Analysis and correction of gradient nonlinearity and B₀ inhomogeneity related scaling errors in two‐dimensional phase contrast flow measurements

Abstract

In the past decade, numerous studies have been devoted to the sources of errors in phase contrast (PC) flow quantification (1-8). Factors affecting the accuracy and precision of these measurements have been investigated extensively and include aliasing due to mismatched encoding velocity, intravoxel phase dispersion, angulation of the imaging plane, inadequate temporal and/or spatial resolution, pulsatility effects, phase offset errors, measurement noise, and spatial misregistration. As far as we know, only one study includes off-center velocity miscalculation related to gradient nonuniformity (9). Our interest in off-center miscalculation of flow was aroused by some inconsistent results of a study in which flow measurements were performed in the loop graft in the forearm of hemodialysis patients (Fig. 1). On average, PC measurements in these grafts were 9% higher than ultrasound dilution measurements (10) and, occasionally, significant differences were observed between the flow values of the arterial and venous limbs. We hypothesized that these observations could have been caused by the nonlinearity of gradients and the inhomogeneity of the main field, as they increase further offcenter. Therefore, we performed a theoretical and experimental analysis of the influence of measurement position on PC flow measurements. In the theoretical part, we will show that scaling of the reconstructed vessel cross-sectional area, caused by inhomogeneity of the main field and nonlinearity of the read and phase-encoding gradients, and scaling of the reconstructed velocity, caused by the nonlinearity of the velocity-encoding gradient, result in incorrect flow values. In the experimental section, we will demonstrate that the associated scaling factors can be determined with a flow phantom and that they can be used to correct the observed flow values. Furthermore, we will show that at off-center positions, concomitant gradients will degrade PC flow measurements. We use the same flow phantom to measure and minimize the sequence-dependent concomitant phase evolution in order to quantify this effect. We will demonstrate concomitant gradient correction in combination with scaling correction, both in the flow phantom and in a volunteer study. THEORYThe volume flow Q through a vessel is the integral of the velocity profile over the cross-sectional area of the vessel. With PC techniques, it is possible to measure velocity, which enables flow quantification by adding the velocity contents over the cross-sectional area. However, the reconstructed cross-sectional area and velocity will be scaled due to the nonlinearity of gradients and inhomogeneity of the main field, resulting in incorrect 2D PC flow values. Inhomogeneity of the Main FieldReichenbach et al. (11) explain distortions of the image in gradient echo imaging as a result of inhomogeneity of the main field, resulting in scaling, translation, and shearing of the object in the read direction. Scaling arises from local, stationary gradients in the read direction, shearing from local,...

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