An image registration framework was developed to perform 3D, affine, intensity-based co registration of multiparametric MRI series using mutual information as the similarity metric. The proposed methods include corrections to compensate for the effects of an endorectal coil, which is commonly used in prostate MRI. Experiments to characterize the registration method demonstrate that it is theoretically accurate to within 1.0 mm (when estimating the translation component). Qualitatively, significant improvements are seen in the co-localization of parametric maps with the anatomic images. The proposed framework may readily be integrated into a CAD system for prostate cancer detection.
Multiparametric MRI data were acquired following previously described protocols.1 Briefly, 34 patients with known PCa received mpMRI scans at 3T. A combination of a surface array coil and an endorectal coil (ERC) was used for signal reception. Imaging sequence parameters are shown in Table 1.
The proposed registration framework seeks to independently register to the anatomic T2w images (target volumes) each of the other imaging series (source volumes), and involves three major steps.
Step 1: A rectangular VOI was defined for each patient that specifies the subvolume on which registration parameters will be optimized. VOI dimensions were chosen to match the prostate extent, which was determined via annotation of the prostate capsule by a experienced radiologist. The VOI was defined on target volumes, then propagated to source volumes.
Step 2: The signal intensity inhomogeneity caused by the ERC sensitivity profile was corrected for. This step was necessary because intensity-based registration would otherwise be biased toward matching coil sensitivity profiles. To perform the correction, the ERC was modeled as two wires, and the Biot-Savart law was used to calculate the differential contribution of a wire segment to the magnetic field in the xy-plane:
$$d\vec{B}=\frac{I\,d\vec{l}\times\vec{R}}{4\pi\left|\vec{R}\right|^3}$$
where $$$I\,d\vec{l}$$$ is the differential element and $$$\vec{R}$$$ is the vector pointing from the element to the voxel of interest. All contributions were then summed to obtain the estimated sensitivity profile. After normalization, the sensitivity profile was registered to each of the imaging series using minimum variation as the similarity metric. Briefly, maximizing minimum variation decreased the dispersion of $$$\log\left(I_{c,i}/I_{s,i}\right)$$$ over the defined VOI, where $$$I_{c,i}$$$ and $$$I_{s,i}$$$ are intensity values of the sensitivity profile and the imaging series, respectively, at voxel $$$i$$$. Lastly, the imaging data were divided by the aligned sensitivity profile (Fig. 1).
Step 3: After intensity correction, each of the source volumes was registered to the target using mutual information as the similarity metric. Multiple echo time TSE series were registered directly. For DWI data, registration was only performed for the b0 image; the transformation was assumed to be identical for the ADC map. For DCE data, registration was only performed for the 2nd time point, assuming (for now) the transformation is identical for other time points and pharmacokinetic maps. Additionally, due to a chemical shift artifact at the prostate-ERC boundary in the DCE data that would otherwise confound intensity-based registration, the translation component along the AP axis was found by calculating the difference between the AP positions of the ERC in the center slice of target and source volumes, which in turn was determined using locally-adaptive thresholding (Fig. 2).
To find the optimal affine transformation in the described registration tasks, a two-step approach was employed to address the non-convexity of the problem. First, a genetic algorithm, using fitness-proportionate selection with a small mutation operator, was used to find candidates for the best mapping. An iterative grid search was then used to sweep for potential local maxima near each candidate.
To validate the proposed methods, random affine transformations $$$T$$$ were applied to select source volumes that were deemed to be aligned (without registration) with the corresponding target volumes. The transformations $$$\hat{T}$$$ that would bring transformed source volumes back into alignment were estimated, and distances between $$$T^{-1}$$$ and $$$\hat{T}$$$ (ideally 0) were quantified using the Frobenius norm (Table 2).
To visually assess registration quality, cases that had obvious misalignment were identified. For each case, ROIs were identified and manually outlined on the target volume, then propagated to the source volumes before and after registration. Figure 3 shows these results plus registered parametric maps for a representative case.
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