Abstract:
A method to quantitatively measure an amount of bio-molecules in a sample includes providing a solution having magnetic nanoparticles; coating bioprobe molecules to surfaces of the magnetic nanoparticles in the solution; measuring a first alternating current (ac) magnetization of the solution at a mixture frequency (γf 1 +βf 2 ), wherein γ or β is independently an integer larger than zero; adding a sample containing the bio-molecules to be detected to the solution, so that the biomolecules in the sample conjugate with the bioprobe molecules coated on the nanoparticles; and measuring a second ac magnetization of the solution at the mixture frequency (γf 1 +βf 2 ) after adding the sample and incubation, so as to obtain an ac magnetization reduction at the mixture frequency (γf 1 +βf 2 ) between the first and the second magnetization to determine the amount of the bio-molecules.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application is a continuation-in-part of U.S. application Ser. No. 11/164,275, filed on Nov. 16, 2005, now pending. The entirety of the above-mentioned patent application is hereby incorporated by reference herein and made a part of this specification. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    1. Field of Invention 
         [0003]    The present invention is related to measuring magnetization of magnetic fluid. More particularly, the present invention relates to device for measuring ac magnetization of materials and method for detecting bio-molecules. 
         [0004]    2. Description of Related Art 
         [0005]    Magnetic fluid is a colloid solution having magnetic nanoparticles dispersed in solvent. The material of magnetic nanoparticles is usually ferromagnetic. Thus, each magnetic nanoparticle owns permanent magnetic moment. In order to disperse stably magnetic nanoparticles in solvent, magnetic nanoparticles are coated with surfactant. For example, hydrophilic organic material is used for surfactant to disperse magnetic nanoparticles into aqueous solution. With aid of surfactant and nano-scale size, magnetic nanoparticles can be dispersed individually in solvent. Due to thermal energy, individual magnetic nanoparticles experience Brownian motion. Although each magnetic nanoparticle is ferromagnetic, i.e. exhibiting permanent magnetic moment, the directions of magnetic moments of magnetic nanoparticles are isotropic in liquid under zero magnetic field, so that the resultant magnetic moment of magnetic nanoparticles in liquid is zero under zero magnetic field. However, as a magnetic field is applied to magnetic fluid, magnetic moment of each magnetic nanoparticle tends to be aligned with the direction of the applied magnetic field. The theoretical analysis for the resultant magnetic moment (hereafter referred as to magnetization) M of magnetic fluid under an applied magnetic field H at temperature T can be expressed as Langevin function 
         [0000]        M (ξ)= M   o (cothξ−1/ξ).   (1) 
         [0006]    In Eq. (1), M o , in which M o =Nm, N is the total numbers of magnetic nanoparticles and m is the averaged magnetic moment of a magnetic particle, denotes the saturated magnetization, and ξ can be written as 
         [0000]      ξ=μ o mH/k B   T,   (2) 
         [0000]    where H is the applied magnetic field, k B  is Boltzmann constant, μ 0  is permeability of free space, and T represents the measurement temperature. 
         [0007]    According to Eq. (1) and Eq. (2), at a given temperature T, the magnetization M of magnetic fluid increases monotonously with the increasing strength H of magnetic field, and then reaches to a saturated value under high H&#39;s. This saturated magnetization is M o  in Eq. (1). When the applied magnetic field H is removed, i.e. H=0, the magnetization of magnetic fluid vanishes. The reversely zero magnetization of magnetic fluid as quenching an applied magnetic field is contributed by the directional randomization of magnetic moment of individual magnetic nanoparticles undergoing Brownian motion in liquid. This feature is so-called superparamagnetism. 
         [0008]    In case of weak magnetic field being in several Gauss at room temperature (T about 300 K.), ξ is around 10 −3  to 10 −2 . Thus, the M in Eq. (1) can be expanded around ξ being zero via Taylor expansion and is written as 
         [0000]        M (ξ→0)= M (0)+ M   (1) (0)·ξ+ M   (2) (0)·ξ 2   +M   (3) (0)·ξ 3   +M   (4) (0)·ξ 4   +M   (5) (0)·ξ 5 +. . .,   (3) 
         [0000]    where M (n)  denotes the n th  derivation of M with respect to ξ at ξ=0. One can find that the even-n th -derivation terms on the right-hand side of Eq. (3) become zero, and M (1) =0.32, M (3) =−0.12. Eq. (3) can be expressed as 
         [0000]        M (ξ→0)=0.32 M   o μ o mH/k B   T− 0.12 M   o (μ o mH/k B   T ) 3   +O   5 (μ o mH/k B   T)+   (4) 
         [0009]    The fifth order of O 5  on the right-hand side in Eq. (4) denotes the term of power 5 of μ o mH/k B T. If the applied magnetic field is generated by alternative-current (ac) and shows a frequency f o , it can be found that the M exhibits non-zero components at frequencies of αf o , where α is positive odd integers. Consequently, magnetic fluid shows magnetization having frequencies of not only f o  but also αf o  under a weak ac magnetic field with frequency f o . 
         [0010]    In Eq. (1) or (4), M o  is proportional to the total numbers N of individual magnetic nanoparticles showing response to the applied ac magnetic field. Thus, in a given volume of magnetic fluid and under a fixed weak ac magnetic field having frequency f o , the amplitude of αf o -component of the magnetization M spectrum decreases when the total numbers N of individual magnetic nanoparticles is reduced. The reduction in the total numbers N of individual magnetic nanoparticles showing a response to the applied ac magnetic field can be achieved by making magnetic nanoparticles clustered or larger through certain reactions in liquid. For example, the certain reactions can be the association between bio-probes and bio-targets in liquid. In such case, bio-probes are coated onto individual magnetic nanoparticles via the binding to the surfactant. Thus, magnetic nanoparticles become bio-functional and are able to bind with conjugated bio-targets. 
         [0011]    For instance, the antibody acts as bio-probes and is coated onto individual magnetic nanoparticles in liquid. These bio-functionalized magnetic nanoparticles can bind with conjugated antigens. Due to the association between antigens and antibodies on individual magnetic nanoparticles, magnetic nanoparticles become clustered or larger. Hence, the total number N of individual magnetic nanoparticles in response to an applied ac magnetic field at certain fixed frequency is definitely reduced. So, it can be deduced that the amplitude of αf o -component of the magnetization M of bio-functionalized magnetic fluid decreases when magnetic nanoparticles bind with bio-targets. Furthermore, the decreasing in the amplitude is enhanced when more individual magnetic nanoparticles bind with bio-targets. Hence, the amount of bio-targets can be determined by measuring the reduction in the αf o -component of the magnetization M of bio-functionalized magnetic fluid. This is the fundamental mechanism for such bio-assay technology as immunomagnetic reduction (IMR). 
         [0012]    In order to measure the ac magnetization of the sample, several conventional apparatus have been proposed.  FIG. 1  schematically shows the conventional architecture to measure the magnetization of magnetic fluid under an ac magnetic field. An excitation solenoid  102  is driven by an ac current generator  100  at frequency f o , so as to generate the ac magnetic field. A pick-up solenoid  104  is co-axially located inside the excitation solenoid  102 . The pick-up solenoid  104  is referred as to magnetometer type. The magnetic fluid  108  is disposed inside the pick-up solenoid  104 . The coil  106  is formed by the solenoids  102  and  104 . The ac current generator  100  applies ac current at the frequency f o  to the solenoid  102  of coil  106 . Due to varying magnetic field, the pick-up solenoid  104  of coil  106  is induced ac voltage for output. However, the output of the ac voltage is relating to the magnetic fluid  108 . As the ac magnetic field of frequency f o  is applied, the magnetic fluid  108  is induced to generate ac magnetizations of various frequencies αf o , α=1, 3, 5, . . . n. The ac magnetizations are detected with the pick-up solenoid  104  of coil  106 , which converts the signals from magnetization to voltage. Thus, ac voltages of frequencies αf 0  are output from the pick-up solenoid  104  of coil  106  to an electronic circuit  110 . The electronic circuit  110  processes the voltage signals, with respect to various frequency components, to obtain the quantity at the component with the target frequency α T f o . 
         [0013]    However, the measurement architecture shown in  FIG. 1  has disadvantages. Firstly, in addition to the magnetizations generated by magnetic fluid, the ambient signals can be detected by the pick-up solenoid. Secondly, the ac magnetic field (at f o ) generated with the excitation solenoid  102  is also probed. Thus, the induced voltage of f o  at the output of the pick-up solenoid  104  is much stronger than those at other frequencies. For the electronic circuit  110 , it usually has amplifying units to amplify the voltage signal at α T f o  for achieving high detection sensitivity. The amplifying units are operation amplifiers, having high-level limitation for the input voltages. The operation amplifiers can not properly work when input voltage is too high. When the input voltage at α T f o  is amplified, the input voltage at f o  is also amplified. With the high-level limitation of operation amplifiers, there is a limitation to amplify the voltage signal at α T f o  in order to keep the total input voltages below the high-level limitation of operation amplifiers. Thirdly, due to the sub-harmonic effect of electronic circuit, there exit output voltages at frequencies of f o , 2f o , 3f o , 4f o , 5f o , . . . etc., when there is input voltage at f o  from the output of the pick-up solenoid  104 . These negative factors cause that the resultant output voltage of α T f o  from the electronic circuit is attributed to the ambient signals, the excitation field, and sub-harmonic signals of electronic circuit. Therefore, the final output voltage at α T f o  is not reliable, or even false. 
         [0014]    To overcome the disadvantages in  FIG. 1 , another conventional design to measure the induced ac magnetization of magnetic fluid is proposed.  FIG. 2  schematically shows the conventional architecture to measure the magnetization of magnetic fluid under an ac magnetic field. In  FIG. 2 , the pick-up solenoid  120  includes two sections: upper section and lower section. The coils in these two sections are wired in opposite direction and connected in series. The magnetic fluid  108  is disposed at one of the two sections, such as the upper section. Thus, ambient signals can be simultaneously sensed by these two sections. Voltages can be induced from out-leads of these two sections, and are cancelled with each other. Besides, by well aligning the position of the pick-up solenoid  120  inside the excitation solenoid  102 , the induced voltage at f o  by the ac magnetic field at f o  generated by the excitation solenoid  102  are cancelled for the gradiometer-type pick-up solenoid  120 . In practical cases, it is impossible to completely cancel the induced voltage at f o  by aligning the pick-up solenoid  120  inside the excitation solenoid  102 . But, the input voltage at f o  to the electronic circuit can be greatly reduced for the measurement architecture in  FIG. 2  as compared to that in  FIG. 1 . This means that the amplification in the electronic circuit can be significantly increased when using gradiometer-type pick-up solenoid. However, the existence of input voltage of f o  also generates the sub-harmonic signals to the output as mentioned before. Thus, the signals from the sample at the target frequency α T f o  usually have unwanted components. 
         [0015]    In conclusion, the conventional designs can measure the ac magnetization of magnetic fluid. However, the target frequency is limited to α T f o , multiple of base frequency f o , resulting in unreliable output voltage at α T f o  and their applications are limited. 
       SUMMARY OF THE INVENTION 
       [0016]    In an aspect, the invention provides a method to quantitatively measure an amount of bio-molecules in a sample. The method includes providing a solution having magnetic nanoparticles; coating bioprobe molecules to surfaces of the magnetic nanoparticles in the solution; measuring a first alternating current (ac) magnetization of the solution at a mixture frequency (γf 1 +βf 2 ), wherein γ or β is independently an integer larger than zero; adding a sample containing the bio-molecules to be detected to the solution, so that the biomolecules in the sample conjugate with the bioprobe molecules coated on the nanoparticles; and measuring a second ac magnetization of the solution at the mixture frequency (γf 1 +βf 2 ) after adding the sample and incubation, so as to obtain an ac magnetization reduction at the mixture frequency (γf 1 +βf 2 ) between the first and the second magnetization to determine the amount of the bio-molecules. 
         [0017]    In an aspect, the present invention also provides an apparatus to measure ac magnetization at mixture frequency. The apparatus includes an ac generating unit to generate at least a first ac current with a frequency f 1  and a second ac current with a frequency f 2 . A co-axial solenoid unit is driven by the first ac current and the second ac current to generate a first magnetic field and a second magnetic field. A gradiometer-type pick-up solenoid is disposed within the co-axial solenoid unit, wherein a sample is disposed in the pick-up solenoid for detection an ac magnetization of the sample. Multiple frequency-component signals corresponding to various frequency combinations of f 1  and f 2  are output. A signal processing circuit receives the signals containing various frequency components, wherein the signal processing circuit processes the signals and obtains the ac magnetization of the sample at a target frequency of (γ T f 1 +β T f 2 ). γ T  and β T  are positive integers and the frequency f 1  and the frequency f 2  are two different frequencies generated by the first and the second ac currents, respectively. 
         [0018]    In an aspect, the present invention also provides a method to establish a relationship between an ac magnetization reduction and a bio-molecular concentration, wherein the ac magnetization reduction is a difference of ac magnetic susceptibilities in measured sample before and after the bio-molecules with known concentration are added into the measured sample. The method includes preparing a plurality of samples, wherein each of the samples include a solution having magnetic nanoparticles with coated bioprobe molecules thereon and bio-molecules with known concentration in the solution, wherein each sample has a different bio-molecular concentration. An ac magnetization reduction for each of the samples is measured. Data of the ac magnetization reductions are fitted by a Sigmoid function, such as logistic function, Equation (5) of: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       I 
                        
                       
                           
                       
                        
                       M 
                        
                       
                           
                       
                        
                       R 
                        
                       
                           
                       
                        
                       
                         ( 
                         % 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           A 
                           - 
                           B 
                         
                         
                           1 
                           + 
                           
                             
                               ( 
                               
                                 φ 
                                 
                                   φ 
                                   o 
                                 
                               
                               ) 
                             
                             ρ 
                           
                         
                       
                       + 
                       B 
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where IMR is the ac magnetization reduction in percentage, φ is the bio-molecular concentration in each sample, and A, B, φ o , and ρ are fitting parameters to be fitted out to obtain a fitted curve. An ac magnetization reduction (IMR) for a to-be-measured sample is measured and a target bio-molecular concentration is obtained by using the fitted curve of the Eq. (5). 
         [0019]    In an aspect, the present invention provides a method to observe reaction between magnetic nanoparticles and bio-molecule in a sample. The method comprises providing a solution having magnetic nanoparticles; coating bioprobe molecules to surfaces of the magnetic nanoparticles in the solution; adding a sample containing the bio-molecules to be detected to the solution for an incubation time; and measuring an alternating current (ac) magnetization of the solution at a mixture frequency (γf 1 +βf 2 ) as function of time, wherein γ and β are independently integers larger than zero, f 1  and f 2  are two different frequencies. The ac magnetization is stable in an initial state and a reaction-completion state, but has a difference between the initial state and the reaction-completion state. 
         [0020]    It is to be understood that both the foregoing general description and the following detailed description are exemplary, and are intended to provide further explanation of the invention as claimed. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS  
         [0021]    The accompanying drawings are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification. The drawings illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention. 
           [0022]      FIG. 1  schematically shows the conventional architecture to measure the magnetization of magnetic fluid under an ac magnetic field. 
           [0023]      FIG. 2  schematically shows the conventional architecture to measure the magnetization of magnetic fluid under an ac magnetic field. 
           [0024]      FIG. 3  schematically shows an architecture to measure the magnetization of magnetic fluid under an ac magnetic field, according to an embodiment of the present invention. 
           [0025]      FIG. 4  schematically shows a circuit block diagram for measuring the magnetization of magnetic fluid, according to an embodiment of the present invention. 
           [0026]      FIG. 5  schematically shows a relationship between magnetization versus concentration in a sample to be measured. 
           [0027]      FIG. 6  schematically shows a reaction mechanism between the magnetic nanoparticles coated with bio-probe and the bio-molecule to be measured, according to an embodiment of the present invention. 
           [0028]      FIG. 7  schematically shows a structure of magnetic nanoparticles coated with bio-probe, according to an embodiment of the present invention. 
           [0029]      FIG. 8  schematically shows a reaction expressed by the magnetization as a function of a time, according to an embodiment of the present invention. 
           [0030]      FIG. 9  schematically shows a behavior of IMR (%) versus a virus concentration, according to an embodiment of the present invention. 
           [0031]      FIG. 10  schematically shows a behavior of IMR nor  (%) in normalization versus a concentration of bio-molecule, according to an embodiment of the present invention. 
       
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0032]    In the invention, a method and an apparatus to measure ac magnetization at mixture frequency are proposed. In addition various applications haven been provided. Several embodiments are provided to depict the present invention. However, the present invention is not limited to the provided embodiments. 
         [0033]    In considering the conventional design to measure the ac magnetization, to further reduce the effect from the excitation field and sub-harmonic signals of electronic circuit to the final output voltage at frequency of α T f o , the present invention propose to use a mixed-frequency excitation technology and the compensation mechanism in the electronic circuit. 
         [0034]    For mixed-frequency excitation, there is more than one frequency used for the applied magnetic field. In fact, at-least two magnetic fields having two different frequencies are applied simultaneously. For example,  FIG. 3  schematically shows an architecture to measure the magnetization of magnetic fluid under an ac magnetic field, according to an embodiment of the present invention. In  FIG. 3 , the example producing the mixed-frequency excitation from two frequencies is illustrated. In this situation, there are two excitation solenoids  204 ,  206  aligned co-axially. The two excitation solenoids  204 ,  206  are respectively driven by ac current generators  200 ,  202  as a driving unit. The two ac current generators  200 ,  202  provide currents having different frequencies f 1  and f 2  separately to these two excitation solenoids  204 ,  206 . Thus, H in Eq. (4) can be replaced with H 1 +H 2 , where H 1 =H 1o  cos(2πf 1 t) and H 2 =H 2o  cos(2πf 2 t) with f 1 ≠f 2 . Eq. (4) turns to be 
         [0000]        M (ξ→0)=0.32 M   o   μ   o   m ( H   1   +H   2 )/ k   B   T− 0.12M o (μ o   m/k   B   T ) 3 ( H   1   +H   2 ) 3 +( H   1   +H   2 ) 5   O   5 (μ o   m/k   B   T )+  (6) 
         [0035]    Eq. (6) reveals the fact that M is a combination of components having frequencies αf 1 , αf 2 , and γf 1 +βf 2 , where α is positive odd integers, and β and γ are non-zero integers. The pick-up solenoid  208  and the magnetic fluid  212  can be like the pick-up solenoid  104  and the magnetic fluid  108  in  FIG. 1 , for example. The coil  210  can be formed by solenoids  204 ,  206 , and  208 . It is clear that, in addition to the odd sub-harmonic frequencies of f 1  and f 2 , the components having such frequencies as the linear combinations of f 1  and f 2  can be relating to the magnetization of magnetic fluid under the mixed-frequency excitation. If the base frequencies f 1  and f 2 , are linear independent, the mixed-frequency components of the output signal from coil  210  are not be disturbed with the sub-harmonic effect in the electronic circuit  214  when these components are amplified with electronic circuit  214 . Furthermore, by suitably selecting f 1  and f 2 , the target frequency γ T f 1 +β T f 2  can be far away from those popularly used in telecommunication, city electric power system, etc. Thus, the contribution from ambience can be prevented to the component of γ T f 1 +β T f 2  for the magnetization of magnetic fluid under mixed-frequency excitation. 
         [0036]    Usually, the amplitudes of the components of γf 1 +βf 2  are much weaker then those of αf 1  and αf 2 , α=1, 2, 3, . . . n. So, the electronic circuit  214  needs to be designed to amplify the signals of components of γf 1 +βf 2 . However, as mentioned above, the sub-harmonic components (i.e. αf 1  and αf 2 ) lead to a bad performance in terms of amplification for the electronic circuit because of the high-level limitation of input signals to operation amplifiers in the electronic circuit  214 . Hence, a compensation mechanism in the electronic circuit  214  is included to cancel the components of αf 1  and αf 2 . 
         [0037]    The block diagram of the electronic circuit designed here is shown in  FIG. 4 . Actually, the electronic circuit in  FIG. 4  also includes the circuit for triggering ac current generators. The triggering signals having frequencies f 1  and f 2  respectively are generated with DSP, which signals are digital type and are converted to analog type through digital-to-analog converter (DAC)  252 . The analog triggering signals f 1  and f 2  make ac current generators  200  and  202  to provide an ac current having frequency f 1  to excitation solenoid  1   204  and an ac current having frequency f 2  to excitation solenoid  2   206  via a power amplifier  254 . The output signals from the gradiometer-type pick-up solenoid  208  are composed of frequencies of αf 1 , αf 2 , and γf 1 +βf 2 . All of these components are processed with the filtering/amplifying/compensating in the electronic circuit  214  to produce the target component at the mixed frequency γ T f 1 +β T f 2 , γ T  and β T  are positive integers. Generally, different choice to the γ T  and β T  to obtain the mixed frequency may have different strength of signal being extracted out. The mixed frequency γ T f 1 +β T f 2  is a general condition and the quantities of γ T  and β T  are the design choices. 
         [0038]      FIG. 4  schematically shows a circuit block diagram for measuring the magnetization of magnetic fluid, according to an embodiment of the present invention. In  FIG. 4 , the apparatus in  FIG. 3  can be shown in electronic block diagram. The electronic circuit  214  in  FIG. 3  includes the circuit  260 , which includes a digital signal processing (DSP) unit  250 , amplifiers  262 ,  270 ,  280 , filters  264 ,  272 ,  274 ,  282 , ADC&#39;s  266 ,  276 ,  284  and digital-to-analog converters (DAC&#39;s)  268 ,  278 , form at least one stage to perform functions of filtering, amplifying, and compensation. In the example, n stages of signal processing are performed. In practical, n can be from 2 to five hundreds. Each filtering/amplifying/compensating part has the amplification factor from 1 to 1000 where 1 means no amplifier being used. For each unit, there is an amplifier and a bandpass filter with a center frequency at the target frequency. 
         [0039]    The DSP unit  250  provides the harmonic frequencies of f 1  and f 2  as the base frequencies per design choice. The frequencies of f 1  and f 2  is converted into analog signal by the DAC  252  to inform the power amplifier  254  to control the ac current generators  200  and  202  for producing ac currents. As a result, the two excitation solenoids  204  and  206  are driven by the ac currents with different base frequencies of f 1  and f 2 . The pick-up solenoid  208  with the magnetic fluid induces the signal spectrum with various resonant components at frequency of αf 1 , αf 2 , and γf 1 +βf 2 , α, γ and β are positive integers, in which one of the components of γf 1 +βf 2  is to be extracted out and amplified as the target frequency γ T f 1 +β T f 2 . 
         [0040]    The signals of components of αf 1 , αf 2 , and γf 1 +βf 2  from the pick-up solenoid  208  are input to the 1 st  stage amplifier (AMP  1 )  262 . All of these components are amplified. However, the filter  1   264  with a central filtering frequency around the target frequency γ T f 1 +β T f 2  filters the other signal components. The 1 st  ADC  1 A  266  converts analog signal into digital signal, which is input to the DSP  250  for finding amplitudes and phases of αf 1  and αf 2 , especially αf 1  and αf 2  near the central frequency, β T f 1 +β T f 2 . To compensate (or offset) the components of αf 1  and αf 2 , the DSP unit  250  generates out-of-phase signals of αf 1  and αf 2  to cancel the components of αf 1  and αf 2  of amplified signals via a digital-to-analog converter DAC  1 B  268 . The 1 st -stage output signal and the out-of-phase signals of αf 1  and αf 2  of the DAC  1 B  268  are output to the 2 nd -stage amplifier  270 , in which the out-of-phase signals can be, for example, an invert phase so as to suppress the other signal component other than the target signal component with the frequency of γ T f 1 +β T f 2 . Thus, the relative amplitude of γ T f 1 +β T f 2  with respect to other components increases. As a result, the amplitudes of αf 1  and αf 2  are not significantly amplified, and may even be reduced due to the compensation process. Moreover, the sub-harmonic effect of electronic circuit is also suppressed. Hence, it is possible to keep the total intensity of the output signal from the 1 st  unit below the high-level limitation of operation amplifiers in the 2 nd -stage amplifier  270 . By using cascading filtering/amplifying/compensating units, the component of target frequency γ T f 1 +β T f 2  can be greatly amplified. The final output signal of all components of αf 1 , αf 2 , and γf 1 +βf 2  is led to DSP via ADC nA  284 . The amplitude of the target component at γ T f 1 +β T f 2  is analyzed and output from DSP unit  250 . 
         [0041]    An example to show the feasibility of the mixed-frequency excitation and filtering/amplifying/compensating electronic circuit is given. The sample to be detected is water-based dextran coated Fe 3 O 4  magnetic fluid in this example, as to be described in  FIG. 7 . In addition to Fe 3 O 4 , the other materials, such as MnFe 2 O 4 , CoFe 2 O 4 , Fe 2 O 3 , . . ., and so on, can also be used for magnetic nanoparticles. Other hydrophilic material such as protein A, protein G, etc. can be used to replace dextran coated onto the surface of magnetic nanoparticles. The mean diameter of magnetic nanoparticles in magnetic fluid is 56 nm for this example. It should be noted that the mean diameter of magnetic nanoparticles are not limited to 56 nm. General speaking, the mean diameter of magnetic nanoparticles can range from 5 nm to 500 nm. The frequencies of f 1  and f 2  can vary from 10 Hz to 10 6  Hz, for example. The output amplitude of target component at γ T f 1 +β T f 2  is measured by using the filtering/amplifying/compensating electronic circuit in  FIG. 4  for magnetic fluids of various concentrations from zero to 0.3 emu/g, or even to higher concentrations. 
         [0042]      FIG. 5  schematically shows a relationship between magnetization versus concentration in a sample to be measured. The magnetic fluids in various concentrations from zero to 0.3 emu/g, are measured by the apparatus in  FIG. 3 . It is noted that the highest concentration of magnetic fluid under detection is not limited to 0.3 emu/g. The higher the concentration is, the more the individual magnetic nanoparticles exist in magnetic fluid. It is expected that the magnetization M T  of the target component at γ T f 1 +β T f 2  increases as the concentration of magnetic fluid increases in a linear relation. 
         [0043]    The apparatus in  FIG. 3  with the circuit architecture in  FIG. 4  can have various applications, such as assay on bio-molecules via immunomagnetic reduction. As evidenced with the results in  FIG. 5 , the M T  become less as the concentration of magnetic fluid, i.e. the number of individual magnetic nanoparticles in liquid, is reduced. The apparatus of the present invention can precisely measure the magnetization of the magnetic fluid and observe the variation. By utilizing this property, a method to detect bio-molecules in liquid is developed. In such method, bio-probes like anti-bodies are coated onto magnetic nanoparticles. 
         [0044]      FIG. 6  schematically shows a reaction mechanism between the magnetic nanoparticles coated with bio-probe and the bio-molecule to be measured, according to an embodiment of the present invention. Thus, the magnetic nanoparticles are specifically bio-functionalized and are able to associate with target bio-molecules. Due to the association, portion of individual bio-functionalized magnetic nanoparticles become physically larger or clustered. In  FIG. 6(   a ), when the magnetic nanoparticles with the coated anti-body do not react with the bio-molecule to be detected, the magnetization is the initial state at M T,o . The magnetic nanoparticles are small and the rotation is easier. In  FIG. 6(   b ), however, if the nanoparticles have reacted with the target bio-molecule, some magnetic nanoparticles are becoming larger or joined together in a cluster. In this situation, the magnetization M T,φ  of the sample is supposed to be less than that of the initial state M T,o , when bio-functionalized magnetic nanoparticles bind with target bio-molecules in magnetic fluid. This is the mechanism to perform assay method as ImmunoMganetic Reduction (IMR). 
         [0045]    An example to show the reduction in M T  caused by the association between bio-functionalized magnetic nanoparticles and target bio-molecules is given.  FIG. 7  schematically shows a structure of magnetic nanoparticles coated with bio-probe, according to an embodiment of the present invention. In  FIG. 7 , for a single magnetic nanoparticle, it can be Fe 3 O 4 , for example. The magnetic nanoparticle is coated with dextran and then bio-probe (or antibody), such as polyclonal anti-H1N2 is used in this example. In addition to polyclonal antibodies, monoclonal antibodies can also be used for bio-probe. The H1N2 is one of swine-influenza viruses as the bio-molecule to be detected in amount. To detect the target bio-molecule H1N2, 40-μl magnetic reagent of 0.02 emu/g in concentration (i.e. magnetic fluid having anti-H1N2 bio-functionalizing magnetic nanoparticles) is mixed with 60-μl H1N2 solution, in which the concentration is 0.032 HAU/50-μl in this example. After mixing, the time-dependence M T  of the mixture of magnetic reagent and H1N2 solution is detected by using the apparatus schematically shown in  FIGS. 3 and 4 .  FIG. 8  shows a reaction expressed by the magnetization as a function of a time, according to an embodiment of the present invention. In  FIG. 8 , the round dots denote the M T  of the mixture of magnetic reagent and H1N2 solution before incubation. The dots distributed at a stable state in time. The M T  before incubation is denoted with M T,o . The time-average value is taken for the collected data 2 hours for example. The M T,o  is measured as 66.18 under the target mixed frequency of γ T f 1 +β T f 2 . The cross dots correspond to the processes that the bio-functionalized magnetic nanoparticles are binding with target bio-molecules H1N2. After the binding/incubation at room temperature, such as 22° C. The M T,φ  represents the averaged M T  for the data after the mixture of magnetic reagent and H1N2 solution has been incubated and reached to another stable state, as shown with square dots. The cross dots represent the transition state. As described in  FIG. 6 , the magnetization M T,φ  becomes smaller after a sufficient incubation time. It must be noted the incubation time generally depends on the quality of bio-probe and the incubation temperature. The incubation temperature can be, for example, from 18° C. to 45° C. and the incubation time can be, for example, 1 minute to 5 hours. If the incubation temperature is increased, the incubation time is expected to be reduced. The time-average value of the square dots is around 64.54 for M T,φ . The significant reduction in M T  evidences the conjugation between bio-functionalized magnetic nanoparticles and bio-molecules H1N2. Moreover, the IMR signal can be obtained as 2.48% via 
         [0000]        IMR (%)=( M   T,o   −M   T,φ )/ M   T,o ×100%.   (7) 
         [0000]    For several tests, the mean value and the standard deviation are 2.48% and 0.09%, respectively. The result approves the presumption made in the present invention. 
         [0046]    In further studies, various concentrations of bio-molecule have been measured in IMR (%).  FIG. 9  shows a behavior of IMR (%) versus a virus concentration, according to an embodiment of the present invention. In  FIG. 9 , the relationship between IMR and the concentration of target bio-molecules, such as virus of H1N2 in this example, is investigated. At concentrations lower than 3×10 −4  HAU/50-μl, IMR signals are near the noise level of the detecting device. As the concentration of H1N2 is higher than 3×10 −4  HAU/50-μl, IMR signal increases exponentially with the increasing concentration of H1N2, and then almost reaches to a saturated value at high concentrations. It is found in the present invention that the relationship between IMR and the concentration φ of target bio-molecules H1N2 in  FIG. 9  behaves following Sigmoid function as the equation (8): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       I 
                        
                       
                           
                       
                        
                       M 
                        
                       
                           
                       
                        
                       R 
                        
                       
                           
                       
                        
                       
                         ( 
                         % 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           A 
                           - 
                           B 
                         
                         
                           1 
                           + 
                           
                             
                               ( 
                               
                                 φ 
                                 
                                   φ 
                                   o 
                                 
                               
                               ) 
                             
                             ρ 
                           
                         
                       
                       + 
                       B 
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where the parameter A in Eq. (8) corresponds to the noise level of this assay and B denotes the saturated IMR signal at high concentrated target bio-molecules. Through fitting the data points in  FIG. 9  to Eq. (8), A, B, φ o , and ρ can be found as 1.06, 3.65, 0.024, and 0.64, respectively. The correlation coefficient R 2  is 0.997 for that in  FIG. 9 . So, the measured quantity of IMR as a function of concentration φ of bio-molecule to be detected is very high and is well defined by Eq. (8). 
         [0047]    The logistic behavior expressed with Eq. (8) for the IMR-φ o  curve is found not only H1N2, but also for other kinds of bio-molecules. The bio-molecules can include, for example, proteins, viruses, nuclei acids, and even chemicals. Of course, the parameters A, B, φ o , and ρ may vary for different kinds of target bio-molecules. However, according to the investigation of the present invention, an universal curve for IMR-φ o  relationships of different bio-molecules or chemicals by scaling IMR to (IMR-A)/(B-A), and φ to φ/φ o  can describe various samples in the same curve in Eq. (8), which is further expressed into Eq. (9): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       I 
                        
                       
                           
                       
                        
                       M 
                        
                       
                           
                       
                        
                       
                         R 
                         nor 
                       
                     
                     = 
                     
                       
                         
                           ( 
                           
                             
                               I 
                                
                               
                                   
                               
                                
                               M 
                                
                               
                                   
                               
                                
                               R 
                             
                             - 
                             A 
                           
                           ) 
                         
                         / 
                         
                           ( 
                           
                             B 
                             - 
                             A 
                           
                           ) 
                         
                       
                       = 
                       
                         1 
                         - 
                         
                           1 
                           
                             1 
                             - 
                             
                               Φ 
                               ρ 
                             
                           
                         
                       
                     
                   
                   , 
                   
                     Φ 
                     = 
                     
                       φ 
                       / 
                       
                         
                           φ 
                           o 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0048]    In Eq. (9), the normalized IMR, denoted as IMR nor  is a function of the normalized concentration Φ without parameters of A, B and φ o . The only parameter to be fitted is ρ in a general form.  FIG. 10  schematically shows a behavior of IMR nor  in normalization versus a normalized concentration of bio-molecules, according to an embodiment of the present invention. In  FIG. 10 , several samples are measured to produce the curve like that in  FIG. 9 . The results show that the universal curve for assaying various bio-molecules. IMR nor  (%) titled in the y axis in  FIG. 10  is (IMR-A)/(B-A) in unit of percents. The parameters A, B, φ o , and ρ for the assays on various bio-molecules shown in  FIG. 10  are tabulated in Table 1. 
         [0000]    
       
         
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
             
             
               
                   
                   
               
               
                   
                 Parameter 
               
             
          
           
               
                 Bio-molecule 
                 Antibody type 
                 A 
                 B 
                 φ o   
                 ρ 
               
               
                   
               
             
          
           
               
                 H1N2 
                 Polyclonal 
                 1.06 
                 3.65 
                 0.024 
                 0.64 
               
               
                 H3N1 
                 Polyclonal 
                 0.96 
                 5.34 
                 0.060 
                 0.50 
               
               
                 Chloramphenicol (CAP) 
                 Monoclonal 
                 0.65 
                 6.26 
                 2.24 
                 0.94 
               
               
                 Leuco-malachite green 
                 Monoclonal 
                 0.75 
                 8.86 
                 1.78 
                 1.01 
               
               
                 (LMG) 
               
               
                 GST-TRIM33 
                 Polyclonal 
                 0.63 
                 3.23 
                 69.46 
                 0.86 
               
               
                 GM-CSF 
                 Monoclonal 
                 0.81 
                 14.53 
                 0.819 
                 0.77 
               
               
                   
               
             
          
         
       
     
         [0049]    In other words, Eq. (9) can be the general curve to describe various bio-molecules. In the practical applications, one can measure the IMR for a sample with respect to a specific bio-molecule by the apparatus as, for example, shown in  FIGS. 3 and 4 . Then, the concentration φ of the bio-molecule to-be-detected can be obtained, according to Eq. (8) or Eq. (9) and a prepared table. The bio-probe provider may prepare the parameter table based on Eq. (8) or Eq. (9), so that the user can simply measure the concentration of the bio-molecule by measuring the quantities IMR. The measuring apparatus can be, for example, the apparatus in  FIG. 3  and  FIG. 4  with solenoids to produce ac magnetic field at the mixed frequency. However, the quantities IMR may be measured by other manner without limited to the solenoid-base. The apparatus in  FIG. 3  and  FIG. 4  is not the only choice in the present invention to measure the IMR. 
         [0050]    It will be apparent to those skilled in the art that various modifications and variations can be made to the structure of the present invention without departing from the scope or spirit of the invention. In view of the foregoing descriptions, it is intended that the present invention covers modifications and variations of this invention if they fall within the scope of the following claims and their equivalents.