Artery active mechanical response: High order finite element implementation and investigation

The active mechanical response of an artery wall resulting from the contraction of the smooth muscle cells (SMCs) is represented by a strain energy function (SEDF) that augments the passive SEDF recently reported in Yosibash and Priel [Z. Yosibash, E. Priel, p-FEMs for hyperelastic anisotropic nearly incompressible materials under finite deformations with applications to arteries simulation, Int. J. Numer. Methods Engrg., 88 (2011) 1152–1174]. The passive–active hyperelastic, anisotropic, nearly-incompressible problem is solved using high-order finite element methods (p-FEMs). A new iterative algorithm, named “p-prediction”, is introduced that accelerates considerably the Newton–Raphson algorithm when combined with p-FEMs. Verification of the numerical implementation is conducted by comparison to problems with analytic solutions and the advantages of p-FEMs are demonstrated by considering both degrees of freedom and CPU.The passive and active material parameters are fitted to bi-axial inflation–extension tests conducted on rabbit carotid arteries reported in Wagner and Humphrey [H.P. Wagner, J.D. Humphrey, Differential passive and active biaxial mechanical behavior of muscular and elastic arteries: basilar versus common carotid, J. Biomech. Engrg., 133 (2011) (Article number: 051009)]. Our study demonstrates that the proposed SEDF is capable of describing the coupled passive–active response as observed in experiments. Artery-like structures are thereafter investigated and the effect of the activation level on the stress and deformation are reported. The active contribution reduces overall stress levels across the artery thickness and along the artery inner boundary.

► Active mechanical response of an artery wall modeled as an inhomogeneous anisotropic hyperelastic material is investigated by p-FEMs.
► A strain energy density function (SEDF) for the phenomenological description is suggested and formulated.
► A new iterative algorithm, is introduced that accelerates considerably the Newton–Raphson method when combined with p-FEMs.
► Verification is conducted and advantages of the p-FEMs are demonstrated both when considering degrees of freedom or CPU.
► Artery-like structures are then investigated and the effect of the activation level and SMCs orientation on the stress and deformation are reported.