Nonlinear mechanical property of tracheal cartilage: a theoretical and experimental study

Despite being the stiffest airway of the bronchial tree, the trachea undergoes significant deformation due to intrathoracic pressure during breathing. The mechanical properties of the trachea affect the flow in the airway and may contribute to the biological function of the lung.

A Fung-type strain energy density function was used to investigate the nonlinear mechanical behavior of tracheal cartilage. A bending test on pig tracheal cartilage was performed and a mathematical model for analyzing the deformation of tracheal cartilage was developed. The constants included in the strain energy density function were determined by fitting the experimental data.

The experimental data show that tracheal cartilage is a nonlinear material displaying higher strength in compression than in tension. When the compression forces varied from -0.02 to -0.03N and from -0.03 to -0.04N, the deformation ratios were 11.03+/-2.18% and 7.27+/-1.59%, respectively. Both were much smaller than the deformation ratios (20.01+/-4.49%) under tension forces of 0.02 to 0.01N. The Fung-type strain energy density function can capture this nonlinear behavior very well, whilst the linear stress-strain relation cannot. It underestimates the stability of trachea by exaggerating the displacement in compression. This study may improve our understanding of the nonlinear behavior of tracheal cartilage and it may be useful for the future study on tracheal collapse behavior under physiological and pathological conditions.