Evaluation Of The Effective Shear Modulus Method: residual Stress In The No-load State and Comparison To The Standard Method

Open Access
Chisena, Robert S
Area of Honors:
Mechanical Engineering
Bachelor of Science
Document Type:
Thesis Supervisors:
  • James Gordon Brasseur, Thesis Supervisor
  • Domenic Adam Santavicca, Honors Advisor
  • Francesco Costanzo, Thesis Supervisor
  • CB13 Method
  • Effective Shear Modulus
  • Tubular Organs
  • Incompressibility
  • Gastrointestinal Tract
It is common in the medical field to search for changes in the elastic response of tubular GI and cardiovascular organs. Many authors in the past have shown that this elastic response changes due to the remodeling of incompressible tissue from disease, aging, or drugs. Hence, a great need exists for a practical quantification of the elastic response of an organ in vivo and in vitro using the parameters measured in a distension test experiment. Often, a modulus of elasticity for a tubular organ is correlated with the remodeling of incompressible tissue. Using the concurrently measured geometric and manometric quantities from the inflation experiment, the Laplace Law (standard method) is used to estimate the total hoop stress corresponding to the Green strain. The elastic modulus is found by curve fitting the distension data and finding the slope. Costanzo and Brasseur [1] show that the Laplace Law method is fundamentally flawed for two reasons: (1) the thin-walled approximation required to use the Laplace Law is not satisfied in physiological organs, and, more importantly, (2) the average hoop stress in the organ includes the redistribution of stress by incompressibility. They show that the elastic response corresponding to the hoop stress in the normal direction measures not only the elastic component of the total stress but also the hydrostatic component. Because the material is incompressible, the hydrostatic component of the stress can pollute the elastic response of the organ to the extent that the elastic response becomes a measure for the incompressibility of the material. In addition to pointing out the flaws in the standard method, Costanzo and Brasseur propose a new, effective shear modulus method (CB13 method) that aims to filter out the hydrostatic component of the stress and to provide a more realistic measure of the elastic response of the tubular organ. This method assumes that the material is isotropic, undistorted, and elastic. Additionally, the method assumes the reference state for the organ is the no-load state (the state in which internal and external pressure equal ii each other). However, as determined by Fung and many other authors, in a physiological setting, organs have residual stress in the no-load state. In this honors thesis, I have examined the effect of residual stress on the evaluation of the CB13 method. It was found that, for the model and deformation class chosen, the CB13 method provided a relatively accurate measure of the shear modulus of the applied constitutive model. Additionally, because Costanzo and Brasseur suggested that the CB13 method should be applied instead of the standard method, the two methods were compared using experimental data provided by Gregersen and Zhao. In applying the two methods to quantify elastic response, the practicality and simplicity of the CB13 method compared to the standard method was evident. Whereas the CB13 method predicted a response directly from the distension test data, the standard method required complex algorithms to accurately curve fit the data points and then find the slope of the fit to determine the elastic modulus. Additionally, because the standard method required curve fitting, significant detail from the data was lost. However, being directly calculated from the data, the CB13 method predicted an initial decrease in the myogenic active tone before tissue stiffness increased. Finally, although trends were similar, the average effective shear modulus was 3-9 times lower than the modulus predicted by the standard method. In summary, the CB13 method was developed to resolve the fundamental flaws associated with the standard, Laplace Law approach. This study found that, even considering a deviation from the initial assumptions of the CB13 method, the CB13 method performed reasonably well in predicting the material property of the applied constitutive model. Finally, using experimental in vitro distension test data, the CB13 method produced different results when compared to the standard method.