This paper discusses the correction of MR images to submillimeter accuracy needed for functional radiosurgery. MR images experience non-linear distortion due to the magnetic field, which becomes more of a problem for newer machines with larger bores and stronger magnetic fields. This paper models the distortion correction parameters using a spherical harmonics basis, which avoids the need to invert the function to correct the image. The coefficients appear linearly for the spherical harmonics so they are solved for in each dimension by least squares techniques for an MR image of a phantom and the measurements of the phantom. Practical considerations in the design are also covered.

Abstract – Functional radiosurgery is a noninvasive stereotactic technique that requires magnetic resonance image (MRI) sets with high spatial resolution. Gradient nonlinearities introduce geometric distortions that compromise the accuracy of MRI-based stereotactic localization. We present a gradient nonlinearity correction method based on a cubic phantom MRI data set. The approach utilizes a sum of spherical harmonics to model the geometrically warped planes of the cube and applies the model to correct arbitrary image sets acquired with the same scanner. In this paper, we give a detailed description of the Matlab distortion correction program, report on its performance in stereotactic localization of phantom markers, and discuss the possibility to accelerate the code using General-Purpose Computing on Graphics Processing Units (GPGPU) techniques. (a) Cube phantom.

A new system for functional proton radiosurgery has been proposed. The goal of the system is to target specific brain areas with high doses of proton beams with submillimeter accuracy. High-energy proton beams have exquisitely sharp lateral penumbra and are, therefore, ideal for functional radiosurgery. Localizing the anatomical target with an MRI-based fiducial system requires correction of gradient nonlinearity distortions inherent in the scanner images. Modern MR scanners are particularly prone to such distortions due to wider bores and stronger gradient fields. The gradient nonlinearity correction described in this work is based on a high-resolution 3D MR scan of a cube phantom. Using a least-squares fitting procedure correction parameters are found that convert the geometrically warped planes of the cube into the ideal planes. In this paper, we describe the initial data processing and quality checks performed before the data is used for estimation of correction parameters. 1.

Abstract—Targeting of brain tumors or diseased brain tissues with neurosurgical instruments or radiosurgery beams requires magnetic resonance image (MRI) sets with high spatial resolution. In recent years, the spatial resolution of MRI scanners has increased considerably with the introduction of highfield (3T) technology. As a result, isotropic submillimeter voxel sizes are more commonly being used for medical procedures. On the other hand, gradient nonlinearities introduce geometric distortions and errors into the image data. As MRI technologies continue to progress, this problem has not been resolved. We have developed a gradient nonlinearity correction method based on a cubic phantom MRI data set. The approach utilizes a sum of spherical harmonics to model the geometrically warped planes of the cube. Once the polynomial parameters are known they can be applied to correct arbitrary image sets acquired with the same scanner. In this paper, we give a detailed description of the Matlab software performing the modeling and correction functions and discuss the possibility to accelerate the code using

AGNETIC resonance imaging (MRI) provides an excellent modality for distinguishing different tissues in the human body, which is essential for medical applications. When MRI is used for stereotactic treatment planning, its geometric accuracy is crucial. Previous studies have been conducted to correct the distortion caused by nonlinearity of the MRI ���������������������������������������������������������ntom [1], [2] and defining distortion correction functions based on the distorted appearance its surfaces. Correct mathematical handling of the distortion correction function required that the cube was centered about the magnetic isocenter, which is defined as the common center of the three magnetic gradient fields and is not very accurately known. New 3Tesla MRI systems have a larger bore, making the previous phantom design impractically small for probing the field nonlinearity in the periphery of the bore, as the phantom cannot be scaled up due to constraints related to weight and cost of manufacturing. We are introducing a new phantom design using a different approach, which can be built to a larger size, improves accuracy of distortion characterization and reduces cost. I. DESIGN The phantom is shaped to be as large as possible, while still fitting in the head coil of the scanner, so as to achieve the maximum quality of signal and largest distortion. The phantom is an octagonal prism with 205mm between opposite sides. Each face of the octagonal prism is composed of 8 high precision NMR tubes that are 5mm in outer diameter and 205 mm in length. These tubes are

AGNETIC resonance imaging (MRI) provides an excellent modality for distinguishing different tissues in the human body, which is essential for medical applications. When MRI is used for stereotactic treatment planning, its geometric accuracy is crucial. Previous studies have been conducted to correct the distortion caused by nonlinearity of the MRI scanner’s magnetic gradient fields by imaging a cubic phantom [1], [2] and defining distortion correction functions based on the distorted appearance its surfaces. Correct mathematical handling of the distortion correction function required that the cube was centered about the magnetic isocenter, which is defined as the common center of the three magnetic gradient fields and is not very accurately known. New 3Tesla MRI systems have a larger bore, making the previous phantom design impractically small for probing the field nonlinearity in the periphery of the bore, as the phantom cannot be scaled up due to constraints related to weight and cost of manufacturing. We are introducing a new phantom design using a different approach, which can be built to a larger size, improves accuracy of distortion characterization and reduces cost. I. DESIGN The phantom is shaped to be as large as possible, while still fitting in the head coil of the scanner, so as to achieve the maximum quality of signal and largest distortion. The phantom is an octagonal prism with 205mm between opposite sides. Each face of the octagonal prism is composed of 8 high precision NMR tubes that are 5mm in outer diameter and 205 mm in length. These tubes are