The framework uses a linear elastic model to simulate brain-shift behavior. The model is driven by cortical surface deformations, which are tracked using a surface-tracking algorithm combined with a laser-range scanner. The framework performance was evaluated using displacements of anatomical landmarks, tumor contours and self-defined evaluation parameters.
The results show that tumor deformations predicted by the present framework agreed well with the ones observed intraoperatively, especially in the parts of the larger deformations. On average, a brain shift of 3. The entire correction process was performed in less than 5 min. The data from this study suggest that the technique is a suitable candidate for intraoperative brain-deformation correction. Citing Literature. Volume 19 , Issue 2 June Pages Related Information. Close Figure Viewer.
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Enter your email address below and we will send you your username. Forgot your password? Moreover, we also implemented a masking of the similarity term in the non-linear registration with a formulation that ensures symmetry. It enhances the robustness of the registration results with respect to intensity artifacts in the boundary of the brain, thereby increasing the sensitivity of the statistical studies done on the longitudinal deformations. We finally showed on an open-access database that the results obtained with this pipeline are consistent with the findings from the literature.
The use of the parallel transport in our pipeline enables us to perform both standard univariate analysis on a scalar map and also statistics directly on the SVFs as illustrated by the multivariate Hoteling's T 2 -test. Therefore, changes other than the ones linked to volumetry like rotations or translations of the brain structures could be studied. Concerning the confidence mask, initializing it with probabilistic masks of the fixed and moving image instead of binary ones could be used to take into account the uncertainty linked to the skull-stripping at the brain boundaries.
However, in our experiment the use of binary masks was sufficient to increase the sensitivity of the statistical group-wise analysis while not decreasing the specificity. Intensities artifacts inside the brain such as prominent blood vessels could also be incorporated in the confidence mask if a blood vessels segmentation was available. The most important issue for the longitudinal processing pipeline is related to the asymmetry biases Ridgway et al. Two types of asymmetries can be distinguished. The first one, described in Reuter and Fischl and Yushkevich et al. In the case of the follow-up images, the transformation used to resample the image is the combination of a rigid and an affine transformation cf.
This aspect of the pipeline has some similarity to that of Rohrer et al. However, this would still imply an implicit internal resampling and in this case we would no longer follow the assumption made in LDDMM and the SVF framework that all the field tends toward zero when we get away from the center of the image i. In practice, we observe edge-effects and a proper way to deal with the problem should be to revise the LCC log-Demons algorithm in order to explicitly handle the two transformations separately and make sure that the criterion and the discretization would be affine invariant.
The second type of bias is related to the non-centrality of the time point where the subject longitudinal deformations are computed also referenced as favoring a particular time point. In these methods, the initial velocity or equivalently the momentum map is different at different time points along a geodesic.
In that case, for more than two time points, it is necessary to choose a time point for the subject-specific template, and this time point is generally the average or median of the observed time points. The momentum maps from the template to all the time points can then be compared in the template reference space only. In the stationary velocity field framework, the velocity field is—by definition—stationary. Thus, the SVF resulting from the registration is the same all along the trajectory: it is not expressed in material coordinates at a specific time point but in Eulerian coordinates which are not attached to a given time point.
Therefore, in the symmetric LCC log-Demons any subject time point can be chosen to perform the pairwise registrations without needing a subject-specific template. Moreover, the annualized log-Jacobian map is valid for all time points even if its value for a material point changes with time along its trajectory. Finally, even if each registration is fundamentally pairwise, the effect of the multiple time points is taken care of using the fully symmetric linear model in time described in Section 2. This model uses all the possible combinations of SVFs in order to avoid favoring any specific time point.
Notice that this approach is sub-optimal with unbalanced data where large variations exist in the number of time points N i between the subjects. This can be corrected using methods like the one described in Guillaume et al. However, in the study presented here, only 13 subjects out of had more than three time points. The majority had two or three time points which did not unbalance the data too much.
At first sight, LDDMM might appear as a better theoretical model for an elastic mechanical deformation since it is based on the conservation of the Hamiltonian. However, it is not completely clear that the longitudinal evolution of a brain intra-subject is an elastic deformation that conserves the energy. Moreover, in practice Lorenzi and Pennec showed that for the longitudinal registration the differences between the two methods are very subtle and the stationary velocity field framework can be used. MH has worked on the design, implementation, and experimental study of the pipeline.
ML, NA, and XP have co-supervised him in the design and revision of the work, and they gave their final approval of the version to be published. The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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