Portable Homemade Magnetic Hyperthermia Apparatus: Preliminary Results

Abstract

This study aims to describe and evaluate the performance of a new device for magnetic hyperthermia that can produce an alternating magnetic field with adjustable frequency without the need to change capacitors from the resonant bank, as required by other commercial devices. This innovation, among others, is based on using a capacitator bank that dynamically adjusts the frequency. To validate the novel system, a series of experiments were conducted using commercial magnetic nanoparticles (MNPs) demonstrating the device’s effectiveness and allowing us to identify new challenges associated with the design of more powerful devices. A computational model was also used to validate the device and to allow us to determine the best system configuration. The results obtained are consistent with those from other studies using the same MNPs but with magnetic hyperthermia commercial equipment, confirming the good performance of the developed device (e.g., consistent SAR values between 1.37 and 10.80 W/gMNP were obtained, and experiments reaching temperatures above 43 °C were also obtained). This equipment offers additional advantages, including being economical, user-friendly, and portable.

Full text

Citation: Castelo-Grande, T.; Augusto,
P.A.; Gomes, L.; Calvo, E.; Barbosa, D.
Portable Homemade Magnetic
Hyperthermia Apparatus:
Preliminary Results. Nanomaterials
2024,14, 1848. https://doi.org/
10.3390/nano14221848
Academic Editors: César de Julián
Fernández and Lyudmila M.
Bronstein
Received: 10 August 2024
Revised: 28 October 2024
Accepted: 3 November 2024
Published: 19 November 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
Portable Homemade Magnetic Hyperthermia Apparatus:
Preliminary Results
Teresa Castelo-Grande
1, 2,
* , Paulo A. Augusto
3,4
, Lobinho Gomes
5
, Eduardo Calvo
6
and Domingos Barbosa
1,2
1LEPABE—Laboratory for Process Engineering, Environment, Biotechnology and Energy,
Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal;
dbarbosa@fe.up.pt
2AliCE—Associate Laboratory in Chemical Engineering, Faculty of Engineering, University of Porto,
Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
3Institute of Molecular and Cellular Biology of Cancer, CSIC/University of Salamanca (GIR Citómica),
37007 Salamanca, Spain; pauloaugusto@usal.es
4CEADIR—Center for Environmental Studies and Rural Revitalization, Avenida Filiberto Villalobos, 119,
37007 Salamanca, Spain
5Faculty of Natural Sciences, Engineering and Technologies, Lusófona University of Porto,
R. de Augusto Rosa 24, 4000-098 Porto, Portugal; lobinho.gomes@sapo.pt
6CEFT—Center of Study of Phenomena’s of Transport, Faculty of Engineering, University of Porto,
Rua Dr. Roberto Frias, 4200-465 Porto, Portugal; ecalvo@edu.fe.up.pt
*Correspondence: castelogrande@sapo.pt
Abstract: This study aims to describe and evaluate the performance of a new device for magnetic
hyperthermia that can produce an alternating magnetic field with adjustable frequency without
the need to change capacitors from the resonant bank, as required by other commercial devices.
This innovation, among others, is based on using a capacitator bank that dynamically adjusts the
frequency. To validate the novel system, a series of experiments were conducted using commercial
magnetic nanoparticles (MNPs) demonstrating the device’s effectiveness and allowing us to identify
new challenges associated with the design of more powerful devices. A computational model was
also used to validate the device and to allow us to determine the best system configuration. The
results obtained are consistent with those from other studies using the same MNPs but with magnetic
hyperthermia commercial equipment, confirming the good performance of the developed device
(e.g., consistent SAR values between 1.37 and 10.80 W/gMNP were obtained, and experiments
reaching temperatures above 43
◦
C were also obtained). This equipment offers additional advantages,
including being economical, user-friendly, and portable.
Keywords: magnetic hyperthermia; cancer treatment; nanotechnologies; nanomaterials; portable
apparatus
1. Introduction
Over the last twenty years, magnetic hyperthermia (MH) has been studied as a po-
tential method for treating cancer. It is undergoing clinical trials in Germany [
1
] and is
also starting to be tested clinically in other countries [
2
]. It is an interdisciplinary field that
demands knowledge integration from diverse areas such as quantum physics, materials
research, electrical engineering, chemical engineering, biology, biochemistry, and medicine.
As a result, scientists face substantial challenges in fully comprehending this technique and
its associated therapies, for which further exploration is thus needed.
Hyperthermia treatment, involving heat generation, holds immense potential. For
cancer therapy, it entails raising the local temperature of the tumor, thus modifying the
physiology of the diseased cells and ultimately causing tissue necrosis. This treatment can
effectively complement existing cancer therapies, including chemotherapy, radiotherapy,
surgery, and immunotherapy.
Nanomaterials 2024,14, 1848. https://doi.org/10.3390/nano14221848 https://www.mdpi.com/journal/nanomaterials

Nanomaterials 2024,14, 1848 2 of 25
Hyperthermia treatments can be categorized into different types based on the extent
of the temperature increase:
(1)
High hyperthermia reaches temperatures above 46
◦
C (up to 56
◦
C), causing direct
tissue necrosis, coagulation, or carbonization of cells.
(2)
Moderate hyperthermia (41
◦
C < T < 46
◦
C) has various effects at the cellular and
tissue levels. In this temperature range, cells undergo heat stress, resulting in the
activation and/or initiation of many extracellular degradation mechanisms, such as
protein denaturation, protein folding, DNA aggregation, and cross-linking.
(3)
Low hyperthermia uses temperatures below 41
◦
C and is applied to treat rheumatic
diseases in physiotherapy. It is important to notice that the effectiveness of any
hyperthermia treatment depends significantly on the temperatures reached in the
targeted sites, the duration of exposure, and the specific characteristics of the cancer
cells [
3
]. The National Cancer Institute (NCI) recognizes three different types of
hyperthermia, which are classified based on the area where it is applied and the
extent of the area to be treated: local, regional, and whole-body hyperthermia. In local
hyperthermia, the primary objective is to heat only tumor cells without damaging
healthy tissues. Local hyperthermia is currently a major focus due to its ability to
target heat within a specified region [4].
Traditionally, hyperthermia treatment was administered through external devices that
transfer energy to the tissues via irradiation with light or electromagnetic waves. Today,
there are various techniques available for inducing hyperthermia, such as ultrasound [
5
],
radio frequencies [
6
], microwave range waves [
7
], infrared radiation [
8
], nanoparticle-
assisted photothermal therapy [
9
–
11
], and the use of magnetically excitable nanoparticles.
However, each of these methods has its own limitations. Oncologists usually combine
hyperthermia treatment with radiotherapy, chemotherapy, or both [
12
]. Some of the
challenges in traditional hyperthermia treatment include:
(1)
The inevitable heating of healthy tissue, resulting in burns, blisters, and discomfort;
(2)
Limited penetration of heat into body tissues by microwave, laser, and ultrasound energy;
(3)
Thermal underdosing in the target area, particularly in areas protected by pelvic or
nape bones, often leads to recurrent tumor growth, remaining largely unresolved.
The potential use of magnetic materials in cancer treatment through hyperthermia
was initially suggested in 1957, aiming to convert magnetic energy into thermal energy [
13
].
The rapid progress in magnetic nanoparticles (MNPs) synthesis has represented significant
advances in this type of hyperthermia. Hyperthermia treatment using MNPs presents
multiple advantages over traditional hyperthermia treatment, as outlined in Table 1.
Table 1. Advantages and disadvantages of magnetic hyperthermia [14–18].
Advantages Disadvantages
Magnetic nanoparticles are absorbed by cancer cells,
allowing for localized therapeutic heat supply, which
increases hyperthermia’s effectiveness
Magnetic hyperthermia encounters challenges in
enhancing nanoparticle heating power, regulating
tumor temperature
Tagging MNPs with tumor-specific binding agents
ensures targeted and efficient treatment, maximizing
its impact.
It is difficult to minimize adverse effects on nearby
healthy tissues.
Harmless passage of alternating magnetic field
frequencies through the body exclusively generates
heat in MNP-containing tissues, ensuring safe and
precise treatment.
It is necessary to monitor temperature changes at the
cellular level using precise and non-invasive
techniques.
MNPs’ ability to traverse the blood–brain barrier
makes them valuable for treating brain tumors.
It is crucial to understand the impact of temperature
on the biological processes of cells.
MNPs can be used to create stable colloids, allowing
for a variety of drug delivery routes.
It is important to comprehend the factors that impact
heat transport from MNPs to cells.
The exploration of new magnetic nanoparticles is currently at the forefront of biomedi-
cal research, particularly in magnetic hyperthermia for cancer treatment. Extensive research

Nanomaterials 2024,14, 1848 3 of 25
is being conducted on superparamagnetic nanoparticles, with an average diameter (
σ
) of
just a few tens of nanometers, to assess their potential in this area. In magnetic hyperther-
mia, these nanoparticles are exposed to an alternating magnetic field (AMF) with high
amplitude (H0) and high-frequency ( f0).
The “tunable” magnetic properties of MNPs are essential for their biomedical appli-
cations. These properties, such as magnetic susceptibility (
χ
), blocking temperature (
TB
),
relaxation time (
τ
), and saturation magnetization (
Ms
), can be tailored through different
synthesis processes to create specific MNPs for magnetic hyperthermia treatments. The
specific absorption rate (SAR), proportional to the nanoparticles’ concentration, is a key
indicator of energy dissipation as heat per unit of mass and can be calculated using the
initial slope method.
Some researchers prefer to calculate the specific loss power (
SLP
) instead of the SAR,
as its definition is less ambiguous. Many studies have measured the
SLP
for different
MNPs. The heating generated by MNPs is attributed to various factors such as eddy
currents, the Brownian effect (Brownian relaxation), the crossing of anisotropic barriers
(Néel relaxation), and magnetic energy losses due to the magnetic hysteresis of the MNPs.
Utilizing the linear response theory (LRT), valid for low-applied fields and/or highly
anisotropic magnetic nanoparticles, this heating power can be mathematically expressed as
detailed by [18].
SLP =π×µ0×χ0×H2
0×2×f0×τ
1+(2×π×f0×τ)2W
g(1)
where
SLP
,
χ0
,
H0
,
µ0
and
f0
represent specific loss power or specific power absorption,
static susceptibility, magnetic field amplitude, vacuum permeability, and frequency, respec-
tively, and
τ
is the relaxation time, as detailed in [
19
,
20
]. Equation (1) demonstrates that
both the field amplitude and field frequency influence the dissipated power of MNPs.
Before conducting
in vivo
experiments, the MNPs must undergo thorough prelimi-
nary studies in chemical laboratories to characterize their physical and chemical properties.
In addition,
in vitro
experiments in cellular biology laboratories are necessary to eval-
uate heating effects and the extent of necrosis or apoptosis in cell cultures. A compact
experimental setup, such as the device developed in our lab, provides an excellent alter-
native for conducting rapid trials and measurements in all these laboratories, making it a
powerful tool.
The main goal for synthesized MNPs is to produce a high SAR with a low concentration
of particles when exposed to an alternating magnetic field. There are various systems
proposed for generating alternating magnetic fields, including single- and double-layer
solenoids, Helmholtz coils, inductors with a ferromagnetic core (in horseshoe shape), and
coils made with Litz wire [
21
,
22
]. The single-layer solenoid refrigerated system is the most
widely used, even in commercial equipment, and it is the primary focus of this work.
The development of MH equipment remains vastly unexplored due to its intricate
technology demands, necessitating both high power and high frequency at the same time.
Commercially available devices are, therefore, complex equipment that also does not
present the desired compactness and portability. Consequently, and due to its complexity
and, hence, associated costs only a handful of companies manufacture this equipment,
leading to significant economic barriers that, among others, impede more in-depth research
and widespread application of this promising technique.
It is already known that in order to create devices that are able to achieve the frequen-
cies and magnetic fields required for magnetic hyperthermia, the best option is to use a
resonant circuit. Many different systems with different configurations have been developed
so far to reach this goal. The current options that exist commercially are complicated (thus
hard to adapt and costly) and/or do not allow for a dynamic change of frequencies, making
the overall device rather complex, expensive, hard to handle, and non-portable. In the last
years, research has been performed trying to innovate and achieve devices where a change
of frequencies does not require the physical change of capacitors, among other concerns;

Nanomaterials 2024,14, 1848 4 of 25
however, all these solutions present limited success only. For example, Mazon et al. [
23
]
present a device where frequency tuning of a magnetic hyperthermia device is achieved
by switching control capacitors. Nonetheless, these and similar cases present the problem
that the tactic used for frequency tunning implies the use of microprocessors with a drive
circuit and an H bridge and an inverter, demanding also the use of a PLL circuit for better
enhancing the results of the output frequencies, making the all-device complex, costly, and
non-portable. In the work that is detailed in this article, we present an innovative system
that was very challenging to design and develop, as it joined the capacity of frequency
tuning by switching control capacitors with the simplified version of a resonant circuit,
without the need to use complex microprocessors, inverters, etc. The outcome is a device
capable of performing magnetic hyperthermia with dynamical frequency tunning based
on a simplified circuit, which makes it low-cost, portable, and flexible, and, thus, allows
for simpler and cheaper magnetic hyperthermia research studies and also for possible
worldwide commercial use.
2. Materials and Methods
2.1. Magnetic Field Simulations
The magnetic field simulations were conducted using the “Magnetic fields” module
from the commercial software COMSOL Multiphysics
®
, version 6.0. For computational
purposes, an HP workstation Z4 (HP Headquarters, Lisbon, Portugal) with an Intel(R)
Xeon(R) W-2295 CPU @ 3.00 GHz was used.
A typical solenoid shape was chosen because it preserves the direction of the magnetic
field within its interior [
24
]. The coil itself is composed of hollow copper tubes with an
inner radius of 1.5 mm and thickness of 1 mm, into which a water pumping system is
connected to control temperature changes due to the Joule effect. To complete the geometry
step, the coil was placed inside a parallelepiped domain composed of air. The example of
S5 is depicted in Figure 1. The simulation of the magnetic field was performed with a finite
element method (FEM), where the domain is discretized into small triangular elements. In
each element, the magnetic field is computed through a frequency domain solver. In our
simulation, we employed a dense mesh to accurately capture the system’s complexities.
For the copper tube and the water domain, we implemented a specialized boundary
condition designed to effectively simulate the skin depth effect associated with the electric
current. This approach allowed us to better represent the penetration of the current into
the conductive material, ensuring a more realistic analysis of the interaction between the
copper tube and the surrounding water. In total, the mesh consists of 365,281 elements
with a minimum relative quality of 0.178 and an average quality of 0.6485, being totally
composed of 3 main domains (water, coil, air), 18 faces, 36 edges, and, finally, by 24 points.
Magnetostatic numerical models:
∇×H=J(2)
B=µrµ0H(3)
B=∇×A(4)
where Jis the current density vector, given by the product of the material’s electrical
conductivity (
σ
) and the electric field (E),
J=σE
. This field is computed based on the type
of excitation in the coil. In this study, the coils are voltage-driven, so the electric field is
derived from the divergence of the electric potential,
E=−∇·V
. To account for the Joule
effect, the electrical losses are calculated using the following equation:
Q=1
TZt+T
t
J·Edt (5)
where Q represents the electromagnetic losses. Finally, magnetic insulation boundary
conditions,
ˆn×A
were applied to the faces of the air parallelepiped domain. The materials

Nanomaterials 2024,14, 1848 5 of 25
were selected from the “built-in” libraries from the COMSOL software. The properties are
listed in Table 2.
Nanomaterials 2024, 14, x FOR PEER REVIEW 5 of 28
(a) (b)
Figure 1. Three-dimensional view of solenoid S5. (a) The copper coil contains interior water for
cooling inside, while the surrounding domain contains air (b) computational mesh.
Magnetostatic numerical models:
∇×𝑯=
𝑱
(2)
𝑩=𝜇
𝜇𝑯 (3)
𝑩= ∇×
𝑨
(4)
where J is the current density vector, given by the product of the material’s electrical con-
ductivity (σ) and the electric field (E), 𝑱=𝜎 𝑬. This field is computed based on the type
of excitation in the coil. In this study, the coils are voltage-driven, so the electric field is
derived from the divergence of the electric potential, 𝑬= −∇∙𝑉. To account for the Joule
effect, the electrical losses are calculated using the following equation:
𝑄= 

𝑱
⋅𝑬 𝑑𝑡

 (5)
where Q represents the electromagnetic losses. Finally, magnetic insulation boundary
conditions, 𝒏
×𝑨 were applied to the faces of the air parallelepiped domain. The materi-
als were selected from the “built-in” libraries from the COMSOL software. The properties
are listed in Table 2.
Table 2. Properties for magnetostatic simulations.
Material Relative Permeability
—𝝁𝒓
Relative Permittivity
—𝜺𝒓
Electric Conductivity
—𝝈 (S/m)
Air 1 1 0
Copper 1 1 6 × 107
Water 1 1 0
2.2. Hyperthermia Studies
The initial examination of the developed magnetic hyperthermia (MH) system as pre-
sented in this article involved the use of commercially available MNPs. These MNPs were
carefully chosen based on a comprehensive review of the literature, highlighting their
positive results [25–29]. Their characteristics and designations are detailed in Table 3.
Hence, seven different iron-oxide-based magnetic liquid samples from Chemicell GmbH
Figure 1. Three-dimensional view of solenoid S5. (a) The copper coil contains interior water for
cooling inside, while the surrounding domain contains air (b) computational mesh.
Table 2. Properties for magnetostatic simulations.
Material Relative Permeability
—µr
Relative Permeability
—εr
Electric Conductivity
—σ(S/m)
Air 1 1 0
Copper 1 1 6×107
Water 1 1 0
2.2. Hyperthermia Studies
The initial examination of the developed magnetic hyperthermia (MH) system as pre-
sented in this article involved the use of commercially available MNPs. These MNPs were care-
fully chosen based on a comprehensive review of the literature, highlighting their positive re-
sults [
25
–
29
]. Their characteristics and designations are detailed in Table 3. Hence, seven differ-
ent iron-oxide-based magnetic liquid samples from Chemicell GmbH (Berlin, Germany) were
evaluated (Table 4), following studies by Kallumadil et al. [
26
]);
Yaremenko, A.V et al. [30];
and
Wang, Huang et al. [31].
These samples varied in size and core-shell configurations, all
featuring a magnetite core. The MNPs had previously undergone comprehensive testing and
characterization, particularly concerning their hydrodynamic diameters.
The heating efficacy is represented by the specific absorption rate (SAR) value, ex-
pressed in W/g
(Magnetic NanoParticles)
. This value corresponds to the amount of energy
converted into heat (J) per unit time (s) and mass (m
mag
) of the magnetic material. The SAR
was calculated using the initial slope method (Figure 2), which considers the first few min-
utes (Equation (6)) within the linear variation range of the heating curve (adiabatic regime).
This period is typically set at 100 s based on theoretical assumptions (low frequency and
magnetic field).
S.A.R(Specific Absortion Rate)=Cmsol ×msol
mmag
dT
dt =(mH2O×CpH2O+mMN P ×Cp MN P)
mMN P ×dT
dt (6)
where
Cmsol
is the specific heat of the solution,
msol
is the mass of the solution,
mmag
is the
mass of the MNPs, and dT
dt is the maximum value of the initial linear slope.

Nanomaterials 2024,14, 1848 6 of 25
Table 3. Properties of the magnetic nanoparticles used in the experiments.
Product Matrix/Cover
Size (Hydrody-
namic
Diameter)
(nm)
Density
(g/cm3)
Functionalization
Particles
Number
Core/vh *
(nm)
Zeta Potential
(mv)
Fluidmag-ara Polysaccharide 150 ~1.25 Glucuronic
acid
~1.8 ×1015/g
−2.2 ×1014/g
23.6 ±5.6/
121 ±40
[30]
−22.65 mV
[30]
Fluidmag-uca No 200 ~5.2 Anionic charge ~2.2 ×1014/g
Fluidmag-dx Dextran 50 ~1.25 Hydroxyl
groups ~1.3 ×1016/g
Fluidmag-cmx
Carboxymethyl–
dextran n.a. ~1.25 Sodium
carboxylate
110.6 ±3.5
[32]–32.3 ±0.1
Fluidmag-lipid Phosphatidyl-
choline 200 ~1.25 Phosphati-
dylcholine ~2.2 ×1014/g
Fluidmag-d50 Starch 50 ~1.25 Hydroxyl
groups ~1.3 ×1016/g
Fluidmag-d100 Starch 100 ~1.25 Hydroxyl
groups ~1.8 ×1015/g
Supermagnetic
ARA
, coated with polysaccharides, distilled water solvent (diam. = 150 nnm, conc = 25 mg/mL and
1.8
×
10
15
particles/g; d = 1.25 g/cm
3
). Supermagnetic
UCA
(diam. = 200 nm, conc = 25 mg/mL and 2.2
×
10
14
particles/g; d = 5.2 g/cm
3
), magnetite as core and uncoated, and are charged to be anionic, solvent distilled water.
* Other average values published CMX-coatedMNPs 0.98 ±0.11 content of iron mgFe/mL.
Table 4. Parameters of the applied solenoids.
Solenoid H (Height)
(mm)
Tube External
Diameter
(mm)
Tube
Internal
Diameter
(mm)
Solenoid
Internal Diameter
(mm)
Number
of Turns
Space
Between
Turns (mm)
Observations
S1 33.0 4.1 ---- 54.6 5 2.7
S2 100.7 6.3 1 73.7 13 2.0 Inductance is
5µH
S3 68.0 6.3 1 50.0 9 2.0
S4 66.0 6.3 1 74.5 8 Variable
S5 73.0 5.0 1 70.0 9 2–2.5 variable
S6 57.0 6.3 1 41.3 7 Variable Inductance is
2.5 µH
S7 100.0 n.a. --- 70.0 11 Variable Foldable
(multiwire)
S8 119.6 5.0 1 42.3 17 Variable Yield the best
results so far
Nanomaterials 2024, 14, x FOR PEER REVIEW 7 of 28
The heating efficacy is represented by the specific absorption rate (SAR) value, ex-
pressed in W/g(Magnetic NanoParticles). This value corresponds to the amount of energy converted
into heat (J) per unit time (s) and mass (mmag) of the magnetic material. The SAR was cal-
culated using the initial slope method (Figure 2), which considers the first few minutes
(Equation (6)) within the linear variation range of the heating curve (adiabatic regime).
This period is typically set at 100 s based on theoretical assumptions (low frequency and
magnetic field).
S.A.R (Specific Absortion Rate) = 𝐶 ×


 = (×  ×)
 ×
 (6)
where 𝐶 is the specific heat of the solution, 𝑚 is the mass of the solution, 𝑚 is
the mass of the MNPs, and 
 is the maximum value of the initial linear slope.
Figure 2. Initial slope method (ISM) for calculating the specific absorption rate (SAR).
The concentration range for measuring the specific absorption rate (SAR) of the of
the MNPs was 5 to 25 mgMNP/mL. This measurement was conducted using the developed
apparatus by determining the heating curve (temperature variation over time). For statis-
tical accuracy, three measurements were taken for each sample.
In Appendix A, details are shown about how magnetic fields were measured and
accounted for.
3. Results and Discussion
3.1. Configuration, Specifications, and Fundamental Operational Principles of an Alternating
Magnetic Field Generator
In the past two decades, there has been remarkable progress in the development of
devices for magnetic hyperthermia applications. These devices utilize alternating mag-
netic fields at high frequencies and power levels [33]. However, most of these devices are
primarily designed for whole-body applications [1]. Due to their large size, these devices
are not suitable for use in research laboratories. Recently, various switched-mode resonant
inverters have been developed for medical use in electromagnetic thermotherapy. These
inverters use voltage-fed high-frequency applicators with power metal-oxide-semicon-
ductor field-effect transistors (MOSFETs) operating based on resonant circuits as further
explained below [34]. To achieve the necessary alternating magnetic field for hyperther-
mia, a high alternating electric current at a specific frequency must be passed through a
coil, typically at high frequencies (>100 kHz). To accomplish this, two main technologies
are commonly used: resonant circuits and H-bridge-based circuits, also known as
Figure 2. Initial slope method (ISM) for calculating the specific absorption rate (SAR).
The concentration range for measuring the specific absorption rate (SAR) of the of the
MNPs was 5 to 25 mg
MNP
/mL. This measurement was conducted using the developed ap-

Nanomaterials 2024,14, 1848 7 of 25
paratus by determining the heating curve (temperature variation over time). For statistical
accuracy, three measurements were taken for each sample.
In Appendix A, details are shown about how magnetic fields were measured and
accounted for.
3. Results and Discussion
3.1. Configuration, Specifications, and Fundamental Operational Principles of an Alternating
Magnetic Field Generator
In the past two decades, there has been remarkable progress in the development of
devices for magnetic hyperthermia applications. These devices utilize alternating magnetic
fields at high frequencies and power levels [
33
]. However, most of these devices are pri-
marily designed for whole-body applications [
1
]. Due to their large size, these devices are
not suitable for use in research laboratories. Recently, various switched-mode resonant
inverters have been developed for medical use in electromagnetic thermotherapy. These in-
verters use voltage-fed high-frequency applicators with power metal-oxide-semiconductor
field-effect transistors (MOSFETs) operating based on resonant circuits as further explained
below [
34
]. To achieve the necessary alternating magnetic field for hyperthermia, a high
alternating electric current at a specific frequency must be passed through a coil, typically
at high frequencies (>100 kHz). To accomplish this, two main technologies are commonly
used: resonant circuits and H-bridge-based circuits, also known as inverters. For more
information on how these circuits work and their components, see Cabrera et al., 2019 [
35
].
In this groundbreaking work, a resonant circuit was employed, harnessing a technique
that has undergone extensive study over the past three decades. This approach has captured
substantial attention from both academic and industrial research communities due to its
remarkable characteristics: smooth waveforms, exceptional efficiency, and high-power
density. Resonant circuits are based on transforming a constant direct current power source
into a sinusoidal wave. This is made possible through a resonant circuit based on a parallel
LC (inductor/capacitor) configuration, as depicted in Figure 3.
Nanomaterials 2024, 14, x FOR PEER REVIEW 8 of 28
inverters. For more information on how these circuits work and their components, see
Cabrera et al. 2019 [35].
In this groundbreaking work, a resonant circuit was employed, harnessing a tech-
nique that has undergone extensive study over the past three decades. This approach has
captured substantial aention from both academic and industrial research communities
due to its remarkable characteristics: smooth waveforms, exceptional efficiency, and high-
power density. Resonant circuits are based on transforming a constant direct current
power source into a sinusoidal wave. This is made possible through a resonant circuit
based on a parallel LC (inductor/capacitor) configuration, as depicted in Figure 3.
Figure 3. Parallel LC resonant circuit.
Resonant converters encompass a diverse and extensive family, which can pose a
straightforward description challenge. However, one common feature shared by most, if
not all, is their reliance on a “resonant inverter” to convert DC voltage into sinusoidal
voltage and deliver AC power. These converters utilize major topologies such as full-
bridge zero voltage switching (ZVS), half-bridge ZVS, full-bridge zero current switching
(ZCS), and half-bridge ZCS series converters [36]. For this project, we opted for the half-
bridge ZVS series converter, a simple yet widely used choice (see Figure 1). The ZVS sys-
tem is typically employed in high-frequency switching applications, offering advantages
including reduced power losses, enhanced reliability, and improved overall performance
of power electronic systems [37].
To aain maximum performance, the converter needs to operate at the resonant fre-
quency. Equations (7) and (8) precisely define the resonance frequency fr and the peak
voltage VM across the coil for the basic ZVS series converter at the operating frequency.
𝑓
=
××√× (7)
𝑉=𝑋
×𝐼
 =2×𝜋×
𝑓
×𝐿×𝐼
 (8)
In Equations (7) and (8), L denotes the coil’s inductance, while C represents the sys-
tem’s capacitance. XL stands for inductive reactance, which varies with frequency.
In our research, we aempted to use the simplest and most efficient system that
would allow us to construct an economical and portable device for use by the scientific
community.
The experimental program initiated with the establishment of a resonant circuit to
generate a sinusoidal wave. The wave’s frequency is contingent on the coil configuration
Qi- Power MOSFET; Ci- condenser; Di- diode; Ri- resistance ; L1,2- shock coils. i = 1–5
Figure 3. Parallel LC resonant circuit.
Resonant converters encompass a diverse and extensive family, which can pose a
straightforward description challenge. However, one common feature shared by most,
if not all, is their reliance on a “resonant inverter” to convert DC voltage into sinusoidal
voltage and deliver AC power. These converters utilize major topologies such as full-
bridge zero voltage switching (ZVS), half-bridge ZVS, full-bridge zero current switching
(ZCS), and half-bridge ZCS series converters [
36
]. For this project, we opted for the
half-bridge ZVS series converter, a simple yet widely used choice (see Figure 1). The ZVS

Nanomaterials 2024,14, 1848 8 of 25
system is typically employed in high-frequency switching applications, offering advantages
including reduced power losses, enhanced reliability, and improved overall performance
of power electronic systems [37].
To attain maximum performance, the converter needs to operate at the resonant
frequency. Equations (7) and (8) precisely define the resonance frequency f
r
and the peak
voltage VMacross the coil for the basic ZVS series converter at the operating frequency.
fr=1
2×π×√L×C(7)
VM=XL×Imax =2×π×fr×L×Imax (8)
In Equations (7) and (8), L denotes the coil’s inductance, while Crepresents the
system’s capacitance. XL stands for inductive reactance, which varies with frequency.
In our research, we attempted to use the simplest and most efficient system that would
allow us to construct an economical and portable device for use by the scientific community.
The experimental program initiated with the establishment of a resonant circuit to
generate a sinusoidal wave. The wave’s frequency is contingent on the coil configuration
and the capacitors positioned in parallel to form the resonant oscillator circuit. Typically, this
circuit maintains a fixed frequency, obstructing the analysis of particle behavior at different
frequencies for identifying the optimal operating value. To surmount this limitation, a
bank of capacitors, managed by a set of switches (six in this scenario), was introduced into
the circuit. These switches enable the parallel placement of more or fewer capacitors with
the test coil, thereby modifying the resonant frequency of the LC circuit and consequently
adjusting the test frequency (see Figure 4). This apparatus has demonstrated remarkable
effectiveness in operating at high powers and high frequencies (frequency range
69–303 khz
and generated magnetic field range 4 mT–16 mT).
Nanomaterials 2024, 14, x FOR PEER REVIEW 9 of 28
and the capacitors positioned in parallel to form the resonant oscillator circuit. Typically,
this circuit maintains a fixed frequency, obstructing the analysis of particle behavior at
different frequencies for identifying the optimal operating value. To surmount this limi-
tation, a bank of capacitors, managed by a set of switches (six in this scenario), was intro-
duced into the circuit. These switches enable the parallel placement of more or fewer ca-
pacitors with the test coil, thereby modifying the resonant frequency of the LC circuit and
consequently adjusting the test frequency (see Figure 4). This apparatus has demonstrated
remarkable effectiveness in operating at high powers and high frequencies (frequency
range 69–303 khz and generated magnetic field range 4 mT–16 mT).
Figure 4. Image of the switch set that controls the capacitor bank.
Upon testing our initial resonant system (see Figure 5a) with a fixed bank of capaci-
tors, we achieved notable positive results. These results were particularly evident when
we modified the coil’s configuration to increase field concentration by adjusting the cur-
rent flow due to lower impedance (2.5 to 5 μH inductance) and by changing the frequency.
In Figure 5, the progression from our initial system prototype to the current develop-
ment stage is depicted, even into a new, more powerful prototype currently under testing.
The magnetic hyperthermia device assembly consists of five key components:
(1) Power source (VELLEMAN, Model: LABPS6030SM);
(2) Electric circuit (designed by us and manufactured by JMP Electronics (Jinhu, China));
(3) Cooling system (designed by us);
(4) Oscilloscope coupled with a probe for measuring the magnetic field (see Appendix
A) and verifying the waveform passing through the coil (Promax Electronics, Model:
OD-624);
(5) Temperature recorder and probe for measuring the sample temperature (Cha-
viun1822 with probe K presenting an accuracy ±2%). In the magnitude range of the
magnetic field, the inference is minimal, as demonstrated in the next section
[32,33,38].
The power source was carefully chosen to ensure the required voltage (ΔV) for gen-
erating an electric current capable of creating a high-intensity magnetic field. The specific
MOSFET selected, IRFP260, can handle a maximum current of 60 A and support a voltage
of 200 V.
The resonant system and coil were meticulously designed to produce a uniform mag-
netic field inside the sample. Several coils were designed and tested, the default system
being composed of a coil, made of copper and comprising a 2 cm diameter, 11 cm length,
and 17 turns, designed to be cooled by flowing water to maintain room temperature. It is
important to notice that under ideal conditions, Equations (7) and (8) are well fied to the
real maximum current and frequency of the resonant circuit, respectively.
The maximum intensity of the magnetic field in the coils is given by Equation (9),
𝐵 =×.×
 (9)
Figure 4. Image of the switch set that controls the capacitor bank.
Upon testing our initial resonant system (see Figure 5a) with a fixed bank of capacitors,
we achieved notable positive results. These results were particularly evident when we
modified the coil’s configuration to increase field concentration by adjusting the current
flow due to lower impedance (2.5 to 5 µH inductance) and by changing the frequency.
Nanomaterials 2024, 14, x FOR PEER REVIEW 10 of 28
N represents the number of turns of the coil, µ0 stands for the magnetic permeability
in a vacuum (4π × 10−7 H/m), Icurr.max denotes the maximum current intensity, and le indi-
cates the length of the solenoid. The high current running through the system causes the
solenoid to heat up due to the Joule effect. To maintain a constant temperature, it is essen-
tial to cool it by circulating water within the solenoid. Priority is given to improve the
insulation system, and currently, we are exploring materials such as mineral wool, AMO-
RIM-expanded cork, and Styrofoam for the sample holder and insulation. Figures 6 and 7
illustrate a diagram of the setup and a schematic representation of the system with the
cooled coil containing a sample inside.
(a) (b) (c)
Figure 5. (a) Initial prototype of our system, (b) the system being currently applied, (c) a new and
more powerful prototype system (resonant) that is being tested.
(a)
Figure 5. (a) Initial prototype of our system, (b) the system being currently applied, (c) a new and
more powerful prototype system (resonant) that is being tested.

Nanomaterials 2024,14, 1848 9 of 25
In Figure 5, the progression from our initial system prototype to the current develop-
ment stage is depicted, even into a new, more powerful prototype currently under testing.
The magnetic hyperthermia device assembly consists of five key components:
(1)
Power source (VELLEMAN, Model: LABPS6030SM);
(2)
Electric circuit (designed by us and manufactured by JMP Electronics (Jinhu, China));
(3)
Cooling system (designed by us);
(4) Oscilloscope coupled with a probe for measuring the magnetic field (see Appendix A) and
verifying the waveform passing through the coil (Promax Electronics, Model: OD-624);
(5) Temperature recorder and probe for measuring the sample temperature (Chaviun1822
with probe K presenting an accuracy
±
2%). In the magnitude range of the magnetic
field, the inference is minimal, as demonstrated in the next section [32,33,38].
The power source was carefully chosen to ensure the required voltage (
∆
V) for gener-
ating an electric current capable of creating a high-intensity magnetic field. The specific
MOSFET selected, IRFP260, can handle a maximum current of 60 A and support a voltage
of 200 V.
The resonant system and coil were meticulously designed to produce a uniform
magnetic field inside the sample. Several coils were designed and tested, the default system
being composed of a coil, made of copper and comprising a 2 cm diameter, 11 cm length,
and 17 turns, designed to be cooled by flowing water to maintain room temperature. It is
important to notice that under ideal conditions, Equations (7) and (8) are well fitted to the
real maximum current and frequency of the resonant circuit, respectively.
The maximum intensity of the magnetic field in the coils is given by Equation (9),
BMAX =µ0×Icurr.max ×N
le(9)
Nrepresents the number of turns of the coil,
µ0
stands for the magnetic permeability in
a vacuum (4
π×
10
−7
H/m), I
curr.max
denotes the maximum current intensity, and l
e
indicates
the length of the solenoid. The high current running through the system causes the solenoid
to heat up due to the Joule effect. To maintain a constant temperature, it is essential to cool it
by circulating water within the solenoid. Priority is given to improve the insulation system,
and currently, we are exploring materials such as mineral wool, AMORIM-expanded cork,
and Styrofoam for the sample holder and insulation.
Figures 6and 7
illustrate a diagram
of the setup and a schematic representation of the system with the cooled coil containing a
sample inside.
Nanomaterials 2024, 14, x FOR PEER REVIEW 10 of 28
N represents the number of turns of the coil, µ0 stands for the magnetic permeability
in a vacuum (4π × 10−7 H/m), Icurr.max denotes the maximum current intensity, and le indi-
cates the length of the solenoid. The high current running through the system causes the
solenoid to heat up due to the Joule effect. To maintain a constant temperature, it is essen-
tial to cool it by circulating water within the solenoid. Priority is given to improve the
insulation system, and currently, we are exploring materials such as mineral wool, AMO-
RIM-expanded cork, and Styrofoam for the sample holder and insulation. Figures 6 and 7
illustrate a diagram of the setup and a schematic representation of the system with the
cooled coil containing a sample inside.
(a) (b) (c)
Figure 5. (a) Initial prototype of our system, (b) the system being currently applied, (c) a new and
more powerful prototype system (resonant) that is being tested.
(a)
Figure 6. Cont.

Nanomaterials 2024,14, 1848 10 of 25
Nanomaterials 2024, 14, x FOR PEER REVIEW 11 of 28
(b)
Figure 6. Overview of the system (a) and photographs of the apparatus and of the system (b): A—
power source; B—system; C—solenoid; D—cooling system; E—equipment for measuring tempera-
ture; F—computer for acquiring and registering the temperature; G and H—oscilloscope coupled
with a probe for measuring the magnetic field and verifying the waveform passing through the coil.
[39].
Figure 7. Insulating system.
To improve the performance of the magnetic hyperthermia system, various experi-
ments were conducted with different coil configurations (see Table 4) that are depicted in
Figure 8. The results of these experiments will be presented throughout the text.
Figure 6. Overview of the system (a) and photographs of the apparatus and of the system (b):
A—power
source; B—system; C—solenoid; D—cooling system; E—equipment for measuring temperature;
F—computer for acquiring and registering the temperature; G and H—oscilloscope coupled with a
probe for measuring the magnetic field and verifying the waveform passing through the coil [39].
Nanomaterials 2024, 14, x FOR PEER REVIEW 11 of 28
(b)
Figure 6. Overview of the system (a) and photographs of the apparatus and of the system (b): A—
power source; B—system; C—solenoid; D—cooling system; E—equipment for measuring tempera-
ture; F—computer for acquiring and registering the temperature; G and H—oscilloscope coupled
with a probe for measuring the magnetic field and verifying the waveform passing through the coil.
[39].
Figure 7. Insulating system.
To improve the performance of the magnetic hyperthermia system, various experi-
ments were conducted with different coil configurations (see Table 4) that are depicted in
Figure 8. The results of these experiments will be presented throughout the text.
Figure 7. Insulating system.
To improve the performance of the magnetic hyperthermia system, various experi-
ments were conducted with different coil configurations (see Table 4) that are depicted in
Figure 8. The results of these experiments will be presented throughout the text.
Nanomaterials 2024, 14, x FOR PEER REVIEW 12 of 28
Figure 8. Images of solenoids described in Table 4.
3.2. Results of Magnetic Field Simulations
This section presents the numerical results obtained for the different coils used in the
hyperthermia studies described in this work.
Parametric frequency studies of solenoid coils
The geometric parameters of each solenoid coil can be found in Table 4. In these nu-
merical studies, only coils S5, S6, and S8 were simulated (see example of S5 in Figure 9),
for reasons detailed in the next sub-section. For coil S8, two simulations were conducted
with different numbers of turns, 12 and 17. To obtain the electric properties of the selected
coils, a parametric frequency run was performed using frequencies of 72, 96, 134, and 302
kHz. The applied voltage to excite the coils was set to a constant value of 60 V.
(a) (b)
Figure 9. Profile of the magnetic field density (mT) of solenoid coil S5 for a driving voltage of 60 V
and an operating frequency of 72 kHz. (a) Three-dimensional view, (b) two-dimensional view for
the plane x = 0.
Comparison of coils at various frequencies
To compare each coil, two criteria were established: the shape of the magnetic field
density at the center of the coil and the electric properties of each coil. The first criterion
involved evaluating the magnetic field density relative to the coil’s length. This method
allowed us to determine whether the magnetic field density inside the coil followed a
horseshoe profile or remained constant along its length. The second criterion focused on
the electrical properties, such as impedance, current, and induction, when different fre-
quencies were applied to the solenoid.
Figure 8. Images of solenoids described in Table 4.

Nanomaterials 2024,14, 1848 11 of 25
3.2. Results of Magnetic Field Simulations
This section presents the numerical results obtained for the different coils used in the
hyperthermia studies described in this work.
Parametric frequency studies of solenoid coils
The geometric parameters of each solenoid coil can be found in Table 4. In these
numerical studies, only coils S5, S6, and S8 were simulated (see example of S5 in Figure 9),
for reasons detailed in the next sub-section. For coil S8, two simulations were conducted
with different numbers of turns, 12 and 17. To obtain the electric properties of the selected
coils, a parametric frequency run was performed using frequencies of 72, 96, 134, and
302 kHz. The applied voltage to excite the coils was set to a constant value of 60 V.
Nanomaterials 2024, 14, x FOR PEER REVIEW 12 of 28
Figure 8. Images of solenoids described in Table 4.
3.2. Results of Magnetic Field Simulations
This section presents the numerical results obtained for the different coils used in the
hyperthermia studies described in this work.
Parametric frequency studies of solenoid coils
The geometric parameters of each solenoid coil can be found in Table 4. In these nu-
merical studies, only coils S5, S6, and S8 were simulated (see example of S5 in Figure 9),
for reasons detailed in the next sub-section. For coil S8, two simulations were conducted
with different numbers of turns, 12 and 17. To obtain the electric properties of the selected
coils, a parametric frequency run was performed using frequencies of 72, 96, 134, and 302
kHz. The applied voltage to excite the coils was set to a constant value of 60 V.
(a) (b)
Figure 9. Profile of the magnetic field density (mT) of solenoid coil S5 for a driving voltage of 60 V
and an operating frequency of 72 kHz. (a) Three-dimensional view, (b) two-dimensional view for
the plane x = 0.
Comparison of coils at various frequencies
To compare each coil, two criteria were established: the shape of the magnetic field
density at the center of the coil and the electric properties of each coil. The first criterion
involved evaluating the magnetic field density relative to the coil’s length. This method
allowed us to determine whether the magnetic field density inside the coil followed a
horseshoe profile or remained constant along its length. The second criterion focused on
the electrical properties, such as impedance, current, and induction, when different fre-
quencies were applied to the solenoid.
Figure 9. Profile of the magnetic field density (mT) of solenoid coil S5 for a driving voltage of 60 V
and an operating frequency of 72 kHz. (a) Three-dimensional view, (b) two-dimensional view for the
plane x = 0.
Comparison of coils at various frequencies
To compare each coil, two criteria were established: the shape of the magnetic field
density at the center of the coil and the electric properties of each coil. The first criterion
involved evaluating the magnetic field density relative to the coil’s length. This method
allowed us to determine whether the magnetic field density inside the coil followed a
horseshoe profile or remained constant along its length. The second criterion focused
on the electrical properties, such as impedance, current, and induction, when different
frequencies were applied to the solenoid.
The initial solenoids (S1–S4) were tested but did not yield significant results; therefore,
simulations were only performed for S5–S8. Solenoid S1 did not produce a satisfactory
magnetic field value and, like S2, exhibited a less concentrated, non-uniform field with high
impedance. S3 presented challenges in implementing an insulation system due to its narrow
design, while S4 had a less concentrated magnetic field compared to S2. Additionally, coil
S7 was discarded because it heated up as the electric current passed through it.
Figure 10 displays the results of the first criterion evaluation. The blue solid lines
represent coils operating at a frequency of 72 kHz, while the red dotted lines, black dashed
lines, and green dashed–dot lines correspond to frequencies of 96 kHz, 134 kHz, and
302 kHz,
respectively. The symbols (*), (
♢
), (
□
), and (
☼
) denote solenoid coils S5, S6, S8
with 12 turns, and S8 with 17 turns, respectively.
Analysis of the image reveals that the magnetic field strength decreases with increasing
frequency, as demonstrated by [
40
]. Overall, coil S6 exhibited the highest magnetic field
density, reaching peaks above 16 mT at 72 kHz and approximately 3.5 mT at 302 kHz. In
contrast, coil S5 had the lowest value, peaking at around 3.5 mT at 72 kHz and below 1 mT
at 302 kHz. However, coil S8, both with 12 turns and 17 turns, demonstrated a consistent
magnetic field strength across all frequencies, showing a flat profile.

Nanomaterials 2024,14, 1848 12 of 25
Nanomaterials 2024, 14, x FOR PEER REVIEW 13 of 28
The initial solenoids (S1–S4) were tested but did not yield significant results; there-
fore, simulations were only performed for S5–S8. Solenoid S1 did not produce a satisfac-
tory magnetic field value and, like S2, exhibited a less concentrated, non-uniform field
with high impedance. S3 presented challenges in implementing an insulation system due
to its narrow design, while S4 had a less concentrated magnetic field compared to S2. Ad-
ditionally, coil S7 was discarded because it heated up as the electric current passed
through it.
Figure 10 displays the results of the first criterion evaluation. The blue solid lines
represent coils operating at a frequency of 72 kHz, while the red doed lines, black dashed
lines, and green dashed–dot lines correspond to frequencies of 96 kHz, 134 kHz, and 302
kHz, respectively. The symbols (*), (◊), (), and () denote solenoid coils S5, S6, S8 with
12 turns, and S8 with 17 turns, respectively.
Figure 10. Magnetic field density (mT) along the center of the simulated coils at various operating
frequencies.
Analysis of the image reveals that the magnetic field strength decreases with increas-
ing frequency, as demonstrated by [40]. Overall, coil S6 exhibited the highest magnetic
field density, reaching peaks above 16 mT at 72 kHz and approximately 3.5 mT at 302 kHz.
In contrast, coil S5 had the lowest value, peaking at around 3.5 mT at 72 kHz and below 1
mT at 302 kHz. However, coil S8, both with 12 turns and 17 turns, demonstrated a con-
sistent magnetic field strength across all frequencies, showing a flat profile.
The second criterion analysis is based on Table 5, which presents the electrical prop-
erties of each solenoid excited by a sinusoidal applied voltage of 60 V. As shown, S6 ex-
hibited the highest current values and consequently the lowest impedance inductance,
ranging from 1.07 μH to 1.08 μH. S8 achieved impedances ranging from 2.13 μH to 2.15
μH for 12 turns and from 3.03 μH to 3.06 μH for 17 turns. Similar to the trend observed in
the first criterion evaluation, S5 demonstrated the poorest performance, with inductances
ranging between 3.91 μH and 3.93 μH. This is consistent with Equation (10), as the imped-
ance varies linearly with the inductance of the coil and the frequency. Additionally, Equa-
tion (11) describes the inductance, indicating a quadratic relationship with the number of
turns and an inverse linear relationship with the length of the coil. Thus, the simulation
results align with the expected outcomes.
Figure 10. Magnetic field density (mT) along the center of the simulated coils at various
operating frequencies.
The second criterion analysis is based on Table 5, which presents the electrical proper-
ties of each solenoid excited by a sinusoidal applied voltage of 60 V. As shown, S6 exhibited
the highest current values and consequently the lowest impedance inductance, ranging
from 1.07
µ
H to 1.08
µ
H. S8 achieved impedances ranging from 2.13
µ
H to 2.15
µ
H for
12 turns and from 3.03
µ
H to 3.06
µ
H for 17 turns. Similar to the trend observed in the first
criterion evaluation, S5 demonstrated the poorest performance, with inductances ranging
between 3.91
µ
H and 3.93
µ
H. This is consistent with Equation (10), as the impedance
varies linearly with the inductance of the coil and the frequency. Additionally, Equation (11)
describes the inductance, indicating a quadratic relationship with the number of turns and
an inverse linear relationship with the length of the coil. Thus, the simulation results align
with the expected outcomes.
Table 5. Electrical properties of solenoid at various frequencies.
f(kHz) Coil Current (A) Coil Resistance (Ω) Coil Impedance (Ω) Coil Inductance (µH)
S5
72 33.684∠−89.305◦2.160 ×10−21.781∠89.305◦3.9372
96 25.311∠−89.403◦2.470 ×10−22.37∠89.403◦3.9296
134 18.167∠−89.512◦2.811 ×10−23.303∠89.512◦3.9226
302 8.081∠−89.739◦3.377 ×10−27.425∠89.739◦3.9127
S6
72 122.183∠−88.89◦9.512 ×10−30.491∠88.89◦1.0853
96 91.917∠−89.046◦1.086 ×10−20.653∠89.046◦1.0820
134 66.04∠−89.22◦1.237 ×10−20.909∠89.22◦1.0790
302 29.423∠−89.58◦1.495 ×10−22.039∠89.58◦1.0747
S8—12 turns
72 61.764∠−88.943◦1.791 ×10−20.971∠88.943◦2.1470
96 46.459∠−89.101◦2.026 ×10−21.291∠89.101◦2.1408
134 33.372∠−89.277◦2.268 ×10−21.798∠89.277◦2.1353
302 14.858∠−89.626◦2.637 ×10−24.038∠89.626◦2.1280
S8—17 turns
72 43.316∠−88.959◦2.516 ×10−21.385∠88.959◦3.0614
96 32.58∠−89.116◦2.841 ×10−21.842∠89.116◦3.0528
134 23.402∠−89.29◦3.178 ×10−22.564∠89.29◦3.0450
302 10.418∠−89.634◦3.676 ×10−25.759∠89.634◦3.0349
3.3. Hyperthermia Essays
In order to assess the effectiveness of the insulation system, a critical component for
adiabatic heating, we conducted tests using distilled water (DW) and observed its heating
patterns. As depicted in Figure 11, over a 10 min heating period at a frequency of 69 kHz,

Nanomaterials 2024,14, 1848 13 of 25
the temperature rose by a mere 2.5
◦
C across three separate days, affirming the consistency
of our measurements. Initially, we meticulously monitored the sample’s temperature on a
minute-by-minute basis to ascertain any signs of heating. Once the device’s reliability was
confirmed, we obtained continuous data and meticulously documented it for the purpose
of calculating temperature variation per second. This approach enabled us to utilize more
precise methodologies, such as the Lucas box method and the increment-corrected method,
to derive the SAR value [39,41].
The initial experiments were conducted using solenoid S5, and the first particles tested
were Fluidmag
ARA
and Fluidmag
UCA
. Fluidmag
ARA
consists of coated particles, while
Fluidmag
UCA
features uncoated particles with anionic charges. The nanoparticle con-
centration used was 25 mg/mL. Fluidmag
ARA
particles are composed of a multi-domain
magnetite core coated with a layer of glucuronic acid [
29
,
42
]. At a frequency of 98 kHz, the
temperature increased by 9.2
◦C
in the Fluidmag
UCA
sample and 6.8
◦C
in the Fluidmag
ARA
sample. These results align with the parameters listed in Table 5, as Fluidmag
ARA
par-
ticles are smaller than UCA particles, resulting in fewer less magnetic domains and a
lower iron percentage. Additionally, it is known that the coating on nanoparticles can
reduce the magnetic saturation value (Ms), which is consistent with the observed results.
The heating curves and SAR values are presented in Figure 12, showing SAR values of
1.76 W/gMNP-UCA and 1.37 W/gMNP-ARA.
Nanomaterials 2024, 14, x FOR PEER REVIEW 14 of 28
Table 5. Electrical properties of solenoid at various frequencies.
f(kHz) Coil Current (A) Coil Resistance (Ω) Coil Impedance (Ω) Coil Inductance (μH)
S5
72 33.684∠−89.305° 2.160 × 10−2 1.781∠89.305° 3.9372
96 25.311∠−89.403° 2.470 × 10−2 2.37∠89.403° 3.9296
134 18.167∠−89.512° 2.811 × 10−2 3.303∠89.512° 3.9226
302 8.081∠−89.739° 3.377 × 10−2 7.425∠89.739° 3.9127
S6
72 122.183∠−88.89° 9.512 × 10−3 0.491∠88.89° 1.0853
96 91.917∠−89.046° 1.086 × 10−2 0.653∠89.046° 1.0820
134 66.04∠−89.22° 1.237 × 10−2 0.909∠89.22° 1.0790
302 29.423∠−89.58° 1.495 × 10−2 2.039∠89.58° 1.0747
S8—12 turns
72 61.764∠−88.943° 1.791 × 10−2 0.971∠88.943° 2.1470
96 46.459∠−89.101° 2.026 × 10−2 1.291∠89.101° 2.1408
134 33.372∠−89.277° 2.268 × 10−2 1.798∠89.277° 2.1353
302 14.858∠−89.626° 2.637 × 10−2 4.038∠89.626° 2.1280
S8—17 turns
72 43.316∠−88.959° 2.516 × 10−2 1.385∠88.959° 3.0614
96 32.58∠−89.116° 2.841 × 10−2 1.842∠89.116° 3.0528
134 23.402∠−89.29° 3.178 × 10−2 2.564∠89.29° 3.0450
302 10.418∠−89.634° 3.676 × 10−2 5.759∠89.634° 3.0349
3.3. Hyperthermia Essays
In order to assess the effectiveness of the insulation system, a critical component for
adiabatic heating, we conducted tests using distilled water (DW) and observed its heating
paerns. As depicted in Figure 11, over a 10 min heating period at a frequency of 69 kHz,
the temperature rose by a mere 2.5 °C across three separate days, affirming the consistency
of our measurements. Initially, we meticulously monitored the sample’s temperature on
a minute-by-minute basis to ascertain any signs of heating. Once the device’s reliability
was con firmed, we obtained continuous data and meticulously documented it for the pur-
pose of calculating temperature variation per second. This approach enabled us to utilize
more precise methodologies, such as the Lucas box method and the increment-corrected
method, to derive the SAR value [39,41].
Figure 11. The temperature variation of dstillated water samples was consistent across three exper-
iments conducted on different days at a frequency of 69 kHz with solenoid S5.
18
18.5
19
19.5
20
20.5
21
21.5
22
024681012
temperature (°C)
time (min)
1st Repetition
2nd Repetition
Destilled Water (DW)
Figure 11. The temperature variation of dstillated water samples was consistent across three experi-
ments conducted on different days at a frequency of 69 kHz with solenoid S5.
Nanomaterials 2024, 14, x FOR PEER REVIEW 15 of 28
The initial experiments were conducted using solenoid S5, and the first particles
tested were FluidmagARA and FluidmagUCA. FluidmagARA con sis ts of coa ted part icl es, whil e
FluidmagUCA features uncoated particles with anionic charges. The nanoparticle concen-
tration used was 25 mg/mL. FluidmagARA particles are composed of a multi-domain mag-
netite core coated with a layer of glucuronic acid [29,42]. At a frequency of 98 kHz, the
temperature increased by 9.2 °C in the FluidmagUCA sample and 6.8 °C in the FluidmagARA
sample. These results align with the parameters listed in Table 5, as FluidmagARA particles
are smaller than UCA particles, resulting in fewer less magnetic domains and a lower iron
percentage. Additionally, it is known that the coating on nanoparticles can reduce the
magnetic saturation value (Ms), which is consistent with the observed results. The heating
curves and SAR values are presented in Figure 12, showing SAR values of 1.76 W/gMNP-
UCA and 1.37 W/gMNP-ARA.
Figure 12. Heating curves for the FluidmagARA and FluidmagUCA samples at a frequency 98 kHz us-
ing solenoid S5.
To verify that the heating was specifically due to the presence of the magnetic parti-
cles, we conducted a control experiment using a blank sample of distilled water (DW) with
the same volume as the analyzed samples. The heating curve for this blank sample
showed a temperature increase of only 2 °C. Additionally, we studied a sample of Fluid-
MagD100nn at a frequency of 69 kHz and repeated the experiment at least three times to
assess its reproducibility. The resulting specific absorption rate (SAR) was 4.34 W/gMNP
(69 kHz), and the system and procedure exhibited excellent reproducibility, consistently
reaching nearly the same final temperature within the last 10 min, even when starting at
a lower temperature. The higher SAR values observed align with those reported by Kal-
lumadil and colleagues [30]. In Figure 13, it can be seen that the temperature did not reach
the expected plateau associated with magnetic hyperthermia, where a stable equilibrium
between heat lost and heat generated is achieved. The main aim of this study was to con-
firm that the heating was indeed caused by the magnetic nanoparticles and to validate
that the device operates correctly with acceptable reproducibility. This was confirmed by
the third repetition: although the initial temperature was lower, the final temperature was
almost the same in the last 10 min. Given more time, the final temperature would likely
have reached a stable state similar to previously observed results.
15
17
19
21
23
25
27
29
024681012
temperature (°C)
time (min)
FluidmagUCA
FluidmagARA
Figure 12. Heating curves for the Fluidmag
ARA
and Fluidmag
UCA
samples at a frequency 98 kHz
using solenoid S5.

Nanomaterials 2024,14, 1848 14 of 25
Nanomaterials 2024, 14, x FOR PEER REVIEW 16 of 28
Figure 13. Heating curves of FluidmagD100nm (25 mg/mL) at 69 kHz using solenoid S5.
15
17
19
21
23
25
27
29
31
33
024681012
temperature (°C)
time(min)
FluidmagD100nm-1st Exp.
FluidmagD100nm-2nd Exp.
FluidmagD100nm-3rd Exp.
Distilled Water(DW)
Figure 13. Heating curves of FluidmagD100nm (25 mg/mL) at 69 kHz using solenoid S5.

Nanomaterials 2024,14, 1848 15 of 25
To verify that the heating was specifically due to the presence of the magnetic particles,
we conducted a control experiment using a blank sample of distilled water (DW) with the
same volume as the analyzed samples. The heating curve for this blank sample showed a
temperature increase of only 2
◦
C. Additionally, we studied a sample of FluidMagD100nn
at a frequency of 69 kHz and repeated the experiment at least three times to assess its
reproducibility. The resulting specific absorption rate (SAR) was 4.34 W/gMNP (69 kHz),
and the system and procedure exhibited excellent reproducibility, consistently reaching
nearly the same final temperature within the last 10 min, even when starting at a lower
temperature. The higher SAR values observed align with those reported by Kallumadil and
colleagues [
30
]. In Figure 13, it can be seen that the temperature did not reach the expected
plateau associated with magnetic hyperthermia, where a stable equilibrium between heat
lost and heat generated is achieved. The main aim of this study was to confirm that
the heating was indeed caused by the magnetic nanoparticles and to validate that the
device operates correctly with acceptable reproducibility. This was confirmed by the third
repetition: although the initial temperature was lower, the final temperature was almost the
same in the last 10 min. Given more time, the final temperature would likely have reached
a stable state similar to previously observed results.
Figure 14 illustrates the heating curve of FluidmagD50 at 69 kHz using solenoid
S5. The SAR values obtained were 2.47 W/g
MNP
for FluidmagD50 and 3.5 W/g
MNP
for
FluidmagD100. Even though distilled water samples were used in all experiments, their
results are not displayed in the graphs to avoid redundancy.
The study investigated how frequency impacts the heating curves of the samples to
find the best frequency. Figure 15 displays the linear fitting that was utilized to find the
initial slope for calculating the SAR value, as outlined in Equation (9).
The slight variation in frequency, ranging from 63 to 138 kHz, leads to a corresponding
change in the final temperature. This change is due to the differences in the current
magnitude at different frequencies. At 63 kHz, the current is higher compared to 138 kHz
due to impedance. To address this issue, it is necessary to either increase the voltage of the
power source or design a new coil. The frequency of 78 kHz produces the best results, as it
is higher than 63 kHz but still maintains a similar current magnitude.
Nanomaterials 2024, 14, x FOR PEER REVIEW 17 of 28
Figure 14 illustrates the heating curve of FluidmagD50 at 69 kHz using solenoid S5.
The SAR values obtained were 2.47 W/gMNP for FluidmagD50 and 3.5 W/gMNP for Fluid-
magD100. Even though distilled water samples were used in all experiments, their results
are not displayed in the graphs to avoid redundancy.
Figure 14. Heating curves of FluidmagD50nm (25 mg/mL) at 69 kHz using solenoid S5.
The study investigated how frequency impacts the heating curves of the samples to
find the best frequency. Figure 15 displays the linear fiing that was utilized to find the
initial slope for calculating the SAR value, as outlined in Equation (9).
The slight variation in frequency, ranging from 63 to 138 kHz, leads to a correspond-
ing change in the final temperature. This change is due to the differences in the current
magnitude at different frequencies. At 63 kHz, the current is higher compared to 138 kHz
due to impedance. To address this issue, it is necessary to either increase the voltage of
the power source or design a new coil. The frequency of 78 kHz produces the best results,
as it is higher than 63 kHz but still maintains a similar current magnitude.
The SAR values obtained are as follows: 2.43 W/gMNP at 63 kHz, 2.22 W/gMNP at 81
kHz, 3.54 W/gMNP at 78 kHz, and 2.03 W/gMNP at 138 kHz. Since the magnetic field is di-
rectly proportional to the current, as described in Equation (4), increasing the current sig-
nificantly impacts this parameter. It is possible that if we had continued the experiment at
138 kHz, the temperature would reach a value like what was observed at 13 min at 78 kHz.
In the case of the FluidMagDx100nn sample, a final temperature of 36.7 °C was reached at 78
kHz using the system configuration with the refrigerated solenoid S5. This produced a
SAR value of 3.54 W/gMNP (refer to Figure 15). These results are promising, as they were
achieved using a lower frequency of 78 kHz and a lower magnetic field compared to the
study by Kallumadil and colleagues. Furthermore, experiments were carried out with var-
ious types of particles to compare heating curves at 138 kHz and to determine the optimal
system for heating studies. The SAR values obtained were as follows: FluidMagCMX = 1.56
W/gMNP, FluidMagLip200nm = 1.92 W/gMNP, FluidMagDx100nn = 2.03 W/gMNP, and Fluid-
MagDx50nm = 2.70 W/gMNP (refer to Figure 16).
Figure 14. Heating curves of FluidmagD50nm (25 mg/mL) at 69 kHz using solenoid S5.

Nanomaterials 2024,14, 1848 16 of 25
Nanomaterials 2024, 14, x FOR PEER REVIEW 18 of 28
Figure 15. Heating curves for the FluidMagD100nm sample at various frequencies using solenoid S5.
Figure 16. Heating curves of various samples at a frequency of 138 kHz.
Figure 16 summarizes the results obtained for the four samples at 138 kHz. Interest-
ingly, the FluidMag200 nm sample seems to exhibit lower heating efficiency, whereas the
FluidMagCMX sample, with a broader size distribution as reported by the manufacturer,
15
17
19
21
23
25
27
29
31
33
024681012141618
temperature (°C)
time (min)
FluidmagD100nm
FluidmagLip200nm
FluidMagD50nm
Fluidmag CMX
Destilled Water (DW)
Figure 15. Heating curves for the FluidMag
D100nm
sample at various frequencies using solenoid S5.
The SAR values obtained are as follows: 2.43 W/g
MNP
at 63 kHz, 2.22 W/g
MNP
at 81 kHz, 3.54 W/g
MNP
at 78 kHz, and 2.03 W/g
MNP
at 138 kHz. Since the magnetic
field is directly proportional to the current, as described in Equation (4), increasing the
current significantly impacts this parameter. It is possible that if we had continued the
experiment at 138 kHz, the temperature would reach a value like what was observed
at 13 min at 78 kHz. In the case of the FluidMag
Dx100nn
sample, a final temperature
of 36.7
◦
C was reached at 78 kHz using the system configuration with the refrigerated
solenoid S5. This produced a SAR value of 3.54 W/
gMNP
(refer to Figure 15). These results
are promising, as they were achieved using a lower frequency of 78 kHz and a lower
magnetic field compared to the study by Kallumadil and colleagues. Furthermore, ex-
periments were carried out with various types of particles to compare heating curves at
138 kHz and to determine the optimal system for heating studies. The SAR values ob-
tained were as follows:
FluidMagCMX = 1.56 W/gMNP,
FluidMag
Lip200nm
= 1.92 W/g
MNP
,
FluidMagDx100nn = 2.03 W/gMNP,
and FluidMag
Dx50nm
= 2.70 W/g
MNP
(refer to Figure 16).
Figure 16 summarizes the results obtained for the four samples at 138 kHz. Interest-
ingly, the FluidMag
200 nm
sample seems to exhibit lower heating efficiency, whereas the
FluidMag
CMX
sample, with a broader size distribution as reported by the manufacturer,
demonstrates a less intense heating effect. This difference may be attributed to magnetic
properties, such as higher magnetization values associated with larger MNPs.
Furthermore, a new set of experiments employing a new coil, designated as S6, with
reduced turns, and narrower and shorter dimensions, was performed. Given that the
inductive reactance
XL
relies on inductance (L) and the length of the solenoid
le
, as
outlined in Equations (10) and (11), it is anticipated that the alterations in the coil design
will impact the heating performance.
XL=2×π×f×L[ohms](10)
L=N2×A×µ
le
[Henry](11)
In Equation (10), the symbol (f) represents the frequency, L denotes the inductance of
the solenoid, N is the number of turns,
µ
is the modulus of the magnetic permeability of the
material, A is the cross-sectional area in m
2
, and
le
is the length of the solenoid. The objective
was to reduce the length of the solenoid, thereby decreasing
le
, and to concentrate the

Nanomaterials 2024,14, 1848 17 of 25
magnetic field by using a narrower inductor and a reduced cross-sectional area with the new
coil, S6. The FluidMag
Dx100nm
sample, with a concentration of
12.5 mgMNP/mL,
was tested
to assess improvements in heating performance. The results showed final temperatures
ranging from
28.8 ◦C
to
29.7 ◦C
on the frequencies 110–170 kHz. The corresponding
SAR values were
2.62 W/gMNP
at
141 kHz, 3.60 W/gMNP
at
110 kHz,
and
3.49 W/gMNP
at
170 kHz (see Figure 17).
Nanomaterials 2024, 14, x FOR PEER REVIEW 18 of 28
Figure 15. Heating curves for the FluidMagD100nm sample at various frequencies using solenoid S5.
Figure 16. Heating curves of various samples at a frequency of 138 kHz.
Figure 16 summarizes the results obtained for the four samples at 138 kHz. Interest-
ingly, the FluidMag200 nm sample seems to exhibit lower heating efficiency, whereas the
FluidMagCMX sample, with a broader size distribution as reported by the manufacturer,
15
17
19
21
23
25
27
29
31
33
024681012141618
temperature (°C)
time (min)
FluidmagD100nm
FluidmagLip200nm
FluidMagD50nm
Fluidmag CMX
Destilled Water (DW)
Figure 16. Heating curves of various samples at a frequency of 138 kHz.
Nanomaterials 2024, 14, x FOR PEER REVIEW 19 of 28
demonstrates a less intense heating effect. This difference may be aributed to magnetic
properties, such as higher magnetization values associated with larger MNPs.
Furthermore, a new set of experiments employing a new coil, designated as S6, with
reduced turns, and narrower and shorter dimensions, was performed. Given that the in-
ductive reactance 𝑋 relies on inductance (L) and the length of the solenoid 𝑙, as out-
lined in Equations (10) and (11), it is anticipated that the alterations in the coil design will
impact the heating performance.
𝑋=2×𝜋×
𝑓
×𝐿 [ohms] (10)
𝐿=(××)
 [Henry] (11)
In Equation (10), the symbol (f) represents the frequency, L denotes the inductance
of the solenoid, N is the number of turns, μ is the modulus of the magnetic permeability
of the material, A is the cross-sectional area in m2, and 𝑙 is the length of the solenoid.
The objective was to reduce the length of the solenoid, thereby decreasing 𝑙, and to con-
centrate the magnetic field by using a narrower inductor and a reduced cross-sectional
area with the new coil, S6. The FluidMagDx100nm sample, with a concentration of 12.5
mgMNP/mL, was tested to assess improvements in heating performance. The results
showed final temperatures ranging from 28.8 °C to 29.7 °C on the frequencies 110–170
kHz. The corresponding SAR values were 2.62 W/gMNP at 141 kHz, 3.60 W/gMNP at 110 kHz,
and 3.49 W/gMNP at 170 kHz (see Figure 17).
Figure 17. Heating curves of FluidMagDx100nn at different frequencies with a concentration of 12.5
mgMNP/mL using solenoid S6.
A new coil configuration, designated as S8, was designed with more turns and a
smaller radius, resulting in a more concentrated magnetic field. This configuration
18
20
22
24
26
28
30
32
0 2 4 6 8 10 12 14
temperature (°C)
time (min)
FluidmagD100nm-110kHZ-12.5 mg/mL
Fluidmag100nm-141kHZ- 12.5mg/mL
FluidmagD100nm-170kHZ-12.5mg/mL
FluidmagD100nm-235kHZ - 12.5 mg/mL
Figure 17. Heating curves of FluidMag
Dx100nn
at different frequencies with a concentration of
12.5 mgMNP/mL using solenoid S6.

Nanomaterials 2024,14, 1848 18 of 25
A new coil configuration, designated as S8, was designed with more turns and a
smaller radius, resulting in a more concentrated magnetic field. This configuration im-
proved system performance, achieving an alternating magnetic field (AMF) H = 4
±
2
mT
.
The heating of the Fluidmag
UCA
sample, with a concentration of 12.5 mg/mL, improved,
reaching 35.5
◦
C in 9 min at 72 kHz, with a SAR of 4.83 W/g
MNP UCA
(see Figure 18). For the
FluidMag
D100nm
sample, the SAR was 3.1 W/g
MNP
, which is consistent with the literature
values [43].
Nanomaterials 2024, 14, x FOR PEER REVIEW 20 of 28
improved system performance, achieving an alternating magnetic field (AMF) H = 4 ±2
mT . The heating of the FluidmagUCA sample, with a concentration of 12.5 mg/mL, im-
proved, reaching 35.5 °C in 9 min at 72 kHz, with a SAR of 4.83 W/gMNP UCA (see Figure 18).
For the FluidMagD100nm sample, the SAR was 3.1 W/gMNP, which is consistent with the lit-
erature values [43] .
These results can be explained by the S8 coil’s 17 turns and smaller diameter, which
concentrate the magnetic field lines. Additionally, the current passing through the sole-
noid is nearly doubled (see Table 5), which is directly proportional to the intensity of the
alternating magnetic field.
Figure 18. Heating curves of FluidMagUCA at 72 kHz with a concentration of 12.5 mgMNP/mL using
solenoid S8.
Regarding the MagFluidD100nm, the previous results were significantly affected, rein-
forcing the notion that the maximum temperature threshold was likely reached within the
frequency range previously observed with coil S6 (see Figure 19).
FluidMagDx50nm samples were used at different frequencies with a concentration of 25
mgMNP/mL in this new device configuration. As anticipated, the results improved, and the
graph also shows the reference for the DW sample and the repeatability in this new con-
figuration (see Figure 20). The SAR values were as follows: 3.55 W/gMNP at 302 kHz, 5.40
W/gMNP at 99 kHz, and 7.74 W/gMNP at 132 kHz. The optimal frequency was around 132
kHz. The Chemicell samples exhibit rapid heating under the 132 kHz applied magnetic
field, consistent with the findings of Eggeman and co-workers [44], with the temperature
notably increase at 132 kHz.
10
15
20
25
30
35
40
0246810
temperature (°C)
time (min)
FluidmagUCA-72kHz
Figure 18. Heating curves of FluidMag
UCA
at 72 kHz with a concentration of 12.5 mg
MNP
/mL using
solenoid S8.
These results can be explained by the S8 coil’s 17 turns and smaller diameter, which
concentrate the magnetic field lines. Additionally, the current passing through the solenoid
is nearly doubled (see Table 5), which is directly proportional to the intensity of the
alternating magnetic field.
Regarding the MagFluid
D100nm
, the previous results were significantly affected, rein-
forcing the notion that the maximum temperature threshold was likely reached within the
frequency range previously observed with coil S6 (see Figure 19).
FluidMag
Dx50nm
samples were used at different frequencies with a concentration of
25 mgMNP/mL
in this new device configuration. As anticipated, the results improved, and
the graph also shows the reference for the DW sample and the repeatability in this new
configuration (see Figure 20). The SAR values were as follows: 3.55 W/g
MNP
at 302 kHz,
5.40 W/g
MNP
at 99 kHz, and 7.74 W/g
MNP
at 132 kHz. The optimal frequency was around
132 kHz. The Chemicell samples exhibit rapid heating under the 132 kHz applied magnetic
field, consistent with the findings of Eggeman and co-workers [
44
], with the temperature
notably increase at 132 kHz. The heating curves for the two samples of FluidMag
DX50nm
are
shown in Figure 21, as a function of average concentration
(5–25 mg/mL)
. The Chemicell
samples were heated using an applied magnetic field at 132 kHz, with a field amplitude of
approximately 8 mT. The initial slope decreases when the sample is diluted from
25 mg/mL
to 5 mg/mL, which aligns with the findings of [
44
]. Therefore, it appears that dilution
does not improve the heating efficiency in this type of MNPs. As state previously, macro-
scopic dilution does not necessarily change the inter-particle distance within a cluster; it

Nanomaterials 2024,14, 1848 19 of 25
may only increase the average cluster spacing, as the MNPs are composed of clusters as
described before.
Nanomaterials 2024, 14, x FOR PEER REVIEW 21 of 28
Figure 19. Heating curves of FluidMagD100nm at different frequencies with a concentration of 12.5
mgMNP/mL using solenoid S8.
Figure 20. Heating curves of FluidMagDx50nm at different frequencies with a concentration of 25
mgMNP/mL using solenoid S8.
The heating curves for the two samples of FluidMagDX50nm are shown in Figure 21, as
a function of average concentration (5–25 mg/mL). The Chemicell samples were heated
using an applied magnetic field at 132 kHz, with a field amplitude of approximately 8 mT.
15
17
19
21
23
25
27
29
31
024681012
temperature (°C)
time (min)
FluidmagD100nm-71kHz
FluidmagD100nm-96kHz
FluidmagD100nm-302kHz
Figure 19. Heating curves of FluidMag
D100nm
at different frequencies with a concentration of
12.5 mgMNP/mL using solenoid S8.
Nanomaterials 2024, 14, x FOR PEER REVIEW 21 of 28
Figure 19. Heating curves of FluidMagD100nm at different frequencies with a concentration of 12.5
mgMNP/mL using solenoid S8.
Figure 20. Heating curves of FluidMagDx50nm at different frequencies with a concentration of 25
mgMNP/mL using solenoid S8.
The heating curves for the two samples of FluidMagDX50nm are shown in Figure 21, as
a function of average concentration (5–25 mg/mL). The Chemicell samples were heated
using an applied magnetic field at 132 kHz, with a field amplitude of approximately 8 mT.
15
17
19
21
23
25
27
29
31
024681012
temperature (°C)
time (min)
FluidmagD100nm-71kHz
FluidmagD100nm-96kHz
FluidmagD100nm-302kHz
Figure 20. Heating curves of FluidMag
Dx50nm
at different frequencies with a concentration of
25 mgMNP/mL using solenoid S8.
At a frequency of 132 kHz, FluidMagDX50nm exhibits a specific absorption rate
(SAR) of 1.95 W/g for a sample concentration of 5 mg/mL and 9.13 W/g for a sample
concentration of 25 mg/mL. The final temperature for the more concentrated sample
reached 47.2 ◦C.

Nanomaterials 2024,14, 1848 20 of 25
Nanomaterials 2024, 14, x FOR PEER REVIEW 22 of 28
The initial slope decreases when the sample is diluted from 25 mg/mL to 5 mg/mL, which
aligns with the findings of [44]. Therefore, it appears that dilution does not improve the
heating efficiency in this type of MNPs. As state previously, macroscopic dilution does
not necessarily change the inter-particle distance within a cluster; it may only increase the
average cluster spacing, as the MNPs are composed of clusters as described before.
Figure 21. Heating curves of FluidmagDX50nm samples with different concentrations (5 and 25
mg/mlMNP) at 132 kHz using solenoid S8.
At a frequency of 132 kHz, FluidMagDX50nm exhibits a specific absorption rate
(SAR) of 1.95 W/g for a sample concentration of 5 mg/mL and 9.13 W/g for a sample con-
centration of 25 mg/mL. The final temperature for the more concentrated sample reached
47.2 °C.
To summarize, we tested the FluidMagDX50nm sample at 101.5 kHz using a new con-
figuration where we changed the capacitors to a specific value determined by us through
Equation (7) to achieve a higher frequency. We selected these particles because they have
previously produced good results [30]. Therefore, we wanted to determine if our device
could achieve comparable or even beer results than those obtained by other researchers.
We conducted a comprehensive experiment for magnetic hyperthermia, which included
heating and cooling curves. The results were very promising, as depicted in Figure 22,
yielding a SAR of 10.8 W/gMNP.
Figure 21. Heating curves of FluidmagDX
50nm
samples with different concentrations (5 and
25 mg/mlMNP) at 132 kHz using solenoid S8.
To summarize, we tested the FluidMag
DX50nm
sample at 101.5 kHz using a new
configuration where we changed the capacitors to a specific value determined by us
through Equation (7) to achieve a higher frequency. We selected these particles because
they have previously produced good results [
30
]. Therefore, we wanted to determine if
our device could achieve comparable or even better results than those obtained by other
researchers. We conducted a comprehensive experiment for magnetic hyperthermia, which
included heating and cooling curves. The results were very promising, as depicted in
Figure 22, yielding a SAR of 10.8 W/gMNP.
Nanomaterials 2024, 14, x FOR PEER REVIEW 23 of 28
Figure 22. Heating and cooling curves of FluidMagDx50nm with the final configuration (S8).
A resume of the final temperature and results obtained from all experiences are pre-
sented in Table 6 with the respective average and deviation; almost all of the experiences
were performed in triplicate as a minimum.
Table 6. Results of the final temperature respective deviations and conditions obtained in the expe-
riences.
Type of Particle Frequency (kHz) Solenoid TFinal (C°) Figure
FluidmagARA 98 S5 27.5 ± 0.4 12
FluidmagUCA 98 S5 23.5 ± 0.5 12
FluidMagD100nm 69 S5 31.0 ± 0.5 13
FluidMagD50nm 69 S5 26.2 ± 0.5 14
FluidMagD100nm 69 S5 31.5 ± 0.4 14
FluidMagD100nm 63 S5 31.0 ± 0.3 15
FluidMagD100nm 78 S5 33.8 ± 0.3 15
FluidMagD100nm 81 S5 25.5 ± 0.4 + 15
FluidMagD100nm 138 S5 28.5 ± 0.4 ++ 15
FluidMagCMX 138 S5 27.7 ± 0.5 * 16
FluidMagLip200nm 138 S5 24.4 ± 0.4 ** 16
FluidMagDx100nn 138 S5 31.80.5
+* 16
FluidMagDX50nm 138 S5 26.9 ± 0.5 +** 16
FluidMagDx100nn a 110 S6 27.0 ± 0.5 17
FluidMagDx100nn a 141 S6 27.0 ± 0.4 17
FluidMagDx100nn a 170 S6 27.5 ± 0.4 17
FluidMagDx100nn a 235 S6 29.7 ± 0.3 17
FluidMagUCA a 72 S8 35.5 ± 0.4 18
FluidMagDx100nm 71 S8 28.7 ± 0.4 19
Figure 22. Heating and cooling curves of FluidMagDx50nm with the final configuration (S8).

Nanomaterials 2024,14, 1848 21 of 25
A resume of the final temperature and results obtained from all experiences are
presented in Table 6with the respective average and deviation; almost all of the experiences
were performed in triplicate as a minimum.
Table 6. Results of the final temperature respective deviations and conditions obtained in
the experiences.
Type of Particle Frequency (kHz) Solenoid TFinal (C◦) Figure
FluidmagARA 98 S5 27.5 ±0.4 12
FluidmagUCA 98 S5 23.5 ±0.5 12
FluidMagD100nm 69 S5 31.0 ±0.5 13
FluidMagD50nm 69 S5 26.2 ±0.5 14
FluidMagD100nm 69 S5 31.5 ±0.4 14
FluidMagD100nm 63 S5 31.0 ±0.3 15
FluidMagD100nm 78 S5 33.8 ±0.3 15
FluidMagD100nm 81 S5 25.5 ±0.4 +15
FluidMagD100nm 138 S5 28.5 ±0.4 ++ 15
FluidMagCMX 138 S5 27.7 ±0.5 * 16
FluidMagLip200nm 138 S5 24.4 ±0.4 ** 16
FluidMagDx100nn 138 S5 31.80.5 +* 16
FluidMagDX50nm 138 S5 26.9 ±0.5 +** 16
FluidMagDx100nn a110 S6 27.0 ±0.5 17
FluidMagDx100nn a141 S6 27.0 ±0.4 17
FluidMagDx100nn a170 S6 27.5 ±0.4 17
FluidMagDx100nn a235 S6 29.7 ±0.3 17
FluidMagUCA a72 S8 35.5 ±0.4 18
FluidMagDx100nm 71 S8 28.7 ±0.4 19
FluidMagDx100nm 96 S8 27.1 ±0.5 19
FluidMagDx100nm 302 S8 27.3 ±0.5 19
FluidMagDx50nm 99 S8 34.3 ±0.4 20
FluidMagDx50nm 132 S8 36.8 ±0.4 20
FluidMagDx50nm 302 S8 31.6 ±0.4 ++** 20
FluidMagDx50nm b132 S8 23 ±0.3 21
FluidMagDx50nm 132 S8 40.9 ±0. 21
FluidMagD50nm 101.5 kHz S8 52.2 ±0.4 22
+
At 10 min,
++
at 13 min.; * 10 min; ** 12 min; +* 13 min; +** 9 min;
a
concentration of 12.5 mgMNP/mL
b
concentration of 5 mg/mL;
++
** The study was stopped for 302 kHz 31.6 in 7 min since at the same time it
obtained 36.8 (132 kHz) and 34.3 (99 kHz); b5 mg/mL.
4. Conclusions
In this study, we developed, built, and tested a new magnetic hyperthermia device.
We evaluated its performance using commercial magnetic nanoparticles and found that
it produced results similar to those of commercial devices. We optimized the system to
achieve higher magnetic fields and frequencies, and the simulation results confirmed our
practical findings. This device is more cost-effective and portable compared to existing
options, and we aim to make this technology more accessible.
According to our findings and previous research [
25
,
26
,
45
], the Chemicell iron oxide
sample FluidMagDx appears to be a suitable material for magnetic hyperthermia (MHT)
applications. The cluster size is large enough to prevent endocytosis at a cell membrane,
yet small enough to avoid activating bacterial defense mechanisms. The coating material,
dextran, makes it biocompatible. However, the stability of the clusters inside biological

Nanomaterials 2024,14, 1848 22 of 25
organisms is still unknown [
46
]. As a result, “FluidMAG” from Chemicell GmbH showed
a significant heating response that can be adjusted by the field and frequency of the AC
driving field and the solution concentration.
Our results confirm that significant optimization can be achieved in a magnetic hyper-
thermia device, such as increasing the frequency, the magnitude of the magnetic field, or
even designing a programmable system.
According to our results, factors such as the size, composition, and shape of particles
may not be enough to accurately predict the magnetic response to different frequencies
and, as a result, the rate of heat generation in an AC magnetic field. We can only make
initial assumptions based on previous research, so our next step is to create various types
of magnetic nanoparticles and see how they affect the heating rate.
The concentration of iron in the sample influences the heating, but local clustering is
also important.
In our upcoming research, we will concentrate on creating MNPs and adjusting their
properties to improve their performance. We are in the process of designing and building
a new apparatus that is similar to the resonant system but capable of generating higher
magnetic fields and frequencies, as outlined in Castelo-Grande et al. [39].
We have encountered an issue with controlling test frequencies and have addressed it
by implementing a circuit based on the H-bridge using MOSFET transistors (IRFP260 or
IRFP4668) as switches. These switches are controlled by a computational system (Arduino
MEGA platform), enabling us to generate square waves at the desired frequency. However,
we faced challenges in controlling the switches on the upper part of the H-bridge (H-bridge
high side or low side).
Based on our analysis, it is evident that there is still significant room for improvement
in the field of magnetic nanoparticle hyperthermia. This could involve developing more
user-friendly devices with a wider range of designs and configurations, thereby paving
the way for further exploration. In terms of MNPs, there is still much to learn in order
to accurately predict the optimal frequency and field for MH, which are closely linked to
intrinsic parameters [47].
For possible future developments, including for example, ex vivo and
in vivo
bio-
logical sample applications, and comparison with simulated data (on the hyperthermia
treatment), collaborations with health institutes of Porto and Salamanca have been initiated.
5. Patents
A patent (reference PPP 20242006604014) was filed concerning the developed innova-
tive magnetic hyperthermia device described in this paper.
Author Contributions: Conceptualization, T.C.-G., P.A.A. and L.G.; methodology, T.C.-G., L.G. and
E.C.; software, L.G. and E.C.; validation, T.C.-G., L.G. and E.C.; formal analysis, T.C.-G., P.A.A. and
D.B.; investigation, T.C.-G., P.A.A. and E.C.; resources, T.C.-G., P.A.A., L.G., E.C. and D.B. data
curation, T.C.-G., P.A.A. and E.C.; writing—original draft preparation, T.C.-G.; writing—review and
editing, T.C.-G., P.A.A. and D.B., visualization, T.C.-G. and P.A.A.; supervision, T.C.-G., P.A.A. and
D.B.; project administration, T.C.-G. and P.A.A.; funding acquisition, T.C.-G., P.A.A. and D.B. All
authors have read and agreed to the published version of the manuscript.
Funding: This work was financially supported by (a) Contract 2021 02188 CEECIND (Teresa
Castelo-Grande); (b) Project MAGLIDUO (POCI-01-0145-FEDER-028020), funded by FEDER funds
through COMPETE2020—Programa Operacional Competitividade e Internacionalização (POCI)
and by national funds (PIDDAC) through FCT/MCTES; (c) LEPABE, UIDB/00511/2020 (DOI:
10.54499/UIDB/00511/2020) and UIDP/00511/2020 (DOI: 10.54499/UIDP/00511/2020) and AL-
iCE, LA/P/0045/2020 (DOI: 10.54499/LA/P/0045/2020); (d) Project MAT2016-76824-C3-2-R, “Dis-
eño de Nanohilos Magneticos para su uso en Tecnologias Limpias”, MINECO, Spain; (e) Project
2019/00057/001—“Application of Magnetic Methods and Magnetic Substances for Environmental
Treatment and Biomedicine”.
Data Availability Statement: Data are contained within the article.

Nanomaterials 2024,14, 1848 23 of 25
Acknowledgments: Helena Sant’Ovaia (Instituto de Ciências da Terra—Pólo da Faculdade de Ciências
U.P.) is gratefully acknowledged for her assistance with measuring the magnetic particle properties.
Conflicts of Interest: The authors declare no conflicts of interest. The funders had no role in the design
of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or
in the decision to publish the results.
Appendix A
Magnetic field measurement
The LF-R 400 H field is a passive near-field probe that has a large diameter (25 mm),
making it highly sensitive and suitable for measurements in ranges of up to 10 cm around
assemblies and fixtures, as it is proven capable of detecting a larger area of the magnetic
field specially comparing with the LF-R 50 (10 mm) or LF-R 3 (3 mm) near-field probes). It
has a current attenuation sheath and is, therefore, electrically shielded. It can be connected
to a spectrum analyzer or an oscilloscope with a 50
Ω
input. An oscilloscope with a 1:1 tip
was used, which recorded the V
value
(peak to peak) and verified the sinusoidal waveform,
as well as the frequency obtained in the coil.
Equations used to calculate the magnetic field
Probe RF-R 400-1- Langer EMV-Technik:
⌈dB⌉== µdBµA
m=Uprobe dBµV+dB µA
µVv m (A1)
A signal attenuator was also used to be able to read the obtained signal. For this we
have to convert the value read by the probe with the attenuator. Since this is 5 dB, the
following equation must be solved:
5(dB)=20 ×log10(x)where we want to obtain x (A2)
Solving, we obtain the value of x= 0.56, which means it attenuates 56% of the value.
or 5(dB)=20 ×log10Vout
Vi n where we want to obtain vin (A3)
For example, if the value read was [
∆
V]
pp
= 95
±
5 V <=>95/0.56 = 169.64, which
gives approximation—[
∆
V]
p
= 85, then it is necessary to resolve the following equation in
order to obtain AMF.
HkA
m=re fvalue(kHz)×10(Vp
20 )/1000 (A4)
where
re fvalue(kHz)
is a value obtained from the data sheet of the equipment and it is
the function of frequency used,
Vp
value of the high of pic of the wavelength shown in
the oscilloscope. In the particular case of this work, the range of magnetic field is from
3.8–6.5 kA/m or 4.6–8 mT depending on the configuration system (different solenoids).
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