Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 129, Issue -, Pages 11-33Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2022.11.006
Keywords
Brinkman equation; Gradient-based optimization; Stabilized finite elements; Boundary reconstruction
Categories
Ask authors/readers for more resources
We reconstructed the unknown shape of a flow domain using partial internal velocity measurements. This inverse problem is motivated by applications in cardiovascular imaging, where motion-sensitive protocols can be used to recover three-dimensional velocity fields in blood vessels. The information about the domain shape is important for quantifying the severity of pathological conditions. We employed a multi-step gradient-based variational method to compute a resistance that minimizes the difference between the computed flow velocity and the available data, and applied post-processing steps to reconstruct the shape of the internal boundaries. The stability and well-posedness of the optimization problem were proven.
We reconstruct the unknown shape of a flow domain using partially available internal velocity measurements. This inverse problem is motivated by applications in cardiovascular imaging where motion-sensitive protocols, such as phase-contrast MRI, can be used to recover three-dimensional velocity fields inside blood vessels. In this context, the information about the domain shape serves to quantify the severity of pathological conditions, such as vessel obstructions. We consider a flow modeled by a linear Brinkman problem with a fictitious resistance accounting for the presence of additional boundaries. To reconstruct these boundaries, we employ a multi-step gradient-based variational method to compute a resistance that minimizes the difference between the computed flow velocity and the available data. Afterward, we apply different post-processing steps to reconstruct the shape of the internal boundaries. To limit the overall computational cost, we use a stabilized equal-order finite element method. We prove the stability and the well-posedness of the considered optimization problem. We validate our method on three-dimensional examples based on synthetic velocity data and using realistic geometries obtained from cardiovascular imaging.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available