Characterization of the diffusion signal of breast tissues using multi-exponential models

Abstract

Purpose: Restriction spectrum imaging (RSI) decomposes the diffusion-weighted MRI signal into separate components of known apparent diffusion coefficients (ADCs). The number of diffusion components and optimal ADCs for RSI are organ-specific and determined empirically. The purpose of this work was to determine the RSI model for breast tissues.

Methods: The diffusion-weighted MRI signal was described using a linear combination of multiple exponential components. A set of ADC values was estimated to fit voxels in cancer and control ROIs. Later, the signal contributions of each diffusion component were estimated using these fixed ADC values. Relative-fitting residuals and Bayesian information criterion were assessed. Contrast-to-noise ratio between cancer and fibroglandular tissue in RSI-derived signal contribution maps was compared to DCE imaging.

Results: A total of 74 women with breast cancer were scanned at 3.0 Tesla MRI. The fitting residuals of conventional ADC and Bayesian information criterion suggest that a 3-component model improves the characterization of the diffusion signal over a biexponential model. Estimated ADCs of triexponential model were D_1,3 = 0, D_2,3 = 1.5 × 10^-3 , and D_3,3 = 10.8 × 10^-3 mm² /s. The RSI-derived signal contributions of the slower diffusion components were larger in tumors than in fibroglandular tissues. Further, the contrast-to-noise and specificity at 80% sensitivity of DCE and a subset of RSI-derived maps were equivalent.

Conclusion: Breast diffusion-weighted MRI signal was best described using a triexponential model. Tumor conspicuity in breast RSI model is comparable to that of DCE without the use of exogenous contrast. These data may be used as differential features between healthy and malignant breast tissues.

Keywords: DW-MRI; DWI; RSI; breast MRI; restriction spectrum imaging.

Figure 1.

Images from diffusion-weighted magnetic resonance imaging (DW-MRI) were averaged over all diffusion directions for each b-value, and noise corrected. Representative images at different b-values and for both sites (top and bottom rows) are shown.

Figure 2.

Boxplot of A) conventional ADC, B) median signal contributions of the components of the bi-exponential and three-component model, and C) median fractional signal contributions within cancer (red) and control (blue) regions of interest (ROIs). In both models, the magnitude of the components of cancer and control ROIs were statistically different (p<0.05, horizontal bars).

Figure 3.

Apparent diffusion coefficients (D_i,N) of a three-component model ($S_{diff}\left(b\right)=C_{\mathrm{1,3}}+C_{\mathrm{2,3}}{e}^{-b·D_{\mathrm{2,3}}}+C_{\mathrm{3,3}}{e}^{-b·D_{\mathrm{3,3}}}$) were determined by simultaneously fitting both control and cancer ROIs of both sites. Values of D_i,N were then fixed (D_2,3=1.4×10⁻³ mm²/s, and D_3,3=10.2×10⁻³ mm²/s) and used to estimate the signal contribution of each component C_i,N. Two-dimensional plots of the magnitude of A) C_1,3 vs C_2,3, B) C_1,3 vs C_3,3, and C) C_2,3 and C_3,3 are shown for fibroglandular tissue (blue circles), fat (yellow squares) and cancer (red squares) ROIs. Circles and bar represent the C_i,N ROI median and 25^th and 75^th percentiles for each subject.

Figure 4.

Processed images from patient from site 1 in Figure 1 including A) T2-weighted and B) dynamic contrast-enhanced (DCE) images, C) conventional apparent diffusion coefficient map, and the signal contributions (C_i,N) of bi-exponential (D-E) and three-component (F-H) models. The fractional signal contributions are also shown for bi-exponential (I-J) and three-component (K-M) models. Arrowheads indicate tumor location. Signal contribution in tumors was higher than surrounding tissues in both C_1,N and C_2,N in both models. The compartment C_3,3 displays vascular flow information.

Figure 5.

Processed images from patient from site 2 in Figure 1 including A) T2-weighted and B) dynamic contrast-enhanced (DCE) images, C) conventional apparent diffusion coefficient map, and the signal contributions (C_i,N) of bi-exponential (D-E) and three-component (F-H) models. The fractional signal contributions are also shown for bi-exponential (I-J) and three-component (K-M) models. Arrowheads indicate tumor location.