A Pseudo-Elastic Effective Material Property Representation of the Costal Cartilage for Use in Finite Element Models of the Whole Human Body

Abstract

Objective: Injury-predictive finite element (FE) models of the chest must reproduce the structural coupling behavior of the costal cartilage accurately. Gross heterogeneities (the perichondrium and calcifications) may cause models developed based on local material properties to erroneously predict the structural behavior of cartilage segments. This study sought to determine the pseudo-elastic effective material properties required to reproduce the structural behavior of the costal cartilage under loading similar to what might occur in a frontal automobile collision.

Methods: Twenty-eight segments of cadaveric costal cartilage were subjected to cantilever-like, dynamic loading. Three limited-mesh FE models were then developed for each specimen, having element sizes of 10 mm (typical of current whole-body FE models), 3 mm, and 2 mm. The cartilage was represented as a homogeneous, isotropic, linear elastic material. The elastic moduli of the cartilage models were optimized to fit the anterior–posterior (x-axis) force versus displacement responses observed in the experiments. For a subset of specimens, additional model validation tests were performed under a second boundary condition.

Results: The pseudo-elastic effective moduli ranged from 4.8 to 49 MPa, with an average and standard deviation of 22 ± 13.6 MPa. The models were limited in their ability to reproduce the lateral (y-axis) force responses observed in the experiments. The prediction of the x-axis and y-axis forces in the second boundary condition varied. Neither the effective moduli nor the model fit were significantly affected (Student's t-test, p < 0.05) by the model mesh density. The average pseudo-elastic effective moduli were significantly (p < 0.05) greater than local costal cartilage modulus values reported in the literature.

Conclusions: These results are consistent with the presence of stiffening heterogeneities within the costal cartilage structure. These effective modulus values may provide guidance for the representation of the costal cartilage in whole-body FE models where these heterogeneities cannot be modeled distinctly.

Keywords:

• Biomechanics
• Chest injury
• Finite elements
• Modeling
• Cartilage
• Experiments

ACKNOWLEDGMENTS

The authors thank Carlos Arregui Dalmases of the Universidad de Navarra for his assistance in a portion of the experiments. All computer modeling and experiments were performed at the University of Virginia Center for Applied Biomechanics. The preparation of this manuscript was partially supported by a Whitaker International Scholars Grant. The analyses and opinions presented here represent those solely of the authors.