# Patent

## Title
Method for stabilizing AC magnetic susceptibility of magnetic fluid

## Abstract

The invention relates to a method for stabilizing ac magnetic susceptibility of a magnetic fluid, comprising the following steps: (A) preparing two reagents of known magnetic concentration, including a first one in a mixture of an xC1 μl, m1-emu/g magnetic fluid and a yC1 μl PBS solution and a second one in a mixture of an xC2 μl, m2-emu/g magnetic fluid and a yC2 μl PBS solution, in addition to a to-be-detected reagent in a mixture of an xS μl, mS-emu/g magnetic fluid and a yS μl PBS solution: (B) detecting alternatively χac,o signals; (C) calculating a new χac,o value, i.e. χac,cal, for S via




  
    
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and (D) repeating steps (B) and (C) to find the χac,cal for a next run, and then finding a time dependent χac,cal for S.

## Background
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method for stabilizing ac magnetic susceptibility of a magnetic fluid, in particular to a method for reducing the coefficient of variation in the ac magnetic susceptibility for a reagent to a rather low value after calibrating.
2. Description of Related Art
By conjugating bio-probes onto magnetic particles, the magnetic particles are able to label specifically bio-targets. With the association between magnetic particles and bio-targets, the magnetic properties of magnetic particles change. This change acts as a parameter for detecting quantitatively proteins, viruses, bacterial, and chemicals by using bio-functionalized magnetic particles.
In early 2000's, some researchers proposed a method for assaying bio-molecules using magnetic particles. This method is so-called immunomagnetic reduction (IMR) [1]. In IMR, the reagent is a solution having homogeneously dispersed magnetic nanoparticles, which are coated with hydrophilic surfactants (e.g. dextran) and antibodies. Under external multiple ac magnetic fields, magnetic nanoparticles oscillate with the multiple ac magnetic fields via magnetic interaction, as shown in FIG. 1(a), which is an illustration of mechanism for immunomagnetic reduction assay before association between magnetic nanoparticles and biotargets. Thus, the reagent under external multiple ac magnetic fields shows a magnetic property, called mixed-frequency ac magnetic susceptibility χac. Hereafter the χac is expressed as χac,o before the association between particles and bio-molecules. Via the antibodies on the outmost shell, magnetic nanoparticles associate with and magnetically label bio-molecules to be detected. Due to the association, magnetic nanoparticles become either larger or clustered, as schematically shown in FIG. 1(b), which is an illustration of mechanism for immunomagnetic reduction assay after the association between magnetic nanoparticles and biotargets. The response of these larger/clustered magnetic nanoparticles to external multiple ac magnetic fields is much less than that of originally individual magnetic nanoparticles. Thus, the χac of the reagent is reduced due to the association between magnetic nanoparticles and detected bio-molecules. Hereafter the χac is expressed as χac,Φ after the association between particles and bio-molecules. It is obvious that χac,Φ should be smaller than χac,o. This is why the method is referred as ImmunoMagnetic Reduction. In principle, when more to-be-detected bio-molecules are mixed with a reagent, more magnetic nanoparticles become larger/clustered. A larger reduction in χac could be expected for reagents. A quantitative parameter related to the amount of to-be-detected bio-molecules is defined in the following Equation as

IMR signal=(χac,o−χac,Φ)/χac,o×100%  (1)

According to the description given above, IMR exhibits several unique merits. Firstly, the unbound to-be-detected bio-molecules and magnetic nanoparticles are not necessarily to be removed. They are still in the reagent. So, the assay process of IMR is simple. Secondly, only one kind of antibody is used. Thirdly, IMR is a direct and homogeneous assay, which usually shows high reliability and sensitivity. Fourth, because the amount of reduction in χac can be accurately measured to correspond to the concentration of the to-be-detected bio-molecules, the concentration of the bio-molecules can thus be measured quantitatively.
The diameter of magnetic nanoparticles used for IMR is tens of nanometers. The magnetic material of the nanoparticles could be ferrite, e.g. Fe3O4. The magnetic nanoparticles are well and homogeneously suspended in a water-based solution. The particle concentration of the magnetic reagent is about 1012 particles/cm3. The distance between two neighboring magnetic nanoparticles is around the order of magnitude of micrometers. Hence, the magnetic interaction between two neighboring magnetic particles is very weak, almost negligible. Therefore, the magnetic particles dispersed in reagent can be regarded as independent particles. But magnetic particles in reagent do experience several kinds of interactions, such as gratify, buoyancy, and thermal motion. The interactions of gravity and buoyancy cancel with each other. The magnetic particles in reagent only experience the thermal motion. Thermal energy UTh, for a magnetic particle in reagent can be expressed as

UTh=kBT,  (2)

where kB is a Boltzmann constant (=1.38×10−23 m2-kg-s−2-K−1), and T is the temperature in unit of Kelvin K. For example, at 25° C. (=298 K), the thermal energy UTh is 4.11×10−21 J for a magnetic particle in regent via Eq. (1).

As a magnetic field B applied to the magnetic reagent, a magnetic energy Um is generated for the magnetic particle in reagent. The Um can be expressed as

Um=−mB,  (3)

where m is a magnetic moment of a magnetic particle. The m can be obtained via

m=vM,  (4)

where v is the volume of a magnetic particle, and M is magnetization of the magnetic material forming the particle. For a magnetic particle of 93 nm in diameter, the volume v is (4/3)π(93/2)3 nm3. If the magnetic material is ferrite, e.g. Fe3O4, the M is 4.75×10−4 A-nm−1. Therefore, the m becomes 200 A-nm2.

In IMR, the amplitude of the applied ac magnetic field is in an order of magnitude of several Gauss's, say 1 Gauss. Thus, the absolute value of Um is found as 2.00×10−20 J via Eq. (3). The Um is just five times as UTh. This implies that the thermal energy plays a role in detecting the ac magnetic susceptibility χac of reagent in IMR. Theoretically, as the temperature rises, the thermal energy is enhanced to depress the magnetic actions of magnetic particles under ac magnetic fields. As a result, the χac of magnetic reagent is reduced as the temperature becomes higher. However, once the temperature is reduced, the magnetic actions become more dominant. Thus, the χac of magnetic reagent goes up at a lower temperature. It is worthy noting that such changes in χac of reagent are due to the variation in temperature, not due to the association between the magnetic particles and bio-targets. This means that the un-stability in temperature easily leads to false reduction or increase in the ac magnetic susceptibility χac of reagent in IMR.
In addition to thermal interaction, there are several factors causing the un-stability for ac magnetic susceptibility of magnetic reagent. These factors include background noise of an analyzer, un-stability of electronic circuits to amplify the detected ac magnetic susceptibility of reagent, etc. Methods to improve these bad issues for IMR are needed to be developed.
One possible method to stabilize the temperature is to use a temperature controller. There have been lots of commercial modules for controlling temperature. However, other control modules are needed to well control the fluctuation in the background noise of the analyzer and the performance of the amplifying circuits. In such a case, the analyzer able to obtain stable signals for ac magnetic susceptibility of reagent would be very complicated, and also costs a lot.
In a known proposed approach, the magnetic reagent used is the dextran-coated Fe3O4 magnetic particles dispersed in a PBS solution. The mean value and the standard deviation for particle diameter are respectively 93.6 nm and 23.8 nm, as shown in FIG. 2, which illustrates distribution for the diameter of dextran-coated Fe3O4 particles. The saturated magnetization of the reagent is 0.1 emu/g.
The reagent is put into the analyzer for detecting the time-dependent ac magnetic susceptibility χac,o. Meanwhile, the time dependent temperature is recorded. The results are shown in FIGS. 3(a) and 3(b), which respectively illustrate time dependent (a) temperature around reagent and (b) detected χac,o. During the detection, the temperature varies with time, as shown in FIG. 3(a). The highest temperature is 25.9° C., and the lowest temperature is 22.6° C. The detected time dependent χac,o is shown in FIG. 3(b). It can be found that the χac,o varies significantly with time. The variation in χac,o is due to not only the temperature fluctuation, but also the noise of the analyzer and the amplifying gain of the electronics. According to the data shown in FIG. 3(b), the maximum and the minimum values for χac,o are 142.1 and 124.3, respectively. The mean value and the standard deviation for the detected χac,o's are 118.0 and 10.68, respectively. Thus, the coefficient of variation for the time dependent χac,o is 9.05%. This means that the noise level for IMR is 9.05%. However, according to the reported papers [Attachments 2-4], the IMR signals are within the range from 0.80% to 3.00% by well controlling the temperature of reagent, background noise of the analyzer, and gain of amplifying circuits. The value of 9.05% for the variation in χac,o found in FIG. 3(b) is much higher than the true IMR signals. It fails to detect the IMR signals if the variation in χac,o could not be reduced.
As far as the related prior art is concerned, references may be referred to the following:
[1] Chin-Yih Hong, C. C. Wu, Y. C. Chiu, S. Y. Yang, H. E. Horng, and H. C. Yang, “Magnetic susceptibility reduction method for magnetically labeled immunoassay”, Appl. Phys. Lett., 88, 212512 (2006).
[2] Chin-Yih Hong, W. H. Chen, Z. F. Jian, S. Y. Yang, H. E. Horng, L. C. Yang, and H. C. Yang, “Wash-free immunomagnetic detection for serum through magnetic susceptibility reduction”, Appl. Phys. Lett., 90, 74105 (2007).
[3] S. Y. Yang, Z. F. Jian, J. J. Chieh, H. E. Horng, H. C. Yang, and Chin-Yih Hong, “Wash-free, antibody-assisted magnetoreduction assays on orchid viruses”, J. Virol. Methods, 149, 334 (2008).
[4] S. Y. Yang, C. B. Lan, C. H. Chen, H. E. Horng, Chin-Yih Hong, H. C. Yang, Y .K. Lai, Y. H. Lin, and K. S. Teng, “Independency of Fe ions in hemoglobin on immunomagnetic reduction assay”, J. Magn. Magn. Mater. 321, 3266 (2009).
Therefore, it is desirable to provide an improved method to stabilize the ac magnetic susceptibility of magnet reagent without using control modules so as to overcome the aforementioned problems.
SUMMARY OF THE INVENTION
The objective of the present invention is to provide an effective method to stabilize the ac magnetic susceptibility of magnet reagent and thus to reduce the variation in χac,o of the magnetic reagent.
To achieve the objective, the method of the present invention includes the following steps:
(A) preparing two reagents of known magnetic concentration, including a first one in a mixture of an xC1 μl (micro liter), m1-emu/ml magnetic fluid and a yC1 μl PBS (Phosphate Buffer Saline) solution and a second one in a mixture of an xC2 μl, m2-emu/ml magnetic fluid and a yC2 μl PBS solution, in addition to a to-be-detected reagent in a mixture of an xS μl, mS-emu/ml magnetic fluid and a yS μl PBS solution, in which the two reagents of known magnetic concentration are respectively referred to as C1 and C2, and the to-be-detected reagent is referred to as S, while meeting with the following requirements:

m1xC1>msxS>m2xC2;

(B) detecting alternatively χac,o signals, denoting mixed-frequency ac magnetic susceptibility χac before association between magnetic nanoparticles and bio-particles, of each of background (without any reagent) and the above-said three reagents in a predetermined sequence of time intervals so as to obtain average values of detected χac,o signals during each interval, which are referred to as χac,o,B, χac,o,C1, χac,o,S, χac,o,C2 for background, C1, S, and C2, respectively;
(C) calculating a new χac,o value, i.e. χac,cal, for S, a to-be-detected reagent via




  
    
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(D) repeating steps (B) and (C) to find the χac,cal for a next run, and then finding a time dependent χac,cal for S.
With the provision of the time dependent χac,cal for S, capable of reducing the coefficient of variation in the ac magetic susceptibility for the reagent to an amount of 0.17% after calibrating the original χac,o to χac,cal, the method of the invention is able to stabilize the ac magnetic susceptibility of magnet reagent without using control modules.
Other objectives, advantages, and novel features of the invention will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is an illustration of mechanism for immunomagnetic reduction assay (a) before and (b) after the association between magnetic nanoparticles and biotargets;
FIG. 2 shows distribution for the diameter of dextran-coated Fe3O4 particles;
FIG. 3 illustrates time dependent (a) temperature around reagent (b) detected χac,o;
FIG. 4 shows sequence for detecting the ac magnetic susceptibility of background and reagents according to the invention;
FIG. 5 shows time dependent χac,cal after calibrating χac,o to χac,cal via Eq. (7) according to the invention;
FIG. 6 shows time-dependent (a) detected ac magnetic susceptibility χac,o and (b) calibrated ac magnetic susceptibility χac,cal of the to-be-detected reagent.



DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
A method to reduce the variation in χac,o of reagent according to the invention comprises the following steps.
1. Preparing two reagents of known magnetic concentration:
For a preferred embodiment, a first one is a mixture of an xC1 μl, mS-emu/ml magnetic fluid and a yC1 μl PBS (Phosphate Buffer Saline) solution. A second one is a mixture of an xC2 μl, mS-emu/ml magnetic fluid and a yC2 μl PBS solution. These two reagents are referred to as C1 and C2, respectively. Notably, a to-be-detected reagent is a mixture of an xS μl, mS-emu/ml magnetic fluid and a yS μl PBS solution. The to-be-detected reagent is referred to as S. It is suggested to follow these requirements:

m1xC1>msxS>m2xC2  (5)

In a preferred embodiment, xC1=42, yC1=58, xC2=38, yC2=62, xS=40, yS=60, and m1=m2=ms=0.1.
2. Detecting alternatively the χac,o signals of background and these three reagents:
As illustrated in FIG. 4, showing sequence for detecting the ac magnetic susceptibility of background and reagents according to the invention, for the time interval from 0 to 1 minute (Interval 1), the χac,o signal of the background (without any reagent) is detected. From the time interval from 1 to 2 minutes (Interval 2), the the χac,o signal of C1 is detected. From the time interval from 2 to 3 minutes (Interval 3), the the χac,o signal of S is detected. From the time interval from 3 to 4 minutes (Interval 4), the the χac,o signal of C2 is detected. The average values of detected χac,o signals during each interval are referred as χac,o,C1, χac,o,S, χac,o,C2 for C1, S, and C2, respectively.
3. Calculating the new χac,o value for S via




  
    
      
        
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4. Repeating steps 2-3 to find the χac,cal for the next run, and then finding the time dependent χac,cal for S:
The results for the time dependent χac,cal for S are plotted in FIG. 5, showing time dependent χac,cal after calibrating χac,o to χac,cal via Eq. (6) according to the invention. It is worthy noting that the original χac,o are the data shown in FIG. 3(b). The maximum and the minimum values for χac,cal in FIG. 5 are 40.73 and 40.46, respectively. The mean value and the standard deviation for the time dependent χac,cal are 40.57 and 0.07, respectively. This results in a value of 0.17% for the coefficient of variation in χac,cal. As compared with the results shown in FIG. 3(b) and FIG. 5, the coefficient of variation in the ac magnetic susceptibility for reagent is reduced from 9.05% to 0.17% after calibrating the original χac,o to χac,cal. As such, the variation in the ac magnetic susceptibility of reagent in the instant invention is much lower than the lowest level for the IMR signal (=0.80%).
In a further preferred embodiment, m1=m2=ms=0.1, xC1=44, yC1=56, xC2=36, yC2=64, xS=40, and yS=60. These reagents are put into the analyzer for detecting the time-dependent ac magnetic susceptibility χac,o for the to-be-detected reagent. The detected time dependent χac,o is shown in FIG. 6(a). It can be found that the χac,o varies significantly with time. According to the data shown in FIG. 6(a), the maximum and the minimum values for χac,o are 130.6 and 110.4, respectively. The mean value and the standard deviation for the detected χac,o's are 118.8 and 5.28. Thus, the coefficient of variation for the time dependent χac,o is 4.44%. This means that the noise level for IMR is 4.44%.
By using the method to reduce the variation in χac,o of to-be-detected reagent developed in this work, the results for the time dependent χac,cal for the to-be-detected reagent S are plotted in FIG. 6(b). The maximum and the minimum values for χac,cal in FIG. 6(b) are 40.00 and 39.79, respectively. The mean value and the standard deviation for the time dependent χac,cal are 39.91 and 0.05. This results in a value of 0.13% for the coefficient of variation in χac,cal. As compare the results shown in FIG. 6(b) and FIG. 6(a), the coefficient of variation in the ac magnetic susceptibility for the to-be-detected reagent is reduced from 4.44% to 0.13% after calibrating the original χac,o to χac,cal.
Although the present invention has been explained in relation to its preferred embodiment, it is to be understood that any other possible modifications and variations can be made without departing from the scope of the invention as hereinafter claimed.

## Claims

1. A method for stabilizing ac magnetic susceptibility of a magnetic fluid, comprising the following steps:
(A) preparing two reagents of known magnetic concentration, including a first one in a mixture of an xC1 micro liter, m1-emu/ml magnetic fluid and a yC1 micro liter Phosphate Buffer Saline solution and a second one in a mixture of an xC2 micro liter, m2-emu/ml magnetic fluid and a yC2 micro liter Phosphate Buffer Saline solution, in addition to a to-be-detected reagent in a mixture of an xS micro liter, mS-emu/ml magnetic fluid and a yS micro liter Phosphate Buffer Saline solution, in which the two reagents of known magnetic concentration are respectively referred to as C1 and C2, and the to-be-detected reagent is referred to as S, while meeting with the following requirements:


m1xC1>mSxS>m2xC2;


(B) detecting alternatively χac,o signals, denoting mixed-frequency ac magnetic susceptibility χac before association between magnetic nanoparticles and bio-particles, of each of background, being without any reagent, and the above-said three reagents in a predetermined sequence of time intervals so as to obtain average values of detected χac,o signals during each interval, which are referred to as χac,o,B, χac,o,C1, χac,o,S, χac,o,C2 for background, C1, S, and C2, respectively;
(C) calculating a new χac,o value, i.e. χac,cal, for S, a to-be-detected reagent via





  
    
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(D) repeating steps (B) and (C) to find the χac,cal for a next run, and then finding a time dependent χac,cal for S.

2. The method for stabilizing ac magnetic susceptibility of a magnetic fluid as claimed in claim 1, wherein xC1=44, yC1=56, xC2=36, yC2=64, xS=40, yS=60 and ms=0.1.

3. The method for stabilizing ac magnetic susceptibility of a magnetic fluid as claimed in claim 1, wherein xC1=42, yC1=58, xC2=38, yC2=62, xS=40, yS=60 and ms=0.1.

4. The method for stabilizing ac magnetic susceptibility of a magnetic fluid as claimed in claim 1, wherein at the predetermined sequence of time intervals, in a first time interval from 0 to 1 minute (Interval 1), the χac,o signal of the background, being without any reagent, is detected, from a second time interval from 1 to 2 minutes, the χac,o signal of C1 is detected, from a time interval from 2 to 3 minutes, the χac,o signal of S is detected, and from a time interval from 3 to 4 minutes, the χac,o signal of C2 is detected.

5. The method for stabilizing ac magnetic susceptibility of a magnetic fluid as claimed in claim 1, wherein a maximum and a minimum values for the time dependent χac,cal for S are 40.73 and 40.46, respectively and a mean value and a standard deviation for the time dependent χac,cal are 40.57 and 0.07, respectively, resulting in a value of 0.17% for a coefficient of variation in χac,cal.