Constitutive models describing the arterial mechanical behavior are important in the development of catheterization products, to be used in arteries with a specific radius. To prove the possible existence of a constitutive model that, provided with a generic set of material and geometric parameters, is able to predict the radius-specific mechanical behavior of a coronary artery, the passive pressure-inner radius (P-r ( i )) and pressure-axial force change (P-ΔF ( z )) relations of seven porcine left anterior descending coronary arteries were measured in an in-vitro set-up and fitted with the model of Driessen et al. in J Biomech Eng 127(3):494-503 (2005), Biomech Model Mechanobiol 7(2):93-103 (2008). Additionally, the collagen volume fraction, physiological axial pre-stretch, and wall thickness to inner radius ratio at physiological loading were determined for each artery. From this, two generic parameter sets, each comprising four material and three geometric parameters, were obtained. These generic sets were used to compute the deformation of each tested artery using a single radius measurement at physiological loading as an artery-specific input. Artery-specific P-r ( i ) and P-ΔF ( z ) relations were predicted with an accuracy of 32 μm (2.3%) and 6 mN (29% relative to ΔF ( z )-range) on average compared to the relations measured in-vitro. It was concluded that the constitutive model provided with the generic parameters found in this study can well predict artery-specific mechanical behavior.

A patient-specific mechanical description of the coronary arterial wall is indispensable for individualized diagnosis and treatment of coronary artery disease. A way to determine the artery's mechanical properties is to fit the parameters of a constitutive model to patient-specific experimental data. Clinical data, however, essentially lack information about the stress-free geometry of an artery, which is necessary for constitutive modeling. In previous research, it has been shown that a way to circumvent this problem is to impose extra modeling constraints on the parameter estimation procedure. In this study, we propose a new modeling constraint concerning the in-situ fiber orientation (β phys ). β phys , which is a major contributor to the arterial stress-strain behavior, was determined for porcine and human coronary arteries using a mixed numerical-experimental method. The in-situ situation was mimicked using in-vitro experiments at a physiological axial pre-stretch, in which pressure-radius and pressure-axial force were measured. A single-layered, hyperelastic, thick-walled, two-fiber material model was accurately fitted to the experimental data, enabling the computation of stress, strain, and fiber orientation. β phys was found to be almost equal for all vessels measured (36.4 ± 0.3) • , which theoretically can be explained using netting analysis. In further research, this finding can be used as an extra modeling constraint in parameter estimation from clinical data.

Knowledge of the mechanical properties of arteries is important to understand vascular function during disease and the effect of interventions, such as PTCA treatment. A mechanical model of the vascular tree would facilitate the improvement of (balloon-)catheters and stents. The aim of this research is to propose general parameter values for the fiber-reinforced material model as proposed by Driessen et al. (2005) that can describe the arterial wall behavior of the porcine left anterior descending coronary artery (LAD, fig. 1a) at physiological axial stretch.

Mechanical characterization of the coronary arterial wall is important for several reasons. Mechanical factors play an important role in the development of atherosclerosis [1]. Atherosclerotic coronary arteries may be treated mechanically with interventions like PTCA and stent implantation, 1265000 PTCA procedures were performed in the United States in 2005 [2]. Furthermore, knowledge of the mechanical properties of the arterial wall is important for modeling of the coronary circulation and explaining its hemodynamics.

To model materials mechanically, it is necessary to determine the parameters of the constitutive model which determine its mechanical behavior. To be able to do this correctly it is important to know the zero-stress state of the material.

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What is the in vivo axial strain of a porcine coronary artery?van den Broek, C.N.; van Tuijl, S.; Rutten, M.C.M.; van de Vosse, F.N.