| By labeling biological molecules, for example, nucleic acid, receptors, enzymes and so on, with radionuclide as the tracer, positron emission tomography (PET) can provides functional information of physiological activity by displaying the concentration distribution of radioisotope labeled tracer, which has shown its great promise in the clinical early diagnosis of diseases, such as cancer, heart disease, neurological and psychiatric disease, and also new drug development. And PET has been one of the outstanding representatives of the current function molecular imaging technology. In the dynamic PET imaging mode, by applying kinetic models, the function parameters of the human tissue, such as local blood flow, material transport rate, metabolic rate, receptor binding rate and so on, can be obtained, and thus directly reflect the metabolism and function state of human body quantitatively at the molecular level.In fact, compared with the tracer activity distribution of the tissues provided by static PET imaging, function parameters provided by quantitative dynamic PET imaging through the kinetic model have more sense for clinical diagnosis. For example, in the diagnosis of lung cancer, the static PET imaging is often suffers from the false-positive and inaccurate staging, especially in the FDG-PET examination, the inflammatory region with high metabolism is often diagnosed as the tumor by mistaken. But the dynamic PET imaging through providing the quantitative functional parameters has been confirmed to effectively reduce the false-positive diagnosis. According to the report in New England Journal of Medicine, in the early diagnosis of major brain diseases such as Alzheimer’s disease, referred to as AD, dynamic brain PET scan played an important role in the diagnosis of AD disease prediction, evaluation, drug treatment and other aspects.However, in order to accurately estimate the function parameters, the dynamic PET scan need to obtain PET activity image distribution of continuous time points within a certain period of time. Therefore, with the dynamic PET scanning time sampling increases, the amount of measured data in the single time frame will decrease, and the reconstructed PET image will suffer more noise effect due to the limited photon counting, and thus directly affect the accuracy and reliability of kinetic parameter estimation. Therefore, to achieve high-quality dynamic PET image reconstruction and accurate kinetic parameter estimation is a major concern for the dynamic PET imaging.At present, the image reconstruction process in clinical routine for the dynamic PET imaging is as follow:first using the measured dynamic sequential projection data, which is called sinogram data, to reconstruct the activity images with analytical reconstruction methods or iterative reconstruction methods frame by frame, and then estimating the quantitative kinetic parameters from the reconstructed dynamic sequence activity images by applying the kinetic models. For one single time frame, the activity image reconstruction is same as the static PET image reconstruction. However, because of the short acquisition duration in single time frame, the measured photon counting rate is very low, the corresponding projection data has low signal-to-noise ratio, which makes the dynamic PET image reconstruction to be an ill-posed inverse problem in theory.For the activity image reconstruction of one single time frame, the the filtered backprojection (FBP) reconstruction algorithm is commonly used for analytical reconstruction as its fast imaging speed, which can satisfy the need fo clinical application, but the existence of large amount of noise in FBP image reconstruction will lead the image quality poor and bring great interference to the clinical diagnosis. Another commonly used reconstruction tactics is the iterative reconstruction. Currently, maximum likelihood expectation maximization (ML-EM) reconstruction algorithm and its improved versions are widely used in clinic. By mathematically modelling for the physical effect of PET imaging system and statistical characteristic of data noise, ML-EM reconstruction can achieve better image quality than traditional FBP reconstruction. However, ML-EM reconstruction algorithm has slow iterative convergence speed, and will cause degradation of the reconstructed image quality during the iterations with the emergence of checkerboard artifact effect, and the iteration is non convergent. In the light of these problems above, incorporating prior information under the Bayesian maximum a posteriori (MAP) framework becomes a research hotspot of PET imaging and even medical images reconstruction. The maximum a posteriori reconstruction algorithm by constructing a regularization term to introduce the prior information of spatial probability distribution of the to-be-reconstructed image can significantly improve the iterative reconstruction image quality and guarantee the convergence of the iterative reconstruction algorithm. In the PET imaging study, the MAP reconstruction algorithm has been proved to be correct in theory and effective in practice. In addition to statistical iterative reconstruction algorithms, according to the statistical characteristics of PET projection data or noise characteristics of activity image, methods based on projection data recovery or image postprocessing also have been proposed to improve PET activity image quality and its signal-to-noise ratio (SNR).The activity image reconstruction of single time frame is difficult to consider the kinetic temporal information within dynamic PET image sequences. Thus, how to explore and use the kinetic temporal information within dynamic PET data has become a hot issue in the recent PET research. As the dynamic PET sequence activity images showing the radioactive tracer activity distribution changes with time within the human tissues, the corresponding sectional anatomy is of the same, and there are lots of redundant information between dynamic sequence images, thus we can use the data redundancy properties for designing corresponding data recovery model or image filter. In addition, because the physiological metabolic processes of radioactive tracer in the same tissue is same or similar in dynamic PET imaging, the pixel-wise time activity curves within the same tissue region have same or similar change tendency, so the pixel-wise time activity curve can be treated as the kinetic feature of corresponding tissue, to design the corresponding filter or prior model. In this thesis, to reconstruct high-quality dynamic PET image, studies have done based on image filtering and statistical iterative reconstruction, respectively.To estimate kinetic parameters in dynamic PET imaging, two commonly used methods are the nonlinear least square method and the Patlak graphical method. In addition, there is a generalized linear least square method, the output function convolution method, the Logan graphical method and so on. The nonlinear least square method establishes the nonlinear relation between kinetic parameters and pixel-wise time activity curve based on the kinetic compartmental model, and solves the values of kinetic parameters from the input pixel-wise or regional time activity curve that extracted from dynamic PET sequence activity images. Patlak graphical method first proposed by Patlak et al. in 1983, mainly used in FDG-PET research, which requires that the FDG phosphorylation to FDG-6-PO4 is irreversible, i.e. k4=0. In practice, when the FDG-6-PO4 concentration is not too high, K4 can be ignored, which meets requirements for the Patlak method. According to Patlak’s theory, when the system reaches the equilibrium state (t>tO, tO is the time to equilibration), the input function and the output function of compartment model satisfies a linear expression, and the glucose metabolic rate can be obtained through calculating the slope of linear function. Pixel-wise parameter estimation forms kinetic parametric images of dynamic PET sequence activity images.The nonlinear least square method and the Patlak graphical method are both derived based on the kinetic compartmental model. Patlak graphical method has fast calculation speed because of its linearity property, but its two assumptions that physiological metabolism process is irreversible and the equilibrium state should be reached limit to its application, and compared with the nonlinear least square method, the result from Patlak graphical method has certain bias, and has less reliability. In this thesis, kinetics parameter estimation is studied based on the nonlinear least squares method.The accuracy of kinetic parameter estimation is closely related to the SNR of the extracted time activity curve. In order to improve the accuracy of kinetic parameter estimation, a direct way is to improve the SNR of time activity curve, which means to improve the SNR of dynamic sequence activity images, and this can be achieved by using maximum a posteriori iterative reconstruction or image denoising. In addition to improve the SNR of time activity curve, researchers have also proposed to introduce the regularization term during parameter estimation, to smooth the estimated parameters in image space, which is also called smoothing constraint. For example, Zhou et al. used spatially smoothed parametric images to reduce spatial variationsin the images; Kamasak investigated the effects of spatial regularization on the kinetic parameter domain, and figured out that it may lead a large difference in kinetic parameter value with its surrounding regions if the region ofinterest is small in size. Therefore, to design an adaptive smoothing regularization for kinetic parameter estimation, which can remove the noise while still well maintain the image edge structure, is the third work in this thesis.In summary, influenced by physical factors of dynamic PET scan, the photon count rate in single timeframe is low, which leads more noise in the dynamic sequence activity images, and thus reduces the accuracy of kinetic parameter estimation, According to the kinetic characteristics of the dynamic PET data, in this thesis, our studies are conducted respectively in three aspects:the filter design for image post-processing, prior modeling for maximum a posteriori reconstruction and adaptive smoothing regularization for kinetic parameter estimation, and achieved good experimental results, effectively improved the reconstruction quality of dynamic PET sequence activity images and also the accuracy and reliability of the kinetic parameter estimation, which provides an exploratory technique reference for high-quality imaging of dynamic PET. To sum up, the main work of this thesis is divided into the following three parts:1) Based on the characteristics of dynamic PET imaging:(1) dynamic sequence images have the same anatomical location for the radioactive tracer activity distribution imaging, and the anatomical location in the image space for all the time frame is fixed, and thus dynamic sequence images have the same spatial distribution characteristics; (2) In dynamic PET imaging the physiological metabolism process in same tissue is the same or similar, namely the kinetic characteristics of the same tissue region is the same, which indicates that the pixel-wise time activity curves within the same tissue region have consistent kinetic parameters, curve shape and change trend; in this work we design a kinetics-induced bilateral filter. The new filtering method is based on the traditional bilateral filtering method, through combining the similarity of the time activity curve and spatial neighborhood between pixels together, constructs an new the filter weights. The new filtering method using time activity curve as the embodiment of the kinetic characteristics of dynamic PET, eliminates the introduction of kinetic compartmental model, and makes the new method more simple and easy to realize. The results of computer simulation and preclinical small animal experiment show that the new filtering method can improve the SNR of dynamic PET sequence activity images, and further improve the accuracy and reliability of the estimation of kinetic parameters, provides strong support for clinical imaging diagnosis and new drug development.2) To introduce reasonable prior information of dynamic PET image sequence under MAP iterative reconstruction framework, and break through the constraint that traditional PET reconstruction prior information depends on the target image spatial neighborhood information, in this work we use spatial and time information within the dynamic image sequence to construct a new spatio-temporal edge preserving prior model based on the characteristics of dynamic PET imaging. The new prior model through incorporating the spatial constraint from the local neighborhood location relationship and the temporal constraint from the time activity curves similarity, combines the information among dynamic sequence images and that of each single frame together, provides a more reasonable and effective regularization for dynamic PET sequence activity image reconstruction. The experimental results of computer simulation with the digital phantom data show that the new method can obtain higher SNR of the reconstructed image and lead more accurate estimation of kinetic parameters, compared with the traditional dynamic PET reconstruction methods.3) In order to reduce the noise interference of dynamic PET activity image sequence to kinetic parameter estimations, in this work we introduce an adaptive smoothing prior constraint on the parametric image domain into the nonlinear least square estimation, and propose a new kinetic parameter estimation method with an adaptive smoothing regularization. The prior model is also based on the characteristic of dynamic PET imaging that the same tissue region has the same kinetic parameters and the parametric images have consistency in spatial distribution, and treats the set of kinetic parameters as one dimension parameter vector to use both the kinetic similarity and the spatial neighborhood between pixels. The new prior model has a smoothing effect for the parameter values within same tissue region, while keeps well the edge information with its surrounding regions, and can be regard as an adaptive smoothing term. The introduction of adaptive smoothing term constrains nonlinear least squares iterative solution and can improve the robustness of parameter estimation. The experimental results of computer simulation with the digital phantom data show that the new kinetic parameter estimation method has more accuracy and higher SNR of parametric images, in comparison with the traditional kinetic parameter estimation method. |
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