10 µm grids give a 67.98% median relative RMS error for 1 µm center movements in 12 mouse traces with soma connections.

We measured how radius-grid spacing and offset change the absolute difference between Sholl profiles after a center movement. The analysis used 12 mouse neuron traces from the Allen Cell Types Database (2015), with 72 repeated comparisons at each movement and spacing. For 1 µm movements with soma connections, the median relative RMS error across uniform grid offset was 10.7785% at 1 µm spacing, 44.5315% at 5 µm, and 67.9780% at 10 µm. At 10 µm spacing, all 72 comparisons had some offset length with error above 50% of the continuous difference; the median such fraction was 42.0624%. These are summaries of this fixed sample, not population estimates or biological error rates. Removing soma connections gave a 56.8436% median at 10 µm spacing for 1 µm movements. The mean grid estimate equals the continuous difference under the uniform-offset calculation, but individual offsets can have large errors. One of 864 numerical extrema differed between binary64 and 50-digit decimal arithmetic (103 versus 102 count·µm); the discrepancy is retained and does not affect the RMS result. The stored paths, movements, coordinate scale, and uniform offset are calculation assumptions. The study does not establish a biological cause or a general radius-spacing rule.

Sholl analysis · neuron morphology · radius grid · sampling offset · numerical integration · sensitivity analysis · Allen Cell Types Database