Optimal Cutoff Frequencies for Filtering Linear Acceleration and Angular Velocity Signals Associated with Head Impacts Measured by Instrumented Mouthguards

Introduction:: Mouthguard- and retainer-style head impact sensors have become increasingly popular because of their potential to couple directly to the upper dentition and hence the skull. Popular sensors available on the market have been compared comprehensively in controlled laboratory environments and on-field. However, the sensors’ inherent signal-processing algorithms vary widely and are an error source between reported measurements and truth. Post-processing differences, especially filtering, make comparison across studies challenging if ignored.

The first goal of this study was to identify an optimal combination of linear acceleration and angular velocity lowpass filter cutoff frequencies for measurements made at the teeth which would minimize the error in linear accelerations transformed to the head center of gravity (CG). The second goal was to identify a set of minimum filter cutoff frequencies for measurements made at the teeth which would limit overall error to less than or equal to five and ten percent in the transformed linear accelerations.


Materials and Methods:: Laboratory head impact tests were conducted using a pendulum impactor and a range of impactor faces against a medium National Operating Committee on Standards for Athletic Equipment (NOCSAE) headform. The headform was modified to mount a custom plate with laboratory instrumentation at the teeth location (Figure 1). Instrumentation included three linear accelerometers (Endevco 7264b-2000) and three angular rate sensors (DTS ARS3 Pro 18k) at the headform’s CG and the teeth (Figure 1). The pendulum impactor was covered with one of three faces: a rigid nylon face or one of two vinyl nitrile foam pads (VN700 or VN1000, Dertex Corporation). These faces generated different linear acceleration durations: approximately 3ms (rigid), 7ms (VN1000), and 11ms (VN700). Four locations were impacted on the headform (Rear, Rearboss, Frontboss, and Front) at four peak resultant linear head acceleration severities (25 g to 100 g in 25 g increments). Each configuration underwent two trials for a total of 96 tests.

A fourth-order phaseless lowpass Butterworth filter was applied to the linear acceleration and angular velocity signals at a range of cutoff frequencies from 5 to 1650 Hz in sequential combination. Angular acceleration was derived from angular velocity using a five-point stencil differentiation method. Error was computed as the difference between the peak values of the transformed linear acceleration signals and the SAE-J211-filtered CG linear acceleration measurements. Percent error was calculated by dividing the error by the CG measurement. The root sum squared (RSS) error was used to weigh both average error and variance equally.


Results, Conclusions, and Discussions:: The optimal cutoff frequency combination for measurements made at the teeth location and transformed to the head CG were cutoff frequencies of 300 Hz for linear acceleration and 310 Hz for angular velocity. This combination had an RSS error of 3.78%. A range of cutoff frequency combinations limited RSS error to 5% or less (Figure 2). The 5% ellipse includes cutoff frequencies of approximately 250 to 400 Hz for linear acceleration signals and 230 to 450 Hz for angular velocity signals. The lowest cutoff frequency combination to remain under 5% RSS error was 255 Hz for linear acceleration and 245 Hz for angular velocity. To limit RSS error to less than ten percent, the linear acceleration cutoff frequency had a minimum (approximately 180 Hz) but no cap before 1650 Hz. However, the angular velocity cutoff frequency had to remain between approximately 200 and 600 Hz. The lowest cutoff frequency combination to stay under 5% RSS error was 255 Hz for linear acceleration and 245 Hz for angular velocity. The lowest cutoff frequency combination to remain under 10% RSS error was 220 Hz for linear acceleration and 155 Hz for angular velocity.

A common filtering approach across instrumentation in laboratory and real-world environments would benefit the field of head impact biomechanics. Filter combinations used to transform linear acceleration to the head CG would allow future studies to produce generalizable data comparable to historical data. When taking measurements at the teeth, we recommend a cutoff frequency of 300 Hz (CFC 180) for both linear acceleration and angular velocity signals, when angular velocity is to be differentiated to calculate angular acceleration. If these filters cannot be used in the field due to noise artifacts, the 5% and 10% RSS error-bounded cutoff frequency combinations can be considered lower limits, with recognition of the resulting bias and variance.

Acknowledgements (Optional): :

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