Research Papers

Development of a Single-Degree-of-Freedom Mechanical Model for Predicting Strain-Based Brain Injury Responses

[+] Author and Article Information
Lee F. Gabler

Department of Mechanical
and Aerospace Engineering,
Center for Applied Biomechanics,
University of Virginia,
P.O. Box 400237,
Charlottesville, VA 22904-4237
e-mail: lfg4dc@virginia.edu

Hamed Joodaki

Department of Mechanical
and Aerospace Engineering,
Center for Applied Biomechanics,
University of Virginia,
P.O. Box 400237,
Charlottesville, VA 22904-4237
e-mail: hj2vq@eservices.virginia.edu

Jeff R. Crandall

Department of Mechanical and Aerospace
Center for Applied Biomechanics,
University of Virginia,
P.O. Box 400237,
Charlottesville, VA 22904-4237
e-mail: jrc2h@virginia.edu

Matthew B. Panzer

Department of Mechanical
and Aerospace Engineering,
Center for Applied Biomechanics,
University of Virginia,
P.O. Box 400237,
Charlottesville, VA 22904-4237
e-mail: mbp2q@virginia.edu

1Corresponding author.

Manuscript received January 30, 2017; final manuscript received October 23, 2017; published online January 17, 2018. Assoc. Editor: Barclay Morrison.

J Biomech Eng 140(3), 031002 (Jan 17, 2018) (13 pages) Paper No: BIO-17-1035; doi: 10.1115/1.4038357 History: Received January 30, 2017; Revised October 23, 2017

Linking head kinematics to injury risk has been the focus of numerous brain injury criteria. Although many early forms were developed using mechanics principles, recent criteria have been developed using empirical methods based on subsets of head impact data. In this study, a single-degree-of-freedom (sDOF) mechanical analog was developed to parametrically investigate the link between rotational head kinematics and brain deformation. Model efficacy was assessed by comparing the maximum magnitude of displacement to strain-based brain injury predictors from finite element (FE) human head models. A series of idealized rotational pulses covering a broad range of acceleration and velocity magnitudes (0.1–15 krad/s2 and 1–100 rad/s) with durations between 1 and 3000 ms were applied to the mechanical models about each axis of the head. Results show that brain deformation magnitude is governed by three categories of rotational head motion each distinguished by the duration of the pulse relative to the brain's natural period: for short-duration pulses, maximum brain deformation depended primarily on angular velocity magnitude; for long-duration pulses, brain deformation depended primarily on angular acceleration magnitude; and for pulses relatively close to the natural period, brain deformation depended on both velocity and acceleration magnitudes. These results suggest that brain deformation mechanics can be adequately explained by simple mechanical systems, since FE model responses and experimental brain injury tolerances exhibited similar patterns to the sDOF model. Finally, the sDOF model was the best correlate to strain-based responses and highlighted fundamental limitations with existing rotational-based brain injury metrics.

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Grahic Jump Location
Fig. 1

sDOF mechanical system with base excitation used as an analog for brain deformation

Grahic Jump Location
Fig. 2

Idealized kinematic pulse applied to the FE and sDOF models (a) and the relationship between pulse parameters (u¨m, u˙m, Δt) in the design space (b). Increasing lines of constant pulse duration are indicated by the arrow and dotted lines. Pulse duration is inversely related to the slope of the dotted lines (π/Δt) where ΔtI<ΔtII. Short-duration pulses are indicated by region I: Δt<ΔtI, moderate duration pulses are indicated by region II: ΔtI<Δt<ΔtII (system natural period is located in this region), and long-duration pulses are indicated by region III: ΔtII<Δt.

Grahic Jump Location
Fig. 3

Design space for numerical simulations (Sec. 2.5) used in the current study. Idealized rotational pulses applied to the sDOF and FE models were constructed using Eqs. (4)(6) for the circular grid points shown above (simulations). Square, triangular, and diamond data points are the directionally dependent (x, y, z) values for u¨m and u˙m, which were taken from the 660 sled, crash, and pendulum tests, and used to define range and distribution of pulses for the parametric study (simulations).

Grahic Jump Location
Fig. 4

Contour plots showing the relationship between u¨m, u˙m, and δm for various combinations of system parameters (Δtn and ζ) using the sDOF model. Contour lines represent constant levels of δm which were normalized by the maximum value within the surface. The slope of the solid line is inversely related to the system natural period (π/Δtn).

Grahic Jump Location
Fig. 5

Contour plots showing the relationship between u¨m, u˙m, and strain-based metrics obtained from numerical simulations using GHBMC and SIMon. Contour lines represent constant levels of MPS or CSDM. Directionally dependent (x, y, z) values for u¨m and u˙m were obtained from the sled, crash, and pendulum data and are plotted (circles) to show the location of real-world head impacts relative to the strain contours generated using the idealized pulses. Dotted lines shown on CSDM plots indicate an MPS value of 25% (100th percentile element), which was used as the threshold for the onset of CSDM.

Grahic Jump Location
Fig. 6

sDOF model responses fit to the subset of GHBMC simulations for each anatomical direction. The solid and dotted lines indicate unity and ±1 root-mean-square error, respectively. Fitted values for the uniaxial parameters of the directionally dependent sDOF models are listed in Table 3.

Grahic Jump Location
Fig. 7

Contour plots showing a comparison between the fitted sDOF model responses (top row) to MPS responses determined from FE simulations using GHBMC (bottom row). Solid lines indicate directionally dependent natural periods obtained from sDOF model fits to the uniaxial GHBMC data.

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Fig. 8

Correlations between existing rotational-based metrics and the sDOF model, and strain-based metrics obtained from GHBMC using the 660 sled, crash, and pendulum tests [12]

Grahic Jump Location
Fig. 9

Contour plots for several existing kinematic-based metrics and the sDOF model. Contour lines indicate constant metric values which have been normalized by the maximum value within the response surface. For directionally dependent metrics (BrIC, HIP, RVCI, and sDOF), only a single direction is shown.



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