Hybrid cone-beam tomographic reconstruction: incorporation of prior anatomical models to compensate for missing data

Abstract

We propose a method for improving the quality of cone-beam tomographic reconstruction done with a C-arm. C-arm scans frequently suffer from incomplete information due to image truncation, limited scan length, or other limitations. Our proposed "hybrid reconstruction" method injects information from a prior anatomical model, derived from a subject-specific computed tomography (CT) or from a statistical database (atlas), where the C-arm X-ray data is missing. This significantly reduces reconstruction artifacts with little loss of true information from the X-ray projections. The methods consist of constructing anatomical models, fast rendering of digitally reconstructed radiograph (DRR) projections of the models, rigid or deformable registration of the model and the X-ray images, and fusion of the DRR and X-ray projections, all prior to a conventional filtered back-projection algorithm. Our experiments, conducted with a mobile image intensifier C-arm, demonstrate visually and quantitatively the contribution of data fusion to image quality, which we assess through comparison to a "ground truth" CT. Importantly, we show that a significantly improved reconstruction can be obtained from a C-arm scan as short as 90° by complementing the observed projections with DRRs of two prior models, namely an atlas and a preoperative same-patient CT. The hybrid reconstruction principles are applicable to other types of C-arms as well.

Fig. 1

The calibration phantom: (a) Mounted on the C-arm XRII. (b) An x-ray image: the grid is used to compute dewarp parameters, and the diamonds and diagonals for pin-hole parameters.

Fig. 2

An outline of the hybrid reconstruction process.

Fig. 3

An outline of the anatomical atlas creation process (images 3,4 courtesy of L.M. Ellingsen).

Fig. 4

Simulated image and registration of model and C-arm x-ray. (a) A DRR image of a mesh model of a dry pelvis specimen. (b) An x-ray image of the specimen, to which the mesh model was rigidly registered by maximization of mutual information. (c) An overlay of the edges of image (a) on image (b). The full dynamic range of each image was normalized independently to [0, 1].

Fig. 5

Distribution of mean errors in deformable 2D-3D registration on the surface of a pelvis model.

Fig. 6

Fusion of a C-arm x-ray image (inside circle) with a DRR projection of a prior model (periphery). (a) Linear scaling of intensities in each modality to the range [0,1]. (b) The DRR image intensities remapped by spline to the dynamic range of x-ray image. (c) Fusion of the x-ray image and the remapped DRR. (d) Fusion done by remapping the x-ray image intensities to the dynamic range of the DRR.

Fig. 7

Matching graph of sorted DRR intensities (on an arbitrary scale) and sorted x-ray image intensities (as normalized logarithm). The control points for spline mapping between them are highlighted in circles.

Fig. 8

Flowchart of the process for compensating limited-arc CBCT scans by “extrapolation” based on a prior anatomical model.

Fig. 9

Transverse cross sectional reconstructions of femur specimen, with a rectangular ROI highlighted. (a) CT volume, resampled in registration with CBCT. (b) CBCT reconstruction using observed x-ray images. (c) CBCT reconstruction from a spline remapping of x-ray images to match CT projection intensities.

Fig. 10

Orthogonal cross sections of femur reconstruction. (a) “Coronal” slice from CT. (b) Coronal slice from CBCT. (c) “Sagittal” slice from CT. (d) Sagittal slice from CBCT.

Fig. 11

Transverse cross sectional midplane reconstructions of dry pelvis specimen. (a) A photograph of the specimen. (b) CT volume, resampled in registration with CBCT. (c) CBCT reconstruction using truncated x-ray images, such as the ones in Fig. 4(b); the ROI for quantitative comparison is highlighted. (d) CBCT reconstruction from a spline remapping of x-ray image intensities to match DRR intensities. (e) CBCT of observed x-ray images fused with projections of a CT-based model. (f) CBCT using x-ray images remapped to DRR intensities and fused with CT-based model projections.

Fig. 12

Images of the fresh pelvis specimen. (a) A photograph of the specimen. (b) An x-ray image, before taking logarithm, highlighting the fiducial screws (magenta circles) and the cement injected near the ilio-sacral joint (yellow outline). (c) An overlay of green edges from an image of an atlas, deformably registered with the x-ray scan. (d) Fusion of x-ray image (at center, after taking logarithm) and a DRR computed from a CT scan of the specimen (periphery). (e) A similar fusion of the x-ray image and the registered atlas; notice the slight misalignment of the iliac crest and the absence of the spine from the atlas.

Fig. 13

Reconstruction of fresh pelvis specimen: the midplane slice. (a) Resampled CT volume, with the similarity ROI highlighted. (b) Reconstruction from truncated x-ray images. (c) Reconstruction from x-ray images fused with CT projections. (d) Reconstruction from x-ray images fused with atlas projections. (e)–(g) Off-midplane slices from the CT, CT-fused CBCT, and atlas-fused CBCT; notice the stronger artifacts in image (g), compared with (f).

Fig. 14

Reconstruction of the fresh pelvis specimen with a reduced arc trajectory, and compensation by a pre-operative scan, an atlas, and a post-operative CT scan, all registered to the original 210° C-arm scan. Two regions of interest, a magenta semicircle and a green rectangle, are highlighted on a slice from the “ground truth” post-operative CT. The semicircle is the “complete” FOV, and the rectangle is the volumetric bounding box of the injected cement. The dynamic range of the images was normalized based on the parameters in Table I.

Fig. 15

Behavior of the correlation coefficient similarity score between the “ground truth” post-operative CT and a number of CBCT reconstructions, involving different sources of prior data: raw x-ray images without a prior, raw data compensated for truncation only, and compensation for reduced arc length using pre-operative CT, statistical atlas and post-operative CT. Notice the contribution of the prior CT and the atlas to the reconstruction from the reduced scan arc of 90°. The regions of interest are (a) the full FOV, and (b) a box containing the injected cement. These are highlighted in Fig. 14.