Well-posedness, ill-posedness, and traveling waves for models of pulsatile flow in viscoelastic vessels

Pulsatile Viscous Flows in Elliptical Vessels and Annuli: Solution to the Inverse Problem, with Application to Blood and Cerebrospinal Fluid Flow

We consider the fully-developed flow of an incompressible Newtonian fluid in a cylindrical vessel with elliptical cross-section (both an ellipse and the annulus between two confocal ellipses). In particular, we address an inverse problem, namely to compute the velocity field associated with a given, time-periodic flow rate. This is motivated by the fact that flow rate is the main physical quantity which can be actually measured in many practical situations. We propose a novel numerical strategy, which is nonetheless grounded on several analytical relations. The proposed method leads to the sol…

Analysis and simulations of a Viscoelastic Model of Angiogenesis

The work analyzes a one-dimensional viscoelastic model of blood vessel growth under nonlinear friction with surroundings, and provides numerical simulations for various growing cases. For the nonlinear differential equations, two sufficient conditions are proven to guarantee the global existence of biologically meaningful solutions. Examples with breakdown solutions are captured by numerical approximations. Numerical simulations demonstrate this model can reproduce angiogenesis experiments under various biological conditions including blood vessel extension without proliferation and blood vess…

Unconditional finite amplitude stability of a viscoelastic fluid in a mechanically isolated vessel with spatially non-uniform wall temperature

We investigate finite amplitude stability of spatially inhomogeneous steady state of an incompressible viscoelastic fluid which occupies a mechanically isolated vessel with walls kept at spatially non-uniform temperature. For a wide class of incompressible viscoelastic models including the Oldroyd-B model, the Giesekus model, the FENE-P model, the Johnson--Segalman model, and the Phan--Thien--Tanner model we prove that the steady state is stable subject to any finite perturbation.

Modeling blood flow in viscoelastic vessels: the 1D augmented fluid-structure interaction system

Mathematical models and numerical simulations are widely used in the field of hemodynamics, representing a valuable resource to better understand physiological and pathological processes. The theory behind the phenomenon is closely related to the study of incompressible flow through compliant thin-walled tubes. The mechanical interaction between blood flow and vessel wall must be properly described by the model. Recent works show the benefits of characterizing the rheology of the vessel wall through a viscoelastic law. Considering the viscous contribution of the wall material and not simply th…

关于斑块生长的流固耦合问题研究

On a fluid-structure interaction problem for plaque growth

该研究针对血管斑块形成对应的带生长自由边界流固耦合问题，采用不可压缩Navier-Stokes方程与黏弹性neo-Hookean材料模型，结合极大正则性理论、形变映射与压缩映射原理证明了非线性问题的适定性。