Neural network-based biomedical parameter imaging and pharmacokinetic analysis method

Abstract

The invention provides a biomedical parameter imaging and pharmacokinetic analysis method based on a neural network. The method comprises the following steps: S10, building a neural network model of an ordinary differential equation based on a medical imaging model; s20, initializing the neural network model; s30, setting a loss function for the neural network model; s40, training the neural network model to complete convergence; and S50, solving estimated values of pharmacokinetic parameters of the medical imaging model by using the converged neural network model. According to the biomedical parameter imaging and pharmacokinetic analysis method, a neural network model is adopted to solve an ordinary differential equation so as to realize accurate inference of pharmacokinetic parameters.

Description

Technical Field

[0001] The present invention relates to the field of medical imaging technology, and in particular to a method for biomedical parameter imaging and pharmacokinetic analysis based on neural network. Background Art

[0002] Pharmacokinetics mainly studies the dynamic changes of drugs entering the body, including the absorption, distribution, biochemical conversion (or metabolism) and excretion of drugs in the body. The drug concentration in the blood is in dynamic change from beginning to end, and the drug disposal process in the body is relatively complex and is affected by internal and external factors. The concentration of drugs at the site of action is affected by the body and thus produces dynamic changes. In order to reveal the dynamic changes of drugs in the body, it is often necessary to use data methods to explain the changes of drug concentration in the body over time. According to the data of drug concentration and time in the body, a certain mathematical model is established, and then the corresponding pharmacokinetic parameters are obtained. These parameters are used to describe the dynamic changes of drugs in the body.

[0003] However, current methods for determining pharmacokinetic parameters place the parameter inference process in a black box and do not pay sufficient attention to the metabolic constraints behind the data. They also lack the ability to generalize data with different time division strategies and different noise levels. Summary of the invention

[0004] The purpose of the present invention is to provide a method for biomedical parameter imaging and pharmacokinetic analysis based on a neural network, using a neural network model to solve ordinary differential equations to achieve accurate inference of pharmacokinetic parameters.

[0005] The present invention provides a method for biomedical parameter imaging and pharmacokinetic analysis based on a neural network, comprising the following steps:

[0006] S10: Build a neural network model of ordinary differential equations based on medical imaging models;

[0007] S20: Initialize the neural network model;

[0008] S30: Setting loss function for the neural network model;

[0009] S40: training the neural network model to complete convergence; and

[0010] S50: Using the converged neural network model to solve the estimated values ​​of the pharmacokinetic parameters of the medical imaging model.

[0011] The method of biomedical parameter imaging and pharmacokinetic analysis based on neural network provided by the present invention solves ordinary differential equations by creating a neural network model and trains the neural network model to achieve convergence by reasonably setting the loss function, thereby achieving accurate inference of pharmacokinetic parameters.

[0012] In another exemplary embodiment of the method for biomedical parameter imaging and pharmacokinetic analysis based on a neural network, in S30 and S40, the neural network model is solved by finite difference discretization, and the following symbols are standardized and defined to generate an assignment table of the coefficient matrix:

[0013] X=[x0,x1,…,x n ] T ∈R n×1 ,

[0014] F(X)=[f(x0),f(x1),…,f(x n )] T ∈R n×1 ,

[0015]

[0016] F′(X)≈WF(X)∈R n×1 ;

[0017] Where X represents the vector of independent variables, F(X) represents the vector-valued function, F′(X) represents the derivative of F(X), and W represents the coefficient matrix;

[0018] For the i ,x i+1}, and solve f′(x i ) is a first-order accurate approximation:

[0019]

[0020] For the i-1 ,x i+1}、{x i ,x i+1 ,x i+2} and {x i-2 ,x i-1 ,x i}, and solve f′(x i ) is an approximation with second-order accuracy:

[0021]

[0022] For the i-1 ,x i ,xi+1 ,x i+2} and {x i-2 ,x i-1 ,x i ,x i+1}, and solve f′(x i ) is an approximation with third-order accuracy:

[0023]

[0024] For the i-2 ,x i-1 ,x i+1 ,x i+2}, and solve f′(x i ) is approximated to fourth order accuracy:

[0025]

[0026] In another schematic embodiment of the method of biomedical parameter imaging and pharmacokinetic analysis based on neural network, in S10, the medical imaging model is a two-chamber model of dynamic PET, the neural network model takes a one-dimensional time point as input, and outputs the plasma input function curve of the two-chamber model of dynamic PET, the tracer time-activity curve in the tissue, and the tracer time-activity curve in the two chambers; when solving the plasma input function curve and the tracer time-activity curve in the tissue, the sampling points of the input time are divided into empirical non-equidistant divisions, and when solving the tracer time-activity curves of the two chambers, the sampling points of the input time are divided into equidistant divisions.

[0027] In another exemplary embodiment of the method for biomedical parameter imaging and pharmacokinetic analysis based on neural network, S30 includes:

[0028] S311: Set delay correction, and optimize the fitting of the plasma input function curve and the tracer time activity curve in the tissue. The loss function is as follows:

[0029]

[0030] Where d0 represents the time difference of the tracer appearing in plasma, d T It represents the time difference of the tracer appearing in the tissue;

[0031] S312: Set 0-point correction. When the input time is 0, the plasma input function curve of the two-chamber model, the tracer time-activity curve in the tissue, and the tracer time-activity curve in the two chambers are 0. The loss function is as follows:

[0032] L init(θ)=‖g(0;θ)‖ 2 = 0; and

[0033] S313: Set physiological constraints and optimize the tracer time activity curves of the two chambers of the two-chamber model. The loss function is as follows:

[0034] L phy (θ,p)=||g T (t c ;θ)-f v g0(t c ;θ)-(1-f v )(g1(t c ;θ)+g2(t c ;θ))|| 2 +‖Wg1(t c ;θ)-[K1g0(t c ;θ)-(k2+k3)g1(t c ;θ)]‖ 2 +‖Wg2(t c ;θ)-k3g1(t c ;θ)‖ 2 ;

[0035] Among them, L phy It indicates guiding the network to learn physiological laws, W indicates the coefficient matrix, and p indicates the kinetic parameters.

[0036] In another exemplary embodiment of the method for biomedical parameter imaging and pharmacokinetic analysis based on neural network, S311 includes:

[0037] S3111: Acquire a set of dynamic PET images sorted by time;

[0038] S3112: Identify the maximum change in pixel activity in dynamic PET images to determine the tracer arrival time, extract the plasma input function curve and the tracer time activity curve in the tissue; and

[0039] S3113: Using the plasma input function curve and the tracer time-activity curve in the tissue output by the neural network model, the extracted plasma input function curve and the tracer time-activity curve in the tissue are fitted to optimize the neural network model.

[0040] In another exemplary embodiment of the method for biomedical parameter imaging and pharmacokinetic analysis based on neural network, S3113 includes:

[0041] S31131: Based on the tracer time activity curve of the extracted tissue, the index of the tracer approximate arrival time frame is selected using the following formula to determine Initial estimate of:

[0042]

[0043] Among them, i0 represents the index of the image frame closest to the moment when the tracer appears;

[0044] S31132: Further determination of tracer arrival time using the Newton-Raphson method:

[0045]

[0046] in, Indicates the time corresponding to the frame of image closest to the moment when the tracer appears, Indicates the tracer appearance time;

[0047] S31133: Calculate the time difference between the appearance of the tracer in plasma and the appearance of the tracer in tissue; and

[0048] S31134: According to the time difference of the tracer appearing in plasma and the time difference of the tracer appearing in tissue, the plasma input function curve output by the neural network model and the tracer time activity curve in the tissue are translated to achieve accurate fitting.

[0049] In another schematic embodiment of the method of biomedical parameter imaging and pharmacokinetic analysis based on neural networks, in S10, the medical imaging model is a two-chamber model of myocardial perfusion MRI, the neural network model takes a one-dimensional time point as input, and outputs an arterial input function curve of the two-chamber model of myocardial perfusion MRI, a contrast agent time-activity curve in myocardial tissue, a contrast agent time-activity curve in plasma, and a contrast agent time-activity curve in the interstitium; when solving the arterial input function curve and the contrast agent time-activity curve in myocardial tissue, the sampling points of the input time are divided into empirical non-equidistant divisions, and when solving the contrast agent time-activity curve in plasma and the contrast agent time-activity curve in the interstitium, the sampling points of the input time are divided into equidistant divisions.

[0050] In another exemplary embodiment of the method for biomedical parameter imaging and pharmacokinetic analysis based on neural network, S30 includes:

[0051] S321: Delay correction is set to optimize the fitting of the pulse input function and the contrast agent time activity curve in the myocardial tissue. The loss function is as follows:

[0052]

[0053] Where d0 represents the time difference of the contrast agent appearing in the plasma, d TIt indicates the time difference for contrast agent to appear in tissue.

[0054] S322: Set 0-point correction. When the input time is 0, the arterial input function curve of the two-chamber model, the contrast agent time-activity curve in the myocardial tissue, the contrast agent time-activity curve in the plasma, and the contrast agent time-activity curve in the interstitium are 0, and the loss function is as follows:

[0055] L init (θ)=‖g(0;θ)‖ 2 = 0; and

[0056] S323: Physiological constraints are set to optimize the contrast agent time activity curves of the two chambers of the two-chamber model. The loss function is as follows:

[0057] L phys (θ,p)=||g T (t c ;θ)-f v g0(t c ;θ)-(1-f v )(g1(t c ;θ)+g1(t c ;θ))|| 2 +||v1Wg1(t c ;θ)-[F p (g0(t c ;θ)-g1(t c ;θ))+PS(g1(t c ;θ)-g1(t c ;θ))]|| 2 +‖v2Wg2(t c ;θ)-[PS(g1(t c ;θ)-g2(t c ;θ)]‖ 2 ,

[0058] Among them, L phys It indicates guiding the network to learn physiological laws, W indicates the coefficient matrix, and p indicates the kinetic parameters.

[0059] In another exemplary embodiment of the method for biomedical parameter imaging and pharmacokinetic analysis based on neural network, S321 includes:

[0060] S3211: Acquire a set of MRI images of myocardial perfusion sorted by time;

[0061] S3212: Identify the maximum change in pixel activity in the MRI image of myocardial perfusion to determine the arrival time of the contrast agent, extract the arterial input function curve and the contrast agent time activity curve in the myocardial tissue; and

[0062] S3213: Using the arterial input function curve and the contrast agent time-activity curve in the myocardial tissue output by the neural network model, the extracted arterial input function curve and the contrast agent time-activity curve in the myocardial tissue are fitted to optimize the neural network model.

[0063] In another exemplary embodiment of the method for biomedical parameter imaging and pharmacokinetic analysis based on neural network, S3213 includes:

[0064] S32131: Based on the extracted arterial input function curve and the contrast agent time activity curve in the myocardial tissue, the following formula is used to select the index of the contrast agent approximate arrival time frame to determine Initial estimate of:

[0065]

[0066] Wherein, i0 represents the index of the image frame closest to the moment when the contrast agent appears;

[0067] S32132: Use the Newton-Raphson method to further determine the contrast agent arrival time:

[0068]

[0069] in, Indicates the time corresponding to the frame of image closest to the moment when the contrast agent appears. Indicates the time of contrast agent appearance;

[0070] S32133: Calculate the time difference between the appearance of the contrast agent in plasma and the appearance of the contrast agent in tissue; and

[0071] S32134: Based on the time difference between the appearance of the contrast agent in plasma and the appearance of the contrast agent in tissue, the arterial input function curve output by the neural network model and the contrast agent time activity curve in the myocardial tissue are translated to achieve accurate fitting.

[0072] In another exemplary embodiment of the method for biomedical parameter imaging and pharmacokinetic analysis based on neural network, S20 includes:

[0073] S21: Preset a set of dynamic parameter values ​​and generate pre-training data;

[0074] S22: setting the initial network weights of the neural network model to random, setting the initial dynamic parameters to random or empirical values, and training the neural network model using pre-training data; and

[0075] S23: Save the network weights and dynamic parameters after the neural network model training iteration as initialization parameters for subsequent training.

[0076] In another schematic embodiment of the method for biomedical parameter imaging and pharmacokinetic analysis based on neural network, it is characterized in that, in S10, the first three layers of the neural network model are composed of linear and nonlinear layers, the linear layer contains several neurons, and uses a nonlinear activation function. The last layer of the neural network model is a linear layer containing four neurons, which is used for dimensionality adjustment to approximate the time activity curve of the tracer or contrast agent.

[0077] In another schematic embodiment of the method of biomedical parameter imaging and pharmacokinetic analysis based on neural network, in S10, the neural network model has a parallel processing structure, which can input an array of one-dimensional time points with different characteristics as input, and output an array of tracers or contrast agents with different characteristics of time activity curves. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] The following drawings are only used to schematically illustrate and explain the present invention, and do not limit the scope of the present invention.

[0079] Figure 1 A flowchart of an exemplary embodiment of a method for biomedical parameter imaging and pharmacokinetic analysis based on a neural network.

[0080] Figure 2 Schematic diagram of the two-chamber model.

[0081] Figure 3 Partial flow chart of the method for neural network-based biomedical parameter imaging and pharmacokinetic analysis.

[0082] Figure 4 is the assignment table of the coefficient matrix.

[0083] Figure 5 Partial flow chart of the method for neural network-based biomedical parameter imaging and pharmacokinetic analysis.

[0084] Figure 6 Partial flow chart of the method for neural network-based biomedical parameter imaging and pharmacokinetic analysis.

[0085] Figure 7 Partial flow chart of the method for neural network-based biomedical parameter imaging and pharmacokinetic analysis.

[0086] Figure 8 A partial flow chart of another exemplary embodiment of a method for biomedical parameter imaging and pharmacokinetic analysis based on a neural network.

[0087] Fig. 9 A partial flow chart of another exemplary embodiment of a method for biomedical parameter imaging and pharmacokinetic analysis based on a neural network.

[0088] Fig.10 A partial flow chart of another exemplary embodiment of a method for biomedical parameter imaging and pharmacokinetic analysis based on a neural network. DETAILED DESCRIPTION

[0089] In order to have a clearer understanding of the technical features, purposes and effects of the invention, the specific embodiments of the present invention are now described with reference to the accompanying drawings. The same reference numerals in the drawings represent components with the same structure or similar structures but the same functions.

[0090] In this document, “exemplary” means “serving as an example, instance or illustration”, and any diagram or implementation described in this document as “exemplary” should not be interpreted as a more preferred or more advantageous technical solution.

[0091] In order to simplify the drawings, each figure only schematically shows the parts related to the present invention, which do not represent the actual structure of the product.

[0092] Figure 1 A flowchart of an exemplary embodiment of a method for biomedical parameter imaging and pharmacokinetic analysis based on a neural network. Figure 1 , a method for biomedical parameter imaging and pharmacokinetic analysis based on neural network, including the following S10 to S50.

[0093] S10: Build a neural network model of ordinary differential equations based on a medical imaging model. The medical imaging model can be a two-chamber model of dynamic PET or a two-chamber model of myocardial perfusion MRI. Taking the two-chamber model of dynamic PET as an example, refer to Figure 2 , the tracer time activity curve in tissue can be decoupled into the following formula:

[0094] C T (t) = f v C0(t)+(1-f v )(C1(t)+C2(t)),

[0095] Among them, C T (t) represents the tracer time-activity curve in the tissue, C0(t) represents the plasma input function curve, and C1(t) and C2(t) represent the tracer time-activity curves in the two chambers.

[0096] The kinetics of the tracer can be expressed by the following ordinary differential equation:

[0097]

[0098] Among them, K1, k2, k3 and k4 represent rate constants, which are the kinetic parameters to be inferred.

[0099] The neural network model takes one-dimensional time points as input and outputs the plasma input function curve, the tracer time activity curve in the tissue and the tracer time activity curve in the two chambers of the two-chamber model of dynamic PET; when solving the plasma input function curve and the tracer time activity curve in the tissue, the sampling points of the input time are divided by empirical non-equidistant division, and when solving the tracer time activity curve in the two chambers, the sampling points of the input time are divided by equidistant division. To meet the above requirements, the first three layers of the neural network model are composed of linear and nonlinear layers. The linear layer contains several neurons and uses a nonlinear activation function. The last layer of the neural network model is a linear layer containing four neurons, which is used for dimensional adjustment to approximate the tracer time activity curve.

[0100] S20: Initialize the neural network model. Figure 3 , S20 specifically includes the following S21 to S23:

[0101] S21: Preset a set of dynamic parameter values ​​and generate pre-training data;

[0102] S22: setting the initial network weights of the neural network model to random, setting the initial dynamic parameters to random or empirical values, and training the neural network model using pre-training data; and

[0103] S23: Save the network weights and dynamic parameters after the training iteration of the neural network model as initialization parameters for subsequent training. Specifically, after adjustment of 10,000 training iterations, save the network weights and dynamic parameters as initialization parameters for subsequent training, thereby accelerating the convergence of the neural network model.

[0104] S30: Setting a loss function for the neural network model. Specifically, the neural network model is solved by finite difference discretization, and the following symbols are standardized and defined to generate an assignment table of the coefficient matrix (refer to Figure 4 ):

[0105] X=[x0,x1,…,x n ] T ∈R n×1 ,

[0106] F(X)=[f(x0),f(x1),…,f(x n )] T ∈R n×1 ,

[0107]

[0108] F′(X)≈WF(X)∈R n×1 ;

[0109] Where X represents the vector of independent variables, F(X) represents the vector-valued function, F′(X) represents the derivative of F(X), and W represents the coefficient matrix;

[0110] For the i ,x i+1}, and solve f′(x i ) is a first-order accurate approximation:

[0111]

[0112] For the i-1 ,x i+1}、{x i ,x i+1 ,x i+2} and {x i-2 ,x i-1 ,x i}, and solve f′(x i ) is an approximation with second-order accuracy:

[0113]

[0114] For the i-1 ,x i ,x i+1 ,x i+2} and {x i-2 ,x i-1 ,x i ,x i+1}, and solve f′(x i ) is an approximation with third-order accuracy:

[0115]

[0116] For the i-2 ,x i-1 ,x i+1 ,x i+2}, and solve f′(x i ) is approximated to fourth order accuracy:

[0117]

[0118] Based on finite difference discretization, refer to Figure 5 , S30 specifically includes the following S311 to S313.

[0119] S311: Set delay correction, and optimize the fitting of the plasma input function curve and the tracer time activity curve in the tissue. The loss function is as follows:

[0120]

[0121] Where d0 represents the time difference of the tracer appearing in plasma, d T Represents the time difference for the tracer to appear in the tissue.

[0122] The two-chamber model of dynamic PET described above is based on an idealized scenario, which assumes that the tracer is instantaneously perfused into various tissues throughout the body through the blood flow. However, in long axial field of view PET scanning, due to the distance between the blood pool and different tissues, there is often a certain time difference between the appearance of the tracer in the blood pool and different tissues. If delay correction is not applied, the model may not fit the measurement results well, especially for tissues far away from the blood pool. In order to apply delay correction, we need to determine the delay value between the blood pool and the tissue, and translate the tracer time activity curve function of the tissue to achieve an accurate fit. Figure 6 , S311 specifically includes the following S3111 to S3113.

[0123] S3111: Acquire a set of dynamic PET images sorted by time.

[0124] S3112: Identify the maximum change in pixel activity in dynamic PET images to determine the tracer arrival time, and extract the plasma input function curve and the tracer time activity curve in the tissue.

[0125] S3113: Using the plasma input function curve and the tracer time activity curve in the tissue output by the neural network model, the extracted plasma input function curve and the tracer time activity curve in the tissue are fitted to optimize the neural network model. Figure 7 , S3113 specifically includes the following S31131 to S31134.

[0126] S31131: Based on the tracer time activity curve of the extracted tissue, the index of the tracer approximate arrival time frame is selected using the following formula to determine Initial estimate of:

[0127]

[0128] Here, i0 represents the index of the image frame closest to the moment when the tracer appears.

[0129] S31132: Further determination of tracer arrival time using the Newton-Raphson method:

[0130]

[0131] in, Indicates the time corresponding to the frame of image closest to the moment when the tracer appears, Indicates the tracer appearance time.

[0132] S31133: Calculate the time difference between the appearance of the tracer in plasma and the appearance of the tracer in tissue.

[0133] S31134: According to the time difference of the tracer appearing in plasma and the time difference of the tracer appearing in tissue, the plasma input function curve output by the neural network model and the tracer time activity curve in the tissue are translated to achieve accurate fitting.

[0134] S312: Set 0-point correction. When the input time is 0, the plasma input function curve of the two-chamber model, the tracer time-activity curve in the tissue, and the tracer time-activity curve in the two chambers are 0, and the loss function is as follows:

[0135] L init (θ)=‖g(0;θ)‖ 2 =0.

[0136] S313: Set physiological constraints and optimize the tracer time activity curves of the two chambers of the two-chamber model. The loss function is as follows:

[0137] L phys (θ,p)=||g T (t c ;θ)-f v g0(t c ;θ)-(1-f v )(g1(t c ;θ)+g2(t c ;θ))|| 2 +‖Wg1(t c ;θ)-[K1g0(t c ;θ)-(k2+k3)g1(t c ;θ)]‖ 2 +‖Wg2(t c ;θ)-k3g1(t c ;θ)‖ 2 ,

[0138] Among them, L phys It indicates guiding the network to learn physiological laws, W indicates the coefficient matrix, and p indicates the kinetic parameters.

[0139] S40: The training of the neural network model completes convergence.

[0140] S50: using the converged neural network model to solve the estimated values ​​of the pharmacokinetic parameters of the medical imaging model, specifically by using finite difference discretization to solve and infer the kinetic parameters K1, k2, k3 and k4.

[0141] The method of biomedical parameter imaging and pharmacokinetic analysis based on neural network provided by the present invention solves ordinary differential equations by creating a neural network model and trains the neural network model to achieve convergence by reasonably setting the loss function, thereby achieving accurate inference of pharmacokinetic parameters.

[0142] As the temporal and spatial resolution of biomedical parameter imaging increases, the amount of computation required for parameter imaging increases. In this exemplary embodiment, the neural network model in S10 has a parallel processing structure, embedding multiple basic networks into a single network, so that it can simultaneously solve multiple sets of ordinary differential equations, input one-dimensional time points of different characteristics of the array as input, and output time activity curves of tracers or contrast agents of different characteristics of the array. This reduces the computation time and improves work efficiency.

[0143] In another exemplary embodiment, the medical imaging model in S10 is a two-chamber model of myocardial perfusion MRI.

[0144] The contrast agent concentration-time activity curve in myocardial tissue can be decoupled into the following formula:

[0145] C T (t) = v1C1(t) + v2C2(t),

[0146] Among them, C T (t) represents the contrast agent concentration-time activity curve in myocardial tissue, C1(t) represents the contrast agent time-activity curve in plasma, C2(t) represents the contrast agent time-activity curve in interstitium, v1 represents the plasma volume fraction, and v2 represents the interstitial volume fraction.

[0147] The kinetics of contrast agents can be expressed by the following ordinary differential equation:

[0148]

[0149]

[0150] Among them, F p represents plasma flow, v1 represents plasma volume fraction, v2 represents interstitial volume fraction, PS represents permeability-surface area, F p , v1, v2 and PS are the kinetic parameters to be inferred.

[0151] The neural network model takes one-dimensional time points as input, and outputs the arterial input function curve of the two-chamber model of myocardial perfusion MRI, the contrast agent time-activity curve in the myocardial tissue, the contrast agent time-activity curve in the plasma, and the contrast agent time-activity curve in the interstitium; when solving the arterial input function curve and the contrast agent time-activity curve in the myocardial tissue, the sampling points of the input time are divided into empirical non-equidistant divisions, and when solving the contrast agent time-activity curve in the plasma and the contrast agent time-activity curve in the interstitium, the sampling points of the input time are divided into equidistant divisions.

[0152] In an exemplary embodiment, based on finite difference discretization, reference is made to Figure 8 , S30 specifically includes the following S321 to S323.

[0153] S321: Delay correction is set to optimize the fitting of the pulse input function and the contrast agent time activity curve in the myocardial tissue. The loss function is as follows:

[0154]

[0155] Where d0 represents the time difference of the contrast agent appearing in the plasma, d T It indicates the time difference for contrast agent to appear in tissue.

[0156] Reference Fig. 9 , S321 specifically includes the following S3211 to S3213.

[0157] S3211: Acquire a set of MRI images of myocardial perfusion sorted by time.

[0158] S3212: Identify the maximum change in pixel activity in MRI images of myocardial perfusion to determine the arrival time of the contrast agent, and extract the arterial input function curve and the contrast agent time activity curve in the myocardial tissue.

[0159] S3213: Using the arterial input function curve and the contrast agent time activity curve in the myocardial tissue output by the neural network model, the extracted arterial input function curve and the contrast agent time activity curve in the myocardial tissue are fitted to optimize the neural network model. Fig.10 , S3213 specifically includes the following S32131 to S32134.

[0160] S32131: Based on the extracted arterial input function curve and the contrast agent time activity curve in the myocardial tissue, the following formula is used to select the index of the contrast agent approximate arrival time frame to determine Initial estimate of:

[0161]

[0162] Here, i0 represents the index of the image frame closest to the moment when the contrast agent appears.

[0163] S32132: Use the Newton-Raphson method to further determine the contrast agent arrival time:

[0164]

[0165] in, Indicates the time corresponding to the frame of image closest to the moment when the contrast agent appears, t i1 Indicates the contrast agent appearance time.

[0166] S32133: Calculate the time difference between the appearance of the contrast agent in plasma and the appearance of the contrast agent in tissue.

[0167] S32134: Based on the time difference between the appearance of the contrast agent in plasma and the appearance of the contrast agent in tissue, the arterial input function curve output by the neural network model and the contrast agent time activity curve in the myocardial tissue are translated to achieve accurate fitting.

[0168] S322: Set 0-point correction. When the input time is 0, the arterial input function curve of the two-chamber model, the contrast agent time-activity curve in the myocardial tissue, the contrast agent time-activity curve in the plasma, and the contrast agent time-activity curve in the interstitium are 0. The loss function is as follows:

[0169] L init (θ)=‖g(0;θ)‖ 2 =0;.

[0170] S323: Physiological constraints are set to optimize the contrast agent time activity curves of the two chambers of the two-chamber model. The loss function is as follows:

[0171] L phys (θ,p)=||g T (t c ;θ)-fv v g0(t c ;θ)-(1-f v )(g1(t c ;θ)+g1(t c ;θ))|| 2 +||v1Wg1(t c ;θ)-[F p (g0(t c ;θ)-g1(t c ;θ))+PS(g1(t c ;θ)-g1(t c ;θ))]|| 2+‖v2Wg2(t c ;θ)-[PS(g1(t c ;θ)-g2(t c ;θ)]‖ 2 ,

[0172] Among them, L phys It indicates guiding the network to learn physiological laws, W indicates the coefficient matrix, and p indicates the kinetic parameters.

[0173] In S50, specifically, the kinetic parameter F is solved and inferred by means of finite difference discretization. p , v1, v2 and PS.

[0174] Although in the exemplary embodiment, the two-chamber model of dynamic PET and the two-chamber model of myocardial perfusion MRI are taken as examples, it is not limited thereto. In other exemplary embodiments, the method of biomedical parameter imaging and pharmacokinetic analysis provided by the present invention is also applicable to other medical imaging models.

[0175] It should be understood that although this specification is described according to various embodiments, not every embodiment contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

[0176] The series of detailed descriptions listed above are only specific descriptions of feasible embodiments of the present invention. They are not intended to limit the scope of protection of the present invention. Any equivalent implementation scheme or changes that do not deviate from the technical spirit of the present invention, such as combination, division or repetition of features, should be included in the scope of protection of the present invention.

Claims

1. A method for biomedical parameter imaging and pharmacokinetic analysis based on a neural network, comprising the steps of: S10: Build a neural network model of ordinary differential equations based on medical imaging models; S20: Initialize the neural network model; S30: Setting a loss function for the neural network model; S40: training the neural network model to complete convergence; and S50: Utilizing the converged neural network model to solve the estimated values ​​of the pharmacokinetic parameters of the medical imaging model.

2. The method for biomedical parameter imaging and pharmacokinetic analysis based on neural network as claimed in claim 1, characterized in that: In S30 and S40, the neural network model is solved by finite difference discretization, and the following symbols are standardized and defined to generate an assignment table of the coefficient matrix: X=[x0,x1,...,x n ] T ∈R n×1 , F(X)=[f(x0),f(x1),...,f(x n )] T ∈R n×1 , F′(X)≈WF(X)∈R n×1 ; Where X represents the vector of independent variables, F(X) represents the vector-valued function, F′(X) represents the derivative of F(X), and W represents the coefficient matrix; For the i , x i+1 }, and solve f′(x i ) is a first-order accurate approximation: For the i-1 , x i+1 }、{x i , x i+1 , x i+2 } and {x i-2 , x i-1 , x i }, and solve f′(x i ) is an approximation with second-order accuracy: For the i-1 , x i , x i+1 , x i+2 } and {x i-2 , x i-1 , x i , x i+1 }, and solve f′(x i ) is an approximation with third-order accuracy: For the i-2 , x i-1 , x i+1 , x i+2 }, and solve f′(x i ) is approximated to fourth order accuracy:

3. The method for biomedical parameter imaging and pharmacokinetic analysis based on neural network as claimed in claim 2, characterized in that: In S10, the medical imaging model is a two-chamber model of dynamic PET, and the neural network model takes a one-dimensional time point as input, and outputs a plasma input function curve of the two-chamber model of dynamic PET, a tracer time-activity curve in the tissue, and a tracer time-activity curve in the two chambers; when solving the plasma input function curve and the tracer time-activity curve in the tissue, the sampling points of the input time are divided into empirical non-equidistant divisions, and when solving the tracer time-activity curves of the two chambers, the sampling points of the input time are divided into equidistant divisions.

4. The method for biomedical parameter imaging and pharmacokinetic analysis based on neural network as claimed in claim 3, characterized in that: S30 includes: S311: Set delay correction, and optimize the fitting of the plasma input function curve and the tracer time activity curve in the tissue. The loss function is as follows: Where d0 represents the time difference of the tracer appearing in plasma, d T It represents the time difference of the tracer appearing in the tissue; S312: Set 0-point correction. When the input time is 0, the plasma input function curve of the two-chamber model, the tracer time-activity curve in the tissue, and the tracer time-activity curve in the two chambers are 0, and the loss function is as follows: L init (θ)=||g(0;θ)|| 2 = 0; and S313: Set physiological constraints and optimize the tracer time activity curves of the two chambers of the two-chamber model. The loss function is as follows: L phys (θ, p)=|| gT (t c ;θ)-f v g0(t c ;θ)-(1-f v )(g1(t c ;θ)+g2(t c ;i))|| 2 +||Wg1(t c ;θ)-[K1g0(t c ;θ)-(k2+k3)g1(t c ;θ)]|| 2 +||Wg2(t c ;θ)-k3g1(t c ;i)|| 2 , Among them, L phys It indicates guiding the network to learn physiological laws, W indicates the coefficient matrix, and p indicates the kinetic parameters.

5. The method for biomedical parameter imaging and pharmacokinetic analysis based on neural network as claimed in claim 4, characterized in that: S311 includes: S3111: Acquire a set of dynamic PET images sorted by time; S3112: Identify the maximum change in pixel activity in dynamic PET images to determine the tracer arrival time, extract the plasma input function curve and the tracer time activity curve in the tissue; and S3113: Utilizing the plasma input function curve and the tracer time-activity curve in the tissue output by the neural network model, the extracted plasma input function curve and the tracer time-activity curve in the tissue are fitted to optimize the neural network model.

6. The method for biomedical parameter imaging and pharmacokinetic analysis based on neural network as claimed in claim 5, characterized in that: S3113 includes: S31131: Based on the tracer time activity curve of the extracted tissue, the index of the tracer approximate arrival time frame is selected using the following formula to determine Initial estimate of: Among them, i0 represents the index of the image frame closest to the moment when the tracer appears; S31132: Further determination of tracer arrival time using the Newton-Raphson method: in, Indicates the time corresponding to the frame of image closest to the moment when the tracer appears, Indicates the tracer appearance time; S31133: Calculate the time difference between the appearance of the tracer in plasma and the appearance of the tracer in tissue; and S31134: According to the time difference of the tracer appearing in the plasma and the time difference of the tracer appearing in the tissue, the plasma input function curve output by the neural network model and the tracer time activity curve in the tissue are translated to achieve accurate fitting.

7. The method for biomedical parameter imaging and pharmacokinetic analysis based on neural network as claimed in claim 2, characterized in that: In S10, the medical imaging model is a two-chamber model of myocardial perfusion MRI, and the neural network model takes a one-dimensional time point as input, and outputs an arterial input function curve of the two-chamber model of myocardial perfusion MRI, a contrast agent time-activity curve in myocardial tissue, a contrast agent time-activity curve in plasma, and a contrast agent time-activity curve in interstitium; when solving the arterial input function curve and the contrast agent time-activity curve in myocardial tissue, the sampling points of the input time are divided into empirical non-equidistant divisions, and when solving the contrast agent time-activity curve in plasma and the contrast agent time-activity curve in interstitium, the sampling points of the input time are divided into equidistant divisions.

8. The method for biomedical parameter imaging and pharmacokinetic analysis based on neural network as claimed in claim 7, characterized in that: S30 includes: S321: Delay correction is set to optimize the fitting of the pulse input function and the contrast agent time activity curve in the myocardial tissue. The loss function is as follows: Where d0 represents the time difference of the contrast agent appearing in the plasma, d T It indicates the time difference of contrast agent appearing in tissue; S322: Set 0-point correction. When the input time is 0, the arterial input function curve of the two-chamber model, the contrast agent time-activity curve in the myocardial tissue, the contrast agent time-activity curve in the plasma, and the contrast agent time-activity curve in the interstitium are 0, and the loss function is as follows: L init (θ)=||g(0;θ)|| 2 = 0; and S323: Physiological constraints are set to optimize the contrast agent time activity curves of the two chambers of the two-chamber model. The loss function is as follows: L phys (θ, p)=||g T (t c ;θ)-f v g0(t c ;θ)-(1-f v )(g1(t c ;θ)+g1(t c ;i))|| 2 +||v1Wg1(t c ;θ)-[F p (g0(t c ;θ)-g1(t c ;θ))+PS(g1(t c ;θ)-g1(t c ;θ))]|| 2 +||v2Wg2(t c ;θ)-[PS(g1(t c ;θ)-g2(t c ;θ)]|| 2 , Among them, L phys It indicates guiding the network to learn physiological laws, W indicates the coefficient matrix, and p indicates the kinetic parameters.

9. The method for biomedical parameter imaging and pharmacokinetic analysis based on neural network as claimed in claim 8, characterized in that: S321 includes: S3211: Acquire a set of MRI images of myocardial perfusion sorted by time; S3212: Identify the maximum change in pixel activity in the MRI image of myocardial perfusion to determine the arrival time of the contrast agent, extract the arterial input function curve and the contrast agent time activity curve in the myocardial tissue; and S3213: Utilizing the arterial input function curve and the contrast agent time-activity curve in the myocardial tissue output by the neural network model, the extracted arterial input function curve and the contrast agent time-activity curve in the myocardial tissue are fitted to optimize the neural network model.

10. The method for biomedical parameter imaging and pharmacokinetic analysis based on neural network according to claim 9, characterized in that: S3213 includes: S32131: Based on the extracted arterial input function curve and the contrast agent time activity curve in the myocardial tissue, the following formula is used to select the index of the contrast agent approximate arrival time frame to determine Initial estimate of: Wherein, i0 represents the index of the image frame closest to the moment when the contrast agent appears; S32132: Use the Newton-Raphson method to further determine the contrast agent arrival time: in, Indicates the time corresponding to the frame of image closest to the moment when the contrast agent appears. Indicates the time of contrast agent appearance; S32133: Calculate the time difference between the appearance of the contrast agent in plasma and the appearance of the contrast agent in tissue; and S32134: According to the time difference of the contrast agent appearing in the plasma and the time difference of the contrast agent appearing in the tissue, the arterial input function curve output by the neural network model and the contrast agent time activity curve in the myocardial tissue are translated to achieve accurate fitting.

11. The method for biomedical parameter imaging and pharmacokinetic analysis based on neural network according to claim 1, characterized in that: The S20 includes: S21: Preset a set of dynamic parameter values ​​and generate pre-training data; S22: setting the initial network weights of the neural network model to random, setting the initial dynamic parameters to random or empirical values, and training the neural network model using the pre-training data; and S23: Save the network weights and dynamic parameters after the neural network model training iterations as initialization parameters for subsequent training.

12. The method for biomedical parameter imaging and pharmacokinetic analysis based on neural network according to claim 1, characterized in that: In S10, the first three layers of the neural network model are composed of linear and nonlinear layers, the linear layer contains several neurons and uses a nonlinear activation function, and the last layer of the neural network model is a linear layer containing four neurons, which is used for dimensionality adjustment to approximate the time activity curve of the tracer or contrast agent.

13. The method for biomedical parameter imaging and pharmacokinetic analysis based on neural network as claimed in claim 1, characterized in that: In S10, the neural network model has a parallel processing structure, can input an array of one-dimensional time points with different characteristics as input, and output an array of time activity curves of tracers or contrast agents with different characteristics.

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