Method and apparatus for estimating the distribution of pharmacokinetic parameters in dynamic enhanced contrast magnetic resonance imaging based on a flow model and applications thereof

Abstract

The present invention discloses a method for estimating the distribution of pharmacokinetic parameters in dynamic contrast-enhanced magnetic resonance imaging based on a flow model: collecting quantitative T1 image data and DCE-MRI data, and calculating C p (t); constructing a simulation data set, including a pharmacokinetic parameter group, #imgabs0#, and C t ; constructing a parameter distribution estimation model FPDEN based on a flow model, and training the FPDEN including a parameter regression model and a flow model after training is completed by using the simulation data set; collecting quantitative T1 image data and DCE-MRI data, and calculating the intravascular contrast agent concentration curve and the corresponding tissue contrast agent concentration curve, and using them as the input of the parameter regression model in the FPDEN, and outputting the mean and standard deviation of the corresponding pharmacokinetic parameters. The present invention also provides an apparatus for estimating the distribution of pharmacokinetic parameters in dynamic contrast-enhanced magnetic resonance imaging based on a flow model. The present invention also provides an application of the above method in glioma grading. The method and apparatus can improve the accurate estimation of the distribution of pharmacokinetic parameters.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetic resonance imaging, and particularly to a method and device for estimating the distribution of pharmacokinetic parameters in dynamic contrast-enhanced magnetic resonance imaging based on a flow model, and applications thereof. Background Art

[0002] Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) technology can provide a large amount of pathological information closely related to clinical diagnosis by fitting time-series MRI signals to a tracer kinetic model. This technology has been widely used in clinical research and diagnosis. However, the pharmacokinetic parameters estimated from DCE-MRI data are affected by various factors, such as signal-to-noise ratio (SNR), native T1, start time, arterial input function, and fitting algorithms. For example, the Patlak model, one of the widely used linear tracer kinetic models, is easily affected by the signal-to-noise ratio. In addition, some non-linear tracer kinetic models, such as the Tofts model and the extended Tofts model (eTofts), have non-convex properties, which further increase the complexity of the problem. Specifically, there may be multiple combinations of pharmacokinetic parameters, and these parameter combinations may have similar fitting residuals when fitting the measured time-series MRI signals, which further increases the uncertainty of the estimation results.

[0003] To solve these problems, researchers have proposed various pharmacokinetic parameter estimation strategies. Among them, non-probabilistic methods use optimization algorithms to find the optimal pharmacokinetic parameters to fit the observed DCE-MRI data to the tracer kinetic model, such as the least squares estimation method. However, the results of these pharmacokinetic parameter estimations may exhibit large variances and do not provide information about uncertainty. The Bayesian estimation method is a classical probabilistic method that has been used in the post-processing of DCE-MRI data and has shown excellent results in terms of consistency and accuracy. The posterior distribution of pharmacokinetic parameters can indicate the probability of the true parameters appearing at any position in the parameter space, where the standard deviation is a descriptor of the uncertainty of parameter estimation. According to Bayes' theorem, the direct calculation of the posterior distribution requires an observation model and a prior distribution, and most of these conditions are unknown. An inappropriate observation model or prior assumption may reduce the accuracy of the estimation. In addition, the numerical calculation of the integral in Bayes' rule is also a relatively difficult problem.

[0004] Another way to estimate the posterior distribution of pharmacokinetic parameters is to approximate the posterior distribution by a predefined class of distributions that have a fixed number of unknown parameters (e.g., mean and variance), and use the expectation-maximization algorithm to solve for the analytical solution of the distribution parameters (KELM B M, MENZE B H, NIX O, et al. Estimating Kinetic Parameter Maps From Dynamic Contrast-Enhanced MRI Using Spatial Prior Knowledge[J / OL]. IEEE Transactions on Medical Imaging, 2009, 28(10): 1534-1547. https: / / doi.org / 10.1109 / TMI.2009.2019957). Additionally, neural network models can also be used to alleviate the complex computational problems in the solution process and have the ability to simultaneously estimate the mean and standard deviation of the posterior distribution of pharmacokinetic parameters (BLIESENER Y, ACHARYA J, NAYAK K S. Efficient DCE-MRI Parameter and Uncertainty Estimation Using a Neural Network[J / OL]. IEEE Transactions on Medical Imaging, 2020, 39(5): 1712-1723.).However, as described in existing literature (ORTON M R, COLLINSD J, WALKER-SAMUEL S, et al. Bayesian estimation of pharmacokineticparameters for DCE-MRI with a robust treatment of enhancement onset time[J / OL]. Physics in Medicine and Biology, 2007, 52(9):2393-2408. and BLIESENER Y, ACHARYA J, NAYAK K S. Efficient DCE-MRIParameter and Uncertainty EstimationUsing a Neural Network[J / OL]. IEEE Transactions on Medical Imaging, 2020, 39(5):1712-1723.), the gap between the true posterior distribution and the assumed posterior distribution may affect the estimation accuracy of pharmacokinetic parameters, so that the estimated standard deviation (uncertainty) may also be inaccurate. When assuming that the pharmacokinetic parameters follow a more general unknown distribution, in order to accurately estimate the pharmacokinetic parameters, it is very necessary to more precisely approximate the posterior distribution.

[0005] Therefore, developing an efficient and flexible method for better approximating and estimating the true posterior distribution of pharmacokinetic parameters is considered crucial. Summary of the Invention

[0006] The object of the present invention is to provide a method and device for estimating the distribution of pharmacokinetic parameters in dynamic contrast-enhanced magnetic resonance imaging based on a flow model, which can improve the accurate estimation of the distribution of pharmacokinetic parameters.

[0007] The present invention adopts the following technical solutions:

[0008] A method for estimating the distribution of pharmacokinetic parameters in dynamic contrast-enhanced magnetic resonance imaging based on a flow model, the method comprising the following steps:

[0009] (1) By collecting quantitative T1 image data and DCE-MRI data, calculating the change curve C p (t) of the intravascular contrast agent concentration;

[0010] (2) Setting the range of the pharmacokinetic model parameters to be estimated, and performing uniform random sampling within the set range to generate a group of pharmacokinetic parameters; According to C p(t) Generate the simulated contrast agent concentration change curve Based on and the pharmacokinetic model to generate the simulated DCE-MRI signal; calculate the corresponding contrast agent concentration curve C in the tissue based on the simulated DCE-MRI signal t ; the pharmacokinetic parameter group, and C t constitute the simulated data set;

[0011] (3) Construct the parameter distribution estimation model FPDEN based on the flow model: including the parameter regression network and the flow model network, and use and C t as the input of the parameter regression network, output the mean and standard deviation, and use the output mean and standard deviation to normalize the pharmacokinetic parameter group and then input it into the flow model network; perform training to obtain the trained FPDEN including the parameter regression model and the flow model;

[0012] (4) Collect the quantitative T1 image data and DCE-MRI data, and calculate the intravascular contrast agent concentration curve and the corresponding tissue contrast agent concentration curve, and use them as the input of the parameter regression model in FPDEN to output the mean and standard deviation of the corresponding pharmacokinetic parameters.

[0013] In the present invention, the pharmacokinetic model can be various pharmacokinetic models such as eTofts and Patlak. The method provided by the present invention is universal for various pharmacokinetic models and can be optionally selected according to needs.

[0014] Further, in step (2), set the range of the pharmacokinetic model parameters as K trans : [0.00001 min -1 , 1 min -1 , V p : [0.0005, 0.1], V e : [0.04, 0.6], and T1: [0.8 s, 3.5 s].

[0015] Further, in step (2), randomly sample from C p (t) and use the random linear combination method to generate the simulated contrast agent concentration change curve; specifically, randomly select two groups of C p (t) and C p1 (t) from the intravascular contrast agent concentration change curve C p2 (t) and perform random linear combination to obtain the simulated angiographic agent concentration data

[0016] Using the eTtofts model as the pharmacokinetic model to generate simulated DCE-MRI signals, specifically:

[0017] The signal of the eTofts model is obtained from the formula where S0 is the fully relaxed signal intensity before the injection of the contrast agent, TR is the echo time, α is the flip angle, and R1 = R 10 + r1C t where, R 10 is the longitudinal relaxation rate of the tissue before the injection of the contrast agent, r1 is the longitudinal relaxation rate of the contrast agent, is the concentration of the contrast agent, where k ep = K trans / v e .

[0018] Furthermore, in step (2), Rice noise is added to the simulated DCE-MRI signals.

[0019] In step (2), the parameter regression network estimates the mean and standard deviation of the parameter distribution, and the flow model network is used to learn the distribution shape of the PK parameters (pharmacokinetic parameters), and calculates the probability value of a given sampling value on the predicted distribution by combining the mean and standard deviation estimated by the regression network.

[0020] Furthermore, in step (3), the parameter regression network includes a one-dimensional convolutional neural network CNN layer, a bidirectional long short-term memory network Bi-LSTM layer, an average layer, and a fully connected layer; the data of two channels and C t are embedded into a high-dimensional space using the CNN layer and then output to the 2-layer Bi-LSTM layer to obtain outputs in two directions; the average layer calculates the average of the outputs in two directions and transmits it to two output branches composed of fully connected layers to estimate the mean and standard deviation of the parameter distribution.

[0021] Furthermore, in step (3), the flow model network uses an adapted RealNVP network structure, including 6 affine coupling layers.

[0022] Furthermore, in step (3), the training of the parameter regression network and the flow model network uses the maximum likelihood estimation loss function, and the training objective is to maximize the log-likelihood value of the given PK parameters on the predicted distribution.

[0023] The specific steps of step (3) are as follows: taking the tissue contrast agent concentration curve and the corresponding intravascular contrast agent concentration curve generated in step (2) as the input of the parameter regression network, outputting the mean value and the standard deviation, taking the PK parameter corresponding to this curve as a sampling value from the true distribution of the parameter, normalizing this sampling value using the output mean value and standard deviation, and then inputting it into the flow model network to calculate its log-likelihood value.

[0024] In step (3), the training of the model uses the maximum likelihood estimation loss function, and the training objective of the model is to maximize the log-likelihood value of the given PK parameter on the predicted distribution. After the network training converges, the optimized model parameters are obtained.

[0025] The specific steps of step (4) are as follows: using the acquired T1 quantitative image and the corresponding DCE-MRI signal collected, calculating the intravascular contrast agent concentration curve. Then, calculate the contrast agent concentration curve of the tissue pixel by pixel. For each pixel, taking the intravascular contrast agent concentration curve and the tissue contrast agent concentration curve as the input of the regression model obtained in step (4), and outputting the mean value and the standard deviation of the corresponding pharmacokinetic parameter.

[0026] The present invention also provides an application of the above-mentioned method for estimating the distribution of pharmacokinetic parameters in dynamic contrast-enhanced magnetic resonance imaging based on the flow model in glioma grading.

[0027] Furthermore, the application is for glioma grading not for the purpose of disease diagnosis.

[0028] Glioma grading can be used in scientific research. For example, by revealing the differences in gene expression and signal pathway activity among gliomas of different grades, it helps researchers conduct more refined patient stratification and data standardization, and further provides strong support in aspects such as drug development, treatment strategy optimization, resource allocation, and multidisciplinary cross-research.

[0029] Furthermore, the mean value of the estimated pharmacokinetic parameter distribution is used as the actual estimated value of the parameter to be estimated, and the standard deviation of the distribution is used as the uncertainty index of the parameter to be estimated, which is used to filter unreliable actual estimated values, and the filtered actual estimated values are applied to glioma grading.

[0030] In the present invention, the distribution of the estimated pharmacokinetic parameters includes two indicators, the mean value and the standard deviation. Among them, the mean value is used as the actual value of the parameter to be estimated for glioma grading, and the standard deviation is the uncertainty, which is used to identify whether the estimated parameter is reliable. Estimated values with greater uncertainty will be excluded and thus do not participate in the calculation of glioma grading, thereby improving the accuracy when using the estimated pharmacokinetic parameters as the basis for glioma grading.

[0031] Further, the glioma grading is to distinguish between low-grade and high-grade gliomas, and between grade III and grade IV gliomas.

[0032] The present invention also provides a device for estimating the distribution of pharmacokinetic parameters in dynamic contrast-enhanced magnetic resonance imaging based on a flow model, comprising:

[0033] An image acquisition and processing module, which calculates the intravascular contrast agent concentration change curve C p (t) by collecting quantitative T1 image data and DCE-MRI data;

[0034] A data set construction module, which sets the range of the pharmacokinetic model parameters to be estimated, performs uniform random sampling within the set range to generate a pharmacokinetic parameter group; generates a simulated contrast agent concentration change curve based on C p (t) Based on and the pharmacokinetic model to generate simulated DCE-MRI signals; calculates the corresponding tissue contrast agent concentration curve C t ; the pharmacokinetic parameter group, and C t constitute a simulated data set;

[0035] A model construction and training module, which constructs a parameter distribution estimation model FPDEN based on a flow model: including a parameter regression network and a flow model network, using and C t as the input of the parameter regression network, outputs the mean and standard deviation, normalizes the pharmacokinetic parameter group using the output mean and standard deviation and inputs it into the flow model network; performs training to obtain the trained FPDEN including the parameter regression model and the flow model;

[0036] A detection module, which collects quantitative T1 image data and DCE-MRI data, calculates the intravascular contrast agent concentration curve and the corresponding tissue contrast agent concentration curve, and uses them as the input of the parameter regression model in FPDEN to output the mean and standard deviation of the corresponding pharmacokinetic parameters.

[0037] The present invention also provides a computing device, comprising a memory and one or more processors, wherein the memory stores executable code, and when the one or more processors execute the executable code, it is used to implement the above-mentioned method for estimating the distribution of pharmacokinetic parameters in dynamic contrast-enhanced magnetic resonance imaging based on a flow model.

[0038] The present invention also provides a computer-readable storage medium, on which a program is stored, and when the program is executed by a processor, it is used to implement the above-mentioned method for estimating the distribution of pharmacokinetic parameters in dynamic contrast-enhanced magnetic resonance imaging based on a flow model.

[0039] In the prior art, there are various uncertainties and variabilities in the estimation methods of PK parameters, which affect their application effects in clinical research and diagnosis. To solve this problem, the present invention provides a method and device for estimating the distribution of pharmacokinetic parameters of DCR-MRI based on a flow model. The parameter distribution estimation model FPDEN based on the flow model is used to adaptively learn and approximate the posterior distribution of pharmacokinetic (PK) parameters: The method provided by the present invention adopts a flow model, which can learn a series of reversible transformations from the dataset and convert the complex parameter distribution into a simple distribution with an analytical solution, thereby realizing the accurate estimation of the PK parameter distribution. In addition, the present invention also introduces a reparameterization strategy to improve the feasibility of the parameter distribution estimation model.

[0040] Therefore, the present invention has the following advantages:

[0041] (1) Highly accurate parameter estimation: The present invention uses a flow model to learn the posterior distribution of PK model parameters in a data-driven manner, which is significantly better than the traditional method that relies on a predefined posterior distribution, thus ensuring a more accurate estimation of PK parameters.

[0042] (2) Enhanced uncertainty assessment: The standard deviation in the pharmacokinetic parameter distribution estimated by the present invention can be used as a reliable uncertainty index, which helps to effectively identify and exclude unreliable parameter (mean) results; further, it can provide a solid basis for medical decision-making.

[0043] (3) The method and device provided by the present invention can also provide valuable uncertainty indicators for downstream tasks (for example, glioma grading of in-vivo data), thereby improving their performance. Such as excellent classification performance: In the World Health Organization (WHO) grading task of glioma, the present method can effectively distinguish different grades, which can be used for scientific research and can also provide more accurate diagnostic references for clinicians. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a schematic diagram of the framework and network structure proposed by the present invention.

[0045] Figure 2 It is the relationship between the average uncertainty and the estimated mean absolute error under different noise levels.

[0046] Figure 3 It is an example of the parameter map, the corresponding uncertainty map, and the parameter SNR map estimated by the method provided in the embodiment.

[0047] Figure 4 The uncertainty estimated by the method provided in the embodiment can be used to improve the glioma classification performance. DETAILED DESCRIPTION OF THE INVENTION

[0048] To make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not limit the protection scope of the present invention.

[0049] The model proposed by the present invention is implemented based on the Pytorch framework.

[0050] The method for estimating the distribution of pharmacokinetic parameters in dynamic enhanced contrast magnetic resonance imaging based on a flow model provided by the present invention mainly includes the following steps:

[0051] S1: By collecting quantitative T1 image data and DCE-MRI data, calculate the change curve C p (t) of the intravascular contrast agent concentration for each subject.

[0052] S1-1: Place the subject in a 3T magnetic resonance imaging system, and use the center of the head as the scanning center point to collect head images. In this embodiment, magnetic resonance data of 53 subjects were collected in total.

[0053] S1-2: Before injecting the contrast agent, set the flash3D sequence to obtain T1 images. The double flip angle fast low angle shot (FLASH) technique was used, and the number of axial slices was 80. The voxel size was 0.9×0.9×1.5mm 3 , the field of view (FOV) was 340×340×120mm 3 , and the matrix size was 384×384. The echo time (TE) was set to 2.46ms, the repetition time (TR) was 6ms, and the flip angles were 2° and 14°. GRAPPA reconstruction was applied, and the acceleration factor (R) was 2 without distortion.

[0054] S1-3: In the contrast agent injection stage, first administer gadopentetate dimeglumine (Gd-DTPA; Bayer, Berlin, Germany) at 0.1 mmol / kg body weight within 48 seconds. Subsequently, flush with 15 mL of saline at a speed of 2.0 mL / s. At the same time, the three-dimensional (3D) CAIPIRINHA-TWIST technique was used, and its voxel size was 0.9×0.9×1.5mm 3 , the FOV was 340×340×120mm 3, the matrix size is 384×384, there are 80 slices, TE is 2.46 ms, TR is 6 ms, and the flip angle is 10°. The TWIST view sharing adopts a forward sharing strategy and adjusts the spatial dimension parameters, thus obtaining a time resolution of 4.5 seconds. The overall scan time is about 10 minutes. To minimize motion artifacts, sponges are placed beside the ears to fix the head. In addition, to overcome the potential noise during MRI scanning, all DCE-MRI data and T1 maps are registered to the baseline (the fourth frame) DCE-MRI 3D data acquired before injecting the contrast agent using a rigid transformation performed by FLIRT in FSL (http: / / www.fmrib.ox.ac.uk / fs1). And the data is checked to ensure that the amplitude of head movement ≤ 2 mm.

[0055] S1-4: Calculate the intravascular contrast agent concentration change curve C p (t) from the experimental DCE-MRI data. Specifically, manually select the key region ROI in the sagittal sinus from the acquired DCE-MRI data, regard it as a single component, average the data within the ROI, and calculate the intravascular contrast agent concentration change curve C p (t) through its signal change.

[0056] Furthermore, to ensure the accuracy of the calculation results, the acquired 3D T1 quantitative images need to be registered to the fourth frame of the DCE-MRI using a registration tool. Similarly, for the DCE-MRI data of other time frames except the fourth frame, they also need to be registered to the fourth frame to reduce the influence of the slight movement of the subject's head during the scanning process on the scanning results.

[0057] S2: Generate a simulation data set: Set the range of the pharmacokinetic model parameters to be estimated, and perform uniform random sampling within the set range to generate a set of pharmacokinetic parameters; Generate a simulated contrast agent concentration change curve based on C p (t) Based on and the pharmacokinetic model to generate simulated DCE-MRI signals; Calculate the corresponding tissue contrast agent concentration curve C t ; The set of pharmacokinetic parameters, and C t constitute a simulation data set.

[0058] S2-1: Set the range of the pharmacokinetic model parameters as K trans : [0.00001 min -1 , 1 min -1 , V p : [0.0005, 0.1], V e: [0.04, 0.6], and T1: [0.8s, 3.5s].

[0059] S2-2: Randomly sample from C p (t) and use the random linear combination method to generate the simulated contrast agent concentration change curve. Specifically: Randomly select two groups of C p (t) from the intravascular contrast agent concentration change curve C p1 (t) and C p2 (t) and perform random linear combination to obtain the simulated angiographic contrast agent concentration data

[0060] S2-3: Use the eTtofts model to generate DCE-MRI data. Among them, the signal of the eTtofts model is obtained from the formula , where S0 is the fully relaxed signal intensity before contrast agent injection, TR is the echo time, α is the flip angle, R1 = R 10 +r1C t , where, R 10 is the longitudinal relaxation rate of the tissue before injecting the contrast agent, r1 is the longitudinal relaxation rate of the contrast agent, is the contrast agent concentration, where k ep =K trans / v e .

[0061] S2-4: Add Rician noise with different intensities to the synthesized signal so that the SNR of the DCE-MRI signal before contrast agent injection varies between 21.8 dB and 36.98 dB (the average SNR is 27.80 dB). This refers to the average SNR of the whole brain of 53 patients in the dataset. This can make the model provided by the present invention robust to a series of SNRs.

[0062] S2-5: Synthesize 500,000 DCE-MRI signals. From the synthesized signals, select 400,000 signals as training data for training and validation, and 100,000 signals as test data to evaluate the model performance. Extract 20% from the training data, that is, 80,000 signals, and set them as the validation set to monitor the training process and prevent overfitting. Specifically, use the C of 46 subjects p (t) to synthesize the training set data, use the C of the remaining 11 subjects p (t) to synthesize the test set data; and calculate the corresponding contrast agent concentration curve in the tissue according to the DCE-MRI signal.

[0063] S3: Construct a flow model-based parameter distribution estimation model (FPDEN): FPDEN includes a parameter regression network and a flow model network.

[0064] Among them, the parametric regression network estimates the mean and standard deviation of the parameter distribution, and the flow model network is used to learn the distribution shape of the parameters and calculate the probability value of the given sampling value on the predicted distribution.

[0065] Specifically, using the Pytorch toolkit in the Python language, construct a parameter distribution estimation network model based on the flow model as shown in Figure 1 : Figure 1 (a) in shows the overall framework and the calculation method of maximum likelihood estimation in the network operation process; Figure 1 (b) in describes the regression network structure based on LSTM; Figure 1 (c) in shows the structure of the affine coupling layer that makes up the flow model.

[0066] In this embodiment, the FPDEN model structure mainly includes a parametric regression network and a flow model network: The regression network shown in Figure 1 (b) first embeds the data C t (t) and C p (t) of two channels into a high-dimensional space using a one-dimensional convolutional neural network (CNN) layer with a kernel size of 3, and uses the ReLU activation function. Then, these high-dimensional features are input into a 2-layer bidirectional long short-term memory network (Bi-LSTM) for time series processing. The average value of the outputs in the two directions of the Bi-LSTM is calculated and transmitted to two output branches composed of fully connected layers to estimate the mean and standard deviation of the parameter distribution, where the uncertainty output branch is defined as logσ, and the output dimensions of the hidden units of the LSTM, the fully connected layers, and the CNN are all 128.

[0067] The flow model network structure uses an adapted RealNVP network structure, which consists of 6 affine coupling layers, and the structure of each coupling layer is as shown in Figure 1 (c). Among them, s k and t k are both implemented by 3 fully connected layers with 64 neurons. In each layer, the specified d reserved dimensions (i.e., the identity transformation dimensions) are randomly selected, and after the model is constructed, these dimensions will be fixed and no longer changed.

[0068] Among them, Figure 1 Regression network in is the regression network, training pathway is the training path, Inference pathway is the inference path, Learned distribution is the learned distribution, Basedistribution is the basic distribution, Affi

[0069] Specifically, the flow model network is constructed using a real-valued non-volume preserving (RealNVP) model. This model consists of a series of simple mappings and can be expressed as:

[0070]

[0071] where g k is the k-th simple mapping g, called the affine coupling layer, representing the composition of functions. In each layer within the flow model, the input is divided into two parts and transformed through the following formula:

[0072] z out，1 = z in，1

[0073]

[0074] where ⊙ represents element-wise multiplication, and s and t are the scale and translation functions. The Jacobian determinant of this transformation can be expressed as:

[0075]

[0076] Due to its triangular shape, its determinant can be efficiently calculated as: where j = 1, 2,..., D - d represents the index variable.

[0077] S4: Network training: Take and C t as the input of the parameter regression network, output the mean and standard deviation, normalize the pharmacokinetic parameter group using the output mean and standard deviation and then input it into the flow model network; perform training to obtain the FPDEN including the parameter regression model and the flow model after training is completed.

[0078] Specifically: Take the tissue contrast agent concentration curve and the corresponding intravascular contrast agent concentration curve generated in the training set in step (2) as the input of the parameter regression network, output the mean and standard deviation, the PK parameter corresponding to this curve is used as a sampling value from the true parameter distribution, normalize this sampling value using the output mean and standard deviation, and then input it into the flow model to calculate its log-likelihood value. The training of the model uses the maximum likelihood estimation loss function, and the training objective of the model is to maximize the log-likelihood value of the given PK parameter on the predicted distribution. After the network training converges, the optimized model parameters are obtained.

[0079] The regression network and the flow model are trained simultaneously in an end-to-end manner. During the training process, both the regression model and the normalizing flow model are trained for 80,000 iterations using the Adam optimizer with a learning rate of 0.0005 and momentum values β1 and β2 of 0.9 and 0.999, respectively. In all network trainings, the batch size is set to 128.

[0080] The network is trained using the maximum likelihood estimation loss function and the reparameterization technique, and its expression is:

[0081]

[0082] where “. / ” is the Hadamard division (i.e., element-wise division), Ψ represents the learnable parameters of FPDEN, p X is the parameter distribution learned by the flow model, x s is the PK parameter value given during the network training process, and are the mean and standard deviation of the distribution estimated by the regression network, respectively.

[0083] Since the uncertainty branch of the parameter regression network may be negative. To avoid this situation, the output of the regression network is defined as The true standard deviation is calculated by taking the exponential power of the output with base e.

[0084] S5: PK parameter estimation: Using the acquired T1 quantitative images and the corresponding DCE-MRI signals collected, calculate the intravascular contrast agent concentration curve. Then, calculate the contrast agent concentration curve of the tissue pixel by pixel. For each pixel, use the intravascular contrast agent concentration curve and the tissue contrast agent concentration curve as the input of the regression model obtained in step (4), and output the mean and standard deviation of the corresponding pharmacokinetic parameters.

[0085] Evaluation of the flow model-based parameter distribution estimation model FPDEN: To prove the effectiveness of the proposed flow model-based distribution estimation network, the maximum likelihood estimation (MLE) loss method based on the flow model is compared with the traditional regression method, that is, using and the method of loss. Specifically, the traditional regression network has a similar regression model structure to the network framework proposed in the present invention, but only has a mean prediction branch and no standard deviation prediction branch.

[0086] In addition, the present invention also compared the influence of the distribution assumption of parameters on the regression performance to prove the accuracy of the present invention. This was achieved by replacing the distribution learned from the flow model with a multivariate Gaussian distribution. This replacement resulted in the use of loss in model training. Finally, the effect of this change in the distribution assumption was compared. In addition, the mean squared error (MSE) between the mean μ of the output of the regression network and the actual value was calculated to evaluate the parameter estimation performance.

[0087] Table 1 shows the quantitative comparison results of the regression model results trained using different loss functions on the test dataset. It can be observed from Table 1 that the models trained using the MLE loss and outperformed the models trained using traditional losses ( and ). The MLE method using the flow model to learn the distribution produced the best parameter estimation, and its performance exceeded the other three methods.

[0088] Table 1 Mean Squared Error (MSE) of the parametric regression model trained using different losses

[0089]

[0090] Verification of the uncertainty of the parametric distribution estimation model FPDEN based on the flow model: To evaluate the uncertainty of the output of the regression network, the σ of each parameter was considered as an index of the degree of uncertainty of the result. The Monte-Carlo (MC) simulation method was used to study the relationship between uncertainty and the signal-to-noise ratio (SNR) in the simulated World Health Organization (WHO) grade IV glioma tissue (K trans =0.158 min -1 , V p =0.106, V e =0.451). In this simulation, DCE-MRI signals with specific parameter values were used, and Rice noise with different degrees was added to the signals. 100 noise addition experiments were conducted for each SNR scenario, and thus the mean absolute error (MAE) and average uncertainty for each SNR scenario were calculated.

[0091] This embodiment simulated the DCE-MRI signals of WHO grade IV glioma tissue, added Rice noise with a specified intensity to simulate different SNRs, and conducted 100 noise realizations for each SNR case to calculate the MAE and average uncertainty. Figure 2The left column of (a)-(c) in [Figure] shows the relationship between uncertainty and SNR. In the right column, the dots represent the predicted MAE for each case of uncertainty (each average uncertainty is from the corresponding SNR). The dashed line represents the result of using linear regression to fit the estimated mean error to the uncertainty of the output, and its correlation coefficient (R^2) is marked in Figure 2 it.

[0092] Figure 2 (a)-(c) in [Figure] reveals that as the SNR decreases, the uncertainties of the three parameters K trans , V p and V e all increase. At the same time, there is a strong correlation between uncertainty and the MAE of the estimated values under 100 signal-to-noise realizations, especially for V p (R 2 = 0.974) and V e (R 2 = 0.938). Uncertainty effectively reflects the estimation error.

[0093] Among them, Figure 2 Mean Uncertainty in [Figure] is the average uncertainty, and MAE (Mean Absolute Error) is the mean absolute error.

[0094] Figure 3 [Figure] shows the parameter maps of the glioma region containing in vivo data. The parameter SNR map is calculated by treating the estimated parameter as the signal and the estimated uncertainty as the noise level. The uncertainty of V e shows the largest difference between the tumor and non-tumor regions, while for V p and K trans , the difference in uncertainty between these two regions is less than that of V e . In the tumor region, all three parameters show relatively high parameter SNR. More specifically, although the proposed model gives the results of V e in both the tumor region and the normal tissue region, the uncertainty generated in the tumor region is lower and that in the non-tumor region is larger. This result indicates that only the V e value in the tumor region is relatively reliable, and this region has a larger K trans and V e parameter SNR.

[0095] Among them, Figure 3 Estimated in [Figure] is the estimated parameter value, Uncertainty is the parameter uncertainty, and SNR is the signal-to-noise ratio of the parameter.

[0096] Verify the parameter distribution estimation model FPDEN based on the flow model on in vivo data. Use the MRI scan parameters described in step (1) to collect DCE-MRI data of 53 subjects who have been clinically diagnosed with glioma. Among them, 11 cases of WHO grade II are defined as low-grade gliomas, and 42 cases including 11 cases of WHO grade III and 31 cases of WHO grade IV are defined as high-grade gliomas. Then, professionals draw the tumor area as the ROI. Calculate the average value of the PK parameters within the ROI as an indicator for glioma grading.

[0097] The uncertainty estimated by the model can be used as the basis for parameter screening in the task of glioma grading using DCE-MRI data. As shown in (a) of Figure 4 , it shows the data processing flow using uncertainty filtering (UF). When using UF, only the PK parameters of some selected pixels within the ROI are used to calculate the PK average value. During this UF process, the uncertainty of each parameter within each voxel is independently evaluated: parameters with higher confidence are retained, while parameters with lower confidence are filtered out. To represent the relative uncertainty, a coefficient of variation (COV) is defined and calculated by the formula (that is . As a measure of parameter uncertainty, the larger the COV, the less reliable the parameter); through the COV (coefficient of variation) threshold, an uncertainty mask is generated using the uncertainty map, and only reliable parameters are used to calculate the average value of the parameters within the tumor area. When the COV value of a parameter exceeds 0.2, the parameter will be excluded in the UF screening. In this experiment, two main glioma grading tasks are used for verification: distinguishing low-grade from high-grade gliomas, and distinguishing grade III from grade IV gliomas. To evaluate the classification accuracy, the receiver operating characteristic curve (ROC) and AUC are applied. And the DeLong test is used to compare the differences in AUC values between the two scenarios of using and not using UF.

[0098] Among them, Figure 4 Parameter Map is the parameter map, Uncertainty Mask is the uncertainty mask, Ucertainty Map is the uncertainty map, Masked Parameter Map is the filtered parameter map, Sensitivity is the sensitivity, and Specificity is the specificity.

[0099] Using uncertainty filtering (UF) can improve the classification performance of glioma grading. As shown in (b) and (c) of Figure 4 , they respectively show the use of Ve The ROC curve for glioma grading. The dashed and solid lines represent the cases without and with UF, respectively. Only after applying UF, V e showed its effectiveness in grading low-grade vs. high-grade and grade III vs. grade IV gliomas (AUC > 0.5, and the AUC values are marked in the legend). UF increased the AUC for classifying low-grade and high-grade gliomas from 0.168 to 0.662, and at the same time, the AUC for classifying grade III and grade IV gliomas increased from 0.418 to 0.711. When using V e for glioma grading, there was a statistically significant difference between the two: the increase in AUC by UF was very significant in low-grade and high-grade gliomas (p < 0.001), while it reached a significant level in grade III and grade IV gliomas (p < 0.05).

[0100] Based on the same inventive concept, an embodiment of the present invention further provides a device for estimating the distribution of pharmacokinetic parameters in dynamic contrast-enhanced magnetic resonance imaging based on a flow model, including:

[0101] An image acquisition and processing module, by acquiring quantitative T1 image data and DCE-MRI data, calculates the change curve C p (t) of the intravascular contrast agent concentration;

[0102] A dataset construction module, sets the range of the pharmacokinetic model parameters to be estimated, and performs uniform random sampling within the set range to generate a set of pharmacokinetic parameters; generates a simulated contrast agent concentration change curve based on C p (t) Based on and the pharmacokinetic model to generate simulated DCE-MRI signals; calculates the corresponding tissue contrast agent concentration curve C t ; the set of pharmacokinetic parameters, and C t constitute a simulated dataset;

[0103] A model construction and training module, constructs a parameter distribution estimation model FPDEN based on a flow model: including a parameter regression network and a flow model network, takes and C t as the inputs of the parameter regression network, outputs the mean and standard deviation, normalizes the set of pharmacokinetic parameters using the output mean and standard deviation and then inputs them into the flow model network; performs training to obtain the trained FPDEN including the parameter regression model and the flow model;

[0104] The detection module collects quantitative T1 image data and DCE-MRI data, calculates the intravascular contrast agent concentration curve and the corresponding tissue contrast agent concentration curve, and uses them as the input of the parameter regression model in FPDEN, and outputs the mean and standard deviation of the corresponding pharmacokinetic parameters.

[0105] Based on the same inventive concept, an embodiment of the present invention further provides a computing device, including one or more processors, and an executable code is stored in the memory. When the processor executes the executable code, it is used to implement the pharmacokinetic parameter distribution estimation method in the dynamic contrast-enhanced magnetic resonance imaging based on the flow model in the above embodiment. Taking software implementation as an example, as a logically meaningful device, it is formed by the processor of any device with data processing capabilities reading the corresponding computer program instructions in the non-volatile memory into the memory and running. In terms of hardware, in addition to the processor, memory, network interface, and non-volatile memory, any device with data processing capabilities where the device in the embodiment is located usually includes other hardware according to the actual functions of the device with data processing capabilities, which will not be elaborated here.

[0106] Based on the same inventive concept, an embodiment of the present invention further provides a computer-readable storage medium, on which a program is stored. When the program is executed by the processor, it implements the pharmacokinetic parameter distribution estimation method in the dynamic contrast-enhanced magnetic resonance imaging based on the flow model in the above embodiment: The computer-readable storage medium can be the internal storage unit of any device with data processing capabilities described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium can also be any device with data processing capabilities, such as a plug-in hard disk, a smart media card (SMC), an SD card, a flash card (Flash8 Card), etc. equipped on the device. Further, the computer-readable storage medium can also include both the internal storage unit of any device with data processing capabilities and external storage devices. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capabilities, and can also be used to temporarily store the data that has been output or will be output.

[0107] The above specific embodiments have detailed the technical solutions and beneficial effects of the present invention. It should be understood that the above is only the most preferred embodiment of the present invention and is not used to limit the present invention. Any modifications, supplements, equivalent replacements, etc. made within the scope of the principles of the present invention should be included in the protection scope of the present invention.

Claims

1. Application of the method for estimating the distribution of pharmacokinetic parameters in dynamic enhanced contrast magnetic resonance imaging based on a flow model in glioma grading, characterized in that, The method includes the following steps: (1) By collecting quantitative T1 image data and DCE-MRI data, calculate the change curve C p (t) of the intravascular contrast agent concentration; (2) Set the range of the pharmacokinetic model parameters to be estimated, and perform uniform random sampling within the set range to generate a group of pharmacokinetic parameters; According to C p (t) Generate a simulated contrast agent concentration change curve Based on and the pharmacokinetic model to generate simulated DCE-MRI signals; Calculate the corresponding contrast agent concentration curve C t in the tissue based on the simulated DCE-MRI signals; The pharmacokinetic parameter group, and C t constitute a simulated data set; (3) Construct a parameter distribution estimation model FPDEN based on a flow model: including a parameter regression network and a flow model network. Take and C t as the input of the parameter regression network, output the mean and standard deviation. After normalizing the pharmacokinetic parameter group using the output mean and standard deviation, input it into the flow model network; perform training to obtain the trained FPDEN including the parameter regression model and the flow model; (4) Acquire quantitative T1 image data and DCE-MRI data, calculate the intravascular contrast agent concentration curve and the corresponding tissue contrast agent concentration curve, and use them as the input of the parameter regression model in FPDEN to output the mean and standard deviation of the corresponding pharmacokinetic parameters; The mean of the estimated pharmacokinetic parameter distribution is used as the actual estimated value of the parameter to be estimated, and the standard deviation of the distribution is used as the uncertainty index of the parameter to be estimated, which is used to filter unreliable actual estimated values, and the filtered actual estimated values are applied to glioma grading.

2. Application of the method for estimating the distribution of pharmacokinetic parameters in dynamic contrast-enhanced magnetic resonance imaging based on a flow model in glioma grading according to claim 1, characterized in that, In step (2), the range of the pharmacokinetic model parameters is set as K trans :[0.00001 min -1 , 1 min -1 , V p :[0.0005, 0.1], V e :[0.04, 0.6], and T1: [0.8 s, 3.5 s].

3. Use of the method for estimating the distribution of pharmacokinetic parameters in dynamic contrast-enhanced magnetic resonance imaging based on a flow model according to claim 1 in glioma grading, characterized in that, In step (2), randomly sample from C p (t), and use the random linear combination method to generate a simulated contrast agent concentration change curve Use the eTtofts model as the pharmacokinetic model to generate simulated DCE-MRI signals, specifically: The signal of the eTofts model is given by the formula where S0 is the fully relaxed signal intensity before contrast agent injection, TR is the echo time, α is the flip angle, and R1 = R 10 + r1C t , where R 10 is the longitudinal relaxation rate of the tissue before contrast agent injection, r1 is the longitudinal relaxivity of the contrast agent, is the contrast agent concentration, and where k ep = K trans / v e .

4. Application of the method for estimating the distribution of pharmacokinetic parameters in dynamic contrast-enhanced magnetic resonance imaging based on a flow model according to claim 1 in glioma grading, characterized in that, In step (2), add Rice noise to the simulated DCE-MRI signals.

5. Use of the method for estimating the distribution of pharmacokinetic parameters in dynamic contrast-enhanced magnetic resonance imaging based on a flow model according to claim 1 in glioma grading, characterized in that, In step (3), the parameter regression network includes a one-dimensional convolutional neural network CNN layer, a bidirectional long short-term memory network Bi-LSTM layer, an average layer, and a fully connected layer; the data of the two channels and C t are embedded into a high-dimensional space using the CNN layer and then output to the 2-layer Bi-LSTM layer to obtain outputs in two directions; The average layer calculates the average of the outputs in two directions and transmits it to two output branches composed of fully connected layers to estimate the mean and standard deviation of the pharmacokinetic parameter distribution.

6. Use of the method for estimating the distribution of pharmacokinetic parameters in dynamic enhanced contrast magnetic resonance imaging based on a flow model according to claim 1 in glioma grading, characterized in that, In step (3), the flow model network uses the adapted RealNVP network structure, including 6 affine coupling layers.

7. Use of the method for estimating the distribution of pharmacokinetic parameters in dynamic contrast-enhanced magnetic resonance imaging based on a flow model according to claim 1 in glioma grading, characterized in that, In step (3), the training of the parameter regression network and the flow model network uses the maximum likelihood estimation loss function, and the training goal is to maximize the log-likelihood value of the pharmacokinetic parameter group on the predicted distribution.

8. Use of the method for estimating the distribution of pharmacokinetic parameters in dynamic contrast-enhanced magnetic resonance imaging based on a flow model according to claim 1 in glioma grading, characterized in that, The glioma grading is to distinguish low-grade and high-grade gliomas, and to distinguish grade III and grade IV gliomas.

9. Application of a device for estimating the distribution of pharmacokinetic parameters in dynamic enhanced contrast magnetic resonance imaging based on a flow model in glioma grading, characterized in that, Including: An image acquisition and processing module calculates the change curve C p (t) of the intravascular contrast agent concentration by collecting quantitative T1 image data and DCE-MRI data; A dataset construction module sets the range of pharmacokinetic model parameters to be estimated, performs uniform random sampling within the set range, and generates a set of pharmacokinetic parameters; according to C p (t) generates a simulated contrast agent concentration change curve Based on and the pharmacokinetic model to generate simulated DCE-MRI signals; based on the simulated DCE-MRI signals, calculate the corresponding contrast agent concentration curve C t in the tissue; the set of pharmacokinetic parameters, and C t constitute a simulated dataset; Model construction and training module, based on the parameter distribution estimation model FPDEN of the flow model: including a parameter regression network and a flow model network, taking and C t as the input of the parameter regression network, outputting the mean and standard deviation, normalizing the pharmacokinetic parameter group using the output mean and standard deviation and then inputting it into the flow model network; Train to obtain the trained FPDEN including a parameter regression model and a flow model; A detection module that acquires quantitative T1 image data and DCE-MRI data, calculates the intravascular contrast agent concentration curve and the corresponding tissue contrast agent concentration curve, and uses them as the input of the parameter regression model in FPDEN to output the mean and standard deviation of the corresponding pharmacokinetic parameters; The mean of the estimated pharmacokinetic parameter distribution is used as the actual estimated value of the parameter to be estimated, and the standard deviation of the distribution is used as the uncertainty index of the parameter to be estimated, which is used to filter unreliable actual estimated values, and the filtered actual estimated values are applied to glioma grading.

10. A computing device, characterized in that, It includes a memory and one or more processors. Executable code is stored in the memory. When the one or more processors execute the executable code, it is used to implement the application of the method for estimating the pharmacokinetic parameter distribution in dynamic contrast-enhanced magnetic resonance imaging based on a flow model according to any one of claims 1-7 in glioma grading.

11. A computer-readable storage medium having a program stored thereon, characterized in that, When the program is executed by the processor, it is used to implement the application of the method for estimating the pharmacokinetic parameter distribution in dynamic contrast-enhanced magnetic resonance imaging based on a flow model according to any one of claims 1-7 in glioma grading.

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