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Piecewise Multivariate Linearity Between Kinematic Features and Cumulative Strain Damage Measure (CSDM) Across Different Types of Head Impacts

  • S.I.: Concussions
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Abstract

In a previous study, we found that the relationship between brain strain and kinematic features cannot be described by a generalized linear model across different types of head impacts. In this study, we investigate if such a linear relationship exists when partitioning head impacts using a data-driven approach. We applied the K-means clustering method to partition 3161 impacts from various sources including simulation, college football, mixed martial arts, and car crashes. We found piecewise multivariate linearity between the cumulative strain damage (CSDM; assessed at the threshold of 0.15) and head kinematic features. Compared with the linear regression models without partition and the partition according to the types of head impacts, K-means-based data-driven partition showed significantly higher CSDM regression accuracy, which suggested the presence of piecewise multivariate linearity across types of head impacts. Additionally, we compared the piecewise linearity with the partitions based on individual features used in clustering. We found that the partition with maximum angular acceleration magnitude at 4706 rad/s2 led to the highest piecewise linearity. This study may contribute to an improved method for the rapid prediction of CSDM in the future.

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Acknowledgments

This research was supported by the Pac-12 Conference’s Student-Athlete Health and Well-Being Initiative, the National Institutes of Health (R24NS098518), Taube Stanford Children’s Concussion Initiative and Stanford Department of Bioengineering.

Author Contributions

XZ, YL and YuL conceived this study, XZ and YL did the experiment and analyzed the data, YL, DC supervised this study, XZ, YL and YL wrote the manuscript, OG, MZ and GG revised the manuscript.

Conflict of interest

The authors declare no competing interests.

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Author notes

  1. Xianghao Zhan and Yiheng Li contributed equally to this work.

Authors and Affiliations

  1. Department of Bioengineering, Stanford University, Stanford, CA, 94305, USA

    Xianghao Zhan, Yuzhe Liu, Nicholas J. Cecchi & David B. Camarillo

  2. Department of Biomedical Data Science, Stanford University, Stanford, CA, 94305, USA

    Yiheng Li & Olivier Gevaert

  3. Stanford Center for Biomedical Informatics Research, Stanford University, Stanford, CA, 94305, USA

    Olivier Gevaert

  4. Department of Radiology, Stanford University, Stanford, CA, 94305, USA

    Michael M. Zeineh

  5. Department of Neurosurgery, Stanford University, Stanford, CA, 94305, USA

    Gerald A. Grant

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  1. Xianghao Zhan
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Correspondence to Yuzhe Liu.

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10439_2022_3020_MOESM1_ESM.pdf

Supplementary file1 (PDF 836 kb) Figure S1 The CSDM regression RMSE with ridge regression and different methods on four different types of head impacts. The CSDM regression RMSE on the simulated impacts (dataset HM, a); on-field test impacts originated from dataset CF (b); dataset MMA (c), and dataset NASCAR (d). Kmeans-1/2/3: the K-means clustering method with the first/second/third critical feature: the maximum resultant angular acceleration, the maximum angular acceleration along the z-axis, the maximum linear acceleration along the y-axis. Figure S2 The CSDM regression \({R}^{2}\) with ridge regression and different methods on four different types of head impacts with different numbers of clusters. The CSDM regression \({R}^{2}\) on the simulated impacts (dataset HM, a); on-field test impacts originated from dataset CF (b); dataset MMA (c); and dataset NASCAR (d). Kmeans2/3/4: the number of clusters equals 2/3/4. It should be noted that the results here are based on clustering on all kinematic features. Figure S3 The averaged CSDM regression \({R}^{2}\) with ridge regression and different methods across four different types of head impacts with different numbers of clusters. Kmeans2/3/4: the number of clusters equals 2/3/4. It should be noted that the results here are based on clustering on all kinematic features

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Zhan, X., Li, Y., Liu, Y. et al. Piecewise Multivariate Linearity Between Kinematic Features and Cumulative Strain Damage Measure (CSDM) Across Different Types of Head Impacts. Ann Biomed Eng 50, 1596–1607 (2022). https://doi.org/10.1007/s10439-022-03020-0

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