Limits...
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.

Show MeSH

Related in: MedlinePlus

Overview of the method. A,The raw data: a retinal outline from an adult mouse (black), two types of data points (red and green circles) from paired injections into the superior colliculus and a landmark (blue line). B, Retinal outline with nasal pole (N) and cuts marked up. Each pair of dark cyan lines connects the vertices and apex of the four cuts. C, The outline after triangulation (shown by grey lines) and stitching, indicated by cyan lines between corresponding points on the cuts. Di, The initial projection of the triangulated and stitched outline onto a curtailed sphere. The strain of each edge is represented on a colour scale with blue indicating compression and red expansion. Cuts are shown in cyan. Dii, The strain plotted on the flat outline with lines of latitude and longitude superposed. Ei,ii, As Di,ii but after optimisation of the mapping. Fi, The data represented on a polar plot of the reconstructed retina. Mean locations of the different types of data points are indicated by diamonds. The nasal (N), dorsal (D), temporal (T) and ventral (V) poles are indicated. Cuts are shown in cyan. Fii, Data plotted on the flat representation, with lines of latitude and longitude superposed. All scale bars are 1 mm.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3585388&req=5

pcbi-1002921-g001: Overview of the method. A,The raw data: a retinal outline from an adult mouse (black), two types of data points (red and green circles) from paired injections into the superior colliculus and a landmark (blue line). B, Retinal outline with nasal pole (N) and cuts marked up. Each pair of dark cyan lines connects the vertices and apex of the four cuts. C, The outline after triangulation (shown by grey lines) and stitching, indicated by cyan lines between corresponding points on the cuts. Di, The initial projection of the triangulated and stitched outline onto a curtailed sphere. The strain of each edge is represented on a colour scale with blue indicating compression and red expansion. Cuts are shown in cyan. Dii, The strain plotted on the flat outline with lines of latitude and longitude superposed. Ei,ii, As Di,ii but after optimisation of the mapping. Fi, The data represented on a polar plot of the reconstructed retina. Mean locations of the different types of data points are indicated by diamonds. The nasal (N), dorsal (D), temporal (T) and ventral (V) poles are indicated. Cuts are shown in cyan. Fii, Data plotted on the flat representation, with lines of latitude and longitude superposed. All scale bars are 1 mm.

Mentions: Historically, the anatomical organisation of the retina was frequently examined using serial sections, with the emphasis on example sections rather than reconstructions [8]. The introduction of retinal flat-mounts, also termed whole-mounts, [9], [10] was a major advance. Briefly, orienting marks are made in the retina whilst in the eye-cup, the retina is then dissected out and flattened with the help of a number of relaxing cuts. The flat-mount facilitated quantitative descriptions of the 2D distributions of different labels and markers across the retina. However, the relaxing cuts, together with tears that can occur during flattening, disturbs the retinal geometry significantly, which not only complicates comparison across retinae, but also can be problematic in interpreting results obtained from individual flat-mounted retinae. For example, various measures are used to quantify the regularity of mosaics of various cell types seen in flat-mounted retinae [11], [12], but these are susceptible to the existence of boundaries [13], both at the rim of the retina and those introduced by the relaxing cuts. In the study of topographic mapping, the locations of ganglion cells labelled by retrograde tracers injected into different locations in the target, the superior colliculus, have been compared in retinal flat-mounts [4], [5]. Foci of labelled cells can be separated, or even split, by relaxing cuts (see Figure 1A), complicating quantitative analyses.


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)

Overview of the method. A,The raw data: a retinal outline from an adult mouse (black), two types of data points (red and green circles) from paired injections into the superior colliculus and a landmark (blue line). B, Retinal outline with nasal pole (N) and cuts marked up. Each pair of dark cyan lines connects the vertices and apex of the four cuts. C, The outline after triangulation (shown by grey lines) and stitching, indicated by cyan lines between corresponding points on the cuts. Di, The initial projection of the triangulated and stitched outline onto a curtailed sphere. The strain of each edge is represented on a colour scale with blue indicating compression and red expansion. Cuts are shown in cyan. Dii, The strain plotted on the flat outline with lines of latitude and longitude superposed. Ei,ii, As Di,ii but after optimisation of the mapping. Fi, The data represented on a polar plot of the reconstructed retina. Mean locations of the different types of data points are indicated by diamonds. The nasal (N), dorsal (D), temporal (T) and ventral (V) poles are indicated. Cuts are shown in cyan. Fii, Data plotted on the flat representation, with lines of latitude and longitude superposed. All scale bars are 1 mm.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002921-g001: Overview of the method. A,The raw data: a retinal outline from an adult mouse (black), two types of data points (red and green circles) from paired injections into the superior colliculus and a landmark (blue line). B, Retinal outline with nasal pole (N) and cuts marked up. Each pair of dark cyan lines connects the vertices and apex of the four cuts. C, The outline after triangulation (shown by grey lines) and stitching, indicated by cyan lines between corresponding points on the cuts. Di, The initial projection of the triangulated and stitched outline onto a curtailed sphere. The strain of each edge is represented on a colour scale with blue indicating compression and red expansion. Cuts are shown in cyan. Dii, The strain plotted on the flat outline with lines of latitude and longitude superposed. Ei,ii, As Di,ii but after optimisation of the mapping. Fi, The data represented on a polar plot of the reconstructed retina. Mean locations of the different types of data points are indicated by diamonds. The nasal (N), dorsal (D), temporal (T) and ventral (V) poles are indicated. Cuts are shown in cyan. Fii, Data plotted on the flat representation, with lines of latitude and longitude superposed. All scale bars are 1 mm.
Mentions: Historically, the anatomical organisation of the retina was frequently examined using serial sections, with the emphasis on example sections rather than reconstructions [8]. The introduction of retinal flat-mounts, also termed whole-mounts, [9], [10] was a major advance. Briefly, orienting marks are made in the retina whilst in the eye-cup, the retina is then dissected out and flattened with the help of a number of relaxing cuts. The flat-mount facilitated quantitative descriptions of the 2D distributions of different labels and markers across the retina. However, the relaxing cuts, together with tears that can occur during flattening, disturbs the retinal geometry significantly, which not only complicates comparison across retinae, but also can be problematic in interpreting results obtained from individual flat-mounted retinae. For example, various measures are used to quantify the regularity of mosaics of various cell types seen in flat-mounted retinae [11], [12], but these are susceptible to the existence of boundaries [13], both at the rim of the retina and those introduced by the relaxing cuts. In the study of topographic mapping, the locations of ganglion cells labelled by retrograde tracers injected into different locations in the target, the superior colliculus, have been compared in retinal flat-mounts [4], [5]. Foci of labelled cells can be separated, or even split, by relaxing cuts (see Figure 1A), complicating quantitative analyses.

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