Idiopathic pulmonary fibrosis (IPF) is a chronic fibrotic lung disease that develops in adults without any known cause. It is an interstitial lung disease in which the lung tissue becomes scarred and stiffens, ultimately leading to respiratory failure. This disease currently has no cure with limited treatment options, leading to an average survival time of 3-5 years after diagnosis. In this paper we employ a mathematical model simulating the lung parenchyma as hexagons with elastic forces applied to connecting vertices and opposing vertices. Using an image registration algorithm, we obtain trajectories of 4D-CT scans of a healthy patient, and one suffering from IPF. Converting the image trajectories into a hexagonal lattice, we fit the model parameters to match the respiratory motion seen for both patients across multiple image slices. We found the model could decently describe the healthy lung slices, with a minimum average error between corresponding vertices to be 1.66 mm. For the fibrotic lung slices the model was less accurate, maintaining a higher average error across all slices. Using the optimized parameters, we apply the forces predicted from the model using the image trajectory positions for each phase. Although the error is large, the spring constant values determined for the fibrotic patient were not as high as we expected, and more often than not determined to be lower than corresponding healthy lung slices. However, the net force distribution for some of those slices was still found to be greater than the healthy lung counterparts. Other modifications to the model, including additional directional components and which vertices were receiving with the limited sample size available, a clear distinction between the healthy and fibrotic lung cannot yet be made by this model.