Experimental investigation and constitutive modeling of the 3D histomechanical properties of vein tissue

Numerous studies have provided material models of arterial walls, but limited information is available on the pseudo-elastic response of vein walls and their underlying microstructure, and only few constitutive formulations have been proposed heretofore. Accordingly, we identified the histomechanics of healthy porcine jugular veins by applying an integrated approach of inflation/extension tests and histomorphometric evaluation. Several alternate phenomenological and microstructure-based strain-energy functions (SEF) were attempted to mimic the material response. Evaluation of their descriptive/predictive capacities showed that the exponential Fung-type SEF alone or in tandem with the neo-Hookean term did not capture the deformational response at high pressures. This problem was solved to a degree with the neo-Hookean and two-fiber (diagonally arranged) family SEF, but altogether the least reliable fit was generated. Fitting precision was much improved with the four-fiber (diagonally, circumferentially, longitudinally arranged) family model, as the inability of neo-Hookean function with force data was alleviated by use of the longitudinal-fiber family. Implementation of a quadratic term as a descriptor of low-pressure anisotropy facilitated the simulation of low-pressure and force data, and the four-fiber families simulated more faithfully than the two-fiber families the physiologic and high-pressure response. Importantly, this SEF was consistent with vein angioarchitecture, namely the occurrence of extensive elastin fibers along the longitudinal axis and few orthogonal fibers attached to them and of three collagen sets with circumferential, longitudinal, and diagonal arrangement, respectively. Our findings help to establish the relationship between vein microstructure and its biomechanical response, yet additional observations are obligatory prior to endeavoring generalizations to other veins.