Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms

JOURNAL OF COMPUTATIONAL PHYSICS

卷:323

Article

Yu, Yue¹  Perdikaris, Paris²  Karniadakis, George Em³ 

[1] Lehigh Univ, Dept Math, Bethlehem, PA 18015 USA

[2] MIT, Dept Mech Engn, Cambridge, MA 02139 USA

[3] Brown Univ, Div Appl Math, Providence, RI 02912 USA

关键词: Fast convolution method;    Fractional differential equations;    Fluid-structure interaction;    Spectral element method;    Patient-specific vasculature;    Brain aneurysm;   

DOI  :  10.1016/j.jcp.2016.06.038

来源: Elsevier

【 摘 要 】

We develop efficient numerical methods for fractional order PDEs, and employ them to investigate viscoelastic constitutive laws for arterial wall mechanics. Recent simulations using one-dimensional models [1] have indicated that fractional order models may offer a more powerful alternative for modeling the arterial wall response, exhibiting reduced sensitivity to parametric uncertainties compared with the integer-calculus-based models. Here, we study three-dimensional (3D) fractional PDEs that naturally model the continuous relaxation properties of soft tissue, and for the first time employ them to simulate flow structure interactions for patient-specific brain aneurysms. To deal with the high memory requirements and in order to accelerate the numerical evaluation of hereditary integrals, we employ a fast convolution method [2] that reduces the memory cost to O(log(N)) and the computational complexity to O(Nlog(N)). Furthermore, we combine the fast convolution with high-order backward differentiation to achieve third-order time integration accuracy. We confirm that in 3D viscoelastic simulations, the integer order models strongly depends on the relaxation parameters, while the fractional order models are less sensitive. As an application to long-timesimulations in complex geometries, we also apply the method to modeling fluid-structure interaction of a 3D patient-specific compliantcerebral artery with an aneurysm. Taken together, our findings demonstrate that fractional calculus can be employed effectively in modeling complex behavior of materials in realistic 3D time-dependent problems if properly designed efficient algorithms are employed to overcome the extra memory requirements and computational complexity associated with the non-local character of fractional derivatives. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free