Microstructural models for diffusion MRI in breast cancer and surrounding stroma: an ex vivo study

Abstract

The diffusion signal in breast tissue has primarily been modelled using apparent diffusion coefficient (ADC), intravoxel incoherent motion (IVIM) and diffusion tensor (DT) models, which may be too simplistic to describe the underlying tissue microstructure. Formalin-fixed breast cancer samples were scanned using a wide range of gradient strengths, durations, separations and orientations. A variety of one- and two-compartment models were tested to determine which best described the data. Models with restricted diffusion components and anisotropy were selected in most cancerous regions and there were no regions in which conventional ADC or DT models were selected. Maps of ADC generally related to cellularity on histology, but maps of parameters from more complex models suggest that both overall cell volume fraction and individual cell size can contribute to the diffusion signal, affecting the specificity of ADC to the tissue microstructure. The areas of coherence in diffusion anisotropy images were small, approximately 1 mm, but the orientation corresponded to stromal orientation patterns on histology.

Keywords: DTI; MRI; anisotropy; breast cancer; diffusion; ex vivo; restriction.

Figure 1

(a) Sample diffusion‐weighted image (DWI) (b = 1076 s/mm ²) with the voxel of interest marked in yellow. (b, d) DWI (each gradient separation Δ is a different colour; all directions for a particular Δ are plotted with a single colour) and DTI (green) data (points) as a function of b value with full lines showing the fit for the Tensor model (b) and the Tensor–Sphere model (d). Corresponding residuals (c and e) show systematic errors for the Tensor model. White scale bars in all magnetic resonance images represent 5 mm

Figure 2

T ₂‐weighted images (first column) and diffusion‐weighted images (second column) for each sample with the main tumour focus outlined in cyan. Maps demonstrate the model that best explains the data in each voxel [third column, Akaike information criterion (AIC); fourth column, Bayesian information criterion (BIC)] and the distribution of relative AICs and BICs (low values indicate better explanation) across the samples. (a, b) Grade 1 ductal/no special type (NST); (c) grade 3 mucinous; (d–g) grade 3 NST. Diffusion data from most voxels are best explained by an anisotropic compartment and a restricted compartment (Zeppelin–Sphere or Tensor–Sphere), although there are several regions, particularly in the grade 3 mucinous carcinoma, in which no restriction is required to explain the data (Zeppelin–Ball, Tensor–Ball). Three samples (b, d and g) contained more fat, with only small tumour areas at the edge of the sample and some voxels exhibiting isotropic restriction (Ball–Sphere)

Figure 3

Histograms of the posterior parameter distributions for each model obtained using the Markov chain Monte Carlo (MCMC) procedure with data for a single voxel. Mean values and parameter distributions are similar for all restricted models (with Sphere compartment), aside from the extracellular diffusion coefficients, D _1–3, demonstrating that increasing model complexity does not affect parameter stability substantially

Figure 4

Parametric maps for the apparent diffusion coefficient (ADC, second row) and selected parameters from the Zeppelin–Sphere model. Regions of low cellularity and correspondingly high ADC are outlined in red and typically correspond to lower f _I in the Zeppelin–Sphere model. However, some regions (e.g. cyan outline) have high cellularity relative to their surroundings, but higher ADC, which may be explained by a larger cell radius, R. Additional samples are shown in Figure S6. Regions without colour were excluded either as fat (orange outline in first column) or as non‐mono‐exponential T ₂ (orange outline in second column), which often corresponded to necrotic regions on histology

Figure 5

Regions from two of the tumours demonstrating different spatial variation in the apparent diffusion coefficient (ADC) and Zeppelin–Sphere model parameters. (a) The black and white boxes show regions of relatively uniform ADC in which the radius R from the Zeppelin–Sphere model suggests smaller cells in the left half of the region, which is supported by the histology, which shows smaller inflammatory cells on the left of the region and an increasing proportion of clusters of larger epithelial cells on the right. (b) Boxes enclose a region in which ADC is lower in the bottom right, but cellularity appears lower on histology. The high magnification histology demonstrates that the cells are smaller in this region, which is consistent with the lower values in this region of the R map

Figure 6

Haematoxylin and eosin (H&E)‐stained histology alongside colour fractional anisotropy (FA) maps from the Zeppelin portion of the Zeppelin–Sphere fit. Remaining samples are shown in Figure S7

Figure 7

Higher magnification histology of two regions (outlined in boxes) with higher fractional anisotropy (FA), demonstrating correspondence between the primary diffusion direction and directional patterns of the fibrous stroma

Figure 8

Higher magnification of the grade 3 mucinous carcinoma showing correspondence between the primary diffusion direction and directional patterns in the fibrous stroma, even in the areas of low cellularity. Note that the colour scale and arrow length have been adjusted from previous figures to better identify regions of coherence

Figure 9

The colour fractional anisotropy (FA) map for the Zeppelin portion of the Zeppelin–Sphere model for the original 0.25 × 0.25 × 0.5 mm ³ data (a) downsampled (by averaging) to 1.0 × 1.0 × 0.5 mm ³ (b) and 2.0 × 2.0 × 0.5 mm ³ (c). At lower resolutions, the anisotropy becomes weaker (colours are less bright) and it is more difficult to discern a coherent direction in the data