Motion estimation for cardiac functional analysis using two x-ray computed tomography scans

Four-dimensional computed tomography of the left ventricle, Part I: Motion artifact reduction

PURPOSE

Standard four-dimensional computed tomography (4DCT) cardiac reconstructions typically include spiraling artifacts that depend not only on the motion of the heart but also on the gantry angle range over which the data was acquired. We seek to reduce these motion artifacts and, thereby, improve the accuracy of left ventricular wall positions in 4DCT image series.

METHODS

We use a motion artifact reduction approach (ResyncCT) that is based largely on conjugate pairs of partial angle reconstruction (PAR) images. After identifying the key locations where motion artifacts exist in the uncorrected images, paired subvolumes within the PAR images are analyzed with a modified cross-correlation function in order to estimate 3D velocity and acceleration vectors at these locations. A subsequent motion compensation process (also based on PAR images) includes the creation of a dense motion field, followed by a backproject-and-warp style compensation. The algorithm was tested on a 3D printed phantom, which represents the left ventricle (LV) and on challenging clinical cases corrupted by severe artifacts.

RESULTS

The results from our preliminary phantom test as well as from clinical cardiac scans show crisp endocardial edges and resolved double-wall artifacts. When viewed as a temporal series, the corrected images exhibit a much smoother motion of the LV endocardial boundary as compared to the uncorrected images. In addition, quantitative results from our phantom studies show that ResyncCT processing reduces endocardial surface distance errors from 0.9 ± 0.8 to 0.2 ± 0.1 mm.

CONCLUSIONS

The ResyncCT algorithm was shown to be effective in reducing motion artifacts and restoring accurate wall positions. Some perspectives on the use of conjugate-PAR images and on techniques for CT motion artifact reduction more generally are also given.

Iterative inversion of deformation vector fields with feedback control

PURPOSE

Often, the inverse deformation vector field (DVF) is needed together with the corresponding forward DVF in four-dimesional (4D) reconstruction and dose calculation, adaptive radiation therapy, and simultaneous deformable registration. This study aims at improving both accuracy and efficiency of iterative algorithms for DVF inversion, and advancing our understanding of divergence and latency conditions.

METHOD

We introduce a framework of fixed-point iteration algorithms with active feedback control for DVF inversion. Based on rigorous convergence analysis, we design control mechanisms for modulating the inverse consistency (IC) residual of the current iterate, to be used as feedback into the next iterate. The control is designed adaptively to the input DVF with the objective to enlarge the convergence area and expedite convergence. Three particular settings of feedback control are introduced: constant value over the domain throughout the iteration; alternating values between iteration steps; and spatially variant values. We also introduce three spectral measures of the displacement Jacobian for characterizing a DVF. These measures reveal the critical role of what we term the nontranslational displacement component (NTDC) of the DVF. We carry out inversion experiments with an analytical DVF pair, and with DVFs associated with thoracic CT images of six patients at end of expiration and end of inspiration.

RESULTS

The NTDC-adaptive iterations are shown to attain a larger convergence region at a faster pace compared to previous nonadaptive DVF inversion iteration algorithms. By our numerical experiments, alternating control yields smaller IC residuals and inversion errors than constant control. Spatially variant control renders smaller residuals and errors by at least an order of magnitude, compared to other schemes, in no more than 10 steps. Inversion results also show remarkable quantitative agreement with analysis-based predictions.

CONCLUSION

Our analysis captures properties of DVF data associated with clinical CT images, and provides new understanding of iterative DVF inversion algorithms with a simple residual feedback control. Adaptive control is necessary and highly effective in the presence of nonsmall NTDCs. The adaptive iterations or the spectral measures, or both, may potentially be incorporated into deformable image registration methods.

Vectors through a cross-sectional image (VCI): A visualization method for four-dimensional motion analysis for cardiac computed tomography

BACKGROUND

Cardiac computed tomography (CT) has the potential for fully four-dimensional (4D for 3D plus time) motion analysis of the heart. We aimed at developing a method for assessment and presentation of the 4D motion for multi-phase, contrast-enhanced cardiac CT data sets and demonstrating its clinical applicability.

METHODS

Four patients with normal cardiac function, old myocardial infarction (OMI), takotsubo cardiomyopathy, and hypertrophic cardiomyopathy (HCM) underwent contrast-enhanced cardiac CT for one heartbeat using a 320-row CT scanner with no tube current modulation. CT images for 10 cardiac phases (with a 10%-increment of the R-R interval) were reconstructed with the isotropic effective resolution of (0.5 mm)³ An image-based motion-estimation (iME) algorithm, developed previously, has been used to estimate a time series of 3D cardiac motion, from the end-systole to the other nine phases. The iME uses down-sampled images with a resolution of (1.0 mm)³ deforms the end-systole images non-rigidly to match images at other phases. Once the agreement is maximized, iME outputs a 3D motion vector defined for each voxel for each phase, that smoothly changes over voxels and phases. The proposed visualization method, which is called "vectors through a cross-sectional image (VCI)," presents 3D vectors from the end-diastole to the end-systole as arrows with an end-diastole CT slice. We performed visual assessment of the VCI with calculated the mean vector lengths to evaluate regional left ventricular (LV) contraction.

RESULTS

The VCI images showed the magnitude and direction of systolic 3D vectors, including the through-plane motion, and successfully visualized the relations of LV wall segments and abnormal regional wall motion. Decreased regional motion and asymmetric motion due to hypokinetic infarct segment, takotsubo cardiomyopathy, and hyper trophic cardiomyopathy was clearly observed. It was easy to appreciate the relation of the abnormal regional wall motion to the affected LV wall segments. The mean vector lengths of the affected segments with pathologies were clearly smaller than the other unaffected segments (1.2-1.7 mm versus 2.5-4.7 mm).

CONCLUSIONS

VCI images could capture the magnitude and direction of through-plane motion and show the relations of LV wall segments and abnormal wall motion.