Phase 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. The 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. The 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. The 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 assessment of cardiovascular blood flow. FVE provides considerably higher signal-to-noise ratio than phase contrast (PC) imaging, is robust to partial-volume effects and can be acquired rapidly using spiral readouts. On the other hand, FVE data do not directly provide a velocity map. These maps are useful for calculating the actual blood flow through a vessel, or for guiding computational fluid dynamics simulations (CFD). In this paper, FVE data were simulated from PC velocity maps from a pulsatile carotid flow phantom; velocity maps were then reconstructed from these FVE data, and used to guide CFD simulations. FVE-guided CFD velocity fields were qualitatively and quantitatively compared with the PC-measured velocity field, with the pure CFD solution, and with PC-guided CFD. The results show that FVE-guided CFD achieves better agreement with the PC-measured velocity field than pure CFD. Compared with PC-guided CFD, FVE provides considerably better results than PC with similar scan time, and equivalent results when compared with PC with 9 times longer scan time.

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.

Apresentamos neste trabalho uma breve revisão sobre o cálculo fracionário e também o método de Adam-Bashforth fracionário para solução de equações diferenciais fracionárias. O método de Adam-Bashforth fracionário é devido a Diethelm et al. [1] e caracteriza-se pela sua eficiência, já que considera os efeitos de memória das derivadas fracionárias. A apresentação do tema é realizada de forma pedagógica, proporcionando a compreensão daqueles que são incipientes no assunto. Nesse contexto, exemplos são apresentados e algumas aplicações são discutidas.

This study aimed to assess the electromyographic feasibility of different hip muscles on transfemoral unilateral lower limb amputees to a possible control of artificial limbs. The volunteers were split into two groups: eight males, physically active amputees and a control group composed of eight males, healthy, non-amputees individuals. The hip muscles were assessed in accordance to the general consensus by SENIAM project, and some adaptations were made in the amputees when the anatomical references were absents, such as the knee articulation. Thus, agonists and antagonists skeleton muscles were evaluated during the isometric contraction of hips movements of extension and flexion, which were controlled by an isokinect chair. The median frequency (F