Ph.D. Public Defense

A Volumetric Expansion Technique Using Vector Divergence Operator for Regional Lung Function Analysis

Rami R. Abu-Aita

Supervised by Kevin J. Parker

Tuesday, October 24, 2023
10 a.m.–11 a.m.

703 Computer Studies Building




Chronic obstructive pulmonary disease (COPD) is the third leading cause of death in the United States, after heart disease and cancer. Pulmonary function tests (PFTs), such as spirometry and body plethysmography, and quantitative computed tomography (CT) indices (QIs) of lung densitometry are typically used in the diagnosis of COPD and have been found to correlate with pulmonary function impairment. The spirometric PFTs are required to diagnose COPD by measuring important parameters such as the forced vital capacity (FVC) and the forced expiratory volume in one second (FEV1). However, the spirometric parameters provide a global measure of lung function rather than regional information. On the other hand, CT lung densitometry provides a quantitative assessment of pulmonary diseases such as emphysema and small airways disease and is used in phenotyping, but lacks functional information. Therefore, the goal of our thesis is to contribute to the functional imaging of the lungs and the regional pulmonary assessment using biomarkers.


Many lung diseases such as COPD and fibrosis are associated with dramatic changes in mechanical properties of lung tissue. Therefore, imaging techniques are continuously being developed to assess the mechanical properties of soft tissue and provide imaging biomarkers for pathological processes. Elastography, a non-invasive medical imaging technique, is used for imaging the elastic properties or stiffness of soft tissues from the tissue displacements, and has been successfully used in imaging liver fibrosis, prostate and breast cancers, and thyroid nodules. Four-dimensional CT (4DCT) and deformable image registration (DIR) are relatively new technologies that allow the estimation of parenchymal tissue displacements from the matching of volumetric lung CT images at different breathing phases. Thus, inspired by Elastography and motivated by the DIR of 4DCT images, we developed a volumetric expansion technique based on the vector divergence operator for evaluating regional lung function. From our phantom studies (0.49× 0.49 × 1.25 mm3 voxels) on compressed open cell lung models, we estimated that for theouter boundary displacements in 3D of greater than 45mm, the models achieve high accuracy with a root-mean-square error of 0.041 for the estimated divergence.


We studied the relationship between the divergence biomarker and the clinical measures of pulmonary function in patients with COPD. To achieve this goal, the mean and median divergence values were tested for correlation with PFTs and QIs using Pearson’s and Spearman’s rank-order correlation analyses. The divergence measure correlated strongly with both PFTs and QIs of COPD patients and therefore is a useful biomarker in analyzing regional lung function. We also found a statistically significant difference in divergence between normal subjects and patients with emphysema (p < .005) and COPD (p < .001), particularly patients with severe obstructive lung disease (p = .0005). 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. Furthermore, we propose the divergence images and divergence volume histograms (DiVHs) as a clear and concise representation for the distribution of divergence within the lung organ in order to facilitate the comparison of pulmonary function impairment amongst individuals with obstructive lung diseases.