CSI-EPT in Presence of RF-Shield for MR-Coils

Abstract

Contrast source inversion electric properties tomography (CSI-EPT) is a recently developed technique for the electric properties tomography that recovers the electric properties distribution starting from measurements performed by magnetic resonance imaging scanners. This method is an optimal control approach based on the contrast source inversion technique, which distinguishes itself from other electric properties tomography techniques for its capability to recover also the local specific absorption rate distribution, essential for online dosimetry. Up to now, CSI-EPT has only been described in terms of integral equations, limiting its applicability to homogeneous unbounded background. In order to extend the method to the presence of a shield in the domain-as in the recurring case of shielded radio frequency coils-a more general formulation of CSI-EPT, based on a functional viewpoint, is introduced here. Two different implementations of CSI-EPT are proposed for a 2-D transverse magnetic model problem, one dealing with an unbounded domain and one considering the presence of a perfectly conductive shield. The two implementations are applied on the same virtual measurements obtained by numerically simulating a shielded radio frequency coil. The results are compared in terms of both electric properties recovery and local specific absorption rate estimate, in order to investigate the requirement of an accurate modeling of the underlying physical problem.

3-D Contrast Source Inversion-Electrical Properties Tomography

“…• Given an initial contrast function χ [0] and contrast source 1] ) < tolerance then stop 2) Update the contrast source according to 183) Compute the electric field strength corresponding to the updated contrast source via (19) 4) Update the contrast function according to (20) The initial guesses in the above algorithm have to be provided, of course. Many choices are possible and any a priori information about the dielectric properties can be included.…”

“…Many choices are possible and any a priori information about the dielectric properties can be included. A general approach that does not take such information into account is to first determine an initial contrast source w [0] via backprojection [24] and subsequently determine the electric field strength and initial contrast via (19) and (20) with n = 0.…”

“…Contrast source inversion (CSI)-EPT is a reconstruction method that avoids the assumption of locally homogeneous media by making use of a global integral approach instead of a local differential approach. This makes the method more reliable near tissue boundaries and, due to the smoothing effect of the integrals, less sensitive to noise [19], [20]. To date, however, CSI-EPT has been implemented for two-dimensional E-polarized RF fields only, which assumes longitudinal invariance of both the sources and the object.…”

Developments in Electrical-Property Tomography Based on the Contrast-Source Inversion Method

“…In this two-dimensional case, object operator G body can easily be identified from the second part of Equation 17and does not contain a gradient-divergence operator as in the three-dimensional case. For 2D data operator G data , we have to substitute the x and y components of the magnetic-flux density as given by the first part of Equation (17) in the definition of theB + 1 -field to obtain…”

Combining deep learning and 3D contrast source inversion in MR‐based electrical properties tomography

“…Inverse methods like contrast source inversion-EPT (CSI-EPT 10,11,12 ) aim at reconstructing EPs by iteratively solving a minimization problem arXiv:1908.04542v1 [physics.med-ph] 13 Aug 2019 where the EP model is fit to the measuredB + 1 field. This avoids the need of computing spatial derivatives of measured data, making these methods in principle more noise-robust.…”