A non-Cartesian MRI dynamic contrast-enhanced intelligent imaging method

Abstract

The present invention relates to the field of magnetic resonance imaging technology, and more particularly to a non-Cartesian magnetic resonance dynamic contrast-enhanced intelligent imaging method. The method comprises the following steps: acquiring multi-coil magnetic resonance k-space data and re-framing it according to the time dimension to obtain undersampled k-space data, k-space label data that satisfies the Nyquist sampling criterion, quantitative parameters, and dynamic signal data, which together form a training set; designing an iterative network and loss function for dual-domain subspace learning based on quantitative parameter constraints, dynamic prior constraints, and k-space constraints; and solving the optimal parameters of the iterative network based on the training set. The framed k-space data is then input into the trained network to reconstruct dynamic images, thereby achieving rapid, high-spatiotemporal resolution, and accurate quantitative reconstruction of magnetic resonance dynamic contrast-enhanced images.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetic resonance imaging, and in particular to a non-Cartesian magnetic resonance dynamic contrast enhancement intelligent imaging method. Background Art

[0002] Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is an advanced medical imaging technique that can capture dynamic changes in the microvascular system within tissues before and after contrast agent injection, reflecting microscopic functional information such as tissue vascular permeability and localized blood perfusion. This imaging modality provides detailed information on the pathophysiological state of microvasculature in diseased tissues, allowing for objective assessment of lesions. Challenges with DCE-MRI include slow imaging speed, resulting in motion artifacts, and limited spatiotemporal resolution, which reduces the accuracy of quantitative parameters. Therefore, rapid reconstruction with high spatiotemporal resolution and improved accuracy of quantitative parameter estimation remain urgent challenges.

[0003] In the past 10 years, many dynamic MRI image reconstruction methods have been proposed, including: 1) Iterative golden angle radial sparse parallel MRI (iGRASP) (Feng L, Grimm R, Block KT, et al. Golden-angle radialsparse parallel MRI: combination of compressed sensing, parallel imaging, and golden-angle radial sampling for fast and flexible dynamic volumetric MRI[J]. Magnetic resonance in medicine, 72(3):707-717, 2014.) This technology combines compressed sensing, parallel imaging, and golden angle radial sampling to achieve higher acceleration capabilities than parallel imaging or coil-by-coil compressed sensing alone. However, this technology is highly dependent on data sparsity, coil sensitivity encoding accuracy, and complex reconstruction algorithms, resulting in increased image artifacts or reduced computational efficiency at high acceleration factors. 2) RACER-GRASP (respiratory-weighted, aortic contrast enhancement-guided and coil-unstreaking golden-angle radial sparse MRI) is a novel dynamic enhancement imaging technique (Feng L, Huang C, Shanbhogue K, et al. RACER-GRASP: respiratory-weighted, aortic contrast enhancement-guided and coil-unstreaking golden-angle radial sparse MRI[J].Magnetic resonance in medicine, 80(1): 77-89, 2018.). This technique extends GRASP to include automatic contrast agent timing, respiratory motion compensation, and spiral weighting to improve the imaging performance of liver MRI. However, this technique is highly dependent on complex multi-parameter synchronization, increases the computational burden, and is sensitive to motion compensation errors, resulting in decreased image quality under high acceleration or complex physiological motion.3) An innovative spatiotemporal flexible sparse constraint parallel compressed sensing reconstruction model (HuY, Zhang X, Chen D, et al. Spatiotemporal flexible sparse reconstruction for rapid dynamic contrast-enhanced MRI [J]. IEEE Transactions on Biomedical Engineering, 69(1): 229-243, 2021.) This technology flexibly adjusts spatiotemporal sparsity by introducing a weight mechanism, and combines it with a fast iterative soft thresholding algorithm (pFISTA) to achieve high-quality and fast reconstruction of brain tumor and liver DCE-MRI images at high acceleration rates. However, this technology is learned in the image domain and the model complexity is relatively high. 4) 4D Golden-AngleRadial MRI (3D+time) method (Feng L. 4D golden-angleradial MRI at subsecondtemporal resolution. NMR in Biomedicine, 36(2): e4844, 2023.) This technology essentially reduces intra-frame motion artifacts in body applications, thereby eliminating the need for explicit motion detection and motion compensation. However, this technology is only based on learning in the image domain and does not have data consistency verification, which may lead to suboptimal reconstruction solutions. 5) An innovative deep learning method GRASPNET (Jafari R, Do RKG, LaGratta MD, et al.GRASPNET: fast spatiotemporal deep learning reconstruction of golden-angle radial data for free-breathing dynamic contrast-enhanced magnetic resonance imaging[J]. NMR in Biomedicine, 36(3): e4861,2023.) Compared with the above methods, this technology achieves efficient reconstruction in the image domain and significantly reduces the reconstruction time. However, this method is only based on image domain learning and does not have data consistency verification, which means that the reconstruction quality needs to be improved.

[0004] Therefore, the current DCE-MRI optimization algorithm has a long reconstruction time, and deep learning reconstruction mainly focuses on learning in the image domain without directly learning the k-space data. In addition, pharmacokinetic quantitative parameters are not introduced as prior constraints of the network. Summary of the Invention

[0005] To solve the above technical problems, the present invention provides a non-Cartesian magnetic resonance dynamic contrast enhanced intelligent imaging method, which is characterized by comprising the following steps:

[0006] S1. Obtain multi-coil magnetic resonance k-space data from the magnetic resonance imaging instrument through magnetic resonance data acquisition. Perform frame rearrangement and dynamic image reconstruction on the multi-coil magnetic resonance k-space data based on the time dimension and Nyquist sampling theory to construct a training set.

[0007] S2. Construct an iterative network and loss function for multi-coil MRI k-space data based on dual-domain subspace learning theory with quantitative parameter constraints, dynamic prior constraints, and k-space constraints.

[0008] S3. Solve the iterative network to obtain the optimal parameters based on the training set obtained in step S1;

[0009] S4. Inputting the frame-rearranged multi-coil MRI k-space data into the iterative network according to the trained iterative network for image reconstruction to obtain a reconstructed MRI dynamic contrast-enhanced image;

[0010] The training set includes undersampled k-space data, k-space label data that meets Nyquist sampling, quantitative parameters, and dynamic image signal data.

[0011] Furthermore, the multi-coil magnetic resonance k-space data is subjected to frame rearrangement and dynamic image reconstruction according to the time dimension and Nyquist sampling theory, and the construction of the training set includes the following steps:

[0012] S101. By acquiring magnetic resonance data, obtain multi-coil magnetic resonance k-space data of a magnetic resonance imaging instrument, expressed as: ;in, is the multi-coil magnetic resonance k-space data, is a complex field, is the number of spokes, is the number of sampling points, is the number of coils, and the multi-coil magnetic resonance k-space data is framed to obtain the undersampled k-space data after framing. The total number of frames of the k-space data after framing is expressed as: ; Where M is the number of spokes, is the number of spokes of the undersampled k-space data after framing, Represents the total number of frames of the k-space data after framing; the multi-coil magnetic resonance k-space data is rearranged and framed along the time dimension to obtain undersampled k-space data, which is expressed as: ; ; ;in, is the undersampled k-space data, is the multi-coil magnetic resonance k-space data, is the time rearrangement operator, For the Frame No. Undersampled k-space data of coils;

[0013] S102. Obtain multi-coil magnetic resonance k-space data from the magnetic resonance imaging instrument through magnetic resonance data acquisition. According to the Nyquist sampling theory, the multi-coil magnetic resonance k-space data is rearranged along adjacent time frames to obtain k-space label data, which is expressed as: ; ;in, The number of spokes for multi-coil MRI k-space data is calculated based on the Nyquist sampling criterion. The operator for rearrangement, is the multi-coil magnetic resonance k-space data, is the rearranged k-space data. The rearranged k-space data is copied according to the total number of frames of the undersampled k-space data after framing to obtain the final k-space label data, which is expressed as: ;

[0014] ;

[0015] in, To satisfy the k-space label data of Nyquist sampling, is the copy operator, is the total number of frames of k-space data after framing, is the number of radial k-space data spokes for each frame in the k-space label data, is the number of sampling points, is the number of coils;

[0016] S103. Optimize the dynamic reconstruction of the undersampled k-space data using an optimized reconstruction algorithm to obtain a dynamic image, which is expressed as: ; ;in, To optimize the reconstruction algorithm, The dynamic image reconstructed by the optimization algorithm is They are the 1st to the 2nd in the dynamic image reconstructed by the optimization algorithm. frame, is the undersampled k-space data, is the total number of frames of the k-space data after framing. Through the extraction algorithm, the values ​​of the pixels at the same position in each frame of the dynamic image along the time dimension are extracted and the dynamic signal data is calculated, which is expressed as: ;in, To extract the algorithm along the time dimension, The dynamic image reconstructed by the optimization algorithm is is dynamic image signal data;

[0017] S104. Based on the dynamic image signal data, an E-tofts model is constructed and quantitative parameters are calculated along the time pixel points by the least squares method;

[0018] S105. A training set is constructed based on the obtained undersampled k-space data, dynamic image signal data, and quantitative parameters.

[0019] Furthermore, the iterative network in step S2 includes a preprocessing module and a network iteration module, and constructing the iterative network for multi-coil magnetic resonance k-space data includes the following steps:

[0020] S201. Construct a preprocessing module, including the following steps:

[0021] S201.1. Split the complex values ​​of the undersampled k-space data into real and imaginary parts, expressed as: ; ; ; ;in, For the Frame No. Undersampled k-space data of coils, is the real part matrix, are the real part values ​​from the 1st sampling point to the Nth sampling point respectively, is the imaginary part matrix, are the imaginary part values ​​from the 1st sampling point to the Nth sampling point, is an imaginary unit;

[0022] S201.2. Arrange the real part matrix and the imaginary part matrix by row to obtain undersampled k-space data arranged by row, which is expressed as: ;

[0023] S201.3. The undersampled k-space data arranged by row splicing are then vector-spliced ​​by column to obtain the target matrix input to the network iteration module, which is expressed as:

[0024] ;in For the Frame No. The target matrix of coils, is the total target matrix, and the total target matrix is ​​input into the network iteration module;

[0025] S202. Construct a network iteration module, including L cascaded iteration blocks, wherein the iteration block includes a k-space learning module and a data consistency check module, including the following steps:

[0026] S202.1. Construct a sector subspace learning module and a ring subspace learning module respectively, including the following steps:

[0027] A. Constructing a fan-shaped subspace learning module includes the following steps:

[0028] A1. According to the total target matrix , rearrange the data blocks to be learned according to d columns, and obtain n data blocks to be learned , expressed as: ;in, is the total target matrix, Represents all the data blocks to be learned, Represents the first data block to be learned, Indicates the nth data block to be learned;

[0029] A2. By cascading multiple CBR structures containing two-dimensional convolution functions, normalization functions, and nonlinear mapping functions, the network structure of each data block to be learned is obtained. Then, data mapping is performed on each data block to be convolved through k-space filling learning. The nonlinear network mapping data for directly predicting the missing sampling points of each data block to be learned is obtained, which is expressed as:

[0030] ;

[0031] in, After learning the cascade CBR structure, the k-space data along the fan is output. represents the network mapping from undersampled k-space to filled k-space, represents the output of the first learning data block, represents the output of the nth learning data block, Represents the network learning parameters of the first learning data block, represents the network learning parameters of the nth learning data block, Represents the first data block to be learned, represents the nth data block to be learned, Indicates the convolutional layer used by the first learning data block, represents the convolutional layer used by the nth learning data block, is the normalization function, is a nonlinear activation function;

[0032] A3. Based on the k-space data obtained after learning the cascaded CBR structure, the k-space data filled along the sector is re-convolved using the convolution algorithm to obtain the k-space data of the re-convolved sector subspace learning module, which is expressed as follows: ;in, is the k-space data after reconvolution, The convolution kernel network learning parameters for the first learning data block, is the convolution kernel network learning parameter of the nth learning data block, is the network output after the first learning data block is convolved, is the network output after the nth learning data block is convolved;

[0033] A4. Based on the reconvolved k-space data, a single iterative block fan-shaped subspace learning module is obtained, which is expressed as: ;in, l Indicates the l Iteration blocks, Indicates the k-space learning submodule l The padded k-space data output by the iterative block, Indicates the l The mapping process of an iterative block fan subspace learning network, is the total target matrix of the network input, Indicates the l The parameters of the fan-shaped subspace network are learned by iterative blocks;

[0034] B. Constructing the annular subspace learning module includes the following steps:

[0035] B1. Based on the obtained target matrix, rearrange it so that e rows form a data block to be learned, and obtain m data blocks to be learned, which can be expressed as: ;in, is the total target matrix, Represents all the data blocks to be learned, Indicates the first data block to be learned, Represents the mth data block to be learned;

[0036] B2. By cascading multiple CBR structures containing two-dimensional convolution functions, normalization functions, and nonlinear mapping functions, the network structure of each data block to be learned is obtained. Then, data mapping is performed on each data block to be convolved through k-space filling learning. The nonlinear network mapping data of the missing sampling points of each data block to be learned is obtained, which is expressed as: ;in, After learning the cascade CBR structure, the k-space data along the ring is output. represents the mapping from undersampled k-space to filled k-space, Represents all the data blocks to be learned, is the total network learning parameter of the learning process, represents the network output of the first learning data block, represents the network output of the mth learning data block, Indicates the first data block to be learned, represents the mth data block to be learned, Represents the network learning parameters of the first learning data block, represents the network learning parameters of the mth learning data block, Indicates the convolutional layer used by the first learning data block, represents the convolutional layer used by the mth learning data block, is the normalization function, is a nonlinear activation function;

[0037] B3. Based on the k-space data obtained after learning the cascaded CBR structure, the k-space data filled along the ring is re-convolved by the convolution algorithm to obtain the k-space data of the sector subspace learning module after re-convolution. The formula is expressed as: ;in, is the k-space data after reconvolution, is the k-space data output by the convolved network of the first learning data block, The network output k-space data after the m-th learning data block is convolved, Indicates that the first learning data block uses the convolutional layer, Indicates that the mth learning data block uses the convolution layer, Represents the network parameters learned by the convolutional layer of the first learning data block, Represents the network parameters learned by the convolutional layer of the mth learning data block;

[0038] B4. Based on the reconvolved k-space data, a single annular subspace learning module is obtained, which is expressed as: ;in, l Indicates the l Iteration blocks, Represents the annular subspace learning module l The padded k-space data output by the iterative block, Indicates the l The network mapping of the submodule is learned by the annular subspace of the iterative blocks, Learning parameters for the annular subspace learning submodule network;

[0039] S202.2. The obtained k-space filling data of the sector subspace learning module is fused with the k-space filling data of the annular subspace learning module to obtain a k-space learning module. The fusion formula is expressed as:

[0040] ;in, and For the l The weighted coefficients learned by the network in iterative blocks, For the l The network mapping relationship of the submodules is learned in the iterative block fan subspace. For the l The network mapping relationship of the submodules is learned in the annular subspace of the iterative block. For the l The network learning parameters of iterative block fan subspace learning, For the l The network learning parameters of the iterative block annular subspace learning, is the total target matrix, For the l Output data after k-space data fusion of iterative blocks;

[0041] S202.3. Perform a data consistency check based on the fused k-space data output by the k-space learning module to obtain a verification result. The verification formula is expressed as:

[0042] ;in, For the l The network mapping relationship of the submodules is learned in the iterative block fan subspace. For the l The network mapping relationship of the submodules is learned in the annular subspace of the iterative block. is the undersampled k-space data, Indicates that the current data point is within the image, Indicates that the current data point is not in the image. and For the l The weighted coefficients learned by the network in iterative blocks, For the l The k-space data output after the data consistency check of the iterative blocks is is the total target matrix, For the l The network learning parameters of iterative block fan subspace learning, For the l The network learning parameters of the iterative block annular subspace learning;

[0043] S202.4. Based on the data verification results, the learning formula for a single iterative block is expressed as:

[0044] ;in, It is the cascade of the learning process of each module in the iterative block, is the undersampled k-space data, represents the total target matrix, For iterative blocks l The learned network parameters, For iterative blocks l The subspace network learns the mapping, For iterative blocks l The data consistency verification process, For iterative blocks l The network outputs k-space data;

[0045] The final filled k-space data is obtained by cascading multiple iterative blocks, which is expressed as:

[0046] ;

[0047] in, Represents the reconstruction mapping process of the entire network, represents the learning parameters of the entire network, represents undersampled k-space data, is the final filled k-space data learned by the network, Represents the network map of the first iteration block, represents the network map of the L-th iteration block, represents the network learning parameters of the first iteration block, Represents the network learning parameters of the Lth iteration block

[0048] S202.5. Final k-space data after filling The dynamic image is reconstructed by non-uniform Fourier transform, and the final dynamic image reconstructed by the network is obtained, which is expressed as: ;in, is the complex conjugate transpose of the sensitivity map, is the non-uniform Fourier transform, is the dynamic image of F frames after reconstruction, D is the density compensation, It is the final filled k-space data for network learning.

[0049] Furthermore, the loss function in step S2 is constructed by quantitative parameter constraints, dynamic signal data constraints, and k-space data constraints. The quantitative parameter constraints are expressed as:

[0050] ;in, is the two-norm term, Respectively represent the corresponding coordinates in the dynamic image, represents the sum operation, Represents dynamic graph reconstruction from the network Calculate quantitative parameters K trans and V p The operator, L represents the total number of iterations, G represents the total number of training samples, Indicates that the coordinates are The optimization algorithm calculates the label in the dynamic graph K trans value, Indicates that the coordinates are Reconstructed dynamic image calculated K trans value; Indicates that the coordinates are The optimization algorithm calculates the label in the dynamic graph V p value, Indicates that the coordinates are Reconstructed dynamic image calculated V p value, represents the quantitative parameter-constrained loss function of the network, Represents the set of learning parameters of the entire network;

[0051] The dynamic signal constraint is expressed as:

[0052] ;in, represents the entire network learning parameter set, represents the two-norm term, L represents the total number of iterations, G represents the total number of training samples, represents the sum operation, is the dynamic signal data extraction operator, Indicates the label dynamic signal data calculated in the optimization algorithm dynamic graph, Indicates that the dynamic signal data is calculated from the dynamic image reconstructed by the network, represents the label dynamic image reconstructed by the optimization algorithm, represents the reconstructed dynamic image, represents the dynamic signal constraint loss function;

[0053] The k-space constraint is expressed as:

[0054] ;in, is the two-norm term, l Indicates the l Iteration blocks, L represents the total number of iterations, G represents the total number of training samples, represents the sum operation, represents the labeled k-space data that meets the Nyquist sampling criterion, represents the k-space data after network learning, represents the loss function of the k-space constraint, Represents the entire network learning parameter set;

[0055] The loss function is expressed as:

[0056] ;in, 、 and is the adjustable weight coefficient, represents the total loss function of the network, represents the entire network learning parameter set, Indicates the label dynamic signal data calculated in the optimization algorithm dynamic graph, Indicates that the dynamic signal data is calculated from the dynamic image reconstructed by the network, represents the labeled k-space data that meets the Nyquist sampling criterion, represents the k-space data after network learning, Indicates that the coordinates are The optimization algorithm calculates the label in the dynamic graph K trans value, Indicates that the coordinates are Reconstructed dynamic image calculated K trans value; Indicates that the coordinates are The optimization algorithm calculates the label in the dynamic graph V p value, Indicates that the coordinates are Reconstructed dynamic image calculated V p value, L represents the total number of iterations, G represents the total number of training samples, Represents a sum operation.

[0057] Furthermore, the step S3 solves the iterative network by using the Adam optimizer, according to the training set obtained in step S1, combined with the loss function constraint in step S2, to obtain the optimal network training parameters of the iterative network, and reconstruct the optimal filled k-space data. .

[0058] Furthermore, in step S4, the multi-coil magnetic resonance k-space data after frame rearrangement is input into the iterative network according to the trained iterative network, and image reconstruction is performed to predict and reconstruct the filled k-space data. ,right The reconstructed magnetic resonance dynamic contrast enhanced image is obtained by performing non-uniform Fourier transform, and the formula is as follows: ;

[0059] ;in, is the operator for density compensation of the Fourier space data of each coil in each time dimension, is the non-uniform Fourier transform, This is the MRI dynamic contrast enhanced image after network reconstruction. is the final k-space data after network learning and filling, is the complex conjugate transpose of the sensitivity map, 、 and Represent the MRI dynamic contrast-enhanced images of frame 1, frame f, and frame F, respectively.

[0060] A computer-readable storage medium is used to store a computer program, which, when executed on a computer, enables the computer to execute a non-Cartesian magnetic resonance dynamic contrast-enhanced intelligent imaging method as described above.

[0061] An electronic device comprises: a memory for storing a computer program; and a processor for executing the computer program to implement a non-Cartesian magnetic resonance dynamic contrast enhanced intelligent imaging method as described in any one of the above.

[0062] The beneficial effects of the present invention are:

[0063] (1) The present invention avoids the frame rate limitation of traditional Nyquist sampling by adopting dynamic frame rearrangement and undersampling strategies, combined with deep learning-driven k-space data intelligent filling technology, and achieves dynamic imaging with a high acceleration factor (AF=W / b) under non-Cartesian trajectories, significantly shortening the scanning time while avoiding the time-consuming iterative process of traditional compressed sensing reconstruction.

[0064] (2) The present invention constructs a dual-domain subspace learning framework and uses fan-shaped and annular subspace modules to capture the temporal continuity characteristics of radial spokes and the spatial global correlation of annular trajectories respectively, effectively solving the spatiotemporal signal aliasing problem in non-Cartesian dynamic MRI and significantly improving the temporal resolution and spatial detail fidelity of dynamic images.

[0065] (3) The present invention utilizes dual-domain subspace learning with quantitative parameter constraints, dynamic prior constraints, and k-space constraints to greatly accelerate the speed of dynamic magnetic resonance imaging. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 , a flow chart of a non-Cartesian magnetic resonance dynamic contrast enhanced intelligent imaging method of the present invention;

[0067] Figure 2 , a continuous sampling non-Cartesian golden angle sampling DCE-MRI-k-space data diagram according to an embodiment of the present invention;

[0068] Figure 3 , a schematic diagram of an iterative network for multi-coil magnetic resonance k-space data based on a dual-domain subspace learning theory of quantitative parameter constraints, dynamic prior constraints, and k-space constraints according to an embodiment of the present invention;

[0069] Figure 4 , a schematic diagram of a network iteration module according to an embodiment of the present invention;

[0070] Figure 5 , a comparison diagram of images before and after reconstruction according to an embodiment of the present invention;

[0071] Figure 6 , a schematic diagram of the terminal device structure of a non-Cartesian magnetic resonance dynamic contrast enhancement intelligent imaging method proposed in an embodiment of the present invention;

[0072] Figure 7 , a schematic diagram of the computer-readable storage medium structure of a non-Cartesian magnetic resonance dynamic contrast enhancement intelligent imaging method proposed in an embodiment of the present invention;

[0073] In the figure, 200 - terminal device, 210 - memory, 211 - RAM, 212 - cache memory, 213 - ROM, 214 - program / utility, 215 - program module, 220 - processor, 230 - bus, 240 - external device, 250 - I / O interface, 260 - network adapter, 300 - program product. DETAILED DESCRIPTION

[0074] In order to make the objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention is further described in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only intended to explain the present invention and are not intended to limit the present invention. That is, the embodiments described herein are only some embodiments of the present invention, not all embodiments. Generally, the components of the embodiments of the present invention described and illustrated in the drawings herein may be arranged and designed in various different configurations.

[0075] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but is merely intended to represent selected embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0076] Furthermore, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion such that a process, method, article, or machine that comprises a list of elements includes not only those elements but also other elements not expressly listed or inherent to such process, method, article, or machine.

[0077] The features and performance of the present invention are further described in detail below with reference to the embodiments.

[0078] Example 1:

[0079] This example uses a 3T magnetic resonance imaging system to image the livers of 150 volunteers. The MRI sequence parameters used in this example are: echo time TE = 1.71 ms, repetition time TR = 3.83 ms, field of view 370 × 370 mm, and number of coils 12. The liver images of the 150 volunteers after MRI scans were then processed using a Gold angle sampling trajectory with an acceleration factor of 20.

[0080] like Figure 1 As shown, embodiment 1 of the present invention provides a non-Cartesian magnetic resonance dynamic contrast enhanced intelligent imaging method, comprising the following steps:

[0081] S1. Obtain multi-coil magnetic resonance k-space data from the magnetic resonance imaging instrument through magnetic resonance data acquisition. Perform frame rearrangement and dynamic image reconstruction on the multi-coil magnetic resonance k-space data based on the time dimension and Nyquist sampling theory to construct a training set.

[0082] S2. Construct an iterative network and loss function for multi-coil MRI k-space data based on dual-domain subspace learning theory with quantitative parameter constraints, dynamic prior constraints, and k-space constraints.

[0083] S3. Solve the iterative network to obtain the optimal parameters based on the training set obtained in step S1;

[0084] S4. Inputting the frame-rearranged multi-coil MRI k-space data into the iterative network according to the trained iterative network for image reconstruction to obtain a reconstructed MRI dynamic contrast-enhanced image;

[0085] The training set includes undersampled k-space data, k-space label data that meets Nyquist sampling, quantitative parameters and dynamic image signals.

[0086] Furthermore, the step 1 includes the following steps:

[0087] A. Undersampled k-space data

[0088] Acquiring multi-coil MRI k-space data from a MRI machine with continuously sampled non-Cartesian radial lines , represents the complex domain, 600 represents the number of spokes, 768 represents the number of sampling points, and 12 represents the number of coils. The total number of frames of k-space data after framing (also known as the number of frames of dynamic images) is defined as: ;

[0089] Where, represents the number of spokes in the undersampled k-space data after framing, Indicates the total number of frames of the dynamic image after framing, and M is the number of spokes.

[0090] Then rearrange the frames along time to obtain the rearranged undersampled k-space data , the formula is as follows: , where represents multi-coil MRI k-space data continuously sampled along non-Cartesian radial lines, represents the rearranged undersampled k-space data, Indicates the Frame No. Non-Cartesian k-space data for coils, Represents multi-coil magnetic resonance k-space data Operator that performs time rearrangement.

[0091] The acceleration factor (AF) in magnetic resonance imaging can be defined as:

[0092] ; where c represents the size of the phase encoding dimension of the reconstructed image, b is the number of spokes of the undersampled k-space data, and π is a constant.

[0093] Bk space label data

[0094] Multi-coil MRI k-space data continuously sampled along non-Cartesian radial lines According to the Nyquist sampling criterion, the k-space label data is obtained by rearranging along adjacent time frames. The rearrangement process is expressed as: , where Represents the k-space data sampled continuously according to the number of spokes of the Nyquist sampling criterion The algorithm for rearrangement, is the rearranged k-space data. In order to satisfy the same number of frames as the undersampled k-space data input by the network, Perform the copy operation as follows:

[0095] ;

[0096] in, is the copy operator, It represents the k-space label data that satisfies Nyquist sampling and keeps the same number of frames as the undersampled k-space data input to the network. represents the complex domain, 5 represents the number of k-space data frames after framing, 120 represents the number of radial k-space data spokes of each frame in the k-space label data, 768 represents the number of sampling points, and 12 represents the number of coils.

[0097] C. Calculation of dynamic signals and quantitative parameters and

[0098] Dynamic contrast-enhanced imaging uses multiple continuous dynamic scans after contrast agent injection to evaluate tissue perfusion effects through quantitative parameters, such as 、 The parameter can measure the permeability of blood vessels, and its accurate quantification is an important indicator for clinical diagnosis of dynamic contrast-enhanced imaging. In the present invention, the optimization algorithm is used to reconstruct the dynamic image, and then the dynamic signal data and the dynamic image are calculated along the time dimension. 、 The quantitative parameters are used as the training label data for the prior constraints of the network. The specific process is:

[0099] The optimization algorithm is used to reconstruct the undersampled k-space data after framing to obtain a dynamic image. The process is described as follows: ;

[0100] in, To optimize the algorithm reconstruction process, It is the dynamic image reconstructed by the optimization algorithm. The values ​​of the pixels at the same position in each frame of the image are extracted to calculate the dynamic signal data graph (Dynamic Signal Curve, DSC), the formula is as follows: ,in, It is an extraction algorithm for dynamic reconstruction graph along the time dimension, The dynamic image reconstructed by the optimization algorithm is It is the dynamic signal data extracted from the dynamic reconstruction graph along the time dimension. Assume (u,v) represents the image of the dynamic image at the position (u,v) at time t, and u represents the dynamic image The row, v represents a dynamic image Based on the E-tofts model and the arterial input function (AIF), the least squares method is used Estimate the hemodynamic parameters corresponding to the pixel point (u, v) along time 、 , the process is expressed as:

[0101] ;

[0102] in, and The pixel coordinates are of K trans and V p value, is the image of the dynamic image at position (u, v) at time F.

[0103] Specifically, is the vascular permeability transport constant at position (u, v), which can reflect the ability to transport contrast agents from the blood vessels to the tissue space. is the plasma volume fraction at position (u, v), which can reflect the contrast agent concentration in the plasma. In summary, the undersampled k-space data after the continuous sampling of non-Cartesian radial line multi-coil magnetic resonance k-space data is framed, the dynamic signal data calculated and K trans 、 V p The quantitative parameters together constitute the training set of the network.

[0104] Furthermore, step 2 includes the following steps:

[0105] like Figure 3 As shown in the figure, an iterative network for dual-domain subspace learning based on quantitative parameter constraints, dynamic prior constraints and k-space constraints is designed. The network is composed of a preprocessing module and a network iteration module as the core, and is composed of multiple cascaded network iteration blocks.

[0106] like Figure 4As shown in the figure, the network iteration module consists of two parts: K-space learning (KL) and data consistency verification (DC).

[0107] (a) Preprocessing

[0108] First, the undersampled k-space data after frame division The complex values ​​of are split into real and imaginary matrices, and the split real and imaginary matrices are rearranged by columns. The following are the specific implementation steps:

[0109] The k-space data after frame division Use the plural form to describe: ,in represents the imaginary unit, represents the real part matrix, ,The real part mainly represents the real anatomical structure and tissue information, which is the main part in image reconstruction. Represents the imaginary part matrix. The imaginary part contains the imaging phase information, which is an important component of the magnetic resonance image.

[0110] Arrange the real and imaginary parts of the complex k-space data in rows: ,Will and Concatenate by column vectors to get the target matrix input to the iteration block , which has the following form:

[0111] ;in For the The target matrix of the jth coil of the frame, is the total target matrix, and the total target matrix is ​​input into the network iteration module.

[0112] (b) Network iteration block

[0113] The network iteration block consists of L iteration blocks, each of which includes a k-space learning module (KL) and a data consistency check module (DC). The specific process is as follows:

[0114] A. K-space learning (KL)

[0115] The k-space learning submodule includes the fan-shaped subspace learning submodule and the annular subspace learning submodule. The two submodules are used to learn and fill the missing points in the k-space, and the results of the two subspace learning are fused.

[0116] Sector subspace learning submodule: the total target matrix Input the fan-shaped subspace learning module and transform the total target matrix Rearrange the data blocks according to the d columns, and then there will be n data blocks to be learned, that is, , Represents all the data blocks to be learned, Represents the first data block to be learned, Represents the nth data block to be learned.

[0117] For each data block to be learned, the network adopts a cascade convolutional network structure composed of multiple CBRs. The convolutional network directly fills the k-space of each data block to be convolved and learns, realizing the nonlinear network mapping of direct prediction of the missing sampling points in each data block, and obtaining , the process is described as follows:

[0118] ;in, It indicates that the k-space data that is completely filled along the sector is output after the cascade CBR structure is learned. represents the network mapping from undersampled k-space to filled k-space, represents the output of the first learning data block, represents the output of the nth learning data block, Represents the network learning parameters of the first learning data block, represents the network learning parameters of the nth learning data block, Indicates the convolutional layer used by the first learning data block, represents the convolutional layer used by the nth learning data block, (Batch Normalization) is the normalization function, (Rectified Linear Unit) is a nonlinear activation function.

[0119] Then to Perform convolution again to avoid When the output of the post-convolution network is less than or equal to zero, the output k-space point value is 0. The final input of the post-convolution sector learning submodule is , the formula is as follows:

[0120] ;in, is the k-space data after reconvolution, The convolution kernel network learning parameters for the first learning data block, is the convolution kernel network learning parameter of the nth learning data block, is the network output after the first learning data block is convolved, is the network output after the nth learning data block is convolved.

[0121] Therefore, the fan-shaped subspace learning submodule in a single iteration block can be described as:

[0122] ;in, l Indicates the l Iteration blocks, Indicates the k-space learning submodule l The padded k-space data output by the iterative block, Indicates the l The mapping process of an iterative block fan subspace learning network, is the total target matrix of the network input, Indicates the l The parameters of the fan-shaped subspace network are learned by iterative blocks;

[0123] Ring subspace learning submodule: the total target matrix Input the annular subspace learning module and transform the total target matrix Rearrange the data blocks to be learned according to c rows. After rearrangement, there are m data blocks to be learned, that is, , Represents all the data blocks to be learned, Represents the first data block to be learned, Represents the mth data block to be learned;

[0124] For each data block to be learned, the network adopts a cascade convolutional network structure composed of multiple CBRs. The convolutional network directly fills the k-space of each data block to be convolved, and realizes the nonlinear network mapping of direct prediction of the sampling missing points in each data block to obtain the filled k-space data. , the process is described as follows:

[0125] ;in, It indicates the k-space data that is completely filled along the ring after the cascade CBR structure is learned. represents the mapping from undersampled k-space to filled k-space, Represents all the data blocks to be learned, is the total network learning parameter of the learning process, represents the network output of the first learning data block, represents the network output of the mth learning data block, Indicates the first data block to be learned, represents the mth data block to be learned, Represents the network learning parameters of the first learning data block, represents the network learning parameters of the mth learning data block, Indicates the convolutional layer used by the first learning data block, represents the convolutional layer used by the mth learning data block, (Batch Normalization) is the normalization function, (Rectified LinearUnit) is a nonlinear activation function.

[0126] Then to Perform convolution again to avoid When the output of the network is less than or equal to zero, the output k-space point is 0. The final input of the post-convolutional ring learning submodule is , the formula is as follows: ;in, is the k-space data after reconvolution, is the k-space data output by the convolved network of the first learning data block, The network output k-space data after the m-th learning data block is convolved, Indicates that the first learning data block uses the convolutional layer, Indicates that the mth learning data block uses the convolution layer, Represents the network parameters learned by the convolutional layer of the first learning data block, Represents the network parameters learned by the convolutional layer of the mth learning data block.

[0127] Therefore, the annular subspace learning submodule in a single iteration block can be described as:

[0128] ;in, l Indicates the l Iteration blocks, Represents the annular subspace learning module l The padded k-space data output by the iterative block, Indicates the l The network mapping of the submodule is learned by the annular subspace of the iterative blocks, Learn parameters for the annular subspace learning submodule network.

[0129] After the two subspaces are learned, the filled k-space data output by the two submodules are fused. The fusion formula is as follows:

[0130] ;in, and For the l The weighted coefficient of the network learning in each iterative block is determined by the network's self-learning. For the l The network mapping relationship of the submodules is learned in the iterative block fan subspace. For the l The network mapping relationship of the submodules is learned in the annular subspace of the iterative block. For the l The network learning parameters of iterative block fan subspace learning, Indicates the l The network learning parameters of the iterative block annular subspace learning, is the total target matrix, For the l Output data after k-space data fusion of iterative blocks;

[0131] B. Data consistency (DC)

[0132] To prevent k-space data learning from going astray, a data consistency check (DC) is performed on the fused k-space data to maintain the consistency between the filled k-space data obtained by the two learning methods and the sampled data points in the undersampled k-space data. The formula is as follows:

[0133] ;

[0134] Where, For the l The network mapping relationship of the submodules is learned in the iterative block fan subspace. For the l The network mapping relationship of the submodules is learned in the annular subspace of the iterative block. represents the undersampled k-space data input to the iterative block, Indicates that the current data point is within the image, Indicates that the current data point is not in the image. and For the l The weighted coefficients learned by the network in iterative blocks, is the total target matrix, For the l The network learning parameters of iterative block fan subspace learning, For the l The network learning parameters of the iterative block annular subspace learning, Indicates the l The k-space data is output after the data consistency check of the iterative blocks;

[0135] Therefore, the learning process of a single iterative block can be described as:

[0136] ;in, Represents the cascade of the learning process of each module of the iterative block, represents the total target matrix, is the undersampled k-space data, For iterative blocks l The learned network parameters, For iterative blocks l The subspace network learns the mapping, Iteration Block l The data consistency verification process, For iterative blocks l The network outputs k-space data.

[0137] In summary, the reconstruction formula of the entire network is as follows:

[0138] ; among them, among them, Represents the reconstruction mapping process of the entire network, represents the learning parameters of the entire network, represents undersampled k-space data, is the final filled k-space data learned by the network, Represents the network map of the first iteration block, represents the network map of the L-th iteration block, represents the network learning parameters of the first iteration block, represents the network learning parameters of the Lth iteration block.

[0139] The final reconstructed dynamic image is obtained by non-uniform Fourier transform:

[0140] ;in, is the complex conjugate transpose of the sensitivity map, is the non-uniform Fourier transform, is the dynamic image of F frames after reconstruction, D represents density compensation, It is the final filled k-space data for network learning.

[0141] The three-constraint loss function is constructed by quantitative parameter constraint, dynamic signal data constraint and k-space data constraint. The specific process is as follows: A. Quantitative parameter constraint Loss1

[0142] Using the quantitative parameters obtained in step 1) K trans and V pThe quantitative parameters of the labeled training set and the dynamic graph reconstructed by the network are estimated with Loss1 constraints:

[0143] ;in, is the two-norm term, Respectively represent the corresponding coordinates in the dynamic image, represents the sum operation, Represents dynamic graph reconstruction from the network Calculate quantitative parameters K trans and V p The operator, L represents the total number of iterations, G represents the total number of training samples, Indicates that the coordinates are The optimization algorithm calculates the label in the dynamic graph K trans value, Indicates that the coordinates are Reconstructed dynamic image calculated K trans value; Indicates that the coordinates are The optimization algorithm calculates the label in the dynamic graph V p value, Indicates that the coordinates are Reconstructed dynamic image calculated V p value, represents the quantitative parameter-constrained loss function of the network, Represents the set of learning parameters of the entire network;

[0144] Specifically, because the network is constantly training, the loss function value is calculated as the average of all iterations under all current training samples. Therefore, it is necessary to take the inverse of the product of the total number of iterations and the total number of training samples, which is expressed as .

[0145] B. Dynamic Signal Constraint Loss2

[0146] A series of continuous dynamic images will be reconstructed and the reference image calculated in the training set , extract the pixels at the same position for each frame of image along the time dimension The value of (u, v) is used to obtain the dynamic signal data (Dynamic Signal Curve, DSC). The dynamic signal data generated by the optimization algorithm is constrained with the dynamic signal data output by the network prediction to minimize the difference between the two data. When integrated into the network training process, the loss function is used to constrain the dynamic information to make it more accurate. The loss function is defined as follows:

[0147] The dynamic signal constraint is expressed as:

[0148] ;in, represents the entire network learning parameter set, represents the two-norm term, L represents the total number of iterations, G represents the total number of training samples, represents the sum operation, is the dynamic signal data extraction operator, Indicates the label dynamic signal data calculated in the optimization algorithm dynamic graph, Indicates that the dynamic signal data is calculated from the dynamic image reconstructed by the network, represents the label dynamic image reconstructed by the optimization algorithm, represents the reconstructed dynamic image, represents the dynamic signal constraint loss function.

[0149] C. k-space constrained Loss3

[0150] The network finally outputs the filled k-space data The k-space data satisfying Nyquist sampling obtained in step S1 The formula for performing k-space constraint as k-space reference data is as follows: The k-space constraint is expressed as:

[0151] ;in, is the two-norm term, l Indicates the l Iteration blocks, L represents the total number of iterations, G represents the total number of training samples, represents the sum operation, represents the labeled k-space data that meets the Nyquist sampling criterion, represents the k-space data after network learning, represents the loss function of the k-space constraint, Represents the entire network learning parameter set.

[0152] In summary, the total loss function of the three constraints can be expressed as:

[0153] ;in, 、 and is the adjustable weight coefficient, represents the total loss function of the network, represents the entire network learning parameter set, Indicates the label dynamic signal data calculated in the optimization algorithm dynamic graph, Indicates that the dynamic signal data is calculated from the dynamic image reconstructed by the network, represents the labeled k-space data that meets the Nyquist sampling criterion, represents the k-space data after network learning, Indicates that the coordinates are The optimization algorithm calculates the label in the dynamic graph K trans value, Indicates that the coordinates are Reconstructed dynamic image calculated K trans value; Indicates that the coordinates are The optimization algorithm calculates the label in the dynamic graph V p value, Indicates that the coordinates are Reconstructed dynamic image calculated V p value, L represents the total number of iterations, G represents the total number of training samples, Represents a sum operation.

[0154] Furthermore, step 3 includes the following steps:

[0155] Solve the optimal parameters of the iterative network based on quantitative parameter constraints, dynamic prior constraints and k-space constraints, using the Adam optimizer, using the training set generated in step 1) and the loss function in step 2) Constraints to obtain optimal network training parameters , and reconstruct the optimal filled k-space data .

[0156] Furthermore, step 4 includes the following steps:

[0157] The framed k-space data is input into the trained network to reconstruct dynamic images, achieving fast, high temporal and spatial resolution, and accurate quantitative magnetic resonance dynamic contrast-enhanced images.

[0158] After the network training is completed, the non-Cartesian undersampled k-space data to be reconstructed Input the trained network to reconstruct the dynamic magnetic resonance image and predict and reconstruct the filled k-space data ,right Perform non-uniform Fourier transform to obtain the final dynamic image reconstruction result , the formula is as follows:

[0159] ; where D represents the density compensation operator for the Fourier space data of each coil in each time dimension, represents the inverse non-uniform Fourier transform;

[0160] represents the final reconstructed dynamic magnetic resonance image, represents the magnetic resonance dynamic contrast enhanced image after network reconstruction, Indicates the Frame of MRI dynamic contrast-enhanced imaging image, is the final k-space data after network learning and filling, is the complex conjugate transpose of the sensitivity map, and Represent the MRI dynamic contrast-enhanced images of frame 1 and frame F respectively.

[0161] like Figure 2 As shown, in this embodiment, continuous sampling of non-Cartesian golden angle sampling DCE-MRI k-space data (dimensions are 600×768×12) is adopted, and the network is reconstructed into DCE-MRI dynamic images (20 frames in total) with 30 spoke k-space data as one frame.

[0162] like Figure 5 As shown, in the reconstructed image comparison of this embodiment, Figure 5 (a) in the figure is the undersampled and unreconstructed image of different frames. Figure 5 (b) in the figure shows reconstructed images from different frames. Compared with existing technologies, this embodiment utilizes dual-domain subspace learning of k-space data, leveraging quantitative parameter constraints, dynamic prior constraints, and k-space constraints to accelerate reconstruction speed and improve image reconstruction quality. This enables fast, high-temporal and spatial resolution, and accurate quantitative intelligent DCE-MRI imaging.

[0163] Example 2

[0164] like Figure 6 As shown, based on Example 1, this embodiment proposes a terminal device for a non-Cartesian magnetic resonance dynamic contrast enhancement intelligent imaging method, wherein the terminal device 200 includes at least one memory 210, at least one processor 220, and a bus 230 connecting different platform systems.

[0165] The memory 210 may include a readable medium in the form of a volatile memory, such as a RAM 211 and / or a cache memory 212 , and may further include a ROM 213 .

[0166] The memory 210 also stores a computer program that can be executed by the processor 220, so that the processor 220 performs any of the above-mentioned non-Cartesian magnetic resonance dynamic contrast enhancement intelligent imaging methods in the embodiments of the present application. The specific implementation method is consistent with the implementation method and the technical effect achieved in the embodiments of the above-mentioned method, and some of the contents are not repeated here. The memory 210 may also include a program / utility 214 having a set (at least one) of program modules 215. Such program modules include but are not limited to: an operating system, one or more application programs, other program modules, and program data. Each of these examples or some combination may include the implementation of a network environment.

[0167] Accordingly, the processor 220 may execute the aforementioned computer programs, as well as the program / utility 214 .

[0168] The bus 230 may represent one or more of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, a processor, or a local bus using any of a variety of bus architectures.

[0169] The terminal device 200 can also communicate with one or more external devices 240, such as keyboards, pointing devices, Bluetooth devices, etc., and can also communicate with one or more devices that can interact with the terminal device 200, and / or communicate with any device that enables the terminal device 200 to communicate with one or more other computing devices (such as routers, modems, etc.). Such communication can be carried out through the I / O interface 250. In addition, the terminal device 200 can also communicate with one or more networks (such as local area networks (LANs), wide area networks (WANs) and / or public networks, such as the Internet) through the network adapter 260. The network adapter 260 can communicate with other modules of the terminal device 200 through the bus 230. It should be understood that although not shown in the figure, other hardware and / or software modules can be used in conjunction with the terminal device 200, including but not limited to: microcode, device drivers, redundant processors, external disk drive arrays, RAID systems, tape drives, and data backup storage platforms.

[0170] Example 3

[0171] like Figure 7As shown, based on Example 1, this embodiment provides a computer-readable storage medium for a non-Cartesian MRI dynamic contrast-enhanced intelligent imaging method. The computer-readable storage medium stores instructions that, when executed by a processor, implement any of the aforementioned non-Cartesian MRI dynamic contrast-enhanced intelligent imaging methods. The specific implementation and technical effects achieved are consistent with those described in the aforementioned method embodiments, and some details are omitted for clarity.

[0172] Figure 7 The program product 300 provided in this embodiment for implementing the above method is shown. It can use a portable compact disc read-only memory (CD-ROM) and include program code, and can be run on a terminal device, such as a personal computer. However, the program product 300 of the present invention is not limited to this. In this embodiment, the readable storage medium can be any tangible medium that contains or stores a program, and the program can be used by or in conjunction with an instruction execution system, device, or device. The program product 300 can use any combination of one or more readable media. The readable medium can be a readable signal medium or a readable storage medium. The readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or device, or any combination of the above. More specific examples of readable storage media (a non-exhaustive list) include: an electrical connection with one or more wires, a portable disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0173] A computer-readable storage medium may include a data signal transmitted in baseband or as part of a carrier wave, carrying readable program code. This transmitted data signal may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. The readable storage medium may also be any readable medium other than a readable storage medium, which can transmit, transmit, or transfer a program for use by or in conjunction with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical cable, RF, etc., or any suitable combination thereof. The program code for performing the operations of the present invention may be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, C++, etc., as well as conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user computing device, partially on the user device, as a standalone software package, partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server. Where a remote computing device is involved, the remote computing device may be connected to the user computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computing device (e.g., through the Internet using an Internet service provider).

[0174] The foregoing description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the form disclosed herein and should not be construed as excluding other embodiments. Rather, the present invention can be used in various other combinations, modifications, and environments and can be modified within the scope of the concept described herein through the above teachings or techniques or knowledge in the relevant field. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention are intended to be protected by the appended claims.

Claims

1. A non-Cartesian magnetic resonance dynamic contrast enhanced intelligent imaging method, characterized in that: The following steps are involved: S1. Obtain multi-coil magnetic resonance k-space data from the magnetic resonance imaging instrument through magnetic resonance data acquisition. Perform frame rearrangement and dynamic image reconstruction on the multi-coil magnetic resonance k-space data based on the time dimension and Nyquist sampling theory to construct a training set. S2. Construct an iterative network and loss function for multi-coil MRI k-space data based on dual-domain subspace learning theory with quantitative parameter constraints, dynamic prior constraints, and k-space constraints. S3. Solve the iterative network to obtain the optimal parameters based on the training set obtained in step S1; S4. Inputting the frame-rearranged multi-coil MRI k-space data into the iterative network according to the trained iterative network for image reconstruction to obtain a reconstructed MRI dynamic contrast-enhanced image; The training set includes undersampled k-space data, k-space label data that meets Nyquist sampling, quantitative parameters and dynamic image signal data; The method of performing frame rearrangement and dynamic image reconstruction on the multi-coil magnetic resonance k-space data according to the time dimension and the Nyquist sampling theory, and constructing a training set includes the following steps: S101. By acquiring magnetic resonance data, obtain multi-coil magnetic resonance k-space data of a magnetic resonance imaging instrument, expressed as: Where Y is the multi-coil magnetic resonance k-space data, is a complex domain, M is the number of spokes, N is the number of sampling points, and J is the number of coils. The multi-coil magnetic resonance k-space data is framed to obtain the undersampled k-space data after framing. The total number of frames of the k-space data after framing is expressed as: Where M is the number of spokes, R is the number of spokes of the undersampled k-space data after framing, and F is the total number of frames of the k-space data after framing; The multi-coil magnetic resonance k-space data is rearranged and framed along the time dimension to obtain undersampled k-space data, which is expressed as: Where H is the undersampled k-space data, Y is the multi-coil magnetic resonance k-space data, is the time rearrangement operator, is the undersampled k-space data of the j-th coil in the f-th frame; S102. Obtain multi-coil magnetic resonance k-space data from the magnetic resonance imaging instrument through magnetic resonance data acquisition. According to the Nyquist sampling theory, the multi-coil magnetic resonance k-space data is rearranged along adjacent time frames to obtain k-space label data, which is expressed as: in, is an operator for rearranging the multi-coil magnetic resonance k-space data Y according to the number of spokes of the Nyquist sampling criterion, where Y is the multi-coil magnetic resonance k-space data, is the rearranged k-space data, A is the last dimension of the rearranged k-space data, and the rearranged k-space data is copied according to the total number of frames of the undersampled k-space data after framing to obtain the final k-space label data, which is expressed as: in, To satisfy the Nyquist sampling of k-space label data, is the replication operator, F is the total number of frames of k-space data after framing, W is the number of radial k-space data spokes of each frame in the k-space label data, N is the number of sampling points, and J is the number of coils; S103. Optimize the dynamic reconstruction of the undersampled k-space data using an optimized reconstruction algorithm to obtain a dynamic image, which is expressed as: M=f(H) M=[M1;M2;...;M F ] Where f is the optimized reconstruction algorithm, M is the dynamic image reconstructed by the optimized algorithm, M1; M2; ...; M F are the 1st to F frames in the dynamic image reconstructed by the optimization algorithm, H is the undersampled k-space data, and F is the total number of frames of the k-space data after framing. Through the extraction algorithm, the values ​​of the pixels at the same position in each frame of the dynamic image are extracted along the time dimension and the dynamic signal data is calculated, which is expressed as: in, is the extraction algorithm along the time dimension, M is the dynamic image reconstructed by the optimization algorithm, and Cu is the dynamic image signal data; S104. Based on the dynamic image signal data, an E-tofts model is constructed and quantitative parameters are calculated along the time pixel points by the least squares method; S105. A training set is constructed based on the obtained undersampled k-space data, dynamic image signal data, and quantitative parameters.

2. The non-Cartesian magnetic resonance dynamic contrast enhanced intelligent imaging method according to claim 1, characterized in that: The iterative network in step S2 includes a preprocessing module and a network iteration module. The iterative network for constructing multi-coil magnetic resonance k-space data includes the following steps: S201. Construct a preprocessing module, including the following steps: S201.

1. Split the complex values ​​of the undersampled k-space data into real and imaginary parts, expressed as: H jf =R+Yes R＝[r1,r2…r N ] Among them, H jf is the undersampled k-space data of the j-th coil in the f-th frame, is the real part matrix, r1,r2…r N are the real part values ​​from the 1st sampling point to the Nth sampling point respectively, is the imaginary part matrix, i1,i2i N are the imaginary part values ​​from the 1st sampling point to the Nth sampling point, respectively, and i is the imaginary unit; S201.

2. Arrange the real part matrix and the imaginary part matrix by row to obtain undersampled k-space data arranged by row, which is expressed as: H jf =[r1,r2…r N ,i1,i2…i N ] S201.

3. The undersampled k-space data arranged by row splicing are then vector-spliced ​​by column to obtain the target matrix input to the network iteration module, which is expressed as: Among them O jf is the target matrix of the jth coil in the fth frame, O is the total target matrix, and the total target matrix is ​​input into the network iteration module; S202. Construct a network iteration module, including L cascaded iteration blocks, wherein the iteration block includes a k-space learning module and a data consistency check module, including the following steps: S202.

1. Construct a sector subspace learning module and a ring subspace learning module respectively, including the following steps: A. Constructing a fan-shaped subspace learning module includes the following steps: A1. Based on the obtained total target matrix O, rearrange it so that each column is a data block to be learned, and obtain n data blocks P to be learned, which can be expressed as: P=[P1,…,P n ]=O Among them, O is the total target matrix, P represents all the data blocks to be learned, P1 represents the first data block to be learned, and P n Indicates the nth data block to be learned; A2. By cascading multiple CBR structures containing two-dimensional convolution functions, normalization functions, and nonlinear activation functions, the network structure of each data block to be learned is obtained. Then, data mapping is performed on each data block to be convolved through k-space filling learning. The complete k-space data of each data block to be learned is directly predicted by the missing sampling points. The formula is expressed as: Z=f1(P|θ)=[Z1=ReLU(BN(Conv1(P1|θ1))),...,Z n =ReLU(BN(Conv n (P n |θ n )))] Among them, Z is the k-space data filled along the fan after the cascade CBR structure is learned, f1(P|θ) represents the network mapping process from undersampled k-space to filled k-space, Z1 represents the output of the first learning data block, and Z n represents the output of the nth learning data block, θ represents the network learning parameters of the learning data block, θ1 represents the network learning parameters of the first learning data block, θ n represents the network learning parameters of the nth learning data block, P represents the data block to be learned, P1 represents the first data block to be learned, and P n Indicates the nth data block to be learned, Conv1 indicates the convolutional layer used for the first learning data block, Conv n Represents the convolutional layer used by the nth learning data block, BN is the normalization function, and ReLU is the nonlinear activation function; A3. Based on the k-space data obtained after learning the cascaded CBR structure, the k-space data filled along the sector is re-convolved using the convolution algorithm to obtain the k-space data of the re-convolved sector subspace learning module, which is expressed as follows: Z′=[Z′1,…,Z′ n ]=[Z′1=Conv1(Z1|θ′1),…,Z′ n =Conv n (WITH n |θ′ n )] Among them, Z′ is the k-space data after re-convolution, θ′1 is the convolution kernel network learning parameter of the first learning data block; θ′ n is the convolution kernel network learning parameter of the nth learning data block, Z1′ is the network output after the first learning data block is convolved, and Z′ n is the network output after the nth learning data block is convolved; A4. Based on the reconvolved k-space data, a single iterative block fan-shaped subspace learning module is obtained, which is expressed as: Where l represents the lth iteration block, Z′ (l) represents the padded k-space data output by the lth iteration block of the k-space learning submodule, represents the mapping process of the lth iterative block fan subspace learning network, O is the total target matrix of the network input, represents the fan-shaped subspace network learning parameters of the lth iteration block; B. Constructing the annular subspace learning module includes the following steps: B1. Based on the obtained target matrix, rearrange it so that e rows form a data block to be learned, and obtain m data blocks to be learned, which can be expressed as: Among them, O is the total target matrix, X represents all the data blocks to be learned, X1 represents the first data block to be learned, and X m Represents the mth data block to be learned; B2. By cascading multiple CBR structures containing two-dimensional convolution functions, normalization functions, and nonlinear mapping functions, the network structure of each data block to be learned is obtained. Then, data mapping is performed on each data block to be convolved through k-space filling learning. The nonlinear network mapping data of the missing sampling points of each data block to be learned is obtained, which is expressed as: Wherein, Τ is the k-space data filled completely along the ring after the cascade CBR structure is learned, represents the mapping from undersampled k-space to filled k-space, X represents all the data blocks to be learned, is the total network learning parameter of the learning process, T1 represents the network output of the first learning data block, T m represents the network output of the mth learning data block, X1 represents the first data block to be learned, and X m represents the mth data block to be learned, Represents the network learning parameters of the first learning data block, represents the network learning parameters of the mth learning data block, Conv1 represents the convolutional layer used in the first learning data block, Conv m represents the convolutional layer used by the mth learning data block, BN is the normalization function, and ReLU is the nonlinear activation function; B3. Based on the k-space data obtained after learning the cascaded CBR structure, the k-space data filled along the ring is re-convolved by the convolution algorithm to obtain the k-space data of the sector subspace learning module after re-convolution. The formula is expressed as: Among them, T′ is the k-space data after re-convolution, T′1 is the k-space data output by the network after convolution of the first learning data block, and T′ m The network outputs k-space data after the mth learning data block is convolved. Conv′1 means that the first learning data block uses the convolution layer. Conv′ m Indicates that the mth learning data block uses the convolution layer, Represents the network parameters learned by the convolutional layer of the first learning data block, Represents the network parameters learned by the convolutional layer of the mth learning data block; B4. Based on the reconvolved k-space data, a single annular subspace learning module is obtained, which is expressed as: Where l represents the lth iteration block, T′ (l) represents the padded k-space data output by the lth iteration block of the annular subspace learning module, represents the network mapping of the annular subspace learning submodule of the lth iteration block, Learning parameters for the annular subspace learning submodule network; S202.

2. The obtained k-space filling data of the sector subspace learning module is fused with the k-space filling data of the annular subspace learning module to obtain a k-space learning module. The fusion formula is expressed as: in, and is the weighted coefficient learned by the network in the lth iteration block, The network mapping relationship of the submodule for learning the fan-shaped subspace of the lth iteration block, The network mapping relationship of the submodules in the ring subspace learning of the lth iteration block is: is the network learning parameter for the lth iteration block fan subspace learning, is the network learning parameter of the lth iteration block annular subspace learning, O is the total target matrix, U (l) is the output data after the k-space data fusion of the l-th iteration block; S202.

3. Perform a data consistency check based on the fused k-space data output by the k-space learning module to obtain a verification result. The verification formula is expressed as: in, The network mapping relationship of the submodule for learning the fan-shaped subspace of the lth iteration block, is the network mapping relationship of the annular subspace learning submodule of the lth iteration block, H is the undersampled k-space data, p∈Ω indicates that the current data point is in the image, Indicates that the current data point is not in the image. and is the weighted parameter learned by the network in the lth iteration block, B (l) is the k-space data output after the data consistency check of the lth iteration block, O is the total target matrix, is the network learning parameter for the lth iteration block fan subspace learning, The network learning parameters for the lth iteration block annular subspace learning; S202.

4. Based on the data verification results, the learning formula for a single iterative block is expressed as: in, is the cascade of the learning process of each module of the iterative block, H is the undersampled k-space data, O represents the total target matrix, are the network parameters learned in iterative block l, The subspace network learns the mapping for iterative block l, Iterate the data consistency check process of block l, B (l) Output k-space data for the network of iterative block l; The final filled k-space data is obtained by cascading multiple iterative blocks, which is expressed as: Among them, f all Represents the reconstruction mapping process of the entire network, Θ all represents the learning parameters of the entire network, H represents the undersampled k-space data, and B recon is the final filled k-space data learned by the network, Represents the network map of the first iteration block, represents the network map of the L-th iteration block, represents the network learning parameters of the first iteration block, represents the network learning parameters of the Lth iteration block; S202.

5. Final filling of k-space data B recon The dynamic image is reconstructed by non-uniform Fourier transform, and the final dynamic image reconstructed by the network is obtained, which is expressed as: in, is the complex conjugate transpose of the sensitivity map, for Non-uniform Fourier transform, M recon is the dynamic image of F frames after reconstruction, D is density compensation, B recon It is the final filled k-space data for network learning.

3. The non-Cartesian magnetic resonance dynamic contrast enhanced intelligent imaging method according to claim 2, characterized in that: The loss function in step S2 is constructed by quantitative parameter constraints, dynamic signal data constraints, and k-space data constraints. The quantitative parameter constraints are expressed as: in, is the two-norm term, (u, v) represent the corresponding coordinates in the dynamic image, Σ represents the summation operation, Represents the reconstruction of the dynamic graph M from the network recon Calculate the quantitative parameter K trans and V p operator, L represents the total number of iterations, G represents the total number of training samples, Indicates that the label K is calculated in the optimization algorithm dynamic graph with coordinates (u, v) trans value, Indicates K calculated by reconstructing the dynamic image at coordinates (u, v) trans Value; V p ref (u,v) represents the label V calculated in the optimization algorithm dynamic graph with coordinates (u,v) p Value, V p recon (u,v) represents the V calculated by reconstructing the dynamic image at the coordinate (u,v) p Value, Loss1(Θ) represents the quantitative parameter constraint loss function of the network, Θ represents the learning parameter set of the entire network; The dynamic signal constraint is expressed as: Among them, Θ represents the entire network learning parameter set, represents the two-norm term, L represents the total number of iterations, G represents the total number of training samples, Σ represents the summation operation, is a dynamic signal data extraction operator, Cu ref Indicates the tag dynamic signal data calculated in the optimization algorithm dynamic graph, Cu recon Indicates the dynamic signal data calculated from the network-reconstructed dynamic image; M ref represents the label dynamic image reconstructed by the optimization algorithm, M recon represents the reconstructed dynamic image, and Loss2 represents the dynamic signal constraint loss function; The k-space constraint is expressed as: in, is the two-norm term, l represents the l-th iteration block, L represents the total number of iterations, G represents the total number of training samples, Σ represents the summation operation, B ref represents the labeled k-space data that meets the Nyquist sampling criterion, B recon represents the k-space data after network learning, Loss3 represents the loss function of k-space constraint, and Θ represents the entire network learning parameter set; The loss function is expressed as: Among them, λ1, λ2 and λ3 are adjustable weight coefficients, Loss total Represents the total loss function of the network, Θ represents the set of learning parameters of the entire network, Cu ref Indicates the tag dynamic signal data calculated in the optimization algorithm dynamic graph, Cu recon Indicates the dynamic signal data calculated from the network reconstructed dynamic image, B ref represents the labeled k-space data that meets the Nyquist sampling criterion, B recon represents the k-space data after network learning, Indicates that the label K is calculated in the optimization algorithm dynamic graph with coordinates (u, v) trans value, Indicates K calculated by reconstructing the dynamic image at coordinates (u, v) trans Value; V p ref (u,v) represents the label V calculated in the optimization algorithm dynamic graph with coordinates (u,v) p Value, V p recon (u,v) represents the V calculated by reconstructing the dynamic image at the coordinate (u,v) p value, L represents the total number of iterations, G represents the total number of training samples, and Σ represents the summation operation.

4. The non-Cartesian magnetic resonance dynamic contrast enhanced intelligent imaging method according to claim 1, characterized in that: The step S3 solves the iterative network by using the Adam optimizer, according to the training set obtained in step S1, combined with the loss function constraint in step S2, to obtain the optimal network training parameters of the iterative network, and reconstruct the optimal filled k-space data.

5. The non-Cartesian MRI dynamic contrast enhanced intelligent imaging method according to claim 1, characterized in that: In step S4, the multi-coil magnetic resonance k-space data after frame rearrangement is input into the iterative network according to the trained iterative network to perform image reconstruction, and the filled k-space data B is predicted and reconstructed. predicted , for B predicted The reconstructed MRI dynamic contrast-enhanced image is obtained by performing non-uniform Fourier transform, and the formula is as follows: Where D is the density compensation operator for the Fourier space data of each coil in each time dimension, is the non-uniform Fourier transform, M prediced B is the dynamic contrast-enhanced magnetic resonance image after network reconstruction. predicted is the final k-space data after network learning and filling, is the complex conjugate transpose of the sensitivity map, M1,M f and M F Represent the MRI dynamic contrast-enhanced images of frame 1, frame f, and frame F, respectively.

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