Tailored Magnetic Nanoparticles for Optimizing Magnetic Fluid Hyperthermia

Abstract

Magnetic Fluid Hyperthermia (MFH) is a promising approach towards adjuvant cancer therapy that is based on the localized heating of tumors using the relaxation losses of iron oxide magnetic nanoparticles (MNPs) in alternating magnetic fields (AMF). In this study, we demonstrate optimization of MFH by tailoring MNP size to an applied AMF frequency. Unlike conventional aqueous synthesis routes, we use organic synthesis routes that offer precise control over MNP size (diameter ~ 10–25 nm), size distribution and phase purity. Furthermore, the particles are successfully transferred to the aqueous phase using a biocompatible amphiphilic polymer, and demonstrate long-term shelf life. A rigorous characterization protocol ensures that the water-stable MNPs meet all the critical requirements: (1) uniform shape and monodispersity, (2) phase purity, (3) stable magnetic properties approaching that of the bulk, (4) colloidal stability, (5) substantial shelf life and (6) pose no significant in vitro toxicity. Using a dedicated hyperthermia system, we then identified that 16 nm monodisperse MNPs (σ ~ 0.175) respond optimally to our chosen AMF conditions (f = 373 kHz, H_o = 14 kA/m); however, with a broader size distribution (σ ~ 0.284) the Specific Loss Power (SLP) decreases by 30%. Finally, we show that these tailored MNPs demonstrate maximum hyperthermia efficiency by reducing viability of Jurkat cells in vitro, suggesting our optimization translates truthfully to cell populations. In summary, we present a way to intrinsically optimize MFH by tailoring the MNPs to any applied AMF, a required precursor to optimize dose and time of treatment.

Introduction

Cancer therapeutics relies heavily on the combination of conventional remedies such as radiation, chemotherapy and surgical removal of tumors. Recent cancer statistics [1] show declines in new diagnoses (−1.1% AAPC^b from 2002–06) and death rates (−1.6% AAPC from 2002–06), primarily due to declines in the most common types of cancer (lung, prostate, breast and colorectal). From both technological and clinical perspectives, however, vast room for improvement in treatment options still remains.

The adverse side effects from conventional therapies and the resulting patient discomfort has encouraged researchers to explore site-specific therapies with the aid of magnetic nanoparticles (MNPs)^2–6. Furthermore, MNPs also offer diagnostic and therapeutic monitoring with imaging modalities such as Magnetic Resonance Imaging (MRI) and the emerging technique of Magnetic Particle Imaging (MPI)^2,7–9. Since the idea of site-specific therapy is to restrict treatment to the cancer site, thereby minimizing side effects and patient discomfort, MNPs are an attractive option because they can be remotely targeted by application of external magnetic field gradients¹⁰ or other active^{4, 11, 12} and passive^{12, 13} targeting methods. Once localized, Magnetic Fluid Hyperthermia (MFH), a therapeutic modality that utilizes alternating magnetic fields (AMF) to dissipate heat from the resulting relaxation losses in MNPs, can be used to induce heating^2,6. Heating cancer cells (typically to ~ 42–43°C) is known to disrupt cellular metabolism making adjuvant therapy by conventional established methods more efficient ^{14 , 15}. Thus, hyperthermia is best characterized as a synergistic modality rather than an independent one^16,17. A wide range of ferromagnetic nanoparticles, including metals/alloys with superior magnetic properties, can be synthesized for MFH^2,18–21. However, only iron oxide (γ-Fe₂O₃ or Fe₃O₄) MNPs show minimal toxicity^5,22,23 and are FDA approved for MRI contrast agents²⁴ and more recently for treatment of patients with chronic kidney disease²⁵. Furthermore, due to their modest magnetic characteristics²⁶ when compared to the ferromagnetic elements^27,28, they require the utmost optimization in terms of their morphological (size, size distribution, shape), crystallographic (phase purity) and magnetic (relaxation) characteristics for effective application in MFH.

MFH has been studied on both in vitro^29–32 and in vivo^33,34 platforms. However, the difficulty in delivering a sufficient amount of MNPs at the target site in order to promote a noticeable therapeutic outcome is one of the major hurdles impeding clinical adoption of MFH^2,6. For example, an estimated 32 mW of power dissipation for a treatment time of 10 minutes is required to raise the temperature of 1g of prostate tumor tissue (c_P ~ 3.8 kJ kg⁻¹ s⁻¹)³⁵ by 5°C. This is an underestimation and would be significantly higher if cooling from blood perfusion is taken into account. Nevertheless, based on this rough estimate, a minimum dose of 0.32 mg of MNPs that have a Specific Loss Power (SLP) of 100 W/g, per gram of tumor tissue would be needed to locally raise the temperature by 5°C.

SLP output can be optimized if the effective magnetization relaxation time of MNPs match the applied AMF frequency^{2,6, 36 , 37 , 38} . The effective relaxation time depends on both Néel (magnetization reversal) and Brownian (particle rotation) time components. Brownian relaxation (τ_B) depends linearly on the fluid viscosity (η) and the hydrodynamic particle volume (V_H), and is typically difficult to control due to the dynamic nature of the in vivo environment. It can also be detrimental to SLP output if the hydrodynamic volume is found to increase significantly³⁹. On the other hand, the operating Néel relaxation time (τ_N) is far more reliable as it depends exponentially on the product of magnetic anisotropy constant (K) and the magnetic core volume (V_m), i.e. τ_N ~ exp (KV_m). The core volume remains constant, irrespective of changes in the hydrodynamic volume and can be tailored to optimize the relaxation time. However, due to this exponential dependence even slight variation in the size distribution dramatically alters the effective relaxation time. It is clear from the above discussion that the effective relaxation time is dependent on the particle volume and this dependence is particularly strong if dominated by the Néel component. Thus, it is crucial to tailor particle size and, more importantly, the size distribution for a chosen AMF frequency, and also ensure MNPs do not agglomerate in biological medium in order to maximize SLP output from Brownian component. For instance, according to a model based on the known size-dependence of magnetic relaxation in MNPs³⁷, if size distribution increases from highly monodisperse (σ = 0, where σ represents the standard deviation of the lognormal distribution) to polydisperse (σ = 0.25), heating rate degrades by a factor of 5. This changes our estimate above, which assumes ideally monodisperse MNPs, to ~1.6 mg of polydisperse MNPs (σ = 0.25) per gram of tumor tissue or 5 times more than needed. The decrease in heating rate is especially dramatic for deviations in the size of MNPs at or near the optimum size, i.e. size that matches the applied AMF frequency.

Currently, popular MNP synthesis methods typically involving co-precipitation of iron salts in aqueous solution produce inherently more biocompatible particles but lack the ability to produce monodisperse MNPs^2,3. So far, most studies of MFH utilize MNPs synthesized by such methods, and rely primarily on “extrinsic” augmentations in order to counteract the ineffectiveness of polydisperse MNP dispersions and improve therapeutic efficiency. Such augmentations include, directly injecting tumors with large quantities of MNPs³⁴ or planting “thermoseeds” at tumor sites⁴⁰. However, in most cases the exact tumor location may be either unknown or require invasive methods to be reached. Increasing the administered MNP dose is also limited by the maximum tolerated dose (MTD); alternatively, increasing the applied magnetic field amplitude is also not an option as it can result in non-specific eddy current heating of surrounding tissue³⁴. Thus, the best approach to optimize MFH is to intrinsically tailor the MNPs, which are the actual source of heating.

In order to achieve the latter, we have synthesized highly monodisperse magnetite (Fe₃O₄) MNPs using organic methods and subsequently transferred them to aqueous phase using a biocompatible amphiphilic polymer. The organic synthesis route gives exceptional control over size, size distribution, shape and phase purity, enabling synthesis of MNPs specifically tailored for any chosen AMF frequency. The resulting power output, or SLP, is maximized and optimized for that specific frequency. In order to confirm that the synthesized MNPs possess the necessary characteristics for optimum MFH performance, we systematically characterized them. A dedicated hyperthermia system was used to measure heating capacity of MNPs and identify the optimum size for our chosen AMF conditions (f = 373 kHz, H₀ = 14 kA/m). Finally, we compared the in vitro therapeutic effectiveness of our monodisperse MNPs to induce hyperthermia in cells as a function of concentration and size.

1. Materials and methods

1.1 Chemicals

Iron (III) Chloride, anhydrous (98%) was purchased from Alfa-Aesar. Oleic acid (tech. grade, 90%), 1-octadecene (tech. grade 90%), poly(maleic anhydride-alt-1-octadecene) or PMAO (M_n = 30,000–50,000), Pluronic®-F127 (M_n = 12,600), methoxy poly(ethylene glycol) (M_n = 5,000) and ethylene diamine were purchased from Sigma-Aldrich. 1-Ethyl-3-[3-dimethylaminopropyl]carbodiimide hydrochloride was purchased from Pierce Biotechnology. N-Succinimidyl 3-(2-pyridyldithio)propionate (99+%) was purchased from Molecular Biosciences.

1.2 Synthesis of Fe₃O₄ magnetic nanoparticles (MNPs)

Magnetite MNPs were synthesized according to a procedure based on pyrolysis of metal fatty acid salts; specifically, Fe³⁺-oleate. Fe³⁺-oleate was prepared according to previous methods^41–43 and stored as a stock solution (conc. 18 wt%) in 1-octadecene (ODE, technical grade 90%). We have developed a method that allows us to reproducibly synthesize highly monodisperse Fe₃O₄ nanoparticles of diameters ranging from 10–25 nm by reacting pre-defined amounts of Fe³⁺-oleate and oleic acid (tech. 90%) in ODE. For instance, synthesis of 15 nm particles required 0.2 mmol/g of Fe³⁺-oleate and 3 mmol/g of oleic acid in 2.5 g of reaction solvent (ODE). The mixture was refluxed overnight (≥ 24 hours) at 320°C under an argon blanket and vigorous stirring. Ageing 24 hours typically resulted in narrow size distribution compared to shorter times (~12 hours), which resulted in relatively broader size distribution. Based on this observation, MNPs with different size distributions were synthesized and enabled us to study the effect of size distribution on SLP. Nucleation of nanoparticles was observed as a sudden change in color, from clear to black. The final product was collected and washed to remove excess surfactant and solvent. MNPs were precipitated using an excess of 1:1 (v/v) mixture of chloroform and methanol; they were then separated using a magnet and the washing step was repeated at least four times. MNP powder, obtained by drying in vacuum for 30 minutes, was coated with oleic acid and could be easily dispersed in organic solvents such as toluene or chloroform. X-ray diffraction (XRD – Rigaku) was routinely used to confirm the crystalline phase of Fe₃O₄ and determine size of nanocrystals. For select samples the Fe₃O₄ phase purity was independently confirmed by more sophisticated fine structure analysis of the Fe L_3,2 edges in transmission electron energy-loss spectroscopy⁴⁴. A Vibrating Sample Magnetometer (VSM - Lakeshore) was used to measure magnetic properties of the samples.

1.3 Synthesis of PMAO-PEG

Methoxy-poly(ethylene glycol) (m-PEG, M_n = 5,000) was used to PEG-ylate poly(maleic anhydride-alt-1-octadecene (PMAO (M_n = 30,000–50,000). PEG is considered highly biocompatible as it rejects non-specific protein adsorption, is non-immunogenic and non-toxic⁴⁵. Under acid catalysis, the hydroxyl group on m-PEG forms an ester bond with the anhydride ring on PMAO. In a typical reaction 2 g of PMAO (≈ 50 µmol) was reacted with 3.75 g of m-PEG (≈ 750 µmol) in 20 ml of acetone. A few drops of concentrated sulfuric acid were added to catalyze the reaction. The mixture was refluxed at 58°C in an argon atmosphere. After 24 hours, the mixture was cooled to room temperature and the polymer was obtained by precipitation in excess DI water. After several more DI water washes by sonication and centrifugation, the white polymer cake was freeze dried for 24 hours. The final product was obtained as a white powder and stored at room temperature. Gel Permeation Chromatography (GPC) was used to confirm the increase in molecular weight after PEG-ylation (data not shown).

1.4 Phase transfer of hydrophobic MNP using PMAO-PEG

In a typical phase transfer process, about 10 mg of oleic acid coated MNP (MNP@OA) and 10 mg of PMAO-PEG were dissolved in 1–2 ml of chloroform. The mixture was sonicated in an ultrasonic bath for about 15 minutes and dried under a stream of argon. The dried nanoparticle-polymer complex was dispersed in 1 ml of 1x Tris-acetate-EDTA (TAE) buffer by a 30-minute sonication step. MNP coated PMAO-PEG (MNP@PMAO-PEG) were filtered using a 0.45 µm nylon syringe filter. In order to remove excess unbound polymer, MNP@PMAO-PEG were passed through a Sephacryl™ S-200 HR gel column (GE Healthcare Life Sciences). Either de-ionized (DI) water or 1× phosphate buffered saline (PBS) was used as the eluent. Nanoparticles were stored at 4°C until further use. Iron concentration was determined using an Inductively Couple Plasma Atomic Emission Spectrophotometer (ICP-AES, Jarrell Ash 955). MNPs were analyzed using transmission electron microscope (TEM - FEI Tecnai™ G2 F20) images to gain a visual perspective and confirm the overall uniformity in the iron oxide core diameter and its distribution. However, due to the finite viewing area in a TEM image, statistically significant size analysis is difficult. As a result, two methods that measure the core diameter and distribution with statistical relevance were used. In particular, magnetization curves of liquid samples (containing 100–200 µg MNPs), measured by VSM, were fit to the Langevin function to obtain the magnetic core diameter and distribution. Additionally, the peak width in powder XRD spectra was used to determine the core crystallite size.

1.5 Colloidal stability measurements

In order to understand the colloidal properties of MNP@PMAO-PEG, zeta potential and hydrodynamic size measurements were done using dynamic light scattering (DLS) technique (Zetasizer Nano, Malvern Instruments). For biological relevance, hydrodynamic size measurements were also made in cell culture medium. In a recent study³⁹, we showed that the SLP deteriorates significantly due to reduced Brownian relaxation when MNPs dispersed in biological medium agglomerate.

1.6 Cytotoxicity study

Jurkat cells (human T-cell leukemia cell line) were grown in RPMI 1640 medium+10% fetal bovine serum (FBS) in physiological conditions (37°C and 5% CO₂). Complementary assays were conducted to confirm there is reasonable correlation between cell viability and induced toxicity. A Lactate Dehydrogenase (LDH) assay (Cytotox-ONE®, Promega) was used to determine MNP toxicity to cells by measuring LDH release in medium due to membrane disintegration. Cell viability was determined using a luciferase assay (Celltiter-GLO®, Promega), which measures ATP levels. Cells were seeded at 20,000 cells/well in a 96-well plate. MNP concentrations of 150 µgFe/ml, 300 µgFe/ml and 450 µgFe/ml were tested for 24 hours in physiological conditions. Appropriate controls were included to ensure assay validity and test for any interference MNPs or media may have with the assay. A microplate reader was used to measure fluorescence at λ_ex = 560 nm and λ_em = 590 nm for LDH assay, and a luminometer (TopCount, Perkin-Elmer) was used for measuring luminescence in the luciferase assay.

1.7 Measuring the Specific Loss Power (SLP)

The SLP (watts/g Fe₃O₄) as a function of MNP diameter (Table 1) was measured using a dedicated hyperthermia system (magneTherm™, NanoTherics Limited, UK). The AMF frequency (f) and amplitude (H₀) were set to 373 kHz and 14 kA/m respectively. A sensitive fiber-optic thermocouple (Luxtron, Lumasense Technologies) was used to measure the temperature ramp rate (dT/dt) in samples. Background temperature was averaged over 60 seconds and used as the baseline temperature (T_base), after which the AMF was turned on for 300 seconds. The change in temperature, ΔT (T_actual − T_base), was normalized for concentration (mg Fe₃O₄/ml) to graphically compare the heating rates (Figure 1). SLP was measured using the following equation³⁶:

$$\mathit{\text{SLP}}(\mathit{\text{watts}}/{\mathit{\text{gFe}}}_3{O}_4)=c\frac{{\mathit{\text{mass}}}_{\mathit{\text{Sample}}}}{{\mathit{\text{mass}}}_{{\mathit{\text{Fe}}}_3{O}_4}}\left(\frac{\mathit{\text{dT}}}{\mathit{\text{dt}}}\right)$$ (1)

where c is the specific heat capacity of water (4.187 J g⁻¹ °C⁻¹), (dT/dt) is the initial slope of the heating curve (from 65 to 125 seconds), mass_sample is the mass of the entire sample, and mass_Fe3O4 is mass of Fe₃O₄ in the sample determined by ICP-AES (typically ranged from 1–3 mg Fe₃O₄/ml). Two sets of samples (Table 1) with average standard deviations (σ) of 0.175 and 0.284 were measured to specifically characterize effects of both size and size distribution on the SLP. Such characterization is intended to emphasize the significance of tailoring size to a specific frequency, thus intrinsically optimizing MFH from a material physics perspective rather than augmenting extrinsic factors such as concentration or field amplitude.

Table 1.

Median diameters and standard deviations (σ) of as-synthesized MNPs, derived from Chantrell fitting of magnetization curves.

Median diameter (nm)	Std. Dev. (σ)*	Std. Dev. (σ)*
	σavg = 0.175	σavg = 0.284
9	-	0.29
10	-	0.10
12	0.01	-
13	0.10	-
14	0.21	0.31
15	0.23	-
16	0.16	0.36
16.5	-	0.36
18	0.34	-

^*The distribution of median diameters is given by the lognormal distribution function, where σ is the standard deviation

Figure 1.

Typical heating curves of MNPs with various median diameters, obtained using a dedicated hyperthermia instrument and a fiber optic thermocouple. The temperature increase is normalized for iron oxide concentration.

1.8 In vitro hyperthermia

Jurkat cells were cultured in triplicates at a density of 10,000 cells/well. MNPs of three sizes (12,13 and 16 nm and σ = 0.09, 0.22 and 0.16, respectively) with varying concentrations were added to the cultured cells. Prior to AMF heating, samples and controls were incubated at 37°C for 15 minutes to stabilize temperature. Samples were enclosed in a thermally insulating Styrofoam™ jacket before inserting in the instrument’s coil assembly. After 15 minutes of AMF application, cells were returned to the 37°C incubator for 15 minutes. Cells were allowed to equilibrate with room temperature for 30 minutes prior to viability measurements using the Celltiter-GLO® luciferase assay.

2. Results

2.1 Characterization of magnetite (Fe₃O₄) MNPs

Synthesized MNPs are highly monodisperse as characterized by Transmission Electron Microscopy (TEM; FEI Tecnai™ G2 F20) imaging [Figure 2(A)]. Hydrodynamic size of MNPs, before and after coating with PMAO-PEG, was measured using Dynamic Light Scattering (DLS). Figure 2(B) shows measurement of a 10 nm sample as an example. Magnetization curves, M(H), from VSM measurements were fit to the Langevin function, to obtain median core diameter and the volume-weighted standard deviation (σ). A lognormal distribution of particle diameter was assumed and details of the fitting method can be found in the highly cited work of Chantrell et al⁴⁶. Unlike TEM size analysis, which provides very limited statistics of particle size distribution, the Chantrell method measures the entire sample volume, giving statistically reliable results. Median diameters and corresponding standard deviations, assuming a lognormal distribution, are shown in Table 1. Magnetic properties were reconfirmed after organic to aqueous phase transfer; example of a 12 nm sample, before, after and 5 months after coating, are shown in Figure 2(D). The latter is also an indicator of the excellent shelf life of MNP@PMAO-PEG.

Figure 2.

(A) TEM image of a monodisperse 16 nm sample. Because of very high monodispersity MNPs form close-packed 2D and 3D hexagonal self-assembled arrays. (B) DLS measurement of MNPs before (10 nm) and after (20 nm) phase transfer using PMAO-PEG. (C) Magnetization curves of 13, 15 and 16 nm as synthesized MNPs. (D) Magnetic properties of 12 nm particles are retained even after phase transfer, for up to 5 months.

Powder X-ray diffraction θ-2θ scans of as synthesized MNPs are shown in Figure 3. The scans show a good match with the powder diffraction file (PDF) for magnetite (#019–0629, International Centre for Diffraction Data). As indicated in the figure, scans for MNPs of two sizes are included (top and middle). Since smaller particles (<15 nm) are nearly spherical in shape (TEM data not shown), a modified version of Scherrer’s formula accounting for the spherical geometry⁴⁷ was used to determine crystal size of smaller particles (top spectrum). For quasi-spherical, monodisperse and crystalline particles, the modified method shows good agreement, within 5–7%, between TEM and XRD size measurements. The generalized form^c was used for larger MNPs (middle scan) due to their noticeable non-spherical geometry characterized by faceting as seen in Figure 2(A). It should be noted that the generalized form of Scherrer equation can lead to ~15% error in size measurements^47,48. The peak at 35.42° (θ = 17.71°) was chosen for all crystallite size calculations. The calculated crystal sizes are 13.7 nm and 16.9 nm for the top and middle scans, respectively. These are in good agreement with the corresponding magnetic diameters determined by the Chantrell fitting method, which are 12.9 nm and 15.9 nm, respectively.

Figure 3.

Powder X-ray diffraction, θ-2θ scans, of magnetite nanoparticles. Sizes indicated in legends were determined by Scherrer’s formula using the peak at 2θ=35.4°. The magnetite reference (bottom) was obtained from the International Centre for Diffraction Data (PDF# 019–0629).

2.2 Colloidal stability

MNPs preferentially disperse in the aqueous phase after coating with PMAO-PEG (Figure 4(A)) and show no signs of physical agglomeration or aggregate formation for several months. Long-term colloidal stability of MNPs in water was determined by measuring zeta potential as a function of pH (Figure 4(B)). MNPs display a neutral surface charge across a wide range of pH values (2–12). Additionally, for biological relevance, hydrodynamic size measurements were also done in cell culture medium (RPMI 1640+10% FBS) to ensure MNPs remain stable during in vitro experiments (Figure 4(C)). MNPs show no significant change in hydrodynamic size up to a period of 96 hours of incubation in RPMI 1640 medium.

Figure 4.

(A) MNPs preferentially disperse in the hydrophobic chloroform phase before phase transfer (left), while preferring the aqueous phase after phase transfer (right). (B) Zeta potential of MNP@PMAO-PEG as a function of pH. (B) Hydrodynamic size measurements of MNP@PMAO-PEG in RPMI 1640+10% FBS cell culture medium as a function of time.

2.3 Cytotoxicity

Figure 5 shows results of MNP@PMAO-PEG cytotoxicity in Jurkat cells. Complementary viability (Luciferase assay) and toxicity (LDH release assay) studies were done to confirm validity of the performed assays. Cell viability drops to about 75% for the lowest concentration tested (150 µgFe/ml), while similar levels, within the calculated errors, are maintained for higher concentrations (300 and 450 µgFe/ml). The trend observed in the toxicity measurement agrees reasonably well with that observed in the viability measurement. Additionally, bright field images of cells incubated with MNPs were captured to examine any subsequent morphological alterations (Figure 6). Jurkat cells are suspension cells and do not adhere to culture plates, as indicated by their spherical shape (Figure 6 (A&E)). The cellular structure and shape is consistent with the control (no MNPs) for all concentrations of MNPs (Figure 6 (B–D) & (F–H)).

Figure 5.

In vitro cytotoxicity of MNP@PMAO-PEG in Jurkat cells. Viability measured via Luciferase assay and toxicity measured via LDH assay. MNPs were incubated for 24 hours in physiological conditions (37°C and 5% CO₂)

Figure 6.

Bright field images of Jurkat cells after 24 hours incubation with MNP@PMAO-PEG. Images A–D were taken at 20X and E–H at 60X magnification, respectively.

2.4 Magnetic Fluid Hyperthermia

Figure 7 shows a distinct peak in SLP around 16 nm for MNPs with narrow average size distribution (σ_avg. = 0.175). SLP values drop by ~30% for samples with broader average size distribution (σ_avg. = 0.284). The drop is especially substantial for 16 nm particles.

Figure 7.

Specific loss power (W/g Fe₃O₄) as a function of size and size distribution. Frequency (f) = 373 kHz and H_o = 14 kA/m

These experimental results were compared with a theoretical model for optimizing magnetic hyperthermia, rigorously developed by Carrey et al³⁸. According to this model, the optimum volume (V_opt) for randomly oriented MNPs is given by:

$$V_{\mathit{\text{opt}}}=\frac{-k_{B}T\text{ ln}(\mathrm{\pi }f{\mathrm{\tau }}_0)}{K_{\mathit{\text{eff}}}{\left(1-\frac{1.69{\mathrm{\mu }}_0{H}_{\text{max}}{M}_s}{2K_{\mathit{\text{eff}}}}\right)}^{\frac{4}{3}}}$$ (2)

where, k_B = Boltzmann constant (1.38 × 10⁻²³ J K⁻¹), T = temperature (300 K), f = applied field frequency (kHz), τ₀ = attempt time (~10⁻¹⁰ s), K_eff = anisotropy constant (23–41 kJ m⁻³)³⁷, µ₀H_max = field amplitude (4π × 10⁻⁷ H m⁻¹ * H_max kA m⁻¹), and M_s = saturation magnetization (450 kA m⁻¹)⁴⁹. Depending on the anisotropy constant of magnetite, for an AMF with f = 373 kHz and H_max = 14 kA m⁻¹, the optimum diameter (D_opt = [6*V_opt/π]^1/3) can range from 13 nm (for K_eff = 40 kJ m⁻³) to 17 nm (for K_eff = 23 kJ m⁻³). Our experimental result showing 16 nm as the peak diameter falls within this range and confirms well with the model. Though such a model is useful for identifying the optimum size range for magnetic nanoparticles under fixed field conditions, it is important to note that at the nanoscale, the anisotropy constant varies significantly from bulk values due to shape¹⁹ and surface⁵⁰ contributions to the magnetocrystalline anisotropy.

2.5 In vitro hyperthermia

In order to study the in vitro effect of magnetic fluid hyperthermia, ATP levels in Jurkat cells, as a measure of metabolic activity or cell viability, were compared. Although the controls (no MFH) experienced small declines in viability as a function of MNP concentration, due to some minor toxicity from potential organic residues in the phase transfer, cells exposed to MFH showed distinctly greater decrease in viability compared to controls (Figure 8). More importantly, since the goal of this study is to emphasize the intrinsic optimization of MFH by size tailoring, monodisperse MNPs of three different diameters were compared. 16 nm (σ = 0.16) MNPs, the optimal size for our chosen AMF as per the maximum observed in SLP measurements (Figure 6), were compared with 12 (σ = 0.09) and 13 (σ = 0.22) nm MNPs. The decrease in viability, relative to control, is markedly greater for the 16 nm MNPs compared to 12 and 13 nm MNPs (Figure 9). Also note, MNP concentration is slightly lower for 16 nm sample compared to 12 and 13 nm samples^d.

Figure 8.

In vitro heating of Jurkat cells using MNPs of median diameters (A) 12 nm, (B) 13 nm and (C) 16 nm. AMF was applied for 15 minutes

Figure 9.

Cell viability relative to control calculated as AC OFF_avg. − AC ON_avg.

3. Discussion

The heat generated by magnetic particles when subject to an AMF, which forms the basis of MFH, depends on two parameters: the applied frequency, f, and one that is intrinsic to the magnetic properties of the nanoparticle, i.e. their relaxation time, τ. The relaxation time can be either Néel, which depends exponentially on the magnetic core volume, or Brownian, which depends linearly on the hydrodynamic volume. The faster process dominates the relaxation time and for the sizes (particles exhibiting superparamagnetism at room temperature) and frequencies of interest in MFH, the Néel relaxation time is predominant. Thus the heating of superparamagnetic MNPs in MFH applications depends critically on matching the nanoparticle size to the applied frequency and more importantly, keeping their size distribution as narrow as possible. Specifically, from the perspective of clinical application, to minimize dose and time of application for the required therapeutic outcome, the relatively modest magnetic characteristics of Fe₃O₄ MNPs require utmost optimization of the material parameters (size, size distribution, shape, phase purity, defect free) responsible for enhancing MFH. The extremely stringent criteria discussed here, and the fact that truly monodisperse MNPs can only be reproducibly synthesized via organic routes in toxic organic solvents, demands the need for a thorough physical, chemical and cytotoxicity characterization.

TEM (Figure 2(A)) and XRD (Figure 3) analysis show that the Fe₃O₄ MNPs are highly monodisperse and single phase, respectively. Additionally, magnetic properties of MNPs are superior, with saturation magnetization reaching as high as 75 A m² kg ⁻¹ for 16 nm MNPs (Figure 2(C)), i.e. ~83% of bulk saturation value for magnetite (~90 A m² kg⁻¹). Due to the presence of ~ 0.5 nm layer of disordered spins on the surface of the MNPs that do not contribute to the total saturation magnetization of the sample, superparamagnetic particles often have lower saturation values compared to bulk⁵⁰. It also explains why the crystalline diameter, determined from XRD spectrum (Figure 3), is ~ 1 nm larger than the magnetic core diameter, determined by the Chantrell method. After transfer from the organic to the aqueous phase using the amphiphilic PMAO-PEG polymer, MNPs show exceptional stability in water (up to a year, Figure 4(A)) and retain their superior magnetic properties up to the tested period of 5 months (Figure 2(D)). The magnetic core diameters as determined using the Chantrell method confirm MNPs remain nearly monodisperse even after phase transfer (Table 1), suggesting no aggregation during the phase transfer process. Zeta potential as a function of pH shows MNPs display a near neutral surface charge across a wide pH range (2–12). This suggests MNPs are primarily stabilized via steric repulsion due to the surface PEG layer, and are less prone to adsorption form charged proteins or, in general, non-immunogenic. Hydrodynamic size measurements performed in cell culture medium (Figure 4 (C)) emphasize the biological relevance. To elucidate this further, in a recent study³⁹ we showed that MNPs can exhibit a combination of Néel (moment reversal) and Brownian (particle reversal) relaxation if the size lies within the Néel to Brownian transition³⁷. Thus, for particles agglomerating in culture medium, the Brownian component of the relaxation, which depends on the hydrodynamic volume, is essentially blocked, decreasing the overall SLP output. MNP@PMAO-PEG are relatively stable for up to 96 hours in RPMI 1640+10% FBS cell culture medium (Figure 4 (C)), suggesting consequent decrease in SLP output due to particle agglomeration is not expected.

Cytotoxicity results confirm MNPs exhibit relatively low inherent toxicity in Jurkat cells (Figure 5). Typically, the total amount of iron stores in the human body is approximately 3500 mg and the total amount of iron oxide used for diagnostic imaging is relatively small (~5.6 µgFe/ml) ⁵¹ . The maximum concentration used in our cytotoxicity experiments (up to 450 µgFe/ml) is far greater than the actual in vivo use. This ensures that we are measuring for cytotoxicity beyond current clinically tried levels. Overall, both viability and toxicity assays complement each other reasonably well, within the calculated error. Bright field images of cells (Figure 6) at 20X and 60X magnification confirm that overall cell morphology is preserved after 24 hours of incubation with MNPs of various concentrations.

Our comprehensive experimental SLP data as a function of both size and size distribution (Figure 7) shows that, for the chosen AMF conditions (373 kHz and 14 kA/m), 16 nm monodisperse MNPs exhibit the optimum SLP. More importantly, a clear peak in the heating as a function of MNP size is demonstrated. Additionally, MNPs with broader average size distributions show an overall drop in the peak SLP value. The drop is especially dramatic at 16 nm, which is the peak maximum for samples with narrow average distributions. This is consistent with theoretical models that show significant degradation of heating rates at or near the optimum size compared to non-optimum sizes. As a result, with broader average distribution the peak appears to shift to a lower median size (14 nm), when in fact, it is broadening and flattening out near the maximum. The experimental data presented here also provides strong validity to theoretical models of MFH^2,37, especially the need for size-tuned, monodisperse MNPs for maximizing SLP.

The in vitro therapeutic efficacy of MFH to induce cell death has been rigorously demonstrated in heating experiments with Jurkat cells as a function of both MNP concentration and, most critically, size (Figure 8 & 9). As expected, increasing MNP concentration increases heating rates; consequently reduction in % viability is also enhanced (Figure 8). As described earlier, enhancing MFH by increasing MNP concentration, which is an extrinsic parameter, does not indicate an improvement in the overall therapeutic potency of MFH. The key result, however, is the significant decrease in % viability due to the optimum 16 nm sized MNPs compared to the 12 and 13 nm MNPs under the same AMF conditions. This result (Figure 9) underscores the central idea of tailoring size for a specific frequency in order to intrinsically improve the therapeutic potency of MFH.

4. Conclusion

We have shown with systematic experiments that magnetite MNPs, with optimal magnetic properties and tailored to a specific alternating magnetic field frequency (f = 373 kHz) can show significant enhancement in MFH. Specifically, a peak in the heating rate or SLP as a function of MNP diameter has been clearly demonstrated and in vitro heating shows that optimized MNPs (16 nm) and narrow size distributions (a 30% difference in SLP is observed between τ~0.175 and τ~0.284) have maximum efficiency in reducing cell viability, suggesting our SLP data translates truthfully to cell populations. All this is achieved by synthesizing monodisperse MNPs via organic synthesis routes and successfully transferring them to aqueous phase using a biocompatible amphiphilic polymer. A rigorous characterization protocol, described in detail, ensures that the MNPs meet all the critical requirements: (1) uniform shape and monodispersity, (2) phase purity, (3) stable magnetic properties approaching that of the bulk, (4) colloidal stability, (5) substantial shelf life and (6) pose no significant in vitro toxicity. Finally, the conclusions are general and present a way to tailor/synthesize optimal, biocompatible MNPs for MFH at any applied frequency.