Time resolved phase-contrast magnetic resonance imaging 4D-PCMR (also called 4D Flow MRI) data while capable of non-invasively measuring blood velocities, can be affected by acquisition noise, flow artifacts, and resolution limits. In this paper, we present a novel method for merging 4D Flow MRI with computational fluid dynamics (CFD) to address these limitations and to reconstruct de-noised, divergence-free high-resolution flow-fields. Proper orthogonal decomposition (POD) is used to construct the orthonormal basis of the local sampling of the space of all possible solutions to the flow equations both at the low-resolution level of the 4D Flow MRI grid and the high-level resolution of the CFD mesh. Low-resolution, de-noised flow is obtained by projecting in-vivo 4D Flow MRI data onto the low-resolution basis vectors. Ridge regression is then used to reconstruct high-resolution de-noised divergence-free solution. The effects of 4D Flow MRI grid resolution, and noise levels on the resulting velocity fields are further investigated. A numerical phantom of the flow through a cerebral aneurysm was used to compare the results obtained using the POD method with those obtained with the state-of-the-art de-noising methods. At the 4D Flow MRI grid resolution, the POD method was shown to preserve the small flow structures better than the other methods, while eliminating noise. Furthermore, the method was shown to successfully reconstruct details at the CFD mesh resolution not discernible at the 4D Flow MRI grid resolution. This method will improve the accuracy of the clinically relevant flow-derived parameters, such as pressure gradients and wall shear stresses, computed from in-vivo 4D Flow MRI data.

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The scarcity of organs for transplant has led to large waiting lists of very sick patients. In drug development, the time required for human trials greatly increases the time to market. Drug companies are searching for alternative environments where the in − vivo conditions can be closely replicated. Both these problems could be addressed by manufacturing artificial human tissue. Recently, researchers in tissue engineering have developed tissue generation methods based on 3-D printing to fabricate artificial human tissue. Broadly, these methods could be classified as laser-assisted and laser free. The former have very fine spatial resolutions (10s of µm) but suffer from slow speed ( < 10 2 drops per second). The later have lower spatial resolutions (100s of µ m) but are very fast (up to 5 × 10 3 drops per second). In this paper we review state-of-the-art methods in each of these classes and provide a comparison based on reported resolution, printing speed, cell density and cell viability.

Dynamic Mode Decomposition (DMD) is a data-driven method to analyze the dynamics, first applied to fluid dynamics. It extracts modes and their corresponding eigenvalues, where the modes are spatial fields that identify coherent structures in the flow and the eigenvalues describe the temporal growth/decay rates and oscillation frequencies for each mode. The recently introduced compressed sensing DMD (csDMD) reduces computation times and also has the ability to deal with sub-sampled datasets. In this paper, we present a similar technique based on discrete cosine transform to reconstruct the fully-sampled dataset (as opposed to DMD modes as in csDMD) from sub-sampled noisy and gappy data using l 1 minimization. The proposed method was benchmarked against csDMD in terms of denoising and gap-filling using three datasets. The first was the 2-D time-resolved plot of a double gyre oscillator which has about nine oscillatory modes. The second dataset was derived from a Duffing oscillator. This dataset has several modes associated with complex eigenvalues which makes them oscillatory. The third dataset was taken from the 2-D simulation of a wake behind a cylinder at Re = 100 and was used for investigating the effect of changing various parameters on reconstruction error. The Duffing and 2-D wake datasets were tested in presence of noise and rectangular gaps. While the performance for the double-gyre dataset is comparable to csDMD, the proposed method performs substantially better (lower reconstruction error) for the dataset derived from the Duffing equation and also, the 2-D wake dataset according to the defined reconstruction error metrics.