Giannakopoulos Ilias I, Serralles Jose E Cruz, Paska Jan, Cloos Martijn A, Brown Ryan, Lattanzi Riccardo
IEEE Trans Biomed Eng. 2025 May 26;PP. doi: 10.1109/TBME.2025.3572800.
Global Maxwell Tomography (GMT) is a noninvasive inverse optimization method for the estimation of electrical properties (EP) from magnetic resonance (MR) measurements. GMT uses the volume integral equation (VIE) in the forward problem and assumes that the sample has negligible effect on the coil currents. Consequently, GMT calculates the coil's incident fields with an initial EP distribution and keeps them constant for all optimization iterations. This can lead to erroneous reconstructions. This work introduces a novel version of GMT that replaces VIE with the volume-surface integral equation (VSIE), which recalculates the coil currents at every iteration based on updated EP estimates before computing the associated fields.
We simulated an 8-channel transceiver coil array for 7 T brain imaging and reconstructed the EP of a realistic head model using VSIE-based GMT. We built the coil, collected experimental MR measurements, and reconstructed EP of a two-compartment phantom.
In simulations, VSIE-based GMT outperformed VIE-based GMT by at least 12% for both EP. In experiments, the relative difference with respect to probe-measured EP values in the inner (outer) compartment was 13% (26%) and 17% (33%) for the permittivity and conductivity, respectively.
The use of VSIE over VIE enhances GMT's performance by accounting for the effect of the EP on the coil currents.
VSIE-based GMT does not rely on an initial EP estimate, rendering it more suitable for experimental reconstructions compared to the VIE-based GMT.
全局麦克斯韦层析成像（GMT）是一种用于从磁共振（MR）测量中估计电特性（EP）的非侵入性逆优化方法。GMT在正向问题中使用体积积分方程（VIE），并假设样品对线圈电流的影响可忽略不计。因此，GMT使用初始EP分布计算线圈的入射场，并在所有优化迭代中保持其不变。这可能导致错误的重建结果。本研究引入了一种新型的GMT，它用体积-表面积分方程（VSIE）取代了VIE，该方程在计算相关场之前，根据更新后的EP估计值在每次迭代时重新计算线圈电流。
我们模拟了一个用于7T脑成像的8通道收发线圈阵列，并使用基于VSIE的GMT重建了一个逼真的头部模型的EP。我们构建了线圈，收集了实验性MR测量数据，并重建了双室模型的EP。
在模拟中，基于VSIE的GMT在两种EP方面均比基于VIE的GMT至少高出12%。在实验中，内（外）室的介电常数和电导率相对于探头测量的EP值的相对差异分别为13%（26%）和17%（33%）。
与VIE相比，VSIE的使用通过考虑EP对线圈电流的影响提高了GMT的性能。
基于VSIE的GMT不依赖于初始EP估计，与基于VIE的GMT相比，它更适合于实验重建。
