Ek Tsoon Tan^{1}, Lisa J Wilmes^{2}, Nola Hylton^{2}, Thomas L Chenevert^{3}, and David C Newitt^{2}

Multi-b-valued diffusion-weighted imaging (DWI) of the breast is highly susceptible to image and fitting noise. A multi-compartment approach was developed to denoise multi-b-value breast DWI without spatial smoothing. In human subject exams (N=12), the denoising approach resulted in a significant reduction in variability of all perfusion and diffusion maps in breast tumor and normal fibroglandular tissue with minimal bias to the mean values, and increased statistical separation of diffusivity metrics between tumor and normal tissue. The denoising algorithm provides compartment fractions for tumor, tissue, and vascularity, which may improve visualization of tissue compartments in DWI.

The model-based diffusion denoising method5was proposed with multi-directional-shell neuro-diffusion to provide 3-4 times acceleration and improved diffusivity maps. The method used a generalized, multi-compartment signal model with anisotropic and isotropic tissue compartments, and Richardson-Lucy dampening for optimization:

$$\widehat{s}(b,q)=\sum_{j=1}^J\sum_{n=1}^Nf_{aniso,j,n}exp(-(\lambda_{||}(bq^Tu_n)^2)(-\lambda_{\bot}b(1-(q^Tu_n)^2))+\sum_{j=1}^Jf_{iso}exp(-\lambda_jb)$$

To adapt the method for breast multi-b diffusion where tissue anisotropy is less and diffusion directions are fewer, a model with far fewer compartments and reduced anisotropy was proposed (Table 1), with compartment values approximating normal fibroglandular tissue (NFT), tumors, vascular and fat components as surveyed in the literature^{1,6-7}. As a by-product of the model, the fractional values belonging to each component (f_{fibroglandular}, f_{tumor}, f_{vascular}) could provide visualization of the image signal from each component, as shown in Fig. 1.

Twelve serial multi-b DWI acquisitions from subjects undergoing neoadjuvant chemotherapy for invasive breast cancer (three subjects x 4 time-points) were selected retrospectively for processing. Studies were deidentified per DICOM standard and all subjects gave written informed consent. The acquisitions were obtained from a 1.5T scanner (GE Healthcare, Waukesha WI) with one b=0 acquisition and three-directions per b-value={100,600,800}sec/mm^{2}, FOV=34-35cm, slice thickness=4mm, TR/TE=7500/67.6-67.9ms. Tumor and contralateral NFT were manually segmented on the un-denoised ADC maps. To reduce spatial-bias of diffusivity, gradient nonlinearity correction was applied^{8-9}. The analyzed metrics included: ADC (utilizing b=0 and all b-values), slow ADC (utilizing non-b=0 data), b=100 ADC, and perfusion component fraction^{10} of b=0. In comparing standard vs denoising, pair-wise, non-parametric Wilcoxon signed-rank test (P<0.05 for statistical significance) was performed on the mean difference and coefficient of variation (CV) of each metric. Two-sample t-test was used to compare metrics between tumor and NFT.

As summarized in Table 2, denoising resulted in very small changes (<±1%) to mean ADC and slow ADC for tumor and NFT; denoising increased b=100 ADC by 5.3-10.2% for both tumor and NFT; denoising increased perfusion fraction as well without statistical significance. In all metrics and in both tumor and NFT, the coefficient of variation (CV) within the ROIs were significantly reduced. In particular, the CV reduction was substantial (15.3-21.2%) in both b=100 and perfusion fraction. These quantitative results could be visualized in Fig. 2, wherein denoising resulted in subtle changes to slow ADC, but dramatic reduction in image texture in both the b=100 ADC and perfusion maps; vascular structures became better visualized.

The differences in diffusivity measures between tumor and NFT were overall increased; t-statistic increased, on average by +1.5 for ADC, +3.2 for slow ADC, +3.8 for b=100 ADC and +0.6 for perfusion fraction. The number of instances with significant differences between tumor and normal tissue was unchanged in ADC (12/12) and in slow ADC (11/12); these were increased in b=100 ADC (from 10/12 to 11/12) and perfusion fraction (from 8/12 to 9/12). These effects are shown on the one subject in Fig. 3.

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Figure 1. Images from T2-weighted (b=0), trace diffusivity, and T2-weighted images weighted by the fractional components of the denoising model, showing that the signal components of individual tissue types could be visualized separately and perhaps with improved conspicuity. For example, in the tumor (white arrows) and the mammary vessels (yellow arrows).

Table 1. Generalized, multi-compartment diffusion model for breast diffusivity with components J and N representing the number of assumed diffusivities and the number of directions respectively. In this work, the parameters for denoising optimization were number of iterations = 52, Nesterov’s iteration parameter = 3.5.

Table 2. Differences (denoising minus no denoising) in multi-b-value metrics of tumor and normal fibroglandular tissue, and their coefficient of variation as compared statistically using the pair-wise, non-parametric Wilcoxon signed-rank test.

Figure 2. Maps from subject #1, standard and denoised, with tumor (solid line) and contralateral fibroglandular tissue (dashed line) drawn, showing significant reduction in image texture and outliers in the b=100 and perfusion fraction maps. The lateral mammary vessel was better visualized after denoising (arrow).

Figure 3. Mean and standard error plots of the diffusivity measures from subject #3 at the four time-points (T0 to T3), showing that denoising resulted in reduced standard error (and hence coefficient of variation) across all metrics and in both normal tissue and tumor tissue with minimal bias. The reduced standard error from denoising resulted in large increases in t-statistic between normal and tumor tissue in all metrics.