Reconstruction and Analysis of Interior Flows with Applications in Cardiovascular Hemodynamics

Heart disease is the leading cause of death worldwide, killing 17.9 million annually. Blood flow patterns in the heart have been shown to be associated with disease, but the adoption of blood flow diagnostics in the clinic has been limited by the difficulty of imaging blood flow inside the body. Color-Doppler ultrasound and 4D-flow Magnetic Resonance Imaging (MRI) are currently the two main tools used to image blood flow. Color-Doppler ultrasound is widely-accessible and relatively inexpensive, but traditional ultrasound only collects a single component of velocity on a single plane. 4D-flow MRI collects all three components of velocity in a 3D domain but is much more expensive and difficult to use. Here, we use computational tools to improve image processing and analysis of blood flow in the left ventricle for both color-Doppler ultrasound and 4D-flow MRI data. Specifically, we seek to develop methods for de-noising and reconstructing interior flow fields and for calculating kinetic energy and viscous dissipation as potential diagnostic tools from limited data.First, we investigate tools to augment color-Doppler ultrasound data. We test multiple methods to calculate a second, in-plane component of velocity from the available velocity and geometry information. Previously, methods to reconstruct the second component of velocity were developed using an assumption that through-plane divergence was negligible. We introduce alternative methods to reconstruct the second component of velocity without making the through-plane assumption. However, when compared to previous methods, these alternative methods did not show an improvement in the accuracy of predicting the second component of velocity.Following these results, we propose modifications to estimates of diagnostic measures from color-Doppler ultrasound data. For many diagnostic measures calculated from color-Doppler ultrasound data, the velocity is measured, a second component of velocity is calculated, and a 2D evaluation of the diagnostic measure is performed. Instead, we propose a 1D evaluation of diagnostic measures directly from the single, measured component of velocity. We introduce this metric for kinetic energy and viscous dissipation rate in the left ventricle, two measures that have been shown to be correlated with heart disease. Using computational fluid dynamics simulation results to obtain a true measurement from all three components of velocity in the entire ventricle, virtual ultrasound measurements were taken and the different types of estimates were calculated from the virtual ultrasound. These reduced dimensional estimates were then compared to the true, 3D values. Both the 1D and 2D estimates were correlated with the 3D values and kinetic energy was more robust to noise and lower grid resolution. These results indicate that 1D estimates, and kinetic energy especially, should be continued to be explored for further use in the clinic.Next, we explore a modal analysis method to de-noise and reconstruct 3D flow fields that can be applied to 4D-flow MRI or color-Doppler ultrasound data. While many methods have been introduced to de-noise 3D velocity fields, this modal analysis method provides advantages because it results in a divergence-free flow field, satisfies necessary boundary conditions, and can be applied to multiple types of data. To test the method, it was applied to flow inside a cube, through a stenosis, around a cylinder, and inside the left ventricle using data from computational fluid dynamics simulations. The modal analysis method was shown to reduce noise from noisy velocity fields and to be able to adequately reconstruct velocity fields with missing data points or missing components of velocity. These results are promising for use with 4D-flow MRI data where a 3D flow field on a 3D domain is available. These results are also promising for use with more recent advancements of color-Doppler ultrasound that allow for measurements on multiple parallel planes and for developing capabilities of color-Doppler ultrasound that allow for measurement of a second, in-plane component of velocity.Through reduced dimensional estimates of kinetic energy and viscous dissipation rate in the left ventricle that can be measured using color-Doppler ultrasound data and the introduction of a modal analysis technique to de-noise and reconstruct 3D flow fields, this dissertation advances image processing and analysis tools for blood flow in the left ventricle