Retistruct: A package to reconstruct flattened retinae
David C Sterratt (University of Edinburgh), Daniel Lyngholm (King’s College London), David Willshaw (University of Edinburgh), Ian D Thompson (King’s College London)
We present a computational method, implemented as an R package ("Retistruct"), that overcomes this problem by reconstructing the 3D shape of the retina so that the positions of the labels in the intact retina can be inferred. The input to the algorithm is the line segments of the flattened retinal outline, with incisions and tears marked up by an expert. The retinal outline is split into triangular elements whose positions are then transformed so that they lie on a partial sphere with the expected dimensions of the intact retina. The transformation is adjusted so as to minimise a physically-inspired deformation energy function. Our validation studies indicate that the algorithm is able to estimate the position of a point on the intact retina to within 8 degrees of arc. Once reconstructed, the retina can be visualised as a 3D object or on polar or sinusoidal projections onto the plane. By inversion and rotating of the optic axis, an estimate of the projection of the reconstructed retina into visual space can be obtained.
A number of insights can be gained by using the method. (1) Because retinae are now described in a standard space, it allows for comparison of retrograde tracer experiments from a number of animals and the construction of composite anatomical maps. (2) The regions of the retinae that project onto the left or right dorsal lateral geniculate nucleus (dLGN) can be determined by injecting retrograde tracer into the dLGN (Coleman et al. 2009, Neuroscience 161:561-571; doi:http://dx.doi.org/10.1016/j.neuroscience.2009.03.045). Reconstruction allows regions of visual space that correspond to the monocular and binocular regions of the dLGN to be identified. (3) The correspondence between the density of S-opsin receptors and visual space can be measured.