Residual Simplified Reference Tissue Model

Objectives: Parametric PET image estimates voxel-based physiological kinetic parameters, which can potentially achieve superior performance compared with a traditional standard uptake value (SUV). Due to the total dose limitation, the reconstructed image of each frame using a conventional ordered subset expectation maximization (OSEM) method is very noisy, which severely degrades the performance of parametric image. To achieve reliable parametric imaging, the most widely used method is the low-pass filtering of temporal images prior to kinetic parameter estimation, which sacrifices the resolution of image significantly. To address this issue, we propose a break-through method, so called the residual simplified reference tissue model (R-SRTM) with new derivations based on residual dynamic data. More specifically, the residual dynamic data denotes the full data excluding each time frame data, so that we can utilize the almost full data for all frames in the R-SRTM. We compare the performance of the proposed method with the conventional SRTM method.

Methods: A new derivation of R-SRTM using residual dynamic data starts with this relationship: F_T=C_T(t)+ C[asterisk]_T(t) , F_R=C_R(t)+C[asterisk]_R(t) ,where F_T and F_R denotes total areas (intensity× duration) of time activity curves (TACs) of target and reference (cerebellum) regions, respectively. C_T(t) is the frame data and C[asterisk]_T(t) is the residual frame data of target region. C[asterisk]_T(t) and C[asterisk]_R(t) are reconstructed by OSEM using residual data. Now, we can directly calculate the derivatives: dC_T(t)/dt= -dC[asterisk]_T(t)/dt and dC_R(t)/dt= -dC[asterisk]_R(t)/dt. Using this residual terms, the R-SRTM solves the following equation: -dC[asterisk]_T(t)/dt= -R dC[asterisk]_R(t)/dt+k₂(F_R-C[asterisk]_R(t))-k_2a(F_T-C[asterisk]_T(t)), where R is the ratio parameter and k_2a= k₂/(1+B). B is the binding potential value. To evaluate the proposed method, a digital brain phantom was used with 6 regional TACs in figure 1(a). The simulation geometry was the same as the HRRT scanner (Siemens). We extracted the reference region TACs of C_R(t) and C[asterisk]_R(t) as shown in figure 1(b). C_R(t) is used for the conventional SRTM and C[asterisk]_R(t) is used for R-SRTM.

Results: We compared binding potential images using the conventional SRTM with dynamic images reconstructed by OSEM frame-by-frame and the proposed method with residual dynamic images by OSEM. In comparison of binding potential (BP) images in figure 1(c), the quality of BP image using the proposed method was significantly improved and outperforms the conventional SRTM. In the BP image of the conventional SRTM method, we could not identify details of features. In the proposed method, we observed the cortex structures continuously connected in the BP images. For the quantification, the normalized root mean square errors (NRMSEs) of SRTM and R-SRTM were 31% and 15%. Furthermore, the image quality of the proposed method using the residual dynamic data was very similar to the image quality of OSEM using full data, which demonstrated the robustness of estimating the parametric images in low dose scan.

Conclusions: The parametric PET imaging using the residual simplified reference tissue model outperforms the conventional SRTM method. We demonstrated that the R-SRTM can provide superior results without using smoothing or penalty functions. Therefore, the R-SRTM will be very useful in clinics by fully utilizing the counts of data. In the near future, we will thoroughly validate the proposed method using clinical data.

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