Abstract
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Introduction: Positron emission tomography (PET) is a powerful imaging technique that can quantify and detect the metabolic processes of radiopharmaceuticals injected into a patient. Unlike static scans performed at a certain time point, dynamic PET scans can maximise the potential of the PET data, i.e. fully use temporal information of the PET data. For dynamic PET, the temporal information is expressed by the time-activity curve (TAC), which represents the time course of the tracer's radioactivity concentration. Generally, we use a mathematical model, e.g. compartmental model, that contains different parameters to fit the TAC. The estimations of the parameters inside the mathematical model usually reveal physiological or biochemical information about the human body's tissues. Traditionally, least-squared estimation (LSE) has been used to apply the fitting between the mathematical model and the observations of the PET data. However, since the LSE can neither make use of the neighbourhood information of each voxel nor make use of the property, e.g. the tissue type, of each voxel, the estimations of this method are usually inaccurate and biased especially when the signal-to-noise-ratio (SNR) is low. Therefore, in this work, we proposed a novel probabilistic graphical model (PGM) to improve the accuracy of the parameter estimations.
Methods: In this work, we have proposed a novel PGM to increase the estimation accuracy of kinetic parameters. The PGM is a statistical model that can reveal complex relationships between different parameters using a graphical model. Since this method is under a Bayesian statistical framework, the conditional posterior distribution of each parameter can be fully inferred. In this proposed work, we have further added two more dependencies to increase the accuracy of the estimation. Specifically, we have added spatial information using a Markov random field prior based on an assumption that adjacent voxels have similar physiological properties, i.e. similar values of parameters. We have further added a new parameter, label, to each voxel which represents the type of such voxel, e,g, lung, liver, myocardium, etc. The acquisition of the label is given by state-of-the-art deep learning segmentation methods such as DeepMedic, DeepSCAN and nnUNet. With the label information, we assumed the voxels with the same label follow a certain distribution, e.g. Gaussian distribution, Gamma distribution or Rician distribution. After adding these two dependencies to the PGM, the conditional posterior distributions can be inferred. We finally have used a Markov Chain Monte Carlo (MCMC) method to sample the kinetic parameters.
Results: The proposed PGM has been applied to a synthetic 2D chest image. It is noted that this method is not limited to 2D data. Theoretically, it can be applied to 3D data. The LSE has also been applied to the same set of data as the benchmark method. The proposed method does not limit the selection of the mathematical model that describes the TAC. In this work, we have applied a two-tissue compartmental model (2TCM) as the mathematical model. Five parameters, i.e., K1, k2, k3, k4 and Vb, are estimated by the proposed PGM and LSE. We have used Mean Square Errors (MSE) as the comparison criterion between these two methods. Specifically, the MSE of K1, k2, k3, k4 and Vb generated by the proposed PGM are 0.00205, 0.03449, 0.00087, 0.00147 and 0.00003 respectively. The MSE of K1, k2, k3, k4 and Vb generated by the LSE are 0.00651, 0.16745, 0.00242, 0.00838 and 0.00088 respectively. The MSE generated by the proposed PGM is dramatically lower than the LSE method.
Conclusions: The proposed PGM method has much higher kinetic parameter estimation accuracy and spatial consistency than the traditional LSE method given synthetic 2D chest dynamic PET data.
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