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Computational and Mathematical Methods in Medicine
Volume 2013, Article ID 679308, 12 pages
Research Article

On the Stability of Lung Parenchymal Lesions with Applications to Early Pneumothorax Diagnosis

1Thomas Jefferson High School for Science and Technology, Alexandria, VA 22312, USA
2Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA

Received 1 December 2012; Revised 26 March 2013; Accepted 30 March 2013

Academic Editor: Thierry Busso

Copyright © 2013 Archis R. Bhandarkar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Spontaneous pneumothorax, a prevalent medical challenge in most trauma cases, is a form of sudden lung collapse closely associated with risk factors such as lung cancer and emphysema. Our work seeks to explore and quantify the currently unknown pathological factors underlying lesion rupture in pneumothorax through biomechanical modeling. We hypothesized that lesion instability is closely associated with elastodynamic strain of the pleural membrane from pulsatile air flow and collagen-elastin dynamics. Based on the principles of continuum mechanics and fluid-structure interaction, our proposed model coupled isotropic tissue deformation with pressure from pulsatile air motion and the pleural fluid. Next, we derived mathematical instability criteria for our ordinary differential equation system and then translated these mathematical instabilities to physically relevant structural instabilities via the incorporation of a finite energy limiter. The introduction of novel biomechanical descriptions for collagen-elastin dynamics allowed us to demonstrate that changes in the protein structure can lead to a transition from stable to unstable domains in the material parameter space for a general lesion. This result allowed us to create a novel streamlined algorithm for detecting material instabilities in transient lung CT scan data via analyzing deformations in a local tissue boundary.