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- Combining Models in Discrete Discriminant AnalysisPublication . Marques, Anabela; Ferreira, Ana Sousa; Cardoso, Margarida
- Performance of Combined Models in Discrete Binary ClassificationPublication . Marques, Anabela; Ferreira, Ana Sousa; Cardoso, Margarida
- A velocity tracking approach for the Data Assimilation problem in blood flow simulationsPublication . Tiago, Jorge; Guerra, Telma; Sequeira, AdéliaSeveral 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 profiles
- Existence of optimal boundary control for the Navier-Stokes equations with mixed boundary conditionsPublication . Guerra, Telma; Sequeira, Adélia; Tiago, JorgeVariational approaches have been used successfully as a strategy to takeadvantage from real data measurements. In several applications, this approach allowsto increase the accuracy of numerical simulations. In the particular case of fluid dy-namics, it leads to optimal control problems with non-standard cost functionals which,when subject to the Navier-Stokes equations, require a non-standard theoretical frameto ensure the existence of solution. In this work, we prove the existence of solution fora class of such type of optimal control problems. Before doing that, we ensure the ex-istence and uniqueness of solution for the 3D stationary Navier-Stokes equations, withmixed-boundary conditions, a particular type of boundary conditions very common inapplications to biomedical problems
- Optimal Control in Blood Flow SimulationsPublication . Guerra, Telma; Tiago, Jorge; Sequeira, AdéliaBlood 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 case
- Improving Blood Flow Simulations Using Known DataPublication . Guerra, Telma; Tiago, JorgeNumerical simulations applied to blood flow together with the imaging processing advances are a powerful tool in the prevention and treatment of some diseases. The inclusion of real data in the numerical blood flow simulations allowsthe achievementofmore realistic and accurate results. In the literature, these techniques areknown asData Assimilation (DA)techniques.In this work we solve a variational DA problem to numerically reconstruct the blood flow circulation inside a real artery,deformed by a saccular aneurysm obtained from medical images and then importedto COMSOL Multiphysics®.We propose a weighted cost function that accurately recovers both the velocity and the wall shear stress profiles. The robustness of such cost function is tested with respect to different velocity inlet profiles
- Aplicação de problemas de controlo a uma estenose idealizadaPublication . Guerra, Telma; Tiago, JorgeNeste trabalho apresentamos, de forma sucinta, simulações numé-ricas de fluidos, de problemas do tipo Assimilação de Dados numa aborda-gem variacional. Apresentamos resultados aplicados à Hemodinâmica consi-derando uma geometria tridimensional na forma de uma estenose idealizadae recuperamos o perfil da velocidade do sangue nesta geometria.
- On the Optimal Control of a Class of Non-Newtonian FluidsPublication . Guerra, Telma; Tiago, Jorge; Sequeira, AdéliaWe consider optimal control problems of systems governed by sta-tionary, incompressible generalized Navier-Stokes equations with shear depen-dent viscosity in a two-dimensional or three-dimensional domain. We study ageneral class of viscosity functions including shear-thinning and shear-thickeningbehavior. We prove an existence result for such class of optimal control prob-lems.
- A practical approach to model banking risks using Loss Distribution Approach (LDA) in Basel II frameworkPublication . Barreira, Raquel; Pryer, Tristan; Tang, QiIn Basel II Capital Accord, the Advanced Measurement Approaches (AMA) is stated as one of the pillar stone methods for calculating corporate risk reserves. One of the common yet cumbersome methods is the one known as loss distribution approach (cf. [3]). In this article, we present an easy to implement scheme through electronic means and discuss some of the mathematical problems we encountered in the process together with proposed solution methods and further sought on the issues.