cart2jpolar {visualFields}

The Jansonius map for average path of nerve fiber bundles

Description

Generates a function that renders the average path of a nerve fiber bundle that exits through the optic nerve head (ONH) with a particular angle

Usage

cart2jpolar(coord)

jpolar2cart(rpsi)

bundlePath(psi0, r0 = 4)

loc2psi(coord, r0 = 4)

psi2oct(psi0, diam = 12)

vf2gc(coord, angle = 0)

Arguments

coord

coordinates of locations in the visual field

rpsi

visual field locations in polar coordinates of the distorted space of the Jansonius map

psi0

angle of incidence at the ONH

r0

radius of the ONH. Its default value is 4. Changing it changes the calculated average bundle paths.

diam

diamater in degrees of visual angle of the OCT circular scan centered at the center of the ONH

angle

fovea-disc angle in degrees

Details

• cart2jpolar converts the cartesian coordinates to the polar coordinates in the distorted space used in the Jansonius map

• jpolar2cart converts back from the Jansonius polar coordinates to cartesian coordinates

• bundlePath returns a function describing the expected fiber path given an angle of incidence on the ONH

• loc2psi returns the angle of incidence of the average bundle path that passes through specific locations of the visual field

• psi2oct returns the angle of OCT circular scans corresponding to average bundle paths with specific angle of incidence at the ONH

• vf2gc calculates ganglion-cell soma locations

Value

cart2jpolar: returns the Jansonius modified polar coordinates

jpolar2cart: returns Cartesian coordinates

bundlePath: returns a function describing a retinal ganglion cell bundle path

loc2psi: returns the angle of incidence on the ONH

psi2oct: returns the corresponding angle in the OCT circular scan

vf2gc: returns the ganglion cell soma corresponding to the photoreceptors of a visual field location

References

N. M. Jansonius, J. Nevalainen, B. Selig, L. M. Zangwill, P. A. Sample, W. M. Budde, J. B. Jonas, W. A. Lagreze, P. J. Airaksinen, R. Vonthein, L. A. Levin, J. Paetzold, and U. Schiefer. A mathematical description of nerve fiber bundle trajectories and their variability in the human retina. Vision Research, 49(17):2157-2163, 2009

N. M. Jansonius, J. Nevalainen, B. Selig, L. M. Zangwill, P. A. Sample, W. M. Budde, J. B. Jonas, W. A. Lagreze, P. J. Airaksinen, R. Vonthein, L. A. Levin, J. Paetzold, and U. Schiefer. Erratum to "A mathematical description of nerve fiber bundle trajectories and their variability in the human retina". Vision Research, 50:1501, 2010

N. M. Jansonius, J. Schiefer, J. Nevalainen, J. Paetzold, and U. Schiefer. A mathematical model for describing the retinal nerve fiber bundle trajectories in the human eye: Average course, variability, and influence of refraction, optic disc size and optic disc position. Experimental Eye Research, 105:70-78, 2012

N. Drasdo, C. L. Millican, C. R. Katholi, and C. A. Curcio. The length of Henle fibers in the human retina and a model of ganglion receptive field density in the visual field. Vision Research, 47:2901–2911, 2007

D. C. Hood, A. S. Raza, D. M. C. G. V., J. G. Odel, V. C. Greenstein, J. M. Liebmann, and R. Ritch. Initial arcuate defects within the central 10 degrees in glaucoma. Investigative Ophthalmology and Visual Science, 52(2):940-946, 2011

A. S. Raza, J. Cho, D. M. C. G. V., H. Wang, X. Zhang, R. H. Kardon, J. M. Liebmann, R. Ritch, and D. C. Hood. Retinal ganglion cell layer thickness and local visual field sensitivity in glaucoma. Archives of Ophthalmology, 129(12):1529-1536, 2011

G. Montesano, G. Ometto, R. E. Hogg, L. M. Rossetti, D. F. Garway-Heath, and D. P. Crabb. Revisiting the Drasdo Model: Implications for Structure-Function Analysis of the Macular Region. Translational Vision Science and Technology, 9(10):15, 2020

Examples

# get ganglion-cell soma locations from visual field locations
vf2gc(locmaps$p10d2$coord)
# convert to polar of the distorted space used by Jansonius map and back
coord <- data.frame(x = c(3, 0, -3), y = c(0, 0, 0))
(rpsi <- cart2jpolar(coord))
jpolar2cart(rpsi)

# get an average bundle path from a specific angle of incidence in the ONH
# The object returned is a function that returns polar angles of the
# distorted space of the Jansonius map for distances from the ONH center
pathFun <- bundlePath(-125)
jpolar2cart(data.frame(10:20, pathFun(10:20)))

# get angle of incidence in the ONH from locations of the visual field
loc2psi(coord)

# get the OCT circular scan angles from the angle of incidence in the ONH
# for the 10-2 map of locations, ...
psi2oct(loc2psi(locmaps$p10d2$coord))
# the previous operation was actually fundamentally wrong! We need to
# obtain first the 
psi2oct(loc2psi(vf2gc(locmaps$p10d2$coord)))