To anticipate an unpredicted finding that emerged across both cohorts, we found that the right hemisphere exhibits differential white matter injury compared to the left hemisphere. We used support vector regression (SVR), as implemented in LibSVM for MATLAB (29), to test for a relation between the spatial pattern of hits across the head and hemispheric asymmetries in white matter changes. This analysis was carried out over the RSHI cohort (n = 38), as that was the cohort for which we had accelerometer data. A laterality index was calculated for each participant: ((RightPost-Season – RightPre-Season) – (LeftPost-Season – LeftPre-Season))/(|RightPost-Season – RightPre-Season| + |LeftPost-Season – LeftPre-Season|) [see (30) for review and discussion]. The laterality index scales between −1 and 1 and represents the (Y) values to be predicted in the SVR model. The accelerometer output includes, for each registered hit, the azimuth (360° longitude) and elevation (180° latitude) of the impact: 0° azimuth is referenced to the back of the head, +90° azimuth is referenced to the right side of the head, −90° azimuth is referenced to the left side of the head, −90° elevation is pointing to the ground, and +90° elevation is pointing up. A 3D histogram of the cumulative number of hits in equally spaced 10° bins of azimuth and elevation was calculated for each participant (36 bins for azimuth; 18 bins for elevation). We refer to the 648 locations or bins containing the total number of impacts sustained for each player as the “spatial fingerprint” of hits for that player; those data were converted to a vector (length, 648) and normalized to have sum = 1 for all players. SVR was carried out using a linear kernel and with 20 support vectors (nu-SVR within LibSVM) using 38 folds. On each data fold, the SVR model was trained to map laterality indices to the spatial fingerprints for n − 1 subjects; the model was then tested by providing the nth participant’s spatial fingerprint or feature vector and having the model generate/predicted the laterality index. The squared correlation coefficient, between the model-based predicted and the observed laterality indices, was tested for significance in two ways. First, it was compared to the standard distribution (e.g., the critical r2 for 37 degrees of freedom for an α of 0.01 is 0.17). Second, 100,000 permutation tests were run; for each permutation, laterality indices and feature vectors were randomly shuffled, and then 38-fold cross-validation was carried out. The r2 value between SVR-predicted laterality indices and the ground truth was calculated for each permutation test, and the results were plotted as the null distribution. To visualize the results of the SVR analyses, feature weights from the SVR model for each azimuth-elevation bin were correlated across participants with observed laterality indices. The results are displayed as vectors at each location/bin of azimuth and elevation.

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