Deformable image registration by regarding respiratory motion as 1D wave propagation in an elastic medium

PET/CT attenuation correction factors are derived from the CT image. Difficulties arise in respiratory-gated PET because the attenuation map often needs to be deformed to correct for the non-rigid motion between each gated PET frame. Deformable image registration can be useful for measuring non-rigid motion, however there are some challenges which impact on its accuracy. In this paper we address these issues in noisy gated PET data. We describe an image registration algorithm that satisfies additional constraints arising from the physics of the problem. We represent the lung by a simple mechanical analogue in which a piston drives the lung tissue. Given this model, respiratory motion approximately satisfies a one-dimensional wave equation in the superior-inferior direction. An existing free-form deformation algorithm is modified to impose this constraint. The proposed algorithm for image registration is found to be extremely robust to image noise. Simulations suggest that applying the wave equation constraint is accurate. The resulting images are plausible and the constraints enhance the robustness of the algorithm when applied to clinical respiratory-gated PET.