# Constitutive modeling of an electrospun tubular scaffold used for vascular tissue engineering

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## Abstract

In this study, we sought to model the mechanical behavior of an electrospun tubular scaffold previously reported for vascular tissue engineering with hyperelastic constitutive equations. Specifically, the scaffolds were made by wrapping electrospun polycaprolactone membranes that contain aligned fibers around a mandrel in such a way that they have microstructure similar to the native arterial media. The biaxial stress-stretch data of the scaffolds made of moderately or highly aligned fibers with three different off-axis fiber angles $$\alpha$$α (30$$^\circ$$, 45$$^\circ$$, and 60$$^\circ$$) were fit by a phenomenological Fung model and a series of structurally motivated models considering fiber directions and fiber angle distributions. In particular, two forms of fiber strain energy in the structurally motivated model for a linear and a nonlinear fiber stress–strain relation, respectively, were tested. An isotropic neo-Hookean strain energy function was also added to the structurally motivated models to examine its contribution. The two forms of fiber strain energy did not result in significantly different goodness of fit for most groups of the scaffolds. The absence of the neo-Hookean term in the structurally motivated model led to obvious nonlinear stress-stretch fits at a greater axial stretch, especially when fitting data from the scaffolds with a small $$\alpha$$α. Of the models considered, the Fung model had the overall best fitting results; its applications are limited because of its phenomenological nature. Although a structurally motivated model using the nonlinear fiber stress–strain relation with the neo-Hookean term provided fits comparably as good as the Fung model, the values of its model parameters exhibited large within-group variations. Prescribing the dispersion of fiber orientation in the structurally motivated model, however, reduced the variations without compromising the fits and was thus considered to be the best structurally motivated model for the scaffolds. It appeared that the structurally motivated models could be further improved for fitting the mechanical behavior of the electrospun scaffold; fiber interactions are suggested to be considered in future models.

Original language English 897-913 17 Biomechanics and Modeling in Mechanobiology 14 4 https://doi.org/10.1007/s10237-014-0644-y Published - 29 Aug 2015

## Keywords

• Constitutive modeling
• Electrospun scaffolds
• Fung model
• Hyperelasticity
• Mechanical properties
• Structurally motivated models