Displacement voxelization to resolve mesh-image mismatch: Application in deriving dense white matter fiber strains

It is common to combine biomechanical modeling and medical images for multimodal analyses. However, mesh-image mismatch may occur that prevents direct information exchange. To eliminate mesh-image mismatch, we develop a simple but elegant displacement voxelization technique based on image voxel corner nodes to achieve voxel-wise strain. We then apply the technique to derive dense white matter fiber strains along whole-brain tractography (∼35 k fiber tracts consisting of ∼3.3 million sampling points) resulting from head impact.

Displacements at image voxel corner nodes are first obtained from model simulation via scattered interpolation. Each voxel is then scaled linearly to form a unit hexahedral element. This allows convenient and efficient voxel-wise strain tensor calculation and displacement interpolation at arbitrary fiber sampling points via shape functions. Fiber strains from displacement interpolation are then compared with those from the commonly used strain tensor projection using either voxel- or element-wise strain tensors.

Based on a synthetic displacement field, fiber strains interpolated from voxelized displacement are considerably more accurate than those from strain tensor projection relative to the prescribed ground-truth (determinant of coefficient (R²) of 1.00 and root mean squared error (RMSE) of 0.01 vs. 0.87 and 0.10, respectively). For a set of real-world reconstructed head impacts (N = 53), the strain tensor projection method performs similarly poorly (R² of 0.80-0.90 and RMSE of 0.03-0.07), with overestimation strongly correlated with strain magnitude (Pearson correlation coefficient >0.9). Up to ∼15% of the fiber strains are overestimated by more than the lower bound of a conservative injury threshold of 0.09. The percentage increases to ∼37% when halving the threshold. Voxel interpolation is also significantly more efficient (15 s vs. 40 s for element strain tensor projection, without parallelization).

Voxelized displacement interpolation is considerably more accurate and efficient in deriving dense white matter fiber strains than strain tensor projection. The latter generally overestimates with overestimation magnitude strongly correlating with fiber strain magnitude. Displacement voxelization is an effective technique to eliminate mesh-image mismatch and generates a convenient image representation of tissue deformation. This technique can be generalized to broadly facilitate a diverse range of image-related biomechanical problems for multimodal analyses. The convenient image format may also promote and facilitate biomechanical data sharing in the future.