Submitted on June 16, 2007
Accepted on October 11, 2007
The validation of a generalized Hooke's law for coronary arteries
Chong Wong1, Wei Zhang1, and Ghassan S. Kassab2*
1 Biomedical Engineering, Indiana University Purdue University Indianapolis, Indianapolis, Indiana, United States
2 Biomedical Engineering, SL-174, Indiana University Purdue University Indianapolis, Indianapolis, Indiana, United States
* To whom correspondence should be addressed. E-mail: gkassab{at}iupui.edu.
The exponential form of constitutive model is widely used in biomechanical studies of blood vessels. There are two main issues, however, with this model: 1) the curve fits of experimental data are not always satisfactory and 2) the oversensitivity of material parameters. A new type of strain measure in a generalized Hookes law for blood vessels was recently proposed by our group to address these issues. The new model has one nonlinear parameter and six linear parameters. In this study, the stress-strain equation is validated by fitting the model to experimental data of porcine coronary arteries. Material constants of LAD and RCA for the Hooke's law were computed with a separable nonlinear least square method with an excellent goodness of fit. A parameter sensitivity analysis shows that the stability of material constants is improved as compared to the exponential model and a bi-phasic model. A boundary value problem was solved to demonstrate that the model prediction can match the measured arterial deformation under experimental loading conditions. The validated constitutive relation will serve as a basis for the solution of various boundary value problems of cardiovascular biomechanics.
