Dynamic double-tracing PET self-supervision separation method based on physical information neural network

Abstract

The invention discloses a dynamic double-tracing PET (positron emission tomography) self-supervision separation method based on a physical information neural network, which creatively combines a tracer kinetic model and a deep learning technology, and gives full play to the advantages of the tracer kinetic model and the deep learning technology. By embedding an ordinary differential equation (ODEs) for describing a tracer kinetic process into a neural network and adopting a self-supervised training strategy, network parameters and kinetic parameters can be updated at the same time under the condition that a large-scale clinical data set is not needed, and accurate separation of double-tracer PET images is achieved. According to the method, the dependency on a large-scale clinical PET data set is greatly reduced, so that the problem of acquiring and processing a large amount of high-quality clinical data is solved, and the problem of complexity caused by data registration difference is also avoided. According to the method, a more accurate separation result can be provided for clinical diagnosis, and doctors and technicians are helped to better understand the complex physiological process in the body, so that a more accurate diagnosis decision is made.

Description

Technical Field

[0001] The invention belongs to the technical field of PET imaging, and in particular relates to a dynamic double-tracer PET self-supervised separation method based on physical information neural network. Background Art

[0002] Positron emission tomography (PET) uses radioactive tracers to monitor key parameters such as glucose metabolism, hemodynamics, and hypoxia, and has become an important diagnostic tool for tumors and neurological diseases. PET uses a radioactive isotope-labeled tracer that enters the human body and accumulates in areas requiring higher energy. As the radioisotope decays, the positron and electron released annihilate, generating a pair of 511 keV gamma photons. These photons are captured by an external detector and processed to reconstruct an image, aiding physicians in pathological diagnosis. However, single-tracer PET can only reflect a specific aspect of physiological function and may not be sufficient for a comprehensive assessment of complex diseases. It is typically used as an auxiliary diagnostic tool. In contrast, dual-tracer PET, by combining two tracers, provides richer information, facilitating more accurate diagnosis, treatment planning, and prognosis assessment, demonstrating significant advantages particularly in tumors and neurological diseases. Therefore, the development of dual-tracer and even multi-tracer PET imaging technologies holds significant clinical significance and broad application prospects.

[0003] However, to save patient scan time and costs, processing dual-tracer PET signals within a single scan becomes a critical technology that urgently needs to be addressed. Because the signals from the different radionuclides all have an energy of 511 keV, signal separation within the signal acquisition device is difficult. This makes it impossible to simultaneously capture the spatiotemporal distribution of the two tracers and monitor vital activity.

[0004] At present, the dual-tracer PET separation methods can be mainly divided into: (1) model-based methods, which mainly rely on the kinetic model that describes the metabolism of the tracer in the body. Common practices include methods based on different half-lives of nuclides [1] and methods based on parallel dual-compartment models for kinetic parameter estimation [2]. However, this method has many problems, such as the need for a long injection interval and poor reconstruction accuracy; (2) dual-tracer separation methods based on prompt γ photons. This method utilizes the characteristic that one of the radioactive isotopes of the tracer can release an additional γ photon when it decays. Based on this characteristic, the signal separation of the dual tracers can be achieved. However, this method has high requirements for tracers and detectors, so it is not widely used in clinical practice; (3) data-driven methods. This method mainly uses data-driven deep learning methods, such as 3D CNN framework [3], Multi-task CNN [4], etc. However, these methods require a large amount of data driving, and have problems such as difficulty in end-to-end training data registration and poor generalization. Therefore, it is very important to study a self-supervised learning framework that combines physical models with deep learning neural networks.

[0005] [1]Huang SC,Carson RE,Hoffman EJ,et al.An investigation of adouble-tracer technique for positron computerized tomography[J].Journal ofNuclear Medicine,1982,23(9):816-822.

[0006] [2]Koeppe RA, Raffel DM, Snyder SE, et al. Dual-[11C]tracer single-acquisition positron emission tomography studies[J]. Journal of Cerebral BloodFlow&Metabolism, 2001, 21(12):1480-1492.

[0007] [3] Xu J, Liu H. Deep-learning-based separation of a mixture of dual-tracer single-acquisition PET signals with equal half-lives: a simulationstudy[J]. IEEE Transactions on Radiation and Plasma Medical Sciences, 2019, 3(6): 649-659.

[0008] [4]Zeng F, Fang J, Muhashi A, et al. Direct reconstruction for simultaneous dual-tracer PET imaging based on multi-task learning[J]. EJNMMIresearch, 2023, 13(1):7. Summary of the Invention

[0009] In view of the above, the present invention provides a dynamic dual-tracer PET self-supervised separation method based on a physical information neural network. By combining a dual-compartment model with a neural network, the dynamic dual-tracer PET self-supervised separation is achieved; compared with other deep learning methods, it has stronger generalization ability and better physical interpretability.

[0010] The present invention is achieved through the following technical solutions:

[0011] The present invention discloses a dynamic dual-tracer PET self-supervised separation method based on physical information neural network, comprising the following steps:

[0012] 1) Perform a dynamic PET scan on the biological tissue injected with tracer I and tracer II at the same time to obtain a hybrid dual-tracer PET sinogram sequence Indicates the current frame number. Tracer I and tracer II are labeled with two radionuclides respectively;

[0013] 2) Using PET image reconstruction algorithm to calculate the hybrid dual-tracer PET sinogram sequence Corresponding hybrid dual-tracer PET image sequence

[0014] 3) Obtain the priori kinetic parameters of the two-compartment model corresponding to tracer I and tracer II respectively;

[0015] 4) Constructing a physical information neural network, while setting the two-compartment model kinetic parameters corresponding to tracer I and tracer II as network parameters a priori; inputting the dynamic scanning time t into the network, and the network output is the tracer concentration of tracer I and tracer II in different compartments;

[0016] 5) Calculate boundary condition constraints on the network output; calculate residual loss constraints for the dual-compartment model ordinary differential equation on the network output; combine the network output with the dual-compartment model to calculate the single-tracer PET image sequence corresponding to tracer I and tracer II, and calculate data term constraints on the mixed dual-tracer PET image sequence; integrate the above three constraints to form the loss function of the physical information neural network;

[0017] 6) Training the physical information neural network, updating the network parameters and dynamic parameters simultaneously according to the loss function until the model converges, and obtaining a trained physical information neural network;

[0018] 7) The dynamic scanning time t is input into the trained physical information neural network to obtain the final predicted tracer concentrations of tracer I and tracer II in different compartments, and a single tracer PET image sequence of tracer I and tracer II that conforms to the actual distribution is calculated through a two-compartment model.

[0019] As a further improvement, the PET image reconstruction algorithm in step 2) of the present invention adopts the Kernel EM algorithm.

[0020] As a further improvement, in step 3) of the present invention, for the dual-tracer dual-compartment model, the tracer concentration change in each compartment is represented by the following ordinary differential equation:

[0021]

[0022] in, C E1 (t), C M1 (t) and C P1 (t) represents the concentration change rate constant of tracer I, the concentration of free and nonspecifically bound tracer, the concentration of specifically bound tracer and the arterial blood input function concentration; similarly, C E2 (t), C M2 (t) and C P2 (t) corresponds to tracer II;

[0023] The arterial input function concentration calculation can be expressed as:

[0024]

[0025] in, and represents the eigenvalue of the arterial input function, and represents the coefficient of the arterial input function;

[0026] In addition, the vascular volume fraction V is added to the two-compartment model B , and thus the total tracer concentration in the tissue is calculated:

[0027] C T1 (t)=(1-V B1 )(C E1 (t)+C M1 (t)))+V B1 C P1 (t)

[0028] C T2 (t)=(1-V B2 )(C E2 (t)+C M2 (t))+V B2 C P2 (t);

[0029] Among them, C T1 (t) and C T2 (t) represents the total concentration of tracer I and tracer II in the tissue, V B1 With V B2 represent the vascular volume fractions of tracer I and tracer II, respectively.

[0030] As a further improvement, the priori kinetic parameters of the two-compartment model corresponding to tracer I and tracer II in step 3) of the present invention are:

[0031]

[0032] Here, ω1 corresponds to the prior kinetic parameters of tracer I, and ω2 corresponds to the prior kinetic parameters of tracer II.

[0033] As a further improvement, the physical information neural network in step 4) of the present invention is composed of two identical quadratic residual networks. Time t is input into two parallel networks, and the networks output different compartment tracer concentrations of tracer I and tracer II, expressed as (C E1 (t;θ′1,ω′1),C M1 (t;θ′1,ω′1),C P1 (t;θ′1,ω′1)) and (C E2 (t;θ′2,ω′2),C M2 (t;θ′2,ω′2),C P2(t; θ′2, ω′2)), corresponding to the free and nonspecific binding tracer concentrations, specific binding tracer concentrations, and arterial input function concentrations of tracer I and tracer II, respectively; each quadratic residual network contains 6 hidden layers, each with 1024 neurons, and each hidden layer is followed by a tanh activation function. The model uses a fifth-order Runge-Kutta to improve calculation accuracy; in addition, the total tracer concentration C in the tissue corresponding to tracer I and tracer II is calculated based on the double compartment model calculation formula and the network output T1 (t;θ′1,w′1) and C T2 (t; θ′2, w′2); where (θ′1, ω′1, θ′2, ω′2) represent the network parameters and dynamic parameters during training.

[0034] As a further improvement, the boundary condition loss constraint term in step 5) of the present invention is:

[0035]

[0036] Where i = 1 represents tracer I, i = 2 represents tracer II, N represents the number of image pixels, C represents the number of tracer I, and N represents the number of image pixels. Ei (0), C Ei (0;θ′ i ,ω′ i ) represent the true value of free and nonspecific binding tracer concentrations (0) and the model-predicted free and nonspecific binding tracer concentrations at t = 0, respectively; C Mi (0), C Mi (0;θ′ i ,ω′ i ) represent the true value of the specific binding tracer concentration (0) and the specific binding tracer concentration predicted by the model at t=0, respectively;

[0037] The residual loss constraint for the ordinary differential equation consists of the following three items:

[0038]

[0039] Among them, L Res Ei 、L Res Mi 、L Res Ti are the residual loss functions of the ordinary differential equations for the model-predicted free and nonspecifically bound tracer concentrations, specifically bound tracer concentrations, and total tracer concentrations in tissues, respectively. represents the kinetic parameters predicted by the model, C Ei (t;θ′ i ,ω′ i ) represents the free and nonspecifically bound tracer concentrations predicted by the model, C Mi (t;θ′ i ,ω′i ) represents the specific binding tracer concentration predicted by the model, C Ti (t;θ′ i ,ω′ i ) represents the total tracer concentration in the tissue predicted by the model, C Pi (t;ω′ i ) represents the arterial blood input function predicted by the model; therefore, the ordinary differential equation residual loss constraint is:

[0040]

[0041] Where T represents the total sampling time. i = 1 corresponds to tracer I, and i = 2 corresponds to tracer II;

[0042] Single tracer PET image sequence corresponding to tracer I and tracer II Single tracer PET image sequence and The total tracer concentration in the tissue is integrated by the PET instrument sampling protocol to obtain:

[0043] Among them, f represents the current time frame number, X f T1′ 、X f T2′ They represent the PET images of tracer I and tracer II in the current frame, respectively, f and t f-1 Represents the time of the current frame and the time of the previous frame respectively, C T1 (t; θ′1, ω′1) represents the total concentration of tracer I in the tissue predicted by the model, C T2 (t; θ′2, ω′2) represents the total concentration of tracer II in the tissue predicted by the model, and ρ1 and ρ2 represent the half-lives of the radionuclides in tracer I and tracer II, respectively. Therefore, the data term constraints are:

[0044] Where F represents the total number of scanned frames.

[0045] As a further improvement, the loss function of the entire network in step 5) of the present invention is:

[0046]

[0047] Among them, λ1 and λ2 are the proportional coefficients of the loss function, i = 1 corresponds to tracer I, and i = 2 corresponds to tracer II.

[0048] As a further improvement, the network parameters and dynamic parameters corresponding to the physical information neural network trained in step 6) of the present invention are marked as (θ1, ω1; θ2, ω2).

[0049] As a further improvement, the final predicted concentrations of tracer I and tracer II in different compartments in step 7) of the present invention are (C E1 (t;θ1,ω1),C M1 (t;θ1,ω1),C P1 (t; θ1, ω1)) and (C E2 (t;θ2,ω2),C M2 (t;θ2,ω2),C P2 (t; θ2, ω2)), the single tracer PET image sequence of tracer I and tracer II that conforms to the actual distribution is: and The PET image of the fth frame is represented as:

[0050]

[0051] Among them, V B1 With V B2 The vascular volume fraction corresponding to tracer I and tracer II, X f T1 With X f T2 They represent the f-th frame PET images of tracer I and tracer II respectively.

[0052] The beneficial effects of the present invention are as follows:

[0053] The present invention discloses a dynamic dual-tracer PET self-supervised separation method based on a physical information neural network. The method innovatively combines the tracer kinetic model with deep learning technology, giving full play to the advantages of both. By embedding ordinary differential equations (ODEs) describing the tracer kinetic process into the neural network and adopting a self-supervised training strategy, the present invention can simultaneously update the network parameters and kinetic parameters without the need for large-scale clinical data sets, thereby achieving accurate separation of dual-tracer PET images. The present invention adopts a self-supervised training strategy, which greatly reduces the dependence on large-scale clinical PET data sets. This not only solves the problem of acquiring and processing large amounts of high-quality clinical data, but also avoids the complexity problems caused by differences in data registration. Compared with the existing technology, this method significantly improves the generalization performance of the model, enabling it to adapt to different tracer combinations, biological tissue and organ types, and sampling protocols, and has broad application prospects. Whether it is for different types of tumors or complex neurological diseases, it can provide reliable results. In addition, the present invention introduces the residual loss of the dynamic ordinary differential equation as a constraint in the loss function. Compared with the problem that traditional methods are prone to falling into local optimal solutions when dealing with nonlinear models, the present invention cleverly uses the residual loss constraint instead of directly solving the nonlinear model, effectively avoiding such problems. At the same time, this approach not only ensures that the output results conform to basic physical principles and improves the accuracy and reliability of the prediction, but also enhances the model's ability to understand complex physiological processes, making the separation results more physically interpretable, which is particularly important in medical clinical diagnosis. The present invention can provide more accurate separation results for clinical diagnosis, helping doctors and technicians to better understand the complex physiological processes in the body, and thus make more accurate diagnostic decisions. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 Schematic diagram of the process of dual-tracer PET separation of the present invention;

[0055] Figure 2 This is the network structure diagram of dynamic dual-tracer PET self-supervised separation based on physical information neural network;

[0056] Figure 3 The following are the simulation experiment results of different phantoms and different tracer combinations;

[0057] Figure 4 It is the TAC curve diagram under different sampling protocols;

[0058] Figure 5 Single tracer PET concentration maps separated by the present invention and traditional supervised training methods (multi-task learning 3D convolution method) on simulated unregistered data. DETAILED DESCRIPTION

[0059] In order to describe the present invention more specifically, the technical solution of the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0060] A dynamic dual-tracer PET self-supervised separation method based on physical information neural network, Figure 1 The specific implementation flow chart of the present invention is shown, which includes the following steps:

[0061] (1) Data acquisition.

[0062] 1.1 Perform a dynamic PET scan on the biological tissue injected with tracer I and tracer II at the same time to obtain a hybrid dual-tracer PET sinogram sequence Indicates the current frame number, the tracer I and tracer II are labeled with two radionuclides respectively;

[0063] 1.2 Using PET image reconstruction algorithm to calculate the hybrid dual-tracer PET sinogram sequence Corresponding hybrid dual-tracer PET image sequence The PET image reconstruction algorithm uses the KernelEM algorithm.

[0064] (2) Obtain the priori kinetic parameters of the two-compartment model corresponding to tracer I and tracer II respectively.

[0065] For the two-compartment model with two tracers, the change in tracer concentration in each compartment can be expressed by the following ordinary differential equation:

[0066]

[0067] in, C E1 (t), G M1 (t) and G P1 (t) represents the concentration change rate constant of tracer I, the concentration of free and nonspecifically bound tracer, the concentration of specifically bound tracer and the arterial blood input function concentration; similarly, C E2 (t), C M2 (t) and C P2 (t) represents the concentration change rate constant of tracer II, the concentration of free and nonspecifically bound tracer, the concentration of specifically bound tracer, and the arterial input function concentration. The arterial input function concentration can be calculated as:

[0068]

[0069] in, and represents the eigenvalue of the arterial input function, and represents the coefficient of the arterial input function; in addition, the vascular volume fraction V is added to the two-compartment model B , and thus the total tracer concentration in the tissue is calculated:

[0070] C T1 (t)=(1-V B1 )(C E1 (t)+C M1 (t))++V B1 C P1 (t)

[0071] C T2 (t)=(1-V B2 )(C E2 (t)+C M2 (t))+V B2 C P2 (t);

[0072] Among them, C T1 (t) and C T2 (t) represents the total concentration of tracer I and tracer II in the tissue, V B1 With V B2 represent the vascular volume fractions of tracer I and tracer II, respectively;

[0073] Therefore, the two-compartment model kinetic parameters required for tracer I and tracer II are a priori:

[0074]

[0075] Among them, ω1 corresponds to the prior kinetic parameters of tracer I, and ω2 corresponds to the prior kinetic parameters of tracer II.

[0076] (3) Construct a physical information neural network framework.

[0077] like Figure 2 As shown in the figure, the physical information neural network consists of two independent parallel quadratic residual networks; the two quadratic residual networks have exactly the same structure, both containing 6 hidden layers, each with 1024 neurons, and each hidden layer is connected to an activation layer, and the activation function uses tanh; time t is used as the model input, and the two quadratic residual networks are input at the same time, and the kinetic parameters of tracer I and tracer II are set as network parameters a priori, and the fifth-order Runge-Kutta is used to improve the calculation accuracy; the two networks are represented by f1(θ′1, ω′1) and f2(θ′2, ω′2), respectively, where θ′1 and θ′2 represent the parameters of the two networks during training, respectively. They represent the kinetic parameters corresponding to tracer I and tracer II during training. The network output includes three items, corresponding to different compartment tracer concentrations. Specifically, the network f1(θ′1, ω′1) output corresponding to tracer I (C E1 (t;θ′1,ω′1),C M1 (t;θ′1,ω′1),C P1 (t; θ′1, ω′1)), respectively, represents the free and nonspecific binding tracer concentrations, the specific binding tracer concentration and the arterial input function concentration of tracer I; similarly, the output (C E2 (t; θ′2, ω′2), (t; θ′2, ω′2), C P2 (t; θ′2, ω′2)) represent the tracer concentrations in different compartments of tracer II (same as tracer I). In addition, according to the calculation formula of the two-compartment model, combined with the outputs of the networks f1(θ′1, ω′1) and f2(θ′2, ω′2), the total tracer concentration C in the tissues corresponding to tracer I and tracer II is calculated. T1 (t;θ′1,ω′1) and C T2 (t; θ′2, ω′2); During the model training process, the kinetic parameters and network parameters of the two tracers are updated simultaneously, thereby realizing the prediction of tracer concentrations in different compartments.

[0078] (4) Construct the loss function of the physical information neural network.

[0079] 4.1 Calculate the boundary condition constraints for the network output; calculate the loss function between the model prediction results and the true values ​​of the tracer concentrations in the two compartments of free and nonspecific binding ligands and specific binding ligands at time t = 0, and obtain the boundary condition loss constraint term as follows:

[0080]

[0081] Where i = 1 represents tracer I, i = 2 represents tracer II, N represents the number of image pixels, C represents the number of tracer I, and N represents the number of image pixels. Ei (0), C Ei (0;θ′ i ,ω′ i ) represent the actual free and nonspecific binding tracer concentrations and the free and nonspecific binding tracer concentrations predicted by the model at t = 0, respectively. Mi (0), C Mi (0;θ′ i ,ω′ i ) represent the actual specific binding tracer concentration and the specific binding tracer concentration predicted by the model at t = 0, respectively; in order to be consistent with the actual situation, C Ei (0) and CMi (0) are all set to 0;

[0082] 4.2 Calculate the residual loss constraint of the ordinary differential equation of the dual-compartment model for the network output; Subtract the left and right sides of the ordinary differential equation corresponding to the double-tracer dual-compartment model, that is,

[0083]

[0084] Among them, L ResEi 、L ResMi 、L ResTi are the residual loss functions of the ordinary differential equations for the model-predicted free and nonspecifically bound tracer concentrations, specifically bound tracer concentrations, and total tracer concentrations in tissues, respectively. represents the dynamic parameters during training, C Ei (t;θ′ i ,ω′ i ) represents the free and nonspecifically bound tracer concentrations predicted by the model during training, C Mi (t;θ′ i ,ω′ i ) represents the specific binding tracer concentration predicted by the model during training, C Ti (t;θ′ i ,ω′ i ) represents the total tracer concentration in the tissue predicted by the model during training, C Pi (t;ω′ i ) represents the arterial blood input function predicted by the model during training; therefore, the ODE residual loss constraint is:

[0085]

[0086] Where T represents the total sampling time; i = 1 corresponds to tracer I, and i = 2 corresponds to tracer II;

[0087] 4.3 According to the PET instrument sampling protocol, the total tracer concentration in the tissue predicted by the model is integrated to obtain the predicted dynamic PET image sequence of tracer I. Dynamic PET image sequence with tracer II The PET image of the fth frame can be expressed as:

[0088]

[0089] Among them, X f T1′ With T f T2′ They represent the PET images of tracer I and tracer II at the fth frame during model training, respectively, and t f and t f-1Represents the time of the current frame and the time of the previous frame respectively, C T1 (t; θ′1, ω′1) represents the total concentration of tracer I in the tissue predicted by the model during training, C T2 (t; θ′2, ω′2) represents the total concentration of tracer II in the tissue predicted by the model during training, and ρ1 and ρ2 represent the half-lives of the radionuclides in tracer I and tracer II, respectively; therefore, the dynamic single-tracer PET image sequence of tracer I and tracer II predicted by the model is added to the mixed dynamic dual-tracer PET image sequence obtained in step (1) Compute data item constraints:

[0090]

[0091] Where F represents the total number of scanned frames;

[0092] 4.4 Integrate the three constraints described in 4.1, 4.2, and 4.3 to form the loss function of the physical information neural network:

[0093]

[0094] Where λ1 and λ2 are the proportional coefficients of the loss function. For boundary condition constraints and ordinary differential equation residual loss constraints, i = 1 corresponds to tracer I and i = 2 corresponds to tracer II.

[0095] (5) Train the physical information neural network, minimize the loss function of the model, back-propagate, and update the network parameters and dynamic parameters (θ′1, w′1; θ′2, ω′2) until the model converges, and obtain the final trained physical information neural network, whose corresponding network parameters and dynamic parameters are (θ1, w1; θ2, ω2).

[0096] (6) The dynamic scanning time t is input into the trained physical information neural network. The two parallel networks in the trained model are represented as f1(θ1, ω1) and f2(θ2, ω2); the network outputs the final predicted concentrations of tracers I and II in different compartments; f1(θ1, ω1) outputs the concentration of tracer I corresponding to (C E1 (t;θ1,ω1),C M1 (t;θ1,ω1),C P1 (t; θ1, ω1)), f2(θ2, ω2) outputs the tracer II corresponding to (C E2 (t;θ2,ω2),C M2 (t;θ2,ω2),C P2 (t; θ2, ω2)); then calculate the total concentration of tracer I in the tissue C by the two-compartment model T1 (t; θ1, ω1) and the total concentration of tracer II C T2(t; θ2, ω2):

[0097]

[0098] Among them, V B1 With V B2 The corresponding model predicts the vascular volume fraction of tracer I and tracer II; finally, according to the PET instrument sampling protocol, C T1 (t; θ1, ω1) and C T2 (t; θ2, ω2) integration, the predicted dynamic PET image sequence of tracer I and tracer II is obtained and To achieve the separation of dynamic dual-tracer PET, the PET image of the fth frame is expressed as:

[0099]

[0100] Among them, X T 1f With X T 2f They represent the f-th frame PET images of tracer I and tracer II predicted by the model, respectively.

[0101] The following simulation experiments verify the present invention. All experiments were conducted in the following experimental environment: PyTorch 1.13.0 framework, using Python 3.9 as the programming language, and executed on the Windows 11 operating system. The training and testing processes were performed in the following environment: 64GB of memory, an Intel(R) Core(TM) i9-14900, and an NVIDIA GeForce RTX4070SUPER with 12GB of video memory.

[0102] (1) Experiments combining different phantoms with different tracers.

[0103] This experiment primarily used three different phantoms and two different tracer combinations to demonstrate the generalizability of the present invention. Four experimental groups were included: (a) Zubal Brain phantom (90×90), tracer combination (18F-FDG / 11C-MET); (b) Zubal Brain phantom (90×90), tracer combination (18F-FDG / 18F-FLT); (c) Template Brain phantom (90×90), tracer combination (18F-FDG / 11C-MET); and (d) Hoffman Brain phantom (64×64), tracer combination (18F-FDG / 11C-MET). A two-compartment model was used to simulate the in vivo motion of two single and dual tracers, and a system of kinetic differential equations was used to solve the in vivo concentration profiles of the radionuclides after decay. Each set of experiments used identical parameters and the same sampling protocol, sampling 18 frames over 60 minutes for a photon count of 80 million. Simultaneously, scattering was simulated using the SimSET software package, selecting 20% ​​uniform random events and employing the Kernel EM reconstruction algorithm. Dual-tracer PET images were incorporated into the model's loss function as a standard, and the model was trained for self-supervised separation of dual-tracer PET images. The separation results were compared with simulated single-tracer PET images.

[0104] The separation results are as follows Figure 3 As shown, Figure 3 (a) Dual tracer separation results of the Zubal brain phantom and tracer combination (18F-FDG / 11C-MET); Figure 3 (b) Dual tracer separation results of the Zubal brain phantom and tracer combination (18F-FDG / 18F-FLT); Figure 3 (c) Double tracer separation results of the Template Brain phantom and tracer combination (18F-FDG / 11C-MET); Figure 3 (d) shows the dual-tracer separation results for the Hoffman Brain phantom and a tracer combination (18F-FDG / 11C-MET). In each set of results, the first row shows the PET image from frame 3, the second row shows the PET image from frame 14, the first three columns show the separation results for 18F-FDG, and the last three columns show the separation results for 11C-MET or 18F-FLT. For each tracer, the true value, predicted value, and error plot are shown from left to right. This demonstrates that the present invention can accurately separate dual-tracer PET images and generalizes well to different phantoms and tracer combinations, demonstrating its strong generalization capabilities.

[0105] (2) Experiments with different sampling protocols.

[0106] This experiment uses the Zubal Brain phantom (containing 5 regions of interest (ROIs)) and randomly generates a 6×6 tumor in it, so there are a total of 6 ROIs. The tracer combination of 18F-FDG / 11C-MET is selected. The simulation data is generated using the same method as experiment (1), except that three sets of results with different sampling protocols are generated. The sampling protocol settings are shown in the following table:

[0107] Table 1 Sampling protocol

[0108]

[0109]

[0110] Use the data from Sampling Protocol 1 to train a physical information constrained neural network model that can achieve dual-tracer PET separation. Set the time t to 40 minutes and input the trained model. Use Sampling Protocol 1 to integrate the separation results. Calculate the average TAC curve for each ROI and compare the predicted results with the true value, as shown in the following example: Figure 4 As shown in (a); the time t is set to 60min and input into the trained model, the separation results are obtained by integration using sampling protocol 2, the average TAC curve of each ROI is calculated, and the predicted results are compared with the true values, as shown in Figure 4 As shown in (b); the time t is set to 60min and input into the trained model, the sampling protocol 3 is used for integration to obtain the separation results, the average TAC curve of each ROI is calculated, and the predicted results are compared with the true values, as shown in Figure 4 (c) is shown. Figure 4 In (a), (b), and (c), six regions of interest are represented from top to bottom, and each figure includes four curves. The solid dot mark curve and the dashed dot mark curve represent the predicted TAC curve and the true TAC curve of tracer I, and the solid triangle mark curve and the dashed triangle mark curve represent the predicted TAC curve and the true TAC curve of tracer II. The results show that the present invention can be well generalized from the sampling results of a shorter time to the sampling results of a longer time.

[0111] (3) Comparative experiment on unregistered data

[0112] This experiment uses the Zubal Brain phantom (containing 5 regions of interest (ROIs)) and randomly generates a 6×6 tumor in it, so there are a total of 6 ROIs. The tracer combination of 18F-FDG / 11C-MET is selected, and 1200 sets of simulation data are generated using the same method as experiment (1) for training the multi-task learning 3D convolution method, of which 960 sets of data are used as training sets and 360 sets of data are used as validation sets. In order to simulate the situation of data misalignment, the Zubal Brain phantom with the tumor inserted is rotated 4° instantaneously, and a set of unregistered data is generated using the same method as experiment (1). The unregistered mixed dual-tracer PET image is added as a label to the loss function of the physical information constrained neural network, and the model is trained to obtain its separated single-tracer PET image; the mixed dual-tracer PET sinusoid of the unregistered data is input into the multi-task learning 3D convolution network trained with 1200 sets of registered data to obtain its separated single-tracer PET image. The comparison of the two sets of separation results is as follows: Figure 5 shown. Figure 5 In the figure, from top to bottom, the ground truth, the separation results of the present invention, and the separation results of the multi-task learning 3D convolution method are shown. From left to right, the PET concentration maps of the separated tracer 18F-FDG in the third, ninth, and fifteenth frames, and the PET concentration maps of the tracer 11C-MET in the third, ninth, and fifteenth frames, respectively, are shown. The results show that compared to the multi-task learning 3D convolution method, the present invention can achieve better separation results, demonstrating its ability to address the data registration issues faced by existing deep learning methods based on supervised training strategies.

[0113] The three sets of experimental results demonstrate from different perspectives that the dynamic dual-tracer PET self-supervised method proposed in this invention has high generalization ability, can be applied to a variety of tracer combinations, a variety of biological tissues and various sampling protocols, and performs better than existing methods on unregistered datasets, solving the complexity problem brought by data registration.

[0114] The above description of the embodiments is intended to facilitate understanding and application of the present invention by those skilled in the art. It will be apparent that those skilled in the art can readily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without requiring inventive effort. Therefore, the present invention is not limited to the above embodiments, and improvements and modifications made by those skilled in the art based on the disclosure of the present invention should fall within the scope of protection of the present invention.

Claims

1. A dynamic dual-tracer PET self-supervised separation method based on a physical information neural network, comprising the following steps: 1) Perform a dynamic PET scan on the biological tissue injected with tracer I and tracer II at the same time to obtain a hybrid dual-tracer PET sinogram sequence f=1, ..., F represents the current frame number, and the tracer I and tracer II are labeled with two radioactive nuclides respectively; 2) Using PET image reconstruction algorithm to calculate the hybrid dual-tracer PET sinogram sequence Corresponding hybrid dual-tracer PET image sequence 3) Obtain the priori kinetic parameters of the two-compartment model corresponding to tracer I and tracer II respectively; 4) Constructing a physical information neural network, while setting the two-compartment model kinetic parameters corresponding to tracer I and tracer II as network parameters a priori; inputting the dynamic scanning time t into the network, and the network output is the tracer concentration of tracer I and tracer II in different compartments; 5) Calculate boundary condition constraints on the network output; calculate residual loss constraints for the dual-compartment model ordinary differential equation on the network output; combine the network output with the dual-compartment model to calculate the single-tracer PET image sequence corresponding to tracer I and tracer II, and calculate data term constraints on the mixed dual-tracer PET image sequence; integrate the above three constraints to form the loss function of the physical information neural network; 6) Training the physical information neural network, updating the network parameters and dynamic parameters simultaneously according to the loss function until the model converges, and obtaining a trained physical information neural network; 7) The dynamic scanning time t is input into the trained physical information neural network to obtain the final predicted tracer concentrations of tracer I and tracer II in different compartments, and a single tracer PET image sequence of tracer I and tracer II that conforms to the actual distribution is calculated through a two-compartment model.

2. The dual-tracer PET self-supervised separation method according to claim 1, characterized in that: The PET image reconstruction algorithm in step 2) adopts the Kernel EM algorithm.

3. The dual-tracer PET self-supervised separation method according to claim 1 or 2, characterized in that: In step 3), for the dual-tracer dual-compartment model, the tracer concentration change in each compartment is expressed by the following ordinary differential equation: in, C E1 (t), C M1 (t) and C P1 (t) represents the concentration change rate constant of tracer I, the concentration of free and nonspecifically bound tracer, the concentration of specifically bound tracer and the arterial blood input function concentration; similarly, C E2 (t), C M2 (t) and C P2 (t) corresponds to tracer II; The arterial input function concentration calculation can be expressed as: in, and represents the eigenvalue of the arterial input function, and represents the coefficient of the arterial input function; In addition, the vascular volume fraction V is added to the two-compartment model B , and thus the total tracer concentration in the tissue is calculated: C T1 (t)=(1-V B1 )(C E1 (t)+C M1 (t))+V B1 C P1 (t) C T2 (t)=(1-V B2 )(C E2 (t)+C M2 (t))+V B2 C P2 (t); Among them, C T1 (t) and C T2 (t) represents the total concentration of tracer I and tracer II in the tissue, V B1 With V B2 represent the vascular volume fractions of tracer I and tracer II, respectively.

4. The dual-tracer PET self-supervised separation method according to claim 3, characterized in that: The priori kinetic parameters of the two-compartment model corresponding to tracer I and tracer II in step 3) are: Here, ω1 corresponds to the prior kinetic parameters of tracer I, and ω2 corresponds to the prior kinetic parameters of tracer II.

5. The dual-tracer PET self-supervised separation method according to claim 4, characterized in that: In step 4), the physical information neural network is composed of two identical quadratic residual networks. Time t is input into two parallel networks, and the network outputs different compartment tracer concentrations of tracer I and tracer II, which are expressed as (C E1 (t;θ′1,ω′1),C M1 (t;θ′1,ω′1),C P1 (t;θ′1,ω′1)) and (C E2 (t;θ′2,ω′2),C M2 (t;θ′2,ω′2),C P2 (t; θ′2, ω′2)), corresponding to the free and nonspecific binding tracer concentrations, specific binding tracer concentrations, and arterial input function concentrations of tracer I and tracer II, respectively; each quadratic residual network contains 6 hidden layers, each with 1024 neurons, and each hidden layer is followed by a tanh activation function. The model uses a fifth-order Runge-Kutta to improve calculation accuracy; in addition, the total tracer concentration C in the tissue corresponding to tracer I and tracer II is calculated based on the double compartment model calculation formula and the network output T1 (t;θ′1,w′1) and C T2 (t; θ′2, w′2); where (θ′1, ω′1; θ′2, ω′2) represent the network parameters and dynamic parameters during training.

6. The dual-tracer PET self-supervised separation method according to claim 1, 2, 4 or 5, characterized in that: The boundary condition loss constraint term in step 5) is: Where i = 1 represents tracer I, i = 2 represents tracer II, N represents the number of image pixels, C represents the number of tracer I, and N represents the number of image pixels. Ei (0), C Ei (0;θ′ i ,ω′ i ) represent the true value of free and nonspecific binding tracer concentrations (0) and the model-predicted free and nonspecific binding tracer concentrations at t = 0, respectively; C Mi (0), C Mi (0;θ′ i ,ω′ i ) represent the true value of the specific binding tracer concentration (0) and the specific binding tracer concentration predicted by the model at t=0, respectively; The ordinary differential equation residual loss constraint consists of the following three items: Among them, L ResEi , L ResMi , L ResTi are the residual loss functions of the ordinary differential equations for the model-predicted free and nonspecifically bound tracer concentrations, specifically bound tracer concentrations, and total tracer concentrations in tissues, respectively. represents the kinetic parameters predicted by the model, C Ei (t;θ′ i ,ω′ i ) represents the free and nonspecifically bound tracer concentrations predicted by the model, C Mi (t;θ′ i ,ω′ i ) represents the specific binding tracer concentration predicted by the model, C Ti (t;θ′ i ,ω′ i ) represents the total tracer concentration in the tissue predicted by the model, C Pi (t;ω′ i ) represents the arterial blood input function predicted by the model; therefore, the ordinary differential equation residual loss constraint is: Where T represents the total sampling time. i = 1 corresponds to tracer I, i = 2 corresponds to tracer II; Single tracer PET image sequence corresponding to the tracer I and tracer II Single tracer PET image sequence and The total tracer concentration in the tissue is integrated by the PET instrument sampling protocol to obtain: Among them, f represents the current time frame number, X f T1′ 、X f T2′ They represent the PET images of tracer I and tracer II in the current frame, respectively, f and t f-1 Represents the time of the current frame and the time of the previous frame respectively, C T1 (t; θ′1, ω′1) represents the total concentration of tracer I in the tissue predicted by the model, C T2 (t; θ′2, ω′2) represents the total concentration of tracer II in the tissue predicted by the model, and ρ1 and ρ2 represent the half-lives of the radionuclides in tracer I and tracer II, respectively. Therefore, the data term constraints are: Where F represents the total number of scanned frames.

7. The dual-tracer PET self-supervised separation method according to claim 6, characterized in that: The loss function of the entire network in step 5) is: Among them, λ1 and λ2 are the proportional coefficients of the loss function, i = 1 corresponds to tracer I, and i = 2 corresponds to tracer II.

8. The dual-tracer PET self-supervised separation method according to claim 7, characterized in that: The network parameters and dynamic parameters corresponding to the physical information neural network trained in step 6) are marked as (θ1, ω1; θ2, ω2).

9. The dual-tracer PET self-supervised separation method according to claim 7 or 8, characterized in that: The final predicted concentrations of tracer I and tracer II in different compartments in step 7) are (C E1 (t;θ1,ω1),C M1 (t;θ1,ω1),C P1 (t;θ1,ω1)) and (C E2 (t;θ2,ω2),C M2 (t;θ2,ω2),C P2 (t; θ2, ω2)), the single tracer PET image sequence of tracer I and tracer II that conforms to the actual distribution is: and , the PET image of the fth frame is expressed as: Among them, V B1 With V B2 The vascular volume fraction corresponding to tracer I and tracer II, X f T1 With X f T2 They represent the f-th frame PET images of tracer I and tracer II respectively.

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