One registration multi-atlas-based pseudo-CT generation for attenuation correction in PET/MRI

Abstract

Purpose

The outcome of a detailed assessment of various strategies for atlas-based whole-body bone segmentation from magnetic resonance imaging (MRI) was exploited to select the optimal parameters and setting, with the aim of proposing a novel one-registration multi-atlas (ORMA) pseudo-CT generation approach.

Methods

The proposed approach consists of only one online registration between the target and reference images, regardless of the number of atlas images (N), while for the remaining atlas images, the pre-computed transformation matrices to the reference image are used to align them to the target image. The performance characteristics of the proposed method were evaluated and compared with conventional atlas-based attenuation map generation strategies (direct registration of the entire atlas images followed by voxel-wise weighting (VWW) and arithmetic averaging atlas fusion). To this end, four different positron emission tomography (PET) attenuation maps were generated via arithmetic averaging and VWW scheme using both direct registration and ORMA approaches as well as the 3-class attenuation map obtained from the Philips Ingenuity TF PET/MRI scanner commonly used in the clinical setting. The evaluation was performed based on the accuracy of extracted whole-body bones by the different attenuation maps and by quantitative analysis of resulting PET images compared to CT-based attenuation-corrected PET images serving as reference.

Results

The comparison of validation metrics regarding the accuracy of extracted bone using the different techniques demonstrated the superiority of the VWW atlas fusion algorithm achieving a Dice similarity measure of 0.82 ± 0.04 compared to arithmetic averaging atlas fusion (0.60 ± 0.02), which uses conventional direct registration. Application of the ORMA approach modestly compromised the accuracy, yielding a Dice similarity measure of 0.76 ± 0.05 for ORMA-VWW and 0.55 ± 0.03 for ORMA-averaging. The results of quantitative PET analysis followed the same trend with less significant differences in terms of SUV bias, whereas massive improvements were observed compared to PET images corrected for attenuation using the 3-class attenuation map. The maximum absolute bias achieved by VWW and VWW-ORMA methods was 06.4 ± 5.5 in the lung and 07.9 ± 4.8 in the bone, respectively.

Conclusions

The proposed algorithm is capable of generating decent attenuation maps. The quantitative analysis revealed a good correlation between PET images corrected for attenuation using the proposed pseudo-CT generation approach and the corresponding CT images. The computational time is reduced by a factor of 1/N at the expense of a modest decrease in quantitative accuracy, thus allowing us to achieve a reasonable compromise between computing time and quantitative performance.

Appendix

The geometric distances obtained from pair-wise registrations are used to form an N × N distance matrix (D) (whose elements d _ij stand for geometric distances between objects i and j) to be processed by multidimensional scaling (MDS). The purpose of the MDS technique is to provide relative spatial locations from a set of pair-wise distances [41]. Since the distance used in MDS does not necessarily need to be metric or based on a system of standard measurements (any set of arbitrary values can be used), the geometric distances calculated from pair-wise registration are valid for use by the MDS procedure. MDS produces a number of coordinates in a user-defined dimension based on the Eigen structure of the distance matrix. Here, we transformed the distance matrix into two most meaningful coordinates computed by MDS where the closest subject to the origin represents the reference image, which is the closest to the mean geometry of the population of subjects using the following procedure:

• 1. The matrix B is computed considering $B=-\frac{1}{2}J{D}^2J\kern0.5em \mathrm{using}\kern0.4em \mathrm{the}\kern0.1em \mathrm{matrix}=I-{N}^{-1}{11}^{\prime }$, where N is the number of subjects, I is the identity matrix and 11′ denotes a square matrix of ones.

• 2. The two largest Eigenvalues λ ₁ and λ ₂ of B and the corresponding two Eigenvectors are extracted,

• 3. A 2-dimensional spatial configuration of the N subjects is derived from the coordinate matrix $X={E}_2\ {\complement}_2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$, where E ₂ is the matrix of 2 Eigenvectors and C ₂ is the diagonal matrix of 2 Eigenvalues of B, respectively.

• 4. The subject residing at the minimum distance to the origin in the new coordinate space is defined as the reference image (Fig. 2).