Redesign of the Laplacian kernel for improvements in conductivity imaging using MRI

Abstract

Purpose To develop an electrical property tomography reconstruction method that achieves improvements over standard method by redesigning the Laplacian kernel. Theory and Methods A decomposition property of the governing PET equation shows the possibility of redesigning the Laplacian kernel for conductivity reconstruction. Hence, the discrete Laplacian operator used for electrical property tomography reconstruction is redesigned to have a Gaussian‐like envelope, which enables manipulation of the spatial and spectral response. The characteristics of the proposed kernel are investigated through numerical simulations and in vivo brain experiments. Results The proposed method reduces textured noise, which hampers observing features of the conductivity image. Furthermore, the proposed scheme can mitigate the propagation of local phase error such as flow‐induced phase. By doing so, the proposed method can recover feature information in conductivity (or resistivity) images. Lastly, the proposed kernel can be extended to other electrical property tomography reconstructions, improving the quality of images. Conclusion An alternative design of the Laplacian kernel for conductivity imaging has been developed to mitigate the textured noise and the propagation of local phase artifact.

Transceive phase mapping using the PLANET method and its application for conductivity mapping in the brain

“…[9][10][11] This relationship has been validated in simulations 3,12,13 and experimentally with MR electrical properties tomography (EPT). 10,11,[14][15][16][17][18][19][20] The transceive phase has been mapped extensively for conductivity reconstruction in different body sites (e.g., in brain, 14,[20][21][22] breast, 23,24 liver, 25 pelvis 26 ), especially because tissue conductivity maps hold relevant information for RF safety, 17,18 diagnostics, 27,28 and therapeutic applications. [29][30][31] Besides conductivity mapping, transceive phase maps can also be beneficial for correction purposes in phase-based quantitative applications such as QSM and MR thermometry.…”

Technical developments for MR-based electrical property mapping

“…The spatial modulation of the transceive phase is primarily induced by the tissue conductivity, as can be derived from Helmholtz equation [56,60,139]. This relationship has been validated in simulations [47,114,118] and experimentally with mr Electrical Properties Tomography (ept) [54,[56][57][58][59][60]91,95,103]. The transceive phase has been mapped extensively for conductivity reconstruction in different body sites (e.g.…”

“…Thus, the higher the B 0 strength [89] and the larger the kernel size [87], the more precise the reconstructed ep map. Denoising strategies include using large kernels [90], large voxel sizes, image filters [83,[91][92][93], polynomial fitting to B + 1 data [94], redesigned Laplacian kernels [95], special acquisition schemes [96] and integration-based solutions [54,60]. Bilateral filters can be applied to constrain the differentiation to voxels with the same ep, thereby reducing boundary errors [81,94].…”

“…The transceive phase has been mapped extensively for conductivity reconstruction in different body sites (e.g. in brain [89,95,103,120], breast [94,129], liver [101], pelvis [97]), especially because tissue conductivity maps hold relevant information for rf safety [54,58], diagnostics [127,130] and therapeutic applications [131,140,141].…”

“…Denoising strategies, e.g. [92,94,95], were proposed and magnitudedriven bilateral filters [81,94] or reformulations of full Helmholtz equation [91,93] were used to reduce boundary errors. Direct ept techniques were employed in recent clinical studies evaluating the potential value of ept-based conductivity in discriminating tumours [127,129] and in hyperthermia treatment planning [131].…”