Toward subject-specific evaluation: methods of evaluating finite element brain models using experimental high-rate rotational brain motion

Abstract

Computational models of the brain have become the gold standard in biomechanics to understand, predict, and mitigate traumatic brain injuries. Many models have been created and evaluated with limited experimental data and without accounting for subject-specific morphometry of the specimens in the dataset. Recent advancements in the measurement of brain motion using sonomicrometry allow for a comprehensive evaluation of brain model biofidelity using a high-rate, rotational brain motion dataset. In this study, four methods were used to determine the best technique to compare nodal displacement to experimental brain motion, including a new morphing method to match subject-specific inner skull geometry. Three finite element brain models were evaluated in this study: the isotropic GHBMC and SIMon models, as well as an anisotropic model with explicitly embedded axons (UVA-EAM). Using a weighted cross-correlation score (between 0 and 1), the anisotropic model yielded the highest average scores across specimens and loading conditions ranging from 0.53 to 0.63, followed by the isotropic GHBMC with average scores ranging from 0.46 to 0.58, and then the SIMon model with average scores ranging from 0.36 to 0.51. The choice of comparison method did not significantly affect the cross-correlation score, and differences of global strain up to 0.1 were found for the morphed geometry relative to baseline models. The morphed or scaled geometry is recommended when evaluating computational brain models to capture the subject-specific skull geometry of the experimental specimens.

Appendix: Morphing technique

A morphing technique was implemented to match the geometry of the specimens to a target geometry. A technique utilized and adapted by Park (2017) (Park et al. 2017) for the subject-specific FE modeling of human femurs was extended to the brain in order to accurately match the geometries. The morphing methodology involved four steps: FE model and specimen geometry preparation, rigid body alignment, surface registration, and 3D volume morphing (Fig. 8). The steps are applied below to morph a specimen geometry to the GHBMC brain model, but the same method can be applied to any FE model or parametric space.

Fig. 8

Representation of the morphing process, with the GHBMC brain model as an example. The morphing process includes four main steps: (1) surface preparation and segmentation, (2) rigid body alignment and scaling, (3) surface registration, and (4) volume morphing and evaluation

In the preparation stage, the inner cranial geometry of the specimen was segmented from the computed tomography (CT) scans using Mimics 19.0 (Materialise, Plymouth, MI). The segmented geometry included everything in the cranial vault up to the inner skull. A thresholding value was used to apply a mask to the desired geometry, followed by manual editing of the mask in areas with inconsistent edges and inferior regions of the cranium. The mask was used to extract the 3D brain cranial geometry of each specimen. The target geometry of the FE brain models was prepared by extracting the outermost layer of the model, the skull or dura.

To align the two surfaces, the specimen geometry was first rotated and centered to match the coordinate system of the FE model. Once the two surfaces were closely aligned using manual rigid body rotation, an iterative closest point approximation (ICP) (Besl and McKay 1992) was used to match the initial rigid body position of the surfaces. The specimen geometry was then scaled to the target external geometry of the FE model in all three directions (x, y, z) to minimize volume differences between the two geometries. The scaling factors were used to scale back the target geometry after the surface registration as to not affect the 3D volume morphing.

Next, control points were selected to map the FE model surface to the specimen surface. In typical biomechanical morphing techniques, control points are chosen based on automated spatial segmentation or a manual assignment based on prominent anatomical features. These methods were difficult for segmented brain CT scans because the shape of the brain may vary significantly, and manual assignment of landmarks may lead to large user error. To minimize errors in the choice of landmarks, an iterative registration method based on the 3D generalization of Burr’s elastic registration (Bryan et al. 2010), was used to match the external geometry of the two surfaces. All the points in each model, which were mapped in the surface registration, were utilized as landmarks to convert the FE brain model geometry to the specimen brain geometry using the registration algorithm. The accuracy of the registration method was evaluated using an average minimum distance error which was the average distance between nodes on the target surface and the surface of the specimen geometry.

The transformations used to match the control points in the registration step were then applied to the internal nodes of the FE brain model to morph the 3D volume to the external geometry of the specimen using radial basis functions with thin-plate splines (Rohr et al. 2001). The normalized Jacobian ratio of all elements in the morphed model was quantified to ensure comparable element quality of the morphed model to the original FE brain models.

The morphing methodology implemented to account for specimen anthropometry provides an important advancement in FE brain modeling. The technique facilitates matching the exact inner cranium shape of the model and specimens, not only the size and volume. The average minimum distance between the surface of the FE model and the surface of each specimen CT was less than 1 mm. While morphing has been attempted through conventional control point morphing (Horgan and Gilchrist 2004; Li et al. 2011) and the generation of new voxel models (Ghajari et al. 2017; Miller et al. 2016), the use of an automated process of picking and registering control points is important in generating an accurate specimen-specific model. The researcher does not have to manually select control points, which can be laborious and error-prone. Instead, all the nodes of the specimen geometry and model are used as control points, to generate a smooth, accurate morphed model automatically. A limitation of the morphing methodology for FE brain models is that it does not address the differences in internal anatomy between subjects, such as ventricle size, regional organization of brain regions, and size of the brain. The morphing methodology only registers the outside surface. Consequently, the internal anatomy is scaled according to the surface. Future methods that incorporate subject-specific morphing or model development of the brain using MRI scans are needed to accurately model and predict subject-specific brain injury.