A kinematically coupled time-splitting scheme for fluid–structure interaction in blood flow

We present a new time-splitting scheme for the numerical simulation of fluid–structure interaction between blood flow and vascular walls. This scheme deals in a successful way with the problem of the added mass effect. The scheme is modular and it embodies the stability properties of implicit schemes at the low computational cost of loosely coupled ones.     

Stable loosely-coupled-type algorithm for fluid–structure interaction in blood flow

We introduce a novel loosely coupled-type algorithm for fluid–structure interaction between blood flow and thin vascular walls. This algorithm successfully deals with the difficulties associated with the “added mass effect”, which is known to be the cause of numerical instabilities in fluid–structure interaction problems involving fluid and structure of comparable densities. Our algorithm is based on a time-discretization via operator splitting which is applied, in a novel way, to separate the fluid sub-problem from the structure elastodynamics sub-problem. In contrast with traditional loosely-coupled schemes, no iterations are necessary between the fluid and structure sub-problems; this is due to the fact that our novel splitting strategy uses the “added mass effect” to stabilize rather than to destabilize the numerical algorithm. This stabilizing effect is obtained by employing the kinematic lateral boundary condition to establish a tight link between the velocities of the fluid and of the structure in each sub-problem. The stability of the scheme is discussed on a simplified benchmark problem and we use energy arguments to show that the proposed scheme is unconditionally stable. Due to the crucial role played by the kinematic lateral boundary condition, the proposed algorithm is named the “kinematically coupled scheme”.     

Existence of a Weak Solution to a Nonlinear Fluid–Structure Interaction Problem Modeling the Flow of an Incompressible, Viscous Fluid in a Cylinder with Deformable Walls

We study a nonlinear, unsteady, moving boundary, fluid–structure interaction (FSI) problem arising in modeling blood flow through elastic and viscoelastic arteries. The fluid flow, which is driven by the time-dependent pressure data, is governed by two-dimensional incompressible Navier–Stokes equations, while the elastodynamics of the cylindrical wall is modeled by the one-dimensional cylindrical Koiter shell model. Two cases are considered: the linearly viscoelastic and the linearly elastic Koiter shell. The fluid and structure are fully coupled (two-way coupling) via the kinematic and dynamic lateral boundary conditions describing continuity of velocity (the no-slip condition), and the balance of contact forces at the fluid–structure interface. We prove the existence of weak solutions to the two FSI problems (the viscoelastic and the elastic case) as long as the cylinder radius is greater than zero. The proof is based on a novel semi-discrete, operator splitting numerical scheme, known as the kinematically coupled scheme, introduced in Guidoboni et al. (J Comput Phys 228(18):6916–6937, 2009) to numerically solve the underlying FSI problems. The backbone of the kinematically coupled scheme is the well-known Marchuk–Yanenko scheme, also known as the Lie splitting scheme. We effectively prove convergence of that numerical scheme to a solution of the corresponding FSI problem.     

Comparative biochemical characterization of 5'-phosphodiesterase and phosphomonoesterase from barley malt sprouts

A comparative biochemical characterization is described of two competing enzymes in the production of flavoring 5'-ribonucleotides, barley malt sprouts 5'-phosphodiesterase (5'-PDE) and phosphomonoesterase (PME). Fractionation of these two enzymes and partial purification of 5'-PDE were achieved by a combination of thermal treatments and precipitation with acetone. With synthetic substrates, under standard assay conditions, 5'-PDE and PME had maximum activities at pH 8.9, 70 degrees C and 55 degrees C, and Km of 0.26 mM and 0.19 mM, respectively. In the presence of 10 mM Mg2+ ions, barley malt sprouts 5'-PDE was activated by up to 160% of the original activity, while PME was inhibited. Zn2+ activated PME by up to 125% of the original activity. Both enzymes were moderately inhibited after addition of Cu2+, Co2+, Ca2+, and Mn2+ ions (10 mM), but, significantly, by addition of the chelating agent EDTA. In the absence of substrate and up to 80 degrees C, barley malt sprouts 5'-PDE showed excellent stability and retained 70% of its original activity at 70 degrees C after 120 min.