A narrowband multi-harmonic magnetic particle imaging method

Abstract

The present invention relates to the field of medical imaging technology, and in particular to a narrowband multi-harmonic magnetic particle imaging method, comprising: determining a magnetic particle imaging region, obtaining a first region and a second region based on the magnetic particle imaging region; placing a magnetic nanoparticle sample in the first region and applying an external magnetic field, extracting harmonic signals to construct a system matrix; placing a test object in the second region and applying an external magnetic field, extracting harmonic signals to construct a test object harmonic signal matrix; constructing an equation to be solved based on the system matrix and the test object harmonic signal matrix and performing an inverse solution to obtain an image of the magnetic nanoparticle concentration distribution. The present invention adopts narrowband imaging technology, which reduces the bandwidth requirements of the magnetic particle imaging system compared to broadband imaging technology, solving the problem of insufficient bandwidth faced under high-frequency excitation.

Description

Technical Field

[0001] The present invention relates to the technical field of medical imaging, and in particular to a narrow-band multi-harmonic magnetic particle imaging method. Background Art

[0002] Magnetic particle imaging (MPI) is a novel medical imaging technology that measures the magnetic response spectrum of magnetic nanoparticles and inverts the spatial distribution of multiple parameters, such as nanoparticle concentration and biomarker concentration. This technology can be applied to early tumor diagnosis, real-time monitoring of treatment progress, and precise evaluation of therapeutic efficacy. Compared to existing medical imaging technologies such as magnetic resonance imaging (MRI), CT, and ultrasound, MPI offers high sensitivity, high spatiotemporal resolution, no tissue depth limitations, and is non-radioactive, demonstrating great potential in various biomedical applications.

[0003] Based on the bandwidth of the received signal, MPI technology can be divided into narrowband magnetic particle imaging and broadband magnetic particle imaging. However, broadband magnetic particle imaging requires receiving signals within a wider spectral range, which places high demands on the bandwidth of the magnetic particle imaging system, increasing the complexity of system design and the difficulty of noise processing. Single-harmonic narrowband imaging methods are subject to interference from feedthrough signals, limiting further improvements in signal-to-noise ratio. Since only one harmonic imaging system is used to construct matrix imaging, insufficient spectral information is obtained, limiting further improvements in resolution.

[0004] Based on the above technical problems, the present invention provides a narrowband-based multi-harmonic magnetic particle imaging method. Summary of the Invention

[0005] The purpose of the present invention is to provide a narrowband-based multi-harmonic magnetic particle imaging method, which uses the narrowband multi-harmonic method to construct a system matrix, solves the problem of insufficient spectrum information obtained by narrowband single harmonic, improves the data measurement dimension, and effectively improves the detection sensitivity and imaging resolution of the magnetic particle imaging system. The implementation process is convenient and concise.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] A narrowband multi-harmonic magnetic particle imaging method, comprising:

[0008] determining a magnetic particle imaging region, and dividing the region into a first region and a second region according to a low-frequency sinusoidal scanning magnetic field;

[0009] Placing the magnetic nanoparticle sample in the first area and applying a magnetic field, extracting harmonic signals and constructing a system matrix;

[0010] Placing the object under test in the second area and applying a magnetic field, extracting harmonic signals and constructing a harmonic signal matrix of the object under test;

[0011] According to the system matrix and the harmonic signal matrix of the measured object, an equation to be solved is constructed and an inversion solution is performed to obtain an image of the concentration distribution of the magnetic nanoparticles.

[0012] Optionally, placing the magnetic nanoparticle sample in the first region and applying a magnetic field, extracting harmonic signals to construct a system matrix includes:

[0013] The first area is grid-divided into a number of imaging units, and a high-frequency excitation magnetic field and a low-frequency scanning magnetic field in a preset direction are applied, and the unit volume of the magnetic nanoparticle sample is moved to traverse the entire first area to construct the system matrix, wherein the system matrix includes the specific harmonic kf0 and sideband harmonic signals kf0±nf1 of the unit volume of the magnetic nanoparticle sample in each imaging unit in the first area, n=1,2…,N, wherein k is an integer greater than or equal to 2, f0 represents the frequency of the high-frequency excitation magnetic field, f1 represents the frequency of the low-frequency scanning magnetic field, and N is the maximum integer detected by the sideband harmonic signal.

[0014] Optionally, obtaining specific harmonic and sideband harmonic signals includes:

[0015] Placing the magnetic nanoparticle sample of unit volume in the imaging unit of the first region and applying a high-frequency excitation magnetic field and a low-frequency scanning magnetic field in a preset direction to obtain a voltage signal generated by a magnetization response signal;

[0016] Performing Fourier transform on the voltage signal generated by the magnetization response signal to obtain the specific harmonic and sideband harmonic signals.

[0017] Optionally, the object under test is placed in the second area and a magnetic field is applied externally, and harmonic signals are extracted to construct a harmonic signal matrix of the object under test, including: gridding the second area into a plurality of imaging units, applying a high-frequency excitation magnetic field and a low-frequency scanning magnetic field in a preset direction, and moving the object under test to traverse the entire second area to construct the harmonic signal matrix of the object under test, wherein the harmonic signal matrix of the object under test includes specific harmonics and sideband harmonic signals of each imaging unit of the object under test in the second area.

[0018] Optionally, the equation to be solved includes:

[0019] U = A·c;

[0020] Among them, U is the harmonic signal matrix of the measured object, A is the system matrix, and c is the concentration distribution of magnetic nanoparticles.

[0021] Optionally, performing inverse solution on the equation to be solved includes: performing Tikhonovz regularization on the equation to be solved, solving the normalized equation to be solved using an algebraic reconstruction algorithm, and obtaining an image of the concentration distribution of the magnetic nanoparticles.

[0022] Optionally, performing Tikhonovz regularization on the equation to be solved includes:

[0023] ;

[0024] Among them, α is the regularization parameter, I is the identity matrix, and A H is the adjoint matrix of the system matrix A, and c is the concentration distribution of magnetic nanoparticles.

[0025] The beneficial effects of the present invention are:

[0026] 1. The present invention adopts narrowband imaging technology, which reduces the bandwidth requirements of the magnetic particle imaging system compared to broadband imaging technology, and solves the problem of insufficient bandwidth faced under high-frequency magnetic field excitation.

[0027] 2. The present invention adopts a multi-harmonic construction system matrix approach. Compared with the narrow-band single-harmonic magnetic particle imaging method, by increasing the number of measured harmonics, richer spectral information is obtained, which can improve image resolution.

[0028] 3. The harmonic frequencies used in the present invention are the kth harmonic and the sideband harmonic signals. The sideband harmonic signals have a higher signal-to-noise ratio (SNR) than the kth harmonic, which can improve the sensitivity of the magnetic particle imaging system. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0030] Figure 1 This is a flow chart of a narrowband multi-harmonic magnetic particle imaging method according to an embodiment of the present invention;

[0031] Figure 2 This is embodiment N of the present invention x =2,N y =2, schematic diagram of the area division of narrow-band multi-harmonic magnetic particle two-dimensional imaging;

[0032] Figure 3 This is a basic principle diagram of narrowband multi-harmonic magnetic particle imaging based on an embodiment of the present invention;

[0033] Figure 4 This is embodiment N of the present invention x =2,N y =2,N z =1, schematic diagram of the area division of narrow-band multi-harmonic magnetic particle three-dimensional imaging. DETAILED DESCRIPTION

[0034] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0035] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0036] like Figure 1 As shown, this embodiment provides a narrowband-based multi-harmonic magnetic particle imaging method, including:

[0037] determining a magnetic particle imaging region, and acquiring a first region and a second region according to the magnetic particle imaging region;

[0038] A unit volume of magnetic nanoparticle sample is placed in the first area and a magnetic field is applied, and harmonic signals are extracted to construct a system matrix;

[0039] Placing the object under test in the second area and applying a magnetic field, extracting harmonic signals and constructing a harmonic signal matrix of the object under test;

[0040] According to the system matrix and the harmonic signal matrix of the measured object, the equation to be solved is constructed and the inversion solution is performed to obtain the image of the concentration distribution of the magnetic nanoparticles.

[0041] Specifically, determine the FOV of the imaging area of ​​the magnetic particle imaging system x ×FOV y ×FOV z , determine the amplitude, waveform, phase and direction of the low-frequency scanning magnetic field and the high-frequency excitation magnetic field, the direction of the low-frequency scanning magnetic field can be any one of the x, y or z axes, and the direction of the high-frequency excitation magnetic field can also be any one of the x, y or z axes, and divide the first area I and the second area II according to it; determine the size of the first area I including: along the direction of the low-frequency scanning magnetic field and the range of the imaging area, the size of the other directions is twice the range of the imaging area; determine the size of the second area II including: along the direction of the low-frequency scanning magnetic field, it becomes the size of a pixel unit, and the size of the other directions is consistent with the range of the imaging area.

[0042] Furthermore, the magnetic nanoparticle sample is placed in the first area and a magnetic field is applied, and the harmonic signal is extracted to construct a system matrix including:

[0043] The first area is grid-divided into a number of imaging units, and a high-frequency excitation magnetic field and a low-frequency scanning magnetic field in a preset direction are applied, and the unit volume of the magnetic nanoparticle sample is moved to traverse the entire first area to construct a system matrix, wherein the system matrix includes the specific harmonics and sideband harmonic signals of each imaging unit of the unit volume of the magnetic nanoparticle sample in the first area.

[0044] Furthermore, obtaining specific harmonic and sideband harmonic signals includes:

[0045] Placing a unit volume of a magnetic nanoparticle sample in an imaging unit in the first region and applying a high-frequency excitation magnetic field and a low-frequency scanning magnetic field in a preset direction to obtain a voltage signal generated by a magnetization response signal;

[0046] The voltage signal generated by the magnetization response signal is Fourier transformed to obtain the specific harmonic kf0 and the sideband harmonic signal kf0±nf1, n=1,2…,N, where k is an integer greater than or equal to 2, f0 represents the frequency of the high-frequency excitation magnetic field, f1 represents the frequency of the low-frequency scanning magnetic field, and N is the maximum integer detected by the sideband harmonic signal.

[0047] Specifically, in this embodiment, constructing the system matrix includes:

[0048] Step S1: performing grid division processing on the first area I to divide it into a plurality of imaging units;

[0049] Step S2: placing a unit volume of magnetic nanoparticle sample in the first area I, and applying a high-frequency excitation magnetic field and a low-frequency scanning magnetic field in a preset direction, for example, applying a high-frequency excitation magnetic field in the x-direction and a low-frequency scanning magnetic field in the y-direction;

[0050] Step S3: The detection coil collects the magnetization response signal generated by the object under test, and extracts the harmonic and sideband harmonic signals of the specific frequency through Fourier transform;

[0051] Step S4: driving the three-dimensional mechanical translation stage to adjust the position of the unit volume of the magnetic nanoparticle sample in the first area I. If the unit volume of the magnetic nanoparticle sample has traversed all imaging units, then go to step S5; otherwise, go to step S2.

[0052] Step S5: constructing a system matrix A based on the harmonic signal and sideband harmonic signal of the specific frequency extracted in step S3.

[0053] Furthermore, the object under test is placed in the second area and a magnetic field is applied externally, and the harmonic signal is extracted to construct a harmonic signal matrix of the object under test, including: gridding the second area into a plurality of imaging units, applying a high-frequency excitation magnetic field and a low-frequency scanning magnetic field in a preset direction, and moving the spatial position of the object under test to traverse the entire second area to construct a harmonic signal matrix of the object under test, wherein the harmonic signal matrix of the object under test includes specific harmonics and sideband harmonic signals of each imaging unit of the object under test in the second area.

[0054] Specifically, constructing the harmonic signal matrix of the measured object includes:

[0055] S1: Performing grid division processing on the second area II to divide it into a number of imaging units, the size of which is consistent with the imaging unit in the first area I;

[0056] S2: The object to be measured is placed in the second area II and a high-frequency excitation magnetic field in the x-direction and a low-frequency scanning magnetic field in the y-direction are applied to it;

[0057] S3: The detection coil collects the magnetization response signal generated by the measured object, and extracts the specific harmonic and sideband harmonic signals through Fourier transform;

[0058] S4: driving the three-dimensional mechanical translation stage to adjust the position of the object under test in the second area II. If the object under test has traversed all imaging units in the second area II, proceed to step S5; otherwise, proceed to step S2.

[0059] S5: Obtain the harmonic signal matrix U of the measured object according to the specific harmonic and sideband harmonic signals extracted in step S3.

[0060] Furthermore, the equations to be solved include:

[0061] U = A·c;

[0062] Among them, U is the harmonic signal matrix of the measured object, A is the system matrix, and c is the concentration distribution of magnetic nanoparticles.

[0063] Furthermore, performing inverse solution on the equation to be solved includes: normalizing the equation to be solved, solving the normalized equation to be solved using an algebraic reconstruction algorithm, and obtaining an image of the concentration distribution of the magnetic nanoparticles.

[0064] Normalizing the equation to be solved includes:

[0065] ;

[0066] Among them, α is the regularization parameter, I is the identity matrix, and A H is the adjoint matrix of the system matrix A, and c is the concentration distribution of magnetic nanoparticles.

[0067] This embodiment utilizes a narrowband multiharmonic magnetic particle imaging method, utilizing noise matching techniques to achieve a signal-to-noise ratio superior to that of the kth harmonic. This method places low bandwidth requirements on the magnetic particle imaging system, is relatively simple to design and implement, and can address the bandwidth constraints encountered with high-frequency magnetic field excitation. This method utilizes a multiharmonic system matrix. Compared to single-harmonic narrowband magnetic particle imaging methods, this method increases the number of measured harmonics to obtain richer spectral information, significantly improving image resolution.

[0068] The method of this embodiment is further described below by applying the narrowband multi-harmonic magnetic particle imaging method to two-dimensional imaging:

[0069] Step S10: Determine the range of the imaging field of view (FOV) of the magnetic particle imaging system x ×FOV y , divide it into (2N x +1)×(2N y +1) imaging units, where N x and N y is a positive integer; using the magnetic particle imaging system, a gradient magnetic field H is applied to the imaging area G (x, y), a low-frequency sinusoidal scanning magnetic field H is applied to the imaging area in the y direction s (t)=H s sin(2πf1t), a high-frequency sinusoidal excitation magnetic field H is applied in the x direction ac (t)=H ac sin(2πf0t), the low-frequency sinusoidal scanning magnetic field controls the movement of the zero magnetic field point, and the high-frequency excitation magnetic field drives the particles to generate a magnetization response signal, where H s and f1 are the low-frequency scanning magnetic field amplitude and frequency respectively, H ac and f0 are the high-frequency excitation magnetic field amplitude and frequency respectively, t is the time, and the total magnetic field H(x,y,t) can be expressed as:

[0070] ;

[0071] Step S20: Sine scanning magnetic field H s The range of the first area I is 2FOV x ×FOV y , the range of the second area II is FOV x ; Grid division is performed on the first area I, and the imaging unit size is consistent with the imaging field of view (FOV), and it is divided into (4N x +1)×(2N y+1) imaging units; the second area II is grid-divided, and the imaging unit size is consistent with the imaging field of view (FOV), and it is divided into (2N x +1) × 1 imaging unit; such as Figure 2 As shown, it means N x It is 2, N y The relationship between the imaging field of view (FOV), the first region I, and the second region II when is 2. A unit volume of SPION sample is placed in the first region I, and a total magnetic field H(x, y, t) is applied.

[0072] When the unit volume of SPION sample is located at position (x a ,y b ), the magnetization response signal generated Mathematically, it can be described by the Langevin equation:

[0073] ;

[0074] Among them, M s is the saturation magnetization, It is the Langevin function ℒ(x)=coth(x)-1 / x, is the magnetic energy of a particle with magnetic moment m and the Boltzmann constant k B The ratio of the heat energy given by the temperature T, μ0 is the vacuum permeability. According to Faraday's law of electromagnetic induction, the detection coil collects the voltage signal generated by the magnetization response signal. It can be expressed as:

[0075] ;

[0076] Where s(x,y) is the spatial sensitivity of the receiving coil, and V is the spatial volume element covered by the detection coil and associated with the magnetization response signal. After Fourier transform processing, it can be expressed as:

[0077] ;

[0078] Where i is the imaginary unit, a m,n represents the Fourier coefficient of the frequency component mf0+nf1. M and N represent the maximum integer multiples of the detectable harmonic signal and sideband harmonic signal, respectively. Based on the hardware design of the magnetic particle imaging system, the kth harmonic kf0 and the sideband harmonic signals kf0±nf1 (n=1,2…,N) are extracted for imaging, where k is an integer greater than or equal to 2.

[0079] The three-dimensional mechanical translation stage is driven to adjust the position of the SPION sample per unit volume in the first region I until all imaging units in the first region I are traversed, and the system matrix A is constructed. The system matrix A can be expressed as:

[0080] ;

[0081] Among them, u0(x a , y b ) represents the position of the SPION sample per unit volume in the first region I (x a , y b ), x a ∈(-2N x ,2N x ), y b ∈(-N y ,N y ), the extracted kth harmonic kf0 and sideband harmonic signals kf0±nf1 (n=1,2…,N).

[0082] Step S30: The SPION concentration distribution of the object to be measured is c(x, y). The object to be measured is placed in the second area II and its position is recorded. , and apply a total magnetic field H(x, y, t), the object under test generates a magnetization response signal M(x, y, t); the detection coil collects the magnetization response signal M(x, y, t), and the generated voltage signal is processed by Fourier transform to extract the kth harmonic kf0 and the sideband harmonic signal kf0±nf1 (n=1, 2…, N). In this embodiment, the third harmonic 3f0 and the sideband harmonic signal 3f0±nf1 (n=1,…, N) are extracted; the three-dimensional mechanical translation stage is driven to adjust the position of the object under test in the second area II until all imaging units in the second area II are traversed, and the harmonic signal matrix U of the object under test is calculated. U can be expressed as:

[0083] ;

[0084] in, Indicates that the position of the measured object in area II is When , the kth harmonic and sideband harmonic signals are extracted, and the superscript T represents transposition.

[0085] Step S40: Based on the system matrix A and the harmonic signal matrix U of the measured object, construct the equation to be solved:

[0086] ;

[0087] Perform Tikhonov normalization on the equation U = A·c:

[0088] ;

[0089] Among them, α is the regularization parameter, I is the identity matrix, and A H is the adjoint matrix of the system matrix A. The algebraic reconstruction algorithm (ART algorithm) is used to solve this equation and invert the image of the magnetic nanoparticle concentration distribution c.

[0090] The method of this embodiment is further described below by applying the narrowband multi-harmonic magnetic particle imaging method to three-dimensional imaging:

[0091] Step S10: Determine the range of the imaging field of view (FOV) of the magnetic particle imaging system x ×FOV y ×FOV z , divide it into (2N z +1) layers, each divided into (2N x +1)×(2N y +1) imaging unit, N z is a positive integer; using the magnetic particle imaging system, a gradient magnetic field H is applied to the imaging area G (x, y), a low-frequency sinusoidal scanning magnetic field H is applied to the imaging area in the y direction s (t)=H s sin(2πf1t), a high-frequency sinusoidal excitation magnetic field H is applied in the x direction ac (t)=H ac sin(2πf0t), the low-frequency sinusoidal scanning magnetic field controls the movement of the zero magnetic field point, and the high-frequency excitation magnetic field drives the particles to generate a magnetization response signal, where H s and f1 are the low-frequency scanning magnetic field amplitude and frequency respectively, H ac and f0 are the high-frequency excitation magnetic field amplitude and frequency respectively, t is the time, and the total magnetic field H(x, y, z, t) can be expressed as:

[0092] ;

[0093] Step S20: Figure 4 As shown, according to the sinusoidal scanning magnetic field H s The range of the first area I is 2FOV x ×FOV y ×2FOV z , the range of the second area II is FOV x ×FOV z; Grid division is performed on the first area I, and the imaging unit size is consistent with the imaging field of view, and it is divided into (4N z +1) layer, each layer (4N x +1)×(2N y +1) imaging unit.

[0094] A unit volume of SPION sample is placed in the first region I and a total magnetic field H(x, y, z, t) is applied. When the unit volume of SPION sample is located at a certain position (x a ,y b ,z c ), the generated magnetization response signal M0(x a ,y b ,z c ,t). According to Faraday's law of electromagnetic induction, the detection coil collects the voltage signal generated by the magnetization response signal. The voltage signal is Fourier transformed to extract the kth harmonic kf0 and the sideband harmonic signals kf0±nf1 (n=1,2…,N) for imaging, where k is an integer greater than or equal to 2. The three-dimensional mechanical translation stage is driven to adjust the position of the unit volume of the SPION sample in the first region I until all imaging units in the first region I are traversed. The system matrix A is calculated and constructed. The system matrix A can be expressed as:

[0095] ;

[0096] in, N represents the unit volume of SPION sample in the first region I z The two-dimensional system matrix when the layer is .

[0097] Step S30: Grid division is performed on the second area II. The imaging unit size is consistent with the imaging field of view (FOV), and it is divided into (2N x +1)×(2N z +1) imaging units, the SPION concentration distribution of the measured object is c(x,y), the measured object is placed in the second region II, and a total magnetic field H(x,y,z,t) is applied. The measured object generates a magnetization response signal M(x,y,z,t); the detection coil collects the magnetization response signal, and the generated voltage signal is processed by Fourier transform to extract the third harmonic 3f0 and sideband harmonic signals 3f0±nf1 (n=1,…,N); the three-dimensional mechanical translation stage is driven to adjust the position of the measured object in the second region II until all imaging units in the second region II are traversed. The harmonic signal matrix U of the measured object is calculated, which can be expressed as:

[0098] ;

[0099] in, N represents the unit volume of SPION sample in the second region II z The two-dimensional harmonic signal matrix at the layer.

[0100] Step S40: Based on the system matrix A and the harmonic signal matrix U of the measured object, construct the equation to be solved:

[0101] ;

[0102] Perform Tikhonov normalization on the equation U = A·c:

[0103] ;

[0104] Among them, α is the regularization parameter, I is the identity matrix, and A H is the adjoint matrix of the system matrix A. The algebraic reconstruction algorithm (ART algorithm) is used to solve this equation and invert the image of the magnetic nanoparticle concentration distribution c.

[0105] The basic principle of narrowband multiharmonic magnetic particle imaging, such as Figure 3 For two-dimensional imaging, a gradient magnetic field H is applied in the xy plane. G Generate FFP and perform spatial encoding. In the x direction, a high-frequency excitation magnetic field H with a frequency of f0 is applied. ac To excite the SPION, a scanning magnetic field H with a low frequency f1 is applied in the y direction. s Used to scan the FFP along the y-axis. Under the influence of the gradient magnetic field, SPIONs located at different positions within the imaging field of view (FOV) will generate different magnetization response signals, M0. The detection coil collects this magnetization response signal, and the generated voltage signal is Fourier transformed to generate a spectrum signal around the third harmonic 3f0.

[0106] This invention utilizes narrowband imaging technology, which reduces the bandwidth requirements of magnetic particle imaging systems compared to broadband imaging techniques, addressing the bandwidth shortage problem encountered with high-frequency excitation. This invention employs a multi-harmonic approach to construct a system matrix, using the kth harmonic and its surrounding spectrum. By increasing the number of measured harmonics, richer spectral information is obtained, thereby improving image resolution and lowering the detection limit of the magnetic particle imaging system.

[0107] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A narrowband multi-harmonic magnetic particle imaging method, characterized in that: include: determining a magnetic particle imaging region, and dividing the region into a first region and a second region according to a low-frequency sinusoidal scanning magnetic field; Placing the magnetic nanoparticle sample in the first area and applying a magnetic field, extracting harmonic signals and constructing a system matrix; Placing the object under test in the second area and applying a magnetic field, extracting harmonic signals and constructing a harmonic signal matrix of the object under test; According to the system matrix and the harmonic signal matrix of the measured object, an equation to be solved is constructed and an inversion solution is performed to obtain an image of the concentration distribution of magnetic nanoparticles; The inverse solution of the equation to be solved includes: performing Tikhonov regularization on the equation to be solved, solving the normalized equation to be solved by using an algebraic reconstruction algorithm, and obtaining an image of the concentration distribution of the magnetic nanoparticles.

2. The narrowband multi-harmonic magnetic particle imaging method according to claim 1, characterized in that: Placing the magnetic nanoparticle sample in the first area and applying a magnetic field, extracting harmonic signals to construct a system matrix includes: The first area is grid-divided into a number of imaging units, and a high-frequency excitation magnetic field and a low-frequency scanning magnetic field in a preset direction are applied, and the unit volume of the magnetic nanoparticle sample is moved to traverse the entire first area to construct the system matrix, wherein the system matrix includes the specific harmonic kf0 and sideband harmonic signals kf0±nf1 of the unit volume of the magnetic nanoparticle sample in each imaging unit in the first area, n=1,2…,N, wherein k is an integer greater than or equal to 2, f0 represents the frequency of the high-frequency excitation magnetic field, f1 represents the frequency of the low-frequency scanning magnetic field, and N is the maximum integer detected by the sideband harmonic signal.

3. The narrowband multi-harmonic magnetic particle imaging method according to claim 2, characterized in that: Obtaining specific harmonic and sideband harmonic signals includes: Placing the magnetic nanoparticle sample of unit volume in the imaging unit of the first region and applying a high-frequency excitation magnetic field and a low-frequency scanning magnetic field in a preset direction to obtain a voltage signal generated by a magnetization response signal; Performing Fourier transform on the voltage signal generated by the magnetization response signal to obtain the specific harmonic and sideband harmonic signals.

4. The narrowband multi-harmonic magnetic particle imaging method according to claim 3, characterized in that: Placing the object under test in the second area and applying a magnetic field, extracting harmonic signals and constructing a harmonic signal matrix of the object under test includes: gridding the second area into a plurality of imaging units, applying a high-frequency excitation magnetic field and a low-frequency scanning magnetic field in a preset direction, and moving the object under test to traverse the entire second area to construct the harmonic signal matrix of the object under test, wherein the harmonic signal matrix of the object under test includes specific harmonics and sideband harmonic signals of each imaging unit of the object under test in the second area.

5. The narrowband multi-harmonic magnetic particle imaging method according to claim 1, characterized in that: The equations to be solved include: U = A·c; Among them, U is the harmonic signal matrix of the measured object, A is the system matrix, and c is the concentration distribution of magnetic nanoparticles.

6. The narrowband multi-harmonic magnetic particle imaging method according to claim 1, characterized in that: Performing Tikhonov regularization on the equation to be solved includes: ； Among them, α is the regularization parameter, I is the identity matrix, and A H is the adjoint matrix of the system matrix A, and c is the concentration distribution of magnetic nanoparticles.

Images