Sensitivity of scale factor choice on injury response for equal-stress equal-velocity scaling

Abstract

Objective

This study aims to evaluate the assumption of geometric similitude inherent to equal-stress equal-velocity scaling by determining if scale factors created with different anthropometry metrics result in different scaled injury tolerance predictions. This assumption will be evaluated when equal-stress equal-velocity scaling is employed across dissimilar (e.g., 50^th male to small female) and similar (e.g., small female to a reference small female anthropometry) anthropometries.

Methods

Three average male and three small female lower extremity specimens that were tested in ankle inversion/eversion were selected for scaling analysis. Three additional female specimens were selected as a reference dataset, such that the accuracy of the scaled data could be compared to an independent measured dataset. The failure moments, total height and total weight for these donors were determined from literature. Additional anthropometry metrics (leg length, calcaneus height, and bimalleolar width) were taken from each of their respective CT scans. Scale factors were calculated from these previously determined anthropometric metrics for the six donors selected for scaling analysis by targeting the averaged anthropometry metrics of the reference small female dataset. Equal-stress equal-velocity scaling was applied to the failure moments from literature using different scale factors. The mean predicted failure tolerance and standard deviation for scaled data using different scale factors were compared to one another and to the mean failure tolerance from the reference (unscaled) small female dataset.

Results

When using average male data to predict ankle failure moment for a small female anthropometry, scaled moments were statistically significantly different from measured small female failure moment. Furthermore, scaled failure moments predicted using scale factors based on different anthropometry metrics were found to be significantly different from one another. Conversely, predicted mean failure moment using scaled female data of a similar size to the reference data was not significantly different from measured female failure moment, and the predicted failure moments were not significantly affected by choice of scale factor.

Conclusions

This study shows that an injury metric predicted with equal-stress equal-velocity scaling is sensitive to choice of scale factor when employing scaling across occupants of dissimilar size and sex. This conclusion suggests error can be introduced into scaled response due to choice of anthropometry metric used to create a scale factor, and therefore, anthropometry metrics used to create scale factors should be justified mechanistically and shown to apply across size and sex before being employed.

Keywords:

• Scaling
• injury tolerance
• sex differences
• geometric similitude

Additional information

Funding

This work was supported by Autoliv Research, for which we thank them. The views expressed here are those solely of the authors.