Multimodal Surface Matching with Higher-Order Smoothness Constraints

The accurate alignment of brains is fundamental to the statistical sensitivity and spatial localisation of group studies in brain imaging, and cortical surface-based alignment is generally accepted to be superior to volume-based approaches at aligning cortical areas. However, human subjects have considerable variation in cortical folding, and in the location of cortical areas relative to these folds, which makes aligning cortical areas based on folding alone a challenging problem. The Multimodal Surface Matching (MSM) tool is a flexible spherical registration approach that enables accurate registration of surfaces based on a variety of different features. Using MSM, we have previously shown that using areal features such as resting state-networks and myelin maps to drive cross-subject surface alignment improves group task fMRI statistics and map sharpness. However, the initial implementation of MSMs regularisation function did not penalize all forms of surface distortion evenly. In some cases, this allowed peak distortions to exceed neurobiologically plausible limits unless the regularisation strength was increased, in which case this prevented the algorithm from fully maximizing surface alignment. Here, we propose a new regularisation penalty, derived from physically relevant equations of strain (deformation) energy, and demonstrate that its use leads to improved and more robust alignment of multi-modal imaging data. In addition, since spherical warps incorporate projection distortions that are unavoidable when mapping from a convoluted cortical surface to the sphere, we also propose constraints to enforce smooth deformation of cortical anatomies. We test the impact of this approach for longitudinal modeling of cortical development for neonates (born between 32 and 45 weeks) and demonstrate that the proposed method increases the biological interpretability of the distortion fields and improves the statistical significance of population-based analysis relative to other spherical methods.