Purpose The purpose of this study is to provide a standard method for flow velocity measurements with phase‐contrast (PC) MRI. This method can be used for in vitro studies that place high demands on measurement accuracy. Clinically relevant PC MRI techniques can be validated using this method before being applied in vivo. Methods Many motion‐related errors in PC MRI, particularly flow misregistration, depend on the timing of the encoding gradients in the pulse sequence. By synchronizing all encoding gradients and shortening the overall encoding interval, these errors can be significantly reduced. Based on this concept, a single‐point PC MRI method is proposed. Results Flow experiments were conducted in vitro. No considerable errors were found in the velocity data of the proposed method. For comparison, a conventional PC MRI technique showed up to 100% local velocity deviation and up to 35% flow rate deviation in the same experiments. Conclusions With the proposed method, the overall measurement accuracy is significantly increased compared to conventional PC MRI techniques. Due to long acquisition times and high specific absorption rates, this method can only be applied in vitro.

This study focuses on the measurement accuracy of Magnetic Resonance Velocimetry (MRV) in high-speed turbulent flows. One of the most prominent errors in MRV is the displacement error, which describes the misregistration of spatial coordinates and velocity components in moving fluids. Displacement errors are particularly critical for experiments with high flow velocity and high spatial resolution. The degree of displacement error also depends on the sequence structure of the MRV technique. In this study, two MRV sequence types are examined regarding their measurement capabilities in highspeed turbulent flows: a conventional MRV sequence based on the popular "4D FLOW" technique, and a newly developed sequence, named "SYNC SPI". Compared to conventional MRV, SYNC SPI is designed for high measurement accuracy, and not for imaging speed, which limits its application to statistically stationary flows. Both sequence types are evaluated in a flow experiment with a converging-diverging nozzle. Time-averaged results are presented for velocities up to 12 m/s at the throat. Supported by Particle Imaging Velocimetry, it is shown that SYNC SPI is capable of acquiring accurate velocity data in these highly turbulent flows. In contrast, the data from the conventional MRV sequence exhibits substantial displacement errors with a maximum displacement of 21 mm. The long acquisition time is the main disadvantage of the SYNC SPI sequence. Therefore, it is examined if undersampling and non-linear reconstruction, known as Compressed Sensing, can be utilized to make data acquisition more efficient. In the presented measurements, Compressed Sensing is successfully applied to shorten the acquisition time by up to 70% with almost no reduction in measurement accuracy.

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Magnetic Resonance Imaging (MRI) provides an insight into opaque structures and does not only have a large number of applications in the field of medical examinations but also in the field of engineering. In technical applications, MRI enables a contactless measurement of the two-or threedimensional velocity field within minutes. However, various measurement methods would benefit from an acceleration of the measurement procedure. Compressed Sensing is a promising method to fit this need. A random undersampling of the sampled data points enables a significant reduction of acquisition time. As this method requires a nonlinear iterative reconstruction of unmeasured data to obtain the same data quality as for a conventional fully sampled measurement, it is essential to estimate the influence of uncertainty on the quantitative result. This paper investigates the implementation of interval arithmetic approaches with a focus on the applicability in the frame of compressed sensing techniques. These approaches are able to handle bounded uncertainty not only in the case of linear relationships between measured data and the computed outputs but also allow for solving the necessary optimality criteria for the fluid velocity reconstruction in an iterative manner under the assumption of set-valued measurement errors and bounded representations of noise.