Ultra-short pulse magnetic fields on effective magnetic hyperthermia for cancer therapy

Abstract

Alternating magnetic fields can deliver magnetic energy deeper inside the body for magnetic hyperthermia cancer therapy by using magnetic nanoparticles (MNPs). In this study, we proposed a highly effective heat generation method for the MNPs by the application of an ultra-short pulse wave. We numerically evaluated the heating power with a variety of parameters, such as pulse width, field amplitude, and frequency. The hysteresis curve and magnetization dynamics clearly indicate larger energy dissipation. Hysteresis loss and the input energy increase with increasing field strength and duty ratio and there is a large efficiency power condition. To evaluate the effective heat generation and practical temperature increment, a larger imaginary part of magnetic susceptibility (χ″ > 30) and specific loss power (SLP > 10 ⁵ W/kg) are required. In addition, larger intrinsic loss power (100 nHm ² /kg) is achieved. The results indicate that the contribution of magnetic harmonics signals on the ultra-short pulse wave significantly enhances the heat generation of MNPs for cancer therapy.

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AIP Advances ARTICLE scitation.org/journal/adv
Ultra-short pulse magnetic fields on effective
magnetic hyperthermia for cancer therapy
Cite as: AIP Advances 13, 025145 (2023); doi: 10.1063/9.0000558
Submitted: 3 October 2022 •Accepted: 13 January 2023 •
Published Online: 9 February 2023
Akihiro Kuwahata,a) Yuui Adachi, and Shin Yabukami
AFFILIATIONS
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
Note: This paper was presented at the 67th Annual Conference on Magnetism and Magnetic Materials.
a)Author to whom correspondence should be addressed: akihiro.kuwahata.b1@tohoku.ac.jp
ABSTRACT
Alternating magnetic fields can deliver magnetic energy deeper inside the body for magnetic hyperthermia cancer therapy by using magnetic
nanoparticles (MNPs). In this study, we proposed a highly effective heat generation method for the MNPs by the application of an ultra-short
pulse wave. We numerically evaluated the heating power with a variety of parameters, such as pulse width, field amplitude, and frequency.
The hysteresis curve and magnetization dynamics clearly indicate larger energy dissipation. Hysteresis loss and the input energy increase with
increasing field strength and duty ratio and there is a large efficiency power condition. To evaluate the effective heat generation and practical
temperature increment, a larger imaginary part of magnetic susceptibility (χ′′ >30) and specific loss power (SLP >105W/kg) are required. In
addition, larger intrinsic loss power (100 nHm2/kg) is achieved. The results indicate that the contribution of magnetic harmonics signals on
the ultra-short pulse wave significantly enhances the heat generation of MNPs for cancer therapy.
©2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license
(http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/9.0000558
INTRODUCTION
Magnetic hyperthermia (MH) with magnetic nanoparticles
(MNPs) and alternating magnetic fields (AMF) have been widely
introduced to cancer treatment.1–5 Potentially, MH enables less-
invasive treatment compared with other treatment methods, such as
surgical operations, chemotherapy, and radiation therapy.6The dis-
sipated magnetic energy of AMF based on the magnetic relaxation
yields cancer degeneration due to heat generation.2In addition, the
magnetic signal originating from the MNPs inside the living tissues
provides noninvasive cancer diagnosis,7–13 offering a theranostics
technology.14
For effective treatment, the improvement of magnetic proper-
ties, such as size, component, and shape, of the MNPs is also very
important.15 At the same time, it is required to explore the wave-
form of the magnetic fields applied to the MNPs. To date, typically,
a sinusoidal wave was widely employed for MH and some research
demonstrated the application of the rectangular wave to improve
the effective heating.16–18 The heating power is large enough to
treat cancer in animal experiments and clinical trials. To establish
a medical device, there is a need to improve the efficiency of heat
generation.
In this study, we proposed a highly effective heat generation
method for the MNPs by the application of an ultra-short pulse
wave of AMF. We numerically evaluated the heating power with
a variety of parameters, such as field amplitude, frequency, and
pulse width. The efficacy of the short pulse magnetic fields strongly
depends on the pulse width, and the optimal parameter achieved
one order larger than heat generation compared with a typical sinu-
soidal wave. Our proposed novel MH with short pulse magnetic
fields will offer effectively generate heating power for future clinical
applications.
METHODS
To demonstrate the effectiveness of the proposed ultra-short
pulse waves of AMF, we employ numerical evaluation based on
energy state.19–21 Figure 1 shows the three kinds of waveforms and
a proposed ultra-short pulse wave of applied magnetic fields for
magnetic hyperthermia. While both the sinusoidal and rectangu-
lar waves have positive and negative magnetic fields [Figs. 1(a) and
1(b)], a pulse wave (a rectangular wave with only positive polarity)
and ultra-short pulse waves represent only positive magnetic fields
[Figs. 1(c) and 1(d)].
AIP Advances 13, 025145 (2023); doi: 10.1063/9.0000558 13, 025145-1
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FIG. 1. Waveforms of applied magnetic fields for magnetic hyperthermia: (a)
conventional sinusoidal wave, (b) rectangular wave with positive and negative
polarities, (c) pulse wave with only positive polarity, and (d) ultra-short pulse wave
(duty ratio is 2%). Parameters are as follows: 250 kHz and 15 kA/m.
Numerical calculation is based on the magnetic potential
energy with Zeeman energy, anisotropy energy, and orienta-
tion probability. The potential energy Uis simply expressed by
U=−μ0MSe⋅H−Keff V(n⋅e)2, where μ0is the magnetic perme-
ability in a vacuum, Ms[A/m] is the saturation magnetic fields,
eis the unit vector, H[A/m] is the applied magnetic fields,
Keff [J/m3] is the effective uniaxial anisotropy constant, and n
is the unit vector along the easy axis. Note that Keff contains
three kinds of anisotropy energy, such as the shape, surface mag-
netic, and crystalline anisotropy energy.22 To demonstrate dynamic
magnetization of the MNPs under AMF, the orientation probabil-
ity ρ(e)of the direction of e1,2,3 is introduced by a Boltzmann factor
exp(−U(n,e,H))kBTand the two-level approximation for energy
reversals between lower energy (e1,e2)through the middle energy
point (e3). Here, kBis the Boltzmann constant and T[K] is the
temperature and we define that the easy axis is the directions of e1
and e2, the hard axis is e3, and applied magnetic fields are along the
easy axis. The reversal probability from e1to e2and from e2to e1
are obtained by v12 =0.5f0exp[((U(n,e1,H)−U(n,e3,H))]kBT,
v21 =0.5f0exp[((U(n,e2,H)−U(n,e3,H))]kBT, respectively. We
can calculate the probability ρ(e)at each time step by using Δρ(e1)
=(v12ρ(e2)−v21ρ(e1))Δtand simply assume ρ(e2)=1−ρ(e1).
The time evolution of the magnetization dynamic is obtained as
M(t)=MsNV[ρ(e1)e1⋅H
H+ρ(e2)e2⋅H
H], where Nis the num-
ber of particles, and Vis the particle volume. f0is the attempt
frequency of 1010 [1/s].
To evaluate the effective heat generation, we employed mag-
netic dissipated energy. The most important magnetic energy
dissipation for heating of MNPs is the hysteresis loss Phys [W/m3]
based on the phase lag originates from MNPs relaxation mech-
anisms.23 The hysteresis loss Phys, which is proportional to the
frequency fof applied magnetic fields and loop area on the M-H
curve, is expressed by
Phys =μ0f∫M dH. (1)
We define the Input magnetic energy to MNPs Pinput [W/m3] as
Pinput =1
2μ0H2f=μ0f
2∫H(t)2dt. (2)
Basically, we can obtain the efficiency of the magnetic energy
dissipation from the calculation Eqs. (1) and (2),PhysPinput . For an
additional important parameter on magnetic relaxation dynamics,
we can introduce the nonlinear magnetic susceptibility χ′′ (out-of-
phase component of susceptibility)24,25 given by
χ′′ =Phys
μ0fπH2=∫MdHπH2. (3)
Furthermore, the specific loss power (SLP) [W/kg] and intrinsic
loss power (ILP) [nHm2/kg] are widely used for the evaluation of
temperature increment of MNPs and are defined as follows:24–27
SLP =Physρϕ, (4)
ILP =SLPH2f. (5)
Here, ρis the density of MNPs and ϕis the volume fraction of
MNPs. Considering the demonstration of typical characteristics of
magnetite multicore nanoparticles,23,28–32 such as Resovist33 that is
commercially available and clinically approved in Japan and consists
of magnetite and maghemite, we employed the following parameters
for numerical calculations. The saturation magnetic field MSis
300 kA/m, effective anisotropy constant Keff is 28 kJ/m3, and par-
ticle diameter dis 14.5 nm. The numerical result is validated by the
comparison with the experimental result under the application of a
typical sinusoidal wave.
RESULTS & DISCUSSION
Figure 2 shows the calculated typical dynamics of the mag-
netization of a sinusoidal, rectangular, pulse, and proposed ultra-
short pulse wave. Numerical parameters are as follows. The applied
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FIG. 2. Magnetization dynamics of (a) conventional sinusoidal wave, (b) rectangular wave with both polarities, (c) pulse wave, and (d) ultra-short pulse wave. For each
figure, Hysteresis curve (top-left), applied magnetic field (bottom-left), magnetization signal as a function of time (top-right), and Fourier analysis (bottom-right). Typical
parameters: H=17 kA/m, d=14.5 nm, Ms=300 kA/m, Keff =28 kJ/m3,andT=300 K.
magnetic field His 17 kA/m, temperature T is 300 K, and fre-
quency is 160 kHz. In Fig. 2(a), we can observe the hysteresis loss
on the M-H curve under the application of the sinusoidal wave.
The magnetization Mas a function of time shows the distorted
magnetic dynamics due to the nonlinear magnetic characteristics of
MNPs based on the Langevin profile.34 This small distortion pro-
duces the even harmonic small signal, mainly third harmonics, as
shown in Fourier analysis. The important parameters of SLP =2.0
×105[W/kg], ILP =5.5 [nHm2/kg] are large enough to heating
the MNPs for magnetic hyperthermia treatment, showing conven-
tional heating efficiency. In Fig. 2(b) for the rectangular wave with
positive and negative polarities, the hysteresis loss increases on the
M-H curve due to a larger lag between the applied magnetic fields
and the magnetization dynamics of MNPs under the application
of rapid rising of AMF. The magnetization signal is also distorted
and the relatively larger third and fifth harmonic components of the
magnetic dynamics appear. The important parameters of SLP =6.8
×105[W/kg], ILP =9.5 [nHm2/kg] shows better performance rather
than the sinusoidal wave.
For the pulse wave as shown in Fig. 2(c), we numerically obtain
the hysteresis loss on the M-H curve in the first quadrant and the
magnetization signal as a function of time is significantly distorted.
In addition, the even as well as odd harmonics appear due to the
break of the symmetry on the magnetic moments, as experimen-
tally described in some research.13,35,36 The characteristics show the
better performance: SLP =2.6 ×105[W/kg], ILP =4.7 [nHm2/kg],
resulting in typical heating performance for magnetic hyperthermia
experiment. The result does not suggest the typical duty ratio of
50% enables higher efficiency. To generate the larger lag effectively,
we need to control the duty ratio (pulse width) of the pulse wave.
During the period under the application of the constant applied
magnetic fields (zero value of the time derivative of the applied
magnetic fields), the magnetic dynamics do not change, indicating
that no energy dissipation and the meaningless of the input energy.
In this comparison of the above three waveforms (sinusoidal, rect-
angular, and pulse wave) the rectangular wave yields the largest
hysteresis loss due to the larger phase lag based on rapid rising and
falling with positive and negative polarities of AMF.
The application of the ultra-short pulse, the pulse width of
2% duty ratio, significantly produces the larger efficiency of the
magnetic energy dissipation, as shown in Fig. 2(d). We obtain
a significantly larger ILP of 73.2 [nHm2/kg] in the presence of
SLP of 8.2 ×105[W/kg] which is large enough to heat cancer
tissue. In addition, we report larger even and odd harmonic com-
ponents compared to the fundamental frequency component on
the magnetization dynamics, suggesting the harmonics potentially
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FIG. 3. Optimization of ultra-short pulse wave on two-dimensional parameter spaces of field strength and duty ratio; (a) hysteresis loss [W/m3], (b) input magnetic energy
[W/m3], (c) power ratio of hysteresis loss to input energy, (d) imaginary part of magnetic susceptibility χ′′, (e) specific loss power [W/kg], and (f) intrinsic loss power
[nHm2/kg].
enhance the efficiency of the magnetic energy dissipation. The
results indicate that an ultra-short pulse wave enables the intro-
duction of a higher efficiency method for magnetic hyperthermia
treatment.
To evaluate the dependency on duty ratio (corresponding to
pulse width) and optimize the waveform, we investigate the detailed
characteristics of magnetic energy dissipation as a function of the
two-dimensional parameter space of applied magnetic field strength
and duty ratio, as shown in Fig. 3. The hysteresis loss and the
input energy increases increasing with field strength and duty ratio
[Figs. 2(a) and 2(b)] and there is a large efficiency power condition
[Fig. 2(c)]. To evaluate the effective heat generation and practi-
cal temperature increment, a larger imaginary part of magnetic
susceptibility (χ′′ >30) and specific loss power (SLP >105W/kg)
are required [Figs. 2(d) and 2(e)]. In addition, larger intrinsic loss
power (100 nHm2/kg) is achieved [Fig. 2(f)]. Finally, we found the
optimal condition of applied AMF (duty ratio =1.2% and H =16
kA/m) considering the practical uses. The results indicate that mag-
netic harmonics signals with a higher frequency range significantly
enhance the heat generation of MNPs.
For a safety issue, our condition exceeds the Atkinson-
Brezovich criterion (4.85 ×108[A m−1s−1]).37 However, R. Hergt
et al. provides 5 ×109[A m−1s−1] for the limitation of safety usage.38
Therefore, our proposed technique would be clinically acceptable
considering typical treatment time of 10 min (less than an hour).
As future prospects, we will develop a temperature measure-
ment system with an infrared camera39 and thermometry based
on magnetic response,40 and investigate the impact of the har-
monic component in the phantom experiment by using MNPs
to evaluate the heating efficiency. We explore further studies
of the development of an effective pulse generator for clinical
applications and the evaluation of the heating effect in animal
experiments.
CONCLUSION
We proposed an ultra-short pulse wave of AMF for a highly
effective heat generation method for the MNPs-mediated mag-
netic hyperthymia cancer treatment. We numerically evaluated the
heating power with a two-dimensional parameter space, such as
pulse width and field amplitude. The hysteresis curve and magne-
tization dynamics of the ultra-short pulse wave clearly demonstrate
a larger energy dissipation. The Hysteresis loss and the input energy
increases increasing with field strength and duty ratio and there is
a large efficiency power condition. To evaluate the effective heat
generation and practical temperature increment, we achieved a
larger imaginary part of magnetic susceptibility (χ′′ >30), spe-
cific loss power (SLP >105W/kg), and larger intrinsic loss power
(100 nHm2/kg) simultaneously for the effective heating of the
AIP Advances 13, 025145 (2023); doi: 10.1063/9.0000558 13, 025145-4
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MNPs. The results indicate that the contribution of magnetic har-
monics signals on the ultra-short pulse wave significantly enhances
the heat generation of MNPs for cancer therapy. We will investigate
the effect of harmonic components in the phantom experiment by
using MNPs to evaluate the heating efficiency.
ACKNOWLEDGMENTS
This work was supported by the Uehara Memorial Founda-
tion, Hitachi Global Foundation, AMED (Japan Agency for Medical
Research and Development) Grant Number 22ym0126802j0001,
and the Comprehensive Growth Program for Accelerator Sciences
and the Joint Development Research 2022-ACCL-1 at High Energy
Accelerator Research Organization (KEK).
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Akihiro Kuwahata: Conceptualization (lead); Data curation (lead);
Funding acquisition (lead); Project administration (lead); Software
(lead); Supervision (lead); Writing – original draft (lead); Writing –
review & editing (lead). Yuui Adachi: Data curation (equal). Shin
Yabukami: Funding acquisition (equal); Writing – review & editing
(equal).
DATA AVAILABILITY
The data that support the findings of this study are available
from the corresponding author upon reasonable request.
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