BackgroundPhase contrast magnetic resonance imaging (PC-MRI) is used clinically for quantitative assessment of cardiovascular flow and function, as it is capable of providing directly-measured 3D velocity maps. Alternatively, vascular flow can be estimated from model-based computation fluid dynamics (CFD) calculations. CFD provides arbitrarily high resolution, but its accuracy hinges on model assumptions, while velocity fields measured with PC-MRI generally do not satisfy the equations of fluid dynamics, provide limited resolution, and suffer from partial volume effects. The purpose of this study is to develop a proof-of-concept numerical procedure for constructing a simulated flow field that is influenced by both direct PC-MRI measurements and a fluid physics model, thereby taking advantage of both the accuracy of PC-MRI and the high spatial resolution of CFD. The use of the proposed approach in regularizing 3D flow fields is evaluated.MethodsThe proposed algorithm incorporates both a Newtonian fluid physics model and a linear PC-MRI signal model. The model equations are solved numerically using a modified CFD algorithm. The numerical solution corresponds to the optimal solution of a generalized Tikhonov regularization, which provides a flow field that satisfies the flow physics equations, while being close enough to the measured PC-MRI velocity profile. The feasibility of the proposed approach is demonstrated on data from the carotid bifurcation of one healthy volunteer, and also from a pulsatile carotid flow phantom.ResultsThe proposed solver produces flow fields that are in better agreement with direct PC-MRI measurements than CFD alone, and converges faster, while closely satisfying the fluid dynamics equations. For the implementation that provided the best results, the signal-to-error ratio (with respect to the PC-MRI measurements) in the phantom experiment was 6.56 dB higher than that of conventional CFD; in the in vivo experiment, it was 2.15 dB higher.ConclusionsThe proposed approach allows partial or complete measurements to be incorporated into a modified CFD solver, for improving the accuracy of the resulting flow fields estimates. This can be used for reducing scan time, increasing the spatial resolution, and/or denoising the PC-MRI measurements.

Fourier velocity encoding (FVE) is a promising magnetic resonance imaging (MRI) method for measurement of cardiovascular blood flow. FVE provides considerably higher SNR than phase contrast imaging, and is robust to partial-volume effects. FVE data is usually acquired with low spatial resolution, due to scan-time restrictions associated with its higher dimensionality. Thus, FVE is capable of providing the velocity distribution associated with a large voxel, but does not directly provides a velocity map. Velocity maps, however, are useful for calculating the actual blod flow through a vessel, or for guiding computational fluid dynamics simulations. This work proposes a method to derive velocity maps with high spatial resolution from low-resolution FVE data using a hyper-Laplacian prior deconvolution algorithm. Experiments using numerical phantoms, as well simulated spiral FVE data derived from real phase contrast data, acquired using a pulsatile carotid flow phantom, show that it is possible to obtain reasonably accurate velocities maps from low-resolution FVE distributions.

No abstract

No abstract

Resumo Problemas de valores inicial e de contorno são muito comuns na Física, Matemática e Engenharia. Eles podem modelar diversos tipos de problemas relacionados a difusão de calor e a vibração de membranas, por exemplo. Quando se deseja encontrar a solução analítica desses problemas podemos encontrar dificuldades extras quando as equações e também as condições de contorno que descrevem os fenômenos são não-homogêneas. Desta forma, neste trabalho apresentamos uma técnica de solução de problemas de valores iniciais e de contorno por meio de transformações integrais. O diferencial da apresentação está na construção da transformada integral apropriada à solução do problema. Essas transformadas são conhecidas como transformadas finitas e neste caso elas estão relacionadas a um problema de Sturm–Liouville associado com o operador diferencial ligado à equação diferencial. Como exemplo do desenvolvimento e aplicação da ferramenta, resolvemos dois problemas de difusão de calor em coordenadas espaciais distintas. A apresentação do trabalho segue de forma pedagógica e autocontida. Sendo assim, esperamos que o leitor compreenda a técnica e possa utilizá-la na resolução de outros problemas envolvendo equações diferencias parciais.