Cardiovascular Diseases (CVD), including stroke, coronary/peripheral artery diseases, are currently the leading cause of mortality globally. CVD are usually correlated to abnormal blood flow and vessel wall shear stress, and fast/accurate patient-specific 3D blood flow quantification can provide clinicians/researchers the insights/knowledge for better understanding, prediction, detection and treatment of CVD. Experimental methods including mainly ultrasound (US) Vector Flow Imaging (VFI), and Computational Fluid Dynamics (CFD) are usually employed for blood flow quantification. However current US methods are mainly 1D or 2D, noisy, can only obtain velocities at sparse positions in 3D, and thus have difficulties providing information required for research and clinical diagnosis. On the other hand while CFD is the current standard for 3D blood flow quantification it is usually computationally expensive and suffers from compromised accuracy due to uncertainties in the CFD input, e.g., blood flow boundary/initial condition and vessel geometry.
To bridge the current gap between the clinical needs of 3D blood flow quantification and measurement technologies, this thesis aims at: 1) developing a fast and accurate 3D full field flow reconstruction algorithm, using existing sparse 1D/2D US velocity measurements; 2) developing GPU based and US augmented Lattice Boltzmann Method (LBM) solver for faster and more accurate blood CFD computation. The thesis has made the following contributions:
(1) Chapter 2 proposed a new algorithm for 3D flow reconstruction using Divergence Free Interpolation (DFI) of sparse 2D in-plane velocity vectors obtained from US particle imaging velocimetry (UIV), with interpolation spatial basis functions which satisfy mass conservation. It is validated via two numerical reconstruction cases, and the reconstruction has similar accuracy with CFD and is ~4 times faster than CFD simulation for a range of problems. The proposed algorithm is also demonstrated and evaluated using experimental 2D UIV measurements.
(2) Chapter 3 has conducted optimizations to improve the DFI based 3D flow reconstruction approach in terms of accuracy and the time-to-solution, through optimizing the interpolation spatial basis function parameters and using a highly optimized iterative solver Generalized Minimal Residual method (GMRES) which is faster than the SVD solver used in the Chapter 2. The optimized algorithm is validated by successfully reconstructing 3D flows of in silico and in vitro UIV measurement cases, and the results show improved accuracy of ~3% and up to 728-fold speedup compared with previous method in Chapter 2. In Appendix A1 3D flow reconstruction using 1D vector US Doppler imaging has also been studied, and the feasibility of the method is demonstrated numerically by reconstructing 3D flow of a widely used benchmark (i.e., lid driven cavity flow). The method has a typical reconstruction time of <1s and error of ~5%, and can be ~800 times faster than CFD with slightly reduced but still acceptable accuracy.
(3) Patient-specific CFD suffers from high computational overheads and compromised accuracy due to input uncertainties. A measurement augmented GPU based Lattice Boltzmann Method (LBM) CFD solver is developed in order to speed up LBM simulation and reduce LBM error caused by such uncertainties, as shown in Chapter 4. We assume CFD inlet/outlet velocities and internal flow measurements are from the same US measurements and thus have similar level of fidelity. US VFI internal measurements are integrated into LBM CFD solver to constrain the simulation and augment it in terms of convergence speed and accuracy. The algorithm is validated with both in silico and in vitro cases, and the results show significant improvements of convergence speed (>30%) and accuracy compared with similar CFD without measurement augmentation. Comparing to the divergence free interpolation method, such estimation combines the advantages of the full physics in CFD and the sparse US measurements. In Appendix A2 the solver is then extended to consider the non-Newtonian rheological effects and validated in silico with a low error of ~1% using well-known commercial CFD software as a reference.
The proposed algorithms can be potentially employed to clinical applications/research, for faster and more accurate 3D blood flow quantifications.