Method for optimizing sampling trajectory of molecular exchange magnetic resonance measurement, and molecular exchange magnetic resonance measurement method and apparatus

Abstract

Disclosed in the present invention is a method for optimizing a sampling trajectory of molecular exchange magnetic resonance measurement. The method comprises: (1) determining the number of physiological / physical parameters of a molecular exchange system and a corresponding range, and generating a data set of simulated physiological / physical parameters; (2) determining a molecular exchange magnetic resonance measurement method, and setting collection parameters; (3) constructing an end-to-end unified network model, which comprises a sampling trajectory optimization network, a noise signal generation network and a parameter estimation network; and (4) using the simulated physiological / physical parameters as an input for training, and completing the training until the network converges, so as to obtain an optimized sampling trajectory and a corresponding parameter estimation network. Further disclosed in the present invention are a molecular exchange magnetic resonance measurement method and apparatus. The method for optimizing a sampling trajectory of molecular exchange magnetic resonance measurement that is provided in the present invention improves the efficiency and accuracy for estimating physiological / physical parameters, and can be applied to different molecular exchange magnetic resonance measurement methods.

Description

A method for optimizing molecular exchange magnetic resonance measurement sampling trajectory, molecular exchange magnetic resonance measurement method and device Technical Field

[0001] The present invention belongs to the technical field of magnetic resonance quantitative measurement, and in particular relates to a method for optimizing a molecular exchange magnetic resonance measurement sampling trajectory, a molecular exchange magnetic resonance measurement method and a device. Background Art

[0002] Multidimensional nuclear magnetic resonance (NMR) spectroscopy can provide comprehensive and detailed analysis of complex molecular systems and is widely favored in biological research as a non-invasive technique [Bai R, Benjamini D, Cheng J, et al. Fast, accurate 2D-MR relaxation exchange spectroscopy (REXSY): Beyond compressed sensing [J]. The Journal of chemical physics, 2016, 145(15): 154-202]. However, the long acquisition time of multidimensional spectroscopy techniques limits their application to analyzing fast dynamics under specific physical conditions and studying human / animal in vivo. For example, the diffusion exchange spectroscopy (DEXSY) method [Callaghan PT, Furo I. Diffusion-diffusion correlation and exchange as a signature for local order and dynamics [J]. The Journal of chemical physics, 2004, 120 (8): 4032-4038] measures the molecular exchange process based on the different apparent diffusion rates of molecules in different microenvironments or chambers. The sequence diagram is shown in (a) of Figure 2. It consists of two independent diffusion coding modules and is separated by a time mixing module. It is a three-dimensional acquisition sequence including a first diffusion module-mixing module-second diffusion module. The corresponding acquisition variables of each module are diffusion weight b1, exchange / mixing time tm, and diffusion weight b2. For each signal point, it is necessary to collect separately under specific first and second diffusion codes and mixing time, so the DEXSY technology is very time-consuming.

[0003] Real-time measurement of molecular exchange is of great significance in the study of dynamic chemical processes and in vivo biological studies. Currently, many studies have proposed methods to accelerate the measurement of molecular exchange. Ultrafast nuclear magnetic resonance (UF NMR) spectroscopy uses the basic principles of magnetic resonance imaging (MRI) to spatially encode the incremental evolution time into each layer of the sample, thereby obtaining a multidimensional spectrum within a single scan [Mankinen O, Zhivonitko VV, Selent A, et al. Ultrafast diffusion exchange nuclear magnetic resonance [J]. Nature Communications, 2020, 11 (1): 3251]. However, the sensitivity of the results obtained by a single scan of UF NMR technology is limited, and it is impossible to achieve short scanning time and high resolution at the same time [Giraudeau P, Akoka S. Sources of sensitivity losses in ultrafast 2D NMR [J]. Journal of Magnetic Resonance, 2008, 192 (1): 151-158]. Therefore, the application of this technology in exploring complex systems is hindered. Another group of studies proposed to shorten the scanning time by downsampling in the b1-b2 space, for example, a sampling ratio of 10% corresponds to a 10-fold speedup. S. Ramadan proposed Diffusion-Exchange Weighted Imaging (DEWI) [Ramadan S. Diffusion-exchange weighted imaging [J]. Magnetic Resonance Insights, 2009, 3: MRI. S3504], which requires that the b-values ​​of the first diffusion coding module and the second diffusion coding module are equal, for example, b1 = b2. Nilsson et al. proposed filter-exchange spectroscopy (FEXSY) [Nilsson M, J, van Westen D, et al. Noninvasive mapping of water diffusional exchange in the human brain using filter-exchange imaging [J]. Magnetic resonance in medicine, 2013, 69 (6): 1572-1580], this technology sets the b-value of the first diffusion coding module to a fixed value, shortening the scanning time by reducing the number of scanning parameters to be set. Cai et al. proposed an antidiagonal sampling mode (ANTI) [Williamson NH, Ravin R, Cai TX, et al. Real-time measurement of diffusion exchange rate in biological tissue [J]. Journal of Magnetic Resonance, 2020, 317: 106782], the characteristic of this sampling mode is that the sum of the b-values ​​of the first diffusion coding module and the second diffusion coding module is the colonization. Ordinola et al. proposed a uniform undersampling strategy (UNIFORM) [A. Ordinola, S. Cai, R. Bai, and E. The 15th International Bologna Conference on Magnetic Resonance in Porous Media, 15, Hangzhou, China (2022)] proposed a sampling pattern that uniformly distributes samples in the upper triangle of the b1-b2 space. However, the optimality of these heuristic sampling patterns could not be proven.

[0004] Recently, the emergence of deep learning has provided a new data-driven optimization technique for sampling pattern optimization. Under specific experimental conditions, studies have successfully optimized the spatial sampling pattern in the frequency domain of MRI using this technique [Xue S, Cheng Z, Han G, et al. 2D probabilistic undersampling pattern optimization for MR image reconstruction [J]. Medical Image Analysis, 2022, 77:102346]. The quality of magnetic resonance (MR) images reconstructed using this technique is superior to images obtained using other sampling patterns.

[0005] Therefore, how to further improve the efficiency and accuracy of parameter estimation is currently a research hotspot in this field.

[0006] Summary of the Invention

[0007] The object of the present invention is to provide a method for optimizing the sampling trajectory of molecular exchange magnetic resonance measurement, which improves the efficiency and accuracy of physiological / physical parameter estimation and can be applied to different molecular exchange magnetic resonance measurement methods.

[0008] The present invention provides the following technical solutions:

[0009] A method for optimizing a molecular exchange magnetic resonance measurement sampling trajectory, the method comprising:

[0010] (1) Determine the number and corresponding range of physiological / physical parameters of the molecular exchange system as simulation parameters, perform independent uniform random sampling within the specified range, and generate a simulated physiological / physical parameter data set;

[0011] (2) Determine the molecular exchange magnetic resonance measurement method and set the acquisition parameters;

[0012] (3) Construct an end-to-end unified network model, including a sampling trajectory optimization network, a noise signal generation network, and a parameter estimation network: the sampling trajectory optimization network simulates the process of signal generation by the molecular exchange magnetic resonance measurement method, and generates magnetic resonance signals according to the corresponding physiological / physical parameters, sampling trajectory, and acquisition parameters; the noise signal generation network simulates the noise distribution in the real magnetic resonance measurement scene and generates a noisy magnetic resonance signal; the parameter estimation network implements the magnetic resonance signal fitting function and outputs physiological / physical parameters according to the noisy magnetic resonance signal;

[0013] (4) Based on the end-to-end unified network model in step (3), the simulated physiological / physical parameters in step (1) are used as input for training under specified acquisition parameters until the network converges and the training is completed, thereby obtaining the optimized sampling trajectory and the corresponding parameter estimation network.

[0014] The method for optimizing the sampling trajectory of molecular exchange magnetic resonance measurement provided by the present invention mainly includes two parts: a sampling trajectory optimization network that simulates the process of signal generation in the molecular exchange magnetic resonance measurement method; and a parameter estimation network that implements the magnetic resonance signal fitting process. The two networks are connected by a noise signal generation network, thereby combining sampling trajectory optimization and parameter estimation into an end-to-end unified network model, realizing network training with the direct goal of improving parameter estimation accuracy, and obtaining an optimized sampling trajectory and parameter estimation network.

[0015] In step (1), in order to ensure the diversity of data and the generalization of the method, all parameters are obtained by average random sampling independently within the corresponding range.

[0016] In the present invention, physiological / physical parameters refer to relevant parameters that describe the molecular exchange system.

[0017] The molecular exchange system is a dual-chamber exchange system or a multi-chamber exchange system; the magnetic resonance measurement method is a diffusion exchange spectrum DEXSY sequence or a relaxation exchange spectrum REXSY sequence; in the dual-chamber exchange system, the physiological parameters / molecular exchange related parameters are: fast component diffusion rate D f , the diffusion rate of the slow component D s , the exchange rate k from the fast component to the slow component fs , the fast component ratio coefficient in equilibrium state and the signal S0 without diffusion-encoded gradient.

[0018] Since the relaxation exchange spectrum REXSY sequence is very similar to the diffusion exchange spectrum DEXSY sequence, and the constructed unified network model is also similar, the diffusion exchange spectrum DEXSY sequence will be mainly used as an example for explanation in the present invention.

[0019] In step (2), the acquisition parameters include the exchange time value and number, the number and distribution constraints of sampling trajectory points under a single exchange time, and the signal-to-noise ratio of a single magnetic resonance acquisition.

[0020] In step (3), the sampling trajectory optimization network simulates the process of generating signals by the molecular exchange magnetic resonance measurement method DEXSY sequence, and generates magnetic resonance signals according to the corresponding physiological / physical parameters, sampling trajectory and acquisition parameters. The expression is as follows:

[0021] S DEXSY =IOD2 O E O D1 S0

[0022] Where I = (1,1),

[0023] Operator O D1 and O D2 Representing the signal evolution process in the first and second diffusion coding modules of the DEXSY sequence, the expression is as follows:

[0024] in is the diffusion matrix, b1 and b2 represent the b-value in the first and second diffusion coding modules respectively. The number of sampling points b1 and b2 is set according to the number of sampling trajectory points under a single exchange time in step (2). The numerical values ​​of the sampling points b1 and b2 are the parameters related to the sampling trajectory to be optimized and are set as trainable parameters.

[0025] Operator O E The signal evolution process in the hybrid module of the DEXSY sequence is described as follows:

[0026] where t m It's exchange time. is the switching matrix, is the longitudinal relaxation matrix, R 1,s(f) =1 / T 1,s(f) , T 1,s(f) is the longitudinal relaxation time.

[0027] In order to ensure that b1 and b2 can be fully optimized simultaneously within the range of sampling trajectory distribution constraints, the present invention makes the following definition in the sampling pattern optimization network: In step (3), in the sampling trajectory optimization network, b1 and b2 meet the following conditions:

[0028] b 1(2) =(b max -b min )σ(v)+b min

[0029] The value range of variable v is [-∞, +∞], σ represents the sigmoid activation function, and b max and b min Represents the distribution constraints of the sampling trajectory, which are the maximum and minimum values ​​of the value range of b1 and b2 respectively.

[0030] In step (3), the noise signal generation network simulates a real magnetic resonance scanning scene, adds independent and identically distributed Gaussian noise to the real and imaginary parts of the signal, and obtains a magnetic resonance signal with Rice noise, as shown in the following formula:

[0031] where n re and n im Represents independent and identically distributed Gaussian noise added to the real and imaginary parts respectively, and the standard deviation of the Gaussian noise is σ=S0 / SNR, where SNR is the signal-to-noise ratio, S DEXSY represents the noise-free magnetic resonance signal output by the sampling pattern optimization network in step (3), represents the magnetic resonance signal with Rice noise.

[0032] In step (3), the parameter estimation network is constructed using a fully connected layer, including an input layer, five hidden layers, and an output layer; the number of neurons in the input layer is equal to the number of magnetic resonance signals, and the number of neurons in the output layer is equal to the number of physiological / physical parameters. Based on the input magnetic resonance signal with Rice noise, the physiological / physical parameters are output:

[0033] in and represents the estimated physiological parameter, f DNN represents the parameter estimation network, θ represents f DNN The network parameters to be optimized.

[0034] Preferably, in order to accelerate the convergence of the network, the output layer neuron values ​​are not directly physiological / physical parameters, but are scaled values ​​of physiological / physical parameters: in step (3), the output physiological / physical parameters to be estimated are obtained by scaling the maximum-minimum values, as shown below:

[0035] P=(P max -P min )*Output P +P min

[0036] Among them, P max and P min Represents the upper and lower boundaries of the physiological / physical parameter range, Output P Represents the neuron value corresponding to the parameter P in the output layer.

[0037] In step (4), the optimization goal is to improve the accuracy of parameter estimation. The training loss function is based on the traditional mean square error, which consists of the losses of all physiological / physical parameters:

[0038] The loss of a single physiological parameter is defined as follows:

[0039] Where P represents the true value of the physiological parameter, represents the physiological parameter estimated by the network, and N represents the number of physiological parameters P.

[0040] Preferably, in step (4), after the unified network model is trained, the obtained optimized sampling trajectory is discretized into the b1-b2 sampling space, and b1 and b2 in the sampling trajectory optimization network are set according to the discretized sampling trajectory, and fixed as non-trainable parameters, and then the parameter estimation network is trained until the network converges and the training is completed, and the optimal parameter estimation network corresponding to the discretized sampling trajectory is obtained.

[0041] Preferably, the method further comprises: in step (2), adjusting the signal-to-noise ratio of the signal acquired by a single magnetic resonance imaging in the acquisition parameters, setting the Gaussian noise standard deviation in the noise signal generation network described in step (3), and performing step (4) to train the unified network model to obtain optimized sampling trajectories and corresponding parameter estimation networks under different signal-to-noise ratios.

[0042] Preferably, the method further comprises: in step (2), adjusting the number of sampling trajectory points under a single exchange time in the acquisition parameters, setting the number of sampling points in the b1-b2 space in the sampling trajectory optimization network described in step (3), and performing step (4) to train a unified network model to obtain optimized sampling trajectories and corresponding parameter estimation networks under different sampling ratios.

[0043] The method for optimizing molecular exchange magnetic resonance measurement sampling trajectories provided by the present invention is based on a data-driven approach. A unified network model is trained under a specified experimental setting to obtain an optimized sampling trajectory and a corresponding parameter estimation network. The distribution characteristics of the optimal sampling trajectory under different numbers of sampling trajectory points and signal-to-noise ratios are analyzed. This technology has certain versatility and can be used to optimize other molecular exchange magnetic resonance measurement sampling trajectories.

[0044] The present invention also provides a molecular exchange magnetic resonance measurement method, which comprises:

[0045] For the molecular exchange system to be measured, the sampling trajectory optimized by the above method for optimizing the sampling trajectory of molecular exchange magnetic resonance measurement is set as the sampling trajectory in the molecular exchange magnetic resonance measurement to collect magnetic resonance signals;

[0046] The collected signal is used as input, and the corresponding parameter estimation network in the above-mentioned method for optimizing the molecular exchange magnetic resonance measurement sampling trajectory outputs the physiological / physical parameter to be measured.

[0047] The present invention also provides a molecular exchange magnetic resonance measurement device, which includes a memory and one or more processors. The memory stores executable code, and when the one or more processors execute the executable code, they are used to implement the above-mentioned molecular exchange magnetic resonance measurement method.

[0048] In the above device, the processor needs to be equipped with Intel(R) Xeon(R) CPU@3.20GHz, 256GB memory, and an Nvidia Tesla P4 (8GB) GPU.

[0049] Compared with the prior art, the present invention has the following technical effects:

[0050] In the method for optimizing the sampling trajectory of molecular exchange magnetic resonance measurement proposed in the present invention: the sampling trajectory optimization network that simulates the signal generation process of the molecular exchange magnetic resonance measurement method overcomes the problems of high degree of freedom and complex model of the parameters to be optimized in traditional optimization methods by setting the sampling trajectory-related parameters as trainable parameters; the parameter estimation network proposed in the present invention that realizes the magnetic resonance signal fitting process utilizes the advantages of deep learning in solving inverse problems, and improves the efficiency and accuracy of parameter estimation compared with traditional parameter estimation methods; the unified network model proposed in the present invention realizes the training of the network with parameter estimation accuracy as the direct goal in a specific molecular exchange magnetic resonance measurement method, thereby obtaining an optimized sampling trajectory and parameter estimation network.

[0051] Compared to existing sampling trajectory and parameter estimation methods, the sampling trajectory and parameter estimation method based on the present invention can provide the most reliable parameters at the same sampling ratio. Therefore, the present invention, when applied to molecular exchange magnetic resonance measurement methods, provides an efficient and accurate method for real-time monitoring and quantitative measurement of molecular exchange in different microenvironments or compartments. This method also has a certain degree of versatility and can be adapted to various molecular exchange magnetic resonance measurement methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] FIG1 is a flow chart showing the application of the method for optimizing the molecular exchange magnetic resonance measurement sampling trajectory to molecular exchange magnetic resonance measurement in an embodiment.

[0053] Figure 2 is a structural diagram of a unified network model provided by the present invention: (a) DEXSY scanning sequence optimized by the embodiment; (b) network structure diagram proposed by the present invention: input layer, sampling pattern optimization network of DEXSY sequence, noise signal generation network, parameter estimation network, output layer.

[0054] Figure 3 shows a two-chamber exchange system based on a cell model.

[0055] Figure 4 shows the comparative b1-b2 spatial sampling patterns and the b1-b2 spatial sampling patterns optimized based on the present invention under different experimental conditions: (a) comparative sampling modes: FEXSY, DEWI, ANTI and UNIFORM; (b) the optimization results obtained by repeating the experiment 100 times when the number of b1-b2 spatial sampling points is fixed at 12 and the SNR is 10, 40 and 400 respectively; (c) the optimization results obtained by repeating the experiment 100 times when the SNR is fixed at 40 and the number of b1-b2 spatial sampling points is 3, 6, 12 and 18 respectively.

[0056] Figure 5 shows a set of sampling patterns obtained by optimization when the SNR is 40 and the number of sampling points in the b1-b2 space is 12.

[0057] FIG6 shows the parameter error results estimated based on different sampling modes under different SNRs and parameter estimation methods.

[0058] Figure 7 shows the repeatability performance of parameter estimation for different sampling modes: (a) repeatability performance of parameter estimation based on simulated data; (b) repeatability performance of parameter estimation based on real data. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to 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 scope of protection of the present invention.

[0060] The model proposed in this paper is implemented based on the Pytorch framework.

[0061] FIG1 is a flow chart showing the application of the method for optimizing the sampling trajectory of molecular exchange magnetic resonance measurement to molecular exchange magnetic resonance measurement according to an embodiment, which mainly includes the following steps:

[0062] (1) Aiming at optimizing the sampling trajectory of molecular exchange magnetic resonance measurement, the physiological / physical parameters and corresponding ranges of the molecular exchange system to be measured are determined as simulation parameters. Independent uniform random sampling is performed within the specified range to generate a certain number of simulated physiological / physical parameters, which are randomly divided into three parts: training set, validation set and test set.

[0063] This embodiment uses a dual-chamber exchange system as the experimental model, as shown in Figure 3, which includes two components: fast (f); slow (s). The physiological parameters / molecular exchange-related parameters to be measured in this system and their reasonable ranges are: the diffusion rate of the fast component D f ∈[1.5,2.0]×10 -3 mm 2 / s, slow component diffusion rate D s∈[0.03,0.06]×10 -3 mm 2 / s, the exchange rate k from the fast component to the slow component fs ∈[0, 10]s -1 The fast component ratio coefficient in equilibrium state Signal S0∈[500,1500] without diffusion-encoded gradient.

[0064] Independent uniform random sampling was performed according to the specified range of each physiological parameter to generate a simulation data set, from which 1,000,000 groups were selected as training sets, 10,000 groups as validation sets, and 10,000 groups as test sets.

[0065] (2) Optimize the sampling trajectory of molecular exchange magnetic resonance measurement and determine the relevant experimental settings in the molecular exchange magnetic resonance measurement experiment (or express it in other words, determine the molecular exchange magnetic resonance measurement method and set the acquisition parameters), including the exchange time value and number, the number and distribution constraints of sampling trajectory points under a single exchange time, and the signal-to-noise ratio of a single magnetic resonance acquisition.

[0066] This embodiment uses the DEXSY sequence as the molecular exchange magnetic resonance measurement method, and the acquisition parameters include: exchange time t m The time interval is fixed to [10, 100, 200, 350] ms. The number of sampling trajectory points in a single exchange time is 12. The sampling space is b1-b2 space, satisfying b min ≤b1,b2≤b max , where b min =100s / mm 2 , b max =1200s / mm 2 , the sampling interval of the discrete b1-b2 space is 100s / mm 2 The signal-to-noise ratio of a single magnetic resonance acquisition is 40.

[0067] (3) Construct a sampling trajectory optimization network to simulate the signal generation process of the molecular exchange magnetic resonance measurement method, and generate magnetic resonance signals according to the corresponding physiological / physical parameters, sampling trajectory and experimental conditions (acquisition parameters).

[0068] This embodiment uses the DEXSY sequence as the molecular exchange magnetic resonance measurement method, and the magnetic resonance signal generation expression is as follows:

[0069] S DEXSY =IO D2 O E O D1 S0

[0070] Where I = (1, 1),

[0071] Operator O D1 and O D2 The signal evolution process in the first and second diffusion coding modules of the DEXSY sequence is described as follows:

[0072] in is a diffusion matrix, b1 and b2 represent the b-value in the first and second diffusion coding modules respectively. According to the experimental setting in step (2), the number of sampling trajectory points in the b1-b2 space is fixed to 12, indicating that the numerical values ​​of b1 and b2 of the sampling trajectory are parameters to be optimized. In order to ensure that b1 and b2 can be fully optimized within the range of the sampling trajectory distribution constraints, this embodiment defines b1 and b2 in the sampling trajectory optimization network to meet the following conditions:

[0073] b 1(2) =(b max -b min )σ(v)+b min

[0074] The variable v ranges from [-∞, +∞], σ represents the sigmoid activation function, and according to the experimental settings in step (2), b max =1200s / mm 2 , b min =100s / mm 2 .

[0075] Operator O E Describes the signal evolution process in the hybrid module, the expression is as follows:

[0076] where t m is the exchange time, which is fixed to [10, 100, 200, 350] ms according to the experimental setting in step (2), is the switching matrix, is the longitudinal relaxation matrix, R 1,s(f) =1 / T 1,s(f) , T 1,s(f) is the longitudinal relaxation time. In this embodiment, the relaxation times of the fast and slow components are set to 1.8 s and 0.9 s, respectively.

[0077] (4) Construct a noise signal generation network to simulate the noise distribution in a real magnetic resonance experiment scenario. Take the magnetic resonance signal output by the sampling trajectory optimization network in step (3) as input, add independent and identically distributed Gaussian noise to the real and imaginary parts of the signal, and output a signal with Rice noise:

[0078] where n re and nim represent the independent and identically distributed Gaussian noise added to the real and imaginary parts respectively. The standard deviation of the Gaussian noise is σ = S0 / SNR, where SNR is the signal-to-noise ratio (SNR), which is fixed to 40 according to the experimental setting in step (2). DEXSY represents the noise-free magnetic resonance signal output by the sampling trajectory optimization network in step (3), represents the magnetic resonance signal with Rice noise.

[0079] (5) Construct a parameter estimation network to realize the magnetic resonance signal fitting function, use the signal with Rice noise generated in step (4) as the input of the network, and output the physiological / physical parameter value to be estimated:

[0080] in and represents the estimated physiological / physical parameter, f DNN represents the parameter estimation network, θ represents f DNN The network parameters to be optimized.

[0081] Specifically, this embodiment only uses a fully connected layer to construct a parameter estimation network, which includes an input layer, five hidden layers and an output layer. The number of neurons in the input layer is equal to the number of collected signals, which is equal to the product of the number of exchange times and the number of sampling trajectory points under a single exchange time in this embodiment. According to the experimental setting in step (2), the number of exchange times is 4, and the number of sampling trajectory points under a single exchange time is 12, then the number of neurons in the input layer is set to 48. The number of neurons in the five hidden layers is set to 128, 256, 512, 256 and 128 respectively, and each layer is followed by an exponential linear unit (ELU) activation function. The number of neurons in the output layer is equal to the number of molecular exchange-related parameters / physiological parameters to be estimated. According to the experimental model description in step (1), it is set to 5 in this embodiment, corresponding to the estimated physiological / physical parameters. and

[0082] (6) Integrate the three networks in steps (3)-(5) into an end-to-end unified network. Under specified acquisition parameters, train the network based on the simulation data set obtained in step (1) until the network converges and obtains the optimized sampling trajectory.

[0083] Write a computer program to implement the three networks in steps (3), (4), and (5), and build an end-to-end unified network model, as shown in Figure 2(b). In a specific molecular exchange magnetic resonance measurement method, the network is trained with parameter estimation accuracy as the direct target, and an optimized b1-b2 spatial sampling trajectory and parameter estimation network are obtained. The training loss function is based on the mean square error of the parameter estimation and is composed of the loss of all physiological parameters:

[0084] The loss of a single physiological parameter is defined as follows:

[0085] Where P represents the true value of the physiological parameter, represents the physiological parameter estimated by the network, P max and P min They represent the upper and lower boundaries of the physiological parameter range, and N represents the number of physiological parameters P.

[0086] (7) According to the distribution constraint of the sampling trajectory in step (2), the sampling trajectory optimized in step (6) is discretized into the b1-b2 sampling space to meet the sampling interval constraint, and b1 and b2 in the sampling trajectory optimization network are set according to the discretized sampling trajectory and fixed as non-trainable parameters. The unified network model is trained based on the simulation data set in step (1) until the network converges, and the optimal parameter estimation network corresponding to the discretized sampling trajectory is obtained.

[0087] To demonstrate the superior performance of the sampling trajectories optimized using the data-driven approach proposed in this paper, we compared four currently proposed b1-b2 space sampling trajectories: FEXSY, DEWI, ANTI, and UNIFORM (as shown in Figure 4(a)). To ensure a fair comparison, b1 and b2 in the sampling trajectory optimization network were set according to the different sampling trajectories and fixed as non-trainable parameters. The corresponding parameter estimation network was trained under the same experimental parameters. The performance of the sampling trajectories was evaluated from the perspectives of accuracy and repeatability on a simulated dataset. In addition, the repeatability of the sampling trajectories was evaluated on real data.

[0088] As shown in Figure 6, the parameter estimation accuracy test results on the simulation data set under different signal-to-noise ratios and different parameter estimation methods are shown. From the results, it can be seen that the sampling trajectory proposed in the present invention can significantly improve the accuracy of parameter estimation, whether it is based on the parameter estimation network or the traditional nonlinear least squares method for model fitting.

[0089] FIG7 shows the repeatability experimental results on simulated data and real data. FIG7 shows that the present invention exhibits the best parameter repeatability in both data sets, demonstrating its stability and proving that the sampling trajectory optimized based on the present invention has a certain universality.

[0090] In order to qualitatively analyze the relationship between the optimal sampling trajectory, the signal-to-noise ratio (SNR) of a single magnetic resonance acquisition, and the number of sampling trajectory points within a single exchange time, the present invention sets the SNR and the number of sampling trajectory points to constant values, and changes another parameter to analyze the relationship between the optimal sampling trajectory and the two. The specific steps are as follows:

[0091] (8) The number of sampling trajectory points in the b1-b2 sampling space in the sampling trajectory optimization network in step (3) is fixed to 12, the SNR of the noise signal generation network in step (4) is set to 10, 40 and 400 respectively, and step (6) is repeated to train the network 100 times to obtain the optimized b1-b2 space sampling trajectory under different signal-to-noise ratios.

[0092] (9) Fix the SNR of the noise signal generation network in step (4) to 40, set the number of sampling trajectory points in the b1-b2 sampling space in the sampling trajectory optimization network in step (3) to 3, 6, 12 and 18 respectively, repeat step (6) to train the network 100 times, and obtain the optimized b1-b2 space sampling trajectory under different sampling ratios.

[0093] (9) Qualitatively analyze the rules and characteristics of the optimal sampling trajectory corresponding to different sampling ratios and signal-to-noise ratios.

[0094] For a specific SNR and sampling ratio, the network is repeatedly trained 100 times based on step (6). Because the training of deep neural networks is a random process, different network weights may be obtained for the same data. In order to obtain statistically significant results, the training is repeated 100 times for the same experimental parameter settings.

[0095] The distribution of the optimal sampling trajectories under different SNRs obtained in step (8) is highly regular. When the SNR is low, the sampling trajectory tends to improve the signal-to-noise ratio by repeated sampling in important areas. When the SNR is high, the sampling trajectory tends to obtain more information by uniformly sampling in the b1-b2 space.

[0096] The distribution of the optimal sampling trajectory under different sampling ratios obtained in step (9) shows that the importance of each sampling point in the b1-b2 space is different.

[0097] The results are shown in Figures 4(b) and 4(c), respectively. As can be seen in Figure 4(b), when the number of sampling trajectory points is fixed, the optimal sampling trajectory is affected by the SNR. When the SNR is low, the sampling trajectory tends to repeat sampling in certain important areas to reduce the impact of noise on the signal. When the SNR is high, the optimal sampling trajectory tends to be evenly distributed, thereby increasing signal diversity. However, the sampling density is still relatively high in high b-value areas because high b-value areas are more significantly affected by noise than low b-value areas. As can be seen in Figure 4(c), when the SNR is fixed, the optimal sampling trajectory is affected by the sampling rate. When the sampling rate is low, the sampling trajectory mainly exhibits a distribution similar to ANTI. As the sampling rate gradually increases, the sampling trajectory gradually expands along the diagonal of the b1-b2 sampling space and the optimization results at low sampling rates. From these two results, it can be seen that it is necessary to design an optimal sampling trajectory for a specific experimental environment.

[0098] The apparatus for optimizing molecular exchange magnetic resonance measurement sampling trajectories provided in this embodiment includes one or more processors, and a memory storing executable code. When the processors execute the executable code, they are used to implement the method for optimizing molecular exchange magnetic resonance measurement sampling trajectories described in the above-described embodiment. Taking software implementation as an example, as a logical device, the apparatus is formed by the processor of any device with data processing capabilities in which the apparatus is located reading corresponding computer program instructions from non-volatile memory into the memory and executing the instructions. From a hardware perspective, in addition to the processor, memory, network interface, and non-volatile memory, the device with data processing capabilities in which the apparatus is located in the embodiment may also include other hardware, typically based on the actual functions of the device with data processing capabilities, and this will not be described in detail.

[0099] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A method for optimizing the sampling trajectory of molecular exchange magnetic resonance measurement, characterized in that: The method comprises: (1) Determine the number and corresponding range of physiological / physical parameters of the molecular exchange system as simulation parameters, perform independent uniform random sampling within the specified range, and generate a simulated physiological / physical parameter data set; (2) Determine the molecular exchange magnetic resonance measurement method and set the acquisition parameters; (3) Construct an end-to-end unified network model, including a sampling trajectory optimization network, a noise signal generation network, and a parameter estimation network: the sampling trajectory optimization network simulates the process of signal generation by the molecular exchange magnetic resonance measurement method, and generates magnetic resonance signals according to the corresponding physiological / physical parameters, sampling trajectory, and acquisition parameters; the noise signal generation network simulates the noise distribution in the real magnetic resonance measurement scene, and generates a noisy magnetic resonance signal; the parameter estimation network implements the magnetic resonance signal fitting function, and outputs physiological / physical parameters according to the noisy magnetic resonance signal; (4) Based on the end-to-end unified network model in step (3), the simulated physiological / physical parameters in step (1) are used as input for training under specified acquisition parameters until the network converges and the training is completed, thereby obtaining an optimized sampling trajectory and a corresponding parameter estimation network.

2. The method for optimizing the molecular exchange magnetic resonance measurement sampling trajectory according to claim 1, characterized in that: The molecular exchange system is a dual-chamber exchange system or a multi-chamber exchange system; the magnetic resonance measurement method is a diffusion exchange spectrum DEXSY sequence or a relaxation exchange spectrum REXSY sequence; in the dual-chamber exchange system, the physiological / physical parameters are: the fast component diffusion rate D f , the diffusion rate of the slow component D s , the exchange rate k from the fast component to the slow component fs , the fast component ratio coefficient in equilibrium state and the signal S0 without diffusion-encoded gradient.

3. The method for optimizing the molecular exchange magnetic resonance measurement sampling trajectory according to claim 1, characterized in that: In step (2), the acquisition parameters include the exchange time value and number, the number and distribution constraints of sampling trajectory points under a single exchange time, and the signal-to-noise ratio of a single magnetic resonance acquisition.

4. The method for optimizing the molecular exchange magnetic resonance measurement sampling trajectory according to claim 3, characterized in that: In step (3), the sampling trajectory optimization network simulates the process of generating signals by the molecular exchange magnetic resonance measurement method DEXSY sequence, and generates magnetic resonance signals according to the corresponding physiological / physical parameters, sampling trajectory and acquisition parameters, and the expression is as follows: S DEXSY =IO D2 O E O D1 S0 Where I = (1,1), Operator O D1 and O D2 Represents the signal evolution process in the first and second diffusion coding modules of the DEXSY sequence, and the expression is as follows: in is a diffusion matrix, b1 and b2 represent the b-value in the first and second diffusion coding modules respectively. The number of sampling points b1 and b2 is set according to the number of sampling trajectory points in a single exchange time in step (2). The numerical values ​​of the sampling points b1 and b2 are the parameters related to the sampling trajectory to be optimized, so they are set as trainable parameters and meet the following conditions: b 1(2) =(b max -b min )σ(v)+b min The variable v ranges from [-∞, +∞], σ represents the sigmoid activation function, and b max and b min Represents the distribution constraints of the sampling trajectory, which are the maximum and minimum values ​​of the value range of b1 and b2 respectively; Operator O E The signal evolution process in the exchange module of the DEXSY sequence is described as follows: where t m It's exchange time. is the switching matrix, is the longitudinal relaxation matrix, R 1,s(f) =1 / T 1,s(f) , T 1,s(f) is the longitudinal relaxation time.

5. The method for optimizing the molecular exchange magnetic resonance measurement sampling trajectory according to claim 4, characterized in that: In step (3), the noise signal generation network simulates a real magnetic resonance scanning scene, adds independent and identically distributed Gaussian noise to the real and imaginary parts of the magnetic resonance signal, and obtains a magnetic resonance signal with Rice noise, the formula is as follows: Where n re and n im represents independent and identically distributed Gaussian noise added to the real part and the imaginary part respectively, and the standard deviation of the Gaussian noise is σ = S0 / SNR, where SNR is the signal-to-noise ratio, S DEXSY represents the noise-free magnetic resonance signal output by the sampling trajectory optimization network in step (3), Represents a magnetic resonance signal with Rice noise.

6. The method for optimizing the molecular exchange magnetic resonance measurement sampling trajectory according to claim 5, characterized in that: In step (3), the parameter estimation network is constructed using a fully connected layer, including an input layer, five hidden layers and an output layer; the number of neurons in the input layer is equal to the number of magnetic resonance signals, and the number of neurons in the output layer is equal to the number of physiological / physical parameters. According to the input magnetic resonance signal with Rice noise, the physiological / physical parameters are output: in and represents the estimated physiological parameter, f DNN represents the parameter estimation network, θ represents f DNN The network parameters to be optimized.

7. The parameter estimation network in the method for optimizing the molecular exchange magnetic resonance measurement sampling trajectory according to claim 1, characterized in that: In step (3), the output physiological / physical parameter is obtained by scaling the maximum-minimum value, as shown below: P = (P max -P min )*Output P +P min Where P max and P min Represent the upper and lower boundaries of the physiological / physical parameter range, Output P Represents the neuron value corresponding to parameter P in the output layer.

8. The method for optimizing the molecular exchange magnetic resonance measurement sampling trajectory according to claim 1, characterized in that: In step (4), the optimization goal is to improve the accuracy of parameter estimation. The training loss function is based on the traditional mean square error, which consists of the losses of all physiological / physical parameters: The loss of a single physiological parameter is defined as follows: Where P represents the true value of the physiological parameter, represents the physiological parameter estimated by the network, and N represents the number of physiological parameters P.

9. The method for optimizing the molecular exchange magnetic resonance measurement sampling trajectory according to claim 1, characterized in that: In step (4), after the unified network model is trained, the optimized sampling trajectory is discretized into the b1-b2 sampling space, and b1 and b2 in the sampling trajectory optimization network are set according to the discretized sampling trajectory and fixed as non-trainable parameters. Then, the parameter estimation network is trained until the network converges and the training is completed, and a parameter estimation network corresponding to the discretized sampling trajectory is obtained.

10. The method for optimizing the molecular exchange magnetic resonance measurement sampling trajectory according to claim 1, characterized in that: The method further includes: in step (2), adjusting the signal-to-noise ratio of a single magnetic resonance acquisition in the acquisition parameters, setting the Gaussian noise standard deviation in the noise signal network generated in step (3), and performing step (4) of training a unified network model to obtain optimized sampling trajectories and corresponding parameter estimation networks under different signal-to-noise ratios.

11. The method for optimizing the molecular exchange magnetic resonance measurement sampling trajectory according to claim 1, characterized in that: The method further includes: in step (2), adjusting the number of sampling trajectory points under a single exchange time in the acquisition parameters, setting the number of sampling points in the b1-b2 space in the sampling trajectory optimization network described in step (3), and performing step (4) to train a unified network model to obtain optimized sampling trajectories and corresponding parameter estimation networks under different sampling ratios.

12. A molecular exchange magnetic resonance measurement method, characterized in that: The method is: For the molecular exchange system to be measured, the optimized sampling trajectory described in any one of claims 1 to 11 is set as the sampling trajectory in the molecular exchange magnetic resonance measurement to collect the magnetic resonance signal; The collected signal is used as input, and the physiological / physical parameter to be measured is outputted based on the corresponding parameter estimation network described in any one of claims 1-11.

13. A molecular exchange magnetic resonance measurement device, characterized in that: The device includes a memory and one or more processors, wherein the memory stores executable code, and when the one or more processors execute the executable code, they are used to implement the molecular exchange magnetic resonance measurement method according to claim 12.

Images