Viscoelastic Models for Passive Arterial Wall Dynamics
D. Valdez-Jasso1 1, H. T. Banks 1, M.A. Haider 1, D. Bia 2, Y. Zocalo 2, R. L. Armentano 3, M.S. Olufsen 1*1 Department of Mathematics and Center for Research in Scientific Computation, NC State University, Campus Box 8205, Raleigh, NC 27695.
2 Departmento de Fisiologia, Facultad de Medicina, Universidad de La Republica, General Flores 2125, PC: 11800, Montevideo, Uruguay
3 Facultad de Ingenieria y Ciencias Exactas y Naturales, Universidad Favaloro, Avda. Belgrano 1723, Capital Federal, Buenos Aires, Argentina.
Received 13 December 2008; Accepted (in revised version) 16 January 2009
This paper compares two models predicting elastic and viscoelastic properties of large arteries. Models compared include a Kelvin (standard linear) model and an extended 2-term exponential linear viscoelastic model. Models were validated against in-vitro data from the ovine thoracic descending aorta and the carotid artery. Measurements of blood pressure data were used as an input to predict vessel cross-sectional area. Material properties were predicted by estimating a set of model parameters that minimize the difference between computed and measured values of the cross-sectional area. The model comparison was carried out using generalized analysis of variance type statistical tests. For the thoracic descending aorta, results suggest that the extended 2-term exponential model does not improve the ability to predict the observed cross-sectional area data, while for the carotid artery the extended model does statistically provide an improved fit to the data. This is in agreement with the fact that the aorta displays more complex nonlinear viscoelastic dynamics, while the stiffer carotid artery mainly displays simpler linear viscoelastic dynamics.AMS subject classifications: 74D05, 74J25, 62J02, 93A30,92C10, 74L15
Key words: Arterial wall modeling, dynamic viscoelastic models, inverse problems, statistical analysis for model comparison.
Email: firstname.lastname@example.org (D. Valdez-Jasso), email@example.com (H. T. Banks), firstname.lastname@example.org (M.A. Haider), email@example.com (D. Bia), firstname.lastname@example.org (Y. Zocalo), email@example.com (R. L. Armentano), firstname.lastname@example.org (M. S. Olufsen)