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


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.

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Correspondence to Matthew B. Panzer.

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Associate Editor Stefan M. Duma oversaw the review of this article.

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Gabler, L.F., Crandall, J.R. & Panzer, M.B. Development of a Second-Order System for Rapid Estimation of Maximum Brain Strain. Ann Biomed Eng 47, 1971–1981 (2019).

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  • Brain deformation
  • Finite element model
  • Head kinematics
  • Second-order system