A method for estimating dynamic parameters of hepatocellular carcinoma PETCT imaging based on Bayesian inference

Abstract

The present invention relates to a method for estimating the kinetic parameters of hepatocellular carcinoma PET / CT imaging based on Bayesian inference. The present invention first extracts tracer time-radioactivity curve data of normal liver tissue, hepatic artery, portal vein, and hepatocellular carcinoma from patients. Secondly, the posterior distribution of the kinetic parameters of hepatocellular carcinoma PET / CT imaging is derived based on Bayesian theory, and the Markov chain Monte Carlo (MCMC) method is used to sample the parameter posterior distribution. The sampling algorithm adopted is the delayed rejection adaptive sampling algorithm (DRAM) to estimate the kinetic parameters. Finally, the differences in the tracer kinetic parameters between the hepatocellular carcinoma tissue images and the surrounding healthy liver tissue images are analyzed and compared. The present invention improves the reliability of the estimation of the kinetic parameters of PET / CT imaging.

Description

Technical Field

[0001] The present invention relates to a method for estimating dynamic parameters of hepatocellular carcinoma PET / CT imaging based on Bayesian inference, and belongs to the technical field of liver cancer auxiliary diagnosis. Background Art

[0002] Primary liver cancer (PHC) is a highly prevalent and devastating malignant tumor in my country. It primarily originates from the epithelial or mesenchymal tissues of the liver. The etiology and precise molecular mechanisms of PHC are not fully understood. Its pathogenesis is currently believed to be a complex, multifactorial, multistep process influenced by both environmental and dietary factors. Symptoms of early-stage PHC are nonspecific, while those of mid- to late-stage PHC are more diverse. Common clinical manifestations include liver pain, abdominal distension, fatigue, and weight loss. Some patients experience low-grade fever, jaundice, diarrhea, upper gastrointestinal bleeding, and acute abdominal pain after rupture of the liver. The vast majority of PHCs are hepatocellular carcinomas (HCCs), which can present with subtle symptoms or only present as metastatic disease. With the development of positron emission tomography (PET) technology, tracer kinetics have become an important tool for studying human functional information. Using tracer kinetic models, it is possible to quantitatively analyze and calculate physiologically relevant indicators such as glucose metabolism, which plays a crucial role in the study of diseases such as HCC. Current methods for quantitatively calculating kinetic parameters require users to pre-set initial values for each parameter. However, accurate initialization is difficult for users, which directly impacts the reliability of kinetic modeling. Therefore, the present invention employs Bayesian inference to improve the reliability of parameter estimation for hepatocellular carcinoma tracer kinetic model calculations. Summary of the Invention

[0003] The present invention provides a method for estimating dynamic parameters of hepatocellular carcinoma PET / CT imaging based on Bayesian inference, so as to improve the reliability of PET / CT imaging dynamic parameter estimation.

[0004] The technical solution of the present invention is: a method for estimating dynamic parameters of hepatocellular carcinoma PETCT imaging based on Bayesian inference, and the specific steps of the method are as follows:

[0005] Step 1: Extract tracer time-radioactivity curve data of normal liver tissue images, hepatic artery, portal vein, and hepatocellular carcinoma images from PET / CT imaging;

[0006] Step 2: Based on Bayesian theory, the posterior distribution of the dynamic parameters of HCC PET / CT imaging was derived. The Markov Chain Monte Carlo (MCMC) method was used to sample the posterior distribution of the parameters. The sampling algorithm used was the delayed rejection adaptive sampling algorithm (DRAM) to estimate the dynamic parameters.

[0007] The specific steps of the adaptive sampling algorithm DRAM are as follows:

[0008] Step 2.1. Select initial values θ0 and covariance matrix C0 with physical meanings, and determine the prior probability non - adaptive stage N0 of relevant parameters;

[0009] Step 2.2. Assume that at time t, the current state of the Markov chain is θ t , and the candidate point generated according to the first - layer proposal distribution is x1 = N(·|θ t , cov t );

[0010] Step 2.3. Calculate the acceptance probability α1;

[0011]

[0012] Step 2.4. Generate a random variable u from the uniform distribution u(0, 1). When α ≥ u, accept the candidate point θ t+1 = x1, and then enter Step 2.6. When α < u, reject the candidate point and enter Step 2.5;; p(θ t+1 |y) represents the posterior probability distribution of the kinetic model parameter θ t+1 , and t represents the number of iterations;

[0013] Step 2.5. Generate a candidate point x i = N i (·|θ n , x1, x2, …, x i-1 , cov ti ), where cov ti = λ i cov t and λ i < 1. Calculate the acceptance probability α i , and return to Step 2.4;

[0014] Step 2.6. Enter the next time t + 1. If t + 1 ≥ N0, adjust the covariance matrix cov n+1 autonomously according to the formula, otherwise cov n+1 = C0;

[0015]

[0016] s d is a scaling factor, cov(θ0, θ1, …, θ t-1 ) is a historical covariance matrix, ε is a very small positive number, and I d is the n - dimensional identity matrix;

[0017] Step 2.7. Repeat steps 2.4-2.6 until enough converged samples are generated.

[0018] The beneficial effects of the present invention are as follows: the present invention uses the delayed rejection adaptive sampling algorithm DRAM to sample the parameter posterior distribution, estimates the dynamic parameters, and improves the reliability of the PET / CT imaging dynamic parameter estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is the overall flow chart of the DRAM algorithm of the present invention;

[0020] Figure 2 This is the posterior probability distribution diagram of the hepatocellular carcinoma kinetic parameters of the present invention. DETAILED DESCRIPTION

[0021] Example 1: The patient data used in this invention are as follows: Patient data were provided by the PET / CT center of a certain hospital. They included 31 case data from 18 HCC patients. Written informed consent was obtained from all patients.

[0022] The PET / CT scanning protocol used was as follows: after the patient had fasted for more than 6 hours and their blood glucose levels stabilized, a liver CT scan (120 kV, 50 mA) was performed. A 5-minute list-mode PET scan was performed, followed by an artificial infusion of 5.5 mbq / kg of 18F-fluorodeoxyglucose (18F-FDG) in 0.9% saline (2 mL / s). Sixty minutes after the 18F-FDG injection, a whole-body CT scan (120 kV, 100 mA) was performed, encompassing six to eight sites, each undergoing a 1.5-minute PET scan. All CT images were reconstructed onto a 512 × 512 matrix using filtered back projection, attenuation correction was performed based on the CT data, and all PET images were reconstructed onto a 200 × 200 matrix using the ordered subset expectation maximization principle. The dynamic PET image acquisition time was 5 minutes, and the PET imaging data were reconstructed into 15s×4 frames and 60s×4 frames by dynamic software.

[0023] Data processing: Time-activity curves of hepatocellular carcinoma images, normal liver tissue images, aorta and portal vein images were extracted from 8-frame serial PET / CT images.

[0024] like Figure 1-Figure 2 As shown, a method for estimating dynamic parameters of hepatocellular carcinoma PETCT imaging based on Bayesian inference is described, and the specific steps of the method are as follows:

[0025] Step 1: Extract tracer time-radioactivity curve data of normal liver tissue images, hepatic artery, portal vein, and hepatocellular carcinoma images from PET / CT imaging;

[0026] Step 2: Based on Bayesian theory, the posterior distribution of the dynamic parameters of HCC PET / CT imaging was derived. The Markov Chain Monte Carlo (MCMC) method was used to sample the posterior distribution of the parameters. The sampling algorithm used was the delayed rejection adaptive sampling algorithm (DRAM) to estimate the dynamic parameters.

[0027] Using Bayes’ theorem, we can estimate the posterior probability distribution of the model parameters θ given the data y:

[0028]

[0029] where θ = (k1, k2, k3, k4, fa) are the parameters of the dynamics model, P(θ) is the prior, which refers to the parameter distribution that captures the prior knowledge about the value of any new data before considering it, and is usually constructed from the literature or other data sources;

[0030] P(y|θ) is called the likelihood function, which is the probability of observing data y given a set of parameters θ;

[0031] P(y) is called evidence, P(y) = ∫P(y|θ)P(θ)dθ.

[0032] Since it is impossible to directly apply the Bayesian formula to solve the parameters, the Markov Chain Monte Carlo method (MCMC) is used to couple the Bayesian method with the tracer kinetic three-compartment model. Commonly used MCMC algorithms include the Metropolis-Hastings algorithm and Gibbs sampling. Based on these algorithms, the adaptive Metropolis (AM) algorithm and the delayed rejection (DR) algorithm have been developed. The present invention adopts the delayed rejection adaptive Metropolis (DRAM) algorithm. The overall algorithm flow is as follows: Figure 1 shown.

[0033] The specific steps of the adaptive sampling algorithm DRAM are as follows:

[0034] Step 2.1, select the initial value θ0 and covariance matrix C0 with physical meaning, and determine the prior probability of the relevant parameters in the non-adaptive stage N0;

[0035] Step 2.2, assume that at time t, the current state of the Markov chain is θ t , the candidate point generated according to the first layer proposal distribution is x1=N(·|θ t ,cov t);

[0036] Step 2.3. Calculate the acceptance probability α1;

[0037]

[0038] Step 2.4. Generate a random variable u from the uniform distribution u(0, 1). When α ≥ u, accept the candidate point θ t+1 = x1, and then proceed to Step 2.6. When α < u, reject the candidate point and enter Step 2.5;

[0039] Step 2.5. Generate a candidate point x according to the proposal distribution of the i-th layer i = N i (·|θ n , x1, x2, …, x i-1 , cov ti ) where cov ti = λ i cov t and λ i < 1. Calculate the acceptance probability α i of each layer and return to Step 2.4;

[0040] Step 2.6. Enter the next time t + 1. If t + 1 ≥ N0, adjust the covariance matrix cov n+1 automatically according to the formula, otherwise cov n+1 = C0;

[0041]

[0042] s d is a scaling factor, cov(θ0, θ1, …, θ t-1 ) is a historical covariance matrix, ε is a very small positive number, and I c is an n-dimensional identity matrix;

[0043] Step 2.7. Repeat Steps 2.4 - 2.6 until enough convergent samples are generated.

[0044] Result analysis: Conduct an independent-samples t-test using SPSS and a ROC analysis using the software Medcalc version 13.0.0.0. If P < 0.05, it is considered to have a statistical difference.

[0045] Table 1 shows the kinetic parameter results of hepatocellular carcinoma images and normal liver tissue PET / CT imaging

[0046]

[0047] The results of the dynamic parameters of PET / CT imaging of hepatocellular carcinoma images and surrounding normal liver tissue are shown in Table 1; in hepatocellular carcinoma images, k1 (P = 0.011), k2 (P < 0.001), k3 (P < 0.001), and fa (P < 0.01) were all higher than those in the surrounding normal liver tissue images; compared with the surrounding normal liver tissue images, k4 in hepatocellular carcinoma images increased but was not statistically significant (P = 0.231); compared with the surrounding normal liver tissue images, ki in hepatocellular carcinoma images increased but was not statistically significant (P = 0.221). The blood supply of hepatocellular carcinoma mainly comes from the hepatic artery rather than the portal vein. This study showed that fa (0.708 ± 0.142 vs 0.311 ± 0.062) in hepatocellular carcinoma images was significantly higher than that in normal liver tissue images. These values are consistent with the results of previous studies on the dynamic parameters of liver PET / CT imaging, and the posterior distribution of parameters provided by the Bayesian method can better analyze uncertainty, such as Figure 2 .

[0048] The specific embodiments of the present invention are described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the knowledge of ordinary technicians in this field without departing from the scope of the present invention.

Claims

1. A method for estimating dynamic parameters of hepatocellular carcinoma PETCT imaging based on Bayesian inference, characterized by: The specific steps of the method are as follows: Step 1: Extract tracer time-radioactivity curve data of normal liver tissue images, hepatic artery, portal vein, and hepatocellular carcinoma images from PET / CT imaging; Step 2: Based on Bayesian theory, the posterior distribution of the dynamic parameters of HCC PET / CT imaging was derived. The Markov Chain Monte Carlo (MCMC) method was used to sample the posterior distribution of the parameters. The sampling algorithm used was the delayed rejection adaptive sampling algorithm (DRAM) to estimate the dynamic parameters. Using Bayes' theorem, estimate the posterior probability distribution of the model parameters θ given the data y: Where θ is the dynamics model parameter, P(θ) is the parameter distribution that captures the prior knowledge of its value before considering any new data; P(y|θ) is called the likelihood function, which is the probability of observing data y given a set of parameters θ; P((y)) is called evidence, P(y) = ∫P(y|θ)P((θ)dθ; Since the Bayesian formula cannot be directly applied to solve the parameters, the Markov chain Monte Carlo method (MCMC) was used to couple the Bayesian method with the three-compartment model of tracer kinetics; The specific steps of the adaptive sampling algorithm DRAM are as follows: Step 2.1, select the initial value θ0 and covariance matrix C0 with physical meaning, and determine the prior probability of the relevant parameters in the non-adaptive stage N0; Step 2.2: Assume that at time t, the current state of the Markov chain is θ t , the candidate point generated according to the first layer proposal distribution is x1=N(·|θ t ,cov t ); Step 2.3, calculate the acceptance probability α1; Step 2.

4. Generate a random variable \(u\) from the uniform distribution \(u((0, 1))\). When \(\alpha\geq u\), accept the candidate point \(\theta t+1 = x1, and then proceed to Step 2.

6. When \(\alpha < u\), reject the candidate point and proceed to Step 2.5; Step 2.5: Generate candidate points x based on the proposed distribution of the i-th layer i =N i ((·|θ n ,x1,x2,…,x i-1 ,cov ti ), where cov ti =λ i cov t And λ i <1, calculate the acceptance probability α of each layer i , return to Step 2.4; Step 2.6, enter the next moment t+1, if t+1 ≥ N0, adjust the covariance matrix cov according to the formula n+1 , otherwise cov n+1 =C0; s d is a scaling factor, cov(θ0,θ1,…,θ t-1 ) is a historical covariance matrix, ε is a very small positive number, I d is the n-dimensional identity matrix; Step 2.

7. Repeat steps 2.4-2.6 until enough converged samples are generated.

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