Mass preserving nonrigid registration of CT lung images using cubic B-spline

The authors propose a nonrigid image registration approach to align two computed-tomography (CT)-derived lung datasets acquired during breath-holds at two inspiratory levels when the image distortion between the two volumes is large. The goal is to derive a three-dimensional warping function that can be used in association with computational fluid dynamics studies. In contrast to the sum of squared intensity difference (SSD), a new similarity criterion, the sum of squared tissue volume difference (SSTVD), is introduced to take into account changes in reconstructed Hounsfield units (scaled attenuation coefficient, HU) with inflation. This new criterion aims to minimize the local tissue volume difference within the lungs between matched regions, thus preserving the tissue mass of the lungs if the tissue density is assumed to be relatively constant. The local tissue volume difference is contributed by two factors: Change in the regional volume due to the deformation and change in the fractional tissue content in a region due to inflation. The change in the regional volume is calculated from the Jacobian value derived from the warping function and the change in the fractional tissue content is estimated from reconstructed HU based on quantitative CT measures. A composite of multilevel B-spline is adopted to deform images and a sufficient condition is imposed to ensure a one-to-one mapping even for a registration pair with large volume difference. Parameters of the transformation model are optimized by a limited-memory quasi-Newton minimization approach in a multiresolution framework. To evaluate the effectiveness of the new similarity measure, the authors performed registrations for six lung volume pairs. Over 100 annotated landmarks located at vessel bifurcations were generated using a semiautomatic system. The results show that the SSTVD method yields smaller average landmark errors than the SSD method across all six registration pairs.