Development of a Second-Order System for Rapid Estimation of Maximum Brain Strain

  • Lee F. Gabler
  • Jeff R. Crandall
  • Matthew B. PanzerEmail author
State-of-the-Art Modeling and Simulation of the Brain's Response to Mechanical Loads


Diffuse brain injuries are assessed with deformation-based criteria that utilize metrics based on rotational head kinematics to estimate brain injury severity. Although numerous metrics have been proposed, many are based on empirically-derived models that use peak kinematics, which often limit their applicability to a narrow range of head impact conditions. However, over a broad range of impact conditions, brain deformation response to rotational head motion behaves similarly to a second-order mechanical system, which utilizes the full kinematic time history of a head impact. This study describes a new brain injury metric called Diffuse Axonal Multi-Axis General Evaluation (DAMAGE). DAMAGE is based on the equations of motion of a three-degree-of-freedom, coupled 2nd-order system, and predicts maximum brain strain using the directionally dependent angular acceleration time-histories from a head impact. Parameters for the effective mass, stiffness, and damping were determined using simplified rotational pulses which were applied multiaxially to a 50th percentile adult human male finite element model. DAMAGE was then validated with a separate database of 1747 head impacts including helmet, crash, and sled tests and human volunteer responses. Relative to existing rotational brain injury metrics that were evaluated in this study, DAMAGE was found to be the best predictor of maximum brain strain.


Brain deformation Finite element model Head kinematics Second-order system 

Supplementary material

10439_2018_2179_MOESM1_ESM.pdf (90 kb)
Supplementary material 1 (PDF 89 kb)


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Copyright information

© Biomedical Engineering Society 2018

Authors and Affiliations

  • Lee F. Gabler
    • 1
  • Jeff R. Crandall
    • 1
  • Matthew B. Panzer
    • 1
    Email author
  1. 1.Department of Mechanical and Aerospace Engineering, Center for Applied BiomechanicsUniversity of VirginiaCharlottesvilleUSA

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