Technical Note: Harmonic analysis applied to MR image distortion fields specific to arbitrarily shaped volumes

Abstract

A novel harmonic analysis approach relying on finite element methods was introduced and validated for multiple volumes with surface shape functions ranging from simple to highly complex. Since a boundary value problem is solved the method requires input data from only the surface of the desired domain of interest. It is believed that the harmonic method will facilitate (a) the design of new phantoms dedicated for the quantitation of MR image distortions in large volumes and (b) an integrative approach of combining multiple imaging tests specific to radiotherapy into a single test object for routine imaging quality control.

MRI-Guided Online Adaptive Stereotactic Body Radiation Therapy of Liver and Pancreas Tumors on an MR-Linac System

“…The composite image distortions due to system-related and patient-induced distortion fields were assessed for all clinical scenarios: 2D cine for fast sampling of organ and target motion, 3D acquisitions for planning, and simulated 4D data for facilitating the accurate generation of internal target volume (ITV) margins. Specifically, the MRID 3D phantom (Modus QA, London, UK, ON), which is based on harmonic analy-sis [9], was used to quantify system-related distortion fields due to gradient non-linearities (GNL) and magnetic field uniformity (i.e., B 0 mapping) in a large imaging field of view (FOV) [10]. Patient-induced geometric distortions caused by variation in tissue magnetic susceptibility (χ) properties were modeled numerically by means of finite difference methods (FDM), using patient-specific susceptibility maps derived from CT images [11].…”

Quantification of magnetic susceptibility fingerprint of a 3D linearity medical device

“…Since the phantom's inner volume is hollow, free of any other fiducials, it provides 3D distortion field information only on its cylindrical boundary, i.e., ∂D . The distortion field is subsequently computed inside D by using a previously reported harmonic analysis (HA) based on finite element methods (FEM) [13]. Fig.…”

“…Therefore, by applying the δ ∂D χ (r) correction to the phantom measurements with mirrored G E polarity it is possible to directly measure both GNL and B 0 mapping values corresponding to ∂D (r), i.e., δ ∂D GNL (r) and δ ∂D B0 (r), respectively. Knowing the boundary values of such a field (i.e., δ GNL and/or δ B0 ), a harmonic analysis consisting of solving an interior Dirichlet problem was applied to compute the field within the entire phantom domain D [13]. The overall accuracy of the HA-derived 3D distortion field was previously reported to be better than the voxel size of the phantom image data.…”

“…The MRID 3D χ correction δ ∂D χ (r) was computed as detailed in Section 2.3 and then subtracted from δ ∂D B0 (r) +δ ∂D χ (r) to determine δ ∂D B0 (r). Each of the three DVFs were used to perform corresponding harmonic analysis to derive its field inside the entire phantom volume D i.e., δ GNL (r), δ B0 (r) and δ χ (r) [13].…”

Application of Discrete Mathematical Model in Edge Distortion Correction of Moving Image

“…ere are many reasons for the degradation of image quality. If there is relative motion between the camera and the object during the shooting, the image blur is called motion blur [2][3][4][5]. Because the image is often accompanied by noise, the existence of noise not only reduces the image quality but also a ects the acquisition of image degradation model and then a ects the restoration e ect of blurred image [6][7][8].…”