The tumor is segmented differently (panels a–c) and the registration results (panels d–f) are similar, indicating the registration algorithm is robust to the tumor delineation. Compared to the tumor in the target image (panel g), the tumor in the deformed image is preserved successfully. Moreover, without the constraint, the tumor is substantially compressed (panel h).
The flow chart of the validation procedure, which includes data acquisition, simulation, transformation, and comparison. The tumor in the pretreatment image is contracted to generate the simulated image in the simulation step. The RPM algorithm is then applied to coregister and the true post-treatment image. This step produces the simulated post-treatment image with known deformation, allowing comparison of the original and modified ABAs on a voxel-by-voxel basis.
The contracted area is filled using texture from nearby healthy appearing tissue in a postcontrast, fat-suppressed THRIVE image. For each voxel in the contracted area, the closest point on the tumor contour is detected and used to find the voxel in the healthy tissue. The voxel is then filled using the intensity of .
The original pretreatment, postcontrast, fat-suppressed THRIVE images from four different patients (upper row), the simulated image with tumor contracted by different percentages (middle row), and the close-up views of the tumor regions (lower row). Note that even when the tumor is fully contracted (first column), the simulated image still appears realistic.
(a) The original postcontrast, fat-suppressed THRIVE breast image, (b) the corresponding simulated image with tumors shrunk by , (c) the simulated post-treatment image after the breast deformation is simulated using the robust point matching algorithm, and (d) the true post-treatment image.
The histogram of errors of ABA with and without constraint when the tumors are contracted by 95% for six patients. Note that the constrained ABA leads to more compact error distributions, with considerably smaller maximum errors.
One central slice of tumor contracted by 95% with the color-coded errors (voxel shifts in mm) superimposed on a postcontrast, fat-suppressed THRIVE. In this slice, the original ABA leads to errors up to 7.01 mm, while the ABA with constraint results in errors only up to 2.71 mm.
The original source image (left panel), the image after the rigid body registration (middle panel), and the image after both the rigid and nonrigid registration (right panel), respectively. The green contour is segmented from the target image (not shown) and copied onto the following images for comparison.
Three axial, postcontrast, fat-suppressed THRIVE slices at three different time points after rigid body registration (column 1), after nonrigid registration without the constraint (column 2), and with the constraint (column 3). In the fourth row, the zoom-in deformation field without and with the constraint at (the first and second panels) and (the third and fourth panels) are shown, respectively. It is clear that the rigid registration can only provide an approximate registration result, and the original ABA compresses the tumor significantly, although the normal tissues are registered accurately. The modified ABA can perform well on both normal tissues and the tumor.
The mean errors (mm) and standard deviations of ABA with and without constraint over the tumor area when the tumors are contracted by different percentages for six patients. Note that the mean voxel shift errors were calculated through averaging over all voxels of the tumor area from all patients instead of directly averaging the mean shift error of each patient. The nonparametric Wilcoxon signed rank test is applied to each simulated case.
The tumor volume changes using ABA with and without constraint when the tumors are contracted by different percentages for six patients. Note that tumor is compressed notably using the unconstrained ABA compared to the constrained ABA.
The tumor volume changes, the constraint values, and the bending energy are calculated for the experimental data, after the registration using ABA with and without constraint, respectively. The nonparametric Wilcoxon signed rank test is applied to all data and the values are listed. The results of all the three validation approaches show that the ABA with constraint leads to significantly smaller tumor volume changes, constraint values, and bending energies, indicating the efficiency of the constraint term.
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