# Embedded Finite Elements for Modeling Axonal Injury

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## Abstract

The purpose of this paper is to propose and develop a large strain embedded finite element formulation that can be used to explicitly model axonal fiber bundle tractography from diffusion tensor imaging of the brain. Once incorporated, the fibers offer the capability to monitor tract-level strains that give insight into the biomechanics of brain injury. We show that one commercial software has a volume and mass redundancy issue when including embedded axonal fiber and that a newly developed algorithm is able to correct this discrepancy. We provide a validation analysis for stress and energy to demonstrate the method.

## Keywords

Embedded element Volume redundancy Mass redundancy Force redundancy Finite element Brain tissue anisotropy## Notes

### Acknowledgment

The authors gratefully acknowledge the support provided by CFDRC, Inc. under a sub-contract funded by the Department of Defense, Department of Health Program through Contract W81XWH-14-C-0045, the U.S. Army Research Laboratory (ARL) at the Aberdeen Proving Grounds under Contract W15P7T-10-D-D416, the Defense Health Agency under the Contract W81XWH-14-C-0045 and the US Department of Defense through the Contracts W15P7T-10-D-D416, W81XWH-17-C-0216, DOTC-17-01-INIT0086. Neuroimaging data show in Fig. 2 was provided by The Pennsylvania State University Center for Sports Concussion Research and Service, University Park, USA. The authors thank Dr. Sam Slobounov and Dr. Brian D. Johnson for the data provided. We would also like to acknowledge The Pennsylvania State University Social, Life, and Engineering Sciences Imaging Center (SLEIC), High Field MRI Facility for providing access to the imaging equipment. The authors also thank The Pennsylvania State University Institute for Cyberscience for providing the computational resources required for this work.

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