Application of Electrical Properties Mapping
1GE Global Research Center, United States, 2Sungkyunkwan University, Suwon, Korea, Republic of
Synopsis
The contrast in electrical properties (EP’s) between regions of interest (ROI’s) is typically limited to less than 30%; within-subject and between-subject variability is also on the order of 30%. The SNR of reconstructed EP’s depends on the reconstruction method used; for Laplacian-based EP reconstruction, SNR depends on field strength, absolute value of EP’s and (ROI_size)3.5. At 3T and 7T, some applications for which relatively large ROI EP’s are sought have promising results using standard EP reconstruction. In order for EP mapping to become a reality at spatial resolutions useful for clinical diagnosis, more advanced reconstruction methodologies are likely needed.
Target Audience
Scientists and clinicians developing reconstruction approaches for electrical property (EP) imaging and employing the resulting methodology for pathology characterization and electromagnetic simulationsOutcome/Objectives
This review will focus on conveying four separate points. First, the diagnostic areas that could benefit from a means for non-invasive, non-contact EP mapping are reviewed. Secondly, the contrast available in vivo for different anatomies and diagnostic/interventional applications is summarized, with particular attention paid to literature reports attempting to distinguish benign from malignant breast tissue based on their EP’s. Third, a theoretical assessment of our current measurement capability for “classical”, Laplacian-based EP mapping is presented, linking the expected EP’s SNR to field strength, incoming data SNR, region of interest (ROI) dimensions and EP’s themselves. Last, a literature survey of in vivo EP mapping studies is presented; these are consistent with theoretical predictions and point to the stringent need for improved reconstruction methodologies.Introduction
MR based imaging of electrical properties relies on the fact that the presence of a body within a scanner alters the distribution (magnitude and the phase) of the radio-frequency fields; mapping of these alterations can result in an estimation of the local distribution of the EP’s. While various direct (in which the measured B1 is directly used to compute EP’s) and indirect EP reconstruction approaches (EP’s are estimated by fitting a model to the measured data) have been proposed, the “classical”, Laplacian-based EP reconstruction methodology is by far the most commonly used in vivo. In this approach, conductivity and permittivity are assumed to be spatially homogeneous, and recovered by solving the homogeneous Helmholtz equation. A theoretical assessment of this method’s capability is performed, and compared to the signal strength and variability expected in vivo. A minimum field strength and ROI size are determined, over which the expected 10-30% changes in EP’s in vivo can be reliably measured.In vivo utility of EP mapping
There are two fundamental classes of applications that can benefit from knowledge of spatially resolved EP’s in vivo: electromagnetic (EM) simulations and separating cancerous lesions from benign tissue. EM simulations are typically conducted for two purposes. The first one aims to determine the local specific absorption rate (SAR), which is proportional to the local conductivity and the square of electric field; higher SAR levels than planned can result in tissue damage. The second one is to assess the thermal dose for hyperthermia planning. Tissue temperature increase is related to the absorbed power by the Pennes bio-heat equation; lower temperature increases than planned will reduce the benefit of hyperthermia as an adjunct to radiation therapy, e.g. Evidence already exists [1,2], indicating that the use of literature values for performing such simulations can lead to undesired SAR hot spots and reduced thermal dose, pointing to the need to perform EM simulation with spatially resolved, patient specific EP’s as input.Available EP contrast
While multiple literature references tend to suggest 100%+ contrast between normal and malignant tissues, the reality is likely less rosy. Typically referenced EP values [3-5] sometimes contain ambiguous entries, whose disambiguation significantly reduces the contrast. For example, Figure 1 presents a more comprehensive summary of the literature values for normal breast and breast cancer conductivity values; one can readily conclude that “normal breast” is sometimes defined as fatty tissue in the literature. Its conductivity is thus significantly below the one of normal glandular tissue and can easily be differentiated from tumors by much simpler MR acquisitions. Careful literature inspection, in particular considering recent in vivo EP measurements [6-8], points to the fact that the available EP contrast at field strengths between 1.5T and 7T is not likely to exceed 30% for most applications (with the possible exception of breast); the within and between subject variability is also in the 30% range, imposing significant demands on the EP reconstruction capability.Laplacian-based EPT reconstruction capability
The most common approach for reconstructing EP’s in vivo relies on solving the Helmholtz equation, with a few underlying assumptions. These include (1) EP’s are constant over the computation ROI and (2) the transmit phase is approximated as half of the transceiver phase (the only one measurable by MRI). The numerical computation of the Laplacian is performed as an inner product between the measured transmit field and a predefined kernel; as demonstrated in [9], the minimum uncertainty Laplacian kernel is the 3D Savitsky-Golay Laplacian kernel; Laplacian estimation using this kernel is equivalent to calculating the Laplacian through quadratic least-squares fitting of the input data. Assuming that data is reconstructed using this kernel, and that noise is uncorrelated, the SNR of the permittivity and conductivity measurements is displayed in Figure 2 (details of this computation are presented in [9]). Note a few salient features of these relationships:
a) SNR is proportional to the square of the field strength for permittivity but only depends linearly on the field strength for conductivity.
b) SNR is very strongly dependent on the ROI size, essentially depending on ROI_size3.5
Using the formula of Figure 2, Figure 3 presents a table with the SNR of electrical properties for grey and white matter at 1.5T, 3T and 7T, assuming an SNR of 100 for both the magnitude and the phase of the transmit field, N=1000 voxels in a 2cm spherical ROI (G=91.65), acquired at a spatial resolution of 1.6mm3 . As a quick statistics detour, if one desires to determine if a given measurement (conductivity or permittivity) X, with a historical mean m and standard deviation s, is the same as the previously established mean, a Z score is computed as Z=(X-m)/s. Looking up the probability in a table of Z scores, for p=0.05, one needs a Z score of 1.65; Figure 4 summarizes the needed measurement SNR (as 1/standard deviation of the measurement) to detect, at 95% level, a 10, 20 and 30% change, respectively. By inspecting Figure 3 and 4 in parallel, it becomes evident that EP measurements at 1.5T are not capable of highlighting 30% differences, even in 2cm ROI’s; conversely, 3T is marginally acceptable, while 7T gets significantly better. Note, however, that results at 7T will likely be dominated by systematic errors (such as the transmit phase becoming significantly non-equivalent to half of the transceive phase [10]), which were not accounted for in the equations of Figure 2. In addition, note that the EP SNR results of Figure 3 become less than 1 for both 1.5T and 3T, and less than 3 for 7T, should the ROI size decrease to 1cm (N=125, while keeping input SNR and spatial resolution identical to the ones used for the 2cm computation). With Laplacian-based reconstruction methodologies, accurate determination of EP’s in 1cm ROI’s is likely impossible.
In vivo demonstration, limitations and future outlook
Given the limitations of the EP reconstruction methodology, there are relatively few reports documenting results other than EP’s of phantoms or normal human brain. The notable exceptions are two extensive studies aiming to differentiate breast cancer tumors from normal fibroglandular tissue [8], and to understand the electric conductivity of cervical cancer patients [6]. They were both conducted at 3T, using Laplacian-based EP reconstruction; they both assessed EP’s in ROI’s larger than 1cm [8]/3cm [6], respectively. Encouragingly, it became apparent that there may be close to 50% contrast between normal parenchyma and breast cancer tumors [8], rendering this as one of the more promising early applications of EP mapping. Less encouragingly [6], the mean value of cervical tumor conductivity was found to be 13% higher than the one of healthy cervical tissue, with the within population variability standing at ~30%. Despite the paucity of in vivo studies, there is general agreement highlighting relatively constant tumor-normal tissue conductivity contrast at field strength spanning 1.5T-7T, and decreasing permittivity contrast (from ~30% at 1.5T to close to nothing at 7T) [7,11]. While permittivity may effectively discriminate between cancer and normal tissue at 1.5T (where it is currently impossible to measure accurately), it becomes less than useful at 7T (where it is easier to measure, at the expense of vanishing contrast) [7]. Additionally, there is an interesting agreement between two studies [7,12], showcasing an inverse proportionality relationship between conductivity and the apparent diffusion coefficient (ADC). While there is little theoretical justification for this experimental finding (naively one may expect conductivity increasing with ADC, as demonstrated in the low frequency case [13]), the simplicity of determining ADC’s, and the fact conductivity may not add much in the quest to better separate cancer from normal tissue on top of what ADC already brings [7], should nonetheless be further considered. Given the current state of EP mapping, it becomes obvious that investing in improved reconstruction approaches is absolutely crucial. A few promising steps forward include the reconstruction of electrical properties using gradient EPT [11]; with this approach, where the gradient of the electrical properties is first reconstructed, then integrated, the assumption of homogeneous EP’s is dropped. This comes at the expense of needing multiple transmit/receive coils, and having to rotate the subject by 180 degrees; it yields, however, promising in vivo EP reconstructions in ~1cm ROI’s. In addition, an inverse reconstruction approach, which bypasses the need to compute the field Laplacian [14], or local Maxwell tomography, where all assumptions about the RF phase and coil/field/magnetization structure are dropped, at the expense of solving a linear system of at least ten unknowns for each voxel [15] represent valuable, yet still-in-their- infancy approaches for improved EP reconstruction.Conclusions
The contrast in electrical properties between ROI’s is limited, generally not exceeding 30%; within-subject and between-subject variability is also on the order of 30%. The SNR of reconstructed electrical properties depends on the reconstruction method used; for Laplacian-based EPT reconstruction, SNR depends on field strength, absolute value of EP’s and (ROI_size)3.5. At 1.5T, standard EPT is therefore incapable to distinguish EP values that less than 30% apart, even for ROI’s as large as 2cm. At 3T, some applications, for which relatively large ROI EP’s are sought, have realistic and promising results using standard EPT reconstruction. In order for EP mapping to become a reality with spatial resolutions and contrast-to-noise ratio meaningful for a clinical diagnosis, better reconstruction methodologies are sorely needed.Acknowledgements
No acknowledgement found.References
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