A Simplified Motion Model for Estimating Respiratory Motion from Orbiting Views

Abstract

We have shown previously that the internal motion caused by a patient’s breathing can be estimated from a sequence of slowly rotating 2D cone-beam X-ray projection views and a static prior of of the patient’s anatomy.1, 2 The estimator iteratively updates a parametric 3D motion model so that the modeled projection views of the deformed reference volume best match the measured projection views. Complicated motion models with many degrees of freedom may better describe the real motion, but the optimizations assiciated with them may overfit noise and may be easily trapped by local minima due to a large number of parameters. For the latter problem, we believe it can be solved by offering the optimization algorithm a good starting point within the valley containing the global minimum point. Therefore, we propose to start the motion estimation with a simplified motion model, in which we assume the displacement of each voxel at any time is proportional to the full movement of that voxel from extreme exhale to extreme inhale. We first obtain the full motion by registering two breathhold CT volumes at end-expiration and end-inspiration. We then estimate a sequence of scalar displacement proportionality parameters. Thus the goal simplifies to finding a motion amplitude signal. This estimation problem can be solved quickly using the exhale reference volume and projection views with coarse (downsampled) resolution, while still providing acceptable estimation accuracy. The estimated simple motion then can be used to initialize a more complicated motion estimator.