Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms

Journal of Computational Physics
Yue YuG E Karniadakis

Abstract

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(N log(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 ...Continue Reading

References

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Jan 15, 2014·Annals of Biomedical Engineering·Paris Perdikaris, George Em Karniadakis
Aug 1, 2015·AJNR. American Journal of Neuroradiology·J R CebralA M Robertson

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Citations

Dec 12, 2019·Royal Society Open Science·Karen LarsonAnastasios Matzavinos
Jul 9, 2020·Soft Matter·A BonfantiA Kabla
Mar 25, 2021·Mathematical Biosciences and Engineering : MBE·Guoyi KeWenrui Hao

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