these measurements. Note that rim angle is measured from the optic pole (*). D, Rim colatitude  that minimises reconstruction error versus the rim angle  determined from eye measurements. Solid line shows equality and grey lines indicate ±10° and ±20° from equality. E, Minimum reconstruction error  obtained by optimising rim angle versus reconstruction error  obtained when using the rim angle from eye measurements. Solid line indicates equality.
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pcbi-1002921-g003: Deformation of reconstructions and the effect of rim angle. A,Histogram of the reconstruction error measure obtained from 288 successfully reconstructed retinae. B, Relationship between deformation measure and age. “A” indicates adult animals. C, Schematic diagram of eye, indicating the measurements and made on mouse eyes at different stages of development, and the rim angle derived from these measurements. Note that rim angle is measured from the optic pole (*). D, Rim colatitude that minimises reconstruction error versus the rim angle determined from eye measurements. Solid line shows equality and grey lines indicate ±10° and ±20° from equality. E, Minimum reconstruction error obtained by optimising rim angle versus reconstruction error obtained when using the rim angle from eye measurements. Solid line indicates equality.

Mentions: Thus the deformation measure gives some indication of the apparent quality of the reconstruction. A value greater than 0.2 indicates a problem with the stitching part of the algorithm; the 2 such reconstructions were rejected and are not included in the 288 successful reconstructions. Noticeably bad reconstructions tend to have . We recommend checking the mark-up of cuts and tears in any retinae with . The mean deformation measure was 0.071, the median was 0.070 (Figure 3A), and 27 out of 288 retinae had a deformation measure exceeding 0.1, including the retina illustrated in Figure 2E–H as an, intentionally, poor dissection. With  = 0.118, it falls above the 97.5th percentile of the retinae illustrated in Figure 3A. The larger deformations tend to come from younger animals (Figure 3B), reflecting the difficulty of dissecting retinae out of these animals cleanly due to the more delicate nature of younger tissue.


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)

Deformation of reconstructions and the effect of rim angle. A,Histogram of the reconstruction error measure  obtained from 288 successfully reconstructed retinae. B, Relationship between deformation measure and age. “A” indicates adult animals. C, Schematic diagram of eye, indicating the measurements  and  made on mouse eyes at different stages of development, and the rim angle  derived from these measurements. Note that rim angle is measured from the optic pole (*). D, Rim colatitude  that minimises reconstruction error versus the rim angle  determined from eye measurements. Solid line shows equality and grey lines indicate ±10° and ±20° from equality. E, Minimum reconstruction error  obtained by optimising rim angle versus reconstruction error  obtained when using the rim angle from eye measurements. Solid line indicates equality.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002921-g003: Deformation of reconstructions and the effect of rim angle. A,Histogram of the reconstruction error measure obtained from 288 successfully reconstructed retinae. B, Relationship between deformation measure and age. “A” indicates adult animals. C, Schematic diagram of eye, indicating the measurements and made on mouse eyes at different stages of development, and the rim angle derived from these measurements. Note that rim angle is measured from the optic pole (*). D, Rim colatitude that minimises reconstruction error versus the rim angle determined from eye measurements. Solid line shows equality and grey lines indicate ±10° and ±20° from equality. E, Minimum reconstruction error obtained by optimising rim angle versus reconstruction error obtained when using the rim angle from eye measurements. Solid line indicates equality.
Mentions: Thus the deformation measure gives some indication of the apparent quality of the reconstruction. A value greater than 0.2 indicates a problem with the stitching part of the algorithm; the 2 such reconstructions were rejected and are not included in the 288 successful reconstructions. Noticeably bad reconstructions tend to have . We recommend checking the mark-up of cuts and tears in any retinae with . The mean deformation measure was 0.071, the median was 0.070 (Figure 3A), and 27 out of 288 retinae had a deformation measure exceeding 0.1, including the retina illustrated in Figure 2E–H as an, intentionally, poor dissection. With  = 0.118, it falls above the 97.5th percentile of the retinae illustrated in Figure 3A. The larger deformations tend to come from younger animals (Figure 3B), reflecting the difficulty of dissecting retinae out of these animals cleanly due to the more delicate nature of younger tissue.

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