Magnetic resonance acoustic radiation force imaging reconstruction method and system

Abstract

The invention belongs to the technical field related to medical magnetic resonance image reconstruction, and discloses a magnetic resonance acoustic radiation force imaging reconstruction method and system, and the method comprises the steps: obtaining two groups of undersampling data; a model is built based on the undersampled data and the variables to be decided, the model is a weighted summation of a minimization function, the data consistency function is used for measuring the deviation between each group of undersampled data and k space data under the same undersampled template calculated based on the corresponding complex diagram to be solved, and the k space data is used for calculating the k space data under the same undersampled template; the fitting consistency function is used for measuring the deviation between any complex image and a fitting image thereof, the fitting image is obtained by fitting the other complex image and the phase difference, and the phase difference sparsity function is used for measuring the sparsity of the phase difference; and solving the model, and reconstructing an acoustic radiation force image of the sample based on a solving result. By adopting the method provided by the invention, the imaging speed can be accelerated while the positioning precision is ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field related to medical magnetic resonance image reconstruction, and more specifically, relates to a magnetic resonance acoustic radiation force imaging reconstruction method and a system thereof. Background Art

[0002] Ultrasound neuromodulation is a non-invasive, well-targeted deep brain stimulation technology that has great potential for the treatment of neurodegenerative diseases such as Alzheimer's disease and epilepsy. However, due to the reflection and scattering of the skull, the ultrasound action point will be offset, and the safety and effectiveness of ultrasound neuromodulation cannot be guaranteed. Magnetic resonance acoustic radiation force (impulse) imaging (MR-ARFI) can provide precise positioning and guidance for ultrasound neuromodulation. However, at present, a full sampling scan of MR-ARFI requires multiple ultrasound activations, a large ultrasound dose, and a long scanning time.

[0003] The article "A fast imaging method for magnetic resonance acoustic radiation force imaging for ultrasonic neuromodulation[D]. Journal of the Chinese Academy of Sciences, 2022. DOI: 10.27822 / d.cnki.gszxj.2022.000038." mentioned the k-space undersampling acceleration method, but it requires the acquisition of four sets of k-space data, and the scanning time still needs to be optimized.

[0004] Therefore, how to ensure the positioning accuracy of MR-ARFI while speeding up the imaging speed has become an urgent need in the field of ultrasonic neuromodulation. Summary of the invention

[0005] In view of the above defects or improvement needs of the prior art, the present invention provides a magnetic resonance acoustic radiation force imaging reconstruction method and system thereof, which aims to speed up the imaging speed while ensuring the positioning accuracy.

[0006] To achieve the above object, the present invention provides a magnetic resonance acoustic radiation force imaging reconstruction method, which comprises:

[0007] Acquire two groups of under-sampling data, wherein the two groups of under-sampling data are k-space data respectively acquired by performing two different motion encoding gradient scans on the sample by turning on two ultrasonic pulses, and the amplitudes of the two motion encoding gradients are the same but the polarities are opposite;

[0008] A model is constructed based on the under-sampled data and variables to be decided, wherein the variables to be decided include two complex images reconstructed under different motion coding gradients and a phase difference between the two complex images, the model is a weighted sum of minimization functions, the functions include a weighted sum of a data consistency function, a fitting consistency function and a phase difference sparsity function, the data consistency function is used to measure the deviation between each group of under-sampled data and the k-space data under the same under-sampled template calculated based on the corresponding complex image to be solved, the fitting consistency function is used to measure the deviation between any of the complex images and its fitting image, the fitting image is obtained by fitting based on another complex image and the phase difference, and the phase difference sparsity function is used to measure the sparsity of the phase difference;

[0009] The model is solved, and an acoustic radiation force image of the sample is reconstructed based on the solution result.

[0010] Optionally, the deviation between different data is calculated by calculating the L2 norm.

[0011] Optionally, sparsity is calculated by computing the L1 norm.

[0012] Optionally, the model is:

[0013]

[0014] In the formula, y 10 ,y 20 are the k-space data collected by positive and negative polarity motion encoding gradient scanning, respectively. Y1 and Y2 are the complex images reconstructed under positive and negative polarity motion encoding gradients, respectively. F represents the Fourier transform operator, θ is the phase difference, and λ and ε are the set weight coefficients.

[0015] Optionally, the alternating direction multiplier method is used to solve the model, and the alternating direction multiplier method converts the weighted sum of the functions in the model into an augmented Lagrangian function. Based on the augmented Lagrangian function, the model solution is converted into a local subproblem of solving the complex graph Y1 and a local subproblem of solving the complex graph Y2. Each decision variable is optimized by alternating iteration until convergence, and the final iterative result is output to complete the solution.

[0016] Optionally, the weight coefficient of the weighted summation is determined by a grid optimization method.

[0017] The present invention also provides a magnetic resonance acoustic radiation force imaging reconstruction system, which comprises:

[0018] Receiving unit: two groups of under-sampled data, wherein the two groups of under-sampled data are k-space data respectively acquired by performing two different motion encoding gradient scans on the sample by turning on two ultrasonic pulses, and the amplitudes of the two motion encoding gradients are the same but the polarities are opposite;

[0019] A modeling unit: used for building a model based on the under-sampled data and variables to be decided, wherein the variables to be decided include two complex images reconstructed under different motion coding gradients and the phase difference between the two complex images, the model is a weighted sum of minimization functions, the functions include a weighted sum of a data consistency function, a fitting consistency function and a phase difference sparsity function, the data consistency function is used to measure the deviation between each group of under-sampled data and the k-space data under the same under-sampled template calculated based on the corresponding complex image to be solved, the fitting consistency function is used to measure the deviation between any one of the complex images and its fitting image, the fitting image is obtained by fitting based on another complex image and the phase difference, and the phase difference sparsity function is used to measure the sparsity of the phase difference;

[0020] Solving unit: used for solving the model and reconstructing the acoustic radiation force image of the sample based on the solution result.

[0021] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program implements the steps of any of the above methods when executed by a processor.

[0022] The present invention also provides a computer program product, comprising a computer program or instructions, wherein when the computer program or instructions are executed by a processor, the steps of any of the above methods are implemented.

[0023] In general, compared with the prior art, the above technical solutions conceived by the present invention mainly have the following beneficial effects:

[0024] The magnetic resonance acoustic radiation force imaging reconstruction method proposed in the present invention collects two sets of k-space data by undersampling, substitutes them into the model for solution, obtains the value of the quantity to be decided, and based on the solution result, the image reconstruction can be quickly realized. The above method only needs to collect two sets of undersampling data. Compared with the current full sampling and undersampling methods (at least four sets of undersampling data), the scanning speed is improved, and the model comprehensively considers the data consistency, fitting consistency and the sparsity of the phase difference, and the reconstruction accuracy is higher. In general, the sampling method proposed in the present invention can ensure the positioning accuracy while speeding up the imaging speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a flowchart of the steps of a magnetic resonance acoustic radiation force imaging reconstruction method in one embodiment of the present invention. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0027] The present invention provides a magnetic resonance acoustic radiation force imaging reconstruction method, such as Figure 1 FIG. 1 is a flowchart of a method for reconstructing magnetic resonance acoustic radiation force imaging in an embodiment of the present invention. Figure 1 This method is introduced in detail.

[0028] Step S1: Acquire two groups of under-sampling data, which are k-space data respectively acquired by performing two different motion encoding gradient scans on the sample by turning on two ultrasonic pulses. The gradient amplitudes of the two motion encodings are the same but the polarities are opposite.

[0029] Among them, undersampling is generally used in compressed sensing. It is a sampling method with a sampling rate much lower than the Nyquist sampling rate. Under the premise of meeting the prerequisites of compressed sensing, the original signal is reconstructed from a small number of sampled values ​​in conjunction with the optimization algorithm. Compressed sensing needs to meet the following key conditions: (1) Signal sparsity: The signal is sparse in a certain transform domain, which means that the signal can be represented by very few non-zero coefficients; (2) Randomness of sampling: The measurement matrix of compressed sensing needs to satisfy the constraint of equidistance so that the structure of the measured signal is maintained in the sampled signal. Random undersampling can meet this requirement; (3) The effectiveness of the reconstruction algorithm: An effective reconstruction algorithm is required to restore the original signal from the sampled values.

[0030] In magnetic resonance acoustic radiation force imaging, the ultrasonic beam acts on a tiny area of ​​tissue, and the tissue displacement caused by it has only a small number of non-zero values ​​within the focal area, so the magnetic resonance acoustic radiation force displacement map is approximately sparse in space, satisfying the sparsity of the signal. The undersampling template is applied to the acquisition of the k-space of magnetic resonance acoustic radiation force images, and the overall approximation satisfies the randomness of the sampling. Then, by designing an effective reconstruction algorithm, it is jointly guaranteed that the magnetic resonance image data can be completely and accurately reconstructed even at a low sampling rate. Finally, these data are used to reconstruct the tissue displacement map. Compared with full sampling, undersampling can effectively shorten the sampling time and speed up the imaging speed.

[0031] In the present invention, the amplitude of the motion encoding gradient (MEG) used in the two undersamplings is the same but the polarity is different, wherein the motion encoding gradient used in one undersampling is positive and the motion encoding gradient used in the other undersampling is negative. The k-space data under two sets of different motion encoding gradients are collected, i.e., bipolar displacement encoding is used, in order to enhance the sensitivity of displacement measurement.

[0032] For the convenience of explanation, the k-space data acquired by the positive polarity motion encoding gradient scanning is recorded as y 10 , the k-space data acquired by the negative polarity motion encoding gradient scan is recorded as y 20 .

[0033] Step S2: construct a model based on the undersampled data and the variables to be decided, the variables to be decided include two complex images reconstructed under different motion coding gradients and the phase difference between the two complex images, the model is a weighted summation of minimization functions, and the functions for weighted summation include data consistency function, fitting consistency function and phase difference sparsity function.

[0034] Among them, the data consistency function is used to measure the deviation between each group of under-sampled data and the k-space data under the same under-sampling template calculated based on the corresponding complex image. The fitting consistency function is used to measure the deviation between any complex image and its fitting image. The fitting image is obtained by fitting based on another complex image and the phase difference. The phase difference sparsity function is used to measure the sparsity of the phase difference.

[0035] The variables to be determined in this model include two complex images reconstructed under different motion coding gradients and the phase difference between the two complex images. For the convenience of explanation, the complex image reconstructed under the positive polarity motion coding gradient is denoted as Y1, the complex image reconstructed under the negative polarity motion coding gradient is denoted as Y2, and the phase difference between Y1 and Y2 caused by ultrasound is denoted as θ. The above three parameters are all variables to be solved.

[0036] The following is a description of each function.

[0037] The data consistency function is used to measure the deviation between each group of under-sampled data and the k-space data under the same under-sampled template calculated based on the corresponding complex image.

[0038] The k-space image is the spectrum diagram of the complex magnetic resonance image in two-dimensional space, and is the result of a two-dimensional Fourier transform of the complex image. Similarly, the complex magnetic resonance image can be obtained by performing a two-dimensional inverse Fourier transform on its k-space data. Any point on the complex image is obtained by weighted summing all points in the k-space according to certain coefficients / weights (Fourier coefficients and phase). Based on the complex image and the undersampling template used during sampling, the k-space data under the same motion encoding gradient and the corresponding undersampling template can be reversely calculated, and the relationship is as follows:

[0039] y1 ′ 0 = FY1;

[0040] y2 ′ 0 = FY2;

[0041] Where F represents the Fourier transform operator, y1 ′ 0 is the k-space data under the positive polarity motion encoding gradient calculated based on the complex image Y1, y2 ′ 0 is the k-space data under the negative polarity motion encoding gradient calculated based on the complex image Y2.

[0042] The more accurate the reconstructed complex image is, the closer the k-space data inferred from the complex image is to the acquired k-space data. Therefore, this model considers the data consistency function, which is used to measure y1 ′ 0 and y 10 The deviation between ′ 0 and y 20 The smaller the deviation, the more accurate the result reconstructed by the model is usually.

[0043] The L2 norm can well measure the Euclidean distance between two sets of data and is currently a commonly used measurement method for measuring the distance between two sets of data. In specific operations, the data consistency function f1 can be introduced into the L2 norm to measure y1 ′ 0 and y 10 The deviation between ′ 0 and y 20 The deviation between them is specifically expressed as follows:

[0044]

[0045] The fit consistency function is used to measure the deviation between any of the complex images and its fitted image, which is obtained by fitting based on another complex image, phase difference and eddy current intensity coefficient.

[0046] Since the phase difference between the two images Y1 and Y2 under different motion coding gradients is a fixed constant θ, if one of Y1 and Y2 is known, the other can be fitted. Therefore, the smaller the deviation between the complex graph and the fitting result, the more accurate the result reconstructed by the model is.

[0047] In specific operations, the fitting result of Y2 can be obtained based on Y1, and the deviation between Y2 and its fitting result can be calculated. Alternatively, the fitting result of Y1 can be obtained based on Y2, and the deviation between Y1 and its fitting result can be calculated.

[0048] In specific operations, the fitting consistency function f2 can also introduce the L2 norm to measure the deviation between the complex graph and the fitting result, which is specifically expressed as follows:

[0049]

[0050] The phase difference sparsity function is used to measure the sparsity of the phase difference.

[0051] Since the phase difference generated by the ultrasonic beam acting on the tissue is sparse in space, the sparsity of the phase difference can be used to constrain and suppress the noise in the image.

[0052] The L1 norm is the sum of the absolute values ​​of each element in the calculation vector, and is a sparse rule operator commonly used in the optimization solution process. In specific operations, the phase difference sparsity function f3 can introduce the L1 norm to calculate the sparsity of the phase difference, which is specifically expressed as follows:

[0053] f3=||θ||1.

[0054] Combining the above examples, the model can be expressed as:

[0055]

[0056] Among them, the weight coefficients λ and ε can be used to find the optimal parameters through grid search.

[0057] In this model, data consistency, fitting consistency and sparsity of phase difference are comprehensively considered, and the reconstruction accuracy is higher. Moreover, this model only uses two sets of k-space data. Compared with traditional technology, the scanning speed is faster and the imaging time is shorter.

[0058] Step S3: Solve the model and reconstruct the acoustic radiation force image of the sample based on the solution result.

[0059] After the model is built, it is necessary to solve the model and obtain the solution of the decision variable to be determined, so that the image can be reconstructed. Specifically, it is only necessary to obtain the phase difference θ in the solution result and calculate it through the following formula to obtain the acoustic radiation force image:

[0060]

[0061] Where x is the average displacement during tissue encoding time, γ is the proton gyromagnetic ratio, G MEG is the motion coding gradient amplitude; t is the coding duration.

[0062] The alternating direction method of multipliers (ADMM) is usually used to solve problems with multiple optimization variables. In the present invention, the model has multiple variables to be solved, including a complex graph Y1, a complex graph Y2, and a phase difference θ. The alternating direction method of multipliers can also be used to solve the model.

[0063] Specifically, when using the alternating direction multiplier method, the weighted sum of the functions in the model will be converted into an augmented Lagrangian function. Based on the augmented Lagrangian function, the model solution will be converted into a local subproblem of solving the complex graph Y1 and a local subproblem of solving the complex graph Y2. By alternatingly optimizing each decision variable until convergence, the final iterative result is output to complete the solution.

[0064] Among them, the augmented Lagrangian function can be expressed as:

[0065]

[0066] In the formula, ξ1, ξ2, u1, u2 are newly introduced variables, and λ2 is the set weight coefficient.

[0067] The local subproblem of solving Y1 can be expressed as:

[0068]

[0069] The local subproblem of solving Y2 can be expressed as:

[0070]

[0071] Wherein, the superscript k represents the kth iteration.

[0072] By alternately iteratively optimizing each decision variable until convergence, the final iterative result is output, the solution is completed, and the solution results of each decision variable are obtained.

[0073] Accordingly, the present invention also relates to a magnetic resonance acoustic radiation force imaging reconstruction system, comprising:

[0074] Receiving unit: two groups of under-sampling data, the two groups of under-sampling data are k-space data collected by turning on two ultrasonic pulses to perform two different motion encoding gradient scans on the sample, and the amplitudes of the two motion encoding gradients are the same but the polarities are opposite;

[0075] Modeling unit: used to build a model based on undersampled data and variables to be decided, the variables to be decided include two complex images reconstructed under different motion coding gradients and the phase difference between the two complex images, the model is a weighted sum of minimization functions, and the functions for weighted summation include a data consistency function, a fitting consistency function, and a phase difference sparsity function. The data consistency function is used to measure the deviation between each group of undersampled data and the k-space data under the same undersampled template calculated based on the corresponding complex image to be solved. The fitting consistency function is used to measure the deviation between any of the complex images and its fitting image. The fitting image is obtained by fitting based on another complex image and the phase difference. The phase difference sparsity function is used to measure the sparsity of the phase difference;

[0076] Solving unit: used to solve the model and reconstruct the acoustic radiation force image of the sample based on the solution results.

[0077] The above system can be used to implement the magnetic resonance acoustic radiation force imaging reconstruction method introduced above, and each unit therein can implement the corresponding steps in the method. The specific process can be referred to the above introduction and will not be repeated here.

[0078] The present invention also relates to a computer-readable storage medium having a computer program stored thereon, and the computer program implements the steps of the above method when executed by a processor.

[0079] Specifically, the memory may include a high-speed random access memory, and may also include a non-volatile memory, such as a hard disk, an internal memory, a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card (Flash Card), at least one disk storage device, a flash memory device, or other volatile solid-state storage devices.

[0080] The present invention also provides a computer program product or a computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the computer device performs the steps of the method of the above embodiment of the present invention.

[0081] It should be pointed out that, for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all fall within the protection scope of the present invention.

Claims

1. A magnetic resonance acoustic radiation force imaging reconstruction method, characterized in that: include: Acquire two groups of under-sampling data, wherein the two groups of under-sampling data are k-space data respectively acquired by performing two different motion encoding gradient scans on the sample by turning on two ultrasonic pulses, and the amplitudes of the two motion encoding gradients are the same but the polarities are opposite; A model is constructed based on the under-sampled data and variables to be decided, wherein the variables to be decided include two complex images reconstructed under different motion coding gradients and a phase difference between the two complex images, the model is a weighted summation of minimization functions, and the function for performing the weighted summation includes a data consistency function, a fitting consistency function, and a phase difference sparsity function, wherein the data consistency function is used to measure the deviation between each group of under-sampled data and the k-space data under the same under-sampled template calculated based on the corresponding complex image to be solved, the fitting consistency function is used to measure the deviation between any of the complex images and its fitting image, the fitting image is obtained by fitting based on another complex image and the phase difference, and the phase difference sparsity function is used to measure the sparsity of the phase difference; The model is solved, and an acoustic radiation force image of the sample is reconstructed based on the solution result.

2. The magnetic resonance acoustic radiation force imaging reconstruction method according to claim 1, characterized in that: The deviation between different data is calculated by calculating the L2 norm.

3. The magnetic resonance acoustic radiation force imaging reconstruction method according to claim 1, characterized in that: Sparsity is calculated by computing the L1 norm.

4. The magnetic resonance acoustic radiation force imaging reconstruction method according to claim 1, characterized in that: The model is: In the formula, y 10 ,y 20 are the k-space data collected by positive and negative motion encoding gradient scanning, respectively. Y1 and Y2 are the complex images reconstructed under positive and negative motion encoding gradients, respectively. U is the undersampling template, F represents the Fourier transform operator, θ is the phase difference, and λ and ε are the set weight coefficients.

5. The magnetic resonance acoustic radiation force imaging reconstruction method according to claim 1, characterized in that: The model is solved by an alternating direction multiplier method, which converts the weighted sum of the functions in the model into an augmented Lagrangian function. Based on the augmented Lagrangian function, the model solution is converted into a local subproblem of solving the complex graph Y1 and a local subproblem of solving the complex graph Y2. Each decision variable is optimized by alternating iteration until convergence, and the final iterative result is output to complete the solution.

6. The magnetic resonance acoustic radiation force imaging reconstruction method according to claim 1, characterized in that: The weight coefficient of the weighted summation is determined by a grid optimization method.

7. A magnetic resonance acoustic radiation force imaging reconstruction system, characterized in that: include: Receiving unit: two groups of under-sampled data, wherein the two groups of under-sampled data are k-space data respectively acquired by performing two different motion encoding gradient scans on the sample by turning on two ultrasonic pulses, and the amplitudes of the two motion encoding gradients are the same but the polarities are opposite; A modeling unit: used for building a model based on the under-sampled data and variables to be decided, wherein the variables to be decided include two complex images reconstructed under different motion coding gradients and the phase difference between the two complex images, the model is a weighted summation of minimization functions, and the function for performing the weighted summation includes a weighted summation of a data consistency function, a fitting consistency function, and a phase difference sparsity function, wherein the data consistency function is used to measure the deviation between each group of under-sampled data and the k-space data under the same under-sampled template calculated based on the corresponding complex image to be solved, the fitting consistency function is used to measure the deviation between any one of the complex images and its fitting image, the fitting image is obtained by fitting based on another complex image and the phase difference, and the phase difference sparsity function is used to measure the sparsity of the phase difference; Solving unit: used for solving the model and reconstructing the acoustic radiation force image of the sample based on the solution result.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

9. A computer program product comprising a computer program or instructions, characterized in that When the computer program or instruction is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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