There have been three sub-projects carried out with the following achievements:
Sub-project 1 aims to develop blood flow models from raw MRI data for simpler fluid and fluid-solid problems. The team found a new way to estimate the properties of blood flowing in the body using MRI measurements, including artifacts in the images. They also started developing a way to use raw MRI measurements to estimate blood flow properties, tested this approach on simulated data, and will soon use experimental data to confirm its accuracy. In addition, they developed a way to accelerate the MRI measurement process and found that they don't need to take many measurements to get accurate results in academic tests. However, further testing is still needed on fluid flow models.
Sub-project 2 aimed to develop new inverse problems for shape estimation of cardiac valves, first from velocity data, and then extending the results of sub-project 1 from raw MRI data. The team made a simple model of the aortic valve that can be used in computer simulations of blood flow and tested it on patients with aortic stenosis using images from CT scans. They also created a new method for finding obstacles in the flow of fluid inside the body, like in the heart. This method adds a term to the equations that makes it easier to find these obstacles, even when there is limited information from MRI or ultrasound scans. They tested this method on simulated heart valves.
Sub-project 3 aimed to develop new inverse problems for cardiac mechanics, first from velocity data, and then extending the results of sub-project 1 from MRI data. The team developed a new algorithm that can simulate how fluids and solids interact with each other in large, deformable structures like the heart. They tested the program and found that it works well for modeling how blood flows through the heart. They also created a new computer method that can estimate the properties of fluids and solids in the heart by analyzing how they interact with each other. They found that when they include measurements of how the fluid flows, they can get much better results than with just measurements of the solid's motion.
