Magnetic resonance acoustic radiation force imaging reconstruction method and system thereof

Abstract

The application belongs to the technical field of medical magnetic resonance image reconstruction, and discloses a magnetic resonance acoustic radiation force imaging reconstruction method and a system thereof. The method comprises the following steps: acquiring two groups of undersampling data; constructing a model based on the undersampling data and to-be-decided variables, wherein the model is a weighted sum of minimization functions, a data consistency function is used to measure the deviation between each group of undersampling data and k-space data under the same undersampling template calculated based on a corresponding to-be-solved complex number graph, a fitting consistency function is used to measure the deviation between any one complex number graph and a fitting graph thereof, the fitting graph is obtained by fitting based on another complex number graph and a phase difference, and a phase difference sparsity function is used to measure the sparsity of the phase difference; solving the model, and reconstructing the acoustic radiation force image of the sample based on the solving result. According to the method, the positioning accuracy can be ensured, and the imaging speed is accelerated.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of medical magnetic resonance image reconstruction, and more particularly relates to a magnetic resonance acoustic radiation force imaging reconstruction method and system thereof. BACKGROUND

[0002] Ultrasound neuromodulation is a non-invasive and targeted deep brain stimulation technology, which has great application potential in 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 deviate, and the safety and effectiveness of ultrasound neuromodulation cannot be guaranteed. Magnetic resonance acoustic radiation force imaging (MR-ARFI) can provide precise positioning and guidance for ultrasound neuromodulation. However, the current MR-ARFI full sampling scan needs to open the ultrasound multiple times, and the used ultrasound dose is large and the scanning time is long.

[0003] In the article "Fast imaging method of magnetic resonance acoustic radiation force imaging for ultrasound neuromodulation[D]. Chinese Academy of Sciences, 2022. DOI:10.27822 / d.cnki.gszxj.2022.000038.", a k-space undersampling acceleration method is mentioned, but it needs to collect four groups of k-space data, and the scanning time still needs to be optimized.

[0004] Therefore, how to make MR-ARFI accelerate the imaging speed while ensuring the positioning accuracy has become an urgent need in the field of ultrasound neuromodulation. SUMMARY

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

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

[0007] Two groups of undersampling data are obtained, the two groups of undersampling data being k-space data collected by twice different motion encoding gradient scanning of the sample by opening twice ultrasound pulses, the amplitudes of the two motion encoding gradients being the same but the polarities being opposite;

[0008] constructing a model based on the undersampling data and to-be-decided variables, the to-be-decided variables including two complex images reconstructed under different motion encoding gradients respectively and a phase difference between the two complex images, the model being a weighted sum of minimization functions, the functions including a data consistency function, a fitting consistency function and a phase difference sparsity function, the data consistency function being used to measure a deviation between each group of undersampling data and k-space data under a same undersampling template calculated based on a corresponding to-be-solved complex image, the fitting consistency function being used to measure a deviation between any one of the complex images and a fitting image thereof, the fitting image being fitted based on the other complex image and the phase difference, and the phase difference sparsity function being used to measure a sparsity of the phase difference;

[0009] solving the model and reconstructing a sound radiation force image of the sample based on a solving result.

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

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

[0012] Optionally, the model is:

[0013]

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

[0015] Optionally, the model is solved by using an alternating direction multiplier method, the alternating direction multiplier method converts the weighted sum of functions in the model into an augmented Lagrangian function, converts model solving into solving a local sub-problem of the complex image Y1 and solving a local sub-problem of the complex image Y2 based on the augmented Lagrangian function, optimizes each to-be-decided variable by alternating iteration until convergence, outputs a final iteration result, and completes solving.

[0016] Optionally, the weight coefficients of the weighted sum are determined by a gridding optimization method.

[0017] The application further provides a magnetic resonance sound radiation force imaging reconstruction system, which comprises:

[0018] a receiving unit: two groups of undersampling data, the two groups of undersampling data being k-space data collected by twice different motion encoding gradient scanning on a sample by opening twice ultrasonic pulses, the amplitudes of the two times of motion encoding gradient being the same but the polarities being opposite.

[0019] a modeling unit configured to construct a model based on the undersampled data and decision variables, the decision variables including two pairs of complex maps reconstructed under different motion encoding gradients respectively and a phase difference between the two pairs of complex maps, the model being a weighted sum of minimization functions, the functions including a data consistency function, a fitting consistency function and a phase difference sparsity function, the data consistency function being used to measure a deviation between each set of undersampled data and k-space data under a same undersampling template calculated based on a corresponding to-be-solved complex map, the fitting consistency function being used to measure a deviation between any one of the complex maps and a fitting map fitted based on the other complex map and the phase difference, the phase difference sparsity function being used to measure a sparsity of the phase difference;

[0020] a solving unit configured to solve the model, and reconstruct a sound radiation force image of the sample based on a solving result.

[0021] The application further provides a computer readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the method according to any one of the preceding embodiments.

[0022] The application further provides a computer program product comprising a computer program or instructions, which, when executed by a processor, implement the steps of the method according to any one of the preceding embodiments.

[0023] Overall, compared with the prior art, the above technical scheme conceived by the application mainly has the following beneficial effects:

[0024] The magnetic resonance acoustic radiation force imaging reconstruction method provided by the application acquires two sets of k-space data in an undersampling manner, substitutes the data into a model for solving, obtains values of to-be-decided variables, and based on a solving result, can quickly reconstruct an image. The above method only needs to acquire two sets of undersampling data, compared with the current full sampling and undersampling manner (at least four sets of undersampling data), the scanning speed is improved, and the model comprehensively considers data consistency, fitting consistency and sparsity of the phase difference, and the reconstruction accuracy is higher. Overall, the method provided by the application can guarantee positioning accuracy while speeding up imaging. BRIEF DESCRIPTION OF DRAWINGS

[0025] Figure 1 is a step flow chart of the magnetic resonance acoustic radiation force imaging reconstruction method in an embodiment of the application. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical scheme and advantages of the present application more clear, the present application is further described in detail below with reference to the drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application and do not limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0027] The present application provides a magnetic resonance acoustic radiation force imaging reconstruction method, as shown in Figure 1 The present application provides a magnetic resonance acoustic radiation force imaging reconstruction method, as shown in Figure 1 The method is described in detail below.

[0028] Step S1: acquiring two groups of undersampled data, the two groups of undersampled data being k-space data respectively acquired by twice different motion encoding gradient scanning of the sample by opening twice ultrasound pulses, the gradient amplitudes of the two motion encodings being the same but the polarities being opposite.

[0029] Among them, undersampling is generally applied in compressed sensing, which is a sampling method with a sampling rate much lower than the Nyquist sampling rate. Under the premise of meeting the conditions of compressed sensing, an optimization algorithm is used to reconstruct the original signal from a small amount of sampling values. Compressed sensing needs to meet the following key conditions: (1) sparsity of signal: the signal is sparse in a certain transform domain, which means that the signal can be represented by a few non-zero coefficients; (2) randomness of sampling: the measurement matrix of compressed sensing needs to meet the constraint equidistance to keep the structure of the measured signal in the sampled signal, and random undersampling can meet this point; (3) effectiveness of reconstruction algorithm: an effective reconstruction algorithm is needed to recover the original signal from the sampling values.

[0030] In magnetic resonance acoustic radiation force imaging, the ultrasound beam acts on a small area of the tissue, and the tissue displacement caused thereby has only a small number of non-zero values inside the focal domain, so the magnetic resonance acoustic radiation force displacement map is approximately sparse in space, meeting the sparsity of the signal. Applying the undersampling template to the acquisition of the k-space of the magnetic resonance acoustic radiation force image approximately meets the randomness of the sampling. By designing an effective reconstruction algorithm, the complete and accurate reconstruction of the magnetic resonance image data is ensured at a low sampling rate, and finally the tissue displacement map is reconstructed using these data. Compared with full sampling, undersampling can effectively shorten the sampling time and speed up the imaging speed.

[0031] In the present application, the motion encoding gradient (MEG) used in the two times of undersampling has the same amplitude but different polarities, where the motion encoding gradient used in one time of undersampling is positive, and the motion encoding gradient used in the other time of undersampling is negative. The k-space data under two different motion encoding gradients are acquired, i.e., bipolar displacement encoding is used, aiming to enhance the sensitivity of displacement measurement.

[0032] For convenience of description, the k-space data acquired in the positive-polarity motion encoding gradient scan is denoted as y 10 The k-space data acquired in the negative-polarity motion encoding gradient scan is denoted as y 20 .

[0033] Step S2: constructing a model based on the undersampled data and the to-be-decided variables, the to-be-decided variables including two pairs of complex images reconstructed under different motion encoding gradients respectively and the phase difference between the two pairs of complex images, the model being a weighted sum of functions to be minimized, the functions to be summed including a data consistency function, a fitting consistency function and a phase difference sparsity function.

[0034] The data consistency function is used to measure the deviation between each set of undersampled data and the k-space data under the same undersampling template calculated based on the corresponding complex image, the fitting consistency function is used to measure the deviation between any one of the complex images and its fitting image, the fitting image being obtained by fitting based on the other complex image and the phase difference, and the phase difference sparsity function is used to measure the sparsity of the phase difference.

[0035] The to-be-decided variables to be solved in the model include two pairs of complex images reconstructed under different motion encoding gradients respectively and the phase difference between the two pairs of complex images. For convenience of description, the complex image reconstructed under the positive-polarity motion encoding gradient is denoted as Y1, the complex image reconstructed under the negative-polarity motion encoding gradient is denoted as Y2, and the phase difference between Y1 and Y2 caused by the action of ultrasound is denoted as θ, all of the above three parameters being variables to be solved.

[0036] The functions therein are described below.

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

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

[0039] y1 ′ 0 = FY1;

[0040] y2 ′ 0 = FY2;

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

[0042] The more accurate the reconstructed complex image is, the closer the k-space data inversely calculated based on the complex image is to the k-space data actually acquired. Therefore, the present model considers a data consistency function, which is used to measure the deviation between y1 ′ 0 and y 10 , and the deviation between y2 ′ 0 and y 20 . The smaller the deviation is, the more accurate the result reconstructed by the model is.

[0043] The L2 norm can well measure the Euclidean distance between two groups of data, and is a commonly used measurement method for measuring the distance between two groups of data. In specific operation, the data consistency function f1 can introduce the L2 norm to measure the deviation between y1 ′ 0 and y 10 , and the deviation between y2 ′ 0 and y 20 . The specific representation is as follows:

[0044]

[0045] The fitting consistency function is used to measure the deviation between any one of the complex images and a fitting image thereof, and the fitting image is obtained based on another complex image, a phase difference and a vortex intensity coefficient.

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

[0047] In specific operation, the deviation of Y2 and its fitting result can be calculated based on the fitting result of Y2 obtained from Y1, or the deviation of Y1 and its fitting result can be calculated based on the fitting result of Y1 obtained from Y2.

[0048] In specific operation, the fitting consistency function f2 can also introduce the L2 norm to measure the deviation between the complex image and the fitting result, which is specifically represented 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 ultrasound beam acting on the tissue has sparsity in space, the sparsity of the phase difference can be used for constraint, and can also suppress the noise in the image.

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

[0053] f3 = ||θ||1.

[0054] Based on the above examples, the model can be represented as:

[0055]

[0056] Wherein, the weight coefficients λ, ε can be found by grid search method to find the optimal parameters.

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

[0058] Step S3: solving the model, and reconstructing the acoustic radiation force image of the sample based on the solving result.

[0059] After modeling, the model needs to be solved to obtain the solving result of the to-be-decided variable, so as to realize the reconstruction of the image. Specifically, only the phase difference θ in the solving result needs to be obtained, and the acoustic radiation force image can be calculated by the following formula:

[0060]

[0061] where x is the average displacement in the encoding time, gamma is the proton gyromagnetic ratio, G MEG is the motion encoding gradient amplitude; t is the encoding time length.

[0062] The alternating direction multiplier method (ADMM) is usually used to solve problems with multiple optimization variables, and in the present application, the model has multiple variables to be solved, including complex image Y1, complex image Y2 and phase difference theta, and the alternating direction multiplier method can also be used to solve the model.

[0063] Specifically, when the alternating direction multiplier method is used, the weighted sum of the functions in the model is converted into an augmented Lagrangian function, and based on the augmented Lagrangian function, the model solving is converted into solving a local subproblem of complex image Y1 and solving a local subproblem of complex image Y2, and each decision variable is optimized by alternating iteration until convergence, and the final iteration result is output, and the solving is completed.

[0064] wherein the augmented Lagrangian function can be expressed as:

[0065]

[0066] In the formula, xi, x2, u1, u2 are newly introduced variables, and lambda2 is a set weight coefficient.

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

[0068]

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

[0070]

[0071] In the formula, the superscript k represents the kth iteration.

[0072] By alternating iteration, each decision variable is optimized until convergence, and the final iteration result is output, and the solving is completed, and the solving result of each decision variable is obtained.

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

[0074] The receiving unit: two groups of undersampled data, the two groups of undersampled data are k-space data respectively collected by two different motion encoding gradient scans on the sample by opening two ultrasonic pulses, and the amplitudes of the two motion encoding gradients are the same but the polarities are opposite;

[0075] The modeling unit is configured to construct a model based on the undersampled data and the to-be-decided variables, the to-be-decided variables including two pairs of complex images reconstructed under different motion encoding gradients respectively and a phase difference between the two pairs of complex images, the model being a weighted sum of functions to be minimized, the functions to be summed including a data consistency function, a fitting consistency function and a phase difference sparsity function, the data consistency function being configured to measure a deviation between each set of undersampled data and k-space data under the same undersampling template calculated based on a corresponding to-be-solved complex image, the fitting consistency function being configured to measure a deviation between any one of the complex images and a fitting image thereof, the fitting image being fitted based on the other complex image and the phase difference, and the phase difference sparsity function being configured to measure a sparsity of the phase difference;

[0076] The solving unit is configured to solve the model and reconstruct the acoustic radiation force image of the sample based on a solving result.

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

[0078] The present application also relates to a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement the steps of the above method.

[0079] Specifically, the memory can include a high-speed random access memory, and can also include a non-volatile memory, for example, a hard disk, a memory, a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, at least one magnetic disk storage device, a flash memory device, or other volatile solid-state memory devices.

[0080] The present application 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 to enable the computer device to perform the steps of the above-mentioned embodiment method of the present application.

[0081] It should be noted that, for those skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are all within the protection scope of the present application.

Claims

1. A magnetic resonance acoustic radiation force imaging reconstruction method, characterized in that, include: Two sets of undersampled data are obtained. The two sets of undersampled data are k-space data collected by performing two different motion coding gradient scans on the sample with two ultrasonic pulses. The amplitudes of the two motion coding gradients are the same but the polarities are opposite. A model is constructed based on the undersampled data and the decision variables, which include two complex graphs reconstructed under different motion coding gradients and the phase difference between the two complex graphs. The model is a weighted summation of minimizing functions, including a data consistency function. Consistency function for fitting and the phase difference sparsity function The data consistency function The fitting consistency function is used to measure the deviation between each group of undersampled data and the k-space data calculated based on the same undersampled template using the corresponding complex graph to be solved. This is used to measure the deviation between any one of the complex graphs and its fitted graph, which is obtained by fitting another complex graph and a phase difference, wherein the phase difference sparsity function... Used to measure the sparsity of phase difference; function , , for: ； ； ； The model is as follows: ； In the formula, These are k-space data collected by positive and negative polarity motion coding gradient scans, respectively. These are complex graphs reconstructed under positive and negative polarity motion coding gradients, respectively. For undersampling templates, This represents the Fourier transform operator. It's the phase difference. , All of these are set weighting coefficients. It is an L1 norm. It is an L2 norm; Solve the model, based on the phase difference in the solution results. The acoustic radiation force image of the sample is reconstructed using the following formula: ； In the formula, The average displacement over the organization's coding time. The proton gyromagnetic ratio, Encodes the gradient magnitude for motion; This represents the encoding duration.

2. The magnetic resonance acoustic radiation force imaging reconstruction method as described in claim 1, characterized in that, The model is solved using the alternating direction multiplier method, which transforms the weighted summation of functions in the model into an augmented Lagrangian function. Based on the augmented Lagrangian function, the model solution is then transformed into solving a complex graph. Local subproblems and solving complex graphs The local subproblem is solved by iteratively optimizing each decision variable in an alternating manner until convergence, and then outputting the final iterative result.

3. The magnetic resonance acoustic radiation force imaging reconstruction method as described in claim 1, characterized in that, The weighting coefficients for the weighted summation are determined through a grid-based optimization method.

4. A magnetic resonance acoustic radiation force imaging reconstruction system, characterized in that, include: Receiving unit: Two sets of undersampled data, which are k-space data collected by performing two different motion coding gradient scans on the sample with two ultrasonic pulses. The amplitudes of the two motion coding gradients are the same but the polarities are opposite. Modeling Unit: Used to construct a model based on the undersampled data and the decision variables, including two complex graphs reconstructed under different motion coding gradients and the phase difference between the two complex graphs. The model is a weighted summation of minimization functions, including a data consistency function. Consistency function for fitting and the phase difference sparsity function The weighted summation of the data, the data consistency function is used to measure the deviation between each group of undersampled data and the k-space data calculated based on the same undersampled template based on the corresponding complex graph to be solved, the fitting consistency function is used to measure the deviation between any complex graph and its fitting graph, the fitting graph is obtained by fitting based on another complex graph and the phase difference, and the phase difference sparsity function is used to measure the sparsity of the phase difference. function , , for: ； ； ； The model is as follows: ； In the formula, These are k-space data collected by positive and negative polarity motion coding gradient scans, respectively. These are complex graphs reconstructed under positive and negative polarity motion coding gradients, respectively. For undersampling templates, This represents the Fourier transform operator. It's the phase difference. , All of these are set weighting coefficients. It is an L1 norm. It is an L2 norm; Solver unit: Used to solve the model, based on the phase difference in the solution results. The acoustic radiation force image of the sample is reconstructed using the following formula: ； In the formula, The average displacement over the organization's coding time. The proton gyromagnetic ratio, Encodes the gradient magnitude for motion; This represents the encoding duration.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 3.

6. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the steps of the method as described in any one of claims 1 to 3.

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