Adaptive Voxel-Weighted Loss Using L1 Norms in Deep Neural Networks for Detection and Segmentation of Prostate Cancer Lesions in PET/CT Images

This study proposes a new loss function for deep neural networks, L1-weighted Dice Focal Loss (L1DFL), that leverages L1 norms for adaptive weighting of voxels based on their classification difficulty, towards automated detection and segmentation of metastatic prostate cancer lesions in PET/CT scans. We obtained 380 PSMA [18-F] DCFPyL PET/CT scans of patients diagnosed with biochemical recurrence metastatic prostate cancer. We trained two 3D convolutional neural networks, Attention U-Net and SegResNet, and concatenated the PET and CT volumes channel-wise as input. The performance of our custom loss function was evaluated against the Dice and Dice Focal Loss functions. For clinical significance, we considered a detected region of interest (ROI) as a true positive if at least the voxel with the maximum standardized uptake value falls within the ROI. We assessed the models' performance based on the number of lesions in an image, tumour volume, activity, and extent of spread. The L1DFL outperformed the comparative loss functions by at least 13% on the test set. In addition, the F1 scores of the Dice Loss and the Dice Focal Loss were lower than that of L1DFL by at least 6% and 34%, respectively. The Dice Focal Loss yielded more false positives, whereas the Dice Loss was more sensitive to smaller volumes and struggled to segment larger lesions accurately. They also exhibited network-specific variations and yielded declines in segmentation accuracy with increased tumour spread. Our results demonstrate the potential of L1DFL to yield robust segmentation of metastatic prostate cancer lesions in PSMA PET/CT images. The results further highlight potential complexities arising from the variations in lesion characteristics that may influence automated prostate cancer tumour detection and segmentation. The code is publicly available at: https://github.com/ObedDzik/pca_segment.git.