A network-based response feature matrix as a brain injury metric

  • Shaoju Wu
  • Wei Zhao
  • Bethany Rowson
  • Steven Rowson
  • Songbai JiEmail author
Original Paper


Conventional brain injury metrics are scalars that treat the whole head/brain as a single unit but do not characterize the distribution of brain responses. Here, we establish a network-based “response feature matrix” to characterize the magnitude and distribution of impact-induced brain strains. The network nodes and edges encode injury risks to the gray matter regions and their white matter interconnections, respectively. The utility of the metric is illustrated in injury prediction using three independent, real-world datasets: two reconstructed impact datasets from the National Football League (NFL) and Virginia Tech, respectively, and measured concussive and non-injury impacts from Stanford University. Injury predictions with leave-one-out cross-validation are conducted using the two reconstructed datasets separately, and then by combining all datasets into one. Using support vector machine, the network-based injury predictor consistently outperforms four baseline scalar metrics including peak maximum principal strain of the whole brain (MPS), peak linear/rotational acceleration, and peak rotational velocity across all five selected performance measures (e.g., maximized accuracy of 0.887 vs. 0.774 and 0.849 for MPS and rotational acceleration with corresponding positive predictive values of 0.938, 0.772, and 0.800, respectively, using the reconstructed NFL dataset). With sufficient training data, real-world injury prediction is similar to leave-one-out in-sample evaluation, suggesting the potential advantage of the network-based injury metric over conventional scalar metrics. The network-based response feature matrix significantly extends scalar metrics by sampling the brain strains more completely, which may serve as a useful framework potentially allowing for other applications such as characterizing injury patterns or facilitating targeted multi-scale modeling in the future.


Concussion Brain structural network Traumatic brain injury Support vector machine Worcester head injury model 



Funding is provided by the NIH Grant R01 NS092853. The authors are grateful to Dr. David B. Camarillo at Stanford University for data sharing. They also thank Dr. Zheyang Wu at Worcester Polytechnic Institute for help on statistical analysis.

Compliance with ethical standards

Conflict of interest

We have no competing interests.


  1. Agoston DV, Langford D (2017) Big Data in traumatic brain injury; promise and challenges. Concussion (London, England) 2:CNC45. CrossRefGoogle Scholar
  2. Bain AC, Meaney DF (2000) Tissue-level thresholds for axonal damage in an experimental model of central nervous system white matter injury. J Biomech Eng 122:615–622. CrossRefGoogle Scholar
  3. Beckwith JG, Greenwald RM, Chu JJ (2012) Measuring head kinematics in football: correlation between the head impact telemetry system and Hybrid III headform. Ann Biomed Eng 40:237–248. CrossRefGoogle Scholar
  4. Beckwith JG, Greenwald RM, Chu JJ et al (2013) Head impact exposure sustained by football players on days of diagnosed Concussion. Med Sci Sports Exerc 45:737–746. CrossRefGoogle Scholar
  5. Beckwith JG, Zhao W, Ji S et al (2018) Estimated brain tissue response following impacts associated with and without diagnosed concussion. Ann Biomed Eng 46:819–830. CrossRefGoogle Scholar
  6. Bigler ED (2016) Systems biology, neuroimaging, neuropsychology, neuroconnectivity and traumatic brain injury. Front Syst Neurosci 10:1–23. CrossRefGoogle Scholar
  7. Bigler ED, Maxwell WL (2012) Neuropathology of mild traumatic brain injury: relationship to neuroimaging findings. Brain Imaging Behav 6:108–136. CrossRefGoogle Scholar
  8. Cai Y, Wu S, Zhao W et al (2018) Concussion classification via deep learning using whole-brain white matter fiber strains. PLoS ONE 13:e0197992. CrossRefGoogle Scholar
  9. Chen Y, Lin C (2006) Combining SVMs with various feature selection strategies. Strategies 324:1–10. CrossRefGoogle Scholar
  10. Cloots RJH (2011) Multi-scale mechanics of traumatic brain injury. Technische Universiteit EindhovenGoogle Scholar
  11. Cloots RJH, van Dommelen JAW, Kleiven S, Geers MGD (2012) Multi-scale mechanics of traumatic brain injury: predicting axonal strains from head loads. Biomech Model Mechanobiol 12:137–150. CrossRefGoogle Scholar
  12. Crisco JJ, Chu JJ, Greenwald RM (2004) An algorithm for estimating acceleration magnitude and impact location using multiple nonorthogonal single-axis accelerometers. J Biomech Eng 126:849–854CrossRefGoogle Scholar
  13. Duhaime A-C, Beckwith JG, Maerlender AC et al (2012) Spectrum of acute clinical characteristics of diagnosed concussions in college athletes wearing instrumented helmets. J Neurosurg 117:1092–1099. CrossRefGoogle Scholar
  14. Fornito A, Zalesky A, Bullmore E (eds) (2016) Fundamentals of brain network analysis. Elsevier/Academic Press Amsterdam, BostonGoogle Scholar
  15. Ganpule S, Daphalapurkar NP, Ramesh KT et al (2017) A three-dimensional computational human head model that captures live human brain dynamics. J Neurotrauma 34:2154–2166. CrossRefGoogle Scholar
  16. Giordano C, Kleiven S (2014) Evaluation of axonal strain as a predictor for mild traumatic brain injuries using finite element modeling. Stapp Car Crash J 58:29–61Google Scholar
  17. Giordano C, Kleiven S (2016) Development of an unbiased validation protocol to assess the biofidelity of finite element head models used in prediction of traumatic brain injury. Stapp Car Crash J 60:363–471Google Scholar
  18. Giordano C, Zappalà S, Kleiven S (2017) Anisotropic finite element models for brain injury prediction: the sensitivity of axonal strain to white matter tract inter-subject variability. Biomech Model Mechanobiol 16:1269–1293. CrossRefGoogle Scholar
  19. Greenwald RM, Gwin JT, Chu JJ, Crisco JJ (2008) Head impact severity measures for evaluating mild traumatic brain injury risk exposure. Neurosurgery 62:789–798. CrossRefGoogle Scholar
  20. Hastie T, Tibshirani R, Friedman J (2008) The elements of statistical learning, data mining, inference, and prediction, 2nd edn. Springer, BerlinzbMATHGoogle Scholar
  21. Hernandez F, Wu LC, Yip MC et al (2015) Six degree-of-freedom measurements of human mild traumatic brain injury. Ann Biomed Eng 43:1918–1934. CrossRefGoogle Scholar
  22. Hernandez F, Giordano C, Goubran M et al (2019) Lateral impacts correlate with falx cerebri displacement and corpus callosum trauma in sports-related concussions. Biomech Model Mechanobiol. CrossRefGoogle Scholar
  23. Hira ZM, Gillies DF (2015) A review of feature selection and feature extraction methods applied on microarray data. Adv Bioinformatics 2015:198363. CrossRefGoogle Scholar
  24. Ho J, Kleiven S (2009) Can sulci protect the brain from traumatic injury? J Biomech 42:2074–2080. CrossRefGoogle Scholar
  25. Ji S, Ghadyani H, Bolander R et al (2014) Parametric comparisons of intracranial mechanical responses from three validated finite element models of the human head. Ann Biomed Eng 42:11–24. CrossRefGoogle Scholar
  26. Ji S, Zhao W, Ford JC et al (2015) Group-wise evaluation and comparison of white matter fiber strain and maximum principal strain in sports-related concussion. J Neurotrauma 32:441–454. CrossRefGoogle Scholar
  27. Khvostikov A, Aderghal K, Benois-Pineau J, Krylov A, Catheline G (2018) 3D CNN-based classification using sMRI and MD-DTI images for Alzheimer disease studies. arXiv preprint arXiv:1801.05968
  28. Kimpara H, Iwamoto M (2012) Mild traumatic brain injury predictors based on angular accelerations during impacts. Ann Biomed Eng 40:114–126. CrossRefGoogle Scholar
  29. King AIAI, Yang KHKH, Zhang L et al (2003) Is head injury caused by linear or angular acceleration? In: IRCOBI conference. Lisbon, Portugal, Portugal, pp 1–12Google Scholar
  30. Kleiven S (2007) Predictors for traumatic brain injuries evaluated through accident reconstructions. Stapp Car Crash J 51:81–114Google Scholar
  31. Koerte IK, Lin AP, Willems A et al (2015) A review of neuroimaging findings in repetitive brain trauma. Brain Pathol 25:318–349. CrossRefGoogle Scholar
  32. Kraft RH, Mckee PJ, Dagro AM, Grafton ST (2012) Combining the finite element method with structural connectome-based analysis for modeling neurotrauma: connectome neurotrauma mechanics. PLoS Comput Biol 8:e1002619. MathSciNetCrossRefGoogle Scholar
  33. Kuo C, Wu L, Zhao W et al (2017) Propagation of errors from skull kinematic measurements to finite element tissue responses. Biomech Model Mechanobiol 17:235–247. CrossRefGoogle Scholar
  34. Leemans A, Jeurissen B, Siibers J, Jones D (2009) ExploreDTI: a graphical tool box for processing, analyzing, and visualizing diffusion MR data. In: 17th annual meeting of the international society of magnetic resonance in medicine. Hawaii, USAGoogle Scholar
  35. Levin HS, Williams D, Crofford MJ et al (1988) Relationship of depth of brain lesions to consciousness and outcome after closed head injury. J Neurosurg 69:861–866. CrossRefGoogle Scholar
  36. Mao H, Zhang L, Jiang B et al (2013) Development of a finite element human head model partially validated with thirty five experimental cases. J Biomech Eng 135:111002–111015. CrossRefGoogle Scholar
  37. Miller LE, Urban JE, Stitzel JD (2016) Development and validation of an atlas-based finite element brain model. Biomech Model 15:1201–1214. CrossRefGoogle Scholar
  38. Mohammadipour A, Alemi A (2017) Micromechanical analysis of brain’s diffuse axonal injury. J Biomech 65:61–74. CrossRefGoogle Scholar
  39. Montanino A, Kleiven S (2018) Utilizing a structural mechanics approach to assess the primary effects of injury loads onto the axon and its components. Front Neurol 9:643. CrossRefGoogle Scholar
  40. Montenigro PH, Alosco ML, Martin BM et al (2017) Cumulative head impact exposure predicts later-life depression, apathy, executive dysfunction, and cognitive impairment in former high school and college football players. J Neurotrauma 13:55. CrossRefGoogle Scholar
  41. Newman JA, Beusenberg MC, Shewchenko N et al (2005) Verification of biomechanical methods employed in a comprehensive study of mild traumatic brain injury and the effectiveness of American football helmets. J Biomech 38:1469–1481. CrossRefGoogle Scholar
  42. NRC I (2014) Sports-related concussions in youth: improving the science, changing the culture. Washington, DCGoogle Scholar
  43. Park HJ, Friston K (2013) Structural and functional brain networks: from connections to cognition. Science. CrossRefGoogle Scholar
  44. Qi S, Meesters S, Nicolay K et al (2015) The influence of construction methodology on structural brain network measures: a review. J Neurosci Methods 253:170–182. CrossRefGoogle Scholar
  45. Rathore S, Habes M, Iftikhar MA et al (2017) A review on neuroimaging-based classification studies and associated feature extraction methods for Alzheimer’s disease and its prodromal stages. Neuroimage 155:530–548CrossRefGoogle Scholar
  46. Rowson B (2016) Evaluation and application of brain injury criteria to improve protective headgear design. Virginia TechGoogle Scholar
  47. Rowson S, Duma SM (2013) Brain injury prediction: assessing the combined probability of concussion using linear and rotational head acceleration. Ann Biomed Eng 41:873–882. CrossRefGoogle Scholar
  48. Rowson S, Duma SM, Beckwith JG et al (2012) Rotational head kinematics in football impacts: an injury risk function for concussion. Ann Biomed Eng 40:1–13. CrossRefGoogle Scholar
  49. Rowson S, Duma SM, Stemper BD et al (2018) Correlation of concussion symptom profile with head impact biomechanics: a case for individual-specific injury tolerance. J Neurotrauma 35:681–690. CrossRefGoogle Scholar
  50. Rowson S, Campolettano ET, Duma SM et al (2019) Accounting for variance in concussion tolerance between individuals: comparing head accelerations between concussed and physically matched control subjects. Ann Biomed Eng. CrossRefGoogle Scholar
  51. Sabet AA, Christoforou E, Zatlin B et al (2008) Deformation of the human brain induced by mild angular head acceleration. J Biomech 41:307–315. CrossRefGoogle Scholar
  52. Sahoo D, Deck C, Willinger R (2014) Development and validation of an advanced anisotropic visco-hyperelastic human brain FE model. J Mech Behav Biomed Mater 33:24–42. CrossRefGoogle Scholar
  53. Sahoo D, Deck C, Willinger R (2016) Brain injury tolerance limit based on computation of axonal strain. Accid Anal Prev 92:53–70. CrossRefGoogle Scholar
  54. Sanchez EJ, Gabler LF, McGhee JS et al (2017) Evaluation of head and brain injury risk functions using sub-injurious human volunteer data. J Neurotrauma 34:2410–2424. CrossRefGoogle Scholar
  55. Sanchez EJ, Gabler LF, Good AB et al (2018) A reanalysis of football impact reconstructions for head kinematics and finite element modeling. Clin Biomech. CrossRefGoogle Scholar
  56. Shattuck D, Mirza M, Adisetiyo V et al (2008) Construction of a 3D probabilistic atlas of human cortical structures. Neuroimage 39:1064–1080CrossRefGoogle Scholar
  57. Šimundić A-M (2009) Measures of diagnostic accuracy: basic definitions. EJIFCC 19:203–211Google Scholar
  58. Smith SM, Jenkinson M, Woolrich MW et al (2004) Advances in functional and structural MR image analysis and implementation as FSL. Neuroimage 23:S208–S219CrossRefGoogle Scholar
  59. Sporns O (2013) Structure and function of complex brain networks. Dialogues Clin Neurosci 15:247–262Google Scholar
  60. Stemper BD, Shah AS, Harezlak J et al (2018) Comparison of head impact exposure between concussed football athletes and matched controls: evidence for a possible second mechanism of sport-related concussion. Ann Biomed Eng. CrossRefGoogle Scholar
  61. Takhounts EG, Ridella SA, Tannous RE et al (2008) Investigation of traumatic brain injuries using the next generation of simulated injury monitor (SIMon) finite element head model. Stapp Car Crash J 52:1–31Google Scholar
  62. Takhounts EGG, Craig MJJ, Moorhouse K et al (2013) Development of brain injury criteria (Br IC). Stapp Car Crash J 57:243–266Google Scholar
  63. Versace J (1971) A review of the severity index. In: 15th stapp car crash conference. Coronado, CA, USA, p SAE paper 710881Google Scholar
  64. Viano DC, Casson IR, Pellman EJ et al (2005) Concussion in professional football: brain responses by finite element analysis: part 9. Neurosurgery 57:891–915. CrossRefGoogle Scholar
  65. Wu LC, Nangia V, Bui K et al (2015) In vivo evaluation of wearable head impact sensors. Ann Biomed Eng 44:1234–1245. CrossRefGoogle Scholar
  66. Wu LC, Kuo C, Loza J et al (2018) Detection of american football head impacts using biomechanical features and support vector machine classification. Sci Rep 8:1–14. CrossRefGoogle Scholar
  67. Wu T, Alshareef A, Giudice JS, Panzer MB (2019) Explicit modeling of white matter axonal fiber tracts in a finite element brain model. Ann Biomed Eng. CrossRefGoogle Scholar
  68. Yanaoka T, Dokko Y, Takahashi Y (2015) Investigation on an injury criterion related to traumatic brain injury primarily induced by head rotation. SAE Tech Pap 2015-01-1439.
  69. Zhang L, Yang KHH, King AII (2004) A proposed injury threshold for mild traumatic brain injury. J Biomech Eng 126:226–236. CrossRefGoogle Scholar
  70. Zhao W, Ji S (2017) Brain strain uncertainty due to shape variation in and simplification of head angular velocity profiles. Biomech Model Mechanobiol 16:449–461. CrossRefGoogle Scholar
  71. Zhao W, Ji S (2019a) Mesh convergence behavior and the effect of element integration of a human head injury model. Ann Biomed Eng 47:475–486. CrossRefGoogle Scholar
  72. Zhao W, Ji S (2019b) White matter anisotropy for impact simulation and response sampling in traumatic brain injury. J Neurotrauma 36:250–263. CrossRefGoogle Scholar
  73. Zhao W, Ford JC, Flashman LA et al (2016) White matter injury susceptibility via fiber strain evaluation using whole-brain tractography. J Neurotrauma 33:1834–1847. CrossRefGoogle Scholar
  74. Zhao W, Cai Y, Li Z, Ji S (2017) Injury prediction and vulnerability assessment using strain and susceptibility measures of the deep white matter. Biomech Model Mechanobiol 16:1709–1727. CrossRefGoogle Scholar
  75. Zhao W, Choate B, Ji S (2018) Material properties of the brain in injury-relevant conditions—experiments and computational modeling. J Mech Behav Biomed Mater 80:222–234. CrossRefGoogle Scholar
  76. Zhao W, Bartsch A, Benzel E et al (2019) Regional brain injury vulnerability in football from two finite element models of the human head. IRCOBI. Florence, Italy, pp 619–621Google Scholar
  77. Zhou Z, Li X, Kleiven S, Hardy WN (2018) A reanalysis of experimental brain strain data: implication for finite element head model validation. Stapp Car Crash J 62:1–26Google Scholar
  78. Zhu F, Gatti DL, Yang KH (2016) Nodal versus total axonal strain and the role of cholesterol in traumatic brain injury. J Neurotrauma 33:859–870. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Biomedical EngineeringWorcester Polytechnic InstituteWorcesterUSA
  2. 2.Department of Biomedical Engineering and MechanicsVirginia TechBlacksburgUSA
  3. 3.Department of Mechanical EngineeringWorcester Polytechnic InstituteWorcesterUSA

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