Extra‐dimensional Demons: A method for incorporating missing tissue in deformable image registration
Authors: Nithiananthan Sajendra , Schafer Sebastian , Mirota Daniel J. , Stayman J. Webster , Zbijewski Wojciech , Reh Douglas D. , Gallia Gary L. , Siewerdsen Jeffrey H. 
Published: August 2012

Purpose:A deformable registration method capable of accounting for missing tissue (e.g., excision) is reported for application in cone‐beam CT (CBCT)‐guided surgical procedures. Excisions are identified by a segmentation step performed simultaneous to the registration process. Tissue excision is explicitly modeled by increasing the dimensionality of the deformation field to allow motion beyond the dimensionality of the image. The accuracy of the model is tested in phantom, simulations, and cadaver models.Methods:A variant of the Demons deformable registration algorithm is modified to include excision segmentation and modeling. Segmentation is performed iteratively during the registration process, with initial implementation using a threshold‐based approach to identify voxels corresponding to “tissue” in the moving image and “air” in the fixed image. With each iteration of the Demons process, every voxel is assigned a probability of excision. Excisions are modeled explicitly during registration by increasing the dimensionality of the deformation field so that both deformations and excisions can be accounted for by in‐ and out‐of‐volume deformations, respectively. The out‐of‐volume (i.e., fourth) component of the deformation field at each voxel carries a magnitude proportional to the excision probability computed in the excision segmentation step. The registration accuracy of the proposed “extra‐dimensional” Demons (XDD) and conventional Demons methods was tested in the presence of missing tissue in phantom models, simulations investigating the effect of excision size on registration accuracy, and cadaver studies emulating realistic deformations and tissue excisions imparted in CBCT‐guided endoscopic skull base surgery.Results:Phantom experiments showed the normalized mutual information (NMI) in regions local to the excision to improve from 1.10 for the conventional Demons approach to 1.16 for XDD, and qualitative examination of the resulting images revealed major differences: the conventional Demons approach imparted unrealistic distortions in areas around tissue excision, whereas XDD provided accurate “ejection” of voxels within the excision site and maintained the registration accuracy throughout the rest of the image. Registration accuracy in areas far from the excision site (e.g., > ∼5 mm) was identical for the two approaches. Quantitation of the effect was consistent in analysis of NMI, normalized cross‐correlation (NCC), target registration error (TRE), and accuracy of voxels ejected from the volume (true‐positive and false‐positive analysis). The registration accuracy for conventional Demons was found to degrade steeply as a function of excision size, whereas XDD was robust in this regard. Cadaver studies involving realistic excision of the clivus, vidian canal, and ethmoid sinuses demonstrated similar results, with unrealistic distortion of anatomy imparted by conventional Demons and accurate ejection and deformation for XDD.Conclusions:Adaptation of the Demons deformable registration process to include segmentation (i.e., identification of excised tissue) and an extra dimension in the deformation field provided a means to accurately accommodate missing tissue between image acquisitions. The extra‐dimensional approach yielded accurate “ejection” of voxels local to the excision site while preserving the registration accuracy (typically subvoxel) of the conventional Demons approach throughout the rest of the image. The ability to accommodate missing tissue volumes is important to application of CBCT for surgical guidance (e.g., skull base drillout) and may have application in other areas of CBCT guidance.