A magnetic nanoparticle imaging method and system based on multi-harmonic system matrix fusion

Abstract

The application belongs to the field of magnetic nanoparticle imaging, and discloses a magnetic nanoparticle imaging method and system based on multi-harmonic system matrix fusion, which comprises the following steps: placing a unit volume of sample at a zero magnetic field point, moving the zero magnetic field point through the whole imaging field of view by scanning the field to obtain system matrices of different harmonics; placing a sample to be measured at the zero magnetic field point, moving the zero magnetic field point through the whole imaging field of view by scanning the field to obtain voltage vectors of different harmonics; fusing the system matrices of different harmonics and the voltage vectors of the sample to be measured; calculating a weight factor for the fused matrix and constructing a weight matrix; and reconstructing the magnetic nanoparticle concentration distribution of the sample to be measured based on the weight matrix by an algebraic iterative reconstruction algorithm. The application fuses system matrices of different orders of harmonics, fully utilizes multi-harmonic information in the nonlinear magnetization response of magnetic nanoparticles, and improves the utilization rate of imaging signals.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of magnetic nanoparticle imaging, and particularly relates to a magnetic nanoparticle imaging method and system based on multi-harmonic system matrix fusion. BACKGROUND

[0002] Magnetic particle imaging (MPI) is a new type of non-radiation molecular imaging technology, which can quantitatively invert the spatial distribution information of superparamagnetic iron oxide nanoparticles (SPIONs) in the imaging space by measuring the nonlinear magnetization response signal of the SPIONs. Compared with traditional medical imaging technologies such as CT, ultrasound, magnetic resonance imaging (MRI) and positron emission tomography (PET), MPI has significant advantages such as high sensitivity, high spatial and temporal resolution, no depth limitation and no radioactivity, and shows great application potential in clinical medical scenarios such as early tumor detection, angiography, targeted drug delivery, cell tracking and magnetic hyperthermia.

[0003] At present, MPI imaging mainly includes wideband imaging and narrowband imaging. Wideband MPI can obtain more complete particle response information by using a non-tunable high-bandwidth receiving coil to collect multi-harmonic signals, but the system bandwidth requirement is high and the noise interference is large. Narrowband MPI has advantages in improving signal-to-noise ratio and reducing system complexity by selectively collecting specific harmonics in a certain frequency band. However, single-harmonic imaging has inherent limitations: low-harmonic signals have large amplitude and high signal-to-noise ratio, but the spatial resolution is poor; high-harmonic can provide better spatial resolution, but the signal amplitude is weak and the signal-to-noise ratio is low, and the reconstructed image is easily disturbed by noise. Therefore, using only a single-harmonic system matrix for reconstruction, artifacts are easily produced in the image, and the resolution and signal-to-noise ratio are difficult to balance.

[0004] Therefore, there is an urgent need for a new magnetic nanoparticle imaging method that can fuse the high signal-to-noise ratio advantage of low-harmonic and the high-resolution characteristic of high-harmonic, so as to significantly improve the spatial resolution while ensuring the imaging signal-to-noise ratio, which is of great significance for promoting the application of MPI in precision medical imaging. SUMMARY

[0005] To solve the problem that spatial resolution and imaging signal-to-noise ratio are difficult to be considered in existing magnetic nanoparticle imaging, the application provides a magnetic nanoparticle imaging method and system based on multi-harmonic system matrix fusion, which fuses system matrices of different orders of harmonics, fully utilizes multi-harmonic information in nonlinear magnetization response of magnetic nanoparticles, and improves utilization rate of imaging signals. The method can combine the advantages of low-harmonic high signal-to-noise ratio and high-harmonic high spatial resolution, so that the reconstructed image has high spatial resolution and less artifact interference, and provides technical support for medical applications such as disease diagnosis and precise treatment of magnetic nanoparticle imaging.

[0006] To achieve the above object, the application provides the following scheme:

[0007] A magnetic nanoparticle imaging method based on multi-harmonic system matrix fusion, the method comprising:

[0008] Placing a unit volume of sample at a zero magnetic field point, moving the zero magnetic field point through the entire imaging field of view by scanning the field, and obtaining system matrices of different harmonics;

[0009] Placing a sample to be measured at a zero magnetic field point, moving the zero magnetic field point through the entire imaging field of view by scanning the field, and obtaining voltage vectors of different harmonics;

[0010] Fusing the system matrices of different harmonics and the voltage vectors of the sample to be measured corresponding to the system matrices;

[0011] Calculating a weight factor for the fused matrix and constructing a weight matrix;

[0012] Based on the weight matrix, reconstructing the magnetic nanoparticle concentration distribution of the sample to be measured by an algebraic iterative reconstruction algorithm.

[0013] Preferably, the method for fusing the system matrices of different harmonics and the voltage vectors of the sample to be measured corresponding to the system matrices comprises:

[0014] Splicing the system matrices of different harmonics of magnetic nanoparticles in the direction of matrix rows to obtain a new system matrix ; correspondingly, splicing the voltage vectors of different harmonics of the sample to be measured to obtain a new voltage vector :

[0015] , ;

[0016] wherein, is the system matrix of the third harmonic of the magnetic nanoparticles, is the system matrix of the fifth harmonic, is the system matrix of the seventh harmonic, The system matrix of the ninth harmonic, note that the elements in the system matrix contain both real and imaginary parts; the corresponding 、 、 and correspond to the voltage vectors of the third, fifth, seventh and ninth harmonics of the sample to be measured, respectively;

[0017] For the fused system matrix and the voltage vector , it is expressed as:

[0018] ;

[0019] wherein, c is the particle concentration distribution.

[0020] Preferably, the method for calculating the weight factor and constructing the weight matrix based on the fused matrix comprises:

[0021] Based on the obtained fused system matrix , the weight factor is calculated:

[0022] ;

[0023] wherein, is the maximum modulus value of the elements in the first row of the system matrix i ;

[0024] Based on the obtained weight factor, the weight matrix is calculated:

[0025] ;

[0026] wherein, W is a diagonal matrix composed of weight factors corresponding to different harmonics, is the weight factor in the first n row on the diagonal of the j th harmonic.

[0027] Preferably, the method for reconstructing the magnetic nanoparticle concentration distribution of the sample to be measured based on the weight matrix through an algebraic iterative reconstruction algorithm comprises:

[0028] Based on the obtained fused system matrix , the voltage vector and the weight matrix W , a model for solving the magnetic nanoparticle concentration distribution to be measured is constructed:

[0029] ;

[0030] wherein, As a relaxation factor, For residuals;

[0031] The algebraic reconstruction algorithm ART is used to iteratively reconstruct the concentration distribution of magnetic nanoparticles to be solved. The iterative formula is as follows:

[0032] ;

[0033] ;

[0034] in, k For the number of iterations, Representing the k The magnetic nanoparticle concentration distribution obtained in the next iteration N The number of columns in the system matrix. For the first k The concentration distribution obtained in the nth iteration is the first n The value of each pixel. For the system matrix, the first i The first line n One element, For the voltage vector i Row elements, The residual vector is the first i The elements of a row.

[0035] The present invention also provides a magnetic nanoparticle imaging system based on multi-harmonic system matrix fusion, the system being used to implement the aforementioned method, the system comprising: a first building module, a second building module, a fusion module, a third building module, and an iteration module;

[0036] The first construction module is used to place a unit volume sample at the zero magnetic field point, and move the zero magnetic field point through the scanning field to traverse the entire imaging field of view to obtain the system matrix of different harmonics.

[0037] The second construction module is used to place the sample to be tested at the zero magnetic field point, and to move the zero magnetic field point through the scanning field to traverse the entire imaging field of view to obtain the voltage vectors of different harmonics.

[0038] The fusion module is used to fuse the system matrix of different harmonics and the voltage vector of the corresponding sample under test;

[0039] The third construction module is used to calculate weight factors and construct a weight matrix from the fused matrix.

[0040] The iterative module is used to reconstruct the magnetic nanoparticle concentration distribution of the sample under test based on the weight matrix and an algebraic iterative reconstruction algorithm.

[0041] Preferably, the process of fusing the system matrix of different harmonics and the voltage vector of the corresponding sample to be measured comprises:

[0042] The system matrix of the magnetic nanoparticles of different harmonics is spliced to obtain a new system matrix in the direction of the matrix row ; correspondingly, the voltage vectors of the different harmonics of the sample to be measured are spliced to obtain a new voltage vector :

[0043] , ;

[0044] wherein, is the system matrix of the third harmonic of the magnetic nanoparticles, is the system matrix of the fifth harmonic, is the system matrix of the seventh harmonic, is the system matrix of the ninth harmonic, and it is noted that the elements in the system matrix include real and imaginary parts; correspondingly , , and correspond to the voltage vectors of the third, fifth, seventh and ninth harmonics of the sample to be measured, respectively;

[0045] For the fused system matrix and the voltage vector , it is expressed as:

[0046] ;

[0047] wherein, c is the particle concentration distribution.

[0048] Preferably, the process of calculating the weight factor and constructing the weight matrix for the fused matrix comprises:

[0049] Based on the obtained fused system matrix , the weight factor is calculated:

[0050] ;

[0051] wherein, is the maximum modulus value of the first row element of the system matrix i ;

[0052] Based on the obtained weight factor, the weight matrix is calculated:

[0053] ;

[0054] wherein, WIt is a diagonal matrix composed of weighting factors corresponding to different harmonics. The nth harmonic on the diagonal j The weighting factor of the row.

[0055] Preferably, the process of reconstructing the magnetic nanoparticle concentration distribution of the sample under test based on the weight matrix and using an algebraic iterative reconstruction algorithm includes:

[0056] Based on the obtained fused system matrix Voltage vector and weight matrix W A model is constructed to solve for the concentration distribution of the magnetic nanoparticles to be measured:

[0057] ;

[0058] in, As a relaxation factor, For residuals;

[0059] The algebraic reconstruction algorithm ART is used to iteratively reconstruct the concentration distribution of magnetic nanoparticles to be solved. The iterative formula is as follows:

[0060] ;

[0061] ;

[0062] in, k For the number of iterations, Representing the k The magnetic nanoparticle concentration distribution obtained in the next iteration N The number of columns in the system matrix. For the first k The concentration distribution obtained in the nth iteration is the first n The value of each pixel. For the system matrix, the first i The first line n One element, For the voltage vector i Row elements, The residual vector is the first i The elements of a row.

[0063] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0064] This invention fully utilizes spectral information by fusing and jointly inverting the system matrix and response voltage vector of multiple harmonics of magnetic nanoparticles. It combines the advantages of high signal strength and high signal-to-noise ratio of low-order harmonics with the advantages of good spatial resolution of high-order harmonics, so that the reconstructed image of magnetic nanoparticle concentration distribution has both good resolution and reduced artifact interference, thus improving the signal-to-noise ratio of the image.

[0065] This invention enhances the role of higher harmonics in the reconstruction process and improves the spatial resolution of the reconstructed image by weighting and fusing the system matrices of multiple harmonics with their corresponding voltage vectors. After weighting the system matrix, the singular values ​​of the matrix decrease more slowly, the condition number decreases, which reduces the amplification of high-frequency noise during the inverse problem solution and improves the reconstruction accuracy. After weighting the system matrix, the orthogonality between different harmonics increases, which accelerates the convergence speed of the ART algorithm for iterative reconstruction and improves the image reconstruction speed for solving the magnetic nanoparticle concentration distribution. Attached Figure Description

[0066] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0067] Figure 1 This is a flowchart of a magnetic nanoparticle imaging method based on multi-harmonic system matrix fusion according to an embodiment of the present invention;

[0068] Figure 2 This is a flowchart of the weighted algebraic reconstruction algorithm according to an embodiment of the present invention. Detailed Implementation

[0069] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0070] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0071] Example 1

[0072] like Figure 1 As shown, this embodiment discloses a magnetic nanoparticle imaging method based on multi-harmonic system matrix fusion, comprising: placing a unit volume magnetic nanoparticle sample at the center of a permanent magnet, i.e., at the zero magnetic field point; applying an excitation magnetic field to induce a nonlinear magnetization response in the magnetic nanoparticles; and applying a scanning magnetic field to change the relative position between the zero magnetic field point and the particles; wherein, the magnetization response generated by the magnetic nanoparticles at different positions relative to the zero magnetic field point is a point spread function; and constructing a system matrix based on the point spread functions of different harmonics of the point-like magnetic nanoparticle sample. , , and ; the measured magnetic nanoparticle sample is measured in the same way to obtain the magnetic response voltage vector of different harmonics , , and ; the system matrix of the magnetic nanoparticle of different harmonics , , and and the corresponding voltage vector , , and are spliced to obtain a new system matrix and a new voltage vector ; the system matrix of different harmonics is weighted to obtain a weighted matrix ; the weighted system matrix and voltage vector are iteratively reconstructed to obtain the particle concentration distribution of the sample to be measured c , the elements in c correspond to the position of the zero magnetic field point, and the reconstructed particle concentration distribution image is obtained.

[0073] Specifically, the embodiment discloses a magnetic nanoparticle imaging method based on multi-harmonic system matrix fusion, comprising:

[0074] Step S10: using a magnetic nanoparticle imaging system, moving a point-like unit volume magnetic nanoparticle sample to the center position of a permanent magnet, i.e. the zero magnetic field point position, by a displacement table, applying a sinusoidal excitation magnetic field to excite the magnetic nanoparticle sample to generate a nonlinear magnetization response, and receiving the response by a receiving coil; at the same time, a scanning field is applied to make the zero magnetic field point move through the entire imaging field of view, and the magnetization response signal of the magnetic nanoparticle sample relative to different positions of the zero magnetic field point is obtained, i.e. a point spread function (PSF). The system matrix , , and is constructed by the point spread function of different harmonics;

[0075] The construction equation of the n th harmonic system matrix is:

[0076] ;

[0077] wherein, is the response of the j th harmonic point spread function on the i th pixel point when the zero magnetic field point (FFP) is located at the n th pixel point.N The number of pixels corresponding to the point spread function.

[0078] Step S20: Place the magnetic nanoparticle sample to be tested in the center of the field of view of the magnetic nanoparticle imaging system, and apply the excitation field and scanning field in the same manner to obtain the magnetization response voltage vectors of different harmonics of the sample to be tested. , , and ;

[0079] No. n The magnetization response voltage vector of the subharmonic The construction equation is:

[0080] ;

[0081] in, Corresponding to The first pixel n Induced voltage response of subharmonics. p and q These correspond to the number of rows and columns of the voltage vector, respectively.

[0082] Step S30: Combine the multiple harmonic system matrices obtained in steps S10 and S20 above. , , and and the corresponding voltage vector , , and By splicing them together, a new system matrix is ​​obtained. and voltage vector ;

[0083] Step S40: The new system matrix obtained in step S30 and voltage vector Construct new equations to solve for the particle concentration distribution. c ;

[0084] Further, step S30 includes:

[0085] Step S31: The system matrix of different harmonics of the magnetic nanoparticles is... , , and The new system matrix is ​​obtained by concatenating the matrices according to the direction of the matrix rows. Correspondingly, the different harmonic voltage vectors of the sample under test are... , , and The same splicing is performed to obtain a new voltage vector :

[0086] , ;

[0087] wherein, is a system matrix of the third harmonic of the magnetic nanoparticle, is a system matrix of the fifth harmonic, is a system matrix of the seventh harmonic, is a system matrix of the ninth harmonic, and it is noted that the elements in the system matrix include both real and imaginary parts; and the corresponding , , and correspond to the voltage vectors of the third, fifth, seventh and ninth harmonics of the sample to be measured, respectively.

[0088] In step S32, for a single harmonic, the voltage vector can be expressed as a convolution of a point spread function and a concentration distribution of the particle to be measured. After converting the point spread function into a system matrix, the voltage vector can be expressed as a product of the system matrix and the concentration distribution to be measured. For the spliced system matrix and the voltage vector , it can be expressed as:

[0089] ;

[0090] Further, obtaining the concentration distribution of the magnetic nanoparticle to be measured includes: obtaining a weight factor and constructing a weight matrix according to the new system matrix, constructing a concentration distribution solving model of the sample to be measured based on the weight matrix, the new system matrix and the voltage vector, and iteratively reconstructing the model to solve the concentration distribution of the magnetic nanoparticle sample to be measured.

[0091] Specifically, step S40 includes:

[0092] In step S41, the weight factor is calculated based on the system matrix obtained in step S30:

[0093] ;

[0094] wherein, is the maximum modulus value of the elements in the first row of the system matrix i .

[0095] In step S42, the weight matrix is calculated based on the weight factor obtained in step S41:

[0096] ;

[0097] in, W It is a diagonal matrix composed of weighting factors corresponding to different harmonics. For the first n The second harmonic on the diagonal j The row weighting factor.

[0098] Step S43, based on the system matrix obtained in steps S30, S41 and S42 Voltage vector and weight matrix W A model is constructed to solve for the concentration distribution of the magnetic nanoparticles to be measured:

[0099] ;

[0100] in, As a relaxation factor, It represents the residual.

[0101] Step S44: The Algebraic Reconstruction Algorithm (ART) is used to iteratively reconstruct the concentration distribution of the magnetic nanoparticles to be solved. The iterative formula is as follows:

[0102] ;

[0103] ;

[0104] in, k For the number of iterations, Representing the k The magnetic nanoparticle concentration distribution obtained in the second iteration N The number of columns in the system matrix. For the first k The concentration distribution obtained in the nth iteration is the first n The value of each pixel. For the system matrix, the first i The first line n One element, For the voltage vector i Row elements, The residual vector is the first i The elements of a row.

[0105] The practical application of this invention is an extension of single-harmonic narrowband magnetic nanoparticle imaging, and this will be explained using single-harmonic narrowband magnetic nanoparticle imaging as an example.

[0106] First, a sample of magnetic nanoparticles per unit volume is placed in the center of the magnetic nanoparticle imaging system. The excitation magnetic field strength and imaging field width are set. These parameters determine the magnitude of the excitation magnetic field and the scanning magnetic field. After the scanning magnetic field drives the zero magnetic field point to traverse the entire imaging field, the point spread function (PSF) of the third, fifth, seventh and ninth harmonics of the magnetization response signal is extracted.

[0107] The magnetic nanoparticle sample to be measured is placed in the imaging field of view. The sample is excited under the same excitation conditions, and the voltage vectors of the third, fifth, seventh, and ninth harmonics of its magnetization response signal are extracted. Taking the third harmonic as an example, the PSF and the voltage vector can be represented by convolution:

[0108] ;

[0109] By using zero-field point (FFP) meshing, the convolution relationship can be transformed into a matrix multiplication relationship. Taking the third harmonic as an example, the PSF is transformed into the system matrix. S The formula is:

[0110] ;

[0111] in, When FFP is in the position of j When the nth pixel is in the imaging field of view i The magnetization response of the third harmonic of each pixel N It refers to the number of pixels in the image.

[0112] Taking the third harmonic as an example, the system matrix and voltage vector The relationship between them can be represented as:

[0113] ;

[0114] Similarly, the same expressions can be used for the fifth, seventh, and ninth harmonics, and these expressions contain... c They are the same, namely, the particle concentration distribution to be solved.

[0115] After acquiring the system matrices and magnetization response voltage vectors for different harmonics, the multi-harmonic system matrices are fused. This fully leverages the advantages of high signal-to-noise ratio for low-order harmonics and high resolution for high-order harmonics to perform a joint inversion of the concentration distribution to be measured. The multi-harmonic system matrix fusion equation can be expressed as:

[0116] ;

[0117] in, The system matrix for the third harmonic of magnetic nanoparticles. System matrix for the fifth harmonic, System matrix for the seventh harmonic, System matrix for the ninth harmonic, Note that the elements in the system matrix contain both real and imaginary parts; the corresponding , , and correspond to the voltage vectors of the third, fifth, seventh, and ninth harmonics of the sample to be measured, respectively. The fused system matrix and voltage vectors can be expressed as and :

[0118] , ;

[0119] In actual systems, the intensity of low-order harmonics is greater than that of high-order harmonics, for example, the intensity of the third harmonic is about ten times that of the ninth harmonic, and the system matrices of different harmonics need to be weighted to balance their roles in the reconstruction process. The weight factor can be obtained:

[0120] ;

[0121] where is the maximum modulus value of the th row of the system matrix. i

[0122] By calculating the weight factors of different rows of the system matrix , the weight matrix can be obtained:

[0123] ;

[0124] where W is a diagonal matrix composed of weight factors corresponding to different harmonics, is the weight factor of the n th row on the diagonal of the j th harmonic.

[0125] The spliced system matrix , voltage vector , and weight matrix W can be used to construct a model for solving the concentration distribution of the magnetic nanoparticles to be measured:

[0126] ;

[0127] where is the relaxation factor, is the residual error.

[0128] ​The algebraic reconstruction technique (ART) can be used to iteratively reconstruct the magnetic nanoparticle concentration distribution to be solved, and the specific algorithm flow is as shown in Figure 2

[0129] First, input the system matrix of different harmonics , , and and the voltage vector , , and , input the maximum iteration number k , the convergence error and the relaxation factor ;

[0130] Splice the multi-harmonic system matrix and the voltage vector into a new system matrix and a voltage vector , and calculate the weight factor and the weight matrix of different harmonics according to the system matrix W .

[0131] Initialize the residual , and traverse the projection according to the number of system equations, such as the concentration distribution obtained after a certain traversal c satisfies the convergence error, then the iteration process is exited, otherwise it is iterated until the maximum iteration number. The specific iteration expression is as follows:

[0132] ;

[0133] ;

[0134] Wherein, k is the iteration number, represents the magnetic nanoparticle concentration distribution obtained by the k th iteration, N is the column number of the system matrix, is the value of the k th pixel point of the concentration distribution obtained by the n th iteration, is the i th element of the n th row of the system matrix, is the element of the i th row of the voltage vector, is the element of the i th row of the residual vector.

[0135] ​The application provides a magnetic nanoparticle imaging method based on multi-harmonic system matrix fusion, which effectively utilizes the advantages of low-harmonic high signal-to-noise ratio and high-harmonic high spatial resolution by fusing the system matrices of multiple harmonics and corresponding voltage vectors and jointly inverting, so that the spatial resolution of the reconstructed image is better and the artifacts are less, the condition number is reduced and the orthogonality of the system matrix is improved through system matrix weighting, the high-harmonic noise amplification effect in the inverse problem solving is effectively reduced, and the convergence speed of the iterative reconstruction is accelerated, which has important significance for promoting the clinical application of magnetic nanoparticle imaging.

[0136] Embodiment two

[0137] The application also provides a magnetic nanoparticle imaging system based on multi-harmonic system matrix fusion, which is used to realize the method in embodiment one, and comprises a first construction module, a second construction module, a fusion module, a third construction module and an iteration module.

[0138] The first construction module is used to place a unit volume of sample at a zero magnetic field point, move the zero magnetic field point through the whole imaging field of view by scanning the field, and obtain the system matrices of different harmonics.

[0139] The second construction module is used to place the sample to be measured at a zero magnetic field point, move the zero magnetic field point through the whole imaging field of view by scanning the field, and obtain the voltage vectors of different harmonics.

[0140] The fusion module is used to fuse the system matrices of different harmonics and the voltage vectors of the sample to be measured.

[0141] The third construction module is used to calculate a weight factor for the fused matrix and construct a weight matrix.

[0142] The iteration module is used to reconstruct the magnetic nanoparticle concentration distribution of the sample to be measured based on the weight matrix through an algebraic iterative reconstruction algorithm.

[0143] In this embodiment, the process of fusing the system matrices of different harmonics and the voltage vectors of the sample to be measured comprises:

[0144] The system matrices of different harmonics of the magnetic nanoparticles are spliced in the direction of the matrix rows to obtain a new system matrix ; correspondingly, the voltage vectors of different harmonics of the sample to be measured are spliced to obtain a new voltage vector :

[0145] , ;

[0146] wherein, is the system matrix of the third harmonic of the magnetic nanoparticles, System matrix for the fifth harmonic, System matrix for the seventh harmonic, System matrix for the ninth harmonic, Note that the elements in the system matrix contain both real and imaginary parts; correspondingly , , and correspond to the voltage vectors of the third, fifth, seventh and ninth harmonics of the sample to be measured, respectively;

[0147] For the fused system matrix and the voltage vector , it is expressed as:

[0148] ;

[0149] wherein, c is the particle concentration distribution.

[0150] In this embodiment, the process of calculating the weight factor and constructing the weight matrix based on the fused matrix includes:

[0151] Based on the obtained fused system matrix , the weight factor is calculated:

[0152] ;

[0153] wherein, is the maximum modulus value of the elements in the first row of the system matrix i ;

[0154] Based on the obtained weight factor, the weight matrix is calculated:

[0155] ;

[0156] wherein, W is a diagonal matrix composed of weight factors corresponding to different harmonics, is the weight factor in the first n row on the diagonal of the first j harmonic.

[0157] In this embodiment, based on the weight matrix, the process of reconstructing the magnetic nanoparticle concentration distribution of the sample to be measured by the algebraic iterative reconstruction algorithm includes:

[0158] Based on the obtained fused system matrix , the voltage vector and the weight matrix W , the model for solving the magnetic nanoparticle concentration distribution to be measured is constructed:

[0159] ;

[0160] in, As a relaxation factor, For residuals;

[0161] The algebraic reconstruction algorithm ART is used to iteratively reconstruct the concentration distribution of magnetic nanoparticles to be solved. The iterative formula is as follows:

[0162] ;

[0163] ;

[0164] in, k For the number of iterations, Representing the k The magnetic nanoparticle concentration distribution obtained in the second iteration N The number of columns in the system matrix. For the first k The concentration distribution obtained in the nth iteration is the first n The value of each pixel. For the system matrix, the first i The first line n One element, For the voltage vector i Row elements, The residual vector is the first i The elements of a row.

[0165] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A magnetic nanoparticle imaging method based on multi-harmonic system matrix fusion, characterized in that, The method comprises: placing a unit volume of sample at a zero magnetic field point, moving the zero magnetic field point through the entire imaging field of view by scanning the field to obtain a system matrix of different harmonics; placing the sample to be measured at a zero magnetic field point, moving the zero magnetic field point through the entire imaging field of view by scanning the field to obtain a voltage vector of different harmonics; fusing the system matrix of different harmonics and the voltage vector of the sample to be measured corresponding thereto; calculating a weight factor for the fused matrix and constructing a weight matrix; reconstructing the magnetic nanoparticle concentration distribution of the sample to be measured based on the weight matrix through an algebraic iterative reconstruction algorithm; The method for fusing the system matrix of different harmonics and the voltage vector of the sample to be measured corresponding thereto comprises: The system matrix of different harmonics of the magnetic nanoparticles is spliced according to the direction of the matrix row to obtain a new system matrix ; accordingly, the voltage vectors of different harmonics of the sample to be measured are spliced to obtain a new voltage vector : ， ； wherein, is the system matrix for the third harmonic of magnetic nanoparticles, is the system matrix for the fifth harmonic, is the system matrix for the seventh harmonic, is the system matrix for the ninth harmonic, note that the elements in the system matrix contain both real and imaginary parts; correspondingly , , and correspond to the voltage vectors of the third, fifth, seventh, and ninth harmonics of the sample to be measured, respectively. For the fused system matrix and voltage vector is expressed as: ； wherein c is the particle concentration distribution.

2. The method of claim 1, wherein, The method for calculating a weight factor for the fused matrix and constructing a weight matrix comprises: based on the obtained fused system matrix , a weight factor is calculated ； wherein is the system matrix the i maximum modulus value of the row elements Based on the obtained weight factors, a weight matrix is calculated : ； wherein, W is a diagonal matrix composed of weight factors corresponding to different harmonics, is the weight factor on the diagonal of the n th harmonic for the j th row.

3. The method of claim 2, wherein, The method for reconstructing the magnetic nanoparticle concentration distribution of the sample to be measured based on the weight matrix through an algebraic iterative reconstruction algorithm comprises: Based on the obtained fused system matrix , voltage vector and weight matrix W , a model for solving the concentration distribution of the magnetic nanoparticles under test is constructed: ； wherein is a relaxation factor, is a residual; An algebraic reconstruction algorithm ART is used to iteratively reconstruct the magnetic nanoparticle concentration distribution to be solved, and the iterative formula is: ； ； in, k For the number of iterations, Representing the k The magnetic nanoparticle concentration distribution obtained in the second iteration N The number of columns in the system matrix. For the first k The concentration distribution obtained in the nth iteration is the first n The value of each pixel. For the system matrix, the first i The first line n One element, For the voltage vector i Row elements, The residual vector is the first i The elements of a row.

4. A multi-harmonic system matrix fusion based magnetic nanoparticle imaging system for implementing the method of any one of claims 1-3, characterized in that, The system comprises a first construction module, a second construction module, a fusion module, a third construction module, and an iteration module. The first construction module is configured to place a unit volume of sample at a zero magnetic field point, move the zero magnetic field point through the entire imaging field of view by scanning the field, and obtain a system matrix of different harmonics. The second construction module is configured to place the sample to be measured at a zero magnetic field point, move the zero magnetic field point through the entire imaging field of view by scanning the field, and obtain a voltage vector of different harmonics. The fusion module is configured to fuse the system matrix of different harmonics and the voltage vector of the sample to be measured corresponding thereto. The third construction module is configured to calculate a weight factor for the fused matrix and construct a weight matrix. The iteration module is configured to reconstruct the magnetic nanoparticle concentration distribution of the sample to be measured based on the weight matrix through an algebraic iterative reconstruction algorithm. The process for fusing the system matrix of different harmonics and the voltage vector of the sample to be measured corresponding thereto comprises: The system matrix of different harmonics of the magnetic nanoparticles is spliced according to the direction of the matrix row to obtain a new system matrix ; accordingly, the voltage vectors of different harmonics of the sample to be measured are spliced to obtain a new voltage vector : ， ； wherein, is the system matrix for the third harmonic of magnetic nanoparticles, is the system matrix for the fifth harmonic, is the system matrix for the seventh harmonic, is the system matrix for the ninth harmonic, note that the elements in the system matrix contain both real and imaginary parts; correspondingly , , and correspond to the voltage vectors for the third, fifth, seventh, and ninth harmonics of the sample under test, respectively. For the fused system matrix and voltage vector is expressed as: ； wherein c is the particle concentration distribution.

5. The system of claim 4, wherein, The process for calculating a weight factor for the fused matrix and constructing a weight matrix comprises: based on the obtained fused system matrix , a weight factor is calculated ； wherein is the system matrix the i maximum modulus value of the row elements Based on the obtained weight factors, a weight matrix is calculated : ； wherein, W is a diagonal matrix composed of weight factors corresponding to different harmonics, is the weight factor on the diagonal of the nth harmonic for the mth row. j is the weight factor on the diagonal of the nth harmonic for the mth row.

6. The system of claim 5, wherein, The process for reconstructing the magnetic nanoparticle concentration distribution of the sample to be measured based on the weight matrix through an algebraic iterative reconstruction algorithm comprises: Based on the obtained fused system matrix , voltage vector and weight matrix W , a model for solving the concentration distribution of the magnetic nanoparticles under test is constructed: ； wherein is a relaxation factor, is a residual; An algebraic reconstruction algorithm ART is used to iteratively reconstruct the magnetic nanoparticle concentration distribution to be solved, and the iterative formula is: ； ； wherein, k is the number of iterations, represents the magnetic nanoparticle concentration distribution obtained at the k th iteration, N is the number of columns of the system matrix, is the value of the n-th pixel of the concentration distribution obtained at the k th iteration, is the element of the system matrix in the i th row and the n th column, is the element of the voltage vector in the i th row, is the element of the residual vector in the i th row.

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