![]() This amounts to a reduction of the total scanning time by a factor of 27. We show that the method is capable of reconstructing and segmenting the low SNR images, producing noiseless velocity fields and a smooth segmentation, with negligible errors compared with the high SNR images. Then we conduct a magnetic resonance velocimetry (MRV) experiment to acquire images of an axisymmetric flow for low (≃6) and high (>30) SNRs. We first test the method for synthetic noisy images of two-dimensional (2-D) flows and observe that the method successfully reconstructs and segments the noisy synthetic images with a signal-to-noise ratio (SNR) of three. ![]() This allows us to estimate the uncertainties of the unknowns by approximating their posterior covariance with a quasi-Newton method. To regularize the problem, we use a Bayesian framework with Gaussian random fields. We formulate and solve a generalized inverse Navier–Stokes problem for the joint velocity field reconstruction and boundary segmentation of noisy flow velocity images. We find that the method is capable of reconstructing and segmenting the velocity fields from sparsely-sampled (15% $k$-space coverage), low ($\sim$$10$) signal-to-noise ratio (SNR) signals, and that the reconstructed velocity field compares well with that derived from fully-sampled (100% $k$-space coverage) high ($>40$) SNR signals of the same flow. We create an algorithm that solves this reconstruction problem, and test it for noisy and sparse $k$-space signals of the flow through a converging nozzle. This prior information is updated using the Navier-Stokes problem, an energy-based segmentation functional, and by requiring that the reconstruction is consistent with the $k$-space signals. Using a Bayesian framework, we regularize the problem by introducing a priori information about the unknown parameters in the form of Gaussian random fields. The method solves an inverse Navier-Stokes boundary value problem, which permits us to jointly reconstruct and segment the velocity field, and at the same time infer hidden quantities such as the hydrodynamic pressure and the wall shear stress. We formulate a physics-informed compressed sensing (PICS) method for the reconstruction of velocity fields from noisy and sparse phase-contrast magnetic resonance signals. These functions should facilitate the robot’s usage in new distal endovascular operations. #KINEMATIC VISCOSITY FORMULA ACTIVATOR#Furthermore, variants of the robot could release the tissue plasminogen activator on-demand locally for thrombolysis and function as flow diverters, initiating promising therapies towards acute ischemic stroke, aneurysm, arteriovenous malformation, dural arteriovenous fistulas, and brain tumors. These locomotion capabilities are confirmed in porcine arteries ex vivo. The robot can also withstand the flow when the magnetic actuation is turned off. We investigate shape-adaptively controlled locomotion in phantoms emulating the physiological conditions here, where the lumen diameter shrinks from 1.5 mm to 1 mm, the radius of curvature of the tortuous lumen gets as small as 3 mm, the lumen bifurcation angle goes up to 120°, and the pulsatile flow speed reaches up to 26 cm/s. Therefore, we propose a wireless stent-shaped magnetic soft robot to be deployed, actively navigated, used for medical functions, and retrieved in the example M4 segment of the middle cerebral artery. However, with tortuous routes far from the arterial puncture site, the distal vascular regions remain challenging for safe catheter access. Microcatheters have enabled diverse minimally invasive endovascular operations and notable health benefits compared with open surgeries. A Matlab script is provided that enables the easy implementation of this method in other works. The model fluids are designed for large throughput experiments of industrial units, and low-cost solutions were considered. The main novelties of this work are (1) the development and validation of a set of equations to predict the rheological and physical properties of model fluids for flow studies involving dissimilar fluids (2) the introduction of an algorithm to match the refractive index of fluids using calcium chloride. In the second part, calcium chloride was added to aqueous solutions of glycerol, and the variations of density, viscosity, and refractive index with the mass fraction of calcium chloride were reported, which is a new contribution to literature. Refractive index, viscosity, and density were measured for a mass fraction of glycerol in a range from 0 to 1 and compared to the data in the literature. The first part of this paper describes the physical properties of aqueous solutions of glycerol. The design of these experiments involves the description of the physical properties of liquids and the refractive index matching using a salt, i.e., calcium chloride. ![]() Aqueous solutions of glycerol are widely used as model fluids in flow phenomena experiments. ![]()
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