A method for improving coincidence time resolution of a PET system based on GRU

Abstract

The application discloses a PET system coincidence time resolution improvement method based on a GRU, which acquires waveform data and true value labels for training, verification and testing by setting point sources at specific positions, and adopts a GRU model composed of a GRU unit and a full connection layer for training, so that the estimation of a PET system TOF time is realized. The application uses a Monte Carlo simulation experiment to acquire coincidence event waveform data of a point source on a center connecting line by setting a pair of PET system crystals and SiPM photodetectors, then uses a training set to train a GRU model, tests the GRU model on a verification set to obtain a trained model, and finally verifies, through a test set, that compared with a traditional CFD method, the accuracy of TOF time estimation of the GRU model and the improvement effect on the coincidence time resolution of the PET system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of PET imaging, and particularly relates to a PET system coincidence time resolution improvement method based on GRU. BACKGROUND

[0002] Positron Emission Tomography (PET) system is a nuclear medical imaging technology for achieving the diagnosis purpose by marking the substances necessary for the metabolism of the living body, injecting into the biological body for detection. The specific drugs marked with radionuclides are usually called tracers, and the commonly used tracers include 18 F, 11 C, 15 O and the like. When the biological body is metabolized, the radionuclide has a probability of decaying and releasing a positron. The positron will undergo a short-time drift and then annihilate with the surrounding negative electrons to produce a pair of γ photons with opposite directions and equal energy. Then, the photon pair will be detected by a detection system composed of a scintillation crystal and a detector and converted into an electrical signal input into a circuit. After a certain signal processing, the concentration, position and time information of the radioactive substance in the life activity can be obtained.

[0003] Further, if the time difference of the arrival of the two γ photons at the detector can be determined, the exact position of the annihilation site can be calculated through the time difference information. Such a PET detection system is called Time of Flight (TOF) PET system. However, the TOF-PET system has a high requirement on time. In actual situations, the detection of γ photons has the following errors: ① conversion depth, the γ photon propagates a distance before being absorbed after entering the crystal; ② crystal scintillation process, the crystal has a rise time and decay time in the process of scintillation and light emission; ③ transmission time, the time used by the photon from the crystal to the photodetector; and ④ single photon dispersion time of the photodetector. These information is finally contained in the waveform of the photodetector.

[0004] Currently, the main methods for timing the waveform of a photodetector are the following two methods mentioned in the paper Signal processing for picosecond resolution timing measurements (Genat, JF, et al. published in the journal Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, volume 607, issue 2, pages 387-393, June 11, 2009):

[0005] Frontier timing method; this method first sets a certain voltage threshold V th , and takes the time t1, t2 when a pair of waveforms first exceeds the threshold as the photon arrival time, and the difference between the two is the TOF time.

[0006] Constant ratio timing method; this method sets the threshold V th as a percentage of the maximum value of the waveform, and also takes the time t1, t2 when a pair of waveforms first exceeds the threshold as the photon arrival time, and the difference between the two is the TOF time.

[0007] In addition to the above-mentioned constant ratio timing method, there are zero-crossing constant ratio timing method and interpolation constant ratio timing method mentioned in the paper Neural network-featured timing systems for radiation detectors: performance evaluation based on bound analysis (Ai, P, et al. published in the journal Journal of Instrumentation, volume 16, issue 9, pages 09-19, September 2021).

[0008] Zero-crossing constant ratio timing method; this method copies each waveform into two groups, multiplies the first group of waveforms by a percentage for scaling, multiplies the second group of waveforms by a negative number and delays, then adds the two groups of waveforms to obtain the final waveform, and the zero-crossing point of the waveform is regarded as the photon arrival time, finally, a pair of waveforms are respectively subjected to zero-crossing constant ratio timing to obtain t1, t2, and the difference between the two is the TOF time.

[0009] Interpolation constant fraction timing method; since the waveform is a digital signal, the time when the waveform first exceeds the threshold in the ordinary constant fraction timing method is not accurate as the photon arrival time, the interpolation constant fraction timing method performs linear interpolation between the sampling points on both sides of the threshold in the waveform, improves the equivalent sampling rate, and obtains more accurate photon arrival times t1 and t2, and the difference between the two is obtained TOF time.

[0010] However, the above methods do not utilize the potential information contained in the waveform; therefore, it is necessary to learn the potential features in the waveform through some deep learning methods to further improve the coincidence time resolution of the PET system. SUMMARY

[0011] In view of the above, the present application provides a GRU-based PET system coincidence time resolution improvement method, which can effectively improve the coincidence time resolution of the PET system.

[0012] A GRU-based PET system coincidence time resolution improvement method, comprising the following steps:

[0013] (1) A pair of PET detectors are used to detect coincidence events generated by a point source, and the detected coincidence waveforms and corresponding point source positions are saved;

[0014] (2) The coincidence waveforms are cropped and the TOF true value corresponding to each group of coincidence waveforms is calculated;

[0015] (3) A large number of samples are obtained according to steps (1) and (2), each sample including coincidence waveform data and TOF true value, and all samples are divided into a training set and a test set;

[0016] (4) A GRU-based network model is constructed, which is composed of multiple cascaded GRU units and linear layer connections;

[0017] (5) The coincidence waveform data in the training set sample is used as the model input, and the TOF true value is used as the label to train the above network model;

[0018] (6) The coincidence waveform data in the test set sample is input into the trained network model, and the corresponding TOF time can be directly predicted.

[0019] Further, the step (1) is specifically implemented as follows: a radioactive point source is placed on the connecting line of a pair of PET detectors, the point source is moved on the connecting line at a certain step interval, and the coincidence events generated by the point source are detected by the two detectors at each position to obtain a plurality of sets of coincidence waveforms, each set of coincidence waveforms comprising two waveform sequences generated by the two detectors in response to the paired gamma photons of the same coincidence event, and the time delay of the two waveform sequences represents the PET flight time.

[0020] Further, the clipping processing in the step (2) is to take the maximum value of each of the two waveform sequences of the coincidence waveform, and take the maximum value point as a reference, sample forward for a time length of t1 and sample backward for a time length of t2 to form a waveform with a length of t1+t2, so as to ensure that most of the waveforms obtained after clipping are rising edges; if the position of the point source corresponding to any set of coincidence waveforms is Δx, then the TOF true value of the coincidence waveform is c is the speed of light.

[0021] Further, the GRU unit includes an input layer, a hidden layer, a reset gate, an update gate and an output layer, and the specific calculation process is as follows:

[0022] z t =σ(W z ·[h t-1 ,x t ])

[0023] r t =σ(W r ·[h t-1 ,x t ])

[0024] h′ t =tanh(W h ·[r t ·h t-1 ,x t ])

[0025] h t =(1-z t )*h t-1 +z t *h′ t

[0026] wherein x t is the input data of the input layer at time t, i.e., the input of the GRU unit at time t, h t and h t-1 are the output results of the output layer at time t and time t-1, i.e., the outputs of the GRU unit at time t, h′ t is the intermediate result of the hidden layer at time t, r t is the intermediate result of the reset gate at time t, and z tThe intermediate result generated by the update gate at time t is W z , W r , W h are the weight matrix of the update gate, the reset gate and the hidden layer respectively, σ() represents the sigmoid function, tanh() represents the hyperbolic tangent function, t is a natural number and 0 < t < t1+t2.

[0027] Further, the output of each layer of GRU units in the network model is used as the input of the next layer of GRU units, and the input of the first layer of GRU units is the coincidence waveform data in the training set sample, which is stored in the form of a two-dimensional array with a width of 2 and a length of t1+t2 after being cut from two waveform sequences of the coincidence waveform.

[0028] Further, the process of training the network model in step (5) is as follows:

[0029] 5.1 Initialize the model parameters, including the bias vector and weight matrix of each layer, the learning rate and the optimizer;

[0030] 5.2 Input the coincidence waveform data in the training set sample into the model, and the model outputs the corresponding prediction result, i.e. TOF time, by forward propagation, and calculates the loss function L between the prediction result and the label;

[0031] 5.3 According to the loss function L, the model parameters are continuously updated by the gradient descent method using the optimizer until the loss function L converges, and the training is completed.

[0032] Further, the loss function L adopts mean square error.

[0033] Further, the optimizer adopts Adam optimizer.

[0034] The present application estimates the TOF of the PET system based on the GRU-based neural network model, extracts the potential features in the waveform, and provides help for better timing. The present application enables the PET system to obtain better coincidence time resolution, thereby obtaining better spatial resolution using TOF information, so that the PET system can provide more accurate information in medical imaging and provide better help for clinical diagnosis. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 Fig. 1 is a schematic diagram of PET system coincidence event waveform and TOF true value data detection.

[0036] Figure 2 Fig. 3 is a structure diagram of the GRU unit in the network model of the present application.

[0037] Figure 3 Fig. 4 is a schematic diagram of the overall structure of the network model of the present application.

[0038] Figure 4 The TOF prediction results of the present application and the conventional method are compared at the point source positions of -50 mm, 0 mm and 50 mm. DETAILED DESCRIPTION

[0039] In order to more specifically describe the present application, the technical solutions of the present application are described in detail below in combination with the drawings and specific embodiments.

[0040] The PET system TOF time resolution improvement method based on GRU of the present application comprises the following steps:

[0041] (1) A radioactive point source is placed on the connecting line of a pair of PET detectors, the position of the point source is moved at a certain interval, and the waveforms of the two detectors when meeting the coincidence events are collected, and the point source position Δx and the waveforms of each group of coincidence events are saved.

[0042] The position of the point source is on the connecting line of the two detectors, and after collecting enough coincidence events each time, the next batch of coincidence event waveform data is collected by moving along the connecting line of the two detectors at a certain step.

[0043] (2) For each coincidence event, each pair of collected waveforms is cut, and a pair of waveform data with a length of t1+t2 is formed by taking t1 and t2 time length waveforms forward and backward from the time t0 when the waveform reaches the maximum value. According to the saved point source position Δx, the value of TOF true value Δt is calculated using the following formula:

[0044]

[0045] Wherein: c is the speed of light.

[0046] (3) The waveform data and TOF true value of all collected coincidence events are randomly allocated as a training set, a validation set and a test set; the data set division requirements: non-repeated, the training set, the validation set and the test set are divided according to the ratio of 7:2:1.

[0047] The waveform data of each coincidence event is composed of a pair of cut waveforms and TOF true value Δt, and the pair of waveform sequences is stored in the form of a two-dimensional array with a width of 2 and a length of t1+t2.

[0048] (4) Take out the coincidence event data in the training set, take the waveform as the input sample, and take the TOF true value Δt as the true value label, train the gated recurrent neural network (GRU), and finally obtain the PET system TOF time estimation model based on GRU according to the performance of the model on the validation set, specifically:

[0049] 4.1 Construct the GRU model, which is composed of multiple layers of GRU units and linear layers, and each GRU unit is composed of hidden state, update gate, reset gate and candidate hidden state.

[0050] 4.2 Initialize the parameters of the above GRU model, including the bias vector and weight matrix of each GRU unit and fully connected layer;

[0051] 4.3 Train the GRU model under the guidance of the true value label in the training set, and verify the training state of the model through the validation set. Input each waveform of the coincidence event in the training set into the GRU multi-layer model to obtain the prediction result Δt' of the GRU model, calculate the mean square error L of the output result and the true value label Δt, and optimize the parameters of each GRU unit through the Adam optimizer. After each step of training, use the waveform of the coincidence event in the validation set as input to obtain the prediction value Δt'' of the GRU model and calculate the mean square error L' of the true value label; when the error of the model on the validation set no longer decreases, the final GRU model is obtained.

[0052] The expression of the error function L is:

[0053]

[0054] The expression of the error function L' is:

[0055]

[0056] Wherein: is the square of the L2 norm.

[0057] (5) Take out the coincidence event data in the test set, input the waveform as the input sample into the trained GRU model, and output to obtain the TOF time value estimated by the GRU model.

[0058] In the following examples, we use Monte Carlo simulation to obtain waveform data, and the detection and acquisition of coincidence event data are as shown in Figure 1 In the simulation, the PET detector is composed of LYSO crystal and SiPM photodetector, taking the center of the connecting line of a pair of PET detectors as the origin and the connecting line as the z axis, placing a point source every 1 cm and collecting 3000 groups of coincidence event data, a total of 21 positions and 63000 groups of coincidence event data.

[0059] The collected each pair of waveforms is cut to form a pair of waveform data with a length of 5 ns, taking the time t0 when the waveform reaches the highest value as the reference point, and taking the waveforms with a length of 3.5 ns and 1.5 ns forward and backward. Since the waveform sampling interval is 0.05 ns, a pair of waveform data can be represented by a two-dimensional matrix of 2x100; then, according to the point source position Δx, the value of the TOF true value Δt is calculated using the following formula.

[0060]

[0061] Wherein: c is the speed of light.

[0062] The collected 63000 sets of coincidence event data are divided into a training set, a validation set and a test set according to a ratio of 7:2:1.

[0063] A GRU unit is constructed; each GRU unit is composed of an input layer, a hidden layer and an output layer, as shown in Figure 2 , wherein h t-1 is the hidden layer state at t-1, h t is the hidden layer state at t, x t is the voltage data of a pair of coincidence waveforms at t, and h0 is a full 0 matrix. In the GRU unit, there are a reset gate r t , an update gate z t and a candidate hidden state h' t , and their calculation formulas are as follows:

[0064] z t =σ(W z ·[h t-1 ,x t ])

[0065] r t =σ(W r ·[h t-1 ,x t ])

[0066] h′ t =tanh(W h ·[r t ·h t-1 ,x t ])

[0067] h t =(1-z t )*h t-1 +z t *h′ t

[0068] Wherein: [ ] means splicing matrices, σ is a sigmoid function, tanh is a hyperbolic tangent function, W z , Wr , W h are weight matrices.

[0069] The whole model is composed of six GRU units and two linear layers, as shown in Figure 3 , where the first layer GRU input is x t and the hidden state h 1,t-1 at time t-1, and the output is h 1,t ; at this time h 1,t again as input into the second GRU unit, and so on to obtain the weight value h 6,t of the last GRU unit at time t. In this embodiment, a pair of waveform data has 100 time points, and after obtaining the hidden state at all 100 time points, a one-dimensional vector is spliced, and the one-dimensional vector is obtained through two linear layers to obtain the final TOF time prediction value Δt'.

[0070] Under the guidance of the true value label in the training set, the GRU model is trained, and the training state of the model is verified through the validation set. The waveform of each coincidence event in the training set is input into the GRU model to obtain the prediction result Δt' of the GRU model, the mean square error L of the prediction result and the true value label Δt is calculated, and the parameters of each GRU unit and linear layer are optimized through the Adam optimizer. After each step of training, the waveforms of the coincidence events in the validation set are used as input to obtain the prediction value Δt" of the GRU model and calculate the mean square error L' with the true value label. When the error of the model on the validation set no longer decreases, the final GRU model is obtained; the mean square error L and L' calculation formula is as follows:

[0071]

[0072]

[0073] Wherein: is the square of the L2 norm.

[0074] Finally, the coincidence event data in the test set is taken out and input into the trained GRU model to output the TOF time value predicted by the GRU model; the time difference distribution spectrum of the predicted TOF time value at each position is counted, and the time difference distribution spectrum at-50mm, 0mm and 50mm is shown in Figure 4 The comparison method is constant fraction discrimination (CFD), and it can be clearly seen that the time difference distribution spectrum after GRU prediction is obviously more concentrated, and the full width at half maximum (FWHM) is lower.

[0075] The half-height full-width of the time difference distribution spectrum of the GRU model and the traditional CFD method from-100mm to 100mm is shown in Table 1:

[0076] Table 1

[0077] Position / mm CFD method FWHM / ps GRU method FWHM / ps Relative improvement -100 109.62 60.97 44.38％ -90 114.18 79.60 30.29％ -80 114.44 89.16 22.09％ -70 113.08 94.20 16.70％ -60 119.44 94.62 20.78％ -50 116.05 93.55 19.39％ -40 115.66 92.84 19.73％ -30 117.97 92.94 21.21％ -20 114.47 84.99 25.75％ -10 126.63 98.35 22.33％ 0 123.05 96.42 21.64％ 10 121.39 89.18 26.54％ 20 114.96 99.41 13.53％ 30 112.66 86.71 23.03％ 40 125.26 100.11 20.08％ 50 111.86 86.13 23.00％ 60 117.32 92.98 20.74％ 70 118.72 91.29 23.11％ 80 114.86 90.96 20.80％ 90 122.56 83.32 32.02％ 100 116.35 58.31 49.88％

[0078] From the above experimental results, we can see that the TOF time estimation method of the PET system based on the GRU of the present application effectively improves the full width at half maximum of the PET system at each position, and improves the coincidence time resolution of the PET system.

[0079] The above description of the embodiments is to facilitate those of ordinary skill in the art to understand and apply the present application, and those skilled in the art can easily make various modifications to the above embodiments, and apply the general principles described herein to other embodiments without creative labor. Therefore, the present application is not limited to the above embodiments, and the improvements and modifications of the present application made by those skilled in the art according to the disclosure of the present application should be within the scope of protection of the present application.

Claims

1. A method for improving coincidence time resolution of a PET system based on GRU, comprising the following steps: (1) detecting coincidence events of a point source by a pair of PET detectors, and saving the detected coincidence waveforms and corresponding point source positions, specifically: placing a radioactive point source on the line connecting a pair of PET detectors, moving the point source on the line at a certain step interval, detecting coincidence events of the point source at each position by the two detectors, and obtaining a plurality of sets of coincidence waveforms, each set of coincidence waveforms containing two waveform sequences of paired gamma photons emitted by the two detectors in response to the same coincidence event, and the time delay of the two waveform sequences representing the PET time of flight; (2) clipping the coincidence waveforms and calculating the TOF true value corresponding to each set of coincidence waveforms; (3) obtaining a large number of samples according to steps (1) and (2), each sample including coincidence waveform data and a TOF true value, and dividing all samples into a training set and a test set; (4) constructing a network model based on GRU, which is composed of a plurality of cascaded GRU units and a linear layer connection; (5) using the coincidence waveform data in the training set samples as model input and the TOF true value as label to train the above network model; (6) inputting the coincidence waveform data in the test set samples into the trained network model to directly predict the corresponding TOF time.

2. The PET system coincidence resolution improvement method of claim 1, wherein: The clipping processing in the step (2) is that the maximum value of each of the two waveform sequences conforming to the waveform is taken, and the maximum value point is taken as a reference, and the waveform of t1+t2 length is composed by sampling forward for t1 length and sampling backward for t2 length, so as to ensure that most of the waveform obtained after clipping is a waveform rising edge; if the point source position corresponding to any set of conforming waveforms is Δx, then the TOF true value of the conforming waveform is c is the speed of light.

3. The PET system coincidence resolution improvement method of claim 2, wherein: The GRU unit includes an input layer, a hidden layer, a reset gate, an update gate, and an output layer, and the specific calculation process is as follows: z t = σ(W z · [h t-1 , x t ]) r t = σ(W r · [h t-1 , x t ]) h' t = t anh(W h ·[r t ·h t-1 ,x t ]) h t = (1 - z t )*h t-1 + z t ·h′ t wherein: x t is the input data of the input layer at time t, i.e., the input of the GRU unit at time t, h t and h t-1 are the output results of the output layer at time t and time t-1, respectively, i.e., the output of the GRU unit at time t, h' t is the intermediate result generated by the hidden layer at time t, r t is the intermediate result generated by the reset gate at time t, z t is the intermediate result generated by the update gate at time t, W z , W r , and W h are the weight matrices of the update gate, the reset gate, and the hidden layer, respectively, σ() represents a sigmoid function, tanh() represents a hyperbolic tangent function, t is a natural number, and 0 < t < t1+t2.

4. The PET system coincidence resolution improvement method of claim 2, wherein: The output of each layer of GRU units in the network model is used as the input of the next layer of GRU units, and the input of the first layer of GRU units is the coincidence waveform data in the training set samples, which is stored in the form of a two-dimensional array with a width of 2 and a length of t1+t2 after clipping the two waveform sequences of the coincidence waveforms.

5. The PET system coincidence resolution improvement method of claim 1, wherein: The process of training the network model in step (5) is as follows: 5.1 initializing model parameters, including the bias vector and weight matrix of each layer, learning rate, and optimizer; 5.2 inputting the coincidence waveform data in the training set samples into the model, and obtaining the corresponding prediction result, i.e. TOF time, by forward propagation of the model, and calculating the loss function L between the prediction result and the label; 5.3 continuously updating the model parameters by gradient descent method according to the loss function L using the optimizer until the loss function L converges, and the training is completed.

6. The PET system coincidence resolution improvement method of claim 5, wherein: The loss function L adopts mean square error.

7. The PET system coincidence resolution improvement method of claim 5, wherein: The optimizer adopts Adam optimizer.

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