  Breast density, which is the ratio between fibroglandular tissue (FGT) and
total breast volume, can be assessed qualitatively by radiologists and
quantitatively by computer algorithms. These algorithms often rely on
segmentation of breast and FGT volume. In this study, we propose a method to
directly assess breast density on MRI, and provide interpretations of these
assessments.
  We assessed breast density in 506 patients with breast cancer using a
regression convolutional neural network (CNN). The input for the CNN were
slices of breast MRI of 128 x 128 voxels, and the output was a continuous
density value between 0 (fatty breast) and 1 (dense breast). We used 350
patients to train the CNN, 75 for validation, and 81 for independent testing.
We investigated why the CNN came to its predicted density using Deep SHapley
Additive exPlanations (SHAP).
  The density predicted by the CNN on the testing set was significantly
correlated with the ground truth densities (N = 81 patients, Spearman's rho =
0.86, P < 0.001). When inspecting what the CNN based its predictions on, we
found that voxels in FGT commonly had positive SHAP-values, voxels in fatty
tissue commonly had negative SHAP-values, and voxels in non-breast tissue
commonly had SHAP-values near zero. This means that the prediction of density
is based on the structures we expect it to be based on, namely FGT and fatty
tissue.
  To conclude, we presented an interpretable deep learning regression method
for breast density estimation on MRI with promising results.
