PET / CT kinetic parameter estimation Bayesian optimization method based on regret-alpha ratio

Abstract

The invention relates to a PET / CT kinetic parameter estimation Bayesian optimization method based on a regret-alpha ratio. According to the method, a reversible double-input three-atrioventricular model is used for modeling the metabolic activity of the liver tissue, and an optimization target is determined in combination with real TAC data. A regret-alpha ratio and a net inflow rate are introduced as weights, high and low weight distinguishing is carried out on an initial sampling point, different optimization strategies are adopted respectively, the strategies are fused into a Bayesian optimization framework, and a Gaussian process is utilized to carry out modeling on an objective function and predict optimal parameters. And after the preliminary optimization is completed, whether an overfitting condition exists or not is judged by combining an objective function value for a parameter estimation result which does not meet physiological rationality, and multi-objective optimization is carried out for an overfitting result. According to the method, a mathematical optimization model is combined with physiological parameters, kinetic parameters are accurately estimated, hepatocellular carcinoma and background liver tissue are more effectively distinguished, and a reliable basis is provided for analysis of hepatocellular carcinoma.

Description

Technical Field

[0001] The invention relates to a Bayesian optimization method for estimating PET / CT dynamic parameters based on regret-alpha ratio, and belongs to the technical field of machine learning and dynamic parameter optimization. Background Art

[0002] Liver cancer is a global health challenge, with an estimated incidence of more than 1 million cases by 2025. Hepatocellular carcinoma (HCC) is the most common form of liver cancer, accounting for approximately 90% of cases. Although malignant and benign tumors can be distinguished by conventional imaging techniques such as computed tomography (CT) and magnetic resonance imaging (MRI), the pathological diagnosis and analysis of HCC in the clinic remains quite challenging. Dynamic PET / CT technology provides more precise and dynamic information for the diagnosis and treatment of HCC by reconstructing image sequences at multiple time points and capturing the time-radioactivity curve (TAC) of real-time tracer distribution changes in the body.

[0003] Estimating kinetic model parameters through optimization algorithms and exploring pharmacokinetic models in PET / CT imaging have attracted widespread attention. However, traditional parameter estimation methods mainly focus on finding a fitting optimal point, lack a comprehensive exploration of the parameter space, and rely on initial points and fixed sampling strategies, which are prone to fall into local optimal solutions. Therefore, although these methods may be ideal in fitting effects, they still have certain limitations in accurately estimating pharmacokinetic parameters that conform to physiological characteristics.

[0004] In terms of technology, the present invention uses Bayesian optimization algorithm to perform pharmacokinetic modeling and parameter estimation on PET / CT data. Currently, there is no research on applying Bayesian optimization to the field of pharmacokinetics and making improvements on this basis. Summary of the invention

[0005] The present invention provides a Bayesian optimization method for PET / CT dynamic parameter estimation based on regret-alpha ratio, which is used for parameter estimation of liver PET / CT dynamic modeling. The present invention applies different optimization strategies according to weights to search the solution space, detects and optimizes parameters that are not in line with physiological rationality, significantly improves the global search capability of the algorithm, and obtains accurate parameter estimation results that are in line with physiological characteristics. The obtained parameter estimation results can significantly assist in distinguishing hepatocellular carcinoma from background liver tissue.

[0006] The technical solution of the present invention is: a Bayesian optimization method for estimating PET / CT dynamic parameters based on regret-alpha ratio, and the specific steps of the method are as follows:

[0007] Step 1: Use a reversible two-input three-compartment model to model the metabolic activity of liver tissue, and combine it with real TACs data to construct an objective function for optimization;

[0008] Step 2, weight calculation is performed on the initial sampling points to determine the corresponding optimization strategy; the weight is calculated based on the regret-alpha ratio and the tracer net inflow rate of each point, so as to determine whether the exploration parameter space is more inclined to development or exploration during the optimization process;

[0009] Step 3: For sampling points with high weights, the lower confidence limit LCB is used as the acquisition function to predict the current optimal point and add it to the parameter space, so as to be more inclined to exploration; for sampling points with low weights, the multi-objective optimization method combining LCB and regret-α ratio is used to guide the prediction of the optimal point. While minimizing both, more attention is paid to developing the area near the current optimal solution;

[0010] Step 4: Perform overfitting detection on the parameter estimation results of all patients and extract all overfitting parameter results;

[0011] Step 5. For patient data that were detected to be overfitted in the preliminary optimization results, the net inflow rate and regret-α ratio were combined with the lower confidence limit (LCB) into the Bayesian optimization framework, and the multi-objective optimization was re-executed to ultimately obtain more accurate kinetic parameter estimation results.

[0012] Furthermore, in the Step 1, the objective function is defined by minimizing the root mean square error (RMSE) between the TAC value predicted by the calculation model and the measured TAC value.

[0013] Furthermore, in Step 2, the regret-α ratio measures the relative difference between the current sampling point and the optimal solution to evaluate the contribution of the point to the optimization result at the current stage; the regret-α ratio is related to the tracer net inflow rate K i This physiological parameter is multiplied to finally calculate the weight value of each sampling point. The optimization strategy adjusts the weight of exploration and development according to the weight value, thereby guiding the search direction of the parameter space and gradually optimizing the accuracy of the solution.

[0014] Furthermore, the calculation formula of the weight W is: W = α RSR (x)×K i ; Among them, α RSR (x) is the regret-α ratio, and Ki represents the net influx rate of the tracer.

[0015] Furthermore, the calculation formula of the regret-α ratio is: Among them, y minis the minimum objective function value in the current solution space, μ(x) is the mean function of the Gaussian process probability model of the black box objective function to be optimized, is the standard deviation, and k(x,x') is the covariance function.

[0016] Furthermore, in the Step 4, those parameter points that obtain excellent RMSE values ​​but whose parameter estimation results obviously deviate from physiological rationality are defined as overfitting points.

[0017] Furthermore, in Step 4, the definition of the overfitting point is:

[0018]

[0019] Among them, combined with the actual clinical measurement information type∈{tumor,normal}, and are the K of all patients in tumor tissue and normal tissue respectively. i The mean value and θ are the threshold values ​​of RMSE.

[0020] Furthermore, in Step 5, the physiological parameter K i express 18 The net influx rate of F-FDG tracer, FDG PET uptake, is proportional to tissue glucose metabolism and is not affected by measurement time or input function; therefore, K i The Bayesian optimization framework is introduced to guide the search of the solution space and effectively correct the parameter estimation results.

[0021] Furthermore, in Step 5, the objective function formula of the multi-objective optimization is:

[0022] For patient data of type normal, the objective function formula of multi-objective optimization is:

[0023]

[0024] For patient data of type tumor, the objective function formula of multi-objective optimization is:

[0025]

[0026] where D is the total number of parameter points evaluated in the solution space, α LCB (x; β|D) and α RSR (x|D) are the lower confidence limit LCB and regret-α ratio RSR of the parameter point calculated based on the current D, and λ1 and λ2 represent the weights of multiple optimization objectives.

[0027] The beneficial effects of the present invention are:

[0028] 1. The present invention uses a reversible two-input three-compartment model to model the metabolic activity of liver tissue and determines the optimization target in combination with real TAC data;

[0029] 2. The present invention introduces the regret-alpha ratio and the net inflow rate as weights to distinguish the initial sampling points with high and low weights, and adopts different optimization strategies respectively. These strategies are integrated into the Bayesian optimization framework, and the Gaussian process is used to model the objective function and predict the optimal parameters;

[0030] 3. After the preliminary optimization is completed, the present invention determines whether there is overfitting in combination with the objective function value for the parameter estimation results that do not meet the physiological rationality, and performs multi-objective optimization for the overfitting results;

[0031] 4. The present invention can combine mathematical optimization models with physiological parameters to more accurately estimate pharmacokinetic parameters, significantly distinguish hepatocellular carcinoma from background liver tissue, and provide reliable data support for the evaluation, grading and prognostic analysis of hepatocellular tumor characteristics after resection. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a schematic diagram of the process of the present invention;

[0033] Figure 2 It is a reversible double-input three-compartment model of the present invention;

[0034] Figure 3 It is the TAC curve fitting result of normal liver tissue of the present invention and the traditional nonlinear least square method;

[0035] Figure 4 It is the TAC curve fitting result of hepatocellular carcinoma lesions by the present invention and the traditional nonlinear least square method. DETAILED DESCRIPTION

[0036] Example 1: A Bayesian optimization method for estimating PET / CT dynamic parameters based on the regret-α ratio. The experiment used real PET data of hepatocellular carcinoma patients. A total of 23 HCC patients were included, of which 21 patients had 1 tumor (including 1 follow-up patient), 1 patient had 2 tumors, and 1 patient had 3 tumors. The tumor size ranged from 1.6 cm to 17.0 cm, with an average of 6.75 cm.

[0037] The present invention uses the ordered subset expectation maximization (OSEM) algorithm for PET image reconstruction. After the patient is intravenously injected with 18F-FDG, the first minute of data is reconstructed into 12 frames with an interval of 5 seconds, and the last 4 minutes of data is reconstructed into 4 frames with an interval of 60 seconds; in order to better analyze the metabolism of 18F-FDG in the patient's body with a kinetic model, a 60-minute static PET image of the liver is selected. 17 frames of PET images are obtained, fused, and aligned with the CT image. After all patients complete the PET / CT scan, professional doctors manually outline the area of ​​interest. During the outlining process, interference from the standard uptake value (SUV) of the intrahepatic blood vessels is avoided as much as possible. The TAC composed of the maximum standard uptake value (SUVmax) of each frame is obtained from the region of interest of the PET / CT image.

[0038] like Figure 2 The reversible two-input three-compartment model shown in the figure can simulate the complex distribution and metabolism of the tracer in liver tissue. a represents the proportion of hepatic arterial blood flow, C i (t) represents the tracer in the total blood 18 Functional relationship between F-FDG concentration and time, C a (t) and C v (t) represents the blood in the hepatic artery and portal vein, respectively. 18 The functional relationship between F-FDG concentration and time. 18 The relationship between F-FDG concentration and time is shown in C f (t) indicates liver tissue 18 The relationship between the concentration of F-FDG-6P and time is shown in C p (t) represents. The total blood input function of the model is obtained by weighted summation of the hepatic artery and portal vein blood supply functions:

[0039] C i (t) = f a ×C a (t)+(1-f a )×C v (t)(1)

[0040] K1(ml / min / ml) represents 18 The rate constant of F-FDG transport from blood to liver tissue, k2 represents 18 The rate constant of F-FDG returning from liver tissue to blood, k3 represents the rate constant of hexokinase in liver tissue to 18 F-FDG is phosphorylated to 18 The rate constant of F-FDG-6P, k4 represents the conversion of phosphokinase into 18 Rate constant of F-FDG.

[0041] according to Figure 2 The reversible two-input three-compartment model shown in Figure 1 gives the differential equation:

[0042]

[0043] Solving the differential equation gives C T (t), which represents the curve of the tracer concentration in the tissue measured from the PET image over time, is the output function of the kinetic model:

[0044]

[0045] In the formula, v b is the blood volume fraction, α1 and α2 can be described as follows:

[0046]

[0047] Parameter estimation for liver PET activity curve data was modeled based on the above two-input three-compartment model.

[0048] A Bayesian optimization method for estimating PET / CT dynamic parameters based on regret-alpha ratio, wherein the specific steps of the method are as follows:

[0049] Step 1: Use a reversible two-input three-compartment model to model the metabolic activity of liver tissue, and combine the real TACs data to construct an objective function for optimization. In Step 1, the objective function is defined by minimizing the root mean square error RMSE between the TAC value predicted by the calculation model and the measured TAC value.

[0050] Specifically, in Step 1, the objective function is defined as:

[0051]

[0052] where θ is the set of all kinetic parameters to be estimated (K1, k2, k3, k4, f a ,v b ), c i is the real TAC data obtained from n=17 frames of PET / CT images, C T (θ,t i ) is the above-mentioned double-input three-compartment kinetic model data used in the liver.

[0053] Step 2: Calculate the weights of the initial sampling points to determine the corresponding optimization strategy. The weights are calculated based on the regret-alpha ratio and the net inflow rate of the tracer at each point to determine whether the exploration parameter space is more inclined to development or exploration during the optimization process. In Step 2, the regret-alpha ratio measures the relative difference between the current sampling point and the optimal solution to evaluate the contribution of the point to the optimization result at the current stage; the regret-alpha ratio is related to the net inflow rate K i This physiological parameter is multiplied to finally calculate the weight value of each sampling point. The optimization strategy adjusts the weight of exploration and development according to the weight value, thereby guiding the search direction of the parameter space and gradually optimizing the accuracy of the solution.

[0054] Specifically, in Step 2, first construct the Gaussian process probability model GP(μ, k) of the black box objective function to be optimized, μ(x) is the mean function of the Gaussian process probability model of the black box objective function to be optimized, and k(x, x') is the covariance (kernel) function. The regret-α ratio is the ratio of the interpolation (regret) of the objective function between the current optimal solution and the predicted mean to the predicted standard deviation (α), to ensure that the sampling point has the potential to improve the current solution and provide valuable information. The formula for the regret-α ratio is:

[0055]

[0056] where y min is the minimum objective function value in the current solution space, is the standard deviation.

[0057] And K i It is composed of a set of kinetic parameters (K1, k2, k3) to reflect 18 Physiological parameter of F-FDG tracer net influx rate, K i The formula is:

[0058]

[0059] The weights of the initial sampling points are calculated as the basis for adopting different optimization strategies. The weight calculation formula is:

[0060] W=α RSR (x)×K i (10)

[0061] Step 3: For sampling points with higher weights, the lower confidence limit (LCB) is used as the acquisition function to predict the current optimal point and add it to the parameter space, so as to be more inclined to exploration; for sampling points with lower weights, the multi-objective optimization method combining LCB and regret-α ratio is used to guide the prediction of the optimal point. While minimizing both, more attention is paid to developing the area near the current optimal solution. The LCB formula is:

[0062] α LCB (x; β) = μ(x) - βσ(x) (11)

[0063] The parameter β needs to be adjusted heuristically, and is automatically interpolated from the calculated weight in the present invention.

[0064] Specifically, in Step 3, the Gaussian process probability model constructed in Step 2 will explore the parameter space according to the high and low weight region strategy and predict the optimal parameters. Sampling points with higher weights have the potential to significantly improve the current model solution and may represent areas of physiologically high metabolic activity, so they are worth further exploration, that is, minimizing LCB. Relatively speaking, sampling points with lower weights indicate that the current objective function value is relatively satisfactory, with limited improvement potential, and are more suitable for local fine development. A multi-objective optimization algorithm is used to achieve a balance between LCB and regret-α ratio.

[0065] Step 4: Perform overfitting detection on the parameter estimation results of all patients and extract all overfitting parameter results.

[0066] Specifically, in Step 4, those parameter points where the parameter estimation results obviously deviate from physiological rationality despite obtaining excellent RMSE values ​​are defined as overfitting points. The definition of overfitting points is:

[0067]

[0068] In which, combined with the actual clinical measurement information type∈{tumor,normal}, and are the K of all patients in tumor tissue and normal tissue respectively. i The mean value and θ are the threshold values ​​of RMSE.

[0069] Step 5. For patient data that were detected to be overfitted in the preliminary optimization results, the net inflow rate and regret-α ratio were combined with the lower confidence limit (LCB) into the Bayesian optimization framework, and the multi-objective optimization was re-executed to ultimately obtain more accurate kinetic parameter estimation results.

[0070] Specifically, in Step 5, the physiological parameter K i express 18 The net influx rate of F-FDG tracer, FDG PET uptake, is proportional to tissue glucose metabolism and is not affected by measurement time or input function. i The Bayesian optimization framework is introduced to guide the search of the solution space, which can effectively correct the parameter estimation results. The objective function formula of multi-objective optimization is:

[0071] For patient data of type normal:

[0072]

[0073] For patient data of type tumor:

[0074]

[0075] where D is the total number of parameter points evaluated in the solution space so far, and α LCB (x; β|D) and α RSR (x|D) are the lower confidence limit (LCB) and regret-α ratio (RSR) of the parameter point calculated based on the current D, and λ1 and λ2 represent the weights of multiple optimization objectives.

[0076] According to the experimental steps, the TAC curve fitting results of the present invention and the traditional nonlinear least squares method are as follows Figure 3 and Figure 4 Compared with the traditional method, the method of the present invention can be closer to the real measurement data at each time point, thereby achieving more accurate fitting. More specific parameter estimation results and experimental evaluation indicators are shown in Table 1:

[0077] Table 1 Experimental results of the present invention

[0078] Kinetic parameters <![CDATA[K1]]> <![CDATA[k2]]> <![CDATA[k3]]> <![CDATA[k4]]> fa(%) vb RMSE HCCs 1.307±0.293 1.535±0.232 0.04±0.069 0.11±0.088 82.4±20.6 0.062±0.059 1.226±0.581 Normal liver tissue 1.062±0.418 1.103±0.447 0.005±0.016 0.168±0.065 29.3±18.1 0.024±0.012 1.051±1.026 P 0.016 <0.001 0.014 0.008 <0.001 0.002 /

[0079] The independent sample T test is a statistical test method used to compare whether there is a significant difference between the means of two independent samples. The test accepts two sample data and outputs a P value. When P < 0.05, it means there is a significant difference, indicating that the parameter result value can be used to distinguish hepatocellular carcinoma tissue from normal liver tissue. The table shows that all the kinetic parameter estimation results of the present invention have significant differences. 18 F-FDG-6P can be dephosphorylated to 18 F-FDG, this metabolic process occurs more frequently in normal liver tissue, so the k4 value in normal liver tissue is greater than that in hepatocellular carcinoma tissue. b The parameter value of normal liver tissue will be smaller than that of hepatocellular carcinoma tissue.

[0080] The liver organ requires dual input including the hepatic artery and portal vein to accurately characterize its blood supply. Normal liver tissue receives 70%-80% of its blood supply from the portal vein, while HCC tissue is mainly supplied by the hepatic artery. a The parameter value will be larger.

[0081] All parameter estimation results in the present invention can accurately reflect physiological characteristics and significantly distinguish hepatocellular carcinoma tissue from normal liver tissue while ensuring low RMSE. This method provides reliable data support for the evaluation and grading of hepatocellular carcinoma characteristics and prognosis analysis after resection.

[0082] The specific implementation modes of the present invention are described in detail above, but the present invention is not limited to the above implementation modes, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. A Bayesian optimization method for PET / CT dynamic parameter estimation based on regret-alpha ratio, characterized in that: The specific steps of the method are as follows: Step 1: Use a reversible two-input three-compartment model to model the metabolic activity of liver tissue, and combine it with real TACs data to construct an objective function for optimization; Step 2: Calculate the weights of the initial sampling points to determine the corresponding optimization strategy; The weight is calculated based on the regret-alpha ratio and the net inflow rate of the tracer at each point, so as to determine whether the exploration of the parameter space during the optimization process is more inclined to development or exploration; Step 3: For sampling points with high weights, the lower confidence limit LCB is used as the acquisition function to predict the current optimal point and add it to the parameter space, so as to be more inclined to exploration; for sampling points with low weights, the multi-objective optimization method combining LCB and regret-α ratio is used to guide the prediction of the optimal point. While minimizing both, more attention is paid to developing the area near the current optimal solution; Step 4: Perform overfitting detection on the parameter estimation results of all patients and extract all overfitting parameter results; Step 5. For patient data that were detected to be overfitted in the preliminary optimization results, the net inflow rate and regret-α ratio were combined with the lower confidence limit (LCB) into the Bayesian optimization framework, and the multi-objective optimization was re-executed to ultimately obtain more accurate kinetic parameter estimation results.

2. The Bayesian optimization method for PET / CT dynamic parameter estimation based on regret-alpha ratio according to claim 1, characterized in that: In the Step 1, the objective function is defined by minimizing the root mean square error (RMSE) between the TAC value predicted by the calculation model and the measured TAC value.

3. The Bayesian optimization method for PET / CT dynamic parameter estimation based on regret-alpha ratio according to claim 1, characterized in that: In Step 2, the regret-α ratio measures the relative difference between the current sampling point and the optimal solution to evaluate the contribution of the point to the optimization result at the current stage. The regret-α ratio is related to the tracer net inflow rate K i This physiological parameter is multiplied to finally calculate the weight value of each sampling point. The optimization strategy adjusts the weight of exploration and development according to the weight value, thereby guiding the search direction of the parameter space and gradually optimizing the accuracy of the solution.

4. The Bayesian optimization method for PET / CT dynamic parameter estimation based on regret-alpha ratio according to claim 1, characterized in that: The calculation formula of the weight W is: W = α RSR (x)×K i ; Among them, α RSR (x) is the regret-α ratio, and Ki represents the net influx rate of the tracer.

5. The Bayesian optimization method for PET / CT dynamic parameter estimation based on regret-alpha ratio according to claim 1, characterized in that: The calculation formula of the regret-alpha ratio is: Among them, y min is the minimum objective function value in the current solution space, μ(x) is the mean function of the Gaussian process probability model of the black box objective function to be optimized, is the standard deviation, and k(x,x') is the covariance function.

6. The Bayesian optimization method for PET / CT dynamic parameter estimation based on regret-alpha ratio according to claim 1, characterized in that: In the Step 4, those parameter points that obtain excellent RMSE values ​​but whose parameter estimation results obviously deviate from physiological rationality are defined as overfitting points.

7. The Bayesian optimization method for PET / CT dynamic parameter estimation based on regret-alpha ratio according to claim 6, characterized in that: In the Step 4, the definition of the overfitting point is: Among them, combined with the actual clinical measurement information type∈{tumor,normal}, and are the K of all patients in tumor tissue and normal tissue respectively. i The mean value and θ are the threshold values ​​of RMSE.

8. The Bayesian optimization method for PET / CT dynamic parameter estimation based on regret-alpha ratio according to claim 1, characterized in that: In Step 5, the physiological parameter K i express 18 The net influx rate of F-FDG tracer, FDG PET uptake, is proportional to tissue glucose metabolism and is not affected by measurement time or input function; therefore, K i The Bayesian optimization framework is introduced to guide the search of the solution space and effectively correct the parameter estimation results.

9. The Bayesian optimization method for PET / CT dynamic parameter estimation based on regret-alpha ratio according to claim 1, characterized in that: In Step 5, the objective function formula of multi-objective optimization is: For patient data of type normal, the objective function formula of multi-objective optimization is: For patient data of type tumor, the objective function formula of multi-objective optimization is: where D is the total number of parameter points evaluated in the solution space, α LCB (x; β|D) and α RSR (x|D) are the lower confidence limit LCB and regret-α ratio RSR of the parameter point calculated based on the current D, and λ1 and λ2 represent the weights of multiple optimization objectives.

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