Content uploaded by Daniela Paola Valdés
Author content
All content in this area was uploaded by Daniela Paola Valdés on Mar 20, 2023
Content may be subject to copyright.
Thermographical method to assess the performance of magnetic nanoparticles in hyperthermia
experiments through spatio-temporal temperature profiles
D.P. Valdés and T.E. Torres
Instituto de Nanociencia y Nanotecnología, CNEA-CONICET, Av. Exequiel Bustillo 9500, Bariloche, Argentina.
Instituto Balseiro, Universidad Nacional de Cuyo, Av. Exequiel Bustillo 9500, Bariloche, Argentina.
A.C. Moreno Maldonado
Departamento de Física de la Materia Condensada, Instituto de Nanociencia y Materiales de Aragón,
Universidad de Zaragoza, C/ Mariano Esquillor s/n, Zaragoza, Spain.
G. Urretavizcaya
Instituto Balseiro, Universidad Nacional de Cuyo, Av. Exequiel Bustillo 9500, Bariloche, Argentina. and
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), CNEA,
Centro Atómico Bariloche, Av. Exequiel Bustillo 9500, Bariloche, Argentina.
M.S. Nadal and M. Vasquez Mansilla
Instituto de Nanociencia y Nanotecnología, CNEA-CONICET, Av. Exequiel Bustillo 9500, Bariloche, Argentina.
R.D. Zysler
Instituto de Nanociencia y Nanotecnología, CNEA-CONICET, Av. Exequiel Bustillo 9500, Bariloche, Argentina.
Instituto Balseiro, Universidad Nacional de Cuyo, Av. Exequiel Bustillo 9500, Bariloche, Argentina.
G.F. Goya
Departamento de Física de la Materia Condensada, Instituto de Nanociencia y Materiales de Aragón,
Universidad de Zaragoza, C/ Mariano Esquillor s/n, Zaragoza, Spain.
E. De Biasi
Instituto de Nanociencia y Nanotecnología, CNEA-CONICET,
Av. Exequiel Bustillo 9500, Bariloche, Argentina. and
Instituto Balseiro, Universidad Nacional de Cuyo, Av. Exequiel Bustillo 9500, Bariloche, Argentina.
E. Lima Jr.
Instituto de Nanociencia y Nanotecnología, CNEA-CONICET, Av. Exequiel Bustillo 9500, Bariloche, Argentina.
(*daniela.valdes@ib.edu.ar)
(Dated: December 16, 2022)
The evaluation of the specific power absorption of magnetic nanoparticles (MNPs) for magnetic hyperthermia
(MH) applications has been performed through either local temperature probing or magnetic measurements so
far. Each of these methods has advantages and drawbacks, and the concurrent use of both techniques offers the
most reliable results. In this work, we propose an alternative strategy based on thermographic images to obtain
two-dimensional temperature maps that allow the determination of the power absorption and other relevant ther-
modynamic parameters in MH experiments in a non-invasive way. This procedure and analysis are convenient
to determine the heating performance of MNPs under the viscous conditions of in vitro and in vivo assays and to
follow the time evolution of the temperature spatial distribution in the sample simultaneously. For this purpose,
iron oxide MNPs with 25 nm average diameter were coated with glucose and dispersed into different 8% poly-
acrylamide gels, which serve as phantoms that emulate intracellular viscosity. Power absorption experiments
were performed under ac magnetic fields (H=32 kA/m; f=350 kHz) and the temperature evolution of the
sample was monitored through a commercial thermographic camera (resolution: 240x180 pixels, temperature
accuracy: 2 K). To complement this simple setup, we designed a program consisting of a detailed procedure for
extracting graphical information from the video frames and obtaining spatio-temporal temperature profiles. The
analysis of these profiles allowed us to gather information on temperature, energy, power, and heat flux during
the MH experiments. This method and analysis allowed us to identify spatial inhomogeneities in samples, such
as different local MNP density, which is of utmost importance for the development of the therapy in vitro and
the application in vivo where MNP aggregation is often present.
I. INTRODUCTION
Magnetic nanoparticle (MNP) characterization is usually
performed on colloidal samples, with as prepared carrier
liquids (either organic solvents or water) as the preliminary
step before magnetic hyperthermia (MH) experiments in vitro.
However, the specific power absorption (SPA) values mea-
sured in these colloids are often higher than the ones obtained
2
in cell cultures for the same MNPs. This behavior is gen-
erally attributed to intracellular viscosity being much higher
than that of liquids [1–3] or to the fact that agglomeration pro-
moted by the cellular environment hinders the free rotation
of MNPs [2, 3]. To counter this effect on the performance
in cell cultures, the current consensus is that MNPs for MH
must be engineered to display a low magnetic anisotropy to
ensure a major contribution of Néel’s mechanism in the mag-
netic relaxation [4]. In addition, it has been reported that MNP
agglomerates shaped into elongated clusters can increase the
SPA values of the system [5]. However, shaping the agglomer-
ates often involves placing the cell culture into large DC fields,
which is inconvenient when taking into account the final med-
ical application because it generally promotes MNP-density
inhomogeneities, which implies a non-homogeneus heating in
the sample, culture or tumor. Another cause for these discrep-
ancies is that the SPA is usually obtained through calorimet-
ric methods, where the temperature is measured through local
probes. This method provides information on targeted mea-
suring spots that cannot account for inhomogeneities in tem-
perature and heat generation and is a problem in the current
evaluation of temperature increments as a function of time in
cellular environments as the placement of the local probe (of-
ten a fiber-optic temperature sensor) determines the nature of
the measured curve, added to the culture contamination prob-
lems that interfere with the interpretation of cellular viability
in MH in vitro experiments. These facts can also account for
in vitro experiments where no temperature rise was measured
but a clear diminish in viability was shown [6, 7].
To be able to optimize the experimental conditions for the
application, it is fundamental then to characterize the MNPs in
media with properties similar to the ones encountered inside
cells. There are different characteristics of the intracellular
environment that could be mimicked into a phantom: conduc-
tivity, viscosity, ion concentrations, etc [8–10]. From these,
there is one that is crucial for determining magnetic relax-
ation, and thus the SPA: viscosity [11, 12], which highlights
the importance of emulating it [13]. The viscosity of the cellu-
lar environment ranges from 1 to 10 cP, depending on the cell
type and intracellular localization [14]. The average cytosol
is ∼1.5 times more viscous than water [15] with intracellu-
lar areas with even greater values [16–18]. Polyacrylamide
gel (PAG) viscosity can be adjusted by varying acrylamide
concentration [19]. For this reason, we employed a phantom
composed by PAGs that can reproduce the cytosol viscosity
range [19] for a more realistic study of MNP systems.
Regarding the determination of the power absorption of
MNPs, most of the reported works are based on calorimet-
ric experiments, magnetic ac hysteresigraph measurements, or
both [20–22]. In calorimetric experiments, a local probe (e.g.
a fiber optic thermometer) is used to assess the temperature at
a given point inside the sample. The SPA is then calculated
from the initial temperature increment in time (dT/dt) of the
MH experiment when the system can be assumed to behave
quasi-adiabatically. Heat losses modify dT/dtand make the
determination of the SPA of the system a challenging task,
since they depend on the specificities of the setup, the exter-
nal temperature during experiments, morphology and homo-
geneity of the samples, etc. Many reports have assessed SPA
through the correction of the heat losses [21, 23–25].
There have been numerous articles informing on tempera-
ture spatial profiles in magnetic fluids, tissue phantoms, and
tumors, obtained both experimentally [26, 27] and theoreti-
cally [28, 29], caused by heat propagation to adjacent tissue,
increased tumor vascularization and blood perfusion [29–31].
These intrinsic tumoral conditions result in heat losses that are
detrimental because the effective SPA is significantly lower
in some targeted areas, but also desirable because they pre-
vent the heating, and hence the damage, of the surrounding
healthy tissue [32, 33]. Moreover, heat flux monitoring is crit-
ical for the understanding of the results obtained in biologi-
cal and medical applications, specially for the later because
of the non-adiabatic nature of the system and that a 3D inter-
pretation is mandatory in these cases. However, there are no
reports so far on the assessment of the distribution of SPA val-
ues on the sample through a 1-, 2- or 3D approach neither on
the heat flux during experiments. To assess the temperature in
these kind of experiments, a high-resolution infrared thermo-
graphic camera is often used [26, 27, 34], which allows having
the temperature spatial profiles as a function of time during a
MH experiment but no simultaneous and continuous monitor-
ing is achieved. Thermographic cameras are also beneficial
due to their non-invasive nature and this type of monitoring is
currently preferred over intrusive or destructive local probes
on in vitro testing and in vivo application [35–39], where the
insertion of a fiber-optic sensor into the tissue or tumor is not
posible.
In the present work, we prepared PAGs with dispersed
MNPs and performed MH experiments monitored by a com-
mercial thermographic camera. We developed a method to
gather both spatial and temporal information from the ob-
tained videos and analyzed not only temperature but also the
energy, power, and heat flux of the system in a medium that
emulates intracellular viscosity.
II. EXPERIMENTAL AND METHODS
A. MNP synthesis and characterization
Through the thermal decomposition of iron(III) acetylacet-
onate [Fe(acac)3] in the presence of oleic acid and oleylamine,
using dibenzyl ether as solvent (boiling point ∼570 K) and a
subsequent thermal treatment at 573 K, we obtained iron ox-
ide MNPs (ferrite structure) with an average diameter of 25
nm and a standard deviation of 7 nm. The saturation magneti-
zation at room temperature is MS=68 Am2/kg (for the results
of morphological and magnetic measurements, see Appendix
1).
B. MNP glucose coating
To change the hydrophobic nature of the synthesized
MNPs, their oleic acid coating was removed with an etching
procedure that consisted of several methanol and hot acetone
3
washes and then replaced by glucose coating obtained from
the dispersion of uncoated MNPs with 10 times their mass in
glucose in a pH=12 ammonia solution. The removal of the
organic material through this washing procedure was moni-
tored by Fourier-Transform Infrared Spectroscopy (FTIR, see
Appendix 2). The MNPs in this solution were magnetically
separated and redispersed in Milli-Q water.
C. Polyacrylamide gel preparation
Four 8% PAGs were prepared: a clean PAG without MNPs
(blank), a PAG with dispersed MNPs at a concentration of 0.1
wt% (0.1 wt% - dispersed), another one at 0.5 wt% (0.5 wt%
- dispersed) and, finally, a PAG with oriented MNPs at a con-
centration of 0.5 wt% (0.5 wt% - oriented). For this matter, we
prepared an acrylamide/bisacrylamide solution (30/0.8% w/v)
and used an aliquot of 195
µ
l with 200
µ
l of 0.375 M Tris-
HCl pH 8.8 buffer solution for each of them. Then we added
350
µ
l of Milli-Q with 0, 0.8, or 4.0 mg of dispersed glucose-
coated MNPs, respectively for the blank, the 0.1 wt% or 0.5
wt% PAGs. As the polymerization of acrylamide is given by
a free-radical driven reaction [40], 55
µ
l of ammonium per-
sulfate (APS) was added as a free radical initiator and 6
µ
l of
N,N,N’,N’-tetramethylenediamine (TEMED) to stabilise the
polymerization chain reaction [41]. This produces ∼800
µ
l
of PAG in an acrylic sample holder with a diameter of 1.3 cm.
In the case of the PAG with oriented MNPs, the mixture of
acrylamide/bisacrylamide, Tris-HCl buffer, and Milli-Q water
with MNPs was placed into the sample holder and inside a
coil. Once an ac field of amplitude 32 kA/m and a frequency
of 350 kHz was applied for 2 min, the polymerizers (APS and
TEMED) were added and the elongated MNP arrangements
were fixed.
D. Specific heat determination
A differential scanning calorimeter (DSC) TA Instruments
Q2000 was used to determine the specific heat of the sam-
ples. The specific heat of a blank PAG and PAGs with MNPs
at a concentration of 0.1 and 0.5 wt% was obtained by fol-
lowing the classical Three-Step Procedure [42] that involved
the measurement of the baseline, a sapphire standard, and the
samples. The ramps used were 2, 5, and 10 K/min and the
purge of the cell was done with a nitrogen flux of 50 ml/min.
The measurements were carried out for a temperature range
going from 283 to 308 K. At least 2 determinations were made
for each condition.
E. Thermographic camera measurements
The PAG phantom was centered into a coil with a water
jacket, which had an inlet and an outlet for recirculating water
at ∼15 ◦C, as seen in Figure 1. A power absorption experi-
ment was carried out on an EASYHeat 5060 with an ac field
of amplitude 32 kA/m and a frequency of 350 kHz and was
monitored through a FLIR E50 thermographic camera placed
on a tripod ∼50 cm above the phantom, as seen in Fig. 1.
FIG. 1. Images of the experimental setup with indications to the
corresponding elements. The images represent a power absorption
experiment conducted on a blank PAG and monitored through a ther-
mographic camera placed on a tripod.
This thermographic camera is, as stated by the manufac-
turer, a rugged, handheld camera fit for a routine inspection.
The video recording consisted of 60 s of temperature stabi-
lization, then the power absorption experiment followed by
the shutdown of the magnetic field and the cooling period
of the phantom until the equilibrium (room) temperature was
again reached. The camera didn’t support grayscale record-
ing so one of the available RGB temperature scales was cho-
sen, which required an RGB to grayscale transformation af-
terward.
It is noteworthy that the camera was always used in the op-
timal conditions described by the manufacturer. The camera’s
resolution (240x180 pixels) translated into a spatial resolution
of ∼100
µ
m in the PAG. The temperature accuracy stated by
the manufacturer is 2% of reading or 2 K.
This thermographic camera allowed the temperature scale
to be fixed before the experiment or to be set in automatic
mode (which means that the temperature scale can be updated
on the go, as the temperature increases). However convenient
this might seem, the automatic mode presents a serious prob-
lem regarding temperature calibration because the update rate
is lower than the frame rate. Therefore, the temperature scale
was set to a fixed temperature range (from 290 to 308 K) and
the time span of the experiment was controlled in order to
avoid surpassing the temperature limit.
The camera had an autofocus feature that caused temper-
ature determination problems when recording long videos.
This feature couldn’t be turned off and videos with this kind
of problems had to be repeated. Finally, all artifacts (such as
scope marks or targets) that perturbed the images for process-
ing had to be deactivated.
As the constant operation of the water chiller heated the sur-
roundings, the room where the experiments were conducted
was ventilated after each recording to ensure that the equilib-
rium temperature was more or less the same for each of them.
4
Video Frames
0
1 s
...
x
y
x
y
Distance
Temperature
Distance
Gray value
Temperature
scale
PAG with
MNPs
ROI(x,y)
Sample holder
wall
ROI(x,y)
(a)
(b)
(c)
FIG. 2. Scheme of the different steps in the video processing software. (a) Frame extraction from the video. (b) Image of one frame from the
video where the placement of the PAG with MNPs and the sample holder is indicated, as well as the temperature scale and ROI (shadowed in
yellow) that can be interactively selected by the user. (c) Process of obtaining a temperature profile from the 2D ROI (selected from 1 frame)
through y−averaging and interactive calibration.
F. Video processing
Frames of the video were extracted at 1 s intervals [see Fig.
2(a)]. An interactive software was developed to transform the
information in these images into calibrated grayscale profiles
as a function of time. The software reads all frames as images
and prompts the user to select the temperature scale and the
PAG’s region of interest “ROI(x,y)” in one of the frames [see
Fig. 2(b)].
For this study, the ROI was taken as a rectangle that con-
tains the center of the phantom and was chosen to minimize
parallax problems that could remain even after the alignment
of the setup (for more details, see Sec. II F 1) . Moreover, once
the ROI has been chosen, the user can interactively specify
the placement of the sample holder wall in order to transform
pixel values into distance by taking into account the PAG’s
dimension. The ROI is then converted into a matrix of gray
value information and a grayscale profile is obtained by aver-
aging y-values at a fixed x. To calibrate the gray values into
temperature, the software performs the corresponding trans-
formation with the previously selected temperature scale [see
Fig. 2(c)].
Once calibrated, temperature profiles for each frame were
interpolated to generate a consistent distance grid through
them, which allows the generation of a temperature map as
a function of distance and time. The ac field was turned on at
t=60 s for all experiments. The maps are presented as tem-
perature increment ∆Tas a function of time tand distance r
measured from the center of the PAG, where ∆T=T−Teq.
The equilibrium temperature Teq was calculated by averaging
temperature data from 0 to 60 s, for all points inside the phan-
tom.
However, the map presents temperature bands for certain
time intervals that don’t match the general behavior of the
temporal evolution during the experiment. These bands are
consistent with the temperature sensitivity given by the cam-
era manufacturer (2% of reading or 2 K). The workaround for
this problem is described in detail in the Appendix 3.
After this procedure, a raw temperature map is obtained,
where the temperature evolution through time for a radial re-
gion of a PAG can be observed [see Fig. 3(a)]. As the anal-
ysis of the data required it, the map was smoothed through a
two-step process including: i) a moving average smoothing
and ii) a Gaussian blur filter [see Figs. 3(b-c), respectively],
which was implemented through the corresponding convolu-
tion masks.
1. Important remarks
Although the infrared camera was placed on a tripod and
carefully aligned, potential parallax effects on the final video
were also taken into account by including a frame rotation
feature in our software to allow the selection of the ROI in the
direction that is perpendicular to that of maximum deviation.
Finally, the position and distance calibration of the ROI is
maintained throughout the analysis, which is crucial to avoid
unwanted noise in the final temperature map.
5
(a) (b) (c)
Distance
Time Time Time
Distance
Distance
Temperature
FIG. 3. (a) Raw temperature map (temperature as a function of dis-
tance and time) obtained from interpolated data from video frames.
(b) Temperature map after a moving average smoothing and (c) con-
sequent Gaussian blur filtering.
G. Local probe validation
The temperature increments obtained from thermographi-
cal video data were contrasted with local-probe measurements
as a way of validation. For these measurements, we used a
Neoptix Reflex temperature thermometer with 4 channels and
an accuracy of ±0.8 K and a Neoptix T1 fiber optic tempera-
ture sensor with a diameter of 1.15 mm and PTFE protective
jacket. The fiber-optic measurements were performed in the
same PAG but in a later power absorption experiment, as the
insertion of the fiber optic destroys part of the sample and hin-
ders the video recording.
III. RESULTS
The temperature maps corresponding to the power absorp-
tion experiments performed with the PAGs containing dis-
persed MNPs at a concentration of 0.1 and 0.5 wt% are shown
in Fig. 4 alongside the one from the blank. A dotted line sep-
arates the heating of the PAGs and their cooling.
From their comparison, it is evident that no significant tem-
perature increment is presented for the blank, contrary to the
PAGs with MNPs dispersed. For these last PAGs, a tempera-
ture increment of ∼12 K was attained at ∼200 s for the 0.1
wt% MNP concentration and at ∼40 s for 0.5 wt%, implying
that a larger amount of MNPs can heat the medium faster. This
temperature increment is considerable when talking about me-
dia with viscosity similar to the cytosol one.
The time evolution of the temperature increment measured
with a fiber-optic sensor is shown in Fig. 5 for power absorp-
tion experiments performed with PAGs containing dispersed
MNPs at a concentration of 0.1 and 0.5 wt% and is compared
with the spatial mean temperature obtained from video data. It
is worth noting that temperature increments obtained from the
conventional local probe measurements are, although slightly
lower, similar to the ones obtained from averaging the spatial
information in the temperature maps and have a qualitatively
comparable temporal evolution. The difference between re-
sults can be explained by the presence of spatial temperature
distributions inside samples (as it was evidenced by tempera-
ture maps) and to heat losses being different for each point in-
side them. Furthermore, the temperature differences are con-
sistent when taking into account the error of both instruments.
To contrast temperature maps obtained from thermograph-
ical videos with conventional local probing, a loss of spatial
information was required through averaging data. This high-
lights the two-dimensional character of our analysis.
(a)
(b)
(c)
0.1 wt% - Dispersed
Blank
0.5 wt% - Dispersed
t (s)
t (s)
t (s)
r (cm)
r (cm) r (cm)
ΔT (K)
FIG. 4. Temperature increment maps for power absorption exper-
iments performed in (a) a blank PAG, and PAGs with MNPs at a
concentration of (b) 0.1 and (c) 0.5 wt%. The black dotted line indi-
cates the time at which the ac field was switched off and the cooling
period of the sample begins.
Back to temperature maps in Fig. 4, it can also be seen that
the temperature spatial distribution is approximately symmet-
ric with respect to the center of the sample (r=0), which is
6
coherent with the axial symmetry of the experimental setup
(see Fig. 1). However, it is clearly noticeable that, for a given
time, the temperature increase rate is not the same for the dif-
ferent points in the sample. In fact, temperature decreases
when approaching the sample holder walls, which could be
evidence that heat losses are not only due to the sample being
exposed to the surrounding environment through the open top
of the sample holder but also through its walls.
(a)
(b) 0.5 wt% - Dispersed
0.1 wt% - Dispersed
0 200 400 600 800
t [s]
0
2
4
6
8
10
12
T [K]
Video data (spatial mean)
Fiber optic data (local probe)
0 200 400 600 800
t [s]
0
2
4
6
8
10
12
T [K]
t (s)
ΔT (K)
ΔT (K)
t (s)
FIG. 5. Comparison of spatial mean temperature increment obtained
from video data and the temperature increment measured by a fiber
optic as a function of time for power absorption experiments per-
formed in PAGs with dispersed MNPs at a concentration of (a) 0.1
and (b) 0.5 wt%.
(a) (b)
+δ
0.5 wt% - Dispersed 0.5 wt% - Oriented
FIG. 6. Photographs of PAGs with (a) dispersed and (b) oriented
MNPs at a concentration of 0.5 wt%. The arrow shows an elongated-
agglomerate’s density gradient inside the PAG with oriented MNPs,
which produces a spatial inhomogeneity.
A. Spatial inhomogeneities
Our method proved to be useful for the evaluation of tem-
perature distributions, which is of great interest for MH appli-
cations. While we have used homogeneous samples so far, a
way to assess the presence of aggregates or any kind of spatial
inhomogeneities in the samples is needed as aggregates are
often promoted in the intracellular environment and are key in
the outcome of the treatment [2, 3].
To test the capabilities of our analysis in this field, we
measured a PAG with elongated agglomerates of MNPs (Ori-
ented). Particularly, this PAG shows a zone that is denser in
these aggregates than the others due to a horizontal magnetic
field gradient produced by the coil in which it was polymer-
ized (see Fig. 6).
The temperature map corresponding to an experiment with
the PAG with oriented MNPs was obtained and compared to
the one from a PAG with homogeneously dispersed MNPs at
the same concentration (Dispersed, see Fig. 6). This compar-
ison is shown in Fig. 7.
(a)
(b) 0.5 wt% - Dispersed
0.5 wt% - Oriented
t (s)
t (s)
r (cm)
r (cm)
ΔT (K)
FIG. 7. Temperature increment maps for power absorption experi-
ments performed in PAGs with (a) oriented and (b) dispersed MNPs,
both with a MNP concentration of 0.5 wt%. The black dotted line in-
dicates the time at which the ac field was switched off and the cooling
period of the sample begins.
7
(a)
(b)
(d)
(e)
(g)
(h)
∂E/∂t
(W g-1)10-3 ∂E/∂r
(J cm-1 g-1)
10-3 E
(J g-1)
0.1 wt% - Dispersed
(c) (f) (i)
0.5 wt% - Dispersed
0.5 wt% - Oriented
∂E/∂t
(W g-1)
10-3 ∂E/∂r
(J cm-1 g-1)
10-3 E
(J g-1)
∂E/∂t
(W g-1)
10-3 ∂E/∂r
(J cm-1 g-1)
10-3 E
(J g-1)
r (cm) r (cm)
r (cm)
r (cm)
r (cm)
r (cm)
r (cm)
r (cm)
r (cm)
r (cm)
t (s) t (s) t (s)
t (s)
t (s) t (s)
t (s) t (s) t (s)
FIG. 8. (a-c) Energy E, (d-f) time derivative
∂
E/
∂
t(at fixed distance r) and (g-i) spatial derivative
∂
E/
∂
r(at fixed time t) maps for power
absorption experiments performed in PAGs with dispersed MNPs at a concentration of 0.1 (top panel) and 0.5 wt% (middle panel) and PAGs
with oriented MNPs at a concentration of 0.5 wt% (bottom panel). Black open dots represent the points with maximum |
∂
E/
∂
r|at a given t.
The white dotted line indicates the time at which the ac field was switched off and the cooling period of the sample begins.
As it can be easily seen, the PAG with oriented MNPs in-
creased the temperature in ∼17 K in less time than it took the
dispersed PAG to increase it in ∼12 K.
Another clear difference between them is that the temper-
ature profile for a given fixed tvalue is not symmetrical with
respect to the physical center (r=0) for the PAG with ori-
ented MNPs, as opposed to the dispersed one. This fact can
be explained through the spatial inhomogeneity in the MNP
distribution, showing a hot spot for the region where the elon-
gated agglomerate’s density is higher. This highlights the im-
portance of our methodology and analysis, as this informa-
tion cannot be gathered from usual temperature measurements
with local probes.
B. Thermodynamic approach
A possible dependence of the specific heat cPof the PAGs
with temperature or MNP dispersion was analyzed through
DSC measurements. Several measurements were made in
blank PAGs and PAGs with MNPs at a concentration of
0.1 and 0.5 wt% as a function of temperature for different
ramps. The results for all of these PAGs were cP= (4.1±0.1)
J K−1g−1, showing no temperature or MNP-concentration in-
fluence in the value of the specific heat of the samples in the
working temperature range.
This last remark allows the evaluation of the energy lib-
erated to the media normalized by the mass of MNPs in the
sample mMNPs by calculating E=mcP∆T/mMNPs, where m
is the PAG’s mass. The corresponding maps are presented in
8
Fig. 8(a-c)] for the PAGs with MNPs, along with maps for
its time derivative
∂
E/
∂
t[at fixed r, see Fig. 8(d-f)] and spa-
tial derivative or spatial energy gradient
∂
E/
∂
r[at fixed t,
see Fig. 8(g-i)]. The time derivative
∂
E/
∂
tis related to the
SPA for the heating period of the experiment and to the loss
power for the cooling of the sample. The time evolution of the
points with maximum spatial gradient [black open dots in Fig.
8(g-i)] evidence the radial heat flux.
It is evident by comparing the data obtained for the heat-
ing and the cooling periods of the samples that temperature
increment and cooling rates are not the same. In fact, this can
be seen clearer in the time derivative maps [see Fig. 8(d-f)].
Moreover, from the cooling part of all of these maps, we
can see that there is an important radial heat loss component
through the sample holder walls, evidenced by the faster cool-
ing of the PAG’s borders and the fact that the heat flux is al-
ways towards the borders [see open dots in Fig. 8(g-i)].
By contrasting the released power maps for dispersed PAGs
with different MNP concentrations, even when normalized by
the MNP mass, it can be seen that to raise the temperature by
12 K, the normalized power is not the same for both cases, i.e.
the one with 0.5 wt% in MNPs does not insume 5 times the
power (without normalization) that the 0.1 wt% does. In fact,
the PAG with 0.5 wt% in MNPs shows a lower normalized
effective power. This could indicate the formation of MNP
aggregates that decrease the SPA for the more concentrated
PAG, which was already discussed in Ref. 43, where both
effects (beneficial or detrimental) were seen in MNP aggre-
gated systems. Another way to explain this effect could be
a higher heat loss by the PAG with 0.5 wt% in MNPs. To
effectively compare the results from different samples in all
calorimetric determinations, one of the current challenges is
to produce information on the power lost to the surroundings
during the experiments. This is especially important when the
experiments are not comparable in time scale, as in our case.
Even more, when comparing both experiments at a fixed
time (t=40 s), the released power is ∼285 Wg−1for the 0.1
wt% case and ∼135 Wg−1for the 0.5 wt% in MNPs’ case,
which could evidence a more pronounced heat loss for the
last case. This is coherent with the fact that this PAG reaches
a higher temperature in 40 s than the other one, which incre-
ments the effective heat loss.
For the PAG with oriented MNPs [see Fig. 8(c,f,i)], its
spatial inhomogeneity can be perceived through different fea-
tures: for the energy and power (
∂
E/
∂
t), it is the displace-
ment of the corresponding maximum to one side of the PAG,
while for the spatial gradient (
∂
E/
∂
r) it is more pronounced
for the zone of the PAG with higher elongated agglomerate’s
density (brighter shades of yellow for r<0 than for r>0).
For the power, the values obtained for the PAG with elon-
gated MNP arrangements are larger than the ones for the non-
oriented one with the same MNP concentration. This rein-
forces the idea that, in certain conditions, MNP agglomerates
can exert an effect on the SPA, beneficial in this case [43].
Moreover, when we compare the spatial gradient for the
oriented and dispersed samples, we notice that the oriented
sample possesses a larger temperature gradient inside the PAG
than the dispersed one. Furthermore, if we look at the heat
flux at each side of the PAG (black open dots in Figs. 8(i)]),
we notice that for the PAG with oriented MNPs, there is a
curvature that is not present in the map of the dispersed PAG.
We hypothesized that this curvature, which represents the heat
flux towards the border of the PAG, could be related to the
larger lateral heat loss for this PAG and, as the amount of heat
that needs to be exchanged with the surroundings is greater, it
takes more time to reach the exchange dynamic equilibrium.
Even more, another cause could be the spatial inhomogeneity
of the heat sources due to having zones with only the PAG
and others with macroscopic aggregates, contrarily to the ho-
mogeneous concentration of MNPs for dispersed PAGs (see
Fig. 6).
A camera with better temperature accuracy and spatial res-
olution would be appropriate to evaluate details in finer tem-
poral windows and distances relevant to cell studies, such as
the mechanisms involved in heat propagation from MNPs to
the medium.
IV. CONCLUSIONS
In this work, iron oxide MNPs with 25 nm average diam-
eter and coated with glucose were dispersed into a PAG at
MNP concentrations of 0.1 and 0.5 wt% to study their heating
capabilities in a medium with viscosity similar to that of the
cytosol. Power absorption experiments were performed under
ac magnetic fields with an amplitude of 32 kA/m and a fre-
quency of 350 kHz and followed by the cooling of the sample
with the magnetic field turned off. The temperature evolution
was monitored through an infrared thermographic camera to
allow a two-dimensional thermal study of these phantoms.
We designed and implemented a procedure to gather in-
formation on the thermal evolution of MNPs in these phan-
toms. This method is based on the processing of the camera
videos by frame extraction, interpolation, and smoothing of
data. Furthermore, we remark certain aspects to take into ac-
count to adapt our procedure to other cameras, such as tem-
perature indetermination, parallax problems, working temper-
atures, manufacturer’s recommendations, etc.
Spatio-temporal temperature profiles were obtained from
the videos and the analysis of these profiles allowed us to
gather information on the increment of temperature with re-
spect to the equilibrium temperature of the system. For the
PAGs studied, an increment of ∼12 K was obtained in only
∼200 s for the 0.1 wt% MNP concentration and ∼40 s for
0.5 wt%, which is suitable for the application in MH if we
take into account that an 8% PAG has a viscosity similar to
the cytosol. The spatial mean temperature increments were
compared with the ones obtained through conventional local-
probe measurements, showing good agreement.
Moreover, the measurement of the specific heat of the sam-
ples allowed us to confirm that the map’s spatio-temporal
characteristics were not due to a specific heat dependence with
temperature. In fact, by confirming that the specific heat is not
temperature or MNP-concentration dependent, we could ob-
tain energy maps, as well as the ones for energy’s time and
spatial derivatives. We also observed that there is a heat-loss
9
mechanism through the sample holder wall and envision fu-
ture tools that could complement the present study.
As a final test, we analyzed a sample that was constituted
by oriented MNPs, forming elongated agglomerates that were
denser in one side of the PAG. Through the maps correspond-
ing to its power absorption experiment, we confirmed the spa-
tial inhomogeneity of the sample. This demonstrates that our
non-invasive methodology and analysis allow gathering infor-
mation that is not reachable through plain thermal methods
such as punctual and invasive fiber-optic measurements. For
this inhomogeneous sample, we noticed that the heat flux has
a different behavior when compared with the ones for other
samples, which could evidence a more pronounce d lateral heat
loss and some effect due to the inhomogeneity of heat source
distribution. This highlights that a 2D analysis could benefit
the interpretation of results obtained in biological and medical
uses, going beyond the current state of the art in MH experi-
ments and future applications.
ACKNOWLEDGMENTS
This work is part of a research project supported by Agen-
cia Nacional de Promoción Científica y Tecnológica (Ar-
gentina) under projects No. PICT-2016-0288 and PICT-2015-
0883 and UNCuyo’s project SIIP No.06/C564. The authors
gratefully acknowledge the EU Commission financial support
through Project No. H2020-MSCA-RISE-2020 101007629-
NESTOR.
AUTHOR DECLARATIONS
The authors have no conflicts to disclose.
DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available
from the corresponding author upon reasonable request.
APPENDIX
1. MNP synthesis and characterization
The morphological characterization of the studied iron ox-
ide magnetic nanoparticles (MNPs) was carried out by trans-
mission electron microscopy (TEM). The TEM images were
obtained using a Tecnai F20 transmission electron microscope
equipped with a Schottky field emission gun, operated at 200
kV accelerating voltage. For these experiments, a drop of the
MNP suspension (dispersed in toluene) was deposited on a
holey carbon-coated micro-grid, with the subsequent evapo-
ration of the solvent. One representative image is shown in
Fig. 9(a).
(a) (b)
14 21 28 35 42 49 56
0.0
0.1
0.2
0.3
0.4
0.5
Normalized counts
d (nm)
TEM data
Log-normal Fit
<d> = 25
nm
s
= 7
nm
FIG. 9. (a) Representative TEM image of the sample. (b) Diameter
histogram obtained from the measurements of MNP size in TEM
images and the corresponding fit of the distribution. The solid line
corresponds to the log-normal fit of the distribution and the dashed
line to its mean.
0 50 100 150 200 250 300 350
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
ZFC
FC
T
(K)
M
(A m
2
kg
-1
)
-1000 -500 0 500 1000
-80
-40
0
40
80
M
(A m
2
kg
-1
)
H
(kA m
-1
)
300 K
5 K
(a)
(b)
FIG. 10. (a) Magnetization as a function of temperature measured
through the ZFC-FC protocol. (b) Magnetization loops at room tem-
perature (300 K) and low temperature (5 K).
The MNPs were assumed spherical and the diameter was
obtained through the circular projected area measured in the
TEM images. The diameter histogram was obtained from the
analysis of >300 MNPs and is shown in Fig. 9(b). This
histogram was fitted by a log -normal distribution. The average
diameter obtained was 25 nm and the standard deviation, 7
nm.
Magnetic measurements were performed using both a vi-
10
brating sample magnetometer (VSM) Lakeshore (M vs. H
curve at 300 K) and a superconducting quantum interference
device magnetometer (SQUID) MPMS-5S Quantum Design
(M vs. T and M vs. H curve at 5 K).
Magnetization as a function of temperature was measured
through the zero-field-cooling (ZFC) and field-cooling (FC)
protocols under an applied magnetic field of ∼1.5 kA/m.
Samples were conditioned on a capsule with dispersed MNPs
in epoxy resin at a concentration of ∼0.1 wt%. The results
are presented in Fig. 10(a).
The saturation magnetization (MS) was determined by mea-
suring the magnetization as a function of the applied field at
room temperature (300 K) of a powder sample using the afore-
mentioned VSM, obtaining for our sample MS=68 Am2/kg.
The magnetization loop at 5 K was measured in the SQUID
on the capsule with MNPs dispersed in epoxy we described
before. From this loop, it can be seen that the coercivity is
HC(5 K)∼70 kA/m. The magnetization loops can be seen in
Fig. 10(b).
2. MNP glucose coating
Fourier-Transform Infrared (FTIR) spectra of the MNPs
used were measured before and after the washing procedure
in a uATR PerkinElmer Spectrum Two equipment in the range
of 450–4000 cm−1, with a resolution of 4 cm−1. To perform
these measurements, a drop of ferrofluid was placed over the
uATR crystal and dried with a N2flow, resulting in an MNP
film covering its entire surface. Interactive baseline, ATR cor-
rections and normalization were performed with the software
Spectrum from PerkinElmer. The obtained spectra are shown
in Fig. 11.
3500 3000 2500 2000 1500 1000 500
Transmittance (arb. units)
Wavenumber (cm
-1
)
Oleic-acid coated MNPs
Etched MNPs
Glucose coated MNPs
Fe-OC-HO-H C-O-O-Fe
FIG. 11. FTIR spectra of as prepared MNPs (oleic-acid coated),
the MNPs after a washing procedure with methanol and hot acetone
(etched) and the MNPs after the ammonium and glucose treatment
(glucose coated). Characteristic peaks are labelled in the spectra.
Normalization of the spectra was made through the Fe-
O peak at 555 cm−1. By comparing both of them, it can
be noticed that the C-H stretching peaks at 2921 and 2853
cm−1considerably diminished after washing, which implies
that oleic acid coating was removed from the MNPs and in-
creased after the ammonium and glucose treatment, as well
as the O-H stretching modes around 3300 cm−1. The C-O-
O-Fe peaks around 1600-1300 cm−1also diminished after the
washing procedure.
3. Video processing
As we stated in the main text of this article, the maps ob-
tained from the ordering of the data into a space-time grid
present temperature bands for certain time intervals that don’t
match the general behavior of the temporal evolution during
the experiment. These bands are evidenced through steps in
the temperature profile plotted as a function of time, such as
the ones for the center (r=0) and border (r=0.65 cm) of the
PAG (see Fig. 12).
These steps are consistent with the temperature sensitivity
given by the camera manufacturer (2% of reading or 2 K)
and imply that to generate and process the map, not as many
frames are needed as the camera is idle in several of them.
0 200 400 600 800 1000
t (s)
0
2
4
6
8
10
12
T (K)
Center
Border
II IIII IV
FIG. 12. Temperature increment ∆Tas a function of time tfor the
center (r=0) and border (r=0.65 cm) of a PAG with 0.1 wt% in
MNPs. Zones for subsequent curve fitting are numbered from I to
IV.
A workaround for this problem is to define a custom time
interval between selected frames
δ
tin which the temperature
increment variation is greater than the temperature indetermi-
nation. Knowing that ∆T(t+
δ
t)≈∆T(t) + d(∆T)
dt
δ
tand con-
sidering temperature sensitivity to be at least 2 K, we get:
δ
t≥2 Kd(∆T)
dt −1
.(1)
According to Eq. 1, the lower threshold value for the time
interval between frames depends on the temperature incre-
ment variation rate, thus it should be different for the heating
and cooling periods of the sample. This fact is also evident
by looking at the curves in Fig. 12, where the bands are more
pronounced at the end of the cooling of the sample.
11
300 350 400 450 500
0
5
10
15
T (K)
(a)
600 700 800 900 1000
0
5
10
15
T (K)
Data
Fit
100 150 200 250
t (s)
0
5
10
15
T (K)
t (s) t (s)
(b)
(c)
II III IV
FIG. 13. Temperature increment ∆Tas a function of time tfor the center (r=0) of a PAG with 0.1 wt% in MNPs, dissected into zones for
behavioral fitting. (a) Zone II corresponds to the power absorption experiment and (b-c) zones III and IV to the cooling period of the sample
at zero magnetic field.
To define a consistent time interval between frames, the
profile for the center of the PAG was divided into 4 zones
with distinctive variation rates, as distinguished in Fig. 12.
For Zone I, the sample is in thermal equilibrium with its sur-
roundings, thus no temperature increment is displayed and
no time-interval adjustment is needed. Zone II represents the
power absorption experiment performed in the presence of a
non-null magnetic field.
Consequently, the sample is heated and the data can be fit-
ted through a curve such as a−bexp[−c(t−d)], where a,b,c
and dare variable fitting parameters that have different values
depending on the zone. Zone III and IV are part of the cooling
period of the sample and can be fitted through an exponential
decay of the form bexp[−c(t−d)]. The fitting procedure is
demonstrated in Fig. 13(a-c)].
Once the fitting of the different zones is achieved, the time
interval between frames for each of them is calculated using
Eq. 1 with d(∆T)/dt being the lowest derivative value ob-
tained analytically from the fits. With these intervals deter-
mined for each zone, frames are selected conveniently from
the original data matrix and then the temperature is interpo-
lated in a regular time grid for all rvalues. One of the re-
sulting interpolated temperature profiles (the one for r=0) is
illustrated in Fig. 14.
This procedure to define the time interval between frames
for different parts of the experiment can be adapted to other
experimental setups by considering the corresponding temper-
ature indetermination instead of “2 K” in Eq. 1.
0 200 400 600 800 1000
t (s)
0
2
4
6
8
10
12
T (K)
Data
Obtained through selection
and interpolation
FIG. 14. Temperature increment ∆Tas a function of time tfor the
center (r=0) of a PAG with 0.1 wt% in MNPs before and after the
adjustment of time-frame interval and interpolation.
[1] T. E. Torres, E. Lima, M. P. Calatayud, B. Sanz, A. Ibarra,
R. Fernández-Pacheco, A. Mayoral, C. Marquina, M. R.
Ibarra, and G. F. Goya, “The relevance of Brownian relaxation
as power absorption mechanism in Magnetic Hyperthermia,”
Sci. Rep. 9, 3992 (2019).
[2] B. Sanz, M. P. Calatayud, E. De Biasi, E. Lima,
M. Vasquez Mansilla, R. D. Zysler, M. R. Ibarra, and G. F.
Goya, “In silico before in vivo: how to predict the heating effi-
ciency of magnetic nanoparticles within the intracellular space,”
Sci. Rep. 6, 38733 (2016).
[3] M. P. Calatayud, E. Soler, T. E. Torres, E. Campos-Gonzalez,
C. Junquera, M. R. Ibarra, and G. F. Goya, “Cell damage pro-
duced by magnetic fluid hyperthermia on microglial BV2 cells,”
Sci. Rep. 7, 8627 (2017).
[4] L. H. Nguyen, P. T. Phong, P. H. Nam, D. H. Manh, N. T. K.
Thanh, L. D. Tung, and N. X. Phuc, “The role of anisotropy
in distinguishing domination of Néel or Brownian relaxation
contribution to magnetic inductive heating: Orientations for
biomedical applications,” Materials 14, 1875 (2021).
[5] B. Sanz, R. Cabreira-Gomes, T. E. Torres, D. P. Valdés,
E. Lima, E. De Biasi, R. D. Zysler, M. R. Ibarra, and G. F.
Goya, “Low-dimensional assemblies of magnetic MnFe2O4
nanoparticles and direct in vitro measurements of enhanced
heating driven by dipolar interactions: Implications for mag-
netic hyperthermia,” ACS Appl. Nano Mater. 3, 8719 (2020).
[6] M. Creixell, A. C. Bohórquez, M. Torres-Lugo, and
C. Rinaldi, “EGFR-targeted magnetic nanoparticle heaters
kill cancer cells without a perceptible temperature rise,”
ACS Nano 5, 7124 (2011).
[7] L. Asín, G. F. Goya, A. Tres, and M. R. Ibarra, “Induced cell
12
toxicity originates dendritic cell death following magnetic hy-
perthermia treatment,” Cell Death Dis. 4, e596 (2013).
[8] G. Hu and B. He, “Magnetoacoustic imaging of electrical con-
ductivity of biological tissues at a spatial resolution better than
2 mm,” PLoS One 6, e23421 (2011).
[9] I. J. Bruvera, D. G. Actis, M. P. Calatayud, and P. Men-
doza Zélis, “Typical experiment vs. in-cell like conditions in
magnetic hyperthermia: Effects of media viscosity and agglom-
eration,” J. Magn. Magn. Mater. 491, 165563 (2019).
[10] M. B. Lee, H. J. Kim, and O. I. Kwon, “Decom-
position of high-frequency electrical conductivity into ex-
tracellular and intracellular compartments based on two-
compartment model using low-to-high multi-b diffusion MRI,”
Biomed. Eng. Online 20, 29 (2021).
[11] N. A. Usov and B. Ya. Liubimov, “Dynamics of
magnetic nanoparticle in a viscous liquid: Ap-
plication to magnetic nanoparticle hyperthermia,”
J. Appl. Phys. 112, 023901 (2012).
[12] D. Cabrera, A. Lak, T. Yoshida, M. E. Materia, D. Ortega,
F. Ludwig, P. Guardia, A. Sathya, T. Pellegrino, and F. J. Teran,
“Unraveling viscosity effects on the hysteresis losses of mag-
netic nanocubes,” Nanoscale 9, 5094 (2017).
[13] A. Rousseau, M. Tellier, L. Marin, M. Garrow, C. Made-
laine, N. Hallali, and J. Carrey, “Influence of medium vis-
cosity on the heating power and the high-frequency magnetic
properties of nanobeads containing magnetic nanoparticles,”
J. Magn. Magn. Mater. 518, 167403 (2021).
[14] E. O. Puchkov, “Intracellular viscosity: Meth-
ods of measurement and role in metabolism,”
Biochem. (Mosc.) Suppl. Ser. A 7, 270 (2014).
[15] K. Fushimi and A. S. Verkman, “Low viscosity in the aqueous
domain of cell cytoplasm measured by picosecond polarization
microfluorimetry,” J. Cell Biol. 112, 719 (1991).
[16] M. K. Kuimova, G. Yahioglu, J. A. Levitt, and K. Suhling,
“Molecular rotor measures viscosity of live cells via fluores-
cence lifetime imaging,” J. Am. Chem. Soc. 130, 6672 (2008).
[17] M. K. Kuimova, S. W. Botchway, A. W. Parker, M. Balaz, H. A.
Collins, H. L. Anderson, K. Suhling, and P. R. Ogilby, “Imag-
ing intracellular viscosity of a single cell during photoinduced
cell death,” Nat. Chem. 1, 69 (2009).
[18] M. K. Kuimova, “Mapping viscosity in cells using molecular
rotors,” Phys. Chem. Chem. Phys. 14, 12671 (2012).
[19] T. Yano, H. Kumagai, T. Fujii, and T. Inukai, “Con-
centration dependence of mechanical properties of
polyacrylamide near the Sol-Gel transition point,”
Biosci. Biotechnol. Biochem. 57, 528 (1993).
[20] I. Andreu and E. Natividad, “Accuracy of available methods
for quantifying the heat power generation of nanoparticles for
magnetic hyperthermia,” Int. J. Hyperth. 29, 739 (2013).
[21] R. R. Wildeboer, P. Southern, and Q. A. Pankhurst, “On
the reliable measurement of specific absorption rates and in-
trinsic loss parameters in magnetic hyperthermia materials,”
J. Phys. D: Appl. Phys. 47, 495003 (2014).
[22] I. Rodrigo, I. Castellanos-Rubio, E. Garaio, O. K. Arrior-
tua, M. Insausti, I. Orue, J. Á. García, and F. Plazaola,
“Exploring the potential of the dynamic hysteresis loops via
high field, high frequency and temperature adjustable AC
magnetometer for magnetic hyperthermia characterization,”
Int. J. Hyperth. 37, 976 (2020).
[23] F. J. Teran, C. Casado, N. Mikuszeit, G. Salas, A. Bollero,
M. P. Morales, J. Camarero, and R. Miranda, “Accu-
rate determination of the specific absorption rate in super-
paramagnetic nanoparticles under non-adiabatic conditions,”
Appl. Phys. Lett. 101, 062413 (2012).
[24] A. A. de Almeida, E. De Biasi, M. Vasquez Mansilla, D. P.
Valdés, H. E. Troiani, G. Urretavizcaya, T. E. Torres, L. M.
Rodríguez, D. E. Fregenal, G. C. Bernardi, E. L. Winkler,
G. F. Goya, R. D. Zysler, and E. Lima, “Magnetic hy-
perthermia experiments with magnetic nanoparticles in clar-
ified butter oil and paraffin: A thermodynamic analysis,”
J. Phys. Chem. C 124, 27709 (2020).
[25] C. A. M. Iglesias, J. C. R. de Araújo, J. Xavier, R. L. An-
ders, J. M. de Araújo, R. B. da Silva, J. M. Soares, E. L.
Brito, L. Streck, J. L. C. Fonseca, C. C. Plá Cid, M. Gamino,
E. F. Silva, C. Chesman, M. A. Correa, S. N. de Medeiros,
and F. Bohn, “Magnetic nanoparticles hyperthermia in a non-
adiabatic and radiating process,” Sci. Rep. 11, 11867 (2021).
[26] H. F. Rodrigues, F. M. Mello, L. C. Branquinho, N. Zufelato,
E. P. Silveira-Lacerda, and A. F. Bakuzis, “Real-time infrared
thermography detection of magnetic nanoparticle hyperthermia
in a murine model under a non-uniform field configuration,”
Int. J. Hyperth. 29, 752 (2013).
[27] B. B. Lahiri, S. Ranoo, and J. Philip, “Infrared thermography
based magnetic hyperthermia study in Fe3O4based magnetic
fluids,” Infrared Phys. Technol. 78, 173 (2016).
[28] I. A. Brezovich, J. H. Young, and M. T. Wang, “Temperature
distributions in hyperthermia by electromagnetic induction: a
theoretical model for the thorax,” Med. Phys. 10, 57 (1983).
[29] J. J. Bosque, G. F. Calvo, V. M. Pérez-García, and
M. C. Navarro, “The interplay of blood flow and temper-
ature in regional hyperthermia: a mathematical approach,”
R. Soc. Open Sci. 8, 201234 (2021).
[30] M. Nabil, P. Decuzzi, and P. Zunino, “Modelling mass
and heat transfer in nano-based cancer hyperthermia,”
R. Soc. Open Sci. 2, 150447 (2015).
[31] S. Hassanpour and A. Saboonchi, “Modeling of heat transfer in
a vascular tissue-like medium during an interstitial hyperther-
mia process,” J. Therm. Biol. 62, 150 (2016).
[32] C. W. Song, “Effect of Hyperthermia on Vascular Functions of
Normal Tissues and Experimental Tumors: Brief Communica-
tion,” J. Natl. Cancer Inst. 60, 711 (1978).
[33] Suriyanto, E. Y. K. Ng, and S. D. Kumar, “Physical mecha-
nism and modeling of heat generation and transfer in magnetic
fluid hyperthermia through Néelian and Brownian relaxation: a
review,” Biomed. Eng. Online 16, 36 (2017).
[34] A. Schuster, M. Thielecke, V. Raharimanga, C. E. Ramarokoto,
C. Rogier, I. Krantz, and H. Feldmeier, “High-resolution in-
frared thermography: a new tool to assess tungiasis-associated
inflammation of the skin,” Trop. Med. Health 45, 23 (2017).
[35] R. M. Arthur, W. L. Straube, J. W. Trobaugh, and E. G. Moros,
“Non-invasive estimation of hyperthermia temperatures with
ultrasound,” Int. J. Hyperth. 21, 589 (2005).
[36] G. Maenhout, T. Markovic, and B. Nauwelaers, “Non-
invasive microwave hyperthermia and simultaneous tem-
perature monitoring with a single theranostic applicator,”
in 2021 43rd Annual International Conference of the IEEE
Engineering in Medicine & Biology Society (EMBC) (IEEE,
New York, 2021) p. 1314.
[37] B. D. De Senneville, C. Mougenot, P. Desbarats,
B. Quesson, and C. T. W. Moonen, “On-line mobile
organ tracking for non-invasive local hyperthermia,” in
2006 International Conference on Image Processing (IEEE,
New York, 2006) p. 2845.
[38] J. Delgado-SanMartin, B. Ehrhardt, M. Paczkowski, S. Hack-
ett, A. Smith, W. Waraich, J. Klatzow, A. Zabair, A. Chabok-
dast, L. Rubio-Navarro, A. Rahi, and Z. Wilson, “An innova-
tive non-invasive technique for subcutaneous tumour measure-
ments,” PLoS One 14, e0216690 (2019).
13
[39] C. W. Meyer, Y. Ootsuka, and A. A. Romanovsky, “Body
temperature measurements for metabolic phenotyping in mice,”
Front. Physiol. 8, 00520 (2017).
[40] Y.-L. Wang and R. J. Pelham Jr., “Preparation of a flexible,
porous polyacrylamide substrate for mechanical studies of cul-
tured cells,” Methods Enzymol. 298, 489 (1998).
[41] M. A. Skidmore and J. E. Turnbull, “Chapter 6 - separation
and sequencing of heparin and heparan sulphate saccharides,”
in Chemistry and Biology of Heparin and Heparan Sulfate,
edited by Hari G. Garg, Robert J. Linhardt, and Charles A.
Hales (Elsevier Science, Amsterdam, 2005) p. 179.
[42] G. W. H. Höhne, W. F. Hemminger, and H.-J. Flammersheim,
“Applications of differential scanning calorimetry,” in Differen-
tial Scanning Calorimetry (Springer-Verlag Berlin Heidelberg,
New York, 2003) p. 147.
[43] D. P. Valdés, E. Lima Jr., R. D. Zysler, G. F. Goya,
and E. De Biasi, “Role of anisotropy, frequency, and
interactions in magnetic hyperthermia applications: Non-
interacting nanoparticles and linear chain arrangements,”
Phys. Rev. Applied 15, 044005 (2021).
