Reconstruction of dual-frequency conductivity by optimization of phase map in MREIT and MREPT

Abstract

Background: The spectroscopic conductivity distribution of tissue can help to explain physiological and pathological status. Dual frequency conductivity imaging by combining Magnetic Resonance Electrical Property Tomography (MREPT) and Magnetic Resonance Electrical Impedance Tomography (MREIT) has been recently proposed. MREIT can provide internal conductivity distributions at low frequency (below 1 kHz) induced by an external injecting current. While MREPT can provide conductivity at the Larmor frequency related to the strength of the magnetic field. Despite this potential to describe the membrane properties using spectral information, MREPT and MREIT techniques currently suffer from weak signals and noise amplification as they both reply on differentiation of measured phase data.

Methods: We proposed a method to optimize the measured phase signal by finding weighting factors according to the echo signal for MREPT and MREIT using the ICNE (Injected current nonlinear encoding) multi-echo pulse sequence. Our target weights are chosen to minimize the measured noise. The noise standard deviations were precisely analyzed for the optimally weighted magnetic flux density and the phase term of the positive-rotating magnetic field. To enhance the quality of dual-frequency conductivity images, we applied the denoising method based on the reaction-diffusion equation with the estimated noise standard deviations. A real experiment was performed with a hollow cylindrical object made of thin insulating film with holes to control the apparent conductivity using ion mobility and an agarose gel cylinder wrapped in an insulating film without holes to show different spectroscopic conductivities.

Results: The ability to image different conductivity characteristics in MREPT and MREIT from a single MR scan was shown by including the two objects with different spectroscopic conductivities. Using the six echo signals, we computed the optimized weighting factors for each echo. The qualities of conductivity images for MREPT and MREIT were improved by optimization of the phase map. The proposed method effectively reduced the random noise artifacts for both MREIT and MREPT.

Conclusion: We enhanced the dual conductivity images using the optimally weighted magnetic flux density and the phase term of positive-rotating magnetic field based on the analysis of the noise standard deviations and applying the optimization and denoising methods.

Figure 1

Schematic diagram for ICNE multi-echo pulse sequence to acquire dual-frequency conductivity images. ‘RF’ shows the timing for excitation of 90° and 180° RF pulses. G_z, G_y and G_x are slice selection gradient, phase encoding gradient and readout gradient, respectively. ${\zeta }_j^{\pm }$ is the j-th echo signal. ‘ICNE’ shows the alternating injection currents in the form of pulses synchronized with the RF pulse.

Figure 2

Experimental set-up for a phantom.(a) The phantom configuration at the middle slice of the testing object, (b) a cylindrical phantom with saline solution of 0.2 Sm⁻¹ including a thin film object and an agarose anomaly wrapped by an insulating film, and (c) a magnitude image at the middle slice acquired at T_E=15 ms.

Figure 3

MR magnitude images measured at each echo time. Echo number marked on the upper left part of each image as (1), (2), ⋯, (6). Magnitude images using ICNE multi-echo pulse sequence acquired at the echo time $T_{E_j}=15\times j$ ms for j=1,⋯,6.

Figure 4

Phase images and magnetic flux density images of each echo.(a) Phase images φj+ of H⁺ map in radian and (b) magnetic flux density images $B_{z^j}$ in ’nT’ unit using ICNE multi-echo pulse sequence at the echo time $T_{E_j}=15\times j$ ms for j=1,⋯,6.

Figure 5

Images of weighting factors corresponding to each echo.(a) Images of weighting factors corresponding to each echoes for φj+ and (b) images for magnetic flux density $B_{z^j}$ to produce an optimal φ^+,χ and $B_z^{\xi }$, respectively. The weighting factors were scaled from 0 to 1.

Figure 6

Reconstructed conductivity images of each echo.(a) Reconstructed conductivity images using the multiple echoes φj+ for j=1,⋯,6 at Larmor frequency and (b) conductivity images using $B_{z^j}^d$ for j=1,⋯,6 at the low frequency.

Figure 7

Optimized dual-frequency conductivity images with and without applying the optimization and denoising method.(a) and (e) Normalized noise standard deviation of the optimally weighted phase of H⁺and$B_z^{\xi }$, respectively. (b) and (f) Reconstructed conductivity images without using the optimization and denoising method. (c) and (d) Reconstructed conductivity distributions at Larmor frequency using the optimized φ^+,χwithout denoising and with the proposed denoising technique applying to ∇φ^+,χ, respectively. (g) and (h) Reconstructed low-frequency conductivity distributions without denoising and with the proposed denoising technique applying to$\nabla B_z^{d,\xi },d=1,2$, respectively.