Image-based gradient non-linearity characterization to determine higher-order spherical harmonic coefficients for improved spatial position accuracy in magnetic resonance imaging

Abstract

Purpose Spatial position accuracy in magnetic resonance imaging (MRI) is an important concern for a variety of applications, including radiation therapy planning, surgical planning, and longitudinal studies of morphologic changes to study neurodegenerative diseases. Spatial accuracy is strongly influenced by gradient linearity. This work presents a method for characterizing the gradient non-linearity fields on a per-system basis, and using this information to provide improved and higher-order (9th vs 5th) spherical harmonic coefficients for better spatial accuracy in MRI. Methods A large fiducial phantom containing 5229 water-filled spheres in a grid pattern is scanned with the MR system, and the positions all the fiducials are measured and compared to the corresponding ground truth fiducial positions as reported from a computed tomography (CT) scan of the object. Systematic errors from off-resonance (i.e., B0) effects are minimized with the use of increased receiver bandwidth (±125 kHz) and two acquisitions with reversed readout gradient polarity. The spherical harmonic coefficients are estimated using an iterative process, and can be subsequently used to correct for gradient non-linearity. Test-retest stability was assessed with five repeated measurements on a single scanner, and cross-scanner variation on four different, identically-configured 3T wide-bore systems. Results A decrease in the root-mean-square error (RMSE) over a 50 cm diameter spherical volume from 1.80 mm to 0.77 mm is reported here in the case of replacing the vendor’s standard 5th order spherical harmonic coefficients with custom fitted 9th order coefficients, and from 1.5mm to 1mm by extending custom fitted 5th order correction to the 9th order. Minimum RMSE varied between scanners, but was stable with repeated measurements in the same scanner. Conclusions The results suggest that the proposed methods may be used on a per-system basis to more accurately calibrate MR gradient non-linearity coefficients when compared to vendor standard corrections.

Geometric distortion characterization and correction for the 1.0 T Australian MRI‐linac system using an inverse electromagnetic method

“…However, the results showed that the performance for the high‐order SH such as the 11th order was stable on the large FOV (e.g., 50‐cm DSV) but unstable at smaller FOVs (e.g., 30‐cm DSV). Moreover, fitting for higher‐order coefficients could be challenging because of the convergence difficulty in iterative algorithms . An investigation of the accuracy and stability of higher‐order SH was beyond the scope of this work.…”

“…Some studies used an iterative calibration process to obtain higher‐order SH coefficients for GNL modeling in a larger FOV. However, the results showed that the performance for the high‐order SH such as the 11th order was stable on the large FOV (e.g., 50‐cm DSV) but unstable at smaller FOVs (e.g., 30‐cm DSV). Moreover, fitting for higher‐order coefficients could be challenging because of the convergence difficulty in iterative algorithms .…”

“…The fifth‐order SH correction methods have been shown to work effectively inside of the working DSV for commercial whole‐body systems . However, the fifth‐order SH may not work optimally for the area at the edges and/or outside of the DSV . In the Australian MRI‐Linac system, as the scanner has a smaller DSV (30‐cm DSV, ±4.05 ppm) than commercial whole‐body MRI scanners (50‐cm DSV, 1 ppm) because of the split structure, the GNL‐induced distortions for the target anatomy at the periphery or outside the DSV need to be resolved …”

Improving apparent diffusion coefficient accuracy on a compact 3T MRI scanner using gradient nonlinearity correction

“…The gradient field map tensor can be generally expressed using spherical harmonic polynomial expansion . The model coefficients can be obtained using electromagnetic (EM) simulation or phantom calibration . In general, for conventional whole‐body systems, only model coefficients of odd‐orders (eg, 3 rd order, 5 th order, etc.)…”

“…7,8 The model coefficients can be obtained using electromagnetic (EM) simulation or phantom calibration. 1,9,10 In general, for conventional whole-body systems, only model coefficients of odd-orders (eg, 3 rd order, 5 th order, etc.) are required for distortion correction when imaging the head.…”