Abstract
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Introduction: Dynamic Positron Emission Tomography (PET) with 18F-FDG is widely used to evaluate neurological disease. The irreversible 2 Tissue Compartmental Model (2TCM) originally developed by Sokoloff et al. is used to extract kinetic parameters (influx rate: K1, ml.g-1.min-1; rate constants: k2,k3, min-1; blood fraction: Vb ) from dynamic FDG-PET data (Equations 1 and 2). The model requires an Arterial Input Function (AIF) obtained via invasive arterial blood sampling which is challenging to use clinically. Here, a non-invasive method of estimating the AIF is proposed. We consider the combination of Machine Learning (ML) along with an iterative approach for AIF estimation using multiple Time Activity Curves (TACs) from one subject.
Methods: Ten thousand synthetic TACs were generated based on the 2TCM with a total sampling time of 60 min, including 4×30s, 8×60s, 10×120s and 6×300s frames. The formulation of the input function introduced by Feng et al. was used in this study (Equation 5). Gaussian random noise was added to each noise-free TAC refer to Equation 3. Three noise levels were considered (c = 0.1, 1.0, 2.8). Gaussian Process Regression (GPR) was employed to build the ML kinetic modelling framework. Individual TACs were used as feature vectors, and corresponding kinetic parameters, K1, k2, k3 and Vb were the labelled data. The GPR was trained using the 10,000 noisy synthetic TACs. For testing, two individual subjects including ninety TACs were simulated using two fixed input functions. Each AIF was estimated iteratively as follows. Each of the 90 TACs was fed into the trained GPR network, leading to an initial estimate of the kinetic parameters (K'1, k'2, k'3 and V'b). Ninety tissue impulse responses, Gj(t) where j is TAC number, were generated using the estimated kinetic parameters, refer to Equation 4. Two specific steps were required to extract the AIF. First, the Feng function AIF parameters, A'1, A'2, A'3, λ'1, λ'2, λ'3 were estimated by minimising loss function 1 stated in Equation 6. Second, kinetic parameters were recalculated (K''1, k''2, k''3 and V''b) using the estimated AIF and by minimising loss function 2 stated in Equation 7. Then the recalculated kinetic parameters were employed to refine the estimated AIF parameters in the first loss function. Figure 1 represents the flowchart of ML and iterative approach. The optimisation was performed using the Levenberg-Marquardt algorithm in MATLAB®. This process was repeated resulting in iterative refinement of kinetic parameters until each value had a change less than 0.1% for the iteration.
Results: Figure 2 provides the comparison between extracted and real AIF shapes and, the Mean Squared Error (MSE) is stated as a measure of accuracy. It also shows the mean and standard deviation of Feng function parameters based on two separate experiments considering 90 TACs each. It took six and five iterations to generate the first and second AIFs, respectively. The results show that an excellent agreement between the extracted AIF and the real AIF was obtained in both cases.
Conclusions: Our goal was to extract the AIF from multiple pixel location time activity curves. Our findings show that the AIF can be extracted accurately using the outlined ML approach through iterative updates of the AIF parameters. Future work should investigate how the number of time activity curves and anatomical regions considered in AIF estimation impact accuracy. Acknowledgments: This research was conducted at the Australian Research Council Training Centre for Innovation in Biomedical Imaging Technology (IC170100035) and funded by the Australian Government. The authors also acknowledge the facilities and scientific and technical assistance of the National Imaging Facility, a National Collaborative Research Infrastructure Strategy (NCRIS) capacity, at the Centre for Advance Imaging, the University of Queensland.
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