An inverse hyper-spherical harmonics-based formulation for reconstructing 3D volumetric lung deformations

Abstract

A method to estimate the deformation operator for the 3D volumetric lung dynamics of human subjects is described in this paper. For known values of air flow and volumetric displacement, the deformation operator and subsequently the elastic properties of the lung are estimated in terms of a Green's function. A Hyper-Spherical Harmonic (HSH) transformation is employed to compute the deformation operator. The hyper-spherical coordinate transformation method discussed in this paper facilitates accounting for the heterogeneity of the deformation operator using a finite number of frequency coefficients. Spirometry measurements are used to provide values for the airflow inside the lung. Using a 3D optical flow-based method, the 3D volumetric displacement of the left and right lungs, which represents the local anatomy and deformation of a human subject, was estimated from 4D-CT dataset. Results from an implementation of the method show the estimation of the deformation operator for the left and right lungs of a human subject with non-small cell lung cancer. Validation of the proposed method shows that we can estimate the Young's modulus of each voxel within a 2% error level.