iLogDemons, Experiments on a Real Case
iLogDemons were then used to estimate the 3D left-ventricular myocardium strain from standard anatomical cine MRI of the heart. Such images have good in-plane and temporal resolutions but large slice thickness, which hampers the accurate estimation of cardiac through-plane motion (Figure 1). As the volume of the heart is almost constant during the cardiac cycle, incompressible registration is believed to improve the estimation of the cardiac deformation.
(Data courtesy of King's College London, St Thomas Hospital, Division of Imaging Sciences)
Anatomical short axis cine SSFP MRI (cMRI) of a patient with heart failure were acquired with multiple breath-holds (Achieva, Philips Medical System, 30 frames, 1.5mm2 isotropic in-plane resolution, 10mm slice thickness). 3D tagged MRI (tMRI) were also acquired during the same exam (CSPAMM, 23 frames, 0.9mm isotropic resolution, tag size 3mm). No manual tracking of the tag grids was available since this task is extremely difficult due to the 3D motion. All the images fully covered both ventricles and no slice misalignments were detected. The cMRI were linearly resampled to get isotropic voxel sizes. The tMRI were spatially and temporally aligned to the cMRI using DICOM information. Because the transformations provided by demons algorithm are resampling fields, myocardium deformation was estimated by recursively registering all the frames of the cardiac sequence to the end-diastole (ED) time frame, as in (Mansi et al., 2009) (Figure 1). Registration parameters were σx=1mm, σ2=2mm, σf2=0.5mm (the smoothing was increased to accommodate the lower image quality). A 2-level multi-resolution scheme was used and registration was stopped as soon as RMSE stopped decreasing. Incompressibility constraint was applied only within the myocardium as volume of surrounding structures like blood pools vary.
First, we estimated the myocardium motion by tracking the heart in the 3D tMRI using iLogDemons. For visual assessment, the deformations were applied to virtual planes manually positioned at ED (Figure 3). Realistic deformations consistent with the tag grids were obtained, which was further confirmed by the temporal variation of the radial, circumferiential and longitudinal myocardium strains (Figure 4, green curve). These results were similar to those obtained with logDemons, as the tag grids provided enough texture information in the myocardium to guide the registration. Hence, as no ground truth was available, we considered the iLogDemons estimation as reference. We then estimated the 3D motion of the heart from the cMRI and compared the results with the reference tMRI motion (Figure 4, blue and red curves). Visually, the warped virtual planes showed that incompressibility constraint did help to recover the longitudinal motion despite the large slice thickness of the cMRI. Estimated longitudinal and circumferential strains confirmed this finding. iLogDemons was closer to the reference than the logDemons (59% of improvement for radial strain, 84% for circumferential strain and 42% for longitudinal strain). Radial strain amplitude was more reasonable and the variations of the circumferential and longitudinal strains presented realistic patterns (Moore et al., 2000), where logDemons estimated an abnormal lengthening at the beginning of the cardiac contraction.
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iLogDemons better estimates longitudinal and circumferential motion
(Data courtesy of King's College London, St Thomas Hospital, Division of Imaging Sciences)
Discussion and Conclusion
We have adapted logDemons algorithm to provide incompressible deformations. This has been possible by showing that demons Gaussian smoothing minimises an infinite order Tikhonov regulariser. This framework opens the way to new regularisers, such as elastic regularisation. As a result, incompressibility could be ensured by constraining the velocities to be divergence-free. The proposed incompressibility constraint does not introduce any new parameter. Those listed in this paper are present in any recent demons algorithm (Vercauteren et al., 2008). One could constrain the correspondence velocity to find the optimal incompressible update deformation. Yet, non-reported experiments showed that this does not significantly improve the results compared to iLogDemons: The updates are usually small and thus near-incompressible. The next step is to modify the demons energy to automatically handle incompressibility in subdomains of the image. From a clinical point of view, we are currently validating this method for the automatic estimation of 3D myocardium strain from standard cardiac images.
References
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H. Delingette, J. Blanc, Y. Boudjemline, and
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- T. Mansi, X. Pennec, M. Sermesant, H. Delingette, and N. Ayache. LogDemons Revisited: Consistent Regularisation and Incompressibility Constraint for Soft Tissue Tracking in Medical Images. In Medical Image Computing and Computer Assisted Intervention (MICCAI), Lecture Notes in Computer Science. Springer, 2010. In press.
- C.C. Moore, C.H. Lugo-Olivieri, E.R. McVeigh, and E.A. Zerhouni. Three-dimensional systolic strain patterns in the normal human left ventricle: Characterization with tagged MR imaging. Radiology, 214(2):453-466, 2000.
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Aymeric Perchant, and Nicholas Ayache. Symmetric log- domain
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