Beam-F3 error analysis and validation of Neurally-F3 equations using realistic head models

Accurate localization of the F3 point is critical for non-invasive brain stimulation, particularly in repetitive transcranial magnetic stimulation (rTMS) targeting the dorsolateral prefrontal cortex. The Beam-F3 heuristic is widely adopted due to its simplicity, yet its accuracy across realistic cranial variations has not been systematically assessed. Here, we evaluated Beam-F3 against the standard F3 location defined by the 10-20 International System using 250 realistic head models representing diverse anatomies. Beam-F3 produced significant errors, with mean deviations of 5.59 ± 1.23 mm in female models and 6.09 ± 1.52 mm in male models. The Adjusted Beam-F3 method performed worse, with mean errors of 8.12 ± 1.96 mm in females and 8.96 ± 2.16 mm in males. To address these limitations, we developed sex-specific multiple linear regression equations, termed Neurally-F3, which retain the measurable scalp-distance methodology of Beam-F3. Cross-validation confirmed robustness (R² > 0.98), and validation on an independent set of 128 head models demonstrated sub-millimeter accuracy (0.19 ± 0.11 mm in females; 0.23 ± 0.14 mm in males). Neurally-F3 preserves procedural simplicity while eliminating the systematic bias of Beam-F3. These results establish Neurally-F3 as a precise, practical solution for scalp-based F3 localization with potential to improve targeting reliability in rTMS.