Fig. 3: A model based on Laplace’s equations demonstrates that axonal propagation speed correlates to axonal length.
From: Synchronization of visual perception within the human fovea
a, Examples of solutions to Laplace’s equations and how they linearly combine to yield new solutions. Black lines—field lines of the underlying potential, that is, trajectories along the potential gradient. Red dot, source; blue dot, sink. b, A 3D model of axonal trajectories in the human retina. Top row: left—eye geometry with sources (red circles, highlighted by black triangles) and sink (blue circle); middle—generated mesh for the numerical solution of Laplace’s equation; right—scalar field solution representing the chemical concentration diffusing from the ora serrata and fovea to the OD. Middle row (right to left): right—orientation of the concentration gradient, guiding axonal growth (orange lines); middle—example axonal trajectories following the gradient (black lines); left—RGC density across the retina used to calculate axon numbers per location. Bottom left: axon counts per location. Inset: zoomed view of the OD (small black square). c, Modeled axonal trajectories (black lines) in the foveal region corresponding to Extended Data Fig. 6c. Solid black line, fovea-to-OD axis. d, Superposition of the modeled trajectories from c with the estimated trajectories from the whole mount in Extended Data Fig. 6c. e, Comparison of the modeled and estimated trajectories for the region in d. Solid line, unity; each point represents local orientations of small image patches. f, Foveal speed data from Fig. 1g binned every 15° (mean ± s.e.m., black, axis on the left) overlaid with model axonal length (solid red line, axis on the right). T and N regions are indicated by gray bars. g, Same speed data as in f (mean ± s.e.m.) plotted against model axonal length with linear regression fit (dashed line). h, Speed data (mean ± s.d.) from Extended Data Fig. 5b by RGC type (midget, purple; parasol, green) and for foveal RGCs (black); numbers, RGCs per bin; dashed vertical lines, OD boundaries; solid lines, speeds corresponding to 100% compensation for t.t. of 10 ms (gray) and 15 ms (cyan). OD, optic disc; t.t., travel times.
