This paper proposes a finite-difference (FD)-based method for the design of gradient coils in MRI. The design method first uses the FD approximation to describe the continuous current density of the coil space and then employs the stream function method to extract the coil patterns. During the numerical implementation, a linear equation is constructed and solved using a regularization scheme. The algorithm details have been exemplified through biplanar and cylindrical gradient coil design examples. The design method can be applied to unusual coil designs such as ultrashort or dedicated gradient coils. The proposed gradient coil design scheme can be integrated into a FD-based electromagnetic framework, which can then provide a unified computational framework for gradient and RF design and patient-field interactions.

Background One of the major limitations of MRI is its slow acquisition speed. To accelerate data acquisition, partially parallel imaging (PPI) methods have been widely used in clinical applications such as sensitivity encoding (SENSE) and generalized autocalibrating partially parallel acquisitions (GRAPPA). SENSE is a popular image-domain partially parallel imaging method, which suffers from residual aliasing artifacts when the reduction factor goes higher. Undersampling the k-space data and then reconstruct images with artificial sparsity is an efficient way to accelerate data acquisition. By exploiting artificial sparsity with a high-pass filter, an improved SENSE method is proposed in this work, termed high-pass filtered SENSE (HF-SENSE). Methods First, a high-pass filter was applied to the raw k-space data, the result of which was used as the inputs of sensitivity estimation and undersampling process. Second, the adaptive array coil combination method was adopted to calculate sensitivity maps on a block-by-block basis. Third, Tikhonov regularized SENSE was then used to reconstruct magnetic resonance images. Fourth, the reconstructed images were transformed into k-space data, which was filtered with the corresponding inverse filter. Results Both simulation and in vivo experiments demonstrate that HF-SENSE method significantly reduces noise level of the reconstructed images compared with SENSE. Furthermore, it is found that HF-SENSE can achieve lower normalized root-mean-square error value than SENSE. Conclusions The proposed method explores artificial sparsity with a high-pass filter. Experiments demonstrate that the proposed HF-SENSE method can improve the image quality of SENSE reconstruction. The high-pass filter parameters can be predefined. With this image reconstruction method, high acceleration factors can be achieved, which will improve the clinical applicability of SENSE. This retrospective study (HF-SENSE: an improved partially parallel imaging using a high-pass filter) was approved by Institute Review Board of 2nd Affiliated Hospital of Zhejiang University (ethical approval number 2018–314). Participant for all images have informed consent that he knew the risks and agreed to participate in the research.

Purpose: To develop and validate a fast dynamic MR imaging scheme. A novel approach termed K-T ARTificial Sparsity enhanced GROWL (K-T ARTS-GROWL) is proposed that integrates dynamic artificial sparsity and GROWL-based parallel imaging (PI). Methods: Golden-angle radial k-space data are acquired with the free-breathing sampling scheme and then sorted into a time series by grouping consecutive spokes into temporal frames. The reconstruction framework sequentially applies PI and dynamic artificial sparsity. In the implementation, GROWL is taken as a special PI instance for its high computational efficiency and the K-T sparse is exploited to improve the PI reconstruction performance, because the dynamic MR images are often sparse in the x-f domain. In the final reconstruction procedure, artificial sparsity is constructed and fed back to the previous reconstruction. Results: The K-T ARTS-GROWL results in high spatial and temporal resolution reconstructions. By exploiting dynamic artificial sparsity, the acceleration capability is further improved compared to the PI alone. The experimental results demonstrate that K-T ARTS-GROWL leads to significantly better image quality (P < 0.05) than the frame-by-frame GROWL and frame-by-frame ARTS-GROWL for in vivo liver imaging. Compared with the tested K-T reconstruction algorithms, the K-T ARTS-GROWL results in a better or comparable image quality and temporal resolution with greatly decreased computational costs. Conclusion: The proposed technique enables sparse, fast imaging of high spatial, high temporal resolutions for dynamic MRI.

A volumetric finite-difference based method is presented in this paper for the design of three-dimensional (3D), arbitrarily structured gradient coils in magnetic resonance imaging. In the proposed method, the coil space is discretized with quasi-rectangular elements, and the current density of each element is expressed by a finite-difference based numerical approximation of stream functions. The magnetic flux density at target field points can be calculated by those stream function values at all grids of the coil space. The optimization problem is constructed and solved to determine the stream function and coil patterns. This proposed method has been tested on several designs that include a shielded, ultra-short cylindrical coil, a partially shielded biplanar coil, and an asymmetric head coil with 3D geometries. The numerical results show that the proposed method is straightforward to implement and is versatile and suitable for designing complex structured gradient coils with high electromagnetic performance.

Matrix gradient coils have received increasing interest in generating arbitrary-shaped magnetic fields for various magnetic resonance imaging applications. In this paper, a novel cone-shaped matrix gradient coil is proposed to design a multifunctional insertable system for head imaging. Using a volumetric finite-difference-based method, the matrix coil is designed to have comprised several coil elements that can implement localized imaging and control eddy current, dissipated power, and minimum wire gap. With the lowest total dissipated power, various current configurations are selected to generate multiple gradient fields within a large, spheroidal region of interest (ROI) and two small spherical sub-ROIs. The numerical computation results show that the designed matrix coil offers high flexibility in generating a local gradient field capable of improving the local resolution. In addition, with enhanced coil performance, the cone-shaped structure provides a patient-friendly solution for head imaging.