Advancing Uncertainty Evaluation in Dynamic PET Imaging Through Residual Permutation and Clustering Techniques

Introduction: Quantitative PET imaging plays a vital role in disease management and treatment decision-making, which can potentially benefit from the evaluation of associated uncertainties. By simulating the measurements and the corresponding variability in dynamic PET images, uncertainty assessment typically employs the bootstrap technique combined with joint iterative estimation of multiple parameters. However, these approaches require significant computation costs and are highly sensitive to parameter initialization. In this work, we proposed a residual permutation (RP) method coupled with a clustering-based approach to evaluate the uncertainty in PET imaging, enhancing computational efficiency and robustness against noisy data.

Methods: The uncertainty assessment process includes three steps. First, a clustering-based method identifies the time-activity curves (TACs) with similar shapes, thereby acquiring a basis to represent the mean TAC of the arbitrarily chosen cluster. Second, the individual TAC of PET imaging was fitted by scaling the basis. Considering that the noise in PET imaging typically does not follow a single probability distribution pattern, we employed β-divergence as the loss function to optimize the model. To further improve the robustness and generalizability, a regularization term was integrated to control model complexity and prevent overfitting. After model fitting, a cluster-based RP was introduced to deal with the residual. This method aims to generate multiple sets of kinetic parameter estimates, systematically quantifying and assessing the uncertainty of kinetic parameters. Our method was validated using simulated and clinically acquired data. The image-based bootstrap method as a reference is also provided. The estimates of kinetic parameters V_b and K_i were derived from a 1 h [18F]FDG dynamic scan with a 66-frame scheme (30×2 s, 12×10 s, 6×30 s, 12×120 s, and 6×300 s). Particularly, the simulated data was generated using a noise model, which employs a time-varying Gaussian distribution and incorporates the principles of radioactive decay. We generated 20 samples for each of the three different noise levels (S_c=0.02, 0.1, and 0.3) and calculated the standard deviation (STD) of the estimated parameters based on them.

Results: The uncertainty assessment of parameters V_b and K_i was evaluated. In the simulation study, the boxplot illustrated that the proposed RP yielded kinetic parameter estimates with less dispersion and more consistent distribution properties. The STD of V_b and K_i under different noise levels estimated by RP and the bootstrap method was compared. RP showed a lower STD than bootstrap for both parameters in all noise levels. In terms of K_i distribution, RP reduced STD by 76.3% compared with bootstrap at the highest noise level (S_c=0.3). For real patient data, the parametric image of K_i was generated using fitted data obtained through RP. The histograms indicate the 75th percentile distribution of K_i within normal tissue and tumor regions of interest (ROIs).

Conclusions: This study demonstrates the feasibility of RP in assessing the uncertainty of quantitative PET data. Compared with the reference method, RP excels in terms of reliability and noise resistance.

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