The relevance of Brownian relaxation as power absorption mechanism in Magnetic Hyperthermia

Abstract

The Linear Response Theory (LRT) is a widely accepted framework to analyze the power absorption of magnetic nanoparticles for magnetic fluid hyperthermia. Its validity is restricted to low applied fields and/or to highly anisotropic magnetic nanoparticles. Here, we present a systematic experimental analysis and numerical calculations of the specific power absorption for highly anisotropic cobalt ferrite (CoFe2O4) magnetic nanoparticles with different average sizes and in different viscous media. The predominance of Brownian relaxation as the origin of the magnetic losses in these particles is established, and the changes of the Specific Power Absorption (SPA) with the viscosity of the carrier liquid are consistent with the LRT approximation. The impact of viscosity on SPA is relevant for the design of MNps to heat the intracellular medium during in vitro and in vivo experiments. The combined numerical and experimental analyses presented here shed light on the underlying mechanisms that make highly anisotropic MNPs unsuitable for magnetic hyperthermia.

Full text

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The relevance of Brownian
relaxation as power absorption
mechanism in Magnetic
Hyperthermia
Teobaldo E. Torres
1,2, Enio Lima Jr.3, M. Pilar Calatayud1, Beatriz Sanz1, Alfonso Ibarra1,2,
Rodrigo Fernández-Pacheco1,2, Alvaro Mayoral4, Clara Marquina
5,6, M. Ricardo Ibarra1,2,5 &
Gerardo F. Goya
1,5
The Linear Response Theory (LRT) is a widely accepted framework to analyze the power absorption of
magnetic nanoparticles for magnetic uid hyperthermia. Its validity is restricted to low applied elds
and/or to highly anisotropic magnetic nanoparticles. Here, we present a systematic experimental
analysis and numerical calculations of the specic power absorption for highly anisotropic cobalt
ferrite (CoFe2O4) magnetic nanoparticles with dierent average sizes and in dierent viscous media.
The predominance of Brownian relaxation as the origin of the magnetic losses in these particles is
established, and the changes of the Specic Power Absorption (SPA) with the viscosity of the carrier
liquid are consistent with the LRT approximation. The impact of viscosity on SPA is relevant for the
design of MNPs to heat the intracellular medium during in vitro and in vivo experiments. The combined
numerical and experimental analyses presented here shed light on the underlying mechanisms that
make highly anisotropic MNPs unsuitable for magnetic hyperthermia.
e specic power absorption (SPA), also known as specic absorption rate (SAR) or specic loss power (SLP),
quanties the power absorbed by a system of MNPs due to magnetic losses, taking place when an alternate mag-
netic eld (AMF) it is applied to the sample. Magnetic losses are the main physical phenomena involved in mag-
netic hyperthermia treatments (MHT) to target and kill cancerous cells. e physics behind this mechanism
of heating is related to the structural and magnetic parameters of the MNPs (namely the eective anisotropy
constant Ke, saturation magnetization MS, average particle size 〈d〉) and to the viscosity of the medium (η). ere
are no simple analytical solutions for the SPA under general conditions. Many accepted models aim to calculate
numerically the time-dependent magnetization as a function of the applied magnetic eld, i.e., the hysteresis
loop, as its area is the energy absorbed by the MNPs (i.e., the heat released to the environment) during a single
AMF cycle. A study by J. Carrey et al.1 having the equilibrium functions, the Stoner-Wohlfarth model-based
theories and the linear response theory (LRT)2,3 as starting point to describe the magnetic relaxation dynamics,
has accounted for the power absorbed in the absence of Brownian relaxation. More realistic models developed
by N.A. Usov et al.4 and H. Mamiya5,6 consider both Brownian and Neel relaxation to describe the magnetization
dynamics of a single-domain nanoparticle by the stochastic Landau-Lifshitz equation.
Given the mathematical complexity of the stochastic approach, analytical expressions may be obtained only in
some limits of the model. A frequently used approximation is to assume that the applied eld H0, is small in com-
parison to the anisotropy eld (HK) of the MNPs and therefore, the magnetic Zeeman contribution to the total
energy of the system can be neglected. In this way, H0 does not distort the energy barrier that separates the two
1Instituto de Nanociencia de Aragón (INA), Universidad de Zaragoza, C/Mariano Esquillor s/n, CP 50018, Zaragoza,
Spain. 2Laboratorio de Microscopias Avanzadas (LMA), Universidad de Zaragoza, C/Mariano Esquillor s/n, CP 50018,
Zaragoza, Spain. 3Div. Resonancias Magnéticas, Centro Atómico de Bariloche/CONICET, S.C 8400, Bariloche,
Argentina. 4School of Physical Science and Technology, Shanghai Tech University. 393 Middle Huaxia Road, 201210,
Pudong, Shanghai, China. 5Departamento de Física de la Materia Condensada, Facultad de Ciencias, Universidad
de Zaragoza, CP 50009, Zaragoza, Spain. 6Instituto de Ciencias de Materiales de Aragón (ICMA), Consejo Superior
de Investigaciones Cientícas (CSIC) - Universidad de Zaragoza, Zaragoza, Spain. Correspondence and requests for
materials should be addressed to T.E.T. (email: teobaldotorresmolina@gmail.com)
Received: 3 May 2018
Accepted: 3 December 2018
Published: xx xx xxxx
OPEN
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possible states between which the MNPs magnetic moment uctuates (Néel relaxation). Within this assumption,
the LRT makes use of the eective relaxation time that results when considering both Néel and Brown relaxations
as independent mechanisms2,3,7. For MNPs with high eective anisotropy (i.e. Hk ≫ H0) the power absorption is
driven by the rotation of the particles due to the magnetic torque at moderate or even high elds (which has been
dened by N.A. Usov et al.4 as viscous mode). For MNPs with moderate anisotropies (e.g. iron oxides) the exper-
imental values of H0 satisfying the LRT are roughly
mH10kA/
0
4.
With the aim of analyzing the validity of the LRT in highly anisotropic systems, the SPA of a series of
cobalt-ferrite MNPs has been studied. Bulk cobalt ferrite has the highest magnetocrystalline anisotropy among
all spinel ferrites, with a magnetocrystalline anisotropy constant K1 = 2 × 105 J/m3. First, the SPA has been calcu-
lated, for MNPs of dierent average diameters assuming that their anisotropy and saturation magnetization have
the values of the bulk CoFe2O4. With these input values, the simulations have been performed in a wide range of
H0 and f, obtaining the dependencies of the SPA on these parameters. e SPA has also been measured in a series
of Co-ferrite MNPs (with average diameters 〈d〉 between 5 and 25 nm) dispersed in hexane, in magnetic elds of
amplitude up to 24 kA/m, and frequencies up to 828 kHz. e experimental SPA results have been compared with
the numerical simulations carried out taking as input for our calculations the physicochemical parameters (size,
magnetic anisotropy, and magnetization) obtained from the respective structural and magnetic characterization
of the MNPs previously reported8. As far as we know, the good agreement observed between simulations and
measurements constitutes the rst experimental conrmation of the validity range of the LRT for highly aniso-
tropic MNPs, establishing the strong correlation of the frequency and strength of the magnetic eld in a given
experiment, with the physicochemical parameters of a given MNPs suspension. erefore, besides establishing
the frequency and magnetic eld strength for which the LRT is valid, our numerical simulations make it possible
to nd the optimal MNPs, with magnetic and structural parameters such that result in the maximum SPA for
xed experimental magnetic eld amplitude (H0) and frequency (f) conditions.
When the magnetic anisotropy of MNPs is such that the energy barrier required to ip the magnetic moments
is much larger than thermal energy at room temperature, the Brownian rotation is the predominant mechanism
for magnetic relaxation4. In this situation, the hydrodynamic diameter of the MNPs and the viscosity of the
medium are key parameters to determine the SPA. To explore the actual inuence of these parameters on SPA in
the case of Co-ferrite MNPs we performed systematic numerical simulations in media with dierent viscosities,
nding good agreement with experimental SPA values measured. In vit ro hyperthermia experiments were carried
out on a culture of MNPs-loaded cells to assess the relevance of Brownian relaxation. Once inside the cell, MNP
aggregates (whose presence was conrmed by Focused Ion Beam-FIB 3D reconstruction) are not free to rotate,
due to the high viscosity of the medium. e lack of Brownian relaxation would explain the absence of heating
observed in our experiments.
Results and Discussion
Numerical simulations of power absorption. We performed numerical simulations within the ‘classi-
cal’ SPA (CSPA) model, applied to magnetic colloids by Rosensweig7, which considers that both Néel and Brown
relaxations are the main mechanisms for magnetic relaxation. As shown in the Supplementary Information,
within the CSPA model for the magnetic relaxation of the MNPs the out-of-phase component χ″ of the magnetic
susceptibility under an alternating magnetic eld of amplitude H0 and frequency f is given by:
χχ
πτ
πτ
″= +
f
f
2
[1 (2 )] (1)
02
where χ0 is the equilibrium susceptibility of the MNPs. e CSPA model assumes that the Néel and Brown relax-
ation are independent processes so that the eective relaxation time τe of a single-domain MNP can be expressed
as:
τττ=+
−−− (2)
effN B
111
where
ττ τη
==eV
kT
and3
(3)
N
KV
kT Bh
B
0
M
B
are the Néel and Brown relaxation times and VM and Vh are the magnetic and hydrodynamic volumes, respec-
tively. e parameter τ0 can be considered as an ‘attempt time’ having values of ~10−9–10−11 s. General consid-
erations about the origin of these two mechanisms show that they cannot be independent because the physical
rotation (i.e. Brownian relaxation) of any particle respect to a xed spatial coordinate system implies a change
on the direction of the magnetic moment (i.e. Néel relaxation). For Co-ferrite nanoparticles, the large value of
the magnetocrystalline anisotropy constant of this material gives, for particle sizes d > 5–6 nm, a large contri-
bution from KV to the exponential in Eq. (3) that makes τN exceedingly large (see Fig.S3 in the Supplementary
Information). Under these conditions, Brownian relaxation, is expected to dominate and τe in Eq. (2) is given by
a single contribution. For sizes d < 5–6 nm the two contributions to the relaxation must be considered.
Considering the above arguments and assuming a Gaussian size distribution for the MNPs, the CSPAM yields
an expression for the power absorption of this ensemble of MNPs under an applied magnetic eld of amplitude
H0 and frequency f of the form (see the Supplementary Information).
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∫µπ χπτ
πτ π
=+×
∞




−





−










SPAfHf
fw
expd(d)2
(2 )1
1
/2 d
(4)
eff
eff
w
000
2
02
2dd
0
2
where 〈d0〉 is the statistical mean value of the particle diameter, w gives the size distribution width (full-width
at half maximum), χ0 is the susceptibility of an ensemble of particles in the equilibrium, and χ0 is the magnetic
permeability on the free space.
To explore the validity of the model in purely Brownian systems, we have numerically calculated the SPA using
Eq. (4). e simulations were performed for colloids of Co-ferrite MNPs of diameter 〈d〉 such as 1 ≤ 〈d〉 ≤ 100 nm
and having a size distribution width w = 1.48 nm (see Supplementary Information). e carrier liquid was hex-
ane (η = 2.94 × 10−4 kg/ms)8. e saturation magnetization and eective anisotropy constant were assumed to
be those of the bulk CoFe2O4 phase (i.e., MS = 4.2 × 105 A/m, and Ke = 2 × 105 J/m3)9. From a previous physical
characterization reported elsewhere8 the hydrodynamic volume of the MNPs in hexane was assumed to be that
of the core of diameter 〈d〉 plus an oleic acid surface layer of thickness δ = 2.0 nm as estimated from DLS analysis
(therefore, Vh = π(d + δ)3/6; see TableS1 in the Supplementary Information). e calculations were done for mag-
netic eld amplitudes H0 such as 7.9 × 10−2 ≤ H0 ≤ 38 kA/m and frequencies f such as 10−1 kHz ≤ f ≤ 2 × 105 kHz.
Figure1 presents the resulting simulations of the SPA as a function of the frequency when H0 = 18.5 kA/m
(Fig.1a), and as a function of the eld amplitude when f = 580 kHz (Fig.1b). A common feature of these curves
is that for some 〈d〉 values, the SPA has a maximum. e size that maximizes the SPA depends on the frequency
and, to a less extent, on the magnetic eld intensity H0. Some of the values presented in the Fig.1a,b are beyond
the limit of the LRT in our case because (kBT < μ0MSVH0), Nevertheless, we performed such simulations because
they allow us to understand how is the variation of SPA with H, f and d within a range of reasonable experimental
values.
To address these dependences separately, we will explore rst the shape of the frequency dependence of the
SPA, assuming in this case the expansion of the Langevin function around H0 ≈ 0, so that the susceptibility of
the system is χ0 = χi (i.e., the initial susceptibility, which is by denition a eld-independent parameter; see the
Supplementary Information for details. According to (4) the SPA (H0, f) has a simple dependence:
=Γ +
SPAH
f
f
B
(B )1 (5)
0
2
2
2
where Γ is a eld- and frequency-independent parameter that contains the magnetic properties of the MNPs,
and B = 2πτe. Figure1c shows the frequency dependence of the SPA for the ΓHo2 ≈ 1 condition, calculated
by Eq. (5) for four dierent particle sizes (i.e., for four dierent values of τe in B). ere is an upper limit for
the SPA, whose value are given by Γ (i.e., characteristic of each particle). e green shaded area in Fig.1c com-
prises the most common frequency values reported in SPA measurements, coinciding with the experimental fre-
quency range in this work and includes the points where the SPA has the steepest changes only for particles with
d ≥ 8 nm. e inset of Fig.1c shows that the particle size with maximum derivative shis above f ≥ 1 Mhz values
for d ≤ 8 nm and, for MNPs larger than ≈20 nm the maximum SPA is already attained at ≈50 kHz. Figure1d
shows a semi-logarithmic representation of the frequency dependence of the SPA calculated from Eq. (4) for
MNPs with 〈d〉 up to 50 nm (i.e., below the critical single-domain diameter reported for cobalt ferrites)10.
In this case, all curves have similar dependences: almost no power absorption is observed for f < 101 kHz,
which is followed by a steep increase for frequencies such as
f1010
13
kHz, and a saturation of the SPA for
f > 103 kHz. e shaded area in the Fig.1d shows the frequencies values used in our experiments and in most of
the experiments found in the literature. According to the gure, as the particle diameter increases, the frequency
for which the maximum increase of the SPA is observed shis to lower values. Whereas for diameters around
3–4 nm this region is centered at f ≈ 100 MHz, it shifts to 30–60 MHz for 〈d〉 between 13 and 25 nm. For
〈d〉 ≥ 35 nm the SPA is already saturated at f ≈ 5 MHz.
Figure1e shows the SPA dependence on H0 for f = 580 kHz calculated with Eq.4. Assuming χ0 is
eld-dependent (See Eq.S10). e results show that despite the system fullls the condition H0 ≫ HK, a deviation
of the quadratic dependence of SPA with the magnetic eld strength H0 is observed. is deviation could be due
to the magnetic eld dependence of τB, as was reported by Yoshida and Enpuku11 and was not taken into account
in our model.
ese results were tted with a power law SPA = ΦHλ, with λ between 1.99 and 1.09. Our results show that at
xed frequency, the quadratic eld dependence of the SPA is only fullled up to certain values of the magnetic
eld strength that depend on the particle size. For increasing particle size the maximum magnetic eld for which
∝SPA H0
2
holds decreases. In particular, at f = 580 kHz, the quadratic dependence for elds H0 ≤ 24 kA/m (the
experimental maximum value in this work) is satised only for the particles with d ≤ 8 nm, expected in a certain
way due to the argument mentioned above, (kBT < μ0MSVH0). is region of experimentally achieved elds is
represented in Fig.1f as the green shaded area labeled “experimental”, which denes the attainable (H0, d) values
in our experiments. e black shaded area labeled ‘quadratic’ represents the expected (H0, d) loci for which the
∝SPA H0
2
dependence is fullled, calculated for elds up to 40 kA/m. e diagram shows that only cobalt ferrite
particles with 〈d〉 ≤ 8 nm are expected to obey this quadratic dependence for any applied eld intensity. On the
other hand, for those particles with 〈d〉 ≥ 25 nm the
∝SPA H0
2
condition should never be expected. We under-
stand that this model is not the more rigorous but it is an easy tool in order to explore the frequency and ampli-
tude field dependence of the SPA for systems where the mechanical mechanism of magnetic relaxation is
dominate.
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Comparison to colloids and in vitro experiments. e SPA of seven samples of Co-ferrite MNPs in
hexane with average particle diameters 5 ≤ 〈d〉 ≤ 25 nm was measured at frequencies 229 ≤ f ≤ 828 kHz and
magnetic eld amplitudes 9.5 ≤ H0 ≤ 24 kA/m (see materials and methods section). e experimental values
were compared to the numerical simulations. For each sample, the input parameters for the simulations were
those obtained from the respective structural and magnetic characterization of the MNPs (size, size distribu-
tion width, hydrodynamic radius, anisotropy constant, and saturation magnetization), previously reported else-
where8. e anisotropy constants Ke and saturation magnetization MS of these samples were found to be within
1.2 × 105 < Ke < 3.78 × 105 J/m3, and 24 ≤ MS ≤ 76 Am2/kg, respectively. e corresponding anisotropy elds
HK estimated from these numbers (1.2 × 103 < HK < 1.9 × 103 kA/m) satisfy the condition H0 ≪ HK in the whole
Figure 1. Results of the numerical simulations using Eq.4 of (a) SPA vs. particle diameter and frequency
(H0 = 18.5 kA/m). (b) SPA vs. particle diameter and H0 (f = 580 kHz). (c) SPA vs. frequency and particle
diameter obtained with Eq. (5) for ΓHo2 ≈ 1 condition. e shaded area corresponds to the experimental
frequency range (250–828 kHz) in this work. e inset shows the derivative of the SPA curves. (d) Semi-
logarithmic representation of SPA vs. f at (H0 = 18.5 kA/m) for particle diameters 8 < d < 50 nm (s olid symbols
are calculated data; lines are a visual guide). e shaded area indicates the experimental frequency window in
this work. (e) SPA vs. H0 (f = 580 kHz) for particle sizes 5 ≤ d ≤ 25 nm. Dashed lines represent the best t using
the power law
Φ≅λ
SPA H
. e line is a visual guide. (f) H0 vs. 〈d〉 (f = 580 kHz) plot. e black shaded area
delimits the particle size values for which the condition
SPA H0
2
∝
is fullled. e green shaded area identies
the (H0, d) space of experimental elds H0 ≤ 24 kA/m of this work. All simulations were performed with
MS = 4.2 × 105 A/m, Ke = 2 × 105 J/m3, and η = 2.94 × 10−4 kg/ms (see text).
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range of experimental applied elds. e comparison between numerical calculations and the experimental data
are shown in Figs2 and 3.
A reasonable agreement between the simulated and experimental values of the SPA was achieved for the
whole series of samples, except for the 〈d〉 = 5 nm sample for the reasons discussed below. e agreement between
simulations and experiment for 〈d〉 = 13 nm, i.e. the size of the maximum SPA, is remarkable. For those sam-
ples with intermediate SPA values the dierences could be assigned to partial agglomeration of the MNPs in
the suspension that yields an underestimation of the hydrodynamic diameter and aects the calculated τB (see
TableS1 in Supplementary Information). e large dierences between the calculated and experimental SPA for
the sample with 〈d〉 = 5 nm (5 W/g and 0 W/g respectively, at the maximum eld) are likely to be originated in
the spin surface conguration of this sample. Indeed, the magnetic characterization of this sample showed that
Figure 2. SPA vs. frequency: the experimental data (blue circles) are obtained at H0 = 18.5 kA/m. Dashed lines
are the SPA resulting from the simulations; the respective input parameters are obtained from the respective
sample physicochemical characterization (see text).
Figure 3. SPA vs applied magnetic eld intensity H0: the experimental data (red circles) were obtained at
f = 580 kHz. Dashed lines are the SPA resulting from the simulations; the respective input parameters were
obtained from the respective sample physicochemical characterization (see text).
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the magnetization was largely diminished in comparison to the other samples, and did not saturate even for
applied elds larger than 11.2 × 106 A/m. Also, the M(H) curves for this small MNPs showed an open hysteresis
loop up to that maximum attainable eld8. ese observations are consistent with a spin canted conguration of
the surface magnetic moments, a well-known eect for small-sized ferrite nanoparticles12,13. Moreover for these
particles the corresponding Néel and Brown relaxation times have similar values (see Fig.S3 in Supplementary
Information) and therefore the two mechanisms cannot be considered as independent. A more realistic analysis
of this situation would require numerical simulations using the comprehensive models proposed by N.A. Usov et
al. and H. Mamiya et al.4–6.
We note also that the relaxation mechanisms depend also on the applied magnetic field, as reported by
Yoshida and Enpuku11. According to these authors, nonlinear eects can be expected in Brown relaxation at high
applied magnetic elds, which is supposed to be more signicant for systems driven by Brown relaxation, as is the
case in the Co-ferrite MNPs studied in this work. Accordingly, when analyzing the dependence of the SPA with
applied elds (Fig.3) up to H0 = 24 kA/m (a value 20% larger than that in Fig.2) the discrepancies easier to see,
suggesting that nonlinear eects in τB are operative. Since the values of SPA calculated numerically for particles
with 〈d〉 = 25 nm are of the order of ≈0.01 W/g, these values are well below our experimental resolution (≈2 W/g
for the conditions of this sample), and therefore both sets of data are considered as equivalent.
In a recent work on Fe3O4 MNPs within the LRT framework14 it was shown that dipolar interactions due
to agglomeration lower the SPA. Similar conclusions were drawn by Branquinho et al. in the case of MnFe2O4
MNPs15. Since our model did not include magnetic dipolar interactions, they could partially explain the discrep-
ancies with the experimental SPA in Figs2 and 3. Interestingly, there are also works attributing a SPA increase
to agglomeration eects in MgFe2O4 and NiFe2O4 MNPs16. As mentioned in previous sections, in our samples
the main mechanism involved is the Brownian relaxation, except in the case of the smallest particle volumes. As
shown in Fig.S3, for the smallest particles, Néel and Brown relaxation times have similar values and therefore
the Néel component in the power absorption should be also taken into account. In these cases, the mechanism of
relaxation is more vulnerable to the dipolar interactions and the LRT show limitations for a complete description
of the physical phenomenon i.e., the Specic Power Absorption.
e limitations of the LRT framework to account for dipolar interactions have been discussed previously15,17
and there is consensus on the need to use more realistic models18 as well as to precisely characterize the main
magnetic and physicochemical parameters of each specic magnetic colloid19. Values of SPA in Co-ferrite MNPs
with 〈d〉 between 6 and 41 nm have been reported to range between 6 W/g and 800 W/g20–27. Since these values
have been obtained at dierent H0 and f and being the MNPs dispersed in dierent liquid carriers, the compar-
ison with our SPA experimental values is not straightforward. e reported data show that at xed H0 and f the
maximum SPA is obtained for MNP diameters about 12–13 nm24. e systematic SPA measurements on a series
of Co-ferrite MNPs performed by A Sathya et al.28 show the same size dependence, being the optimal size for the
maximum SPA about 17 nm. In addition, a steep dropping of SPA values below and above the optimal MNP size
has also been reported22,26.
As mentioned above, the viscosity η of the carrier media determines the eective value of SPA when Brownian
relaxation is the dominant mechanism28,29. Our simulations of the SPA vs. 〈d〉 curves in carrier liquids with dif-
ferent viscosities (water, hexane and blood) displayed the expected drop in SPA for increasing η values, keeping
the bell-shaped dependence with a maximum at some optimal size value 〈d〉op (see Fig.S9 in the Supplementary
Information). e maximum of SPA shis to lower values of 〈d〉op for increasing viscosities (Fig.S9a), underlining
the relevance of knowing the actual environment where the MNPs are going to be used. For magnetic hyperther-
mia, this implies to characterize the biological media where the heating by the MNPs is required30,31.
In the following paragraphs of this section, all the in vitro experiments discussed have been performed using
a sample of Co-ferrite MNPs specically chosen because of its high SPA (≈570 W/g in hexane). e crystallo-
graphic structure and magnetic data for this sample are shown in Fig.S2 of the Supplementary Information. e
MNPs were transferred to aqueous suspension following the procedure described in the material and methods
section. e study of the in vitro heating eciency was performed on human neuroblastoma SH-SY5Y cells.
e cell viability aer incubation with the MNPs as a function of the concentration (see FigsS10 and S11 on
Supplementary Information) was consistent with previously reported data on SH-SY5Y cells using Fe3O4 par-
ticles32. However, we mention here that due to the positive surface charge of the magnetite MNPs the eective
amount bonded/incorporated to the cells was much larger in ref.32. In the present case, the intracellular distri-
bution of MNPs aer overnight incubation was scrutinised by Transmission Electron Microscopy (TEM) and
Focused Ion Beam - Scanning Electron Microscopy (FIB-SEM).
For all the MNP concentrations studied, the images showed similar general trends: aer proper washing of
the culture, most of the remaining MNPs were located within the cytoplasm, specically within vesicles, as small
aggregates. A minor amount of MNPs attached to the cell membrane were also observed. e images in Fig.4
correspond to a single cell incubated with 20 µg/ml of MNPs (Fig.4a). Figure4d shows the Energy Dispersive
X-ray spectroscopy (EDS spectra) of a MNP cluster inside a vesicle (Fig.4b) and of a single particle (Fig.4c).
ese EDS–HAADF (High Angle Angular Dark Field) spectra showed the Kα and Lα peaks expected for iron
and cobalt, characteristic of the composition of our nanoparticles. Moreover, it can be observed that the mor-
phology of the MNPs is preserved inside the vesicles, ruling out any signicant particle degradation (see also the
Supplementary Information). e 3-D reconstruction of several cells (VideosVS1 and VS2 in the Supplementary
Information) suggests an endosome-mediated uptake process.
For the power absorption experiments, the cells were incubated with the maximum MNP concentration for
which a negligible cytotoxicity was observed (100 μg/ml), corresponding to a MNP concentration of 2 × 10−2 mg/
ml inside the cells aer incubation. e variation of temperature observed during the power absorption experi-
ments is represented in Fig.5a together with the data corresponding to a control sample (1 ml of pure water). e
water curve represents the background signal arising from the self-heating of the equipment (from the Joule
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heating of the coil), and it was measured to subtract it from the heating data of the samples. e inset of Fig.5a
clearly shows that during the rst ≈5–7 minutes no temperature increase was observed in the sample containing
MNP-loaded cells. Moreover, aer subtracting the control curve the maximum temperature increase measured
aer 2100 s was ΔT ≤ 0.9 °C, much lower than expected from the SPA calculations/measurements on the as syn-
thesized MNPs. e small temperature increase observed is consistent with the distribution of the MNPs inside
the cytoplasm, i.e., forming large agglomerates within vesicles. Together with the high viscosity of this environ-
ment it results in a large increase of the Brown relaxation time,
τ
=
η
B
V
kT
3h
B
, thus hindering viscous losses. To verify
that the nearly-zero temperature increase was due to the blocking of the MNP rotation and not to a low MNP
concentration inside the cell, we dispersed 2 × 10−2 mg/ml of MNPs in hexane. We measured the temperature
increase ΔT in this sample, and subtracted the background heating using pure hexane as a control. e heating
curves are shown in Fig.5b.
ere is a marked dierence between the heating proles of the control sample and the MNPs colloid, even
shortly aer starting the measurement (t < 600 s). A fast temperature increase is observed for the MNPs sample
(about 1.5 °C in the rst minutes). We calculated the SPA of the MNPs sample aer background subtraction,
by tting the dierence curve for t < 400 s, using a Box-Lucas function33, obtaining ΔT/Δt = 0.005 °C/s, which
produces an SPA = 367 W/g. is value is 35% lower than that of the as synthesized sample, probably because
the measured ΔTs are within the resolution limit of our equipment at the experimental conditions described.
Figure 4. (a) STEM image of SH-SY5Y cells incubated with Co-ferrite nanoparticles at 20 µgml−1 for 24 hours.
(b,c) Are zooms of the region selected on (a). (d) EDS spectrum (in blue) of the small group of MNPs selected
in (b) and EDS spectrum (in red) of the particle selected in (c). Both show the presence of iron and cobalt in the
MNPs. (e) Snapshot of the 3D cell reconstruction incubated with Co-ferrite MNPs at 100 µgml−1 for 24 hours.
Red spots correspond to MNP aggregates.
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ese results rule out the low concentration as the reason for the absence of heating of the in vitro experiments.
e eect of the liquid viscosity on the experimental SPA values was assessed by measuring the same MNPs in
dierent solvents (hexane, toluene, chloroform, water and cell culture medium, see Fig.5c). e actual intracel-
lular viscosity used has been assumed to be η = 5 × 10−2 kg/ms as reported in ref. 34. e decrease of SPA with the
increasing viscosity conrms the major contribution from Brown relaxation to the heating mechanism.
Figure 5. (a) Heating curves of SH-SY5Y cells loaded with MNPs (black curve) and of 1 ml of pure water (red
curve) as control sample. e blue curve is the dierence between both experiments. Inset: magnication of the
same curves for t ≤ 7 min. (e applied eld was turned on at t = 0). (b) Heating curves of the as prepared MNPs
sample diluted up to 2 × 10−2 mg/ml in hexane (black); pure hexane (red) and the dierence between both
curves (blue). Inset: heating curves with a modied Box-Lucas t. (c) SPA of the MNPs dispersed in dierent
media as a function of the solvent viscosity, included the cell culture medium DMEM (Dulbecco modied
Eagles minimal essential medium). All the experiment were carried out at H0 = 24 kA/m and f = 571 kHz.
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Conclusions
Our investigation on the heating capability of highly anisotropic Co-ferrite nanoparticles conrmed that the SPA
values up to ≈1300–1400 W/g obtained in low-viscosity media originate in a purely Brownian relaxation mecha-
nism. e numerical simulations provided a good match of the power absorption with the systematic experimen-
tal data. Deviations of the
SPA H0
2
∝
dependence of the SPA with the applied field expected within the LRT
emerged for certain values of H0 and f that depend on the average particle size considered. In vitro SPA measure-
ments conrmed the total suppression of the Brown relaxation at the intracellular level, and the intracellular
distribution of the MNPs within vesicles (either endosomes or lysosomes) provides further support to the
hypothesis that the stalling of the Brown relaxation is due to a high viscosity local environment.
Materials and Methods
Synthesis of Co-ferrite nanoparticles. e cobalt ferrite nanoparticles used here were synthesized by
thermal decomposition of iron acetylacetonate (acac)3 and cobalt acetylacetonate (acac)2 in organic solvents and
in the presence of oleic acid and oleylamine35,36 as surfactants. Dierent organic solvents (phenyl ether, benzy-
lether, 1-octadecene, and trioctylamine) having dierent boiling temperatures, were used in order to control the
nal particle size. e details about the preparation were reported in a previous work8. e method used for their
stabilization in water was the interspersion of an amphiphilic polymer with the oleic acid on the nanoparticle
surface. e general diagram for the transfer process is the following: the hydrophobic part of the polymer, the
monomeric unit of 1-octadecene, has lateral chains of 18 carbon atoms that are insert with the oleic acid inter-
acting hydrophobically. e hydrophilic part, the monomer unit of maleic anhydride, is exposed outside and is
capable to stabilize the nanoparticles in aqueous medium by the carboxyl groups that are generated by hydrolysis
of the anhydrides (made using sodium hydroxide)37. For the present work it is important to mention that, down
to the single-particle analysis, all samples consisted of an homogeneous phase CoxFe3−xO4, with a systematic
deviation from the stoichiometric x = 1. e histograms for all samples showed small size distribution width
(w = 2.9), exemplied with samples AV09 (〈d〉 = 9.5 nm) and AV15 (〈d〉 = 15.0 nm) in Fig.S1 of Supplementary
Information.
Transmission Electron Microscopy (TEM). e detailed structural and morphological characterization
of the samples studied in this work was carried out by transmission electron microscopy TEM and STEM modes.
e TEM images were obtained using a thermoionic LaB6 200 kV Tecnai T20 microscope (FEI Company) operat-
ing at an accelerating voltage of 200 kV. STEM–HAADF images were acquired using an XFEG TITAN 60–300 kV
(FEI Company), operated at 300 kV, equipped with a monochromator and a probe aberration corrector (CEOS).
For these experiments a drop of the MNP suspension (either in hexane or in water) was deposited on a holey
carbon coated micro-grid. TEM images were obtained aer the evaporation of the solvent, when the sample dried
completely. From these images, size histograms were obtained. ey were tted using a Gaussian distribution
function g(x)) of parameters (w, d0) given by:
=π




−




−










gd wexp() 1
(6)
dd
w
0
2
20
2
being w and d0 the FWHM (full-width at half-maximum) and the mean value of the distribution, respectively.
Magnetic Characterization. Magnetization measurements M(H) were performed on a commercial
SQUID magnetometer (MPMSXL Quantum Design) on dried samples. e powder was conditioned inside plas-
tic capsules as described elsewhere8. Magnetic measurements for quantication of the cellular MNP uptake were
done at room temperature in a vibrating sample magnetometer (Lake Shore 7400 Series VSM), as a function of
the eld up to 1.5 T.
Heating Eciency Measurements. Power absorption experiments under ac magnetic elds were per-
formed in a commercial applicator (DM100 from nB nanoscale Biomagnetics, Spain) at frequencies such as
229 ≤ f ≤ 828 kHz and applied magnetic elds such as 7.95 ≤ H0 ≤ 24 kA/m. e SPA values of magnetic colloids
containing a total mass mNP of MNPs dispersed in a mass ml of carrier liquid were calculated as:
==
+




∆
∆





SPA
P
m
mc mc
m
T
t(7)
NP
ll NP NP
NP
where cl and cNP are the specic heat capacities of the liquid carrier and the magnetic nanoparticles, respectively.
ΔT is the temperature increase of the sample measured in a time interval Δt. Since for these experiments the
concentration of MNPs is usually in the range of 1% wt., we can approximate
+≈mcmcs mc
ll NP NP ll
and the Eq.
(7) can be written as
δ
φ
=





∆
∆





SPA
CT
t(8)
ll
where δl and φ are the density of the liquid and the (mass) concentration of the MNPs in the colloid, respectively.
e heating rate ΔT/Δt in °C s−1 is obtained from the initial temperature increase, within the rst 50–100 sec-
onds of the experiment.
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Dynamic Light Scattering. e distribution of hydrodynamic diameters when the nanoparticles are dispersed
in hexane or in water was obtained using a Brookhaven Instruments 90 Plus photon-correlation spectrometer.
MNPs Cell culture. Dulbecco’s modied Eagle’s medium (DMEM) was chosen as the medium for culturing
human neuroblastoma SH-SY5Y cells (ATCC CRL-2266), in a mixture of Ham’s F12 (1:1) mixture with 15%
fetal bovine serum. Aliquots of penicillin (100 IU/ml) and Streptomycin (100 µg/ml) were added to the culture
medium together with 2 mM of L-glutamine. Incubation of the cells was done in all cases maintaining the samples
at 37 °C within an incubation atmosphere composed by 95% air and 5% CO2. e SPA experiments in cell pellets
were performed aer the cells were incubated for 24 hours with dierent concentrations of MNPs, then washed
several times and the culture medium was replaced by fresh, ordinary DMEM composition medium. Cells for
control samples (i.e., without MNPs) were grown simultaneously in each experiment, in order to replicate possi-
ble environmental uctuations from pellet to pellet.
Cell Viability Assays. Cell viability assays were performed aer incubation with MNPs using ≈80 × 103 cells
at the exponential growth phase of the cell cycle. e cells were seeded onto a twelve-well plate and incubated for
24 h. Aer that, culture medium with increasing MNPs concentrations (1, 5, 10, 20, 50 and 100 µg/ml) was used
to replace the modied-DMEM and the cells were incubated for another 24 h. Trypan blue assays were conducted
by diluting 20 ml of cell samples into Trypan blue (1:1) before the viable cells were counted. e fractions of
viable cells as compared to control cells were calculated, assuming 100% viability for the control cells. For ow
cytometry analysis Annexin-binding buer (composed by 5 ml of Annexin and 5 ml of propidium iodide) was
used to incubate the cells for 15 min at room temperature, keeping a dark environment. e resulting viability was
analyzed using a FACS Aria Cytometer and FACS Diva Soware.
For the study of the intracellular MNPs distribution by TEM and FIB-SEM the cells were seeded (1 × 106
cells/well) in a 6-well-plate in 2 ml of culture media. Following the protocol described above, aer 24 h increasing
concentrations of MNPs were added and the cells incubated overnight. Aer incubation, the cells were washed,
detached and xed with 2% glutaraldehyde solution for 2 h at 4 °C. ey were washed again three times in caco-
dylate buer (pH 7.2) and treated with potassium ferrocyanide 2.5% and osmium tetroxide 1% for 1 hour at room
temperature. e cells were then dehydrated with increasing concentrations of acetone 30% (x2), 50% (x2), 70%
(x2), 90% (x2), and a nal dehydration with pure acetone. Aer drying, samples were embedded in a solution
(50:50) of EPOXI resin and acetone (100%) overnight, and then for 4–5 hours in resin EPOXI 100%. ese sam-
ples were maintained for 2 days at 60 °C.
Dual Beam FIB-SEM Analysis. Intracellular distribution of MNPs was assessed using a dual beam FIB/
SEM (Nova NanoLab 200 and Helios 650 ermo Fisher Scientic). For these experiments the SH-SY5Y neu-
roblastoma samples were conditioned. SEM images were taken at 2–5 kV with a FEG column, and a combined
Ga-based 30 kV (10 pA and 0.27–9 nA) ion beam was used to cross-sectioning single cells and resin pellet.
Energy-dispersive x-ray (EDS) spectra were acquired in order to identify the presence of characteristic metal
elements (iron and cobalt) in the MNPs.
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Acknowledgements
is work was partially supported by the Spanish Ministerio de Economia y Competitividad (MINECO) through
project MAT2016-78201-P and by the Aragón Regional Government (DGA), through the Research Groups
grants (E-26 and E28-17R) co-nanced by the FEDER Operational Program Aragón 2014–2020 “Building Europe
from Aragon”. We are grateful to Ms. S. Rivera Fernandez (for her assistance in the water-transfer protocols), and
to the Advanced Microscopy Laboratory (LMA) and the Servicio General de Apoyo a la Investigación of the
University of Zaragoza.
Author Contributions
T.E.T., C.M. and G.F.G. conceived the experimental strategies and supervised the project. T.E.T., E.L., C.M. and
G.F.G. designed experiments. T.E.T. synthesized the colloids. E.L. and T.E.T. performed the numerical simulation.
M.P.C. and B.S. performed in vitro experiments. A.I., R.F., A.M., performed the TEM analysis. T.E.T. performed
the 3D FIB-SEM experiments. M.R.I., C.M. and G.F.G. supervised the experimental and theoretical strategies. All
authors participated in the writing and revision of the manuscript.
Additional Information
Supplementary information accompanies this paper at https://doi.org/10.1038/s41598-019-40341-y.
Competing Interests: e authors declare no competing interests.
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