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The comparison of magnetic circuits used in magnetic hyperthermia
Author’s Accepted Manuscript The comparison of magnetic circuits used in magnetic hyperthermia Andrzej Skumiel, Błażej Leszczyński, Matus Molcan, Milan Timko www.elsevier.com/locate/jmmm
PII: DOI: Reference:
S0304-8853(16)30690-4 http://dx.doi.org/10.1016/j.jmmm.2016.07.018 MAGMA61630
To appear in: Journal of Magnetism and Magnetic Materials Received date: 17 May 2016 Revised date: 1 July 2016 Accepted date: 12 July 2016 Cite this article as: Andrzej Skumiel, Błażej Leszczyński, Matus Molcan and Milan Timko, The comparison of magnetic circuits used in magnetic hyperthermia, Journal of Magnetism and Magnetic Materials, http://dx.doi.org/10.1016/j.jmmm.2016.07.018 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
The comparison of magnetic circuits used in magnetic hyperthermia
Andrzej Skumiel1, Błażej Leszczyński1,2, Matus Molcan3, Milan Timko3*
Institute of Acoustics, Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland,
1
NanoBioMedical Centre at Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
2
Institute of Experimental Physics, SAS, Watsonova 47, 040 01 Košice, Slovak Republic
3
*
Corresponding author: Tel.: +421 55 792 2260; fax: +421 55 633 62 92. [email protected]
Abstract The magnetic nanoparticle hyperthermia experiments require a precise system of magnetic field generation. In this article we present the design of three circuits that can generate an alternating magnetic field (the double-layer solenoid, Helmholtz coils, the inductor with C-shaped ferromagnetic core) and one system of rotating magnetic field. The theoretical calculations have been made to compare the magnetic field intensity distribution along the axis of the coils. Also the inhomogeneity of the magnetic field was determined. Similar calculations have been made for ferromagnetic core inductor. It was also shown the relationship between the intensity of magnetic field and the air gap width of ferrite core. Moreover, it was made a proposal of rotating magnetic field generator consisting of three pairs of phase-tuned inductors. In the experimental section we presented the results of calorimetric measurements performed on water dispersion of SPIONs.
Graphical abstract. The three circuits generating the alternating magnetic field (the double-layer solenoid, Helmholtz coils, the inductor with C-shaped ferromagnetic core) and one system of rotating magnetic field that can be used in the field of magnetic hyperthermia experiments.
Keywords: Magnetic hyperthermia, Specific absorption rate, Two-layer solenoid, Helmholtz coils, Rotating magnetic field, Magnetic hyperthermia setups
1
1. Introduction The main trend in the magnetic hyperthermia research is focused on the design and synthesis of biocompatible magnetic fluid (MF) that exhibits the best heating efficiency. It is mainly motivated by possible in vivo applications of magnetic hyperthermia. Heating of magnetic fluid with the use of alternating magnetic field (AMF) is used to treat tissues containing tumor cells. Such cells are more temperature-sensitive than normal cells and increased temperature (45 42°C) makes tumor cells to be more responsive for radio- and chemotherapy. Degenerated cells reduce its multiplication rate in raised temperatures [1]. Magnetic hyperthermia allows a local temperature increase – the temperature rise is observed only within the volume containing magnetic nanoparticles (MNP) and closely adjacent tissues [2]. There are several designs of magnetic field generators used in experimental studies on magnetic hyperthermia. Custom made and commercial setups always contain one of the following components: single or multilayer solenoid, flat coil, Helmholtz coils or systems with ferrite parts. They are designed to generate AMF of high amplitude which is later converted into heat by relaxational or hysteretic processes occurring in magnetic fluid (MF) [3, 4]. Each of mentioned designs has its advantages and disadvantages mainly related to magnetic field homogeneity and amplitude. In this article we present and compare the spatial uniformity of magnetic field amplitude and the maximum amplitude in the point where the test samples are usually placed in the mentioned generator designs. Recently it was made a research proving that a rotating magnetic field (RMF) generates more heat than AMF in magnetic nanoparticle hyperthermia [5]. In this work we also suggest a simpler thus cheaper setup that can generate RMF. Finally, we are also present the results of calorimetric measurements performed on MF sample with the use of two-layer solenoid generator design. 2. Construction and parameters of magnetic circuits 2.1. The two-layer solenoid The first example of a circuit generating AMF is a two-layer solenoid which cross-section is shown in Fig. 1. For the construction of the solenoid it was used a copper wire consisting of several thin wires with a total cross-section of 2.5 mm2. The outer diameter of the cable with its insulation was l = 3.6 mm. The number of the turns in the first and second layers is n1 = 47 and n2 = 45 respectively. The first layer has a diameter D1 = 44 mm and is wound on a plastic bobbin (Db = 40 mm) while the second diameter is D2 = 51.5 mm. The inner diameter of the solenoid is big enough to enwrap the sample vial with polyurethane foam providing sufficient thermal insulation. The lengths of the solenoid layers are l1 = 170 mm and l2 = 163 mm, respectively. Self-inductance of this solenoid is L = 93.5 H (measured using RLC bridge type MT 4080). Applying 300 W 2
power amplifier AL-300-HF-A, the provided current amplitude is Imax = 15 A and achieved magnetomotive force is 1380 ampere-turns. In order to calculate the amplitude of the magnetic field inside the solenoid we can use the Biot-Savart law [7]. According to this law, the current I flowing through the single turn of radius r produces at x point on the axis by a distance x from the turn component of the field Hx:
HX
I sin 3 . 2r
(1)
In this case, the resultant amplitude of the magnetic field is a sum of (n1 + n2) components originating from all turns. Successive the angles 1, 2, 3, and etc. between the axis of the solenoid and the radii R1, R2, R3, and etc. are determined:
tan1
r1 2r 1, x1 l
tan 2
2r1 l 2 l
,
tan 3
2r1 . l 4 l
(2, 3, 4)
Generally consecutive angles i for the 1st layer of solenoid are r1 (5) i a tan . l l i 1 2 The calculated components of the amplitude from equations (2-5) of the magnetic field Hi inside
the solenoid and generated by all turns are shown in Fig. 2. The sum of these components determined for the maximum current amplitude of the power generator (Imax = 15 A) is i n
H i 1
i
7901 A m 1 . According to equation (4) in order to achieve a high magnetic field inside the
solenoid it is recommended to choose the small radius r of the bobbin. In turn, the amplitude distribution of magnetic field intensity along the x axis of the solenoid for the two layers can be calculated from the expressions (6a, 6b and 6c) [6, 7]:
H x H1 x H 2 x ,
(6a)
H1 x
n1 I l1 2 x l1 2 x l1 2 D 2 l 2 x 2 2 D 2 l 2 x 2 1 1 1 1
, (6b)
H 2 x
n2 I l2 2 x l2 2 x l2 2 D 2 l 2 x 2 2 D 2 l 2 x 2 2 2 2 2
. (6c)
For the parameter values occurring in this case the course of the function H(x) are shown in Fig. 3(a).
3
Assuming that the amplitude of the current flowing through the solenoid is I = 15 A, the amplitude of the magnetic field strength reaches in the center of the bobbin the value of Ho 7963 A·m-1. Taking into account the length of the sample in a vial about 20 mm, a reduction in the magnetic field reachesH = -12.5 A·m-1 and is related with the non-linearity of the magnetic field This change can be considered as sufficiently low value. Therefore, the relative change(Ho Hx)/Ho of the magnetic field over a distance of 10 mm from the center of the bobbin is not more than 0.16%. In turn, Fig. 3(b) shows the derivative dH/dx of the amplitude of the magnetic field along the x axis of the solenoid. In the middle of the coil dH/dt reaches the value of zero. 2.2. The Helmholtz coils. Another solution shown in Fig. 4 allows to obtain a homogeneous magnetic field [8]. The Hermholtz coils consist of two identical short coils connected in series, wherein the magnetic fields are directed in the same direction. At their mutual distance l = r obtained in the central region of the good homogeneity of the magnetic field. Between the coils there is enough space for proper thermal insulation of the sample which can be realized with the use of polystyrene or polyurethane foam. Distribution of the magnetic field intensity along the x axis of the two coils is described by the equation (7) while the graphic course of this function is illustrated in Fig. 5.
H x
nI 2 2 2 r r 0.5 r x 2
3 / 2
r 2 0.5 r x
2 3 / 2
(7)
Shown in Fig. 5(a) the course of the function H(x) is plotted for a radius equal to the average radius values r1 and r2 of double-layer solenoid from Fig. 1. With the same number of ampereturns (1380A·turn) as in the coil of Fig. 1 generated magnetic field reached only a value of 2904 A·m-1. This is significantly less than in the case of two-layer coils (7963 A·m-1). In Fig. 5(b) is presented a derivative of the magnetic field along the axis of Helmholtz coils. At a distance of 10 mm from the center of the Helmholtz-coil the value of magnetic intensity is reduced only by 0.1 A·m-1. However, at the same distance from the center of the coil obtained better homogeneity of the magnetic field than in the case of the double-layer solenoid. In the case of Helmholtz coils the relative change in the magnetic field on a distance of 10 mm is about 0.00344%. Table 1. Comparison of the magnetic field parameters H(x), dH(x)/dx and (Ho - Hx)/Ho for a double-layer solenoid and Helmholtz coils of the same length l = 0.170 m and with the same number of ampere-turns (1380 A·turn). H(x) dH(x)/dx x (Ho - Hx)/Ho A·m-1 cm
double-
Helmholtz
A·m-2 double-
Helmholtz
% double-
Helmholtz 4
-8.5
layer solenoid 3824
-1.0
coils 2746.9
layer solenoid +2447
7950.8
2904.2
0.0
7963.3
+1.0 +8.5
coils
coils
+6254
layer solenoid 52.0
+2550
+16.1
0.16
0.00344
2904.3
0.0
0.0
0.0
0.0
7950.8
2904.2
-2550
-16.1
0.16
0.00344
3824
2746.9
-2447
-6254
52.0
5.4
5.4
2.3. Inductor with a ferromagnetic core Previously shown air coils do not include non-linear ferromagnetic materials, therefore the relationship between the intensity of the magnetic field and the electric current I is linear, which undoubtedly is their advantage. At frequencies from 100 up to 600 kHz sometimes it can be used a solution consisted of soft magnetic ferrite materials [9, 10, 11, 12]. This can produce easily relatively high values of the alternating magnetic field intensity. In this case we use a space of airgap, where the magnetic field is dependent on the number of ampere-turns and of the width of the air gap. An example of a such solution is shown in Fig. 6. Self-inductance coil wound on a ferrite core for n = 12 turns is L = 100 H. Magnetic flux flowing through ferrite elements and via an air gap lg is formed by the flow = nI. For I = 15 A and n = 12 the current flow = 180 ampereturns. According to the flow law the value of this magnetic flux is:
I n RFe R g
,
(8)
where RFe and Rg are magnetic reluctance in part of ferrites and in the air gap, which are defined by the following formulas: RFe
l Fe
o Fe S
, and Rg
lg
o g S
.
(9)
In this case, Fe 2000 and g 1 are relative magnetic permeability of ferrite material (3F3) and free space. Symbols lFe = 0.326 m and lg = 0.0107 m are the lengths of the path line of magnetic flux in the ferrite, and in the air gap respectively. The symbol SFe = 17.910-4 m2 refers to the crosssectional area which magnetic flux flows through. The available magnetic materials 3F3 produced by Ferroxcube are suitable for use at frequencies up to 1 MHz, which the real part of relative magnetic permeability Fe 2000 and the magnetic induction at saturation BS 400 mT for. Substituting numerical data to the equation (9) we get the values of magnetic reluctance: RFe = 72.5 kA·V-1·s-1 and Rg = 4756.3 kA·V-1·s-1. Thus, the resultant value of magnetic reluctance equals to 4829 kA·V-1·s-1. We assume further that along the field lines of the magnetic flux is not 5
dispersed and passes through the same surface in the two parts of the magnetic circuit. In that case, it means that the magnetic induction B is the same in the ferrite and as in the air gap. From equation (8) we get value of magnetic flux flowing through ferrite elements and via an air gap: = 37.27 Vs. Hence the value of the magnetic induction B = ·SFe-1 = 20.82 mT. Thus, the amplitude of the magnetic field in the air gap reaches value Hg = B o-1 = 16.57 kA·m-1. It is noticeable that an inductor with a ferromagnetic core allows to obtain significantly higher magnetic field intensity than air coils, although in this case the current flow = In was several times lower. If we use a ferrite core with a smaller air gap we can (at the same the flow = 180 ampere-turns) get even higher magnetic field strength. For example, when we reduce the gap to 6 mm, the magnetic field increases, reaching a value of about 29 kA·m-1. The course of the dependence of the magnetic field strength amplitude in the air gap Hg(lg) and in the magnetic material HFe(lg) on the gap width lg is shown in Fig. 7. It should be noted that a small air gap width precludes proper thermal insulation of the sample. While unwanted heating occurs (e.g. the ferromagnetic core heating), the reference sample (e.g. water-filled vial) should be used. This system producing a strong alternating magnetic field also has some drawbacks associated with heating of the core and a non-linear relationship between the intensity of the magnetic field in the gap and the electric current. In addition, in the vicinity of the air gap there is a certain dispersion of the magnetic flux, which leads to reduction of field in the gap. Thus, to avoid the measurement error of the magnetic field in the gap Hg we can use the measurement loop located in the center of the gap plane.
2.4. Rotating magnetic field generation Descriptions of a rotary magnetic field generation for use in magnetic hyperthermia have recently appeared in scientific papers [5, 13]. In these studies, the improved efficiency of heat generation is predicted. An interesting type of the applied field (which is "simultaneously rotating and alternating") is given in [14]. In Ref. [15] the authors reported on the circularly polarized field, it was shown that unusual non-linear effects are expected in this case and the increase of heating efficiency near the boundaries of various rotating regimes is expected. In the experimental work [16] is presented that for the rotating field the heat release in the nanopowders on the basis of iron oxides is 2– 3 times greater than for the axial field. In this case the rotating field generating system consists of two pairs of Helmholtz coils whose axes are mutually crossed at 90°. To supply energy two power amplifiers with signals shifted by a phase angle /2 rad were used. Signals controlling two amplifiers were provided from a signal generator, wherein to the input of one of the amplifiers the analog phase shifter was hooked up. In addition, to the each of the Helmholtz coils a variable capacitor to tune the resonance current was connected. Helmholtz coils and capacitors are connected in parallel. 6
The advantage of the parallel connection of coil and capacitor is very high impedance at tuning in resonance that is a small power amplifier overload. On the other hand, it is necessity to use two amplifiers, which raises the cost of the entire system. Within a different way we can produce the rotating magnetic field using three pairs of coils whose axes are mutually offset by an angle of 120° geometrically, as it is shown in Fig. 8. Each of the coils is connected in series with the capacitor C. Serial circuit LC acts as a selective filter, which exhibits minimal impedance for the resonant frequency fr. Therefore, at the resonance frequency through the branch LC flows maximum current. It leads to generation of rotating magnetic field which also achieves high intensity. The advantage of this system is the possibility to stimulate the branch LC by rectangular voltage as in Fig. 9. Furthermore, the system does not require an analog phase shifter, and the square wave signals can be easily generated using digital electronics. Although the currents flowing through the respective branches A, B and C are sine waves mutually displaced in phase by 120° as in Fig. 10. Temporal waveforms of currents flowing through the coils connected in series with the capacitors are described in formulas
2 4 i A t I A sin t , iB t I B sin t , iC t I C sin t 3 3
(10a, b, c)
where IA, IB, IC, the amplitudes of the currents in the branches A, B and C. Due to the high value of the Q-factor of the LC the higher harmonics can be omitted. In current system proposed by the authors a half bridge amplifier with two MOSFET transistors as switchers can be used [12, 17]. Therefore, there is no need to use conventional power amplifier. Each branch tuning to the resonance is done by spacing of the two coils L1 and L2 to the appropriate distance x. As a result, through changing the coefficient of coupling k(x) we achieve the correct frequency fr, which resonance occurs at,
f r x
1 , 2 C L1 2M x L2
(11)
where C is capacity of condenser, L1 and L2 inductance of coils and M x k x L1 L2 is mutual inductance. The value of coupling coefficient can achieve 0 ≤ k(x) ≤ 1. In Fig. 11 is shown the LC branch connected to two MOSFET transistors working as switchers. In practice, six coils with equal inductance L1 = L2 = L can be used for construction and then the resonance frequency equals
f r x
1 . 2 2C L M x
(12)
To compare our system to systems previously discussed, let's assume that we used six flat coils L, whereby a magnetomotive force of each branch of LC is 1380 ampere-turns.
Furthermore, the 7
used coils diameter of 2r = 47.75 mm, ie. as much as the average diameter of the two-layer solenoid in Fig. 1. The configuration of this system is shown in (Fig. 12). Concluding from the geometry shown in the sketch and from the calculations it results that the distance between the flat coils l = 2r·ctan(π/6) = 82.68 mm and magnetic field inside the system is Ho = 7.23 kA·m-1. As we can see, the obtained magnetic field has a substantial non-uniformity, due to the fact that l ≥ r. Unfortunately, if we wanted to approach the coils at a distance l = r, as is in the classic Helmholtz coil system, it would need to adjacent coils overlap. The free volume between the coils allows to thermally insulate the sample with polystyrene or polyurethane foam.
3. Experimental methods and results 3.1. Synthesis of magnetite nanoparticles For calorimetric measurements the magnetic fluid consisting of spherical magnetite particles prepared by the coprecipitation method [18] dispersed in water was used. Briefly, 21g of iron (III) chloride hexahydrate (Sigma-Aldrich 31232) and 10.8g of iron (II) sulfate heptahydrate (Sigma-Aldrich 215422) were dissolved in 400mL of deionized water. The molar ratio of Fe3+ and Fe2+ ions was 2:1 (the same ratio found in magnetite). 100 mL ammonium hydroxide solution 28% (Sigma-Aldrich 221228) was rapidly added while vigorous stirring. The black precipitate occurred. The supernatant was removed and precipitate was washed several times with DI water. A wet precipitate was mixed with 7.5g of sodium oleate (Sigma 26125). The mixture was mechanically stirred and heated until the boiling point was reached. Then the surfactant-stabilized nanoparticles were dispersed in water with the use of immersible sonication horn and homogenizer. Then, the agglomerates were removed by preliminary centrifugation (9 kRPM, 30 min), where the aggregates and large particles were separated. The supernatant was collected to form the initial MF. To increase the concentration of the nanoparticles, the MF was again centrifuged at 35kRPM (2 hours). The supernatants were removed and the sediments were re-dispersed in a small amount of water giving final MF with the concentration of 70mg/mL and the density 1.069 g/cm3 determined by magnetic and spectrophotometric methods [19, 20]. The volume concentration of the magnetite is ΦV = 1.35%.
3.2 Characterization of magnetic fluid The imaging of synthesized MF was performed with JEOL JEM1400 microscope at accelerating voltage of 120 kV. High magnification image (Fig. 14) shows good crystallinity of single nanoparticle. The d-spacing was measured to be 0.485 nm which corresponds to (111) interplanar distance of magnetite. [21]. Particle size distribution (PSD) calculated from TEM and from magnetic measurements are shown on insets of Fig. 14 and Fig. 15. The respective mean
8
values of particle diameter were 8.9 nm and 10.3 nm. The saturated magnetic polarization was measured by SQUID magnetometer and estimated as to be 32.6 mT.
3.3. Calorimetric Experiments Calorimetric investigations were performed in the testing system presented in Fig. 16. The glass vial with the tested sample (magnetic fluid, 1 mL) was placed into a plastic tube with polystyrene or polyurethane foam. Between the inner and outer tube (which wound solenoid coils) flowed water from the thermostat. The coil of the solenoid was connected in series with four different capacitors to the power amplifier. Thus, there were obtained four different frequencies of magnetic field. Depending on the capacity values of capacitors (C = 4, 3, 2 and 1.5 nF) used in experiment, the values of frequency were 254.17, 295, 360 and 415 kHz. The capacitors (type PS40, 5 kVp) operate at a voltage of about 100 times higher than the amplitude of the voltage from the power amplifier due to the resonance voltage in series LC system. For the condition of series voltage resonance, both (inductive and capacitive) reactances diminish and the current reaches its maximum value. Then the magnetic field also attains its maximum value. Additionally, one turn of winding coil was used to measure the magnetic field strength. This voltage is proportional to a magnetic flux value flowing in the magnetic system. The magnetic field intensity amplitude Ho in the solenoid equals Uo 2 f S o , (10) where Uo is the voltage amplitude induced through the magnetic flux in one turn of winding placed Ho
inside of the two-layer solenoid, and S = 13.85 cm2 is a surface of this turn. The temperature was measured with the help of a thermometer with fiber optic sensor produced by FISO Technologies Inc. The measurement uncertainty of the magnetic intensity amplitude equals ± 30 Am-1, whereas the uncertainty of the temperature is equal to ±0.1K. Between the sample of magnetic liquid and the windings of the solenoid we placed a pipe with liquid connected to a thermostat which ensures the constant thermal initial conditions of the test. Fig. 17 shows an example of time-temperature courses registered for f = 254.17 kHz and several intensities of the magnetic field. The slope dT/dt of each waveform T(t) was determined at the time 30 seconds after switching on the magnetic field. In turn, in Fig. 18 shows the experimental values of dT/dt versus the AC magnetic field amplitude (for some frequencies) and the plot of the function type (H/a)n. Parameters a and n obtained by fitting a function of the type (H/a)n to the experimental data are listed in Table. 2. If the sample includes only superparamagnetic nanoparticles, dT/dt = (H/a)n is
9
a square function and the parameter n 2. In our case the obtained value of this parameter shows that losses occur through of thermal energy associated with the magnetic relaxation.
f
Table 2. Results obtained from hyperthermal experiment. a n SAR, W·g-1 dT/dt, Ks-1
kHz
-
for
for 10 kAm-1
for
for 10 kAm-1
4 kAm-1
by extrapolation
4 kAm-1
by extrapolation
254.17 19564
1.81
0.0567
0.2972
3.6
19.0
295.0
14455
1.995
0.0770
0.4794
4.9
30.7
360.0
13823
1.938
0.0905
0.5340
5.8
34.2
415.0
12603
1.916
0.1109
0.6419
7.1
41.1
This table also lists the specific absorption rate (SAR) which is defined by formula (11) [22, 23] for the following frequencies at H = 4 and by extrapolation for 10 kAm-1
SAR
C P S dT , m dt
(11)
where CP andS – is the specific heat and density of the sample respectively, m – is the mass of magnetite per unit volume of the magnetic fluid.
4. Conclusions The calculations of three types of magnetic circuits have shown that they produce a magnetic field of adequate intensity, which can be used in studies of magnetic nanoparticle hyperthermia. With the use of the double-layer solenoid of the same length and the same number of ampere-turns as the Helmholtz coils we can obtain much higher values of magnetic field intensity (2.7 times higher). However, the magnetic field obtained by means of Helmholtz coils has a significantly better homogeneity. Another design with a ferromagnetic core allows to obtain magnetic field of very high amplitude, however the magnetic field is concentrated in a small air gap. Also, due to the limited space in the air gap there are difficulties in thermal insulation and temperature stabilization of the sample. We also presented an alternative method of rotating magnetic field generation that is simpler than the earlier reported one. The new setup involves only one signal amplifier, but 3 sets of Helmholtz coils driven by properly designed circuit. The new design can be applied in the study of magnetic hyperthermia. The amplitude of magnetic field obtained this way is sufficient for magnetic nanoparticle hyperthermia experiments. In the sample of the magnetic fluid prepared by coprecipitation method we found a heat dissipation which was caused by relaxation mechanisms. With increasing frequency of magnetic field also increases parameter SAR. 10
Acknowledgments The studies were supported by the Polish Ministry of Science and Higher Education Grant DEC2015/17/B/ST7/03566, European Social Fund (POKL.04.03.00-00-015/12), Slovak Scientific Grant Agency VEGA (projects No. 00141, 0045), by the European Structural Funds (PROMATECH), PHYSNET No. 26110230097, M-ERA.NET MACOSYS and COST Radiomag TD1402. References [1] Ch.S.S.R. K.umar, F. Mohammad, Magnetic nanomaterials for hyperthermia-based therapy and controlled drug delivery, Advanced Drug Delivery Reviews 2011. [2] A.A. Elsherbini, M. Saber, M. Aggag, A. El-Shahawy, H.A. Shokier, Magnetic nanoparticleinduced hyperthermia treatment under magnetic resonance imaging, Magnetic Resonance Imaging 2011. [3] R.E. Rosensweig, Heating magnetic fluid with alternating magnetic field, Journal of magnetism and Magnetic Materials, 252, 370-374, 2002. [4] S. Dutz, R. Hergt, Magnetic particle hyperthermia – a promising tumor therapy?, Nanotechnology 25, (2014) 452001. [5] M. Bekovic, M. Trlep, M. Jesenik, A. Hamler, A comparison of the heating effec of magnetic fluid between tha alternating and rotating magnetic field, Journal of magnetism and Magnetic Materials, 355, 12-17, 2014. [6] R. Kurdziel, Fundamentals of Electrical Engineering, (in Polish) WNT, Warszawa, 1972. [7] S. Huang, S.Y. Wang, A. Gupta, D.A. Borca-Tasciuc, S.J. Salon, On the measurement technique for specific absorption rate of nanoparticles in an alternating electromagnetic field, Measurement Science and Technology, 23, 035701, 2012. [8] Eva Natividad, Miguel Castro, Arturo Mediano, Accurate measurements of the specific absorption rate using a suitable adiabatic magnetothermal setup, Applied Physics Letters 92, 093116, 2008. [9] G. Glöckl, R. Hergt. M. Zeisberger, S. Dutz, S. Nagel, W. Weitschies, The effect of field parameters, nanoparticle properties and immobilization on the specific heating power in magnetic particle hyperthermia, Journal of Physics: Condensed Matter, 18, S2935-S2949, 2006. [10] L.M. Lacroix, J. Carrey, M. Respaud, A frequency-adjustable electromagnet for hyperthermia measurements on magnetic nanoparticles, Review of scientific instruments 79, 09309, 2008. [11] A. Skumiel, M. Kaczmarek-Klinowska, M. Timko, M. Molcan, M. Rajnak, Evaluation of Power Heat Losses in Multidomain Iron Particles under the Influence of AC Magnetic Field in RF Range, International Journal of Thermophysics, Vol. 34, Issue: 4, Pages: 655-666, 2013
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[12] E.A. Perigo, G. Hemery, O. Sandre, D. Ortega, E. Garaio, F. Plazaola, Fundamentals and advances in magnetic hyperthermia, Applied Physics Reviews 2, 041302, 2015 [13] Y.L. Raikher, V.I. Stepanov, Theory of Magneto-Inductive Hyperthermia Under a Rotating Field, 8th International Coference on the Scientific and Clinical Applications of Magnetic Carriers, 2010 American Institute of Physics. [14] J. Racz, P.F. De Chatel, I.A. Szabo, L. Szunyogh, I. Nandori, Improved efficiency of heat generation in nonlinear dynamics of magnetic nanoparticles, Phys. Rev. E 93, 012607, 2016 [15] T.V. Lyutyy, S.I. Denisov, A.Yu. Peletskyi, C. Binns, Energy dissipation in single-domain ferromagnetic nanoparticles: Dynamical approach, Phys. Rev. B 91, 054425, 2015 [16] V.A. Sharapova, M.A. Uimin, A.A. Mysik, A.E. Ermakov, Heat Release in Magnetic Nanoparticles in AC Magnetic Fields, Physics of Metals and Metallography 110, 5-12, 2010 [17] W. Kardys, A. Milewski, Efficiency Measurements of Ultrasonic Generator for Welding, Acta Physica Polonica A, Vol. 128, (2015), 456-460. [18] R. Massart, Preparation of aqueous magnetic liquids in alkaline and acidic media, IEEE Transactions on Magnetics, Vol. 17, Issue 2, 1981, 1247-1248 [19] R. E. Rosensweig, Ferrohydrodynamics, Dover Publications, Inc., Mineola, New York, 1997, ISBN 0-486-67834-2 [20] C. Riggio, M. P. Calatayud, C. Hoskins, et al., Poly-l-lysine-coated magnetic nanoparticles as intracellular actuators for neural guidance, International Journal of Nanomedicine, 2012;7:3155-3166. [21] Fachinformationszentrum Karlsruhe database, data_26410-ICSD. [22] P. de la Presa, Y. Luengo, M. Multigner, R. Costo, M.P. Morales, G. Rivero, A. Hernando, Study of heating efficiency as a function of concentration, size, and applied field in γ-Fe2O3 nanoparticles, The Journal of Physical chemistry C, 116, 25602-25610, 2012. [23] E.A. Perigo, F.A. Sampaio, M.F. de Campos, On the specific absorption rate of hyperthermia fluids, Applied Physics Letters 103, 264107, 2013.
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Graphical abstract. The three circuits generating the alternating magnetic field (the double-layer solenoid, Helmholtz coils, the inductor with C-shaped ferromagnetic core) and one system of rotating magnetic field that can be used in the field of magnetic hyperthermia experiments.
l , mm -80
40
-60
-40
-20
r, mm
20
40 nd
2
r2 r 20 1
R1
l
0
0
i
1
x1
Hxi Hx1 xn
0
layer
-l/2
-40
D2 D1
H(1) H(i)
st
nd
layer
st
1 layer 2
80
1 layer
Ri
xi
-20
60
+l/2
0
10
20
n
30
40
Fig. 1. Outline of the two-layer solenoid.
400 -1
d1 = 44mm d2 = 51.5mm
300
Hi , A·m
-1
Hi=7901 A·m
200 100 0
0
10
20
30
i - consecutive coils
40
50
Fig. 2. The components of the amplitude of the magnetic field Hi inside the solenoid generated by all the turns.
13
200000
10000
double-layer solenoid lsolen = 170 mm 1380 [A·turn]
7963±13 A/m
5000
double-layer solenoid 1380 [A·turn]
-l/2
-0.05
0.00
-200000
+l/2
0.05
x, m
0
-100000
0
-l/2
-0,05
0,00
x, m
0,05
+l/2
Fig. 3. The distribution of the amplitude of the magnetic field Hi inside the double-layer solenoid (a), and derivative dH/dx along its axis.
Fig. 4. The outline of Helmholtz coils.
3000
(a)
(b) Helmholtz coil
1380 A·turn
Helmholtz coil 1380 A·turn
A·m
-1
-2
5000
-1
H(0) = 2904 A·m
2750
-1
-1
2747 A·m
2500
-0.5·r
dH/dx,
H , A·m
H , A·m
dH/dx , A·m
nd
2 layer, n2 = 45 l2 = 0.163m, d2 = 51,5mm
st
1 layer, n1 = 47 l1 = 0.17m, d1 = 44mm
2500
100000
-2
2cm
-1
7500
2747 A·m
0,00
x, m
l=r 170 mm -5000
l=r 170 mm -0,05
0
0,05
+0.5·r
-0.5·r
-0,05
0,00
x, m
0,05
+0.5·r
Fig. 5. Magnetic field distribution in Helmholtz coils (a) and derivative dH/dx along its axis (b).
14
Fig. 6. A ferromagnetic core (3F3) to concentrate the field into an air gap where the sample is placed.
100
I = 15 A n = 12
-1
100000
Hg, A·m
Hg
10
HFe, A·m
10000
HFe
-1
1000 -3 10
10
-2
lg, m
1
Fig. 7. The dependence of the magnetic field strength amplitude in the air gap Hg(lg) and in the magnetic material HFe(lg) on the gap width lg.
Fig. 8. System of three pairs of inductors connected in series with capacitors for generating a rotating magnetic field.
15
Fig. 9. Temporary voltage waveforms supplied to the LC branches.
1
iA(t)
iC(t)
iB(t)
i(t) 0
-1 0
120 t , deg 240
360
Fig. 10. Temporal waveforms of currents flowing through the coils connected in series with capacitors.
Fig. 11. The LC branch power with adjustable coefficient of coupling with two MOSFET transistors as switchers.
16
Fig. 12. The configuration of LC branch to generating of rotating magnetic field.
r = 23.875 mm
l = 82.68 mm
20000
H, A·m
-1
30000
10000
I·n = 1380 A 0 -0.1
0.0
0.1
x,m Fig. 13. Magnetic field distribution between coils in one branch where l = 2r·ctan(π/6) and a magnetomotive force of each branch LC is 1380 ampere-turns.
Fig. 14. Transmission electron micrograph of MF. Insets: high magnification image of single nanoparticle and lognormal size distribution calculated from nanoparticle sizes measured by TEM. 17
Fig. 15. Magnetization curves measured at 297K. Insert is lognormal particle size distribution (PSD) calculated from Langevin function fit to measured magnetization points.
Fig. 16. Schematic diagram of experimental setup for measuring hyperthermal effect.
o
T, C
40,0 I F D C E A B G
37,5 35,0
MK10/14 C=4nF L=97.5H f= 254.17 kHz
32,5 30,0 0
30
60
t, s
90
120
150
Fig. 17. Time courses of the temperature in magnetic sample at various magnetic field intensity (f = 254.17 kHz).
18
0.100 a = 12603 n = 1.916 f = 415 kHz
0.075
dT/dt , K·s
-1
a = 13823 n = 1.938 f = 360 kHz
0.050 0.025
a = 14455 n = 1.995 f = 295 kHz
a = 19564 n = 1.81 f = 254.2 kHz
0.000 0
1000
2000
3000 -1
H , A·m
4000
5000
Fig. 18. The experimental values of dT/dt versus the AC magnetic field amplitude (for some frequencies)
and the plot of the function type (H/a)n.
Highlights
Various magnetic circuits can produce an AC magnetic field of sufficient intensity.
The design of rotating magnetic field generator is made.
The heat dissipation and SAR parameter of water dispersion of SPIONs are shown.
19
PII: DOI: Reference:
S0304-8853(16)30690-4 http://dx.doi.org/10.1016/j.jmmm.2016.07.018 MAGMA61630
To appear in: Journal of Magnetism and Magnetic Materials Received date: 17 May 2016 Revised date: 1 July 2016 Accepted date: 12 July 2016 Cite this article as: Andrzej Skumiel, Błażej Leszczyński, Matus Molcan and Milan Timko, The comparison of magnetic circuits used in magnetic hyperthermia, Journal of Magnetism and Magnetic Materials, http://dx.doi.org/10.1016/j.jmmm.2016.07.018 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
The comparison of magnetic circuits used in magnetic hyperthermia
Andrzej Skumiel1, Błażej Leszczyński1,2, Matus Molcan3, Milan Timko3*
Institute of Acoustics, Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland,
1
NanoBioMedical Centre at Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
2
Institute of Experimental Physics, SAS, Watsonova 47, 040 01 Košice, Slovak Republic
3
*
Corresponding author: Tel.: +421 55 792 2260; fax: +421 55 633 62 92. [email protected]
Abstract The magnetic nanoparticle hyperthermia experiments require a precise system of magnetic field generation. In this article we present the design of three circuits that can generate an alternating magnetic field (the double-layer solenoid, Helmholtz coils, the inductor with C-shaped ferromagnetic core) and one system of rotating magnetic field. The theoretical calculations have been made to compare the magnetic field intensity distribution along the axis of the coils. Also the inhomogeneity of the magnetic field was determined. Similar calculations have been made for ferromagnetic core inductor. It was also shown the relationship between the intensity of magnetic field and the air gap width of ferrite core. Moreover, it was made a proposal of rotating magnetic field generator consisting of three pairs of phase-tuned inductors. In the experimental section we presented the results of calorimetric measurements performed on water dispersion of SPIONs.
Graphical abstract. The three circuits generating the alternating magnetic field (the double-layer solenoid, Helmholtz coils, the inductor with C-shaped ferromagnetic core) and one system of rotating magnetic field that can be used in the field of magnetic hyperthermia experiments.
Keywords: Magnetic hyperthermia, Specific absorption rate, Two-layer solenoid, Helmholtz coils, Rotating magnetic field, Magnetic hyperthermia setups
1
1. Introduction The main trend in the magnetic hyperthermia research is focused on the design and synthesis of biocompatible magnetic fluid (MF) that exhibits the best heating efficiency. It is mainly motivated by possible in vivo applications of magnetic hyperthermia. Heating of magnetic fluid with the use of alternating magnetic field (AMF) is used to treat tissues containing tumor cells. Such cells are more temperature-sensitive than normal cells and increased temperature (45 42°C) makes tumor cells to be more responsive for radio- and chemotherapy. Degenerated cells reduce its multiplication rate in raised temperatures [1]. Magnetic hyperthermia allows a local temperature increase – the temperature rise is observed only within the volume containing magnetic nanoparticles (MNP) and closely adjacent tissues [2]. There are several designs of magnetic field generators used in experimental studies on magnetic hyperthermia. Custom made and commercial setups always contain one of the following components: single or multilayer solenoid, flat coil, Helmholtz coils or systems with ferrite parts. They are designed to generate AMF of high amplitude which is later converted into heat by relaxational or hysteretic processes occurring in magnetic fluid (MF) [3, 4]. Each of mentioned designs has its advantages and disadvantages mainly related to magnetic field homogeneity and amplitude. In this article we present and compare the spatial uniformity of magnetic field amplitude and the maximum amplitude in the point where the test samples are usually placed in the mentioned generator designs. Recently it was made a research proving that a rotating magnetic field (RMF) generates more heat than AMF in magnetic nanoparticle hyperthermia [5]. In this work we also suggest a simpler thus cheaper setup that can generate RMF. Finally, we are also present the results of calorimetric measurements performed on MF sample with the use of two-layer solenoid generator design. 2. Construction and parameters of magnetic circuits 2.1. The two-layer solenoid The first example of a circuit generating AMF is a two-layer solenoid which cross-section is shown in Fig. 1. For the construction of the solenoid it was used a copper wire consisting of several thin wires with a total cross-section of 2.5 mm2. The outer diameter of the cable with its insulation was l = 3.6 mm. The number of the turns in the first and second layers is n1 = 47 and n2 = 45 respectively. The first layer has a diameter D1 = 44 mm and is wound on a plastic bobbin (Db = 40 mm) while the second diameter is D2 = 51.5 mm. The inner diameter of the solenoid is big enough to enwrap the sample vial with polyurethane foam providing sufficient thermal insulation. The lengths of the solenoid layers are l1 = 170 mm and l2 = 163 mm, respectively. Self-inductance of this solenoid is L = 93.5 H (measured using RLC bridge type MT 4080). Applying 300 W 2
power amplifier AL-300-HF-A, the provided current amplitude is Imax = 15 A and achieved magnetomotive force is 1380 ampere-turns. In order to calculate the amplitude of the magnetic field inside the solenoid we can use the Biot-Savart law [7]. According to this law, the current I flowing through the single turn of radius r produces at x point on the axis by a distance x from the turn component of the field Hx:
HX
I sin 3 . 2r
(1)
In this case, the resultant amplitude of the magnetic field is a sum of (n1 + n2) components originating from all turns. Successive the angles 1, 2, 3, and etc. between the axis of the solenoid and the radii R1, R2, R3, and etc. are determined:
tan1
r1 2r 1, x1 l
tan 2
2r1 l 2 l
,
tan 3
2r1 . l 4 l
(2, 3, 4)
Generally consecutive angles i for the 1st layer of solenoid are r1 (5) i a tan . l l i 1 2 The calculated components of the amplitude from equations (2-5) of the magnetic field Hi inside
the solenoid and generated by all turns are shown in Fig. 2. The sum of these components determined for the maximum current amplitude of the power generator (Imax = 15 A) is i n
H i 1
i
7901 A m 1 . According to equation (4) in order to achieve a high magnetic field inside the
solenoid it is recommended to choose the small radius r of the bobbin. In turn, the amplitude distribution of magnetic field intensity along the x axis of the solenoid for the two layers can be calculated from the expressions (6a, 6b and 6c) [6, 7]:
H x H1 x H 2 x ,
(6a)
H1 x
n1 I l1 2 x l1 2 x l1 2 D 2 l 2 x 2 2 D 2 l 2 x 2 1 1 1 1
, (6b)
H 2 x
n2 I l2 2 x l2 2 x l2 2 D 2 l 2 x 2 2 D 2 l 2 x 2 2 2 2 2
. (6c)
For the parameter values occurring in this case the course of the function H(x) are shown in Fig. 3(a).
3
Assuming that the amplitude of the current flowing through the solenoid is I = 15 A, the amplitude of the magnetic field strength reaches in the center of the bobbin the value of Ho 7963 A·m-1. Taking into account the length of the sample in a vial about 20 mm, a reduction in the magnetic field reachesH = -12.5 A·m-1 and is related with the non-linearity of the magnetic field This change can be considered as sufficiently low value. Therefore, the relative change(Ho Hx)/Ho of the magnetic field over a distance of 10 mm from the center of the bobbin is not more than 0.16%. In turn, Fig. 3(b) shows the derivative dH/dx of the amplitude of the magnetic field along the x axis of the solenoid. In the middle of the coil dH/dt reaches the value of zero. 2.2. The Helmholtz coils. Another solution shown in Fig. 4 allows to obtain a homogeneous magnetic field [8]. The Hermholtz coils consist of two identical short coils connected in series, wherein the magnetic fields are directed in the same direction. At their mutual distance l = r obtained in the central region of the good homogeneity of the magnetic field. Between the coils there is enough space for proper thermal insulation of the sample which can be realized with the use of polystyrene or polyurethane foam. Distribution of the magnetic field intensity along the x axis of the two coils is described by the equation (7) while the graphic course of this function is illustrated in Fig. 5.
H x
nI 2 2 2 r r 0.5 r x 2
3 / 2
r 2 0.5 r x
2 3 / 2
(7)
Shown in Fig. 5(a) the course of the function H(x) is plotted for a radius equal to the average radius values r1 and r2 of double-layer solenoid from Fig. 1. With the same number of ampereturns (1380A·turn) as in the coil of Fig. 1 generated magnetic field reached only a value of 2904 A·m-1. This is significantly less than in the case of two-layer coils (7963 A·m-1). In Fig. 5(b) is presented a derivative of the magnetic field along the axis of Helmholtz coils. At a distance of 10 mm from the center of the Helmholtz-coil the value of magnetic intensity is reduced only by 0.1 A·m-1. However, at the same distance from the center of the coil obtained better homogeneity of the magnetic field than in the case of the double-layer solenoid. In the case of Helmholtz coils the relative change in the magnetic field on a distance of 10 mm is about 0.00344%. Table 1. Comparison of the magnetic field parameters H(x), dH(x)/dx and (Ho - Hx)/Ho for a double-layer solenoid and Helmholtz coils of the same length l = 0.170 m and with the same number of ampere-turns (1380 A·turn). H(x) dH(x)/dx x (Ho - Hx)/Ho A·m-1 cm
double-
Helmholtz
A·m-2 double-
Helmholtz
% double-
Helmholtz 4
-8.5
layer solenoid 3824
-1.0
coils 2746.9
layer solenoid +2447
7950.8
2904.2
0.0
7963.3
+1.0 +8.5
coils
coils
+6254
layer solenoid 52.0
+2550
+16.1
0.16
0.00344
2904.3
0.0
0.0
0.0
0.0
7950.8
2904.2
-2550
-16.1
0.16
0.00344
3824
2746.9
-2447
-6254
52.0
5.4
5.4
2.3. Inductor with a ferromagnetic core Previously shown air coils do not include non-linear ferromagnetic materials, therefore the relationship between the intensity of the magnetic field and the electric current I is linear, which undoubtedly is their advantage. At frequencies from 100 up to 600 kHz sometimes it can be used a solution consisted of soft magnetic ferrite materials [9, 10, 11, 12]. This can produce easily relatively high values of the alternating magnetic field intensity. In this case we use a space of airgap, where the magnetic field is dependent on the number of ampere-turns and of the width of the air gap. An example of a such solution is shown in Fig. 6. Self-inductance coil wound on a ferrite core for n = 12 turns is L = 100 H. Magnetic flux flowing through ferrite elements and via an air gap lg is formed by the flow = nI. For I = 15 A and n = 12 the current flow = 180 ampereturns. According to the flow law the value of this magnetic flux is:
I n RFe R g
,
(8)
where RFe and Rg are magnetic reluctance in part of ferrites and in the air gap, which are defined by the following formulas: RFe
l Fe
o Fe S
, and Rg
lg
o g S
.
(9)
In this case, Fe 2000 and g 1 are relative magnetic permeability of ferrite material (3F3) and free space. Symbols lFe = 0.326 m and lg = 0.0107 m are the lengths of the path line of magnetic flux in the ferrite, and in the air gap respectively. The symbol SFe = 17.910-4 m2 refers to the crosssectional area which magnetic flux flows through. The available magnetic materials 3F3 produced by Ferroxcube are suitable for use at frequencies up to 1 MHz, which the real part of relative magnetic permeability Fe 2000 and the magnetic induction at saturation BS 400 mT for. Substituting numerical data to the equation (9) we get the values of magnetic reluctance: RFe = 72.5 kA·V-1·s-1 and Rg = 4756.3 kA·V-1·s-1. Thus, the resultant value of magnetic reluctance equals to 4829 kA·V-1·s-1. We assume further that along the field lines of the magnetic flux is not 5
dispersed and passes through the same surface in the two parts of the magnetic circuit. In that case, it means that the magnetic induction B is the same in the ferrite and as in the air gap. From equation (8) we get value of magnetic flux flowing through ferrite elements and via an air gap: = 37.27 Vs. Hence the value of the magnetic induction B = ·SFe-1 = 20.82 mT. Thus, the amplitude of the magnetic field in the air gap reaches value Hg = B o-1 = 16.57 kA·m-1. It is noticeable that an inductor with a ferromagnetic core allows to obtain significantly higher magnetic field intensity than air coils, although in this case the current flow = In was several times lower. If we use a ferrite core with a smaller air gap we can (at the same the flow = 180 ampere-turns) get even higher magnetic field strength. For example, when we reduce the gap to 6 mm, the magnetic field increases, reaching a value of about 29 kA·m-1. The course of the dependence of the magnetic field strength amplitude in the air gap Hg(lg) and in the magnetic material HFe(lg) on the gap width lg is shown in Fig. 7. It should be noted that a small air gap width precludes proper thermal insulation of the sample. While unwanted heating occurs (e.g. the ferromagnetic core heating), the reference sample (e.g. water-filled vial) should be used. This system producing a strong alternating magnetic field also has some drawbacks associated with heating of the core and a non-linear relationship between the intensity of the magnetic field in the gap and the electric current. In addition, in the vicinity of the air gap there is a certain dispersion of the magnetic flux, which leads to reduction of field in the gap. Thus, to avoid the measurement error of the magnetic field in the gap Hg we can use the measurement loop located in the center of the gap plane.
2.4. Rotating magnetic field generation Descriptions of a rotary magnetic field generation for use in magnetic hyperthermia have recently appeared in scientific papers [5, 13]. In these studies, the improved efficiency of heat generation is predicted. An interesting type of the applied field (which is "simultaneously rotating and alternating") is given in [14]. In Ref. [15] the authors reported on the circularly polarized field, it was shown that unusual non-linear effects are expected in this case and the increase of heating efficiency near the boundaries of various rotating regimes is expected. In the experimental work [16] is presented that for the rotating field the heat release in the nanopowders on the basis of iron oxides is 2– 3 times greater than for the axial field. In this case the rotating field generating system consists of two pairs of Helmholtz coils whose axes are mutually crossed at 90°. To supply energy two power amplifiers with signals shifted by a phase angle /2 rad were used. Signals controlling two amplifiers were provided from a signal generator, wherein to the input of one of the amplifiers the analog phase shifter was hooked up. In addition, to the each of the Helmholtz coils a variable capacitor to tune the resonance current was connected. Helmholtz coils and capacitors are connected in parallel. 6
The advantage of the parallel connection of coil and capacitor is very high impedance at tuning in resonance that is a small power amplifier overload. On the other hand, it is necessity to use two amplifiers, which raises the cost of the entire system. Within a different way we can produce the rotating magnetic field using three pairs of coils whose axes are mutually offset by an angle of 120° geometrically, as it is shown in Fig. 8. Each of the coils is connected in series with the capacitor C. Serial circuit LC acts as a selective filter, which exhibits minimal impedance for the resonant frequency fr. Therefore, at the resonance frequency through the branch LC flows maximum current. It leads to generation of rotating magnetic field which also achieves high intensity. The advantage of this system is the possibility to stimulate the branch LC by rectangular voltage as in Fig. 9. Furthermore, the system does not require an analog phase shifter, and the square wave signals can be easily generated using digital electronics. Although the currents flowing through the respective branches A, B and C are sine waves mutually displaced in phase by 120° as in Fig. 10. Temporal waveforms of currents flowing through the coils connected in series with the capacitors are described in formulas
2 4 i A t I A sin t , iB t I B sin t , iC t I C sin t 3 3
(10a, b, c)
where IA, IB, IC, the amplitudes of the currents in the branches A, B and C. Due to the high value of the Q-factor of the LC the higher harmonics can be omitted. In current system proposed by the authors a half bridge amplifier with two MOSFET transistors as switchers can be used [12, 17]. Therefore, there is no need to use conventional power amplifier. Each branch tuning to the resonance is done by spacing of the two coils L1 and L2 to the appropriate distance x. As a result, through changing the coefficient of coupling k(x) we achieve the correct frequency fr, which resonance occurs at,
f r x
1 , 2 C L1 2M x L2
(11)
where C is capacity of condenser, L1 and L2 inductance of coils and M x k x L1 L2 is mutual inductance. The value of coupling coefficient can achieve 0 ≤ k(x) ≤ 1. In Fig. 11 is shown the LC branch connected to two MOSFET transistors working as switchers. In practice, six coils with equal inductance L1 = L2 = L can be used for construction and then the resonance frequency equals
f r x
1 . 2 2C L M x
(12)
To compare our system to systems previously discussed, let's assume that we used six flat coils L, whereby a magnetomotive force of each branch of LC is 1380 ampere-turns.
Furthermore, the 7
used coils diameter of 2r = 47.75 mm, ie. as much as the average diameter of the two-layer solenoid in Fig. 1. The configuration of this system is shown in (Fig. 12). Concluding from the geometry shown in the sketch and from the calculations it results that the distance between the flat coils l = 2r·ctan(π/6) = 82.68 mm and magnetic field inside the system is Ho = 7.23 kA·m-1. As we can see, the obtained magnetic field has a substantial non-uniformity, due to the fact that l ≥ r. Unfortunately, if we wanted to approach the coils at a distance l = r, as is in the classic Helmholtz coil system, it would need to adjacent coils overlap. The free volume between the coils allows to thermally insulate the sample with polystyrene or polyurethane foam.
3. Experimental methods and results 3.1. Synthesis of magnetite nanoparticles For calorimetric measurements the magnetic fluid consisting of spherical magnetite particles prepared by the coprecipitation method [18] dispersed in water was used. Briefly, 21g of iron (III) chloride hexahydrate (Sigma-Aldrich 31232) and 10.8g of iron (II) sulfate heptahydrate (Sigma-Aldrich 215422) were dissolved in 400mL of deionized water. The molar ratio of Fe3+ and Fe2+ ions was 2:1 (the same ratio found in magnetite). 100 mL ammonium hydroxide solution 28% (Sigma-Aldrich 221228) was rapidly added while vigorous stirring. The black precipitate occurred. The supernatant was removed and precipitate was washed several times with DI water. A wet precipitate was mixed with 7.5g of sodium oleate (Sigma 26125). The mixture was mechanically stirred and heated until the boiling point was reached. Then the surfactant-stabilized nanoparticles were dispersed in water with the use of immersible sonication horn and homogenizer. Then, the agglomerates were removed by preliminary centrifugation (9 kRPM, 30 min), where the aggregates and large particles were separated. The supernatant was collected to form the initial MF. To increase the concentration of the nanoparticles, the MF was again centrifuged at 35kRPM (2 hours). The supernatants were removed and the sediments were re-dispersed in a small amount of water giving final MF with the concentration of 70mg/mL and the density 1.069 g/cm3 determined by magnetic and spectrophotometric methods [19, 20]. The volume concentration of the magnetite is ΦV = 1.35%.
3.2 Characterization of magnetic fluid The imaging of synthesized MF was performed with JEOL JEM1400 microscope at accelerating voltage of 120 kV. High magnification image (Fig. 14) shows good crystallinity of single nanoparticle. The d-spacing was measured to be 0.485 nm which corresponds to (111) interplanar distance of magnetite. [21]. Particle size distribution (PSD) calculated from TEM and from magnetic measurements are shown on insets of Fig. 14 and Fig. 15. The respective mean
8
values of particle diameter were 8.9 nm and 10.3 nm. The saturated magnetic polarization was measured by SQUID magnetometer and estimated as to be 32.6 mT.
3.3. Calorimetric Experiments Calorimetric investigations were performed in the testing system presented in Fig. 16. The glass vial with the tested sample (magnetic fluid, 1 mL) was placed into a plastic tube with polystyrene or polyurethane foam. Between the inner and outer tube (which wound solenoid coils) flowed water from the thermostat. The coil of the solenoid was connected in series with four different capacitors to the power amplifier. Thus, there were obtained four different frequencies of magnetic field. Depending on the capacity values of capacitors (C = 4, 3, 2 and 1.5 nF) used in experiment, the values of frequency were 254.17, 295, 360 and 415 kHz. The capacitors (type PS40, 5 kVp) operate at a voltage of about 100 times higher than the amplitude of the voltage from the power amplifier due to the resonance voltage in series LC system. For the condition of series voltage resonance, both (inductive and capacitive) reactances diminish and the current reaches its maximum value. Then the magnetic field also attains its maximum value. Additionally, one turn of winding coil was used to measure the magnetic field strength. This voltage is proportional to a magnetic flux value flowing in the magnetic system. The magnetic field intensity amplitude Ho in the solenoid equals Uo 2 f S o , (10) where Uo is the voltage amplitude induced through the magnetic flux in one turn of winding placed Ho
inside of the two-layer solenoid, and S = 13.85 cm2 is a surface of this turn. The temperature was measured with the help of a thermometer with fiber optic sensor produced by FISO Technologies Inc. The measurement uncertainty of the magnetic intensity amplitude equals ± 30 Am-1, whereas the uncertainty of the temperature is equal to ±0.1K. Between the sample of magnetic liquid and the windings of the solenoid we placed a pipe with liquid connected to a thermostat which ensures the constant thermal initial conditions of the test. Fig. 17 shows an example of time-temperature courses registered for f = 254.17 kHz and several intensities of the magnetic field. The slope dT/dt of each waveform T(t) was determined at the time 30 seconds after switching on the magnetic field. In turn, in Fig. 18 shows the experimental values of dT/dt versus the AC magnetic field amplitude (for some frequencies) and the plot of the function type (H/a)n. Parameters a and n obtained by fitting a function of the type (H/a)n to the experimental data are listed in Table. 2. If the sample includes only superparamagnetic nanoparticles, dT/dt = (H/a)n is
9
a square function and the parameter n 2. In our case the obtained value of this parameter shows that losses occur through of thermal energy associated with the magnetic relaxation.
f
Table 2. Results obtained from hyperthermal experiment. a n SAR, W·g-1 dT/dt, Ks-1
kHz
-
for
for 10 kAm-1
for
for 10 kAm-1
4 kAm-1
by extrapolation
4 kAm-1
by extrapolation
254.17 19564
1.81
0.0567
0.2972
3.6
19.0
295.0
14455
1.995
0.0770
0.4794
4.9
30.7
360.0
13823
1.938
0.0905
0.5340
5.8
34.2
415.0
12603
1.916
0.1109
0.6419
7.1
41.1
This table also lists the specific absorption rate (SAR) which is defined by formula (11) [22, 23] for the following frequencies at H = 4 and by extrapolation for 10 kAm-1
SAR
C P S dT , m dt
(11)
where CP andS – is the specific heat and density of the sample respectively, m – is the mass of magnetite per unit volume of the magnetic fluid.
4. Conclusions The calculations of three types of magnetic circuits have shown that they produce a magnetic field of adequate intensity, which can be used in studies of magnetic nanoparticle hyperthermia. With the use of the double-layer solenoid of the same length and the same number of ampere-turns as the Helmholtz coils we can obtain much higher values of magnetic field intensity (2.7 times higher). However, the magnetic field obtained by means of Helmholtz coils has a significantly better homogeneity. Another design with a ferromagnetic core allows to obtain magnetic field of very high amplitude, however the magnetic field is concentrated in a small air gap. Also, due to the limited space in the air gap there are difficulties in thermal insulation and temperature stabilization of the sample. We also presented an alternative method of rotating magnetic field generation that is simpler than the earlier reported one. The new setup involves only one signal amplifier, but 3 sets of Helmholtz coils driven by properly designed circuit. The new design can be applied in the study of magnetic hyperthermia. The amplitude of magnetic field obtained this way is sufficient for magnetic nanoparticle hyperthermia experiments. In the sample of the magnetic fluid prepared by coprecipitation method we found a heat dissipation which was caused by relaxation mechanisms. With increasing frequency of magnetic field also increases parameter SAR. 10
Acknowledgments The studies were supported by the Polish Ministry of Science and Higher Education Grant DEC2015/17/B/ST7/03566, European Social Fund (POKL.04.03.00-00-015/12), Slovak Scientific Grant Agency VEGA (projects No. 00141, 0045), by the European Structural Funds (PROMATECH), PHYSNET No. 26110230097, M-ERA.NET MACOSYS and COST Radiomag TD1402. References [1] Ch.S.S.R. K.umar, F. Mohammad, Magnetic nanomaterials for hyperthermia-based therapy and controlled drug delivery, Advanced Drug Delivery Reviews 2011. [2] A.A. Elsherbini, M. Saber, M. Aggag, A. El-Shahawy, H.A. Shokier, Magnetic nanoparticleinduced hyperthermia treatment under magnetic resonance imaging, Magnetic Resonance Imaging 2011. [3] R.E. Rosensweig, Heating magnetic fluid with alternating magnetic field, Journal of magnetism and Magnetic Materials, 252, 370-374, 2002. [4] S. Dutz, R. Hergt, Magnetic particle hyperthermia – a promising tumor therapy?, Nanotechnology 25, (2014) 452001. [5] M. Bekovic, M. Trlep, M. Jesenik, A. Hamler, A comparison of the heating effec of magnetic fluid between tha alternating and rotating magnetic field, Journal of magnetism and Magnetic Materials, 355, 12-17, 2014. [6] R. Kurdziel, Fundamentals of Electrical Engineering, (in Polish) WNT, Warszawa, 1972. [7] S. Huang, S.Y. Wang, A. Gupta, D.A. Borca-Tasciuc, S.J. Salon, On the measurement technique for specific absorption rate of nanoparticles in an alternating electromagnetic field, Measurement Science and Technology, 23, 035701, 2012. [8] Eva Natividad, Miguel Castro, Arturo Mediano, Accurate measurements of the specific absorption rate using a suitable adiabatic magnetothermal setup, Applied Physics Letters 92, 093116, 2008. [9] G. Glöckl, R. Hergt. M. Zeisberger, S. Dutz, S. Nagel, W. Weitschies, The effect of field parameters, nanoparticle properties and immobilization on the specific heating power in magnetic particle hyperthermia, Journal of Physics: Condensed Matter, 18, S2935-S2949, 2006. [10] L.M. Lacroix, J. Carrey, M. Respaud, A frequency-adjustable electromagnet for hyperthermia measurements on magnetic nanoparticles, Review of scientific instruments 79, 09309, 2008. [11] A. Skumiel, M. Kaczmarek-Klinowska, M. Timko, M. Molcan, M. Rajnak, Evaluation of Power Heat Losses in Multidomain Iron Particles under the Influence of AC Magnetic Field in RF Range, International Journal of Thermophysics, Vol. 34, Issue: 4, Pages: 655-666, 2013
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[12] E.A. Perigo, G. Hemery, O. Sandre, D. Ortega, E. Garaio, F. Plazaola, Fundamentals and advances in magnetic hyperthermia, Applied Physics Reviews 2, 041302, 2015 [13] Y.L. Raikher, V.I. Stepanov, Theory of Magneto-Inductive Hyperthermia Under a Rotating Field, 8th International Coference on the Scientific and Clinical Applications of Magnetic Carriers, 2010 American Institute of Physics. [14] J. Racz, P.F. De Chatel, I.A. Szabo, L. Szunyogh, I. Nandori, Improved efficiency of heat generation in nonlinear dynamics of magnetic nanoparticles, Phys. Rev. E 93, 012607, 2016 [15] T.V. Lyutyy, S.I. Denisov, A.Yu. Peletskyi, C. Binns, Energy dissipation in single-domain ferromagnetic nanoparticles: Dynamical approach, Phys. Rev. B 91, 054425, 2015 [16] V.A. Sharapova, M.A. Uimin, A.A. Mysik, A.E. Ermakov, Heat Release in Magnetic Nanoparticles in AC Magnetic Fields, Physics of Metals and Metallography 110, 5-12, 2010 [17] W. Kardys, A. Milewski, Efficiency Measurements of Ultrasonic Generator for Welding, Acta Physica Polonica A, Vol. 128, (2015), 456-460. [18] R. Massart, Preparation of aqueous magnetic liquids in alkaline and acidic media, IEEE Transactions on Magnetics, Vol. 17, Issue 2, 1981, 1247-1248 [19] R. E. Rosensweig, Ferrohydrodynamics, Dover Publications, Inc., Mineola, New York, 1997, ISBN 0-486-67834-2 [20] C. Riggio, M. P. Calatayud, C. Hoskins, et al., Poly-l-lysine-coated magnetic nanoparticles as intracellular actuators for neural guidance, International Journal of Nanomedicine, 2012;7:3155-3166. [21] Fachinformationszentrum Karlsruhe database, data_26410-ICSD. [22] P. de la Presa, Y. Luengo, M. Multigner, R. Costo, M.P. Morales, G. Rivero, A. Hernando, Study of heating efficiency as a function of concentration, size, and applied field in γ-Fe2O3 nanoparticles, The Journal of Physical chemistry C, 116, 25602-25610, 2012. [23] E.A. Perigo, F.A. Sampaio, M.F. de Campos, On the specific absorption rate of hyperthermia fluids, Applied Physics Letters 103, 264107, 2013.
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Graphical abstract. The three circuits generating the alternating magnetic field (the double-layer solenoid, Helmholtz coils, the inductor with C-shaped ferromagnetic core) and one system of rotating magnetic field that can be used in the field of magnetic hyperthermia experiments.
l , mm -80
40
-60
-40
-20
r, mm
20
40 nd
2
r2 r 20 1
R1
l
0
0
i
1
x1
Hxi Hx1 xn
0
layer
-l/2
-40
D2 D1
H(1) H(i)
st
nd
layer
st
1 layer 2
80
1 layer
Ri
xi
-20
60
+l/2
0
10
20
n
30
40
Fig. 1. Outline of the two-layer solenoid.
400 -1
d1 = 44mm d2 = 51.5mm
300
Hi , A·m
-1
Hi=7901 A·m
200 100 0
0
10
20
30
i - consecutive coils
40
50
Fig. 2. The components of the amplitude of the magnetic field Hi inside the solenoid generated by all the turns.
13
200000
10000
double-layer solenoid lsolen = 170 mm 1380 [A·turn]
7963±13 A/m
5000
double-layer solenoid 1380 [A·turn]
-l/2
-0.05
0.00
-200000
+l/2
0.05
x, m
0
-100000
0
-l/2
-0,05
0,00
x, m
0,05
+l/2
Fig. 3. The distribution of the amplitude of the magnetic field Hi inside the double-layer solenoid (a), and derivative dH/dx along its axis.
Fig. 4. The outline of Helmholtz coils.
3000
(a)
(b) Helmholtz coil
1380 A·turn
Helmholtz coil 1380 A·turn
A·m
-1
-2
5000
-1
H(0) = 2904 A·m
2750
-1
-1
2747 A·m
2500
-0.5·r
dH/dx,
H , A·m
H , A·m
dH/dx , A·m
nd
2 layer, n2 = 45 l2 = 0.163m, d2 = 51,5mm
st
1 layer, n1 = 47 l1 = 0.17m, d1 = 44mm
2500
100000
-2
2cm
-1
7500
2747 A·m
0,00
x, m
l=r 170 mm -5000
l=r 170 mm -0,05
0
0,05
+0.5·r
-0.5·r
-0,05
0,00
x, m
0,05
+0.5·r
Fig. 5. Magnetic field distribution in Helmholtz coils (a) and derivative dH/dx along its axis (b).
14
Fig. 6. A ferromagnetic core (3F3) to concentrate the field into an air gap where the sample is placed.
100
I = 15 A n = 12
-1
100000
Hg, A·m
Hg
10
HFe, A·m
10000
HFe
-1
1000 -3 10
10
-2
lg, m
1
Fig. 7. The dependence of the magnetic field strength amplitude in the air gap Hg(lg) and in the magnetic material HFe(lg) on the gap width lg.
Fig. 8. System of three pairs of inductors connected in series with capacitors for generating a rotating magnetic field.
15
Fig. 9. Temporary voltage waveforms supplied to the LC branches.
1
iA(t)
iC(t)
iB(t)
i(t) 0
-1 0
120 t , deg 240
360
Fig. 10. Temporal waveforms of currents flowing through the coils connected in series with capacitors.
Fig. 11. The LC branch power with adjustable coefficient of coupling with two MOSFET transistors as switchers.
16
Fig. 12. The configuration of LC branch to generating of rotating magnetic field.
r = 23.875 mm
l = 82.68 mm
20000
H, A·m
-1
30000
10000
I·n = 1380 A 0 -0.1
0.0
0.1
x,m Fig. 13. Magnetic field distribution between coils in one branch where l = 2r·ctan(π/6) and a magnetomotive force of each branch LC is 1380 ampere-turns.
Fig. 14. Transmission electron micrograph of MF. Insets: high magnification image of single nanoparticle and lognormal size distribution calculated from nanoparticle sizes measured by TEM. 17
Fig. 15. Magnetization curves measured at 297K. Insert is lognormal particle size distribution (PSD) calculated from Langevin function fit to measured magnetization points.
Fig. 16. Schematic diagram of experimental setup for measuring hyperthermal effect.
o
T, C
40,0 I F D C E A B G
37,5 35,0
MK10/14 C=4nF L=97.5H f= 254.17 kHz
32,5 30,0 0
30
60
t, s
90
120
150
Fig. 17. Time courses of the temperature in magnetic sample at various magnetic field intensity (f = 254.17 kHz).
18
0.100 a = 12603 n = 1.916 f = 415 kHz
0.075
dT/dt , K·s
-1
a = 13823 n = 1.938 f = 360 kHz
0.050 0.025
a = 14455 n = 1.995 f = 295 kHz
a = 19564 n = 1.81 f = 254.2 kHz
0.000 0
1000
2000
3000 -1
H , A·m
4000
5000
Fig. 18. The experimental values of dT/dt versus the AC magnetic field amplitude (for some frequencies)
and the plot of the function type (H/a)n.
Highlights
Various magnetic circuits can produce an AC magnetic field of sufficient intensity.
The design of rotating magnetic field generator is made.
The heat dissipation and SAR parameter of water dispersion of SPIONs are shown.
19