CN110705072A - Fokker-Planck-based high-precision magnetic nano temperature estimation method and system - Google Patents

Fokker-Planck-based high-precision magnetic nano temperature estimation method and system Download PDF

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CN110705072A
CN110705072A CN201910907076.5A CN201910907076A CN110705072A CN 110705072 A CN110705072 A CN 110705072A CN 201910907076 A CN201910907076 A CN 201910907076A CN 110705072 A CN110705072 A CN 110705072A
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杜中州
叶娜
孙毅
王丹丹
苏日建
刘文中
甘勇
李娜娜
邹东尧
金保华
朱付保
张志峰
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Zhengzhou University of Light Industry
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Abstract

The invention provides a high-precision magnetic nano-temperature estimation method and system based on Fokker-Planck, wherein a magnetic nano-particle temperature estimation model is constructed through a Fokker-Planck formula, a magnetic field information detection device is used for measuring the magnetization response harmonic amplitude and phase information of magnetic nano-particles for multiple times, and model parameters in the magnetic nano-particle temperature estimation model are fitted; and placing a sample to be detected in a magnetic field information detection device, measuring the harmonic amplitude and phase information of the sample under the excitation of an external magnetic field, substituting the harmonic amplitude and phase information into a preset magnetic nano particle temperature estimation model, and solving the magnetic nano particle temperature information. The invention can accurately acquire the temperature information of the magnetic nanoparticles under the excitation of the medium-high frequency magnetic field, solves the problem that the Langevin Function is not suitable for the application occasions of medium-high frequency excitation in the past, expands the application fields of magnetic nanoparticle temperature measurement and magnetic nanoparticle imaging technology, and improves the measurement precision and the time-space resolution.

Description

Fokker-Planck-based high-precision magnetic nano temperature estimation method and system
Technical Field
The invention relates to the technical field of nanomagnetic detection technology and non-invasive temperature measurement, in particular to a Fokker-Planck-based high-precision magnetic nano temperature estimation method and system, which are suitable for magnetic nano temperature measurement under medium-high frequency excitation or magnetic nano particle imaging technology and solve the bottleneck of application field caused by lower excitation magnetic field of magnetic nano temperature measurement.
Background
The magnetic nanoparticle tumor thermotherapy is considered to be a green therapy for treating tumor and cancer due to the advantages of strong targeting property, no wound, safety, small toxic and side effects and the like. The temperature is a very key physical parameter in the magnetic nano tumor thermotherapy. However, the real-time accurate measurement of the temperature information of the tumor cancerous region is an important prerequisite and basis for accurately applying and controlling the thermal dose, improving the curative effect of the magnetic nano tumor thermotherapy, and selectively inducing the tumor cell apoptosis while maximally retaining normal cells.
In 2009, j.b.weaver et al proposed that temperature measurement was performed based on the ratio of the fifth harmonic amplitude to the third harmonic amplitude in the magnetic nanoparticle ac magnetization response information, and the standard deviation of the measured temperature within the hyperthermia temperature window was 0.3 ℃. Rauwerdink et al, used the combined action of an ac magnetic field and a dc magnetic field to measure the ratio of the fourth harmonic amplitude to the second harmonic amplitude in the magnetization response information, and implemented temperature measurement with a root mean square error of 0.79 ℃, however, the above studies lacked rigorous mathematical models. Liu et al, based on the langevin paramagnetic theorem, constructs a mathematical model for temperature measurement under excitation of a direct-current magnetic field, measures the magnetization of magnetic nanoparticles by using a superconducting quantum interferometer, measures temperature information, and has a root mean square error of 0.55 ℃, thereby solving the problem that the magnetic nanoparticle temperature measurement technology lacks theoretical model support. Subsequently, J.Zhong et al proposed a magnetic nanoparticle temperature measurement correction model, and theoretically the temperature measurement accuracy could reach a standard deviation of 0.017 ℃. Du et al propose a recursive-based fast magnetic nano temperature measurement method to solve the time-consuming problem of magnetic nano temperature measurement. Liu et al propose a magnetic nanoparticle temperature measurement model under dual-frequency excitation, which effectively improves the magnetic nanoparticle temperature measurement accuracy. Du et al further improves the temperature measurement accuracy of magnetic nanoparticles from the perspective of reducing the noise of the measurement system by studying an influence model influencing the temperature measurement accuracy of magnetic nanoparticles from the perspective of error transfer. I.M.Perrerard, L.He and the like respectively provide a magnetic nanoparticle temperature measurement model based on the Debye theory, and the magnetic nanoparticle temperature measurement model is suitable for the field of temperature measurement in medium-high frequency excitation magnetic fields.
In summary, the magnetic nano temperature measurement technology has been developed rapidly in recent years, and careful research finds that the above model is a research on the temperature measurement technology based on langevin function, however, langevin function describes magnetic nanoparticle magnetization response information when the excitation magnetic field is static or quasi-steady state, and langevin function is no longer applicable under the excitation of medium-high frequency magnetic field. I.m. perreard and l.he et al also have difficulty accurately describing magnetization response information under medium and high frequency magnetic field excitation based on debye's theory, which is a linear approximation model. The magnetization response information under the excitation of the medium-high frequency magnetic field cannot be accurately and comprehensively described. Under the excitation of a medium-high frequency alternating current magnetic field, the magnetic nanoparticles have the phenomenon of Brownian magnetic relaxation or Neille magnetic relaxation, which influences the output of the magnetization response harmonic amplitude of the magnetic nanoparticles, and further influences the measurement accuracy and the spatial resolution of the magnetic nanoparticle temperature measurement and magnetic nanoparticle imaging technology. In addition, the magnetization response information of the magnetic nanoparticles under the excitation of the medium-high frequency magnetic field lags behind the excitation magnetic field by a phase angle.
Disclosure of Invention
Aiming at the technical problems that the Brownian magnetic relaxation or Neille magnetic relaxation phenomenon under the excitation of a medium-high frequency magnetic field has influence on the magnetization response harmonic amplitude information, and the Langmuir function can not accurately describe the magnetization response information of the magnetic nano particle size under the excitation of the medium-high frequency, so that the measurement precision is low, the invention provides a Fokker-Planck-based high-precision magnetic nano temperature estimation method and system, the magnetization response harmonic amplitude information is compensated through the harmonic amplitude and phase information in the magnetization response, the magnetization response harmonic information of the magnetic nano particles under the excitation of the medium-high frequency magnetic field can be accurately described, the estimation of the temperature information under the excitation of the medium-high frequency magnetic field is further realized, the technical bottleneck that the measurement precision and the spatial resolution of the magnetic nano temperature are low due to the low excitation frequency in the past is overcome, and the real-time temperature information measurement under the excitation of the, thereby meeting the index requirements of magnetic nano temperature measurement and magnetic nano particle imaging technology, such as measurement precision, real-time property, spatial resolution, and the like, required in the fields of medical biological diagnosis, industry and the like.
In order to achieve the purpose, the technical scheme of the invention is realized as follows: a high-precision magnetic nano temperature estimation method based on Fokker-Planck comprises the following steps:
the method comprises the following steps: placing a magnetic field information detection device on a magnetic nano sample to be detected to detect a magnetization response signal of magnetic nano particles in the magnetic nano sample;
step two: obtaining harmonic amplitude and phase angle information of the magnetization response by using a harmonic amplitude and phase angle detection algorithm;
step three: and constructing a magnetic nanoparticle temperature estimation model by utilizing a Fokker-Planck formula, substituting the extracted harmonic amplitude and phase angle information of each time of the magnetization response signal into a harmonic amplitude fitting model to obtain fitting parameters, substituting the fitting parameters into the magnetic nanoparticle temperature estimation model, and calculating the temperature information of the magnetic nanoparticles.
The method for constructing the magnetic nanoparticle temperature estimation model by utilizing the Fokker-Planck formula comprises the following steps:
according to a Fokker-Planck formula, drawing a magnetization response curve of the magnetic nanoparticles under different Brownian magnetic relaxation times;
respectively extracting odd harmonic amplitudes A in the magnetization response curve according to the harmonic amplitude and phase detection algorithmiAnd phase information thetaiWherein i is 1,3,5, …, N represents the harmonic order;
drawing a magnetization response curve of the magnetic nanoparticles according to a Langevin function;
extracting each odd harmonic amplitude B according to harmonic amplitude and phase detection algorithmi；
Fitting function according to harmonic amplitude
Figure BDA0002213580660000021
Amplitude ratio of opposite harmonics Ai/BiCarrying out harmonic amplitude information fitting to obtain fitting parameters; wherein, ai、bi、ciModel parameters in the ith harmonic amplitude information fitting function are respectively shown, H is the alternating current magnetic field intensity of the medium-high frequency excitation magnetic field, and T is the absolute temperature of the magnetic nanoparticles;
obtaining a fitting function of the magnetic nanoparticle magnetization response harmonic amplitude by fitting the harmonic amplitude information into
Figure BDA0002213580660000031
Obtaining a magnetic nanoparticle temperature estimation model through inversion calculation
Figure BDA0002213580660000032
The fitting method of the model parameters in the fitting function comprises the following steps:
s1: measuring magnetization response signals of the magnetic nanoparticles under the excitation of an external excitation magnetic field;
s2: extracting amplitude and phase angle information of each harmonic in the magnetization response signal;
s3: repeating the steps S2-S3 for multiple times, measuring and extracting amplitude and phase angle information of each harmonic;
model parameters in the magnetic nanoparticle temperature estimation model, namely model parameters a of ith harmonic in the magnetic nanoparticle temperature estimation model, are simulated by adopting a method of compensating harmonic amplitude information by phase angle informationi、bi、ci。
The method for calculating the temperature of the magnetic nanoparticles comprises the following steps:
measuring magnetization response signals of the magnetic nanoparticles under the excitation of an external excitation magnetic field; extracting amplitude and phase angle information of each harmonic in the magnetization response signal;
and substituting the extracted amplitude and phase angle information of each harmonic into the magnetic nano particle temperature estimation model to obtain the magnetic nano particle temperature information.
The ith harmonic amplitude A of the magnetization response signaliAnd phase information thetaiThe method comprises the following steps:
when the magnetic nanoparticles are excited by an external alternating magnetic field, the magnetic nanoparticles are influenced by Brownian magnetic relaxation excitation, and the dynamic behavior of the magnetic nanoparticles is described by a Fokker-Planck formula as follows:
Figure BDA0002213580660000033
wherein the content of the first and second substances,is the included angle between the internal magnetic moment of the magnetic nano-particles and the direction of an external magnetic field H,
Figure BDA0002213580660000035
is an included angleXi is the ratio of the energy of the applied magnetic field to the heat energy and xi is mH/KBT, magnetic moment m ═ mu0MsV，μ0Is the magnetic permeability in vacuum, MsIs the saturation magnetization, V is the unit volume, KBIs the Boltzmann constant, T is the absolute temperature of the magnetic nanoparticles, and the Brownian relaxation time τB＝3ηV/KBT, η is the viscosity coefficient;
and (3) performing spherical harmonic expansion on the dynamic behavior of the magnetic nanoparticles described by the Fokker-Planck formula to obtain a distribution function:
Figure BDA0002213580660000037
wherein, an(t) is the coefficient of each spherical harmonic in relation to time,
Figure BDA0002213580660000038
is a Legendre polynomial, n represents the number of terms of the Legendre polynomial;
and substituting the distribution function into the dynamic behavior of the magnetic nanoparticles described by Fokker-Planck formula, and combining and finishing to obtain:
Figure BDA0002213580660000041
here, theThe differential-to-differential equation is obtained as:
Figure BDA0002213580660000043
passing coefficient anIs solved to obtain a distribution function
Figure BDA0002213580660000044
The magnetization response of the magnetic nanoparticles is then:
Figure BDA0002213580660000045
processing the magnetization response M of the magnetic nanoparticles by FFT or DPSD algorithm to obtain the amplitude A of each subharmonic in the magnetization response information of the magnetic nanoparticlesiAnd phase information thetai。
The ith harmonic amplitude B of the magnetization response signaliThe method comprises the following steps:
when the magnetic nanoparticles of the magnetic nano sample are excited by a static or quasi-static magnetic field, the magnetization response information M is described as an approximate function of Frankia:
wherein, mu0Denotes the vacuum permeability, L (ξ) denotes the langevin function, M denotes the effective magnetic moment of the magnetic nanoparticles, M denotes the effective magnetic moment of the magnetic nanoparticlessDenotes saturation magnetization, H ═ Hsin (ω T) denotes an applied alternating-current excitation magnetic field, angular velocity ω ═ 2 π f, T denotes the absolute temperature of the magnetic nanoparticles, k denotes the absolute temperature of the magnetic nanoparticlesBRepresenting boltzmann constant, xi is the ratio of external magnetic field energy to heat energy, and coth (xi) is langevin function;
the taylor series expansion of the magnetization response information M represented by the langevin function can result in:
Figure BDA0002213580660000047
obtaining each subharmonic amplitude B through DPSD algorithmi：
Figure BDA0002213580660000048
A high-precision magnetic nano temperature estimation system based on Fokker-Planck comprises a magnetic field excitation device, a magnetic field information detection device and a signal processing and temperature calculation device, wherein the magnetic field excitation device and the magnetic field information detection device are both arranged in a region where a magnetic nano sample to be detected is located, the magnetic field excitation device generates an excitation magnetic field in the region where the magnetic nano sample to be detected is located, the magnetic field information detection device collects and preprocesses magnetization response signals generated by the magnetic nano sample, the magnetic field information detection device is connected with the signal processing and temperature calculation device, and the signal processing and temperature calculation device calculates magnetic nano temperature information according to a magnetic nano particle temperature estimation model and the obtained magnetization response signals.
The magnetic field exciting device comprises a magnetic field generator, a power amplifier, a signal generator and a passive band-pass filter, wherein the signal generator is connected with the power amplifier, the power amplifier is connected with the passive band-pass filter, and the passive band-pass filter is connected with the magnetic field generator; the magnetic field information detection device comprises a magnetic detection sensor, a low-noise preamplifier, a frequency-selecting amplifier, a band-pass filter and a signal acquisition card, wherein the magnetic detection sensor is connected with the low-noise preamplifier, the low-noise preamplifier is connected with the frequency-selecting amplifier, the frequency-selecting amplifier is connected with the band-pass filter, and the band-pass filter is connected with the signal acquisition card; the signal processing and temperature calculating device comprises a computer, a harmonic amplitude phase angle detection module and a magnetic nano temperature estimation model, wherein the signal acquisition card, the harmonic amplitude phase angle detection module and the magnetic nano temperature estimation model are all connected with the computer;
the magnetic field excitation device outputs sine wave signals by adopting a signal output module of a signal generator or a signal acquisition card, sends the sine wave signals to a power amplifier for signal power amplification, and then carries out signal conditioning through a passive band-pass filter to drive a magnetic field generator to generate an excitation magnetic field;
the magnetic field information detection device adopts a magnetic detection sensor to measure the magnetization response signal of the magnetic nano sample under the excitation of a medium-high frequency sine wave excitation magnetic field in real time, and adopts a band-pass filter, a low-noise preamplifier and a frequency-selecting amplifier to respectively perform signal conditioning of filtering, pre-amplification and frequency-selecting amplification on the obtained magnetization response signal; the signal acquisition card stores the magnetization response signal after signal conditioning;
the signal processing and temperature calculating device adopts a computer to control a data acquisition card to carry out data acquisition on the magnetization response signal after signal conditioning to obtain a discrete signal; extracting harmonic amplitude and phase angle information of the obtained discrete signal by adopting a harmonic amplitude phase angle detection module, substituting the obtained harmonic amplitude and phase angle information into a magnetic nano temperature estimation model
Figure BDA0002213580660000051
Solving magnetic nano temperature information; wherein A isiFor harmonic amplitude, θiFor phase information, i is 1,3,5, …, N denotes the harmonic order; b isiObtaining harmonic amplitude values by drawing a magnetization response curve of the magnetic nanoparticles according to a Langevin function; a isi、bi、ciThe model parameters in the ith harmonic amplitude information fitting function are respectively, H is the alternating current magnetic field intensity of the medium-high frequency excitation magnetic field, and T is the absolute temperature of the magnetic nanoparticles.
The excitation magnetic field is a medium-high frequency sine wave excitation magnetic field: h' ═ H sin (2 pi ft), where H is the alternating excitation field strength at frequency f; the alternating excitation magnetic field strength H is in the range of below 0.01 Tesla, and the frequency f is in the range of below 20 KHz.
The magnetic detection sensor is one of an air coil, a magnetoresistive sensor or a SQUID sensor; and a harmonic amplitude and phase angle detection algorithm is arranged in the harmonic amplitude and phase angle detection module, and adopts a digital phase-sensitive detection algorithm, a fast Fourier transform algorithm or a least square system identification algorithm.
The invention has the beneficial effects that: magnetic nano solid powder particles or magnetic nano colloid or magnetic nano liquid samples are placed at an object to be measured, medium-high frequency magnetic field excitation is applied to the region where the object to be measured is located, the magnetization intensity information of the magnetic nano particles contains rich information of various subharmonics, however, due to the fact that the Brownian magnetic relaxation or Neille magnetic relaxation phenomenon affects the amplitude information of magnetization response harmonics, and the phase lag problem exists at the same time, the amplitude and phase angle information of the required various subharmonics are extracted through a high-precision harmonic and phase angle detection algorithm, the amplitude information of the contaminated various subharmonics obtained through measurement is compensated and corrected based on the harmonic information compensation of the magnetic nano particles, magnetic nano temperature information is obtained, the influence of the Brownian magnetic relaxation or Neille magnetic relaxation phenomenon generated under the medium-high frequency sine wave magnetic field excitation is overcome, and the magnetic nano temperature measurement cannot be applied to the medium-high frequency measurement field, the method expands the application range of magnetic nanoparticle temperature measurement, improves the accuracy of magnetic nanoparticle temperature information measurement, is expected to solve the problem of low accuracy of magnetic nanoparticle temperature measurement under the excitation of medium-high frequency magnetic fields in medical biological diagnosis technology, and is also suitable for other non-invasive high-accuracy magnetic nanoparticle temperature measurement occasions in the industrial field. The method obtains the harmonic information compensation model under the excitation of the medium-high frequency magnetic field, breaks through the situation that the traditional method can only be suitable for lower frequencies, is expected to fundamentally solve the problem of lower temperature measurement precision of the magnetic nanoparticles under the excitation of the medium-high frequency magnetic field, avoids the problem of difficult higher harmonic measurement, and realizes high-precision real-time temperature measurement of the magnetic nanoparticles.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a graph based on the information ratio of Fokker-Planck to the langevin function to the actual magnetization response of the magnetic nanoparticles.
Fig. 3 is a simulation temperature error diagram of a temperature estimation model, wherein (a) is a comparison result of a magnetic nanoparticle magnetization response harmonic information compensation model and a langevin harmonic model at different temperatures, and (b) is an error between a temperature point to be solved and a temperature true value obtained by using parameters obtained by fitting and the temperature estimation model.
FIG. 4 is a comparison result of a harmonic information compensation model under 200Hz alternating magnetic field excitation and a langevin harmonic model of a sample model SHP-20, wherein (a) is a first harmonic amplitude, (b) is a third harmonic amplitude, (c) is a fifth harmonic amplitude, and (d) is a parameter estimation value.
Fig. 5 is a comparison effect graph of a harmonic information compensation model and a langevin harmonic model under the excitation of an alternating magnetic field of 200Hz with a sample model of MS1, wherein (a) is a first harmonic amplitude, (b) is a third harmonic amplitude, (c) is a fifth harmonic amplitude, and (d) is a parameter estimation value.
Fig. 6 is a comparison effect graph of a harmonic information compensation model and a langevin harmonic model under the excitation of an alternating magnetic field of 200Hz with a sample model of MS2, wherein (a) is a first harmonic amplitude, (b) is a third harmonic amplitude, (c) is a fifth harmonic amplitude, and (d) is a parameter estimation value.
FIG. 7 is a comparison result diagram of a harmonic information compensation model and a langevin harmonic model under the excitation of a 3KHz alternating magnetic field with a sample model of SHP-20, wherein (a) is a first harmonic amplitude, (b) is a third harmonic amplitude, (c) is a fifth harmonic amplitude, and (d) is a parameter estimation value.
Fig. 8 is a comparison effect graph of a harmonic information compensation model and a langevin harmonic model under excitation of a 3KHz alternating magnetic field of a sample model MS1, wherein (a) is a first harmonic amplitude, (b) is a third harmonic amplitude, (c) is a fifth harmonic amplitude, and (d) is a parameter estimation value.
Fig. 9 is a comparison effect graph of a harmonic information compensation model and a langevin harmonic model under excitation of a 3KHz alternating magnetic field of a sample model MS2, where (a) is a first harmonic amplitude, (b) is a third harmonic amplitude, (c) is a fifth harmonic amplitude, and (d) is a parameter estimation value.
FIG. 10 is a graph showing the comparison effect between the harmonic information compensation model with the model number of SHP-20 excited by the 20KHz alternating magnetic field and the langevin harmonic model, where (a) is the first harmonic amplitude, (b) is the third harmonic amplitude, (c) is the fifth harmonic amplitude, and (d) is the parameter estimation value.
Fig. 11 is a comparison effect graph of a harmonic information compensation model under the excitation of a 20KHz alternating magnetic field and a langevin harmonic model of a sample model MS1, wherein (a) is a first harmonic amplitude, (b) is a third harmonic amplitude, (c) is a fifth harmonic amplitude, and (d) is a parameter estimation value.
Fig. 12 is a comparison result graph of a harmonic information compensation model under the excitation of a 20KHz alternating magnetic field and a langevin harmonic model of a sample model MS2, wherein (a) is a first harmonic amplitude, (b) is a third harmonic amplitude, (c) is a fifth harmonic amplitude, and (d) is a parameter estimation value.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without inventive effort based on the embodiments of the present invention, are within the scope of the present invention.
In this application, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, the statement that there is an element defined as "comprising" … does not exclude the presence of other like elements in the process, method, article, or apparatus that comprises the element.
Embodiment 1, as shown in fig. 1, a method for estimating a magnetic nano temperature with high precision based on Fokker-Planck includes the following steps:
the method comprises the following steps: and placing the magnetic field information detection device in a magnetic nano sample to be detected to detect the magnetization response signals of the magnetic nano particles in the magnetic nano sample.
The magnetic nano sample comprises magnetic nano solid powder particles, magnetic nano colloid or magnetic nano liquid and is suitable for a magnetic nano particle temperature measuring system comprising a magnetic field excitation device and a magnetic field information detection device, the magnetic nano sample is placed in the measuring system, and the excitation device in the measuring system applies a medium-high frequency excitation magnetic field to the magnetic nano sample.
The magnetic field excitation device generates a medium-high frequency excitation magnetic field H 'by utilizing an electrified Helmholtz coil, a solenoid or a Maxwell coil, wherein the H' can be a single frequency f or a medium-high frequency excitation magnetic field excited by combining direct current and alternating current. In order to obtain the signal-to-noise ratio of higher harmonic amplitude and phase angle, the range of the alternating current excitation magnetic field strength H is below 0.01 Tesla, and the frequency f range is below 20 KHz.
And measuring by using a magnetic nanoparticle temperature measuring system to obtain the harmonic amplitude and phase angle information of the magnetization response of the magnetic nanoparticles. A differential structure, namely an air-core type spiral coil or a three-section type detection coil or a gradient coil or a giant magnetoresistance sensor is adopted as a magnetic detection sensor to obtain the magnetization response information of the magnetic nanoparticle sample under the excitation of a medium-high frequency magnetic field in real time.
Respectively carrying out signal conditioning of filtering, pre-amplifying and frequency-selecting amplifying on the magnetization response signal obtained in the step two by adopting a band-pass filter, a low-noise preamplifier and a frequency-selecting amplifier; and carrying out data acquisition on the conditioned signals by using a data acquisition card to obtain discrete signals.
Due to the superparamagnetic property of the magnetic nanoparticles, the magnetization response information of the magnetic nanoparticle sample under the excitation of the medium-high frequency sine wave magnetic field contains rich harmonic information, namely, each subharmonic signal with the frequency f as the fundamental frequency. And carrying out band-pass filtering on the magnetization response signal to filter noise outside the frequency bandwidth of the signal. Then, because the signal is weak, the detected useful signal needs to be sent to a low-noise preamplifier and a frequency-selecting amplifier for signal preprocessing such as signal amplification, frequency selection and the like, so that signal conditioning is realized, and finally, the conditioned signal is discretely acquired through a data acquisition card, so that the subsequent processing is facilitated.
Step two: and obtaining the harmonic amplitude and phase angle information of the magnetization response by using a harmonic amplitude and phase angle detection algorithm.
And extracting the information of each harmonic amplitude and phase angle of the magnetization response signal by adopting a digital phase-sensitive detection algorithm, a fast Fourier transform algorithm or a least square system identification algorithm.
Step three: and constructing a magnetic nanoparticle temperature estimation model by utilizing a Fokker-Planck formula, substituting the extracted harmonic amplitude and phase angle information of each time of the magnetization response signal into a harmonic amplitude fitting model to obtain fitting parameters, substituting the fitting parameters into the magnetic nanoparticle temperature estimation model, and calculating the temperature information of the magnetic nanoparticles.
According to a preset magnetic nanoparticle temperature estimation model, substituting the obtained harmonic amplitude and phase angle information into the preset magnetic nanoparticle temperature estimation model to obtain magnetic nanoparticle temperature information;
the magnetic nanoparticle temperature estimation model construction process comprises the following steps:
the Fokker-plane Equation is used for drawing the magnetization response curves of the magnetic nanoparticles under different Brownian magnetic relaxation times;
respectively extracting each subharmonic amplitude A according to the harmonic amplitude and phase detection algorithmiAnd phase information thetai1,3,5, …, N denotes the harmonic order;
drawing a magnetization response curve of the magnetic nanoparticles according to the Langevin Function;
extracting each subharmonic amplitude B according to harmonic amplitude and phase detection algorithmi1,3,5, …, N denotes the harmonic order;
according to fitting function
Figure BDA0002213580660000091
Amplitude ratio of opposite harmonics Ai/BiFitting harmonic amplitude information, ai、bi、ciParameters in the ith harmonic amplitude information fitting model are respectively, H is the alternating current magnetic field intensity of the medium-high frequency excitation magnetic field, and T is the absolute temperature of the magnetic nanoparticles;
magnetic nanoparticle magnetization response harmonic amplitude fitting function obtained based on the process
Figure BDA0002213580660000092
Further obtaining a magnetic nano particle temperature estimation model
Figure BDA0002213580660000093
The parameter fitting process in the magnetic nanometer temperature estimation model comprises the following steps:
measuring a magnetization response signal curve of the magnetic nanoparticles under the excitation of an external excitation magnetic field; extracting amplitude and phase angle information of each harmonic in the magnetization response signal;
repeating the measurement and extracting harmonic amplitude and phase angle information for multiple times;
method for simulating model parameters in magnetic nanoparticle temperature estimation model by adopting phase angle information to compensate harmonic amplitude information, ai、bi、ciAnd respectively estimating the parameter of the ith harmonic in the model, and establishing a magnetic nanoparticle temperature estimation model.
Magnitude A of ith harmonic of magnetization response signaliAnd phase information thetaiThe calculation process is as follows:
when the magnetic nano-particles are excited by an external alternating magnetic field, the magnetic nano-particles are influenced by the Brownian magnetic relaxation excitation, and the dynamic behavior of the magnetic nano-particles can be described by Fokker-plane Equation as follows:
wherein the content of the first and second substances,is the included angle between the internal magnetic moment of the magnetic nano-particles and the direction of an external magnetic field H,is that
Figure BDA0002213580660000097
Magnetic moment m ═ mu0MsV，μ0Is the magnetic permeability in vacuum, MsIs saturation magnetization, V is unit volume, and the ratio of external magnetic field energy to heat energy isBT，KBIs the Boltzmann constant, T is the absolute temperature, τB＝3ηV/KBT is the Brownian relaxation time and η is the viscosity coefficient.
And (3) carrying out spherical harmonic expansion on the formula to obtain:
wherein, an(t) is the coefficient of each spherical harmonic, n represents the number of terms of the Legendre polynomial, and has a time dependenceAnd off.
Figure BDA0002213580660000102
Is Legendre polynomial, and the two formulas are combined and arranged to obtain:
Figure BDA0002213580660000103
here, the
Figure BDA0002213580660000104
Further, the differential-to-differential equation can be obtained as follows:
Figure BDA0002213580660000105
passing coefficient anIs solved to obtain a distribution functionThe magnetic nanoparticle magnetization response can be obtained by the following formula:
the various harmonics A in the magnetic nanoparticle magnetization response information can be obtained by FFT or DPSD algorithmi，θi。
Magnitude of ith harmonic B of magnetization response signaliThe calculation process is as follows:
when the magnetic nanoparticles of the magnetic nano sample are excited by a static or quasi-static magnetic field, the magnetization response information M can be described by approximating the womb function as follows:
Figure BDA0002213580660000108
wherein, mu0Showing the vacuum permeability, L (xi) showing the langevin function, M showing the effective magnetic moment of the magnetic nanoparticles, MsDenotes saturation magnetization, and H ═ Hsin (ω t) denotes applied ac excitationField, ω ═ 2 π f, T denotes the absolute temperature of the magnetic nanoparticles, kBRepresenting Boltzmann constants, i.e. 1.38X 10-23JK-1. Xi is the ratio of the energy of the applied magnetic field to the heat energy, and coth (xi) is a function of langevin.
By performing taylor series expansion on the magnetization response information M, it is possible to obtain:
Figure BDA0002213580660000109
amplitude of each harmonic BiCan be obtained by the DPSD algorithm:
Figure BDA0002213580660000111
using the obtained amplitude A of each harmoniciAnd phase information thetaiAnd obtaining the temperature information of the magnetic nanoparticles according to the magnetic nanoparticle temperature estimation model.
Example 2
A high-precision magnetic nano temperature estimation system based on Fokker-Planck comprises a magnetic field excitation device, a magnetic field information detection device and a signal processing and temperature calculation device, wherein the magnetic field excitation device and the magnetic field information detection device are both arranged in a region where a magnetic nano sample to be detected is located, the magnetic field excitation device generates an excitation magnetic field in the region where the magnetic nano sample to be detected is located, the magnetic field information detection device collects and preprocesses magnetization response signals generated by the magnetic nano sample, the magnetic field information detection device is connected with the signal processing and temperature calculation device, and the signal processing and temperature calculation device calculates magnetic nano temperature information according to a magnetic nano particle temperature estimation model and the obtained magnetization response signals.
The magnetic field exciting device comprises a magnetic field generator, a power amplifier, a signal generator and a passive band-pass filter, wherein the signal generator is connected with the power amplifier, the power amplifier is connected with the passive band-pass filter, and the passive band-pass filter is connected with the magnetic field generator; the magnetic field information detection device comprises a magnetic detection sensor, a low-noise preamplifier, a frequency-selecting amplifier, a band-pass filter and a signal acquisition card, wherein the magnetic detection sensor is connected with the low-noise preamplifier, the low-noise preamplifier is connected with the frequency-selecting amplifier, the frequency-selecting amplifier is connected with the band-pass filter, and the band-pass filter is connected with the signal acquisition card; the signal processing and temperature calculating device comprises a computer, a harmonic amplitude phase angle detection module and a magnetic nano temperature estimation model, wherein the signal acquisition card, the harmonic amplitude phase angle detection module and the magnetic nano temperature estimation model are all connected with the computer;
the magnetic field excitation device outputs sine wave signals by adopting a signal output module of a signal generator or a signal acquisition card, sends the sine wave signals to a power amplifier for signal power amplification, and then carries out signal conditioning through a passive band-pass filter to drive a magnetic field generator to generate an excitation magnetic field; the excitation magnetic field is a medium-high frequency sine wave excitation magnetic field: h ═ Hsin (2 pi ft), where H is the alternating excitation field strength at frequency f; the alternating excitation magnetic field strength H is in the range of below 0.01 Tesla, and the frequency f is in the range of below 20 KHz.
The magnetic field information detection device adopts a magnetic detection sensor to measure the magnetization response signal of the magnetic nano sample under the excitation of a medium-high frequency sine wave excitation magnetic field in real time, and adopts a band-pass filter, a low-noise preamplifier and a frequency-selecting amplifier to respectively perform signal conditioning of filtering, pre-amplification and frequency-selecting amplification on the obtained magnetization response signal; and the signal acquisition card stores the magnetization response signal after the signal conditioning. The magnetic detection sensor is one of an air coil, a magnetoresistive sensor or a SQUID sensor.
The signal processing and temperature calculating device adopts a computer to control a data acquisition card to carry out data acquisition on the magnetization response signal after signal conditioning to obtain a discrete signal; extracting harmonic amplitude and phase angle information of the obtained discrete signal by adopting a harmonic amplitude phase angle detection module, substituting the obtained harmonic amplitude and phase angle information into a magnetic nano temperature estimation model
Figure BDA0002213580660000121
Solving magnetic nano temperature information; wherein A isiIs a harmonic waveAmplitude, θiFor phase information, i is 1,3,5, …, N denotes the harmonic order; b isiObtaining harmonic amplitude values by drawing a magnetization response curve of the magnetic nanoparticles according to a Langevin function; a isi、bi、ciThe model parameters in the ith harmonic amplitude information fitting function are respectively, H is the alternating current magnetic field intensity of the medium-high frequency excitation magnetic field, and T is the absolute temperature of the magnetic nanoparticles. The harmonic amplitude phase angle detection module is internally provided with a harmonic amplitude and phase angle detection algorithm, the harmonic amplitude and phase angle detection algorithm adopts a digital phase-sensitive detection algorithm, a fast Fourier transform algorithm or a least square system identification algorithm, and the harmonic amplitude phase angle detection module is used as a signal processing device for extracting information of each harmonic amplitude and phase angle of the magnetization response signal.
The invention provides a high-precision magnetic nano temperature estimation system based on Fokker-Planck, which comprises a magnetic field driving device, a driven element and a signal processing device, wherein the magnetic field driving device is a magnetic field generator or the driven element is a magnetic field detection device, the signal processing device is a computer, and the magnetic field of the computer is connected with the driving device and the driven element.
The invention compensates the harmonic amplitude information by adopting the phase information caused by the magnetic relaxation phenomenon under the medium-high frequency excitation, overcomes the technical problem that the traditional method can not accurately measure the temperature under the medium-high frequency magnetic field excitation, is expected to realize the measurement of the temperature information of the magnetic nano particles under the medium-high frequency magnetic field excitation, ensures the feasibility of the method in practical application, and improves the measurement precision and the time resolution.
Simulation case: 1. simulation conditions, two sets of simulation experiments were conducted to study the effectiveness and superiority of the present invention.
The first set of simulation experiments are based on the magnetic nanoparticle magnetization response of Fock-Planck equation under the influence of different relaxation times, and simulation parameters are as follows: boltzmann constant kB＝1.38×10-23JK-1Magnetic permeability μ in vacuum01, saturation magnetization Ms＝47.7×104A/m, absolute temperature T290K, excitation magnetic field frequency 200Hz, sampling rate 100KHz, excitation magnetic field H' 0.76sin (wt), the relaxation times are 0s, 0.00005s, 0.0001s, 0.0005s, 0.001s, respectively, and a relaxation time of 0s is an ideal state in which no relaxation influence exists.
The second group of simulation experiments are temperature estimation simulation, and simulation parameters are as follows: boltzmann constant kB＝1.38×10-23JK-1Magnetic permeability μ in vacuum01, saturation magnetization Ms＝47.7×104A/m, absolute temperature T290K, excitation magnetic field frequency 200Hz, sampling rate 100KHz, excitation magnetic field H' 0.76sin (2 pi ft), relaxation time 0.0001s, absolute temperature T310K-320K, stepping 1K, temperature points 310K, 312K, 314K, 316K, 318K, 320K for fitting parameter ai、biAnd ciThe temperature points 311K, 313K, 315K, 317K, and 319K are true values of the temperature points to be estimated.
2. Simulation test result
Fig. 2 shows the first set of simulation results, when the excitation magnetic field H' is 0.76sin (wt), and the magnetic nanoparticles have magnetization response information under the non-magnetic phenomenon and different magnetic relaxation time. From fig. 2, it can be found that under the condition of no influence of the magnetic relaxation phenomenon, the magnetization response information of the magnetic nanoparticles can be accurately described by the langevin function, but when the influence of the magnetic relaxation phenomenon exists, the langevin function cannot be accurately described. When the magnetic relaxation time is from 0s to 0.00005s and 0.0001s, the amplitude of the magnetization response information of the magnetic nanoparticles has little influence, only phase delay exists, namely phase included angle exists, and when the magnetic relaxation time is from 0.0001s to 0.0005s and 0.001s, the magnetization response of the magnetic nanoparticles has not only phase lag, but also attenuation of the magnetization response signal. Magnetic nanoparticle magnetization response signal simulation experiments under different magnetic relaxation times verify that the magnetic relaxation phenomenon has amplitude information attenuation and phase lag problems on magnetic nanoparticle magnetization response information, and when the magnetic nanoparticle magnetization response information is excited by a medium-high frequency magnetic field, the langevin function cannot accurately describe the magnetic nanoparticle magnetization response information.
Fig. 3 is a second set of simulation experiment results. Fig. 3(a) comparison results of the magnetic nanoparticle magnetization response harmonic information compensation model and the langevin harmonic model at different temperatures (T: 310K, 312K, 314K, 316K, 318K, 320K) are shown in the figureThe sign is the magnetization response first harmonic amplitude based on the Fockplanck equation, the sign ○ is the magnetization response first harmonic amplitude based on the Langmuir function, the line represents the fitting result of the magnetization response first harmonic amplitude information compensation model, and the fitting parameters are a1＝1.0140、b1＝0.0032、c1-0.4969. It was found that the magnitude of the magnetization response harmonics gradually decreased with increasing temperature. Fig. 3(b) shows the error between the temperature point to be obtained and the true temperature value (T: 311K, 313K, 315K, 317K, 319K) obtained by the temperature estimation model using the fitting parameters, where the temperature error is less than 0.04K.
The first experimental case:
1. conditions of the experiment
To develop three sets of experiments to study the effectiveness and superiority of the invention, the first set of experimental parameters: sample model SHP-20, Boltzmann constant kB＝1.38×10-23JK-1Magnetic permeability μ in vacuum01, 290K of absolute temperature T, 200Hz of excitation magnetic field frequency, 100KHz of sampling rate, 0.002 tesla-0.01 tesla of alternating magnetic field intensity variation range, 0.001 tesla of stepping, and the second set of experimental parameters: sample model MS1, Boltzmann constant kB＝1.38×10-23JK-1Magnetic permeability μ in vacuum01, the absolute temperature T290K, the excitation magnetic field frequency 200Hz, the sampling rate 100KHz, the alternating magnetic field intensity variation range 0.002 tesla-0.01 tesla, the step size 0.001 tesla, the third set of experimental parameters: sample model MS2, Boltzmann constant kB＝1.38×10-23JK-1Magnetic permeability μ in vacuum0The absolute temperature T is 290K, the frequency of the excitation magnetic field is 200Hz, the sampling rate is 100KHz, the variation range of the alternating magnetic field intensity is 0.002 Tesla-0.01 Tesla, and the step is 0.001 Tesla.
2. Results of the Experimental tests
Fig. 4 is a comparison result graph of a harmonic information compensation model and a langevin harmonic model under excitation of a 200Hz alternating magnetic field, the model of a sample is SHP-20, in fig. 4, (a), (b), and (c) are comparison graphs of first harmonic amplitude, third harmonic amplitude, and fifth harmonic amplitude measured by the harmonic information compensation model and the langevin harmonic model respectively, the symbol is experimental data, the symbol is langevin harmonic model, and the line is the harmonic information compensation model, and it can be found that as the excited magnetic field increases, the harmonic amplitude obtained by the langevin harmonic model and the actually measured harmonic amplitude become larger and larger, and the actual magnetization response harmonic data cannot be accurately fitted, and the actual magnetization response harmonic data can be accurately fitted through the harmonic information compensation model. Fig. 4(d) shows the parameter fitting values in the harmonic information compensation model, respectively. Fig. 5 is a comparison result graph of a harmonic information compensation model and a langevin harmonic model under excitation of a 200Hz alternating magnetic field, the model of a sample is MS1, fig. 5(a), (b) and (c) are a comparison graph of a first harmonic amplitude, a third harmonic amplitude and a fifth harmonic amplitude measured by the harmonic information compensation model and the langevin harmonic model respectively, a symbol x is experimental data, a symbol a is the langevin harmonic model, and a line is the harmonic information compensation model, and it can be found that as the excitation magnetic field increases, the harmonic amplitudes obtained by the langevin harmonic model and the actually measured harmonic amplitudes become larger and larger, actual magnetization response harmonic data cannot be accurately fitted, and the actual magnetization response harmonic data can be accurately fitted by the harmonic information compensation model. Fig. 5(d) shows the parameter estimation values in the harmonic information compensation model, respectively. Fig. 6 is a comparison result graph of a harmonic information compensation model and a langevin harmonic model under excitation of a 200Hz alternating magnetic field, the model of a sample is MS2, fig. 6(a), (b) and (c) are a comparison graph of a first harmonic amplitude, a third harmonic amplitude and a fifth harmonic amplitude measured by the harmonic information compensation model and the langevin harmonic model respectively, a symbol x is experimental data, a symbol a is the langevin harmonic model, and a line is the harmonic information compensation model, and it can be found that as the excitation magnetic field increases, the harmonic amplitudes obtained by the langevin harmonic model and the actually measured harmonic amplitudes become larger and larger, actual magnetization response harmonic data cannot be accurately fitted, and the actual magnetization response harmonic data can be accurately fitted by the harmonic information compensation model. Fig. 6(d) shows the parameter estimation values in the harmonic information compensation model, respectively.
Experiment case two:
1. conditions of the experiment
To develop three sets of experiments to study the effectiveness and superiority of the invention, the first set of experimental parameters: sample model SHP-20, Boltzmann constant kB＝1.38×10-23JK-1Magnetic permeability μ in vacuum01, 290K for absolute temperature T, 3KHz for excitation magnetic field frequency, 100KHz for sampling rate, 0.002 tesla to 0.01 tesla for alternating current magnetic field intensity range, 0.001 tesla for stepping, the second set of experimental parameters: sample model MS1, Boltzmann constant kB＝1.38×10-23JK-1Magnetic permeability μ in vacuum01, 290K for absolute temperature T, 3KHz for excitation magnetic field frequency, 100KHz for sampling rate, 0.002 tesla-0.01 tesla for alternating current magnetic field intensity range, 0.001 tesla for stepping, and the third set of experimental parameters: sample model MS2, Boltzmann constant kB＝1.38×10-23JK-1Magnetic permeability μ in vacuum0The absolute temperature T is 290K, the frequency of the excitation magnetic field is 3KHz, the sampling rate is 100KHz, the variation range of the alternating-current magnetic field intensity is 0.002 Tesla-0.01 Tesla, and the step is 0.001 Tesla.
2. Results of the Experimental tests
FIG. 7 is a comparison result diagram of a harmonic information compensation model excited by a 3KHz alternating magnetic field and a langevin harmonic model, wherein the model of the sample is SHP-20, FIG. 7(a), (b), (c) are the comparison graphs of the first harmonic amplitude, the third harmonic amplitude and the fifth harmonic amplitude measured by the harmonic information compensation model and the langevin harmonic model respectively, the symbol is experimental data, the symbol A is the langevin harmonic model, the line is the harmonic information compensation model, it can be found that as the excited magnetic field increases, the harmonic amplitude obtained by the langevin harmonic model and the actually measured harmonic amplitude become larger and larger, the actual magnetization response harmonic data cannot be accurately fitted, the actual magnetization response harmonic data can be accurately fitted by the harmonic information compensation model, and the parameter estimation values in the harmonic information compensation model are respectively given in fig. 7 (d). Fig. 8 is a comparison result graph of a harmonic information compensation model excited by a 3KHz alternating magnetic field and a langevin harmonic model, where the sample model is MS1, fig. 8(a), (b), and (c) are comparison graphs of a first harmonic amplitude, a third harmonic amplitude, and a fifth harmonic amplitude measured by the harmonic information compensation model and the langevin harmonic model, respectively, the symbol x is experimental data, the symbol a is the langevin harmonic model, and the line is the harmonic information compensation model, it can be found that as the excited magnetic field increases, the harmonic amplitudes obtained by the langevin harmonic model and the actually measured harmonic amplitudes become larger and larger, and actual magnetization response harmonic data cannot be accurately fitted, and actual magnetization response harmonic data can be accurately fitted by the harmonic information compensation model, and fig. 8(d) respectively gives parameter estimation values in the harmonic information compensation model. Fig. 9 is a comparison result diagram of a harmonic information compensation model excited by a 3KHz alternating magnetic field and a langevin harmonic model, where the model of the sample is MS2, fig. 9(a), (b), and (c) are comparison diagrams of first harmonic amplitude, third harmonic amplitude, and fifth harmonic amplitude measured by the harmonic information compensation model and the langevin harmonic model, respectively, where symbol x is experimental data, symbol a is langevin harmonic model, and lines are the harmonic information compensation model, it can be found that as the excited magnetic field increases, the harmonic amplitude obtained by the langevin harmonic model and the actually measured harmonic amplitude become larger and larger, and actual magnetization response harmonic data cannot be accurately fitted, and actual magnetization response harmonic data can be accurately fitted by the harmonic information compensation model, and fig. 9(d) gives parameter estimation values in the harmonic information compensation model, respectively.
Experiment case three:
1. conditions of the experiment
To develop three sets of experiments to study the effectiveness and superiority of the invention, the first set of experimental parameters: sample model SHP-20, Boltzmann constant kB＝1.38×10-23JK-1Magnetic permeability μ in vacuum01, 290K of absolute temperature T, 20KHz of excitation magnetic field frequency, 100KHz of sampling rate, 0.002 tesla-0.01 tesla of alternating current magnetic field intensity variation range, 0.001 tesla of stepping, the second set of experimental parameters: sample model MS1, Boltzmann constant kB＝1.38×10-23JK-1Magnetic permeability μ in vacuum01, 290K absolute temperature T, 20KHz exciting magnetic field frequency, 100KHz sampling rate and alternating current magnetic field intensity variationThe chemical range is 0.002 tesla to 0.01 tesla, the step is 0.001 tesla, and the third group of experimental parameters: sample model MS2, Boltzmann constant kB＝1.38×10-23JK-1Magnetic permeability μ in vacuum0The absolute temperature T is 290K, the frequency of the excitation magnetic field is 20KHz, the sampling rate is 100KHz, the variation range of the alternating-current magnetic field intensity is 0.002 Tesla-0.01 Tesla, and the step is 0.001 Tesla.
2. Results of the Experimental tests
FIG. 10 is a graph showing the comparison result between the harmonic information compensation model excited by the 20KHz alternating magnetic field and the langevin harmonic model, the model of the sample is SHP-20, FIG. 10(a), (b), (c) are comparative graphs of the first harmonic amplitude, the third harmonic amplitude, and the fifth harmonic amplitude measured by the harmonic information compensation model and the langevin harmonic model, respectively, where symbol x is experimental data, symbol a is langevin harmonic model, line is harmonic information compensation model, it can be found that as the excited magnetic field increases, the harmonic amplitude obtained by the langevin harmonic model and the actually measured harmonic amplitude become larger and larger, the actual magnetization response harmonic data cannot be accurately fitted, the actual magnetization response harmonic data can be accurately fitted by the harmonic information compensation model, and the parameter estimation values in the harmonic information compensation model are respectively given in fig. 10 (d). Fig. 11 is a comparison result graph of a harmonic information compensation model excited by a 20KHz alternating magnetic field and a langevin harmonic model, where the model of a sample is MS1, fig. 11(a), (b), and (c) are comparison graphs of a first harmonic amplitude, a third harmonic amplitude, and a fifth harmonic amplitude measured by the harmonic information compensation model and the langevin harmonic model, respectively, the symbol x is experimental data, the symbol a is the langevin harmonic model, and the line is the harmonic information compensation model, it can be found that as the excited magnetic field increases, the harmonic amplitudes obtained by the langevin harmonic model and the actually measured harmonic amplitudes become larger and larger, and actual magnetization response harmonic data cannot be accurately fitted, and actual magnetization response harmonic data can be accurately fitted by the harmonic information compensation model, and fig. 11(d) respectively gives parameter estimation values in the harmonic information compensation model. Fig. 12 is a comparison result graph of a harmonic information compensation model excited by a 20KHz alternating magnetic field and a langevin harmonic model, where the model of the sample is MS2, fig. 12(a), (b), and (c) are comparison graphs of a first harmonic amplitude, a third harmonic amplitude, and a fifth harmonic amplitude measured by the harmonic information compensation model and the langevin harmonic model, respectively, the symbol x is experimental data, the symbol a is the langevin harmonic model, and the line is the harmonic information compensation model, it can be found that as the excited magnetic field increases, the harmonic amplitudes obtained by the langevin harmonic model and the actually measured harmonic amplitudes become larger and larger, and actual magnetization response harmonic data cannot be accurately fitted, and actual magnetization response harmonic data can be accurately fitted by the harmonic information compensation model, and fig. 12(d) respectively gives parameter estimation values in the harmonic information compensation model.
Three groups of experimental cases respectively verify three different samples SHP-20, MS1 and MS2, and magnetization response harmonic amplitude compensation models under three different excitation magnetic field frequencies of 200Hz, 3KHz and 20KHz, the effectiveness of the invention is verified through experiments, the measured experimental data are basically consistent with the curve of the harmonic information compensation model, the coincidence is very good, and the effectiveness of the harmonic information compensation model is demonstrated.
The invention has the advantages that under the excitation of a medium-high frequency magnetic field, the harmonic information compensation model can accurately describe the magnetization response harmonic amplitude information of the magnetic nanoparticles, solves the model problem caused by the magnetic relaxation phenomenon under the excitation of the medium-high frequency magnetic field by the Langmuir function, expands the application fields of the magnetic nanoparticle temperature measurement and magnetic nanoparticle imaging technology, and is expected to improve the measurement precision and the time-space resolution. In addition, since the rate of change of the medium-high frequency sine wave excitation magnetic field is fast compared with the rate of change of the direct current or low frequency excitation magnetic field, the measurement time does not depend on the time taken to construct the measurement model, but only on the magnetization response information sampling time. Compared with a temperature measurement method under the excitation of a direct current or low-frequency magnetic field, the time resolution is greatly improved, the temperature measurement precision under the excitation of a medium-high frequency magnetic field can be ensured, the time resolution of the temperature measurement of magnetic nanoparticles is greatly improved, and a new model and a new method are provided for the temperature measurement in the medium-high frequency field.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (10)

1. A high-precision magnetic nano temperature estimation method based on Fokker-Planck is characterized by comprising the following steps:
the method comprises the following steps: placing a magnetic field information detection device on a magnetic nano sample to be detected to detect a magnetization response signal of magnetic nano particles in the magnetic nano sample;
step two: obtaining harmonic amplitude and phase angle information of the magnetization response by using a harmonic amplitude and phase angle detection algorithm;
step three: and constructing a magnetic nanoparticle temperature estimation model by utilizing a Fokker-Planck formula, substituting the extracted harmonic amplitude and phase angle information of each time of the magnetization response signal into a harmonic amplitude fitting model to obtain fitting parameters, substituting the fitting parameters into the magnetic nanoparticle temperature estimation model, and calculating the temperature information of the magnetic nanoparticles.
2. The method for estimating the magnetic nano-temperature with high precision based on the Fokker-Planck as claimed in claim 1, wherein the method for constructing the magnetic nano-particle temperature estimation model by using the Fokker-Planck formula is as follows:
according to a Fokker-Planck formula, drawing a magnetization response curve of the magnetic nanoparticles under different Brownian magnetic relaxation times;
respectively extracting odd harmonic amplitudes A in the magnetization response curve according to the harmonic amplitude and phase detection algorithmiAnd phase information thetaiWherein i is 1,3,5, …, N represents the harmonic order;
drawing a magnetization response curve of the magnetic nanoparticles according to a Langevin function;
extracting each odd harmonic amplitude B according to harmonic amplitude and phase detection algorithmi；
Fitting function according to harmonic amplitude
Figure FDA0002213580650000011
Harmonic vibrationAmplitude ratio Ai/BiCarrying out harmonic amplitude information fitting to obtain fitting parameters; wherein, ai、bi、ciModel parameters in the ith harmonic amplitude information fitting function are respectively shown, H is the alternating current magnetic field intensity of the medium-high frequency excitation magnetic field, and T is the absolute temperature of the magnetic nanoparticles;
obtaining a fitting function of the magnetic nanoparticle magnetization response harmonic amplitude by fitting the harmonic amplitude information into
Figure FDA0002213580650000012
Obtaining a magnetic nanoparticle temperature estimation model through inversion calculation
Figure FDA0002213580650000013
3. The Fokker-Planck-based high-precision magnetic nano temperature estimation method according to claim 2, wherein the fitting method of the model parameters in the fitting function is as follows:
s1: measuring magnetization response signals of the magnetic nanoparticles under the excitation of an external excitation magnetic field;
s2: extracting amplitude and phase angle information of each harmonic in the magnetization response signal;
s3: repeating the steps S2-S3 for multiple times, measuring and extracting amplitude and phase angle information of each harmonic;
model parameters in the magnetic nanoparticle temperature estimation model, namely model parameters a of ith harmonic in the magnetic nanoparticle temperature estimation model, are simulated by adopting a method of compensating harmonic amplitude information by phase angle informationi、bi、ci。
4. The Fokker-Planck-based high-precision magnetic nano-temperature estimation method according to claim 1 or 3, wherein the method for calculating the temperature of the magnetic nano-particles is:
measuring magnetization response signals of the magnetic nanoparticles under the excitation of an external excitation magnetic field; extracting amplitude and phase angle information of each harmonic in the magnetization response signal;
and substituting the extracted amplitude and phase angle information of each harmonic into the magnetic nano particle temperature estimation model to obtain the magnetic nano particle temperature information.
5. The Fokker-Planck-based high-precision magnetic nano temperature estimation method according to claim 2 or 3, wherein the ith harmonic amplitude A of the magnetization response signaliAnd phase information thetaiThe method comprises the following steps:
when the magnetic nanoparticles are excited by an external alternating magnetic field, the magnetic nanoparticles are influenced by Brownian magnetic relaxation excitation, and the dynamic behavior of the magnetic nanoparticles is described by a Fokker-Planck formula as follows:
Figure FDA0002213580650000021
wherein the content of the first and second substances,
Figure FDA00022135806500000211
is the included angle between the internal magnetic moment of the magnetic nano-particles and the direction of an external magnetic field H,
Figure FDA0002213580650000022
is an included angleXi is the ratio of the energy of the applied magnetic field to the heat energy and xi is mH/KBT, magnetic moment m ═ mu0MsV，μ0Is the magnetic permeability in vacuum, MsIs the saturation magnetization, V is the unit volume, KBIs the Boltzmann constant, T is the absolute temperature of the magnetic nanoparticles, and the Brownian relaxation time τB＝3ηV/KBT, η is the viscosity coefficient;
and (3) performing spherical harmonic expansion on the dynamic behavior of the magnetic nanoparticles described by the Fokker-Planck formula to obtain a distribution function:
Figure FDA0002213580650000024
wherein, an(t) is the coefficient of each spherical harmonic in relation to time,
Figure FDA0002213580650000025
is a Legendre polynomial, n represents the number of terms of the Legendre polynomial;
and substituting the distribution function into the dynamic behavior of the magnetic nanoparticles described by Fokker-Planck formula, and combining and finishing to obtain:
here, the
Figure FDA0002213580650000027
The differential-to-differential equation is obtained as:
Figure FDA0002213580650000028
passing coefficient anIs solved to obtain a distribution function
Figure FDA0002213580650000029
The magnetization response of the magnetic nanoparticles is then:
Figure FDA00022135806500000210
processing the magnetization response M of the magnetic nanoparticles by FFT or DPSD algorithm to obtain the amplitude A of each subharmonic in the magnetization response information of the magnetic nanoparticlesiAnd phase information thetai。
6. The Fokker-Planck based high precision magnetic nano temperature estimation method according to claim 2, wherein the ith harmonic amplitude B of the magnetization response signaliThe method comprises the following steps:
when the magnetic nanoparticles of the magnetic nano sample are excited by a static or quasi-static magnetic field, the magnetization response information M is described as an approximate function of Frankia:
Figure FDA0002213580650000031
wherein, mu0Denotes the vacuum permeability, L (ξ) denotes the langevin function, M denotes the effective magnetic moment of the magnetic nanoparticles, M denotes the effective magnetic moment of the magnetic nanoparticlessDenotes saturation magnetization, H ═ Hsin (ω T) denotes an applied alternating-current excitation magnetic field, angular velocity ω ═ 2 π f, T denotes the absolute temperature of the magnetic nanoparticles, k denotes the absolute temperature of the magnetic nanoparticlesBRepresenting boltzmann constant, xi is the ratio of external magnetic field energy to heat energy, and coth (xi) is langevin function;
the taylor series expansion of the magnetization response information M represented by the langevin function can result in:
Figure FDA0002213580650000032
obtaining each subharmonic amplitude B through DPSD algorithmi：
Figure FDA0002213580650000033
7. A high-precision magnetic nano temperature estimation system based on Fokker-Planck is characterized by comprising a magnetic field excitation device, a magnetic field information detection device and a signal processing and temperature calculating device, wherein the magnetic field excitation device and the magnetic field information detection device are both arranged in a region where a magnetic nano sample to be detected is located, the magnetic field excitation device generates an excitation magnetic field in the region where the magnetic nano sample to be detected is located, the magnetic field information detection device collects and preprocesses magnetization response signals generated by the magnetic nano sample, the magnetic field information detection device and the signal processing and temperature calculating device are connected, and the signal processing and temperature calculating device calculates magnetic nano temperature information according to a magnetic nano particle temperature estimation model and the obtained magnetization response signals.
8. The Fokker-Planck-based high-precision magnetic nano temperature estimation system of claim 7, wherein the magnetic field excitation device comprises a magnetic field generator, a power amplifier, a signal generator and a passive band-pass filter, the signal generator is connected with the power amplifier, the power amplifier is connected with the passive band-pass filter, and the passive band-pass filter is connected with the magnetic field generator; the magnetic field information detection device comprises a magnetic detection sensor, a low-noise preamplifier, a frequency-selecting amplifier, a band-pass filter and a signal acquisition card, wherein the magnetic detection sensor is connected with the low-noise preamplifier, the low-noise preamplifier is connected with the frequency-selecting amplifier, the frequency-selecting amplifier is connected with the band-pass filter, and the band-pass filter is connected with the signal acquisition card; the signal processing and temperature calculating device comprises a computer, a harmonic amplitude phase angle detection module and a magnetic nano temperature estimation model, wherein the signal acquisition card, the harmonic amplitude phase angle detection module and the magnetic nano temperature estimation model are all connected with the computer;
the magnetic field excitation device outputs sine wave signals by adopting a signal output module of a signal generator or a signal acquisition card, sends the sine wave signals to a power amplifier for signal power amplification, and then carries out signal conditioning through a passive band-pass filter to drive a magnetic field generator to generate an excitation magnetic field;
the magnetic field information detection device adopts a magnetic detection sensor to measure the magnetization response signal of the magnetic nano sample under the excitation of a medium-high frequency sine wave excitation magnetic field in real time, and adopts a band-pass filter, a low-noise preamplifier and a frequency-selecting amplifier to respectively perform signal conditioning of filtering, pre-amplification and frequency-selecting amplification on the obtained magnetization response signal; the signal acquisition card stores the magnetization response signal after signal conditioning;
the signal processing and temperature calculating device adopts a computer to control a data acquisition card to carry out data acquisition on the magnetization response signal after signal conditioning to obtain a discrete signal; extracting harmonic amplitude and phase angle information of the obtained discrete signal by adopting a harmonic amplitude phase angle detection module, substituting the obtained harmonic amplitude and phase angle information into a magnetic nano temperature estimation modelSolving magnetic nano temperature information; wherein A isiFor harmonic amplitude, θiFor phase information, i is 1,3,5, …, N denotes the harmonic order; b isiObtaining harmonic amplitude values by drawing a magnetization response curve of the magnetic nanoparticles according to a Langevin function; a isi、bi、ciThe model parameters in the ith harmonic amplitude information fitting function are respectively, H is the alternating current magnetic field intensity of the medium-high frequency excitation magnetic field, and T is the absolute temperature of the magnetic nanoparticles.
9. The Fokker-Planck based high-precision magnetic nano temperature estimation system according to claim 8, wherein the excitation magnetic field is a medium-high frequency sine wave excitation magnetic field: h ═ Hsin (2 pi ft), where H is the alternating excitation field strength at frequency f; the alternating excitation magnetic field strength H is in the range of below 0.01 Tesla, and the frequency f is in the range of below 20 KHz.
10. The Fokker-Planck based high precision magnetic nano temperature estimation system of claim 7, wherein the magnetic detection sensor is one of an air coil, a magneto-resistive sensor or a SQUID sensor; and a harmonic amplitude and phase angle detection algorithm is arranged in the harmonic amplitude and phase angle detection module, and adopts a digital phase-sensitive detection algorithm, a fast Fourier transform algorithm or a least square system identification algorithm.
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CN111680444A (en) * 2020-06-12 2020-09-18 福州大学 Magnetic nanoparticle critical heat production value automatic positioning method based on simplex algorithm
CN111680444B (en) * 2020-06-12 2022-10-04 福州大学 Magnetic nanoparticle critical heat production value automatic positioning method based on simplex algorithm
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CN112212996B (en) * 2020-10-10 2022-11-08 郑州轻工业大学 Harmonic amplitude-temperature method for measuring temperature of magnetic nanoparticles in high-frequency excitation magnetic field
CN112924906A (en) * 2021-01-26 2021-06-08 西安交通大学 Wireless flexible magnetic sensor based on magnetocaloric effect, and preparation method and detection method thereof
CN113534025A (en) * 2021-07-21 2021-10-22 北京航空航天大学 Magnetic nanoparticle imaging method based on non-ideal magnetic field-free point
CN114166365A (en) * 2021-11-23 2022-03-11 华中科技大学 Mitochondrial temperature measuring method and system based on magnetic nanoparticle magnetization response
CN114199405A (en) * 2021-11-26 2022-03-18 华中科技大学 Temperature measuring method and system based on GRE (GRE) image and magnetic nanoparticles
CN114199405B (en) * 2021-11-26 2022-08-16 华中科技大学 Temperature measuring method and system based on GRE (GRE) image and magnetic nanoparticles
CN117572309A (en) * 2023-10-20 2024-02-20 暨南大学附属第一医院（广州华侨医院） Magnetic particle spectrometer based on harmonic phase deflection, quantification method and storage medium
CN117572309B (en) * 2023-10-20 2024-04-09 暨南大学附属第一医院（广州华侨医院） Magnetic particle spectrometer based on harmonic phase deflection, quantification method and storage medium

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