Linear and Nonlinear Viscoelastic Modeling of Aorta and Carotid Pressure–Area Dynamics Under In Vivo and Ex Vivo Conditions

Abstract

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 ten ovine aortas and ten human carotid arteries. Ex vivo measurements (from both locations) were made in eleven 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 arterial 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.

Physical determining factors of the arterial pulse waveform: theoretical analysis and calculation using the 1-D formulation

“…The flow at the aortic root can be measured using Doppler ultrasound [44, p. 38] and magnetic resonance (MR) [45]. Blood pressure can be recorded noninvasively in superficial arteries, such as carotid, brachial, radial and femoral, using applanation tonometry [16,25,26,46]. Invasive measurements can be obtained in the aorta and other extracranial arteries using pressuresensing catheters [14].…”

“…The internal luminal area can be measured in superficial arteries using ultrasound-based echo-tracking [16,26,47] and MR [45]. Invasive measurements using piezoelectric crystal transducers have been carried out in animal experiments [26].…”

“…This is, therefore, a limitation of our study, and a full verification of our results using in vivo data remains to be done in future work. Future work could also carry out a similar analysis using more complex visco-elastic models of the arterial wall that account for stress relaxation [10,23,24] and the nonlinear behaviour of the arterial wall [25,26].…”

“…There are, however, more complex models that also account for stress relaxation [10,23,24] and the nonlinear behaviour of the wall [25,26]. Here we use a Voigt-type visco-elastic model since it is the simplest model to reproduce, to first approximation, the main features of visco-elastic effects on blood flow in large arteries [9,16,[20][21][22].…”

A Mathematical Model for Analyzing the Elasticity, Viscosity, and Failure of Soft Tissue: Comparison of Native and Decellularized Porcine Cardiac Extracellular Matrix for Tissue Engineering

“…28 While obtaining large amounts of data on the stress-strain behavior of such biomaterials is straightforward, analyzing it in a uniform, comparable, and user-independent manner is more challenging. 29 Despite significant advancements in highly correlative mechanistic models [30][31][32][33][34][35][36][37][38] for stress-strain analysis, most of the reported literature still relies on stiffness, as measured by the Young's modulus, as the primary mechanical measure for biological tissues. However, as tissues are subjected to many nonelastic deformation modes and their responses may differ significantly from ideal spring behavior, measuring only this characteristic can be misleading, at best.…”