In this paper, a multiscale constitutive framework for one-dimensional blood flow modeling is presented and discussed. By analyzing the asymptotic limits of the proposed model, it is shown that different types of blood propagation phenomena in arteries and veins can be described through an appropriate choice of scaling parameters, which are related to distinct characterizations of the fluid-structure interaction mechanism (whether elastic or viscoelastic) that exist between vessel walls and blood flow. In these asymptotic limits, well-known blood flow models from the literature are recovered. Additionally, by analyzing the perturbation of the local elastic equilibrium of the system, a new viscoelastic blood flow model is derived. The proposed approach is highly flexible and suitable for studying the human cardiovascular system, which is composed of vessels with high morphological and mechanical variability. The resulting multiscale hyperbolic model of blood flow is solved using an asymptotic-preserving Implicit-Explicit Runge-Kutta Finite Volume method, which ensures the consistency of the numerical scheme with the different asymptotic limits of the mathematical model without affecting the choice of the time step by restrictions related to the smallness of the scaling parameters. Several numerical tests confirm the validity of the proposed methodology, including a case study investigating the hemodynamics of a thoracic aorta in the presence of a stent.
Multiscale modeling of blood circulation with cerebral autoregulation and network pathway analysis for hemodynamic redistribution in the vascular network with anatomical variations and stenosis conditions
Advanced Institute for Materials Research, Tohoku University（东北大学先进材料研究所）；Department of Neurosurgery, Kohnan Hospital（郡山医院神经外科）；Department of Neurosurgery, Tohoku University Graduate School of Medicine（东北大学大学院医学研究科神经外科）；Department of Translational Neuroscience, Tohoku University Graduate School of Medicine（东北大学大学院医学研究科转化神经科学）；Department of Neurosurgical Engineering, Graduate School of Biomedical Engineering, Tohoku University（东北大学研究生院生物医学工程学系神经外科工程）；Mathematical Science Center for Co-creative Society, Tohoku University（东北大学共创社会数学科学中心）
