A Deep Learning-Based Method for Calculating the Relaxation Time Distribution of Nuclear Magnetic Resonance Signals

Abstract

This invention provides a deep learning-based method for calculating the relaxation time distribution of nuclear magnetic resonance (NMR) signals. Based on the characteristics of Laplace NMR signals, a mathematical model of an exponentially decaying signal with noise and an ideal relaxation time spectrum are constructed. The ideal relaxation time spectrum serves as a label, and the position of the spectral peak represents the exact value of either the T1 or T2 relaxation time. The full width at half maximum (FWHM) of the spectral peak corresponds to the uncertainty of the result. Simulated signals are generated from the mathematical model, and training and test sets are constructed. A network model is built, and the training data is input into the network model for training. The test data is then input into the network model for testing. The method provided by this invention relies on a mathematical model of the exponentially decaying signal during the relaxation process to construct a dataset for training. This eliminates the need to collect large amounts of real data and allows for NMR relaxation time spectrum calculations to be completed within seconds. Furthermore, it exhibits high robustness to test data with different signal-to-noise ratios.

Description

Technical Field

[0001] This invention relates to the field of nuclear magnetic resonance, and in particular to a method for calculating the relaxation time distribution of nuclear magnetic resonance signals based on deep learning. Background Technology

[0002] Nuclear Magnetic Resonance (NMR) is a non-invasive detection technique widely used in clinical diagnostics and industrial measurement. NMR spectroscopy is commonly used for determining the structure of organic molecules and analyzing the composition of substances. The free induction decay (FID) signal obtained from traditional NMR sampling can be converted into a spectrum using Fourier transform, revealing the relative number of atomic nuclei with specific chemical shifts in the sample. However, relaxation times related to molecular dynamics and spin interactions cannot be directly measured by conventional NMR experiments and are usually provided by Laplace NMR experiments. There are two types of NMR relaxation times involved in the study: longitudinal (spin-lattice) relaxation time T1, reflecting the rate at which the longitudinal magnetization vector recovers to its equilibrium value, and transverse (spin-spin) relaxation time T2, reflecting the decay rate of the transverse component. Measuring NMR relaxation times reveals important properties of molecules, and related techniques are widely used in many fields such as petroleum, chemical, food, agriculture, medicine, and materials science.

[0003] In Laplace NMR experiments, the measured signal is the Laplace transform of the relaxation time distribution (i.e., the NMR relaxation time spectrum, T1 spectrum, T2 spectrum). Therefore, theoretically, the NMR relaxation time spectrum can be obtained from the measured signal through Laplace inversion. However, Laplace inversion is an ill-posed inverse problem, meaning that a single measured signal may correspond to countless relaxation time spectra. Therefore, the uncertainty of the NMR relaxation time spectrum obtained through Laplace inversion is significant, especially when the signal-to-noise ratio (SNR) of the measured signal is low. To obtain high-resolution NMR relaxation time spectra, current conventional methods add constraints and regularization terms to the objective function of the inverse problem to constrain the properties and form of the solution, such as the maximum entropy method and iterative thresholding algorithms with multiple exponential decay. However, conventional methods still face several challenges. First, they rely on complex optimization algorithms that determine how to search the solution space and when to terminate and output the results, often requiring meticulous mathematical derivation and lengthy iterations during the inversion process. Secondly, different regularization terms require corresponding regularization parameters for trade-off. Mismatched regularization parameters can easily lead to increased uncertainty in the relaxation time spectrum, such as increased peak linewidth.

[0004] Currently, there are methods to optimize such ill-posed inverse problems using untrained neural networks. These methods benefit from the powerful representational capabilities of neural networks in handling complex objective functions; however, for different test data, it is necessary to reinitialize the network weights and iteratively optimize the relevant parameters to obtain the desired results. When performing inversion calculations on a batch of test data, these methods exhibit poor flexibility and stability. Summary of the Invention

[0005] The main objective of this invention is to overcome the aforementioned deficiencies in the prior art and propose a deep learning-based method for calculating the relaxation time distribution of nuclear magnetic resonance (NMR) signals. This method relies on a mathematical model of the exponentially decaying signal during the relaxation process to construct a dataset for training, eliminating the need to collect large amounts of real data. Through a pre-trained network model, the calculation time for the NMR relaxation time spectrum can be controlled within seconds, while also exhibiting high robustness to test data with different signal-to-noise ratios.

[0006] The present invention adopts the following technical solution:

[0007] A deep learning-based method for calculating the relaxation time distribution of nuclear magnetic resonance signals includes:

[0008] Based on the characteristics of Laplace nuclear magnetic resonance signals, a mathematical model and an ideal relaxation time spectrum are constructed for the exponentially decaying signal of the relaxation process with noise. The ideal relaxation time spectrum serves as a label, and the position of the spectral peak in the relaxation time spectrum represents the exact value of the T1 or T2 relaxation time. The full width at half maximum (FWHM) of the spectral peak corresponds to the uncertainty of the result. Simulation signals are generated from the mathematical model to construct training and test set data.

[0009] Build the network model and set the relevant training parameters;

[0010] The training set data is input into the network model for training. The network parameters are adjusted until the loss function decreases to convergence and tends to stabilize, thus obtaining the trained network model.

[0011] The test set data is input into the trained network model for testing. Specifically, the obtained test set data signal is input into the trained network model to obtain the NMR relaxation time spectrum generated by the trained network model through relaxation time inversion. This spectrum is then compared with the position of the spectral peak in the label, i.e., the T1 relaxation time value or T2 relaxation time value, and the full width at half maximum (FWHM) to verify the convergence of the network model. Next, the real acquired NMR transverse relaxation signal is input into the trained network model to obtain the corresponding NMR relaxation time spectrum generated by the trained network model through relaxation time inversion. This spectrum is then compared with the expected value obtained by the fitting method to verify the effectiveness of the network model.

[0012] Specifically, the network model is built, and the relevant training parameters are set, as follows:

[0013] The network model consists of two parts: the main network structure and the loss function. The main network structure comprises a fully connected layer and N layers of feedforward modules stacked together. Each feedforward module is connected to the output of the previous layer via a residual connection, and then normalized before entering the next layer. Each feedforward module includes two fully connected layers, followed by a nonlinear ReLU unit. The loss function of the network framework is:

[0014]

[0015] Where S in (i) represents the magnitude of the i-th point in the network label of the input network, S out (i) represents the magnitude of the i-th point in the network's output.

[0016] Specifically, the training set data is input into the network model for training, and the network parameters are adjusted until the loss function decreases to convergence and tends to stabilize, resulting in a trained network model.

[0017] The network is trained by using the Adam (Adaptive Moment Estimation) optimizer. The network loss is calculated in each iteration and the parameters in the network are updated with this loss. Training is terminated when the predetermined maximum number of iterations is reached, or when the loss function decreases to convergence and tends to stabilize, and the trained network model is obtained.

[0018] As can be seen from the above description of the present invention, compared with the prior art, the present invention has the following beneficial effects:

[0019] (1) This invention provides a deep learning-based method for calculating the relaxation time distribution of nuclear magnetic resonance (NMR) signals. Based on the characteristics of Laplace NMR signals, a mathematical model of the exponentially decaying relaxation process with noise and an ideal relaxation time spectrum are constructed. The ideal relaxation time spectrum serves as a label, and the position of the spectral peak represents the exact value of either the T1 or T2 relaxation time. The full width at half maximum (FWHM) of the spectral peak corresponds to the uncertainty of the result. Simulation signals are generated from the mathematical model, and training and test sets are constructed. A network model is built, and relevant training parameters are set. The training set data is input into the network model for training, and the network parameters are adjusted until the loss function decreases to convergence and stabilizes, resulting in a trained network model. The test set data is then input into the trained network model for testing. The method provided by this invention relies on a mathematical model of the exponentially decaying relaxation process to construct a dataset for training, eliminating the need to collect large amounts of real data. Through the pre-trained network model, the calculation time of the NMR relaxation time spectrum can be controlled within seconds, while also exhibiting high robustness to test data with different signal-to-noise ratios.

[0020] (2) This invention utilizes deep learning to invert the NMR relaxation time spectrum from the noisy NMR relaxation decay signal, which has the characteristics of high accuracy, fast speed and strong universality. Attached Figure Description

[0021] Figure 1 This is an overall framework diagram of a deep learning network according to an embodiment of the present invention.

[0022] Figure 2 This is a comparison chart of the transverse relaxation time T2 values ​​obtained by network model inversion and traditional fitting methods according to an embodiment of the present invention, wherein... Figure 2 (a) represents the expected value obtained by the traditional fitting method. Figure 2 (b) is the predicted value obtained by inversion through the network model.

[0023] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Detailed Implementation

[0024] The present invention will be further described below through specific embodiments.

[0025] The relaxation time includes the transverse relaxation time T2 and the longitudinal relaxation time T1. The sequence corresponding to the transverse relaxation process is a decaying signal (decreasing with time and tending to 0), while the sequence corresponding to the longitudinal relaxation process is a recovering signal (increasing with time and tending to a fixed value). The longitudinal relaxation process and the transverse relaxation process have certain differences in signal model formulas. The mathematical model of the multi-exponential decay signal of the NMR transverse relaxation process is shown in formula (1), and the mathematical model of the multi-exponential decay signal of the NMR longitudinal relaxation process is shown in formula (2).

[0026]

[0027]

[0028] Where τ is the echo interval time, T2 and T1 are the NMR relaxation times, and ε is Gaussian noise. and Let f(T1) be the NMR relaxation signal intensity, and f(T2) be the distribution of NMR relaxation times T1 and T2, corresponding to the NMR relaxation time spectra. Without loss of generality, assuming that the above relaxation signals have all been normalized, we have:

[0029]

[0030] By comparing the mathematical models of the two relaxation signals, it can be seen that the longitudinal relaxation signal can be transformed into a decay model similar to that of the transverse relaxation signal:

[0031]

[0032] in It has the same decay form as the transverse relaxation signal. Therefore, the mathematical models of the training set are all constructed based on the transverse relaxation signal formula (1). When inverting the longitudinal relaxation signal, the longitudinal relaxation signal can be preprocessed by formula (3) to convert it into the same decay form as the transverse relaxation time.

[0033] This specific implementation will take the inversion of NMR transverse relaxation T2 time as an example. A model is trained by generating simulated data, and the trained network model is used to invert the NMR relaxation signal to obtain the NMR relaxation time spectrum. For example... Figure 1 Here is an overall framework diagram of the deep learning network according to an embodiment of the present invention. The specific steps are as follows:

[0034] S1: Generate the dataset.

[0035] The network dataset is generated according to formula (1). The input data is a relaxed multi-exponential decay signal S(τ), with a data dimension of 125×10, where 125 is the batch size, 10 is the number of points for the echo time τ, and the maximum value of the echo time τ is set to 12.8. The number of relaxation times superimposed in each multi-exponential decay signal is randomly selected as 1 or 2, and the relaxation time parameters are randomly generated with a minimum interval of 0.1. The network label is an NMR relaxation time spectrum with an ideal Gaussian line shape, where the position of the spectral peak is the accurate value of the relaxation time, and the half-width at half-maximum (WHM) of the spectral peak is the uncertainty of the result. The data dimension of the network label is 125×140, where 125 is the batch size, 140 is the number of grid points for the lateral relaxation time, and the maximum value of the lateral relaxation time is set to 14. The total number of simulated samples is 30,000, of which 27,000 are the training set, 2,000 are the validation set, and 1,000 are the test set. The training set is used to train the network model, the validation set is used to evaluate the performance of the current network model, and the test set is used to verify the performance of the final network model.

[0036] S2: Build the network model and set the relevant training parameters.

[0037] The overall framework of the network is as follows Figure 1 As shown, the network can be divided into two parts: the main network structure and the loss function. The main network structure consists of a fully connected layer and N layers of feedforward modules stacked together. Each feedforward module is connected to the output of the previous layer via a residual connection, and then normalized before entering the next layer. The first fully connected layer has a dimension of 10×140, which can expand the input signal to a higher-dimensional feature space. Each feedforward module includes two fully connected layers, with 4096 neurons in the hidden layers. Each fully connected layer is followed by a nonlinear unit ReLU (Rectified Linear Unit). The loss function of the network framework is:

[0038]

[0039] Where S in (i) represents the magnitude of the i-th point in the network label of the input network, S out (i) represents the magnitude of the i-th point in the network's output.

[0040] S3: Network training.

[0041] The training process of a deep learning network model is an iterative learning process, which can be divided into two stages: forward propagation and back propagation. Forward propagation refers to the process where each layer of the neural network is processed by multiplying the neural network weights by the input, summing the results, adding the bias vector, and then passing the output through an activation function to obtain the output loss value. Back propagation is the process where the neural network calculates the impact of each layer's neural network weights on the final output using the output loss value (measured by partial derivatives), and then updates the neural network weights using the gradient descent principle, based on the difference and the learning rate.

[0042] The specific method is as follows: input the training set data obtained in step 1) into the network for training, adjust the network parameters until the loss function decreases to convergence and tends to stabilize, and obtain a functional network model; the network training method is as follows: use the Adam optimizer for training, with a learning rate of 1e-3, calculate the network loss in each iteration, and update the parameters in the network with this loss; when the predetermined maximum number of iterations is reached, or the loss function decreases to convergence and tends to stabilize, terminate the training and obtain a functional network model.

[0043] S4: Network test.

[0044] The specific method for network testing is as follows: First, the test set data signal obtained in step 1) is input into the functionalized network model to obtain the NMR transverse relaxation time spectrum generated by the network relaxation time inversion, and compared with the position of the spectral peak in the label (i.e., the T2 relaxation time value) and the full width at half maximum (FWHM) to verify the performance of the network model.

[0045] Then, the actual acquired NMR transverse relaxation signals were input into a functionalized network model to obtain the corresponding transverse relaxation T2-time spectrum generated by network relaxation time inversion. This spectrum was then compared with the expected values ​​obtained by traditional fitting methods to verify the practicality of the network model. The comparison results are as follows: Figure 2 As shown, where Figure 2 (a) represents the expected value obtained by the traditional fitting method. Figure 2 (b) shows the predicted values ​​obtained through network model inversion, with the one-dimensional curve above representing the corresponding hydrogen NMR spectrum. Overall, the deep learning-based NMR relaxation time inversion method exhibits high accuracy and robustness, along with fast computation speed.

[0046] The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains may modify or supplement the described specific embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

[0047] The above are merely specific embodiments of the present invention, but the design concept of the present invention is not limited thereto. Any non-substantial modifications made to the present invention using this concept shall be considered as infringing upon the protection scope of the present invention.

Claims

1. A method for calculating the relaxation time distribution of nuclear magnetic resonance signals based on deep learning, characterized in that, include: Based on the characteristics of Laplace nuclear magnetic resonance signals, a mathematical model and an ideal relaxation time spectrum are constructed for the exponentially decaying signal of the relaxation process with noise. The ideal relaxation time spectrum serves as a label, and the position of the spectral peak in the relaxation time spectrum represents the exact value of the T1 or T2 relaxation time. The full width at half maximum (FWHM) of the spectral peak corresponds to the uncertainty of the result. Simulation signals are generated from the mathematical model to construct training and test set data. Build the network model and set the relevant training parameters; The training set data is input into the network model for training. The network parameters are adjusted until the loss function decreases to convergence and tends to stabilize, thus obtaining the trained network model. The test set data is input into the trained network model for testing. Specifically, the obtained test set data signal is input into the trained network model to obtain the NMR relaxation time spectrum generated by the trained network model through relaxation time inversion. This spectrum is then compared with the position of the spectral peak in the label, i.e., the T1 relaxation time value or T2 relaxation time value, and the full width at half maximum (FWHM) to verify the convergence of the network model. Next, the real acquired NMR transverse relaxation signal is input into the trained network model to obtain the corresponding NMR relaxation time spectrum generated by the trained network model through relaxation time inversion. This spectrum is then compared with the expected value obtained by the fitting method to verify the effectiveness of the network model. The construction of the network model and the setting of the relevant training parameters are as follows: The network model consists of two parts: the main network structure and the loss function. The main network structure comprises a fully connected layer and N layers of feedforward modules stacked together. Each feedforward module is connected to the output of the previous layer via a residual connection, and then normalized before entering the next layer. Each feedforward module includes two fully connected layers, followed by a nonlinear ReLU unit. The loss function of the network framework is: Where S in (i) represents the magnitude of the i-th point in the network label of the input network, S out (i) represents the magnitude of the i-th point in the network's output.

2. The method for calculating the relaxation time distribution of nuclear magnetic resonance signals based on deep learning according to claim 1, characterized in that, The training set data is input into the network model for training. The network parameters are adjusted until the loss function decreases to convergence and tends to stabilize, resulting in a well-trained network model. Specifically: The network is trained as follows: the Adam optimizer is used for training, the network loss is calculated in each iteration, and the parameters in the network are updated with this loss; when the predetermined maximum number of iterations is reached, or the loss function decreases to convergence and tends to stabilize, the training is terminated and the trained network model is obtained.

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