Purpose: Quantify the elastostatic force exerted in the lungs due to the change in elasticity, caused by the diaphragm motion and track the elasticity of the lungs after radiotherapy treatment.
Methods: Four-dimensional Computed Tomography scans of the lungs at different respiratory phases are obtained. Considering full exhale phase as a reference phase and performing deformable image registration deformation vector fields (DVF) for different phases were obtained. Using these DVF the displacement of specific points in the lungs was found for all phases with respect to the reference phase. Assuming lungs as an elastic medium, force was calculated from the displacement using elastic balance equation F = Kx, K being the elasticity constant, and x being the displacement from any phase to the reference phase. The displacements were calculated from the deformation vector field and compared with linear elastic model which is a linear interpolation between the minimum displacement in the upper lung and the maximum displacement in the lower lung.
Results: The deformation was found to be larger towards the lower part of the lungs near diaphragm. It was also observed that larger forces are exerted at peak inspiration as compared to the peak expiration. The force was calculated on the upper, lower, and mid lungs and the force increased from upper to lower lung as the deformation was also increasing in the same order. The maximum difference was 2.70mm in the mid-region of the lungs.
Conclusion: This work presents the distribution of the force exerted on the lungs due to the deformation at different breathing phases. The forces calculated at different regions of the lungs quantify the motion due to respiration and determine the elasticity of the lungs. The determination of force in the lungs before and after radiotherapy helps to find the optimized positions for fiducial marker placement.