Sodium (²³Na) MRI is an important tool to measure tissue sodium content (TSC). Quantification of TSC provides valuable information about cell viability, pathologic changes and cell metabolism. Influences of reception radiofrequency field (B₁^-) inhomogeneities change the accuracy of quantification results and therefore impair clinical interpretation. Due to low sensitivity, ²³Na MRI suffers from low signal-to-noise ratio (SNR) compared to standard hydrogen (¹H) MRI. Consequently, surface coils are mostly used. Furthermore, due to high noise level some standard B₁^- correction methods fail.

In this work we present a novel approach to correct for B₁^- field inhomogeneities by using Ensemble Empirical Mode Decomposition (EEMD), which takes nonlinear B₁^- fields and noise corruption into account. Corrections are carried out offline during postprocessing. No additional scan time is needed.

EEMD [1,2] has been transferred from a 1D signal analysis to a 2D spatial data decomposition [3]. The data $$$f(x,y)$$$ is decomposed in oscillation functions called intrinsic mode functions (IMFs) $$$g_i(x,y)$$$ and a monotonous trend, which remains as residue $$$r(x,y)$$$ (Figure 1): $$f(x,y) = \sum_i(g_i(x,y)) + r(x,y)$$ B₁^- correction uses the information from the fourth IMF, since this mode contains an overlying field variation. The inverse of $$$g_4(x,y)$$$ is normalized and multiplied pixel-by-pixel to the original image (EEMD correction: EEMD-C, see Figure 2).

We compared EEMD-C with the uniform phantom correction (PC) method [4], the Murakami correction (MC) method [5] and the uncorrected original image. For PC, a large (35x35x25 cm³) uniform phantom is scanned with same acquisition parameters as the object that requires correction. Ideally, the uniform phantom should cause identical load into the coils as the object. MC is carried out offline during postprocessing. The B₁^- field of a surface coil in presence of load can be measured if the same field of view is scanned with an ideal volume coil. This is simulated in MC by thresholding and low pass filtering the surface coil image.

Sodium images were acquired with different phantoms (two homogeneous phantoms [round and rectangular cross section], one resolution phantom, and one liver phantom [6]) and in vivo (cardiac scan, healthy female volunteer, 26 years) on a clinical 3 T whole body scanner (Magnetom TIM Trio, Siemens Healthcare, Erlangen, Germany) using a double resonant TxRx ²³Na/¹H body stem coil (Rapid Biomedical, Rimpar, Germany). Sodium signal was acquired with a 4-channel surface array. A 3D density adapted radial gradient echo sequence [7] which allows ultrashort echo times was used with the following parameters: 4 mm isotropic resolution (10 mm for both homogenous phantoms), 150 ms repetition time, 0.7 ms echo time, 90° flip angle and 800 to 25000 projections depending on the size of field of view (no undersampling). For PC additional scan time was necessary, the uniform phantom was scanned with identical acquisition parameters.Qualitative comparison (Figure 3) among results obtained from a liver phantom, a resolution phantom, and cardiac imaging showed a reasonable intensity correction for both EEMD-C and MC. In cardiac scan, a detailed separation between heart chambers can be seen for EEMD-C. The liver phantom is brighter on the upper part for EEMD-C, which leads to a more homogeneous intensity. Tumor imitations can still be separated from healthy liver material. For the resolution phantom, the intensity variations are smallest for MC, but blurring is introduced into the center. Quantitative evaluations (Figure 4 a) and b)) were carried out as analysis of the round and the rectangular phantom. EEMD-C provided slightly superior results compared to MC for the round phantom (reducing the standard deviation from 53% to 32% and 35%, respectively) but for the rectangular phantom MC reduced the standard deviation from 84% to 47%, while EEMD-C decreased it to 52%. The same effect was observed for slice profiles (Figure 4 c) and d)). On average for both homogeneous phantoms, EEMD-C showed a reduction in intensity variations of 39%. MC obtained similar results, while PC decreased variations by 2%.EEMD-C corrects B₁^- field inhomogeneities in sodium MR images. Quantitative results were similar to MC. Qualitative results showed more details than MC and PC. EEMD-C can be applied clinically without causing scheduling issues or increasing patient discomfort by prolonging measurements. In contrast to MC, EEMD-C needs no manual adaption for high noise images and provides a fully automatic correction.A novel B₁^- field correction method is developed, which uses 2D image decomposition into intrinsic mode functions calculated by EEMD. Automatic corrections show promising initial results, feasibility and a straightforward handling.