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1994 Ramesh Bhagwandien

Object induced geometry and intensity distortions in Magnetic Resonance Imaging

Thesis Advisors: J.J. Battermann, Ph.D.; C.J.G. Bakker, Ph.D.; J.J.W. Lagendijk, Ph.D.
Ph. D. awarded October 1994 by University Utrecht, The Netherlands

The excellent soft tissue contrast, the potential for tumor localization and determination of tumor infiltration and the ability to scan in any plane orientation have made magnetic resonance imaging (MRI) a useful tool in various fields of medicine, including radiotherapy. In radiotherapy treatment planning (RTP) geometric accuracy is of major importance, because accurate beam positioning is essential for optimal tumor dose coverage while sparing surrounding healthy tissues as much as possible. However, geometric accuracy and intensity distortions in MRI are complications. Two major factors causing these artifacts are system and object related distortions of the static field. The aim of this study to evaluate the object induced geometry and intensity distortions in magnetic resonance imaging.

Geometry and intensity distortions can be divided into two categories viz. the system related distortions and the object related distortions. The system related distortions stem from the inhomogeneity of the static field (B0) and the non-linearity of the imaging gradients (Gx, Gy, Gz), while the object related distortions depend on the chemical shift and the susceptibility distribution.

A numerical technique is described for calculating the 2D and 3D magnetic field for arbitrary magnetic susceptibility distributions. The technique used is the explicit finite difference method with the addition of the Du Fort-Frankle algorithm. The proposed algorithm is unconditionally stable and has excellent convergence properties. For simple geometries (cylinders and spheres), numerical results were compared against analytical solutions and appeared to be in excellent agreement. As an application cylinders with different ratios of lengths and diameter were studied. The current implementations of the algorithms to calculate the magnetic field and simulating the MR images are time consuming and should be further optimized. The present study also shows a comparison of 2D and 3D B-field calculations; further research is required to determine in which cases 3D B-field calculations can be replaced by 2D calculations.

The consequences of object induced field inhomogeneities (geometry and intensity distortions) were studied in 2D and 3D spin echo and gradient echo imaging. The proposed method incorporates object induced field perturbations in the time domain (k-space) and is very time consuming in its current implementation. The process of data acquisition is demonstrated for infinitely long cylindrical non-uniformities in susceptibility, where analytical B-field calculation is possible (2D), for infinitely long bar shaped non-uniformities, where the B-field is numerically calculated (2D), and for spherical non-uniformities (3D), where slice selection effects are taken into account. Both simulations and experimental results for single slice, multi-slice 2D and 3D imaging of phantoms are provided. The method is a powerful tool for understanding and predicting the effect of object induced and inherent static field inhomogeneities in 2DFT and 3DFT imaging. The method offers a large flexibility in studying the effect of various experimental conditions and parameter settings on the appearance of susceptibility artifacts in SE and GE imaging.

Geometry and intensity distortions in spin echo and gradient echo images of the human body were investigated. Simulated geometry distortions, demonstrated by means of contour images for the head, the neck area and the hand and simulated intensity distortions at the cervical spine and the hand appeared to be in good agreement with experiments. It has also been confirmed that field related geometrical errors are inversely proportional to the gradient strength. The validity of 2D B-field calculations was investigated by comparing with 3D B-field calculations and experiments. 2D B-field calculations slightly overestimate field perturbations, for the particular geometries investigated here, compared to 3D calculations.

The use of markers for image registration in magnetic resonance imaging was theoretically analyzed for the head. Susceptibility induced field inhomogeneities causing shifts and distortions of markers around the head were studied. The marker size and location were varied. The analysis of the B-field around the head showed that the position of a marker should be well considered. For standard machine set-up (B0 = 1.5 T, Greadout = 1.5 mT/m) marker shifts of a few mm can appear depending on the position with respect to the head. Theoretically, the non-disturbed position is along the diagonal of the dipolar field. The use of a 0.5 T scanner instead of a 1.5 T scanner will decrease the marker shifts caused by susceptibility artifacts with a factor of 3.

For the correction of susceptibility induced image distortions a method is proposed that is based on the distorted MR image. The main steps in this method are respectively the conversion of the MR image into a magnetic susceptibility distribution by segmenting the image into air and water equivalent tissue, the calculation of the B-field and the calculation of the corrected MR image by applying a reversed read out gradient. With this method marker shifts are reduced and distorted internal and external contours are rectified. The results of this new method were compared to the results of the method proposed by Chang and proved to be in good agreement. Our method is only approximately correct, since we start with the distorted image and as a consequence with the B-field distribution that differs from the B-field distribution of the undistorted object. For distorted images as encountered in clinical practice the correction works properly. The Jacobian of the transformation between the distorted image and the object determines the degree of distortion this method can handle. The mapping from object space to the image space must remain one to one.

In conclusion:
The magnetic field can be calculated for arbitrary magnetic susceptibility distributions. Object induced geometry and intensity distortions can be predicted and the effect of various experimental and clinical conditions and parameter settings on the appearance of susceptibility artifacts in SE and GE imaging can be studied. A new method for correction of geometrical distortions was proposed.
It was shown that in 1.5 T MR images, acquired with typical gradient strength of 1.5 mT/m, susceptibility artifacts can not be ignored if the images are to be used for radiotherapy treatment planning. Also MRI compatible localization frames perturb the magnetic field, resulting in shifts of the markers that serve as a reference system. In view of the required geometric accuracy for RTP, patients should by preference be scanned on a 0.5 T NMR imager using strong gradients. In that case susceptibility (and chemical shift) artifacts are negligible, so that image distortions caused by the non-linearity of the gradients are the remaining distortions to be corrected. Correction of these distortions can readily be performed (see dissertation Moerland). However, magnetic resonance spectroscopy and new applications of MRI, like magnetic resonance angiography, fast imaging and functional imaging require higher field strengths (B0 > 1.5 T). Therefore, interest in high field NMR scanners will remain and further study of susceptibility induced field inhomogeneities is relevant.