  Pneumothorax is a medical emergency caused by abnormal accumulation of air in
the pleural space - the potential space between the lungs and chest wall. On 2D
chest radiographs, pneumothorax occurs within the thoracic cavity and outside
of the mediastinum and we refer to this area as "lung+ space". While deep
learning (DL) has increasingly been utilized to segment pneumothorax lesions in
chest radiographs, many existing DL models employ an end-to-end approach. These
models directly map chest radiographs to clinician-annotated lesion areas,
often neglecting the vital domain knowledge that pneumothorax is inherently
location-sensitive.
  We propose a novel approach that incorporates the lung+ space as a constraint
during DL model training for pneumothorax segmentation on 2D chest radiographs.
To circumvent the need for additional annotations and to prevent potential
label leakage on the target task, our method utilizes external datasets and an
auxiliary task of lung segmentation. This approach generates a specific
constraint of lung+ space for each chest radiograph. Furthermore, we have
incorporated a discriminator to eliminate unreliable constraints caused by the
domain shift between the auxiliary and target datasets.
  Our results demonstrated significant improvements, with average performance
gains of 4.6%, 3.6%, and 3.3% regarding Intersection over Union (IoU), Dice
Similarity Coefficient (DSC), and Hausdorff Distance (HD). Our research
underscores the significance of incorporating medical domain knowledge about
the location-specific nature of pneumothorax to enhance DL-based lesion
segmentation.
