Automated detection and segmentation of metastatic prostate cancer lesions in PET/CT images via deep neural networks towards accurate and routine quantification of clinical metrics

Detection and segmentation of lesions in metastatic prostate cancer patients via multimodal positron emission tomography (PET)/computed tomography (CT) imaging can have significant value in the clinical management spectrum, including staging, restaging, diagnosis, treatment planning, and prognosis. Conventional manual segmentation methods, such as tumor contouring, are labor intensive and time-consuming, driving interest in automated solutions using artificial intelligence, specifically deep neural networks. However, automated segmentation faces challenges due to tumor variability in size, shape, uptake intensity, and anatomical location, as well as significant class imbalance between lesion and background voxels, and variability in voxel classification difficulty. Loss function design is central to addressing these challenges. While Dice loss effectively handles class imbalance, it struggles with voxel-level classification difficulty. Nevertheless, distribution-based loss functions like cross-entropy and focal loss address classification difficulty but compromise Dice loss's balance of false positives and false negatives. Combining these loss functions into compound forms improves robustness but often trades off specificity for sensitivity, limiting clinical utility. To address these issues, we propose a novel loss function, L1-weighted Dice Focal Loss (L1DFL), which uses L1 norms of predicted probabilities and ground truth labels to prioritize underrepresented classes and hard-to-classify voxels. Performance was evaluated across multiple lesion scenarios, including images with single and multiple lesions, and varying molecular volumes. We also evaluated its robustness across various levels of spatial distribution of lesions, beyond the primary prostatic region. Subsequently, the analysis evaluated the loss function's clinical utility and its ability to reproduce clinical metrics. Experimental results demonstrate that L1DFL outperforms Dice Focal Loss and Dice Loss by 22% and 13%, respectively, on the Dice Similarity Coefficient, and achieves a superior sensitivity-specificity balance, improving F1 scores by 34% and 6%. L1DFL consistently performed well across lesion scenarios, surpassing other loss functions by at least 11%. It also quantified clinically relevant metrics such as the standardized uptake values (SUVmean, SUVmax), total lesion activity, and lesion count within acceptable margins. Coupled with its effectiveness across diverse neural network architectures (SegResNet, U-Net, Attention U-Net), the results highlight L1DFL's potential to enhance automated segmentation and support clinical decision-making in metastatic prostate cancer management.