On the Optimal Control of a Class of Non-Newtonian Fluids

We consider optimal control problems of systems governed by stationary, incompressible generalized Navier-Stokes equations with shear dependent viscosity in a two-dimensional or three-dimensional domain. We study a general class of viscosity functions including shear-thinning and shear-thickening behavior. We prove an existence result for such class of optimal control problems

Existence of optimal boundary control for the Navier-Stokes equations with mixed boundary conditions

Variational approaches have been used successfully as a strategy to take advantage from real data measurements. In several applications, this approach gives a means to increase the accuracy of numerical simulations. In the particular case of fluid dynamics, it leads to optimal control problems with non standard cost functionals which, when constraint to the Navier-Stokes equations, require a non-standard theoretical frame to ensure the existence of solution. In this work, we prove the existence of solution for a class of such type of optimal control problems. Before doing that, we ensure the existence and uniqueness of solution for the 3D stationary Navier-Stokes equations, with mixed-boundary conditions, a particular type of boundary conditions very common in applications to biomedical problems

An overview of some mathematical models of blood rheology

Experimental investigations over many years reveal that blood flow exhibits non-Newtonian characteristics such as shear-thinning, viscoelasticity and thixotropic behaviour. The complex rheology of blood is influenced by numerous factors including plasma viscosity, rate of shear, hematocrit, level of erythrocytes aggregation and deformability. Hemodynamic analysis of blood flow in vascular beds and prosthetic devices requires the rheological behaviour of blood to be characterized through appropriate constitutive equations relating the stress to deformation and rate of deformation. The objective of this paper is to present a short overview of some macroscopic constitutive models that can mathematically characterize the rheology of blood and describe its known phenomenological properties. Some numerical simulations obtained in geometrically reconstructed real vessels will be also presented to illustrate the hemodynamic behaviour using Newtonian and non-Newtonian inelastic models under a given set of physiological flow conditions.info:eu-repo/semantics/publishedVersio

Optimal Control in Blood Flow Simulations

preprintBlood flow simulations can be improved by integrating known data into thenumerical simulations. Data assimilation techniques based on a variationalapproach play an important role in this issue. We propose a nonlinear optimalcontrol problem to reconstruct the blood flow profile from partial observationsof known data in idealized 2D stenosed vessels. The wall shear stress isincluded in the cost function, which is considered as an important indicatorfor medical purposes. To simplify we assume blood flow as an homogeneousfluid with non-Newtonian behavior. Using a Discretize then Optimize (DO)approach, we solve the nonlinear optimal control problem and we proposea weighted cost function that accurately recovers both the velocity and thewall shear stress profiles. The robustness of such cost function is tested withrespect to different velocity profiles and degrees of stenosis. The filteringeffect of the method is also confirmed. We conclude that this approach canbe successfully used in the 2D caseinfo:eu-repo/semantics/submittedVersio

Data-Driven Computations in the Life Sciences

Mathematical modeling and simulations in the Life Sciences is a very ambitious and rapidly developing interdisciplinary research field that connects mathematics, computational sciences and engineering to biology and medicine. Starting from high-resolution volumetric medical imaging, the development of spatially realistic physiological models for predictive medicine leads to complex mathematical models to capture heterogeneous processes of multiscale nature, that require highly efficient numerical algorithms and high performance computing techniques for their simulation. The aim of he School is to bring together doctoral candidates, postdoctoral scientists and graduates in applied mathematics, bioengineering and medicine, who wish to be involved in this fascinating research field, giving them the opportunity to make scientific interactions and new connections with established experts in the different topics covered by these events

A velocity tracking approach for the Data Assimilation problem in blood flow simulations

preprintSeveral advances have been made in Data Assimilation techniques applied to blood flow modeling. Typically,idealized boundary conditions, only verified in straight parts of the vessel, are assumed. We present ageneral approach, based on a Dirichlet boundary control problem, that may potentially be used in differentparts of the arterial system. The relevance of this method appears when computational reconstructions ofthe 3D domains, prone to be considered sufficiently extended, are either not possible, or desirable, due tocomputational costs. Based on taking a fully unknown velocity profile as the control, the approach uses adiscretize then optimize methodology to solve the control problem numerically. The methodology is appliedto a realistic 3D geometry representing a brain aneurysm. The results show that this DA approach may bepreferable to a pressure control strategy, and that it can significantly improve the accuracy associated totypical solutions obtained using idealized velocity profilesinfo:eu-repo/semantics/submittedVersio