Modeling lung deformation: A combined deformable image registration method with spatially varying Young's modulus estimates

Purpose: Respiratory motion introduces uncertainties in tumor location and lung deformation, which often results in difficulties calculating dose distributions in thoracic radiation therapy. Deformable image registration (DIR) has ability to describe respiratory-induced lung deformation, with which the radiotherapy techniques can deliver high dose to tumors while reducing radiation in surrounding normal tissue. The authors' goal is to propose a DIR method to overcome two main challenges of the previous biomechanical model for lung deformation, i.e., the requirement of precise boundary conditions and the lack of elasticity distribution. Methods: As opposed to typical methods in biomechanical modeling, the authors' method assumes that lung tissue is inhomogeneous. The authors thus propose a DIR method combining a varying intensity flow (VF) block-matching algorithm with the finite element method (FEM) for lung deformation from end-expiratory phase to end-inspiratory phase. Specifically, the lung deformation is formulated as a stress-strain problem, for which the boundary conditions are obtained from the VF block-matching algorithm and the element specific Young's modulus distribution is estimated by solving an optimization problem with a quasi-Newton method. The authors measure the spatial accuracy of their nonuniform model as well as a standard uniform model by applying both methods to four-dimensional computed tomography images of six patients. The spatial errors produced by the registrations are computed using large numbers (>1000) of expert-determined landmark point pairs. Results: In right-left, anterior-posterior, and superior-inferior directions, the mean errors (standard deviation) produced by the standard uniform FEM model are 1.42(1.42), 1.06(1.05), and 1.98(2.10) mm whereas the authors' proposed nonuniform model reduces these errors to 0.59(0.61), 0.52(0.51), and 0.78(0.89) mm. The overall 3D mean errors are 3.05(2.36) and 1.30(0.97) mm for the uniform and nonuniform models, respectively. Conclusions: The results indicate that the proposed nonuniform model can simulate patient-specific and position-specific lung deformation via spatially varying Young's modulus estimates, which improves registration accuracy compared to the uniform model and is therefore a more suitable description of lung deformation.