R2* mapping is emerging as a rapid and accurate biomarker of iron content and distribution in the liver. However, conventional voxelwise R2* mapping methods are often impacted by relatively low signal-to-noise ratio (SNR) in source echo images, and thus result in inaccurate and noisy R2* maps. Image smoothing prior to R2* mapping can improve noise performance, but degrades spatial resolution. The purpose of this work was to improve the noise performance of liver R2* mapping, while preserving spatial resolution, using a novel noise-corrected model incorporating neighborhood information.

Theory: In multi-coil systems, fitting the expectation value of noisy signal to the first-moment noise-corrected model (M¹NCM)^1-3 has been demonstrated to produce accurate an­­­­­­­d precise estimates of R2*. To reduce the impact of noise induced signal fluctuations on curve fitting of each target voxel in R2* mapping, neighboring voxels are taken into consideration with weights determined according to their similarities to the target voxel. The proposed method is given by minimizing the cost function:

$$\min_{S_0, R2^*}\sum_{x_j\in\Omega_i}w(x_i, x_j)\parallel{S_{x_j}-f(S_0, R2^*)}\parallel_2^2,$$

where x_j denotes the neighboring voxels in search window Ω_i centered at target voxel x_i, S_xj=[S_TEmin,xj, …, S_TEmax,xj], f is the M¹NCM model function (right-hand side of Equation [4] in Reference (1)), and the weight w(x_i, x_j) is determined as follows

$$w(x_i,x_j)=\left\{\begin{array}{} exp(-\frac{\parallel{S_{x_i}-S_{x_j}}\parallel_2^2}{h^2}) & \forall x_j\in\Omega_i \ and\ x_j\neq x_i,\\ max{\{w(x_i,x_j), \forall x_j \in \Omega_i \ and\ x_j\neq x_i\}} & if x_j=x_i,\end{array}\right.$$

where h acts as a smoothing parameter and controls the decay of the weights. High weights are assigned to voxels that have similar decay signals and small weights to dissimilar voxels.

Simulation Experiments: A mask delineating liver anatomy (including parenchyma and blood vessels) and a nonuniform S₀ reference map­­­ were pre-calculated. Liver parenchyma R2* values were chosen in the range of 100-1000s^-1 and vessel R2* values of 33s^-1. Echo times (TE) were the same as those used as in vivo experiments (below). Multi-echo MR images were simulated by the root-sum-square operation for 8 coils and Gaussian white noise was added to each channel, such that the SNR of echo images at TE=0 were 15, 30 and 60.

In Vivo Experiments: Two subjects with moderate and severe iron loading levels were retrospectively analyzed after IRB approval and informed consent was obtained. In vivo experiments were performed on a 1.5T scanner (Sonata, Siemens Medical Solutions, Erlangen, Germany) using a 6-channel anterior array coil combined a 2-channel spine array coil and 2D spoiled gradient echo acquisition with fat saturation. Scan parameters included: number of echoes=12, TE_min=0.93ms, ΔTE=1.34ms, TR=200ms, flip angle=20°, slice thickness=10mm, number of averages=1, matrix size=64×128, FOV=200×400mm².

The proposed method was compared with two methods: the original M¹NCM model² and nonlocal means (NLM) filter⁴-based M¹NCM model⁵ (two-step operation: denoising multi-echo MR images by the NLM filter, then curve fitting by the original M¹NCM model). Note that for the proposed and NLM-based methods, the search window size was set to 11×11 and smoothing parameter h was determined using root-mean-square error (RMSE)⁵ criterion. Quantitative analysis was performed for both simulation and in vivo data. RMSE and averaged R2* estimates over parenchyma for each combination of SNRs and R2* reference values were calculated in the simulation study. For the in vivo data, the statistical distributions of R2* estimated in liver were shown.

As shown in Figure 1, the proposed method effectively preserves edge information and produces R2* maps with high spatial resolution. Based on the simulations, the proposed method obtained the most accurate mean R2* estimated in parenchyma area and smallest variability (Figure 1a). In addition, the proposed method led to the smallest RMSE for each combination of R2* reference values and SNR levels (Figure 2). In the in vivo study, R2* maps and distribution over liver of one subject with severe iron overload are shown in Figure 3, with less noisy R2* maps as shown by the narrow histogram and sharp edges were achieved using the proposed method. By incorporating neighborhood information into the noise-corrected R2* estimation method, simulation results and preliminary in vivo studies suggest that improved R2* maps with high accuracy and spatial resolution can be obtained using the proposed method. Compared to the original M¹NCM method, the proposed method utilizes neighborhood information and thus produces less noisy R2* maps. Unlike the two-step operation in the NLM-based M¹NCM method, the proposed method is a single-step procedure that can avoid error accumulation from denoising to curve fitting. Due to the absence of reference standard for the in vivo study, future work will be needed to validate the reproducibility of the proposed method comprehensively.