@article{valdez-jasso_bia_zocalo_armentano_haider_olufsen_2011, title={Linear and Nonlinear Viscoelastic Modeling of Aorta and Carotid Pressure-Area Dynamics Under In Vivo and Ex Vivo Conditions}, volume={39}, ISSN={["1573-9686"]}, DOI={10.1007/s10439-010-0236-7}, abstractNote={A better understanding of the biomechanical properties of the arterial wall provides important insight into arterial vascular biology under normal (healthy) and pathological conditions. This insight has potential to improve tracking of disease progression and to aid in vascular graft design and implementation. In this study, we use linear and nonlinear viscoelastic models to predict biomechanical properties of the thoracic descending aorta and the carotid artery under ex vivo and in vivo conditions in ovine and human arteries. Models analyzed include a four-parameter (linear) Kelvin viscoelastic model and two five-parameter nonlinear viscoelastic models (an arctangent and a sigmoid model) that relate changes in arterial blood pressure to the vessel cross-sectional area (via estimation of vessel strain). These models were developed using the framework of Quasilinear Viscoelasticity (QLV) theory and were validated using measurements from the thoracic descending aorta and the carotid artery obtained from human and ovine arteries. In vivo measurements were obtained from 10 ovine aortas and 10 human carotid arteries. Ex vivo measurements (from both locations) were made in 11 male Merino sheep. Biomechanical properties were obtained through constrained estimation of model parameters. To further investigate the parameter estimates, we computed standard errors and confidence intervals and we used analysis of variance to compare results within and between groups. Overall, our results indicate that optimal model selection depends on the artery type. Results showed that for the thoracic descending aorta (under both experimental conditions), the best predictions were obtained with the nonlinear sigmoid model, while under healthy physiological pressure loading the carotid arteries nonlinear stiffening with increasing pressure is negligible, and consequently, the linear (Kelvin) viscoelastic model better describes the pressure–area dynamics in this vessel. Results comparing biomechanical properties show that the Kelvin and sigmoid models were able to predict the zero-pressure vessel radius; that under ex vivo conditions vessels are more rigid, and comparatively, that the carotid artery is stiffer than the thoracic descending aorta; and that the viscoelastic gain and relaxation parameters do not differ significantly between vessels or experimental conditions. In conclusion, our study demonstrates that the proposed models can predict pressure–area dynamics and that model parameters can be extracted for further interpretation of biomechanical properties.}, number={5}, journal={ANNALS OF BIOMEDICAL ENGINEERING}, author={Valdez-Jasso, Daniela and Bia, Daniel and Zocalo, Yanina and Armentano, Ricardo L. and Haider, Mansoor A. and Olufsen, Mette S.}, year={2011}, month={May}, pages={1438–1456} }
 @article{steele_valdez-jasso_haider_olufsen_2011, title={PREDICTING ARTERIAL FLOW AND PRESSURE DYNAMICS USING A 1D FLUID DYNAMICS MODEL WITH A VISCOELASTIC WALL}, volume={71}, ISSN={["1095-712X"]}, DOI={10.1137/100810186}, abstractNote={This paper combines a generalized viscoelastic model with a one-dimensional (1D) fluid dynamics model for the prediction of blood flow, pressure, and vessel area in systemic arteries. The 1D fluid dynamics model is derived from the Navier–Stokes equations for an incompressible Newtonian flow through a network of cylindrical vessels. This model predicts pressure and flow and is combined with a viscoelastic constitutive equation derived using the quasilinear viscoelasticity theory that relates pressure and vessel area. This formulation allows for inclusion of an elastic response as well as an appropriate creep function allowing for the description of the viscoelastic deformation of the arterial wall. Three constitutive models were investigated: a linear elastic model and two viscoelastic models. The Kelvin and sigmoidal viscoelastic models provide linear and nonlinear elastic responses, respectively. For the fluid domain, the model assumes that a given flow profile is prescribed at the inlet, that flow is c...}, number={4}, journal={SIAM JOURNAL ON APPLIED MATHEMATICS}, author={Steele, Brooke N. and Valdez-Jasso, Daniela and Haider, Mansoor A. and Olufsen, Mette S.}, year={2011}, pages={1123–1143} }
 @article{valdez-jasso_bia_haider_zocalo_armentano_olufsen_2010, title={Linear and Nonlinear Viscoelastic Modeling of Ovine Aortic Biomechanical Properties under in vivo and ex vivo Conditions}, ISSN={["1557-170X"]}, DOI={10.1109/iembs.2010.5626563}, abstractNote={This study uses linear and nonlinear viscoelastic models to describe the dynamic distention of the aorta induced by time-varying arterial blood pressure. We employ an inverse mathematical modeling approach on a four-parameter (linear) Kelvin viscoelastic model and two five-parameter nonlinear viscoelastic models (arctangent and sigmoid) to infer vascular biomechanical properties under in vivo and ex vivo experimental conditions in ten and eleven male Merino sheep, respectively. We used the Akaike Information Criterion (AIC) as a goodness-of-fit measure. Results show that under both experimental conditions, the nonlinear models generally outperform the linear Kelvin model, as judged by the AIC. Furthermore, the sigmoid nonlinear viscoelastic model consistently achieves the lowest AIC and also matches the zero-stress vessel radii measured ex vivo. Based on these observations, we conclude that the sigmoid nonlinear viscoelastic model best describes the biomechanical properties of ovine large arteries under both experimental conditions considered in this study.}, journal={2010 ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY (EMBC)}, author={Valdez-Jasso, D. and Bia, D. and Haider, M. A. and Zocalo, Y. and Armentano, R. L. and Olufsen, M. S.}, year={2010}, pages={2634–2637} }
 @article{valdez-jasso_haider_banks_santana_german_armentano_olufsen_2009, title={Analysis of Viscoelastic Wall Properties in Ovine Arteries}, volume={56}, ISSN={["1558-2531"]}, DOI={10.1109/TBME.2008.2003093}, abstractNote={In this paper, we analyze how elastic and viscoelastic properties differ across seven locations along the large arteries in 11 sheep. We employ a two-parameter elastic model and a four-parameter Kelvin viscoelastic model to analyze experimental measurements of vessel diameter and blood pressure obtained in vitro at conditions mimicking in vivo dynamics. Elastic and viscoelastic wall properties were assessed via solutions to the associated inverse problem. We use sensitivity analysis to rank the model parameters from the most to the least sensitive, as well as to compute standard errors and confidence intervals. Results reveal that elastic properties in both models (including Young's modulus and the viscoelastic relaxation parameters) vary across locations (smaller arteries are stiffer than larger arteries). We also show that for all locations, the inclusion of viscoelastic behavior is important to capture pressure-area dynamics.}, number={2}, journal={IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING}, author={Valdez-Jasso, Daniela and Haider, Mansoor A. and Banks, H. T. and Santana, Daniel Bia and German, Yanina Zocalo and Armentano, Ricardo L. and Olufsen, Mette S.}, year={2009}, month={Feb}, pages={210–219} }
 @article{valdez-jasso_banks_haider_bia_zocalo_armentano_olufsen_2009, title={Viscoelastic models for passive arterial wall dynamics}, volume={1}, number={2}, journal={Advances in Applied Mathematics & Mechanics}, author={Valdez-Jasso, D. and Banks, H. T. and Haider, M. A. and Bia, D. and Zocalo, Y. and Armentano, R. L. and Olufsen, M. S.}, year={2009}, pages={151–165} }