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Research Papers

Extracting Time-Accurate Acceleration Vectors From Nontrivial Accelerometer Arrangements

[+] Author and Article Information
Jennifer A. Franck

School of Engineering,
Brown University,
Providence, RI 02912
e-mail: Jennifer_Franck@brown.edu

Janet Blume

Associate Professor
School of Engineering,
Brown University,
Providence, RI 02912
e-mail: Janet_Blume@brown.edu

Joseph J. Crisco

Mem. ASME
Professor
Department of Orthopaedics,
Center for Biomedical Engineering,
Brown University,
Providence, RI 02912
e-mail: Joseph_Crisco@brown.edu

Christian Franck

Mem. ASME
Assistant Professor
School of Engineering,
Brown University,
Providence, RI 02912
e-mail: franck@brown.edu

1Corresponding author.

Manuscript received October 6, 2014; final manuscript received June 16, 2015; published online July 14, 2015. Assoc. Editor: Brian D. Stemper.

J Biomech Eng 137(9), 091004 (Sep 01, 2015) (11 pages) Paper No: BIO-14-1499; doi: 10.1115/1.4030942 History: Received October 06, 2014; Revised June 16, 2015; Online July 14, 2015

Sports-related concussions are of significant concern in many impact sports, and their detection relies on accurate measurements of the head kinematics during impact. Among the most prevalent recording technologies are videography, and more recently, the use of single-axis accelerometers mounted in a helmet, such as the HIT system. Successful extraction of the linear and angular impact accelerations depends on an accurate analysis methodology governed by the equations of motion. Current algorithms are able to estimate the magnitude of acceleration and hit location, but make assumptions about the hit orientation and are often limited in the position and/or orientation of the accelerometers. The newly formulated algorithm presented in this manuscript accurately extracts the full linear and rotational acceleration vectors from a broad arrangement of six single-axis accelerometers directly from the governing set of kinematic equations. The new formulation linearizes the nonlinear centripetal acceleration term with a finite-difference approximation and provides a fast and accurate solution for all six components of acceleration over long time periods (>250 ms). The approximation of the nonlinear centripetal acceleration term provides an accurate computation of the rotational velocity as a function of time and allows for reconstruction of a multiple-impact signal. Furthermore, the algorithm determines the impact location and orientation and can distinguish between glancing, high rotational velocity impacts, or direct impacts through the center of mass. Results are shown for ten simulated impact locations on a headform geometry computed with three different accelerometer configurations in varying degrees of signal noise. Since the algorithm does not require simplifications of the actual impacted geometry, the impact vector, or a specific arrangement of accelerometer orientations, it can be easily applied to many impact investigations in which accurate kinematics need to be extracted from single-axis accelerometer data.

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Figures

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Fig. 1

Geometric definitions of rigid-body kinematics and position and orientation of accelerometers

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Fig. 2

(a) Geometry of the representative headform model with the location and direction of ten simulated head impacts and (b) location of the six single-axis accelerometers with the orientation of the tangential configuration indicated (randomly assigned tangential vectors). The orthogonal orientation has the same positions, but the orientation is in the outward normal direction. The mixed configuration has four oriented orthogonal with the two red arrows (two far-right accelerometers) oriented tangentially as indicated.

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Fig. 3

Schematic of the force signal applied to the headform. The pre-impact is applied to the lower right hemisphere to generate an initial rotational velocity of 16 rad/s, and the high-amplitude and short duration impact follows, simulating an in-game impact. The impact is applied over ten different locations on the headform (Fig. 2).

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Fig. 4

Reconstructed signals with (solid lines) and without (dashed lines) the nonlinear term computed and compared to the original signal (□). Simulated accelerometer readings (top) with reconstructed linear (middle) and angular (bottom) signals for a representative impact to the lower left hemisphere. The short duration impact of 10 ms (left) has a relatively small nonlinear term, however, the longer duration impact of 125 ms (right) has a strong nonlinear component. (a) Short duration (10 ms) impact and (b) long duration (125 ms) impact.

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Fig. 5

The percentage RMSE for the reconstructed accelerations with and without the nonlinear term computed as a function of impact duration and configuration for a glancing impact in the upper hemisphere of the headform (inducing high magnitude angular acceleration): (a) linear acceleration and (b) angular acceleration

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Fig. 6

An example of the acceleration reconstruction from the pre-impact and impact signal depicted in Fig. 6. The pre-impact (left column) and impact (right column) signals are shown on separate axis since the magnitudes are orders of magnitude apart. The top row is the constructed single-axis accelerometer data with 10% noise. The reconstructed accelerations (solid lines) are compared to the original data (□) for the linear (second row) and angular (third row) accelerations. (a) Low amplitude pre-impact and (b) high-amplitude impact with nonzero initial angular velocity.

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