The invention relates to a nano measurement field, and more particularly to a temperature measurement method based on magnetic susceptibility of nano superparamagnetic materials.
Temperature information deeply inside objects, especially deeply in vivo, is limited by physical principle of time and space, and information transportation, and this makes it impossible to facilitate non-contact temperature measurement within 1000° C. Temperature is direct evidence that characterizes immune response and life activities. Hyperthermia cancer therapy expects to control temperature at cancerization parts at 45° C.-47° C. during hyperthermia process. Normally 45° C.-47° C. is a critical temperature point that ensures safety of normal cells and causes cancer cells necrosis gradually. Remote detection of temperature field information of cancer cells between lungs and livers are critical for breakthrough of the hyperthermia therapy. However, internal organs, bones, vessels or skin are a natural barrier for the temperature information. In other fields, temperature distribution at outlets of aero engines directly affect lifetime of turbines, fast measurement methods are to greatly improve performance of engines without changing temperature distribution field of turbines. Therefore, a more popularly used method for measuring temperature at deep sites of objects becomes a key technique for promoting development of biomedical and industrial fields.
Technically, it is comparatively difficult to apply the existing temperature measurement technique to temperature measurement of deep sites of objects. The magnetic resonance temperature measurement technique brings twilight for temperature field measurement of human beings, and it is difficult to apply the magnetic resonance temperature measurement to vivo (such as hyperthermia cancer therapy) temperature measurement. However, too weak magnetic property of molecular directly or indirectly leads to technical difficulty of measurement. Temperature characteristic parameters of hydrogen molecular in vivo cannot be pre-obtained, and during test, measurement of temperature difference is implementing by measuring the same point for two times before and after heating, and at the same time, a test point is required to be highly static, which form a main source of error. Researchers notice that magnetic moments of magnetic nanoparticles (tri-iron tetroxide) are three orders of magnitude higher than nuclear magnetic signals of hydrogen molecules soon. Thus, the nano magnetic measurement system is expected to achieve high speed and high signal-noise ratio. J. B. Weaver from America made useful exploration of the nano magnetism, and he used the ratio between the triple harmonic generation and the quintuple harmonic generation after AC magnetization using nano superparamagnetic materials for experiment, and the precision obtained was greater than 1 degree in a range of 20° C. to 50° C. Temperature-related constants of the magnetic nanoparticles, such as size, saturation magnetic moment and so on can be precisely and repeatedly pre-measured outside vivo, and magnetic parameters can be predetermined. Uncertainty of concentration distribution and space distribution of magnetic nanoparticles in vivo is to cause very large error of temperature measurement in vivo. Uncertainty of pixel distribution in vivo causes temperature of nuclear magnetic resonance can only implement measurement of temperature difference.
It is an objective of the invention to provide a paramagnetism-based remote temperature measurement method for a magnetic nanoparticle that is capable of precisely and quickly implementing remote temperature measurement of objects.
A paramagnetism-based remote temperature measurement method for a magnetic nanoparticle, comprising:
where reciprocal of the Langevin's function
c2j-1 is a polynomial coefficient, J+1 is a predetermined polynomial expansion term, N is concentration of the sample, M is atomic magnetic moment of the sample, k is a Boltzmann's constant, and T is temperature of the measured object;
to perform curve fitting on a sequence point
calculating the temperature according to an intercept 3x and a slope ⅕y of the straight line obtained by the curve fitting:
and calculating the concentration of the sample:
Advantageously, 2≦J≦5, and step (5) comprises:
Firstly transforming the equation between the magnetic susceptibility χi and the excited magnetic fields Hi into a matrix equation
1≦Q≦J+1, and A is a coefficient matrix;
Then solving equations
whereby obtaining a and b, where Aq* is the qth row of a generalized inverse A* of the coefficient matrix A; and
Finally calculating the temperature of the measured object:
and the concentration of the sample:
Advantages of the invention comprise:
The invention provides a temperature measurement method based on the magnetic susceptibility of nano superparamagnetic materials, multiple (normally greater than two) times of excited magnetic fields are applied on area of a magnetic nano sample, equations between different excited magnetic fields and corresponding magnetic susceptibility are constructed according to the Langevin's paramagnetic theorem, and information of temperature and sample concentration are obtained via the equations.
The invention makes it possible for implementing precise and quick temperature detection of objects, and especially applicable for detection of thermal motion at biomolecular level. Different from hydrogen molecular sensors used in the MRI technique, the nano magnetic temperature measurement method employs nano superparamagnetic materials in magnetohyperthermia cancer therapy as temperature sensors, and has advantages in many aspects. Magnetic susceptibility measurement is not relaxation response but instant measurement, and therefore features good real-time performance. Constants of magnetic nanoparticles relating to temperature, such as size, saturation magnetic moment and so on are precisely and repeatedly measured outside the object, and magnetic parameters are predetermined. Meanwhile, magnetic moments of the magnetic nanoparticles (tri-iron tetroxide) are three orders of magnitude higher than nuclear magnetic signals of hydrogen molecules. Therefore, a nano magnetic measurement system can implement high speed and a high signal-noise ratio. Average error of the temperature measurement technique after 9 times' repetition is less than 0.56K. Temperature measurement error less than 1K can meet requirement in the hyperthermia cancer therapy for temperature measurement precision. Application prospect of the invention is to implement a temperature measurement technique that can be applied deeply in an object comprising the vivo, and is below the Curie temperature of iron-magnetic materials.
1. Theoretical Basis
Superparamagnetic materials follow the Langevin's function:
where I is magnetization, N is the number of particles per unit volume, M is atomic magnetic moment, is the Langevin's function, in this function
K is the Boltzmann's constant, T is absolute temperature.
The magnetic susceptibility χ follows equation:
A reciprocal of the Langevin's function is
where c2j-1 is a polynomial coefficient, and J+1 is a predetermined polynomial expansion term.
2. Solution
1) Linear Approximation Model of the Langevin's Paramagnetic Theorem:
Assuming J=1,
where χ is magnetic susceptibility,
By replacing
in the above equation:
By setting different excited magnetic fields Hi (i=1, 2 . . . n), the equation is formulated as:
Under moderate intensity, a magnetic susceptibility reciprocal—temperature curve varies, and the curve does not pass an absolute temperature zero point 0 K predicted by the Curie's law, or a fixed Curie point θ described in the Curie-Weiss law. Within certain temperature range, intercept shift exists on the magnetic susceptibility reciprocal—temperature curve, and the shift is related to intensity of the excited magnetic field. This phenomena is defined as magnetic modulation property of the magnetic susceptibility reciprocal—temperature curve. The magnetic modulation property of the magnetic susceptibility reciprocal—temperature curve indicates that under moderate intensity, the magnetic nanoparticles no longer follow the Curie's paramagnetic law.
Assuming
namely substituting
in the equation:
where Hn and χn are both known quantities which can be obtained by instrumental measurement, curve fitting is performed on a sequence point
by using a linear equation
and temperature T and concentration are respectively calculated according to an intercept 3x and a slope ⅕y of a line after curve fitting:
2) Polynomial Approximation Model of the Langevin's Paramagnetic Theorem:
assuming J≧2
By setting different excited magnetic fields Hi (i=1, 2 . . . n), the equation is formulated as:
Assuming
the equation is formulated as:
The binary high overdetermined equation is rewritten as:
If assuming
A* is a generalized inverse of the matrix A, then
Further, if A1*, A2*, A3*, A4* are respectively the first to the fourth vectors of the matrix A*, then
In practice, a and b can be obtained by combining
in the first two equations, namely
Equations {circle around (1)} and {circle around (2)} are combined as a first-degree polynomial approximation model, equations {circle around (1)} and {circle around (3)} are combined as a second-degree polynomial approximation model, equations {circle around (1)} and {circle around (4)} are combined as a third-degree polynomial approximation model, finally the first-stage, the second-stage, or the third-stage polynomial approximation model is solved to obtain a and b, and the equations
are used to calculate and obtain the temperature and the concentration (N, the number of particles per unit volume).
The above method uses the first to the fourth row vector of the matrix A* to construct the approximation model, and is a sample only, but the invention cannot be understood as only selecting the first four row vectors. A general construction mode of the approximation model is given as follows:
Expansion terms of the above polynomial model have no limitation, the invention uses three-term, four-term, five-term, six-term, and ten-term for operation, and calculation results indicate they can all implement the objective of the invention. However, the more the terms are, the easier pathological property of the equation may occur, therefore polynomials having three to six terms are suggested.
3. Simulation Example
1) Simulation Model and Test Explanation
To study effectiveness and optimization design of the temperature measurement method, simulation data containing noise are used to execute experimental test. Defaut samples (unless otherwise specified) during the measurement are EMG1400 (FerroTec, USA), magnetic moment of particles is set to 2.49×10−17. A noise model uses an awgn function in MATLAB to directly apply noise with a preset signal-noise ratio on the magnetic moment during magnetization process. A signal-noise ratio of the magnetization curve is set to 100 dB to 200 dB according to different test targets. The magnetization curve is uniformly divided into 200 points from zero to the maximum value. Taken into account that more polynomial expansions are to increase the number of conditions of a matrix A in a binary overdetermined equation, and thus leading to pathological property of solution. This will cause solution of the equation to be very sensitive to noise. Therefore in polynominal expansion of the Langevin's equation, expansions of the first six terms are used.
Simulation Result and Discussion
Simulation data indicate as the signal-noise ratio is small enough, the above-mentioned temperature prediction model can facilitate any precision. For example, in
The polynomial approximation model exhibits comparatively small system error, this is because it nonlinearly corrects the magnetization process based on the linear approximation model. A magnetic test system is to face thermal noise or external interruption under small magnetic excitation, and thus it is difficult to ensure precision of low-field test. During the test process, it is normally expected to effectively reduce interruption of noise by increasing excited magnetic field. Under comparatively large excited magnetic field, if only a linear model is used, obvious system error is to occur, as shown in
As noise cannot be neglected, different degrees in the polynomial approximation model directly affect suppression of noise. Degree of the polynomial model during test is 1 to 3. It can be seen from prediction algorithms of the first-degree, the second-degree, and the third-degree models in
3) Practical Test and Analysis
To prove applicability of the above-mentioned model in practical precision measurement, magnetic nano solid particle EMG1400 (FerroTec, USA) samples are used. A measurement instrument is a SQUID VSM (Quantum Design, USA) magnetometer. Based on multiple times of measurement and analysis, system parameters are adjusted to the optimum state and thus a final experiment scheme is determined. Excited magnetic field during the experiment is set to −200 Gs-+200 Gs, and every 5 Gs is one point. Temperature range of
Problems with the practical data are that undetermined factors exist in the saturation magnetic moment M in equations
and cannot be known in advance. Different agglomeration states in different environments of the same sample, such as dimer, trimer, or mulltimer, are to affect the saturation magnetic moment. Therefore, off-line measurement of the saturation magnetic moment may fail, and accordingly the actual temperature cannot be obtained accurately. An engineering-oriented method is to use magnetic susceptibility data of a group of known temperature to calculate an average M, and then to substitute M in the equations
as a known quantity. This makes it convenient to operate during practical application.
actual experiment data using the above-mentioned test method indicate that, although error during single temperature measurement is comparatively large, after multiple times of measurement, the measurement error can be less than 1K.
Filing Document | Filing Date | Country | Kind | 371c Date |
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PCT/CN2011/072207 | 3/28/2011 | WO | 00 | 5/2/2012 |
Publishing Document | Publishing Date | Country | Kind |
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WO2012/119329 | 9/13/2012 | WO | A |
Number | Name | Date | Kind |
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20090068114 | Haik | Mar 2009 | A1 |
20100327869 | Kim et al. | Dec 2010 | A1 |
20110098558 | Weaver et al. | Apr 2011 | A1 |
Number | Date | Country |
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101352342 | Jan 2009 | CN |
101601607 | Dec 2009 | CN |
102008049605 | Dec 2009 | DE |
3333875 | Oct 2002 | JP |
2009088062 | Jul 2009 | WO |
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Number | Date | Country | |
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20120239341 A1 | Sep 2012 | US |