Cortical surfaces no longer cross: four meshes deform together, zero collisions in 92% of 560 cases

All four cortical surfaces now move together under one deformation of the ambient space instead of each following its own mesh-level trajectory. Earlier explicit mesh-deformation methods either reconstructed white matter then pial surfaces sequentially or exchanged features only between paired surfaces within a hemisphere, leaving cross-surface relationships unconstrained. Across 560 cases from 14 cohorts, SimCortex v2 showed no detected inter-surface collision in 92.14% (516/560) of cases, while every learning-based baseline produced at least one collision in every case.

Initial mesh quality is raised before deformation, with pial surfaces searched outward from the white-matter distance field. SimCortex v1's accuracy was limited by the quality of initial white-matter surfaces in highly folded regions, where errors propagated through deformation into smoother, shallower sulcal reconstructions. Initialization checks left-right white matter, ipsilateral white-pial, and left-right pial collisions; all 560 evaluated cases passed and no fallback was triggered.

The deformation network reads both the T1 image and a cortical ribbon probability map, fusing the two streams through a learned gate. Supplying the ribbon as an extra input channel alone is not enough; a sufficiently deep dedicated geometry pathway with multi-scale fusion is needed to exploit it. In ablations, removing the dedicated ribbon encoder and gated fusion raised mean symmetric surface distance, and removing the residual normalized backbone raised it further, with the full model ahead on all 14 datasets.

The training objective adds explicit separation and white-pial nesting penalties. Deformation smoothness or feature exchange alone reduces crossings only empirically and cannot constrain the relative position of vertices on different surfaces. Removing these two losses left mean surface distance essentially unchanged but raised mean union collision by roughly three orders of magnitude and dropped the collision-free case rate from 92.14% to zero.

Evaluation covers 560 cases from 14 cohorts, ages 6 to 89, spanning healthy and clinical populations and scanners from three vendors, with 13 cohorts unseen during training. Reference surfaces come from FreeSurfer 7.4.1 and serve as an unedited silver standard, so all distance and thickness metrics are defined relative to it. The method uses T1-weighted MRI mapped to MNI152 space and was not assessed on acquisition protocols or pathology-related morphology far from the training distribution. The reconstructions do not establish vertex-wise correspondence, so vertex-wise group analyses would need an additional surface-registration or resampling step.

Reference surfaces are a FreeSurfer silver standard rather than manually verified ground truth, so distance and thickness metrics inherit its own inaccuracies; cortical thickness is estimated as nearest-surface white-to-pial distance and is not based on anatomical vertex correspondence. Some same-hemisphere white-pial contacts near the medial wall may be anatomically expected yet still counted as collisions, which can slightly inflate collision values, including for the reference pipeline. Baselines were not retrained on the evaluation data, and the training data and silver-standard versions may differ across methods. All training scans were high-quality research-grade T1-weighted images, so the model has not seen the lower resolution, reduced contrast, and motion artifacts common in routine clinical acquisition, and accuracy may degrade there. The method was evaluated on geometric metrics only; its effect on downstream morphometric and population-level analyses was not measured.