Author(s)

Hongyun Wang¹, Corinne Kramer², Jessica Swallow², Wesley A. Burgei³, Hong Zhou^4*

¹Department of Applied Mathematics, University of California, Santa Cruz, CA, USA.
²Institute for Defense Analyses, Alexandria, VA, USA.
³U.S. Department of Defense, Joint Non-Lethal Weapons Directorate, Quantico, VA, USA.
⁴Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA, USA.

We consider the problem of assessing bone fracture risk for a subject hit by a blunt impact projectile. We aim at constructing a framework for integrating test data and Advanced Total Body Model (ATBM) simulations into the risk assessment. The ATBM is a finite element model managed by the Joint Non-Lethal Weapons Directorate for the purpose of assessing the risk of injury caused by blunt impacts from non-lethal weapons. In ATBM simulations, the quantity that determines arm bone fracture is the calculated maximum strain in the bone. The main obstacle to accurate prediction is that the calculated strain is incompatible with the measured strain. The fracture strain measured in bending tests of real bones is affected by random inhomogeneity in bones and uncertainty in measurement gauge attachment location/orientation. In contrast, the strain calculated in ATBM simulations is based on the assumption that all bones are perfectly elastic with homogeneous material properties and no measurement uncertainty. To connect test data and ATBM simulations in a proper and meaningful setting, we introduce the concept of elasticity-homogenized strain. We interpret test data in terms of the homogenized strain, and build an empirical dose-injury model with the homogenized strain as the input dose for predicting injury. The maximum strain calculated by ATBM has randomness due to uncertainty in specifications of ATBM setup parameters. The dose propagation uncertainty formulation accommodates this uncertainty efficiently by simply updating the shape parameters in the dose-injury model, avoiding the high computational cost of sampling this uncertainty via multiple ATBM runs.

Blunt Impact, Bone Fracture, Effects of Loading Rate, Elasticity-Homogenized Strain, Dose Propagation Uncertainty Formulation, ATBM Simulations

Wang, H. , Kramer, C. , Swallow, J. , Burgei, W. and Zhou, H. (2019) Integrating Test Data and ATBM Simulations into Dose Propagation Uncertainty Formulation for Bone Fracture Risk Assessment. Health, 11, 1426-1472. doi: 10.4236/health.2019.1110109.