To show principle feasibility to extend MRI based "Electric Properties Tomography" ("MRI-EPT") determining electric conductivity at high (MHz) frequencies to "Magnetic Particle Imaging" (MPI), thus determining electric conductivity at low (kHz) frequencies ("MPI-EPT").Recently, an MR-based method was developed to measure electric conductivity quantitatively in vivo using “Electric Properties Tomography” (MRI-EPT [1]), based on measuring and post-processing the spatial distribution of the RF field applied. The conductivity obtained with MRI-EPT corresponds to the Larmor frequency of the MR system. At these frequencies, tissue bulk conductivity is obtained, i.e., the conductivity reflects the biochemical content of the tissue, but not its specific cellular structure. Cellular structure of tissue is reflected by conductivity at much lower frequencies (100-500 kHz), which are not accessible with MRI. On the other hand, “Magnetic Particle Imaging” (MPI [2,3]) is working at the desired low frequencies (LF). Similar to MRI, MPI is able to determine the spatial distribution of the LF field applied, and thus, reconstruction of LF conductivity should be possible (“MPI-EPT”) analogously to MRI-EPT. – In this study, the principle feasibility of MPI-EPT at 128 kHz was investigated, and compared with MRI-EPT at 128 MHz.

The relation between a spatial component H of a time harmonic magnetic field H (with frequency ω) and electric properties (i.e., conductivity σ and permittivity ε) reads [1]

$$$-{\nabla}^2 H=μω(ωε-iσ)H$$$ (1)

Here, σ, ε, and magnetic permeability μ are assumed to be constant, as is the case for the phantoms investigated. Eq. (1) is valid for both, MPI and MRI. Utilizing the complex nature of H = |H| exp(iφ), Eq. (1) can be simplified to [4]

$$${\nabla}^2 φ=μωσ$$$ (2)

i.e., parabolic phase profiles are expected for phantoms with constant σ. For MRI, Eq. (2) can be applied to the half transceive phase φ_MRI = (φ⁺ - φ^-)/2 (see [1]). For MPI, any arbitrary component of H can be measured [3] and used for Eq. (2).

Phantoms: Two cylindrical phantoms (both length = 15 cm, diameter = 5.5 cm) were filled with (a) highly concentrated saline (250 g NaCl / liter water) and (b) distilled water. The corresponding conductivity of the saline is 21.9 S/m at both 128 kHz and 128 MHz, and approximately 0 S/m for distilled water [5]. In the center of the phantoms, a small compartment (1×1×1 mm³) was mounted and filled with Resovist ® (Bayer Schering Pharma AG, Berlin, Germany) acting as contrast agent for MPI.

MRI measurements: A steady state free precession sequence has been used to measure φ_MRI of the two phantoms (TR/TE = 3.3/1.6 ms, flip angle 25°, voxel size 1×1×1 mm³) with a commercial 3T MRI system (Philips Ingenia, Best, The Netherlands). Conductivity was estimated applying Eq. (2) to the measured phase maps.

MPI measurements: An experimental MPI scanner (bore size 7 cm) was used [2,3] investigating the mode corresponding to ω=128 kHz [6]. The phase of the contrast agent compartment was measured with a time resolution of 20 ms over 3 minutes. Measurements started with empty phantoms. After 45 seconds, phantoms were filled with the respective fluid. After the next 45 seconds, emptying of phantoms started. Mean phase change between full and empty phantom was taken as φ_MPI(x=0) at iso-center. Phase change at left and right phantom boundary ±x₀ was assumed to be zero φ_MPI(x=±x₀) = 0, thus yielding three values to estimate the parabolic phase shape according to Eq. (2).

Figure 1 shows the MRI phase maps φ_MRI of the two phantoms (2 cm off-isocenter to exclude artefact from Resovist ® compartment) and Fig. 2 the corresponding phase profiles. The indicated, fitted parabola yields a conductivity of 19.2 S/m for the saline phantom. From the time course of the MPI scans (Fig. 3), φ_MPI(x=0) = 0.0051 rad is obtained for the saline phantom. Together with the assumption φ_MPI(x=±x₀) = 0, a parabola can be fitted, which corresponds to a conductivity of 20.6 S/m. Distilled water did not produce a significant phase bending, neither for MPI nor for MRI, as expected (Fig. 2).

Approximately the same conductivity of roughly 20 S/m was measured at both 128 kHz using MPI and 128 MHz using MRI. These values correspond (a) to the applied phantom saline concentration and (b) to the expected frequency dependence, which is negligible for saline [5]. Further studies shall investigate the (non-negligible) frequency dependence of tissue conductivity using MPI and MRI.

In conclusion, the RF conductivity spectrum of MRI-EPT can be extended to low frequencies using MPI, opening a new way to investigate cellular structure of tissue.