Inductive heating of ferrimagnetic particles and magnetic fluids: Physical evaluation of their potential for hyperthermia

Abstract

The potential of colloidal subdomain ferrite particle suspensions (SDP) (‘magnetic fluids’), exposed to an alternating magnetic field, is evaluated for hyperthermia. Power absorption measurements of different magnetic fluids are presented in comparison to multidomain ferrite particles (MDP). Variations with frequency as well as magnetic field strength have been investigated. The experimental results clearly indicate a definite superiority of even non-optimized magnetic fluids over MDP ferrites regarding their specific absorption rate (SAR). Based on the work of [Shliomis, Pshenichnikov, Morozov, Shurubor. Magnetic properties of ferrocolloids. J Magn Magn Mater 1990;85:40–46 and [Hanson The frequency dependence of the complex susceptibility of magnetic fluids. J Magn Magn Mater, 1991;96 (In press).], a solid-state physical model is applied to explain the specific properties of magnetic fluids with respect to a possible use in hyperthermia. The experimentally determined SAR data on magnetic fluids are used to estimate the heating capabilities of a magnetic induction heating technique assuming typical human dimensions and tissue parameters. It is considered that for a moderate concentration of 5 mg ferrite per gram tumour (i.e. 0.5% w/w) and clinically acceptable magnetic fields, intratumoral power absorption is comparable to RF heating with local applicators and superior to regional RF heating (by comparison with clinical SAR measurements from regional and local hyperthermia treatments). Owing to the high particle density per volume, inductive heating by magnetic fluids can improve temperature distributions in critical regions. Furthermore, localized application of magnetic fluids in a tumour might be easier and less traumatic than interstitial implantation techniques.

• inductive heating
• magnetic fluids
• ferrites

Introduction

Two classes of materials are of interest for localized hyperthermia using magnetic induction heating: ferromagnets and ferrites. The magnetic attributes of both materials are determined by an ensemble of interacting magnetic moments in a crystalline structure. In ferrites, adjacent magnetic moments are opposite in direction and unequal in magnitude, yielding a net magnetization in antiferromagnetic coupling [1]. By contrast, magnetic moments of ferromagnets are parallel and equal in magnitude. Particles of 1 µm and more are multidomain ferrite particles (MDP) which consist of magnetic domains representing areas of locally saturated magnetization [2]. When applying an external AC magnetic field, the domain boundaries (Bloch walls) shift down by changing the intrinsic energy of the domain's crystalline structure, named anisotropy energy. During this oscillation, an energy loss occurs, which is the area of the so-called hysteresis curve.

By contrast, magnetic fluids are suspensions of ferromagnetic or ferrite particles of a size much smaller than a magnetic domain (1–100 nm). A carrier liquid (coating) prevents (in its ideal form) the particles from aggregation. In water-based fluids containing subdomain particles with a net magnetization (e.g. ferrites), each particle is a magnetic dipole. In an AC magnetic field, only a rotation of the whole crystal magnetization vector is possible [3]. The external magnetic forces required for this intrinsic change in magnetization depend on the anisotropy energy, size and shape of the subdomain ferrite particle [3]. Furthermore, mechanical rotation of the entire subdomain ferrite particle in an AC magnetic field is expected [4], as has been observed similarly from ferrofluid particles in rotating magnetic fields [5]. Both mechanisms are expected to contribute to energy loss of subdomain particles and can be clearly distinguished from the well-known hysteresis heating of multidomain ferrite particles.

In ferromagnetic implants of larger dimensions (>1 mm diameter) two mechanisms determine the power absorption in an external magnetic field: eddy current loss and hysteresis loss [e.g. [12–14]. The eddy current loss is produced by closed currents, which are induced by alternating magnetic flux in a conductive material of sufficient area (Equation 1). The rate of heat production by hysteresis loss is described by Equation (2). For small ferri- as well as ferromagnetic multidomain particles hysteresis loss dominates because eddy current loss goes to zero with radius a in Equation (1).

The power absorption terms of implants have to be related to the direct inductive heating of the surrounding conductive medium, which behaves as per Equation (3). Note that analysis of Equations [1–3] favours low frequencies (<100 kHz) for typical patient sizes in order to achieve a preferential SAR in the magnetic material in comparison to tissues at risk (i.e. the subcutaneous fat layer at large radius r) [8], [10], [11]. Furthermore, a temperature distribution within an array of thermal implants is determined as a result of hot sources even when self-regulating thermo-seeds are used. To minimize temperature gradients a close package of tiny particles is required.Equation (1). Power absorption of AC magnetic field energy in discrete ferro-seeds of diameter larger than approximately 1 mm, where a is the radius and L the length of the implant, μ is the magnetic permeability, σ_F is the conductivity of the ferromagnetic material, f is the frequency and H₀ is the strength of the external magnetic field [8], [10].

Equation (2). Power absorption of AC magnetic field energy in ferro- or ferrimagnetic material by hysteresis loss, where μ″ is the imaginary part of the complex permeability of magnetizable material as a function of H₀, the external field strength, N_v is the demagnetization factor which strongly depends on the geometry of the particle; f is the frequency and H₀ is the strength of the external magnetic field [1], [2].

Equation (3). Power absorption of AC magnetic field energy in lossy medium (e.g. tissue, ‘tissue load’) where σ_T is the conductivity of tissue and r is the distance from the central axis of the body [8], [11]. This equation is valid only for H₀ = constant and .

Heat production by hysteresis (Equation 2) is not directly limited by the particle size as it is with eddy current heating. Actually, heat production of particles via hysteresis loss is dependent on the average strength of the internal magnetic field H_i = H₀ + H_D, where H_D = − N_vM (H_D: demagnetization field, N_v; demagnetization factor, M, magnetization of the magnetic material, H₀: strength of external AC magnetic field) [2]. H_D reduces H_i, N_v is dependent on the geometry of the particle (e.g. for a sphere N_v is 0.33, for a needle in the x direction it is 0 but for y- and z-directed needles it is 0.5 [2]. We note that H_D = − N_v(μ_r − l)H₀ where μ_r is the relative permeability of the magnetic material. Thus, power absorption by hysteresis is severely limited with increasing μ_r (μ_r > 3) according to Equation (2). Therefore, trying to increase energy loss by increasing the ferrite permeability is, in the case of small spheres, even detrimental. In conclusion, heat production via hysteresis loss requires very strong magnetic fields (should be limited to H₀ f ≤ 4 × 10⁸ A/m s (Brezovich et al. 1984b) and large amounts of material, which may cause unacceptable direct tissue heating and other cytotoxic effects even when the frequency is low [9].

Biological effects of magnetic microparticles, exposed to an alternating magnetic field, have been investigated in animal tumour systems with magnetite [12–14], later with dextran-coated magnetite and ferric hydroxide [15–25], glass-ceramic material [26] and other ferri- or ferromagnetic microparticles [27–30]. Most of the studies show tumoricidal effects of the magnetically heated particles in animal tumours with very few side-effects. However, the main concern was the macroscopic temperature elevation. Only in one case was no correlation of temperature with tumoricidal effect [16] observed.

The findings of these studies are not consistent because of a large variability (or even lack of documentation) of tumour models, application modes, techniques of magnetic field excitation, and ferrite materials. Therefore, the potential of this heating technique is not clearly defined up to now. In particular, heating efficiencies of different materials (i.e. the SAR), as well as mechanisms of energy absorption, have not been systematically investigated.

Specifically, no systematic SAR measurements with regard to the specific particle attributes (particle size, shape, composition, manufacturing details) as well as external parameters (such as H-field and frequency) have been performed till now. This is the primary reason for the present study.

Finally, we note that there are fundamental disadvantages to the clinical application of ferro- or ferrimagnetic materials formed as finite-sized seeds, due to the large thermal gradients between individual seeds spaced 1 cm or more apart. Obviously, well-distributed microparticles are more suitable for producing relatively homogeneous temperature distributions. This is a further motivation for the present study.

Some of the ferrite samples used in this study are under clinical consideration as contrast agents for MR imaging. Cytotoxicity of these fluids at diagnostic levels is known to be low, so far.

For application of magnetic fluids in cancer therapy, uniformity of particle distribution in the target tissue, systemic tolerance of magnetic fluids, biological effects of high AC magnetic fields and a therapeutic effectiveness must be extensively analysed. However, a basic requirement is knowledge of the special SAR characteristics of magnetic fluids in alternating magnetic fields. This is the issue of the present study.

Materials and methods

We measured in vitro the heat production of small subdomain magnetite and composite ferrite particles (diameter 1–10 nm) with and without dextran coating, compared with multi-domain particles (diameter 1–300 µm) in alternating magnetic fields (Tables I and II).

Table I.  Multidomain ferrite particles (MDP) and soft iron powder (no. Fe) used for power absorption measurement in an AC magnetic field. Particle size distribution and surface structure determined by light microscopy.

MDP ferrite no.	Milling	Commercial	Elements	Shape	Size distribution (µm)	Surface	Manufacturer
360G	Yes	Yes	Ni–Zn–Fe-0	Irregular	10–100	Rough	Vogt Electronic
60	No	Yes	Ba–Co–Fe–O	Irregular	100–300	Rough	S + M Components
TK-T4	No	No	Ni–Zn–Fe–O	Spherical	1–100	Smooth	BASF
322	No	Yes	Ni–Zn–Fe–O	Spherical	200–400	Smooth	Vogt Electronic
360	No	Yes	Ni–Zn–Fe–O	Spherical	200–400	Smooth	Vogt Electronic
221G	Yes	Yes	Ni–Zn–Fe–O	Irregular	10–100	Rough	Vogt Electronic
TK-T2	No	No	Ni–Zn–Fe–O	Ellipsoid	1–100	Smooth	BASF
Fe	No	Yes	Fe	Irregular	1–100	Rough	Emerson & Cuming
23	No	No	Ni–Zn–Fe–O	Irregular	1–100	Rough	BASF
1680	No	No	Mn–Zn–Fe–O	Rodshape	0.8–10	Smooth	BASF
KG-T4	No	No	Ni–Zn–Fe–O	Irregular	10–100	Rough	BASF
KG-T2	No	No	Ni–Zn–Fe–O	Spherical	1–100	Smooth	BASF
10 000	No	No	Mn–Zn–Fe–O	Irregular	40–150	Rough	Kaschke

BASF: BASF AG, 6700 Ludwigshafen, Carl-Bosch-Str. 38, Germany.

Emerson & Cuming: Emerson & Cuming Europe, Distr.: EMC-Technik u. Consulting GmbH, 7000 Stuttgart 80, Schultze Delitzsch-Str. 58, Germany.

Kaschke KG: Kaschke KG GmbH & Co., 3400 Göttingen, Rudolf-Winkel-Str. 6, Germany.

S + M Components: Siemens Matsushita Components GmbH & Co. KG, 8000 München 80, Germany.

Schering: Schering AG, 1000 Berlin 65, Müllerstr. 170–178, Germany.

Vogt Electronic: Vogt Electronic AG, 8391 Erlau bei Passau, Postfach, Germany.

Temperature measurement and determination of SAR

Specific absorption rate (SAR) measurements (in mW/mg) were made with the rate of temperature rise method (determination of the linear T-rise after switching on the external power supply, according to the formula SAR = c dT/dt whereby c is the specific heat capacity, dT/dt the temperature increase per unit of time, [31]). In the case of low magnetic field amplitudes (H₀ ≤ 1400 A/m, § 2.4) temperature measurements were performed continuously with the temperature monitoring system including the high-precision three-point calibrated (range 25–50°C, precision ± 0.1°C) Bowman temperature probes of the BSD-2000 (BSD Medical Corp., Salt Lake City, UT 84108, USA) (Figure 1). For different ferrite materials an average value of c was taken as 0.937 J/gK [2]. The c-value of the specimen was defined as the weighted mean of ferrite and water equivalent agar (with c_water = 4.118 J/gK). Since all samples contained less than 10% of ferrite material, only slight differences in c for the whole series were obtained. For the purpose of normalization to the ferrite mass, a density of ρ_ferrite = 5 g/cm³ is assumed.

Figure 1. Experimental set-up for SAR measurements with applicator device 2 for frequencies from 0.3 to 5 MHz. When using the shorter coil of applicator device 1, liquid column (sample volume) was reduced to prevent thermal gradients induced by magnetic field inhomogeneities near the edges of the coil. Surface cooling effects were low because of the effective Styrofoam insulation around the sample tube.

Since the applicator device generating high magnetic fields (>100 A/m, § 2.4.1) was installed in another institute away from the BSD-2000 thermometry system, in this set of experiments a Fluke 87 True RMS Multimeter was used in connection with the Fluke thermocouple module (Fluke 80TK, Ni–Cr–Ni thermosensor, ±0.5°C, J. Fluke Mfg Co., Inc., Washington, USA) calibrated against the thermometry of the BSD-2000. The temperature was measured after inductive heating for 30 s with the thermosensor for a duration of 1 min at the centre of the specimen. During temperature measurement the power was turned off to prevent measuring artifacts of the thermosensor. Temperature did not fall off significantly (≤ 0.5°C) during this interruption of RF heating because of the Styrofoam insulation of the test tube (wall thickness ∼20 mm). This insulation was also used for the experiments with low magnetic field amplitudes (Figure 1).

Table II.  Subdomain ferrite particles suspensions (SDP) used for power absorption measurement in an AC magnetic field. Core sizes determined by transmission electron microscopy (Siemens EM 102). Both types of SDP are of spherical shape.

SD ferrite no.	Dispersion medium	Suspension	Core elements	Commercial	Average core size (nm)	Manufacturer
65IIB	Dextran 4000	Poorly stabilized	Mn–Zn–Fe–O	No	7.6 ± 1.8	BASF†
P6	mod. dextran	Stabilized	Fe–O	No	3.1 ± 0.7	Schering†

†See note for Table I.

With decreasing frequency the magnetic field strength was increased from 200 A/m (5–80 MHz) and 300 A/m (at 5 MHz) to 1400 A/m (at 200 kHz) to warrant significant temperature rise of the sample. Absorption data are normalized to 500 A/m field strength for all frequencies. Normalization is based on an -dependency of the specific absorption rate, which was verified experimentally for different frequencies (see § 3.2, data not shown).

Specimen preparation

Multidomain ferrite particles (MDP) (Table I) were prepared by milling commercial magnetic high permiability high frequency solid ferrite core material (no. 360, no. 221). The materials were assigned as no. 360G and no. 221G, respectively, after milling (Table I). The ferrite sieve fraction had a size distribution of 1–300 µm of irregular shape and rough surface as determined by phase contrast light microscopy. The particles were embedded in a 2% agar matrix containing 4.7 g/l sodium chloride to a total volume of 2 ml (applicator device 1, § 2.4) and 1 ml (applicator device 2). The filling level of the sample in the tube (volume) was adapted to the length of the applicator coil to minimize effects of magnetic field inhomogeneity (Figure 1).

Nearly uniform embedding of the particles in the sample was performed by mixing less than 10% of ferrite particles and 90% of hot liquid agar (60°C) with a non-magnetic stirring apparatus for 1 h. The sample was tempered in a water bath (60°C) during the mixing procedure. The suspension was sonified for 15 min (Branson sonifier B 15, 200 W) and finally it was fast-cooled in a mixture of calcium-6-hydrate and crushed ice (ratio 2 : 1.4, about − 50°C) to prevent sedimentation and reaggregation of particles before the agar gained gel consistency. The agar matrix without ferrite material served as control [32].

The MDP particles other than no. 360 and no. 221 listed in Table I (test materials were not available on the market but were kindly provided by several ferrite manufacturers) did not require milling and were embedded directly in the agar matrix as described above.

Subdomain ferrite particle suspensions (SDP) (test materials were not available on the market but were kindly provided by two German ferrite manufacturers, see Table II) were received in two forms: as stabilized dextran-coated particles and in a poorly stabilized form. The ferrite particle diameters of these two particles are 3.1 ± 0. 7 nm and 7.6 ± 1.8 nm as measured by transmission electron microscopy with a Siemens EM102 (Table II). SDP, MDP and control samples were filled into transparent polystyrene (PS) tubes (average radius 5 mm, length 100 mm, wall thickness less than 1 mm) with volumes of 2 and 1 ml depending on applicator coil used (Figure 1).

Measurement conditions

Coated subdomain particles are stable in suspension, whereas poorly stabilized SDP ferrites tend to begin sedimentation within 2–5 min. Therefore, aqueous suspensions of poorly stabilized ferrite particles were stirred with an electrical glass rod stirring device during the main heating period of 5 min. Control measurements of temperature rise with no applied AC magnetic field showed no heating effect of stirring alone. Furthermore, no SAR difference between samples with or without stirring device was observed in several tests.

The test samples were aligned to the coil axis and individually excited by the AC magnetic field (§ 2.1). Each sample was provided with a closed end catheter and fixed in the centre of the applicator coil (Figure 1). The tubular coils were connected to the water control system of the BSD-2000. A Bowman thermistor was inserted into the catheter. The temperature of the water control system was set to 25°C. The samples were preincubated for 30 min at a temperature of 25.0 ± 0.1°C in a precision water bath (Haake D8, Haake Meßtechnik GmbH, Karlsruhe, Germany). Under these conditions the samples were in thermal equilibrium at 25.0°C. In the measurement cell (Figure 1), constant temperature was demanded for 5 min, as monitored by the Bowman probe at the centre of each sample, until power was turned on and temperature recording continued. Power output, coil current and frequency were monitored during the heating process to guarantee reproducible AC field conditions. Careful positioning of samples at the coil centre was performed. Furthermore, sample size was always small in comparison to the coil length (Figure 1). No dependency on axial position was seen for SAR measurements near the coil centre (≤10% of total coil length). Obviously, the magnetic field homogeneity in the axial direction was adequate according to the sample size. Since the sample radius is some millimetres, radial field inhomogeneities are also minimal.

Water cooling was necessary (≤12°C) to prevent overheating of the coil and ceramic capacitors with high magnetic field amplitudes (>6000 A/m). In order to avoid any thermal influence of the coil on the sample (either by cooling or ohmic losses), a styrofoam coat was used as thermal insulation. There were no significant heating effects of the electric and magnetic fields alone. This was confirmed with control samples of highly conductive (4.7 g/l NaCl in 2% agar) agar, dextran solution (100 mg/ml), distilled water and glycerol without ferrite particles.

The error of the experimental SAR data is around ±10%, which is estimated from variations of at least three independent experiments on various days, separately for every data point under identical conditions.

Magnetic field generation and design of applicators

High AC magnetic field amplitudes with fixed frequency

High magnetic field amplitudes of max. 13.2 kA/m were achieved inside the water-cooled copper induction coil (average radius R = 34.5 mm, N = 7 turns, turn to turn distance a = 12 mm) at a fixed frequency of 520 kHz in a high-voltage matching circuit. The coil current and the voltage were I = 170A and U_ss = 2.5 kV, respectively. The magnetic field amplitude at the z = 0 coil centre was estimated according to Equation (4).Equation (4). Calculation of magnetic field amplitude H(0) at the z = 0 coil centre for short coil devices, where R is the averge coil radius, n to N the number of turns, a the turn-to-turn distance and I is the current through the coil.

Variable frequency low-level AC magnetic field generation

Magnetic field amplitudes of 200–1400 A/m were achieved within a frequency range of 300 kHz to 80 MHz. We used one of the class-A amplifiers (500 W/channel) of the BSD-2000 hyperthermia system as power supply. The AC signal was externally supplied to the amplifier by a Rhode & Schwarz SMX generator (accuracy ±0.5 Hz) or a General Radio Corp. 1163-A frequency generator (accuracy ±1.0 Hz). For frequencies higher than 27 MHz the BSD-system built-in Marconi synthesizer (accuracy ±0.5 Hz) was used. In spite of using external frequency and amplitude input control of the BSD amplifier, we used the BSD-2000 data acquisition software for complete high precision and calibrated thermometry. The feed point potential and frequency were checked by a four-channel Tektronix 11301 A Counter Time Oscilloscope. Most of the magnetic field applicators were part of high-voltage resonance circuits and, for safety reasons, the coil current was determined indirectly by measuring the voltage from a ferrite-coil pickup transformer (copper windings around a toroid wide-band ferrite-core, placed coaxially over the supply wire) using a Fluke 87-Multimeter (±0.1%, J. Fluke Mfg., Co., Inc., Washington, USA). The sense voltage is calibrated by replacing the coil by a 50 Ω coaxial resistor (600 W, model 8401 Bird Electronic Corp., Cleveland, Ohio, USA) as a matched termination. The power was measured simultaneously with a Rhode & Schwarz power reflection meter (using a NAP power head, 1950 W, 0.2–80 MHz, ±5%). For this set-up the current I is calculated from the power P by I = (P/50 Ω)^0.5. Finally, the induction coil of applicator device 1 was integrated into the circuit in series with the 50 Ω load using a suitable matching network in series. The corresponding magnetic field strength was estimated by inserting I into Equation (4). The current calculated via this indirect method was verified by measuring the coil feed point potential U_S directly and calculating the current according to I = U_S/L × f. The inductances L of the coils used were determined by an impedance meter model 252 from the Electro Scientific Industries (ESI), Portland, USA (±0.1 µH). The results of the direct and indirect method were close together in the range of ±10%.

Applicator device 1. For low-level H-field amplitudes we used a short-length water-cooled copper coil (number of turns N = 2.5, turn to turn distance a = 12 mm, average radius R = 14 mm, inductance L < 0.1 µH) over the frequency range of 5–80 MHz. This induction coil is matched to a 50 Ω load in series by use of a suitable series network of two capacitors. Therefore, if the power is adjusted to be 400 W for all frequencies, the current can be estimated as 2.8 A. It results from Equation (4) a magnetic field amplitude of 220 A/m.

Applicator device 2. For frequencies from 0.3 to 5 MHz, a longer coil was used with higher magnetic field strengths than applicator 1 to maintain significant heating of the samples. The water-cooled copper coil had N = 22 turns, turn to turn spacing of a = 7 mm, average coil length l = 155 mm, average radius R = 50 mm, inductance L = 7.5 µH) with an adjustable series capacitance of 330 pF. The current was determined indirectly as outlined above. The field strength (calculated according Equation 4) increased from 300 A/m at 5 MHz to 1400 A/m at 200 kHz. For such a long coil the H-field can also be estimated by the well-known formula H(0) = I × N/l, which gave similar results.

To confirm that SDP heating was exclusively due to the AC magnetic field power absorption, a static magnetic field of 0–900 G was applied simultaneously and positioned perpendicular to the z-axis of the AC magnetic field by a solenoid device.

Results

Power absorption of multidomain ferrite particles (MDP)

Temperature changes were monitored by the rate of temperature rise method [31] and absorbed power was assessed in ferrite-containing agar and in a control sample with no ferrite (see also § 2.1). Different multidomain ferrite particles (Table I) were tested with respect to their power absorption in an alternating magnetic field. The magnetic field amplitude at 520 kHz had to be very high to detect low power absorption of some samples.

At this frequency, large ferrite particles (such as no. 360 and no. 322 with a size distribution of 200–400 µm) had a considerably lower power absorption per mass than smaller particles of the same composition (e.g. no. 360G, 10–100 µm) although both particle size distributions were relatively broad (Table I and Figure 2). Due to their different composition and synthesis ‘history’ large particles (∼200 µm) obviously absorb more power when their permeability is higher (no. 60, Ba–Co–ferrite). By contrast, some unsuitable magnetic materials have low power absorption even when the average particle size is low (≤50 µm for no. Fe, soft iron powder). Particles of variable geometry but similar composition were not available. Therefore, the effect of these two parameters could not be evaluated. Frequency-dependence of MDP power absorption could not be tested since the magnetic field strength of applicators 1 and 2 was too low for detectable temperature rises of the MDP-samples.

Figure 2. SAR of multidomain ferrite particles (MDP) embedded in 2% agar matrix (in 4.7 g/l NaCl). Magnetic field strength ∼13.2 kA/m, frequency 520 kHz.

Power absorption of stibdomain ferrite particle suspensions (SDP)

Figure 3 shows the dependence of power absorption in SDP-ferrite no. P6 (Table II) and MDP-ferrite no. KG-T4 (Table I) on magnetic field amplitude at 520 kHz. No. P6 and no. KG-T4 proved to be the best representative of each ferrite type. The subdomain no. P6 particles show a considerably higher SAR than the 1000 times larger multidomain no. KG-T4 particles. For the case of no. P6 at H₀ > 200 A/m, there is approximately a square dependency of power absorption on field amplitude (exponent 1.9, plot not shown), whereas for no. KG-T4, it increases faster than the amplitude to the third power (exponent 3.6, plot not shown). Furthermore, the SAR of no. P6 increases at much lower field amplitudes (<1000 A/m) than no. KG-T4 which does not have a detectable SAR below a threshold of 6000 A/m (Figure 3).

Figure 3. SAR of multidomain ferrite (MDP) no. KG-T4 compared with subdomain ferrite (SDP) no. P6 (coated) as a function of AC magnetic field strength. Frequency: 520 kHz. Particles embedded in 2% w/v agar matrix (in 4.7 g/l NaCl) and 100 mg/ml dextran solution, respectively. The solid lines are the result of a third-order polynomial regression fit.

Power absorption of subdomain ferrite particle suspensions (SOP) with and without stabilized coatings

Figures 4 and 5 show the SAR measurements of coated and poorly stabilized SDP as a function of the AC magnetic field frequency at a normalized magnetic field strength of 500 A/m. Additionally, Figure 5 shows the SAR of SDP no. P6 and no. 65IIB diluted in suspension media of different viscosity (distilled water, glycerol) for frequencies from 5 to 80 MHz.

Figure 4. SAR of subdomain poorly stabilized ferrite no. 65IIB compared with coated subdomain ferrite no. P6 as a function of AC magnetic field frequency (1–5 MHz), normalized for 500 A/m magnetic field strength. The solid lines are the result of a linear regression fit.

Figure 5. SAR of subdomain poorly stabilized ferrite no. 65IIB and coated subdomain ferrite no. P6 as 1 : 10 dilution in distilled water or glycerol as a function of AC magnetic field frequency (10–80 MHz), normalized for 500 A/m magnetic field strength (§ 2.1). The solid lines are the result of a second-order polynomial regression fit.

Up to frequencies of about 10–30 MHz power absorption of both SDP ferrites no. P6 and no. 65IIB increases linearly with frequency (Figures 4 and 5). From 60 MHz to 80 MHz the increase of SAR with frequency is reduced to a plateau phase for both no. P6 suspensions and for no. 65IIB in distilled water. Only the no. 65IIB sample in glycerol continues nearly linearly over the the whole frequency range (Figure 5).

At lower frequencies ≤5 MHz applied to undiluted SDP samples (Figure 4), the SAR of no. P6 is about 15% higher compared with the poorly stabilized no. 65IIB sample at 5 MHz. For higher frequencies a pronounced medium-dependency occurs between suspensions of poorly stabilized ferrite no. 65IIB in glycerol compared with dilution in distilled water (e.g. at 60 MHz the glycerol-ferrite suspension has a SAR of nearly half the water-ferrite sample). By contrast, there is no significant effect of the suspension medium in the case of coated SDP (no. P6).

Power absorption of AC magnetic jeld excited subdomain ferrite particle suspensions (SDP) in a static magnetic field

To confirm that SDP heating was due exclusively to the magnetic field power deposition, coated SDP (no. P6) was excited by an AC magnetic field of 11 300 A/m at 520 kHz. A static magnetic field of variable strength (0–16 000 A/m) was applied at the same time perpendicular to the z-axis of the AC field (Figure 6). When the strength of the static magnetic field was increased the SAR of the SDP suspension decreased significantly. The ferrite specific absorption rate, P_F dropped to less than 10% of its original value when the static field strength approached the AC field strength (∼13 000 A/m).

Figure 6. SAR of subdomain coated ferrite no. P6 (suspended in 10% (w/v) dextran heated by an AC magnetic field (strength ∼11.3 kA/m, frequency 520 kHz) in dependence on static magnetic field strength H_stat perpendicular to the AC field z-axis. The solid line is the result of a fourth-order polynomial regression fit.

Discussion

Power absorption of multidomain ferrite particles (MDP)

Highly permeable multidomain ferrite particles (MDP) are heated by the well-known hysteresis loss which depends on the internal magnetic field strength H_i and material specific properties, especially geometry and permeability (Figure 2 and Table I).

Spherical ferrimagnetic particles (no. 322, no. 360) have an isotropic demagnetization factor of N_v = 0.33. They transform only a small amount of magnetic field energy into heat due to their strong demagnetization field H_D. By contrast, irregularly shaped ferri-magnetic particles (no. 360G, no. 60, no. 23, no. KG-T4) or anisotropically shaped particles (no. 1680), randomly distributed in the suspension, have a significant portion of particles aligned with the field, i.e. a low demagnetization. This portion is responsible for the heat observed with those particles. Also specific surface properties of the particles might influence the SAR and explain pronounced differences between some ferrite materials of Table I in Figure 2. Since MDP power absorption was low compared with SDP heating, interest was focused on the analysis of SDP power absorption and no attempt was made to explain all differences observed with MDP samples in detail.

Power absorption of subdomain ferrite particle suspensions (SDP)

Subdomain particles (SDP) produce substantially more heat per unit mass than the 1000 times larger multidomain ferrite particles (MDP) of similar composition, especially at low AC magnetic field amplitudes. The fundamentally different physical mechanisms of magnetization in MDP and SDP ferrites have been described in § 1. Permeabilities of magnetic fluids (i.e. subdomain particle suspensions) were measured in dependence on SDP size distribution and on AC magnetic field frequency [4], [33]. The extraordinary specific absorption rate of magnetic fluids cannot be explained by macroscopic parameters known with MDP ferrites or with ensembles of subdomain particles in a magnetic fluid, such as permeability (μ), susceptibilty (χ = 1 + µ), magnetization (M = χB) and hysteresis (B = µH), rather than the dynamic behaviour of the single subdomain particle in an AC magnetic field. Both Shliomis et al. and Hanson report on two distinct mechanisms which occur in magnetic fluids exposed to an AC magnetic field. They are characterized by relaxation time τ_N, which results from the rotation of the magnetic moment within the crystal, called the ‘Neél mechanism’ [4], [34], [35], and the relaxation time τ_B, which represents a mechanical friction component called the ‘Brownian mechanism’ [4], [33]. The Brownian mechanism (Equation 5) is a rotation of the particle as a whole according to the external AC magnetic field [4]. Whereas the Neél mechanism is the counterpart in SDP of the Bloch wall motion in MDP, the Brownian mechanism is possible only with particles small enough not to be limited by the moment of inertia.Equation (5). Relaxation times of the τ_n-component (‘Neél mechanism’) and the τ_B-component (‘Brownian mechanism’) of subdomain ferrite particle suspensions (‘Magnetic fluids’), where K is the anisotropy constant, V particle volume, k Boltzmann constant, T the temperature and η is the medium viscosity [4], [33].

The friction component, and to a much larger extent the Neél mechanism, depends on particle volume. The Brownian mechanism is influenced by medium viscosity and the Neél mechanism by the crystal anisotropy energy (Equation 5). Shliomis et al. conclude that there exists a characteristic particle size d_*, and a characteristic frequency v_*, for the condition τ_N = τ_B. For d < d_*, the Neél mechanism dominates, for d > d_* the Brownian mechanism dominates. As an example for the poorly stabilized SDP ferrite no. 65IIB, the Neél relaxation time is calculated according to Equation (5) as 1 ns, setting τ₀ to 1 ns [4], T = 293.2 K, average particle core diameter d_p = 7.6 mm (determined by transmission electron microscopy, see Table II) and K = 4.7 × 10³ J m⁻³ [4]. Since both the Neél mechanism and the Brownian mechanism contribute to the energy loss per cycle, the net SAR of the fluid depends on the portions of both mechanisms.

The calculated 1/τ_N of about 1 GHz ≫ 80 MHz (maximum frequency used in the experiments) indicates that, for all measurements, the Neél mechanism makes an unweakened contribution to the heat production. By contrast, 1/τ_B indicates a much lower frequency of about 6 MHz in an aqueous medium (setting T = 293.2 K, particle diameter d_p = 7.6 nm, η = 0.001025 Ns m⁻² (20°C) for water). In glycerol, the 1/τ_B frequency is lowered to about 4 kHz (η = 1.528 Ns m⁻² (20°C) for glycerol). The experimentally determined total SAR in an aqueous medium flattens out at frequencies higher than 10–30 MHz, reaching a plateau around 70 MHz, which is higher than the calculated 1/τ_B. This is not unexpected, because the increasing number of cycles compensates for the gradual amplitude decrease with f > 1/τ_B shifting the SAR maximum to higher frequencies. By contrast, the glycerol-suspended sample shows no plateau in the frequency spectrum but increases linearly with frequency. Since a 1/τ_B of 4 kHz is so far below the frequencies tested, no SAR by mechanical friction at all was expected with this sample.

Therefore, the difference between the two curves of no. 65IIB which is nearly a factor two at 60 MHz may represent the portion of heat produced by the r_B mechanical friction component. This friction is strongly dependent on particle size, frequency and medium viscosity. A second possibility to explain the effect of suspension in different media, namely that there is a higher particle aggregation in the more viscous medium, has been excluded by transmission electron microscopy of equal prepared samples of water- and glycerol-suspended no. 65IIB ferrite (i.e. no significant difference in aggregation was observed). Therefore, if aggregation is not the reason for different heating of the samples, a different mechanical contribution to total heat production in an AC magnetic field is probable.

With no. P6, which is a dextran-coated stabilized magnetite suspension (see Table II), no medium effect was seen (Figure 5). Both no. P6 curves were similar for the dilutions in distilled water and glycerol. The slight difference between the no. P6 curves in Figure 5 is smaller than 10% (measurement error) and therefore not significant. Since the surface coating is not destroyed by the dilution procedure (unchanged suspension stability), the coat supplies a constant environment for τ_B. In agreement with the experimental data (Figure 5, upper curves, no. P6), no effect of glycerol medium outside the coat is expected. However, the total amount of heat produced by a coated particle should depend on special attributes of the coat. This addresses a way for optimization by size and coat variation.

Evaluation of power absorption of subdomain ferrite particles P_F compared with inductive tissue load P_T under clinical conditions

The power absorption (P_F) at a given magnetic field strength must be compared with the maximally possible inductive tissue load (P_T), which is calculated according to Equation (3) [e.g. [8], [10], [36]. For a pessimistic evaluation of P_T, the conductivity of tissue σ_T, is set to be 0.4 Ω⁻¹ m⁻¹ assuming high water content [37] for f = 13 MHz; for f < 13 MHz σ_T, is not significantly decreased–e.g. [38] and the body cross-section is set to 30 cm in diameter. For a given P_T of 25 mW/ml at the maximal radius r = 15 cm from the central body axis, the corresponding magnetic field strength is calculated. For H₀ > 200 A/m and f < 10 MHz a proportionality of P_F, to and f is experimentally shown in Figures 3–5, i.e. . The material constant κ is derived from measurements of P_F (calculated from the rate of temperature rise data) as a function of frequency or magnetic field strength (f = 300 kHz–5 MHz: H₀ = 300 … 1400 A/m, f = 520 kHz: H₀ = 1600 … 13 000 A/m). κ was derived and averaged for the ferrite material no. P6 from numerous P_F measurements with different H₀ and f. The P_F in mW for 5 mg ferrite in 1 ml tumour tissue of σ_T = 0.4 Ω⁻¹ m⁻¹ was estimated assuming a P_T of 25 mW/ml at maximal radius r = 15 cm (Figure 7), limiting the magnetic field amplitudes to 15 000 A/m. To estimate an application in the cranium, P_F is calculated in Figure 8 with r = 10 cm, σ_T = 0.4 Ω⁻¹ m⁻¹ (pessimistic assumption, real brain tissue conductivity might be somewhat lower) and 1 mg of ferrite per ml tissue. Note that the ferrite density has been reduced in Figure 8 to 20% of that in Figure 7 because of the more favourable conditions for H-field application in the brain or extremities (e.g. small radius of target volume, cf. Equation 3). Both figures clearly indicate that 1–5 mg/ml of a non-optimized ferrite in tumour tissue yields a SAR of two to three times more than the tissue load of 25 mW/ml with f ≤ 100 kHz and H₀ ≤ 8000 A/m. If a higher tissue load of e.g. 50 mW/ml could be accepted clinically, Ρ_F would be further increased. The inductive tissue load might eventually add some SAR to the tumour, depending on its location. In conclusion, it seems feasible to achieve an SAR > 100 mW/ml in a brain tumour, if the pessimistic estimation of σ_T, and all possibilities to increase the intratumoral ferrite concentration are considered.

Figure 7. Expected power absorption (based on experimental heating data, § 3.2) of 5 mg ferrite no. P6 per ml tumour volume with an inductive tissue load (muscle-equivalent, σ_T = 0.4 Ω⁻¹ m⁻¹) of 25 mW/ml at max. radius r = 15 cm as a function of AC magnetic field frequency and magnetic field strength.

Figure 8. Expected power absorption (based on experimental heating data, § 3.2) of 1 mg ferrite no. P6 per ml tumour volume with an inductive tissue load (muscle-equivalent, σ_T = 0.4 Ω⁻¹ m⁻¹) of 25 mW/ml at max. radius r = 10 cm as a function of AC magnetic field frequency and magnetic field strength.

In vivo SAR measurements by the author [39] under clinical conditions in the Sigma-60 applicator of the BSD-2000 (annular phased array system, E-field heating device, BSD Medical Corp.) indicated for 20 patients in 120 intratumoral measurements (rate of temperature rise method), that the achieved SAR without any ferrite is distributed between 10 and 50 mW/g with a prominent peak between 20 and 30 mW/g. At this SAR level, satisfactory regional heat treatments have been obtained in ∼70% of the patients (i.e. ≥42°C, in at least one measurement point in the tumour). Higher SAR levels (i.e. usually 50–120 mW/g) are required for local hyperthermia treatments of limited treatment volumes. Assuming a ferrite concentration of 5 mg/ml in the tumour, local power deposition is up to three times higher (i.e. 300%!) than the tissue load. By comparison, in the clinical reality of regional RF hyperthermia we are lucky to achieve some 10% more SAR in the tumour in relation to the healthy tissue (and even this is often not obtained). However, the fundamental problem of magnetic fluids will be the accumulation in the target. By using established techniques of interventional radiology, this might be more feasible than focusing approaches of external heating techniques (such as RF heating or ultrasound). Furthermore, usage of externally applied static magnetic fields to accumulate magnetic fluids in malignant tissues of animal tumours is under investigation at the present.

Conclusions and future prospects

The encouraging results indicate that even non-optimized ferrite particles of appropriate size distribution (around 3–10 nm diameter) have a fundamentally different behaviour compared to multidomain particles of a few micrometres or more. The aim of this study was to investigate the parameters, which determine the specific absorption rate of subdomain ferrite material, and to evaluate the feasibility of clinical application from a physical point of view. It is concluded that considerable amounts of power could be delivered in the target tissue. For further improvement of SAR it is important to note that the SDP tested were not in any way screened or modified concerning their heat production capability. The coated ferrite no. P6 represents a completely unoptimized test material used for other purposes. Parameters for further optimization of magnetic fluids are coating attributes (i.e. friction, suspension stability), particle size distribution for the chosen frequency (e.g. ≤100 kHz for deep-seated tumours in humans), composition and magnetization of the SDP crystalline structure.

An important question is the relative biological efficacy of the magnetic fluids compared with the effect from macroscopic temperature elevation alone. Therefore, a presumed additional cytotoxic effect of magnetic fluids is a topic for further investigation. In this case the consequence would be the chance for further reduction of the required ferrite concentration in the tumour. From the pharmacological point of view it is important to determine the infiltration depth of magnetic fluids into malignant tissue or particle phagocytosis into tumour cells. Finally, it is a challenging task for the future to develop techniques for targeting the fluids to malignant cells (e.g. by static magnetic fields, biochemical coat modifications, ferrite-antibody conjugates).

The mechanisms regarding power absorption of subdomain ferrite particle suspensions (magnetic fluids) are well distinguished from the known hysteresis heating. Advantages of the use of magnetic fluids for local hyperthermia are the following: first, the target is precisely defined by the accumulation of ferrite material. Only the inductive load of normal tissue depending on AC magnetic field strength, frequency, tissue conductivity and body cross-section needs to be considered. Therefore, problems in focusing the external field energy into the target volume which are encountered when heating with external E-field techniques [39–42], might be avoided. Secondly, power deposition is controlled by the precalculated amount of ferrite per ml tumour, provided that uniform drug distribution in the target volume can be achieved. This is the most critical issue which is closely related to the biological efficacy, i.e. the number of particles per cell required for a lethal effect. If a relatively large amount of magnetic fluid were administered into the tumour (in accordance to its biological efficacy), the probability of malignant cells coming into contact with a sufficient number of particles, and as a result becoming inactivated, should be high. Intratumoral ferrite application, usage of static magnetic fields at the body surface, particle modifications to enable intracellular ferrite uptake, and pharmacological targeting (e.g. with antibody-ferrite conjugates) are suitable strategies to improve intratumoral accumulation. Thirdly, the large number of nanometre-size particles of a magnetic fluid produce uniform energy deposition within the volume, not a distinct number of hot sources. Fourthly, the ferrites give a contrast in diagnostic imaging (MRT: magnetic resonance tomography). This means that a quantitative assessment of ferrite concentration may be performed by a non-invasive imaging method before application of an AC magnetic field. This is a precondition for a controlled SAR application in a clinical situation. Fifthly, existing data suggest that undesirable systemic toxicity (e.g. spleen, liver) of the non-excited magnetic fluids is not expected (e.g. [43]).

Based on knowledge of the physical potential of magnetic fluids for controlled heating, further development of this technique and the evaluation of its biological effects in vitro and in vivo are needed.

Acknowledgements

This work is supported by Deutsche Krebshilfe, Dr Mildred Scheel Stiftung für Krebsforschung, 5300 Bonn 1, Germany (Grant M31/89/Fe 4). We wish to thank all ferrite manufacturers listed in Tables I and II, especially BASF AG and Schering AG, for the supply of test material, further assistance and helpful discussions. We are grateful for extensive technical support from staff members of the Institut f. Hochfrequenztechnik der Technischen Universitat, Berlin. For assistance in particle examination by transmission electron microscopy we are thankful to Dr B. Tesche of the Fritz-Haber-Institut fur Elektronenmikroskopie der Max-Planck-Gesellschaft, 1000 Berlin 33, Germany. Finally, we thank one of the reviewers for his very constructive and helpful comments.

Declaration of interest: The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.