Vector Divergence of Computed Tomography Measures Pulmonary Function Impairment in Patients with Chronic Obstructive Lung Disease

Chronic obstructive pulmonary disease (COPD) is the third leading cause of death worldwide. Pulmonary function tests (PFTs) and quantitative indices (QIs) of computed tomography (CT) are typically used to diagnose COPD. The purpose of this work was to determine the correlation of the vector divergence operator with PFTs and QIs in COPD patients and compare the divergence of normal lung function to that in COPD. Vector divergence is computed for 73 patients with four-dimensional CT scans retrospectively identified as normal (n = 37) and COPD (n = 36), which includes emphysema (n = 13). The divergence is the flux per unit volume at a point in a vector field and reflects the local lung tissue expansion when the data are taken during inspiration. The divergence measures are strongly correlated with both PFTs and QIs of COPD patients and therefore are a useful biomarker in analyzing regional lung function. In physical terms, the divergence shows that there is a significant difference in lung tissue expansion between normal subjects and patients with airflow obstruction as in emphysema and COPD. The divergence analysis also enables new images using color overlays to provide a functional measure (local expansion capability) to the anatomical CT image.