The negative sigmoid loss for controlling false positive rate in osteolytic lesion segmentation

Multiple Myeloma (MM) is a malignancy that is commonly associated with the development of osteolytic lesions. To support MM diagnosis, low-dose Computed Tomography (CT) is commonly used for lesion localization, but manually evaluating CT scans can be time-consuming and prone to error. Although deep learning methods have delivered promising results in supporting lesion detection, they are likely to produce false positive findings, hindering their usability in clinical practice. To address this, we trained a 2D U-Net on annotated lesions (positive patches) in combination with images of bone tissue without lesions (negative patches). To optimize penalization of segmentations in these negative patches, we propose the "Negative Sigmoid" (NS) loss, a term that can be added to conventional loss functions such as the Combo loss (a combination of the cross-entropy and Dice loss). This NS loss applies a tunable penalty to segmentations in negative patches, and by scaling the contribution of the NS loss to the total loss, the balance between lesion detection and false positive rate can be controlled. Compared to training exclusively on positive patches, we show that training with negative patches slightly reduces the number of false positive lesion segmentations in negative patches when using the Combo loss, but that false positive counts can be further reduced by extending the Combo loss with the NS loss. Although the reduced false-positive rate was accompanied by a lower recall and lesion detection rate, it resulted in a significant improvement in precision. Overall, our work demonstrates advances in the automatic segmentation of osteolytic lesions in low-dose CT data by enabling precise control over the number of true and false positives while maintaining good segmentation performance, both of which are key prerequisites for future clinical application.