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We present a geometric framework for aligning white matter fiber tracts. By registering fiber tracts between brains, one expects to see overlap of anatomical structures that often provide meaningful comparisons across subjects. However, the geometry of white matter tracts is highly heterogeneous, and finding direct tract-correspondence across multiple individuals remains a challenging problem. We present a novel deformation metric between tracts that allows one to compare tracts while simultaneously obtaining a registration. To accomplish this, fiber tracts are represented by an intrinsic mean along with the deformation fields represented by tangent vectors from the mean. In this setting, one can determine a parallel transport between tracts and then register corresponding tangent vectors. We present the results of bundle alignment on a population of 43 healthy adult subjects.

We present a novel method for global diffeomorphic phase alignment of time-series data from resting-state functional magnetic resonance imaging (rsfMRI) signals. Additionally, we propose a multidimensional, continuous, invariant functional representation of brain time-series data and solve a general global cost function that brings both the temporal rotations and phase reparameterizations in alignment. We define a family of cost functions for spatiotemporal warping and compare time-series warps across them. This method achieves direct alignment of time-series, allows population analysis by aligning time-series activity across subjects and shows improved global correlation maps, as well as z-scores from independent component analysis (ICA), while showing new information exploited by phase alignment that was not previously recoverable.

Background: Although nonoperative management after shoulder instability injury allows an athlete to return to play sooner than operative intervention, higher rates of recurrence have been observed after nonoperative management. However, no study has investigated the differences in performance of National Basketball Association (NBA) players after index shoulder instability events managed nonoperatively versus operatively. Purpose/Hypothesis: The purpose of this study was to identify shoulder instability events in NBA athletes and assess differences in performance after injury with nonoperative versus operative management. We hypothesized that players who undergo operative intervention have reduced risk of recurrence and are able to continue their elite level of play as opposed to those who undergo nonoperative management. Study Design: Cohort study; Level of evidence, 3. Methods: Publicly available injury data from the 1986-1987 through 2017-2018 seasons were reviewed to identify NBA athletes sustaining a shoulder instability event. In addition to characteristics, player performance information, including games played, player efficiency rating (PER), and win shares, was analyzed before and for 3 seasons after injury. Statistical learning models were applied to identify performance variables that have the greatest predictive value to determine players who would benefit from surgery. Results: A total of 60 players with shoulder instability events were identified between 1986 and 2018. After injury, 37 players (61.7%) eventually underwent surgery and 23 players (38.3%) did not. Players who were treated nonoperatively had significantly decreased PER, games played, and offensive win shares in the season after injury ( P < .05). Players who underwent surgery did not see a decline in PER, games played, or win shares. Random forest modeling found that true shooting percentage and win shares per 48 minutes were the performance variables most predictive in determining which players would benefit from surgery after shoulder instability. Conclusion: Players who underwent surgical intervention for shoulder instability maintained their PER, games played, and win share performance characteristics, whereas players who did not undergo surgery had declines in these parameters. Given the demands of shoulder function in basketball and the risk of recurrence after an instability event, surgery enhances a player’s opportunity to maintain a high level of performance after injury.