Related papers: A velocity tracking approach for the Data Assimila…
Understanding time-dependent blood flow dynamics in arteries is crucial for diagnosing and treating cardiovascular diseases. However, accurately predicting time-varying flow patterns requires integrating observational data with…
A general setup for deterministic system identification problems on graphs with Dirichlet and Neumann boundary conditions is introduced. When control nodes are available along the boundary, we apply a discretize-then-optimize method to…
Several cardiovascular diseases are caused from localised abnormal blood flow such as in the case of stenosis or aneurysms. Prevailing theories propose that the development is caused by abnormal wall-shear stress in focused areas.…
Patient-specific modeling of cardiovascular flows with high-fidelity is challenging due to its dependence on accurately estimated velocity boundary profiles, which are essential for precise simulations and directly influence wall shear…
Numerical simulations of cardiovascular mass transport pose significant challenges due to the wide range of P\'eclet numbers and backflow at Neumann boundaries. In this paper we present and discuss several numerical tools to address these…
We propose a method to compute optimal control paths for autonomous vehicles deployed for the purpose of inferring a velocity field. In addition to being advected by the flow, the vehicles are able to effect a fixed relative speed with…
The choice of appropriate boundary conditions is a fundamental step in computational fluid dynamics (CFD) simulations of the cardiovascular system. Boundary conditions, in fact, highly affect the computed pressure and flow rates, and…
This article concerns a class of time-optimal state constrained control problems with dynamics defined by an ordinary differential equation involving a three-dimensional steady flow vector field. The problem is solved via an indirect method…
Image-based, patient-specific modelling of hemodynamics can improve diagnostic capabilities and provide complementary insights to better understand the hemodynamic treatment outcomes. However, computational fluid dynamics simulations remain…
Variational data assimilation technique applied to identification of optimal approximations of derivatives near boundary is discussed in frames of one-dimensional wave equation. Simplicity of the equation and of its numerical scheme allows…
Continuous data assimilation addresses time-dependent problems with unknown initial conditions by incorporating observations of the solution into a nudging term. For the prototypical heat equation with variable conductivity and the Neumann…
Understanding and predicting people flow in urban areas is useful for decision-making in urban planning and marketing strategies. Traditional methods for understanding people flow can be divided into measurement-based approaches and…
We introduce a continuous (downscaling) data assimilation algorithm for the 2D B\'enard convection problem using vorticity or local circulation measurements only. In this algorithm, a nudging term is added to the vorticity equation to…
Fast and realistic coupling of blood flow and vessel wall is of great importance to virtual surgery. In this paper, we propose a novel data-driven coupling method that formulates physics-based blood flow simulation as a regression problem,…
We consider an optimal flow control problem in a patient-specific coronary artery bypass graft with the aim of matching the blood flow velocity with given measurements as the Reynolds number varies in a physiological range. Blood flow is…
Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using…
Mathematical models and numerical simulations offer a non-invasive way to explore cardiovascular phenomena, providing access to quantities that cannot be measured directly. In this study, we start with a one-dimensional multiscale blood…
Variational data assimilation technique applied to the identification of the optimal discretization of interpolation operators and derivatives in the nodes adjacent to the boundary of the domain is discussed in frames of the linear shallow…
In meteorological and oceanological studies the classical approach for finding the numerical solution of the regional model consists in formulating and solving the Cauchy-Dirichlet problem. The related boundary conditions are obtained by…
One of the crucial aspects of patient-specific blood flow simulations is to specify material parameters and boundary conditions. The choice of boundary conditions can have a substantial impact on the character of the flow. While no-slip is…