A method for classifying and detecting magnetic nanoparticles based on multi-frequency magnetization response spectrum

Abstract

The application relates to a kind of magnetic nanoparticle classification detection methods based on multi-frequency magnetization response spectrum, comprising: for different kinds of magnetic nanoparticle samples, applying excitation magnetic field f1, f2...f n , respectively acquiring sample magnetization response spectrum signal, and constructing corresponding coefficient matrix A(f1), A(f2)...A(f n ); The coefficient matrix under different frequencies is spliced to obtain a new coefficient matrix A'; for the mixed magnetic nanoparticle to be measured, excitation magnetic field is sequentially applied, and magnetization response spectrum signal U(f1), U(f2)...U(f n ) is obtained, the magnetization response spectrum signals under different frequencies are combined to obtain a new magnetization response spectrum signal U'; through the new coefficient matrix combined with the new magnetization response spectrum signal, a magnetic nanoparticle classification and quantitative detection model is constructed, the magnetic nanoparticle classification and quantitative detection model is solved, and the kind and concentration or content of the mixed magnetic nanoparticle to be measured are obtained. The application can improve the precision of magnetic nanoparticle classification detection, and promote the application process of magnetic nanoparticles in biomedicine.

Description

Technical Field

[0001] This invention relates to the field of magnetic nanoparticle classification and detection technology, and in particular to a method for magnetic nanoparticle classification and detection based on multi-frequency magnetization response spectrum. Background Technology

[0002] Magnetic nanoparticles (MNPs), with their unique superparamagnetism and tunable surface functionalization, have shown broad application potential in the biomedical field, such as as heat sources for thermotherapy, carriers for targeted drug delivery, contrast agents for magnetic resonance imaging (MRI), and tracers for magnetic particle imaging (MPI). The performance of MNPs in practical applications is highly dependent on their magnetic properties and surface modifications; therefore, various characterization methods have been developed to evaluate their key parameters.

[0003] Magnetic Particle Spectroscopy (MPS) is a rapidly developing detection technique originating from Magneto-Particle (MPI). By measuring the nonlinear magnetization response of magnetic nanoparticles (MNPs), it can quantitatively detect the concentration of MNPs in biological tissues or in vitro samples, and achieve highly sensitive, real-time characterization of their magnetic properties and the physical parameters of their environment (such as viscosity, temperature, and hydrodynamic diameter). Initially used for screening and optimizing MPI tracers, MPS has now become an important tool in biomarker detection and magnetic immunoassay due to its advantages of ease of operation, rapid detection, high sensitivity, and low cost.

[0004] In multiplex detection applications, the magnetization response behavior of MNPs is particularly crucial. Based on their dominant relaxation mechanisms, MNPs can be categorized into Niehr relaxation-dominated and Brownian relaxation-dominated types, with significant differences in their magnetization responses at different excitation frequencies: the former exhibits stronger signals and higher signal-to-noise ratios at high frequencies, while the latter performs better at low frequencies. Based on this characteristic, multiplexed magnetization response spectra (MPS) can be used to acquire the magnetization response spectrum signals of different types of MNPs and mixed samples at different excitation frequencies. Mathematical models for classification and quantitative detection can be established and solved to decouple the magnetization response spectrum signals of mixed samples, enabling the classification and quantitative detection of multiple MNPs within the mixed samples.

[0005] Furthermore, by utilizing multiple types of MNP probes functionalized with different antibodies, MPS technology can simultaneously achieve the joint detection of multiple biomolecules, i.e., multiplex detection. In this application context, accurately distinguishing and identifying the signals of different magnetic nanoparticles is crucial for ensuring the accuracy and reliability of multiplex biomolecule detection, and it is also a current technical challenge. Summary of the Invention

[0006] The purpose of this invention is to provide a method for classifying and detecting magnetic nanoparticles based on multi-frequency magnetization response spectrum, so as to solve the difficulties of the current technology, improve the accuracy of magnetic nanoparticle classification and detection, and promote the application of magnetic nanoparticles in biomedicine.

[0007] To achieve the above objectives, the present invention provides the following solution:

[0008] A method for classifying and detecting magnetic nanoparticles based on multi-frequency magnetization response spectrum, comprising:

[0009] For different types of magnetic nanoparticle samples, an excitation magnetic field with an excitation frequency of f1 was applied, and the sample magnetization response spectrum signals S1(f1), S2(f2)...S were obtained respectively. k (f1), and construct the corresponding coefficient matrix A(f1);

[0010] Change the excitation frequency, applying excitation frequencies f2, f3...f in sequence. n The excitation magnetic field was used to obtain the magnetization response spectrum signals of different types of magnetic nanoparticle samples, and the corresponding coefficient matrices A(f2), A(f3)...A(f n );

[0011] The coefficient matrices A(f1), A(f2), ..., A(f) at different frequencies are... n The coefficients are concatenated to obtain a new coefficient matrix A'.

[0012] The hybrid magnetic nanoparticles to be tested are sequentially subjected to frequencies f1, f2…f n The excitation magnetic field was used to obtain the magnetization response spectrum signals U(f1), U(f2)...U(f) respectively. n The mixed magnetic nanoparticles to be tested are composed of different types of magnetic nanoparticles.

[0013] The magnetization response spectrum signals U(f1), U(f2), ... U(f) at different frequencies are used to analyze the magnetization response spectrum signals U(f1), U(f2), ... U(f3) at different frequencies. n By combining these signals, a new magnetization response spectrum signal U' can be obtained;

[0014] By combining the new coefficient matrix A' with the new magnetization response spectrum signal U', a magnetic nanoparticle classification and quantitative detection model is constructed. The magnetic nanoparticle classification and quantitative detection model is solved to obtain the types and concentrations (or contents) of the mixed magnetic nanoparticles to be tested.

[0015] Optionally, the magnetization response spectrum signal is:

[0016] S(f) = [M1 M2… M h ]T

[0017] Where S(f) is the magnetization response spectrum of the magnetic nanoparticles at an excitation frequency of f, and M1, M2…M h These are the magnetization signals of the 1st, 2nd...hth harmonics of the magnetization response spectrum, respectively.

[0018] Optionally, the corresponding coefficient matrix is:

[0019] A(f)=[S1(f) S2(f) … S k (f)]

[0020] Where A(f) is the coefficient matrix, S1(f), S2(f)...S k (f) represents the magnetization response spectrum signals of the first, second to kth types of magnetic nanoparticles, respectively.

[0021] Optionally, the new coefficient matrix is:

[0022]

[0023] Where A' is the new coefficient matrix, A(f1), A(f2)...A(f n The excitation frequencies are f1, f2, ..., f, respectively. n The coefficient matrix at that time.

[0024] Optionally, the new magnetization response spectrum is:

[0025] U(f) = [M1 M2 … M h ] T

[0026]

[0027] Where U(f) is the magnetization response spectrum of the hybrid magnetic nanoparticles to be tested, and M1, M2…M h These are the magnetization signals of the 1st, 2nd...hth harmonics of the magnetization response spectrum, respectively; U' is the new magnetization response spectrum, U(f1), U(f2)...U(f...h) n ) for excitation frequencies of f1, f2...f n The magnetization response spectrum signal under the given conditions.

[0028] Optionally, obtaining the type and concentration (or content) of the mixed magnetic nanoparticles to be tested includes:

[0029] Based on the new coefficient matrix and the new magnetization response spectrum signal, a classification and quantitative detection model for magnetic nanoparticles is constructed.

[0030] The magnetic nanoparticle classification and quantitative detection model is iteratively reconstructed to solve for the particle concentration (or content) of different types of magnetic nanoparticles.

[0031] Optionally, the magnetic nanoparticle classification and quantitative detection model is as follows:

[0032]

[0033] Where A' is the new coefficient matrix, U' is the new magnetization response spectrum, x is the concentration (or content) of different types of magnetic nanoparticles in the sample to be tested, μ is the relaxation factor and μ≥0, and v is the residual.

[0034] Optionally, solving the magnetic nanoparticle classification and quantitative detection model includes:

[0035]

[0036] Where k is the iteration number, 1≤i≤N, and N is the number of rows in the coefficient matrix A'. i Let U' be a vector composed of the elements of the i-th row of the coefficient matrix A'. i Let be the element in the i-th row of the magnetization response spectrum signal U'.

[0037] The beneficial effects of this invention are as follows:

[0038] This invention fully utilizes the different trends exhibited by different types of magnetic nanoparticles (Niell relaxation-dominated and Brown relaxation-dominated) when the applied excitation frequency changes. Based on the characteristics that Niell relaxation particles have a high signal-to-noise ratio at higher frequencies and Brown relaxation particles have a high signal-to-noise ratio at lower frequencies, the accuracy of quantitative detection of magnetic nanoparticles is improved.

[0039] This invention combines the coefficient matrices of different types of magnetic nanoparticles and the nonlinear magnetization response signal of the mixed magnetic nanoparticles under test at excitation frequencies of f1, f2 and more. This utilizes more information about the magnetic nanoparticles, expands the differences between the magnetic nanoparticle signals, avoids crosstalk between particle signals during the reconstruction process, and improves the accuracy of magnetic nanoparticle classification and detection. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other embodiments can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a flowchart of a magnetic nanoparticle classification and detection method based on multi-frequency magnetization response spectrum according to an embodiment of the present invention;

[0042] Figure 2 This is a flowchart of the algebraic reconstruction algorithm according to an embodiment of the present invention. Detailed Implementation

[0043] 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.

[0044] 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.

[0045] like Figure 1 As shown, this embodiment discloses a method for classifying and detecting magnetic nanoparticles based on multi-frequency magnetization response spectrum, including:

[0046] For different types of magnetic nanoparticle samples, an excitation magnetic field was applied, and the magnetization response spectrum signal of the samples was obtained respectively, and the corresponding coefficient matrix was constructed.

[0047] By concatenating the coefficient matrices at different frequencies, a new coefficient matrix is ​​obtained;

[0048] For the mixed magnetic nanoparticles under test, excitation magnetic fields are applied sequentially, and magnetization response spectrum signals are obtained respectively. The mixed magnetic nanoparticles under test are composed of different types of magnetic nanoparticles.

[0049] By combining magnetization response spectrum signals at different frequencies, a new magnetization response spectrum signal can be obtained.

[0050] By combining the new coefficient matrix with the new magnetization response spectrum signal, a magnetic nanoparticle classification and quantitative detection model is constructed. The magnetic nanoparticle classification and quantitative detection model is solved to obtain the types and concentrations (or contents) of the mixed magnetic nanoparticles to be tested.

[0051] Specifically, in this embodiment, a method for classifying and detecting magnetic nanoparticles based on multi-frequency magnetization response spectra includes: moving different types of magnetic nanoparticles (NieR relaxation-dominated and Brownian relaxation-dominated) to the test region of the magnetic particle spectrum, applying an excitation magnetic field with an excitation frequency of f1, and acquiring the sample magnetization response spectrum signals S1(f1), S2(f2)...S1, respectively. k (f1), and construct the corresponding coefficient matrix A(f1); change the excitation frequency, and apply excitation frequencies of f2, f3...f in sequence.n The excitation magnetic field was used to obtain the magnetization response spectrum signals of different types of magnetic nanoparticle samples, and the corresponding coefficient matrices A(f2), A(f3)...A(f n ); The coefficient matrices A(f1), A(f2)...A(f) at different frequencies n The coefficients are spliced ​​together to obtain a new coefficient matrix A'; the hybrid magnetic nanoparticles to be tested are sequentially subjected to frequencies f1, f2...f... n The excitation magnetic field was used to obtain the magnetization response spectrum signals U(f1), U(f2)...U(f) respectively. n The test hybrid magnetic nanoparticles are composed of different types of magnetic nanoparticles; the magnetization response spectrum signals U(f1), U(f2)...U(f) at different frequencies are analyzed. n The new magnetization response spectrum signal U' is obtained by combining the new coefficient matrix A' with the new magnetization response spectrum signal U'. A magnetic nanoparticle classification and quantitative detection model is constructed by combining the new coefficient matrix A' with the new magnetization response spectrum signal U'. The magnetic nanoparticle classification and quantitative detection model is solved to obtain the type and concentration (or content) of the mixed magnetic nanoparticles to be tested.

[0052] Further, in step S10, using a magnetic particle spectrum system, unit volume samples of different types of magnetic nanoparticles are moved to the test area, and an excitation magnetic field with an excitation frequency of f1 is applied to the different types of magnetic nanoparticle samples to obtain the sample magnetization response spectrum signals S1(f1), S2(f1)...S1(f1) respectively. k (f1), and construct the corresponding coefficient matrix A(f1);

[0053] Further, in step S20, the excitation frequency is changed, and excitation frequencies of f2, f3...f are applied sequentially. n The excitation magnetic field was used to obtain the magnetization response spectrum signals of different types of magnetic nanoparticle samples, and the corresponding coefficient matrices A(f2), A(f3)...A(f n );

[0054] The coefficient matrices A(f1), A(f2), ..., A(f) at different frequencies are... n The coefficients are concatenated to obtain a new coefficient matrix A'.

[0055] Further, in step S30, the mixed magnetic nanoparticles to be tested are placed in the test area, and the concentration distribution of different types of magnetic nanoparticles contained in the mixed magnetic nanoparticles to be tested is x1, x2…x k The hybrid magnetic nanoparticles to be tested are sequentially subjected to frequencies f1, f2…f n The excitation magnetic field was used to obtain the magnetization response spectrum signals U(f1), U(f2)...U(f) respectively. n ).

[0056] The magnetization response spectrum signals U(f1), U(f2), ... U(f) at different frequencies are used to analyze the magnetization response spectrum signals U(f1), U(f2), ... U(f3) at different frequencies. n By combining these signals, a new magnetization response spectrum signal U' can be obtained;

[0057] Further, step S40, constructing a magnetic nanoparticle classification and quantitative detection model includes: constructing a magnetic nanoparticle classification and quantitative detection model based on the new coefficient matrix and the new magnetization response spectrum signal.

[0058] Step S41: Different types of magnetic nanoparticles are excited at frequencies f1, f2…f n The coefficient matrices A(f1), A(f2)...A(f) are given at the time. n The new coefficient matrix A' is obtained by concatenating the matrices according to the row directions; correspondingly, the magnetization response spectrum signals U(f1), U(f2)...U(f... n By combining these components, we obtain the magnetization response spectrum U':

[0059]

[0060] U(f) = [M1 M2 … M h ] T

[0061]

[0062] Where A' is the new coefficient matrix, A(f1), A(f2)...A(f n The excitation frequencies are f1, f2, ..., f, respectively. n The coefficient matrix at time, U(f) is the magnetization response spectrum of the hybrid magnetic nanoparticles to be tested, M1, M2…M h These are the magnetization signals of the 1st, 2nd...hth harmonics of the magnetization response spectrum, respectively; U' is the new magnetization response spectrum, U(f1), U(f2)...U(f...h) n ) for excitation frequencies of f1, f2...f n The magnetization response spectrum signal under the given conditions.

[0063] Step S42, the concentration distributions of different types of magnetic nanoparticles x1, x2…x k The particle concentration x is obtained by splicing:

[0064]

[0065] Where x1, x2…x k This refers to the concentration (or content) of different types of magnetic nanoparticles.

[0066] In step S50, based on the coefficient matrix A' and the magnetization response spectrum U', a classification and quantitative detection method for magnetic nanoparticles is constructed:

[0067]

[0068] Where μ is the relaxation factor and μ≥0, and v is the residual.

[0069] In step S60, the method for solving the magnetic nanoparticle classification and quantitative detection model employs an algebraic reconstruction algorithm. Specifically, this includes:

[0070]

[0071] Where k is the iteration number, 1≤i≤N, and N is the number of rows in the coefficient matrix A'. i Let U' be a vector composed of the elements of the i-th row of the coefficient matrix A'. i Let be the element in the i-th row of the nonlinear magnetization response signal U'.

[0072] To improve the accuracy of magnetic nanoparticle classification and detection in mixed samples, the purpose of this embodiment is to provide a magnetic nanoparticle classification and detection method based on multi-frequency magnetization response spectrum.

[0073] By superimposing the magnetization response spectrum signals of magnetic nanoparticles under different excitation frequencies and combining them with the relaxation characteristics of MNPs, more information is introduced, maximizing the difference in magnetization response spectrum signals between different types of magnetic nanoparticles. This effectively increases the available information, improves the accuracy of magnetic nanoparticle detection, and reduces classification detection errors, which is of great significance for the bioimmunoassay of magnetic nanoparticles in biomedical applications.

[0074] The practical application scenarios of this embodiment include measuring the magnetization response spectrum using multiple excitation frequencies, and then classifying and quantitatively detecting various magnetic nanoparticles. Here, we take the classification and quantitative detection of two types of magnetic nanoparticles under two excitation frequencies as an example for illustration:

[0075] First, using a magnetic particle spectrum system, a certain excitation magnetic field strength is set, and different types of unit volume magnetic nanoparticle samples are placed in the test area. An excitation magnetic field with an excitation frequency of f1 is applied to the test area, and the magnetization response spectra S1(f1) and S2(f1) of the magnetic nanoparticles are obtained, and a coefficient matrix A(f1) is constructed based on them. Then, an excitation magnetic field with an excitation frequency of f2 is applied again, and the magnetization response spectra S1(f2) and S2(f2) of the magnetic nanoparticles are obtained, and a coefficient matrix A(f2) is constructed based on them.

[0076] The test object is placed in a magnetic particle spectrum system. Here, the concentrations (or contents) of the two types of magnetic nanoparticles contained in the test object are x1 and x2, respectively. The magnetization response spectra of the test object are obtained under the same excitation conditions, yielding U(f1) and U(f2), particle coefficient matrices A(f1) and A(f2), and the relationship between particle concentrations (or contents) x1 and x2 and magnetization response spectra U(f1) and U(f2) is as follows:

[0077] A(f1)x1 + A(f1)x2 = U(f1)

[0078] A(f2)x1 + A(f2)x2 = U(f2)

[0079] After acquiring the coefficient matrix of the MNPs and the magnetization response spectrum of the object under test, the equations at the two excitation frequencies are concatenated and combined into a new equation:

[0080]

[0081] Wherein, S1(f1) and S2(f1) are the magnetization response spectrum signals of the first and second types of magnetic nanoparticles when the excitation frequency is f1, S1(f2) and S2(f2) are the magnetization response spectrum signals of the first and second types of magnetic nanoparticles when the excitation frequency is f2; U(f1) and U(f2) are the magnetization response spectrum signals at excitation frequencies of f1 and f2 respectively, and x1 and x2 are the concentrations (or contents) of different types of magnetic nanoparticles.

[0082] The new coefficient matrix and magnetization response spectrum can be represented as A' and U', and the particle concentrations (or contents) x1 and x2 are combined as x:

[0083]

[0084] In the actual measurement process, considering the influence of noise, a residual vector v is introduced, and a new solution equation is constructed:

[0085]

[0086] Where μ is the relaxation factor and μ≥0.

[0087] The above equations can be solved using an algebraic reconstruction algorithm. The specific algorithm flowchart is shown below. Figure 2 As shown:

[0088] First, input the coefficient matrix A' of different types of magnetic nanoparticles, the measured magnetization response spectrum U', the number of iterations k, and the relaxation factor μ;

[0089] Initialize the residual vector v = 0, and perform traversal projection based on the set number of iterations and coefficient matrix to calculate the concentration (or content) x of the magnetic nanoparticles. The specific iterative solution formula is as follows:

[0090]

[0091] Where k is the iteration number, 1≤i≤N, and N is the number of rows in the coefficient matrix A'. i Let U' be a vector composed of the elements of the i-th row of the coefficient matrix A'. i Let be the element in the i-th row of the nonlinear magnetization response signal U'.

[0092] This embodiment fully utilizes the differentiated trends exhibited by different types of magnetic nanoparticles (NieR relaxation-dominated and Brownian relaxation-dominated) when the applied excitation frequency changes—where Neirian relaxation particles have a higher signal-to-noise ratio at higher frequencies, while Brownian relaxation particles have a higher signal-to-noise ratio at lower frequencies—and employs magnetization response spectrum signals at multiple excitation frequencies. This effectively utilizes more information from the magnetic nanoparticles, expands the signal differences between particles, avoids signal crosstalk during the reconstruction process, and thus significantly improves the accuracy of magnetic nanoparticle classification and detection.

[0093] The embodiments described above are merely illustrative of one aspect of the present invention and are not intended to limit the scope of the invention. Any 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 invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for classifying and detecting magnetic nanoparticles based on multi-frequency magnetization response spectrum, characterized in that, include: For different types of magnetic nanoparticle samples, an excitation magnetic field with an excitation frequency of f1 was applied, and the magnetization response spectrum signals S1(f1), S2(f1)...S were obtained respectively. k (f1), and construct the corresponding coefficient matrix A(f1); Change the excitation frequency, applying excitation frequencies f2, f3...f in sequence. n The excitation magnetic field was used to obtain the magnetization response spectrum signals of different types of magnetic nanoparticle samples, and the corresponding coefficient matrices A(f2), A(f3)...A(f n ); The coefficient matrices A(f1), A(f2), ..., A(f) at different frequencies are... n The coefficients are concatenated to obtain a new coefficient matrix A'. The hybrid magnetic nanoparticles to be tested are sequentially subjected to frequencies f1, f2…f n The excitation magnetic field was used to obtain the magnetization response spectrum signals U(f1), U(f2)...U(f) respectively. n The mixed magnetic nanoparticles to be tested are composed of different types of magnetic nanoparticles. The magnetization response spectrum signals U(f1), U(f2), ... U(f) at different frequencies are used to analyze the magnetization response spectrum signals U(f1), U(f2), ... U(f3) at different frequencies. n By combining these signals, a new magnetization response spectrum signal U' can be obtained; By combining the new coefficient matrix A' with the new magnetization response spectrum signal U', a magnetic nanoparticle classification and quantitative detection model is constructed. The magnetic nanoparticle classification and quantitative detection model is solved to obtain the types, concentrations or contents of the mixed magnetic nanoparticles to be tested.

2. The method for classifying and detecting magnetic nanoparticles based on multi-frequency magnetization response spectrum according to claim 1, characterized in that, The magnetization response spectrum signal is: S(f)=[M1 M2…M h ] T ; Where S(f) is the magnetization response spectrum of the magnetic nanoparticles at an excitation frequency of f, and M1, M2…M h These are the magnetization signals of the 1st, 2nd...hth harmonics of the magnetization response spectrum, respectively.

3. The method for classifying and detecting magnetic nanoparticles based on multi-frequency magnetization response spectrum according to claim 1, characterized in that, The corresponding coefficient matrix is: A(f)=[S1(f) S2(f) … S k (f)]; Where A(f) is the coefficient matrix, S1(f), S2(f)...S k (f) represents the magnetization response spectrum signals of the first, second to kth types of magnetic nanoparticles, respectively.

4. The method for classifying and detecting magnetic nanoparticles based on multi-frequency magnetization response spectrum according to claim 1, characterized in that, The new coefficient matrix is ​​as follows: Where A' is the new coefficient matrix, A(f1), A(f2)...A(f n The excitation frequencies are f1, f2, ..., f, respectively. n The coefficient matrix at that time.

5. The method for classifying and detecting magnetic nanoparticles based on multi-frequency magnetization response spectrum according to claim 1, characterized in that, The new magnetization response spectrum is: U(f)=[M1 M2…M h ] T ; Where U(f) is the magnetization response spectrum of the hybrid magnetic nanoparticles to be tested, and M1, M2…M h These are the magnetization signals of the 1st, 2nd...hth harmonics of the magnetization response spectrum, respectively; U' is the new magnetization response spectrum, U(f1), U(f2)...U(f...h) n ) for excitation frequencies of f1, f2...f n The magnetization response spectrum signal under the given conditions.

6. The method for classifying and detecting magnetic nanoparticles based on multi-frequency magnetization response spectrum according to claim 1, characterized in that, Obtaining the type, concentration, or content of the mixed magnetic nanoparticles to be tested includes: Based on the new coefficient matrix and the new magnetization response spectrum signal, a classification and quantitative detection model for magnetic nanoparticles is constructed. The magnetic nanoparticle classification and quantitative detection model is iteratively reconstructed to solve for the concentration or content of different types of magnetic nanoparticles.

7. The method for classifying and detecting magnetic nanoparticles based on multi-frequency magnetization response spectrum according to claim 6, characterized in that, The magnetic nanoparticle classification and quantitative detection model is as follows: Where A' is the new coefficient matrix, U' is the new magnetization response spectrum, x is the concentration or content of different types of magnetic nanoparticles in the sample to be tested, μ is the relaxation factor and μ≥0, and v is the residual.

8. The method for classifying and detecting magnetic nanoparticles based on multi-frequency magnetization response spectrum according to claim 6, characterized in that, Solving the classification and quantitative detection model for the magnetic nanoparticles includes: Where k is the iteration number, 1≤i≤N, and N is the number of rows in the coefficient matrix A'. i Let U' be a vector composed of the elements of the i-th row of the coefficient matrix A'. i Let be the element in the i-th row of the nonlinear magnetization response signal U'.

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