Finding the Spatial Co-Variation of Brain Deformation With Principal Component Analysis

Objective: Strain and strain rate are effective traumatic brain injury metrics. In finite element (FE) head model, thousands of elements were used to represent the spatial distribution of these metrics. Owing that these metrics are resulted from brain inertia, their spatial distribution can be represented in more concise pattern. Since head kinematic features and brain deformation vary largely across head impact types (Zhan et al. , 2021), we applied principal component analysis (PCA) to find the spatial co-variation of injury metrics (maximum principal strain (MPS), MPS rate (MPSR) and MPS x MPSR) in four impact types: simulation, football, mixed martial arts and car crashes, and used the PCA to find patterns in these metrics and improve the machine learning head model (MLHM). Methods: We applied PCA to decompose the injury metrics for all impacts in each impact type, and investigate the spatial co-variation using the first principal component (PC1). Furthermore, we developed a MLHM to predict PC1 and then inverse-transform to predict for all brain elements. The accuracy, the model complexity and the size of training dataset of PCA-MLHM are compared with previous MLHM (Zhan et al. , 2021). Results: PC1 explained >80% variance on the datasets. Based on PC1 coefficients, the corpus callosum and midbrain exhibit high variance on all datasets. Finally, the PCA-MLHM reduced model parameters by 74% with a similar MPS estimation accuracy. Conclusion: The brain injury metric in a dataset can be decomposed into mean components and PC1 with high explained variance. Significance: The spatial co-variation analysis enables better interpretation of the patterns in brain injury metrics. It also improves the efficiency of MLHM.

Automated summary

The study utilized principal component analysis (PCA) to analyze the spatial co-variation of injury metrics in four types of head impacts, aiding in the improvement of the machine learning head model (MLHM). PCA-MLHM reduced model parameters by 74% with comparable MPS estimation accuracy.