BMD prediction

Bone mineral density (BMD) prediction in CT images based on deep residual CNN + XAI Interpretation

Paper
Kang, J. W., Park, C., Lee, D. E., Yoo, J. H., & Kim, M. (2023). Prediction of bone mineral density in CT using deep learning with explainability. Frontiers in Physiology, 13, 2735.

Workflow

L1 Segmentation

In order to investigate which area had a great impact on the prediction of BMD, we divided the experiment into three cases.

• Case 1 : Cropped images
• Case 2 : Entire-vertebrae-masked images
• Case 3 : Vertebral-body-masked images

U-Net-based model was applied to segment the L1 region.

BMD Prediction

Deep resiudal CNN for BMD estimation.

We achieved a maximum correlation coefficient of 0.905 for the test set.

• Estimation Network

• Estimation Result

XAI Interpretation

Grad-CAM is well-known XAI technique used to investigate the attention of a DL network toward an image.

We modified Grad-CAM for this study because it is specialized in a classifer, whereas our network is an estimator (regressor).

Grad-RAM converted the ReLU operator in Grad-CAM to an absolute operator because it considered the features that have a significant impact on the estimate, regardless of the direction (sign) of the gradient.

$$L_{Grad-RAM}\left(i,j\right)=\left|\sum_{k}{\alpha_kA_k\left(i,j\right)}\right|,\ \ \ \ \alpha_k=\frac{1}{Z}\sum_{i}\sum_{j}\frac{\partial y}{\partial A_k(i,j)}$$

Grad-RAMP multiplied each gradient with respect to every pixel $(i,j)$ with the corresponding pixels to consider pixel attribution.

$$L_{Grad-RAMP}\left(i,j\right)=\left|\sum_{k}{g_k\odot A_k\left(i,j\right)}\right|,\ \ \ \ g_k=\frac{\partial y}{\partial A_k(i,j)}$$

• $k$ : Channel index of the convolutional layer

• $\alpha_{k}(i,j)$ : $k$ th weight

• Z : The number of pixels in the feature map

• $A_{k}(i,j)$ : Feature map of the last convolutional layer

• $\odot$ : Hadamard product operator

• XAI result