Disk-shaped magnetic particles for cancer therapy

According to the estimates by the U.S. National Cancer Institute, nanotechnology will play a key role in the future of the prevention, diagnosis, and treatment of cancer.¹ Particularly, magnetic nanoparticles and, especially, superparamagnetic iron oxide nanoparticles (SPIONs) seem to hold the greatest potential for success. Among other biomedical applications,² these nanoparticles have the ability to be heated by external magnetic fields for magnetic hyperthermia treatment,³ which is one of the oldest forms of cancer therapy.⁴ In this procedure, the magnetic particles are dispersed throughout the target tissue and then heated by applying an AC magnetic field of sufficient strength and frequency (typically hundreds of kilohertz). The heat is transferred into the surrounding diseased tissue and, if the temperature is maintained above 42 °C for 30 min or more, the cancer cells are destroyed.² However, the increase in the magnetic response of the SPIONs required for biomedical applications is critically limited by their size since, above the superparamagnetic limit, the nanoparticles become coercive and spontaneously aggregate.⁵ Moreover, SPIONs are synthesized by chemical routes⁶ that typically produce nanoparticles with a non-negligible size and shape distribution⁷ and in a relatively low yield,⁸ which prevents their implementation for mass production.

The development of physical fabrication routes, combining a lithographic method with a material deposition technique,⁹ enabled the growth of thin films with an accurate control of the geometry, composition, and crystallographic structure in which effects of perpendicular surface anisotropy¹⁰ and interlayer exchange coupling¹¹ were discovered. Although originally focused on microelectronic applications, these technologies and phenomena inspired material scientists to create new magnetic nanoarchitectures for biomedical applications. In 2008, Wei Hu et al. reported the fabrication of monodisperse Co₉₀Fe₁₀/Ru disk-shaped particles, 100 nm in diameter, with a high magnetic moment well above the typical values of SPIONs, and zero remanence due to their antiferromagneticlike behavior. Remarkably, the zero remanence, i.e., the null magnetic moment in the absence of an external magnetic field, eliminates the problem of particle aggregation. In light of the advantageous characteristics of these synthetic antiferromagnetic (SAF) nanoparticles, the authors predicted their potential biomedical applications, particularly as capture probes for magnetic separation and biosensor labels.¹² This pioneering work opened the way for research on other disk-shaped particles with alternative magnetic configurations, namely magnetic vortex state¹³ and perpendicularly magnetized SAF (P-SAF),¹⁴ both with high magnetic moment and zero remanence. The following paragraph, supported by the text box in Table I, describes in simple terms the basis of the magnetic structures of the three types of disks: SAF, P-SAF, and vortex state.

The synthetic antiferromagnetic (SAF) disks are composed of two ferromagnetic (FM) layers separated by a nonmagnetic spacer layer. Within a critical thickness range of the spacer, the magnetic layers become exchange-coupled and behave as single magnetic moments with opposite magnetization (M) directions, thus canceling each other, as it happens in an antiferromagnetic material. However, when an external magnetic field (H) is applied, the magnetic moments point in the same direction, reaching saturation so they can be manipulated for biomedical applications. Similarly, the P-SAF disks, as those fabricated in Ref. 14, are synthetic antiferromagnets with the only difference of the magnetization being perpendicular to the plane of the disk. Finally, the disks in the magnetic vortex state are characterized by the magnetic moments being curled in the plane of the disk, configured in closed circles to minimize the magnetostatic energy. Only at the center, in the core of the vortex, the magnetic moments get out of the plane and point perpendicularly. This particular spin arrangement is also characterized by a zero remanence. Nevertheless, when an external magnetic field is applied, the vortex core displaces in the plane of the disk until it reaches the edge where it is annihilated and the disk becomes magnetically saturated.

The three types of disks have been used in diverse experiments with cancer cells, either attached to the cell membrane or internalized within the cytoplasm. Figure 1 shows a gallery of P-SAF and vortex disks of different sizes fabricated for biomedical tests. In the majority of the reported experiments, the disks have been remotely actuated by an external magnetic field in order to exert mechanical force on the cancer cell. Beyond the differences encountered for each type of disk and experiment, the results confirm that the disk-shaped magnetic particles are capable of dramatically disrupting cancer cells. Since there is no heat generation, it is claimed that the magnetomechanical actuation avoids the risk of damaging the surrounding healthy tissue as can occur when using magnetic hyperthermia. Moreover, it has been proposed that the mechanical force delivered by the disks leads to the apoptosis of the cells instead of the more likely necrotic pathway induced by heating. Apoptosis is the programed spontaneous cell death where, at the latest stage, the dead cells are phagocytized by macrophages. Consequently, there should not be any cell-leakage in the surrounding extracellular environment, avoiding inflammatory reactions, in contrast to necrosis.¹⁵ 

The present review is divided into three sections. Section II is an overview of the in vitro experiments where the disks are magnetomechanically actuated to exert force on cancer cells. Furthermore, preliminary results of their drug delivery and heating efficiencies (for magnetic hyperthermia) are shown. Although these routes are focused on cancer treatment, magnetic disks could also be used to separate cancer cells from blood samples for early detection, as explained at the end of the section. It is worth mentioning that this review does not deal with the analysis of the interaction of disk-shaped magnetic particles with an in vivo biological environment but focuses on providing a physics perspective of their potential. Thereby, in Sec. III, we will discuss the dispersion capability and torque that disks can exert as a function of their magnetic configuration, dimensions, and the external magnetic field setup (uniaxial or rotational). The aim of the latter section is to orient this research field in its early-stage toward the most efficient magnetic-disk-based system that could evolve into a real cancer therapy. Finally, in Sec. IV, we evaluate the clinical translation possibilities of magnetic disks by addressing the main obstacles that magnetic nanoparticles encounter in the process of turning into an antitumor product.

The most powerful feature of the magnetic disks is their ability to rotate when an external field is applied. Indeed, in the absence of an external magnetic field, the disks are dispersed in the liquid medium (due to the zero remanence), but when a field is applied, the disks magnetize in a direction compatible with their easy axes trying to get aligned with the direction of the field, which generates the rotation of the disk and the concomitant mechanical torque. In the case of SAF and vortex disks, as the easy magnetization axis lies on the plane of the disk, this will tend to orient parallel to the direction of the field [Figs. 2(a) and 2(b)]. In the case of the P-SAF instead, the easy magnetization axis points out of the plane of the disk and the disk will tend to get perpendicular to the direction of the field [Fig. 2(c)]. In any case, the torque generated on the disk is accompanied by a force that can be directly delivered to the cell if the particle is either attached to the surface or internalized within it.

The first work exploiting this ability was presented in the year 2010 by Kim et al.¹⁶ They used Ni₈₀Fe₂₀ disks 1 μm in diameter with magnetic vortex configuration for in vitro experiments with glioma cancer cells. The microdisks, capped with two gold layers of 5 nm (all of the particles reported here are coated with gold), were biofunctionalized with an antibody that matches an antigen overexpressed on the surface of the glioma cells to achieve particle-cell bonding, as schematized in Fig. 6(a). Impressively, a field as small as 9 mT and 10–20 Hz applied for only 10 min induced 90% of cell death. Furthermore, the primary death mechanism was demonstrated to be apoptotic by assaying one of the hallmarks of late apoptotic cascades, namely genomic DNA fragmentation. The authors proposed that the oscillation of the disks may induce calcium influx through membrane ionic channels, or calcium release from the internal cell sources, which results in the total perturbation of cellular calcium homeostasis and the activation of the apoptosis process as illustrated in Fig. 3(a). This work made the difference in the area of magnetic nanoparticles for cancer treatment where, so far, the research was focused on magnetic hyperthermia using chemically synthetized SPIONs.

The large magnetic response of the Ni₈₀Fe₂₀ microdisks, compared to SPIONs, is due to the large saturation magnetization of permalloy. In return, nickel and iron, as well as cobalt, can lead to adverse effects as explained in more detail in Sec. IV of the review. This problem is partially solved by the gold coating; however, the reduction of the metallic mass to be injected in the body, while preserving therapeutic effectiveness, is strongly desired. With that goal, in 2016 we reported on the fabrication of Ni₈₀Fe₂₀ disks¹⁷ almost ten times smaller than those used by Kim et al. still presenting a well-defined vortex configuration.¹⁸ Although not biofunctionalized, the nanodisks were internalized by lung cancer cells¹⁹ during the 24 h of incubation, as demonstrated by the optical micrographs in Fig. 4(a). Probably, the small size of the disks favored their endocytosis and subsequent encapsulation into lysosomes (organelles that function as the digestive system of cells by processing both external and internal compounds). In the in vitro experiments, the application of a 10 Hz oscillating magnetic field of 10 mT for 30 min led to a reduction of 30% in viable cells. Lysosomal membrane rupture was proposed as the main cause of the cell death mechanism, which is illustrated in Fig. 3(b). Indeed, Saftig et al. had previously reported that lysosomal membrane permeabilization can induce the leakage of lysosomal hydrolases into the cytosol, and lead to cell death eventually.^20,21 Accordingly, the oscillation of the nanodisks could be able to disrupt the lysosomal membrane and trigger the cell death as it has been suggested elsewhere.^22,23

Leulmi et al. used Ni₈₀Fe₂₀ disks, 1.3 μm in diameter, with a vortex magnetic configuration for in vitro experiments with renal cancer cells.²⁴ However, in contrast to Refs. 16 and 19 where the authors used a uniaxial magnetic field (UMF) generated by a pair of helmholtz coils, in this paper, the authors applied a rotating magnetic field (RMF) generated by a Halbach array, which rotates around the cells well-plate. The gold-covered disks were biofunctionalized with the antibody anti hCA9 to specifically target carbonic anhydrase CA9, which is a protein overexpressed on the cell surface of a large number of solid tumors. Thus, the particles were attached to the renal cell membranes as shown in Fig. 4(b). The application of a RMF of 30 mT and 20 Hz for 1 h reduced the viable cells by 70%. Moreover, the authors observed an increase in activated caspase levels, which are key components in the latest stage of the apoptotic intracellular cascade. Therefore, this is an additional proof that the magnetomechanical stimulus favors the apoptotic cell death.

Cheng et al. also made use of a RMF to actuate vortex magnetic state Ni₈₀Fe₂₀ microdisks aimed to destroy glioma cells.²⁵ However, in this case the authors did not biofunctionalize the surface of the disks. Despite the large diameter of the disks (2 μm), the brain cancer cells internalized the particles in an average proportion of 39 microdisks per cell. According to the authors, due to the high binding affinity between the gold surface of the particles and biomolecules such as proteins with carboxylate, amine, and thiol groups, the interaction between the microdisks and the plasma membrane is promoted, which induces the internalization of the microdisks into the glioma cells. Moreover, TEM images reported by Y. Cheng et al. [Fig. 4(c)] suggest that the microdisks follow a similar endocytic path as the nanodisks, schematized in Fig. 3(b), since the particles appear to be encapsulated in lysosomes. Interestingly, the internalization of disks did not affect the viability of cells, whereas 5 min of exposure to a RMF of 1 T at 20 Hz caused the death of 26% of cells. Additionally, the authors used terminal deoxynucleotidyl transferase UTP nick end labeling (TUNEL) assay to detect DNA fragmentation, a hallmark of the late apoptotic cascade, resulting in 33% of stained cells. However, some cells showed morphological change but no TUNEL staining, which could be attributed to a necrotic death. The large magnetic field used in this treatment (two orders of magnitude larger than that used in the previously mentioned works) might be too aggressive, deviating from the magnetomechanically triggered apoptosis and leading to the nondesired necrosis.

Recently, Mansell et al. used P-SAF disks, previously reported,¹⁴ to destroy brain cancer cells under a RMF.²⁶ The basic structure of this SAF is a pair of perpendicularly magnetized CoFeB layers coupled by a Pt/Ru/Pt spacer. To increase the total moment, this basic stack was repeated twelve times when fabricating the microdisks. Again, despite the large size of the disks (2 μm in diameter) and their nonfunctionalized surface, the particles were internalized by the cells. After applying a RMF of 1 T for one minute, the viability was assessed indicating a percentage of cell death of approximately 60%. Interestingly, the same authors in collaboration with Muroski et al. proposed that the P-SAF microdisks could be carried inside the brain by neural stem cells.²⁷ Indeed, the authors demonstrated that the neural stem cells internalize microdisks without damaging their migration capability; thus, they could cross the blood brain barrier, which has proven to be extremely difficult in particle-based therapies. Once inside, the disks could be delivered by an external magnetic field and destroy brain cancer cells as described.

The different characteristics and results of the above in vitro experiments are compiled and compared in Table II. It is important to note that each work used different techniques and procedures to assess the cell viability (see table footnotes). For instance, the same experiment assessed by two techniques, Trypan blue (TB) staining and flow cytometry with ADD-7 stain, gave values of viable cell reduction of 26% and 90%, respectively.²⁵ Not only that, each type of cancer cell will most likely respond differently to the same stimulus. Furthermore, the location of the disk in relation to the cell can also play an important role. Since all these are in vitro experiments, one must take into consideration that the viscosity of the cytoplasm or the lysosome will be larger than that of the cell culture medium, whose composition is mainly water. In fact, the effective intracellular fluid viscosity for human brain cancer cells was found to be 0.068 Pa s,²⁸ close to the value measured inside lung cancer cell lysosomes (0.040 Pa s),²⁹ whereas the viscosity of RPMI, a widely used cell culture medium, is 0.00069 Pa s,³⁰ i.e., two orders of magnitude smaller. Therefore, the disks attached to the cellular membrane will have a larger freedom of motion exerting the force more efficiently, although this experimental condition might be far from an in vivo tumor environment. Because of these three variables, no purely quantitative comparison has been made in order to evaluate the efficiency of the treatments. The aim of Table II is to provide the big picture of the most relevant in vitro experiments of magnetomechanically actuated disk-shaped particles to kill cancer cells.

The mechanical oscillation or torque of disks not only serves to exert forces on cells but also to deliver therapeutic molecules. In fact, Kim et al. studied the delivery efficiency of magnetomechanically actuated Ni₈₀Fe₂₀ vortex disks.³¹ In the experiment, thiolated chitosan was assembled on the gold surface of the disks and doxorubicin molecules (typically used as drugs in chemotherapy) were then loaded into the chitosan scaffold. Under a UMF field of 2.8 mT at 30 Hz, 30% of doxorubicin was released to the medium thanks to the disks motion that favors the diffusion of drug molecules (Fig. 5). The mechanical force applied to the cells, that permeabilizes the cancer cell membrane, accompanied by a simultaneous delivery of antitumor drugs could definitely enhance the therapeutic efficiency of the treatment.

The ability of disk-shaped magnetic particles to release loaded molecules on demand could also open up new prospects in emerging cancer therapies such as gene therapy. Gene therapy aims at delivering genetic material into target tissue and to express it with the intention to gain a therapeutic effect. Genes have the advantage over chemotherapeutic drugs due to the fact that they can be administered locally at high therapeutic dose without risking systemic adverse effects. Furthermore, since most gene therapies are single time applications, they can be cost effective in the long run. Currently, more than 60% of all on-going clinical gene therapy trials worldwide are targeting cancer.³² However, its clinical implication has only achieved little success due to the lack of an efficient gene delivery system.³³ Here, we propose the use of disk-shaped magnetic particles to locally deliver genes at tumor sites in a controlled manner based on the mechanism described above.

Disk-shaped particles could also be excellent heating agents for the well-known magnetic hyperthermia therapy. Yang et al. carried out a study to compare the specific absorption rate (SAR) of the most widely used superparamagnetic iron oxide nanoparticles (12 nm), ferrimagnetic nanoparticles (60 nm), which could provide a much larger SAR, and vortex state nanodisks (125 nm in diameter), all of them made of Fe₃O₄.³⁴ Impressively, the nanodisks showed higher SAR values at all measured magnetic field strengths (a frequency of 488 kHz was used in all the measurements). The highest SAR value for the three kinds of particles was found at 47.8 kA/m, being 5 kW/g for the nanodisks, which is more than two times higher than that of ferrimagnetic particles and about four times higher than that of SPIONs. It is known that the major heating mechanism is the hysteresis loss, which is directly proportional to the area of the hysteresis loop. According to the results, when the Fe₃O₄ nanodisks are aligned parallel to the magnetic field, the area of the loop is remarkably larger. Moreover, even if the nanodisks are not strictly parallel to the field, i.e., within a deviation of ±30°, high SAR values are still achieved.

However, it should be noted that even though the SAR values achieved by Y. Yang and co-workers are among the highest values reported in the literature, they are considered insufficient to induce a significant therapeutic effect in a real treatment.³⁵ Furthermore, the product of the field strength and frequency (⁠ $H×f$⁠) in these measurements (ranging from 7.8  $×$ 10⁹ to 2.3  $×$ 10¹⁰ A m⁻¹ s⁻¹) exceeds the upper limitation of 5  $×$ 10⁹ A m⁻¹ s⁻¹ conventionally used in the literature to avoid unwanted nonselective heating of both cancerous and healthy tissues due to generation of eddy currents.³⁵ Thus, the SAR values would be lower under a magnetic field that falls within the clinical limits. This issue is discussed in more detail in Sec. IV.

Besides therapeutic approaches, disk-shaped particles could be used for detection purposes. In the work by Zhang and co-workers,³⁶ SAF nanodisks (150 nm in diameter) of Fe/Ti were encapsulated in silica shells to improve the stabilization in fluid, surface functionalization, and biocompatibility. Afterwards, streptavidin was covalently bonded to the silica surface by carboxylate groups. Streptavidin is a protein that has an extraordinarily high affinity for biotin, a water-soluble B-vitamin; thus cancer cells were labeled with the latter, through biotin-antibody-antigen chaining, for the final nanodisk-cell bonding. The labeling could be also achieved by following the previously mentioned antibody–antigen method, as illustrated in Fig. 6(a). The cells were then suspended in blood samples. For cell separation, a ferromagnetic membrane with micrometer-sized pores was used. When magnetized, the membrane generates an intense magnetic field gradient, effectively capturing magnetic objects flowing through the pores. When the blood samples were sent through the magnetic sifter, the magnetic forces pulled the nanodisks-labeled cells to the sifter, while unlabeled red and white blood cells passed through [Fig. 6(b)]. The authors observed an average capture efficiency of 46.8%. The SAF nanodisks are therefore promising candidates for cell separation from blood samples, followed by optical counting, for early cancer detection. This is possible because of the large magnetic moment of the SAF disks, which is also attributable to P-SAF and vortex disks.

The major goal of the present review is to discuss the torque and dispersion capabilities of each type of magnetic disk in order to promote the investigation toward the most efficient magnetomechanical actuator that could evolve into a real cancer therapy. It should be noted that the conditions in an in vivo biological environment would add numerous variables to the study of these properties. Particularly, the tumor biological environment possesses an extra level of complexity due to the abnormal extracellular matrix, high interstitial fluid pressure,³⁷ and irregular chemical conditions such as a lower extracellular pH.³⁸ However, such sophisticated biophysical analysis, which is also hampered by the very scarce number of in vivo studies in the literature,^25,39 is beyond the scope of the present review. It is our intention then to provide a thorough physical analysis of disk-shaped magnetic particles for the upcoming in vivo studies to be more successful.

One of the major advantages of disk-shaped particles is the net zero magnetization at remanence which, in theory, is translated into the absence of magnetic interactions among the particles and, thus, no agglomeration in fluid. This is essential for biomedical applications in general, and for cancer therapy in particular, where a uniform distribution of the particles through the tumor tissue is required to provide an efficient treatment. The dispersion is also necessary for the proper circulation of the particles inside the body without the risk of embolization of capillary vessels. Besides that, for magnetomechanical-based therapy, the particles must have freedom of motion. Despite their good dispersion capability attributed to the zero remanence, the application of an external magnetic field leads to polarization phenomena that need to be considered. This is addressed in Sec. III A 1, whereas modification of the dispersion capability by adequate surface treatments is discussed afterwards.

Joisten et al. studied the agglomeration/dispersion phenomena in SAF disks of (NiFe/Ru/)_nNiFe 1 μm in diameter.⁴⁰ The number of repeats (n) was varied from 1 to 7, whereas the total magnetic thickness was kept constant. When the magnetic field was applied, the particles got magnetically polarized and started interacting magnetostatically forming long chains parallel to the field. When the field was turned off, the particles kept on interacting and formed large magnetic agglomerates. This phenomenon is due to the very high susceptibility of the particles resulting in self-polarization caused by the magnetostatic stray field from the other neighboring particles. The authors demonstrated that the reduction of the susceptibility reduces self-polarization phenomena, which can be achieved by increasing the repeats number in the multilayered stack (i.e., reducing the thickness of each magnetic layer). For instance, SAF disks with n = 1 [Fig. 7(a)] kept forming chains after turning the field off, whereas disks with n = 7 [Fig. 7(b)] broke chains and redispersed. The authors proposed a model that gives an expression for the susceptibility threshold below which SAF particles agglomeration can be avoided

where d is the lateral dimension of the particle (assuming that the particles have a square shape), N is the number of particles along the chain, t_NiFe is the thickness of each NiFe layer, and K is a numerical factor (1  $≤$ K  $≤$ 4) that describes the fact that the stray field created on a given particle by the others may be reduced because of the misalignment of the particles planes along the chain.

There are no experimental studies of particle agglomeration with P-SAF disks but, since the susceptibility at low field is nearly zero, the self-polarization process occurring in SAF disks is not expected to take place. Agglomeration can in any case be produced by the small hysteresis at low field existing in not perfectly compensated particles.

In contrast to SAF particles, the susceptibility of vortex state disks of Ni₈₀Fe₂₀ can be reduced by increasing the thickness, which was experimentally and theoretically demonstrated by Leulmi et al.⁴¹ Importantly, according to the model the authors proposed, which similarly gives an expression for the susceptibility threshold [Eq. (2)], whatever the particles radius (R) and thickness (t), the actual susceptibility is lower than the critical self-polarization threshold. In other words, the vortex particles should never magnetostatically agglomerate as long as they can keep their reversible magnetic behavior at low fields. In practice, if compared to SAF disks, vortex disks need more time to redisperse when the magnetic field is turned off. However, the general trend is to go toward a complete dispersion provided enough time is left to the system, as shown in the image sequence of Fig. 7(c) 

Recently, we found out that the dispersion time of vortex disks significantly varies with the size of the particles.¹⁹ A light-transmission experiment [schematized in Fig. 8(a)] was performed in order to compare the magnetomechanical motion of disks having 2 μm and 140 nm in diameter. As expected, in both cases, the intensity of the transmitted light reached the maximum when the magnetic field was on and dropped down when turned off, which could be due to the alignment of the disks plane with the magnetic field [Fig. 8(b)]. Surprisingly, spherical magnetic nanoparticles, not having a preferential geometrical orientation, showed the same response [Fig. 8(c)]. This indicated that the change in the light intensity was due to the formation of particles chains along the magnetic field lines, which is consistent with the results of Leulmi et al.⁴¹ Consequently, similar transmitted light plots reported so far^16,31 do not represent the alignment of individual disks, as the authors claim, but (also) the formation of chains that permits the light to pass through the aqueous solution. Another remarkable conclusion of this experiment is that nanosized disks break chains and redisperse instantaneously when the field is turned off, whereas the relaxation time for disks having 2 μm in diameter is close to 0.5 s.

Besides magnetic interactions, the stability of magnetic particles in suspension is also affected by hydrophobic–hydrophilic and van der Waals forces. Due to the large surface area to volume ratio, magnetic nanoparticles tend to aggregate to micrometer-sized clusters through hydrophobic interactions. Furthermore, in order to minimize the total surface energy, nanoparticles aggregate by attractive van der Waals forces. These phenomena can be minimized by modifying the surface of magnetic particles, which has been extensively studied in the literature.^42,43 Surfactants (e.g., oleic acid), natural dispersants (e.g., chitosan), organic dyes (e.g., fluorescein isothiocyanate, FITC), and polymers are widely used for this purpose. Poly(ethylene) glycol (PEG) is a particularly interesting polymer coating because of its amphiphilic nature (it is soluble in a number of organic polar and apolar solvents), chemical stability, and biocompatibility. When bound to surfaces, PEG repels other molecules by steric effects making PEG-modified nanoparticles more stable at high salt concentrations and in biological environments.⁴⁴ Other materials such as silica⁴⁵ and gold⁴⁶ also serve as particle coating for dispersibility enhancement. Since both silica and gold are hydrophilic, silica- and gold-coated particles are better dispersed in aqueous solutions. In addition, silica has hydroxyl groups (silanol) useful for the attachment of further functionalities through covalent bonding. Gold on the other hand possesses a huge affinity to thiol groups, which facilitates the anchoring of additional dispersant molecules. All these surface modification approaches can be similarly applied to disk-shaped particles. Actually, the discoidal shape provides a larger surface available for functionalization with respect to spherical nanoparticles, allowing for a better coating of the surface and higher minimization of the aforementioned attractive forces.

As mentioned previously, the majority of the micro and nanodisks used in experiments with cancer cells are coated with gold to improve biocompatibility and to ease further surface functionalization. Indeed, various works report on subsequent surface modifications and dispersibility results. For instance, Kim et al. attached chitosan on the thiolated gold surface of disks resulting in an enhanced dispersion of the particles in aqueous solution due to the formation of a positive surface charge.³¹ On the other hand, Barrera and co-workers found that FITC derivatized nanodisks showed superior dispersion and change in aggregation compared to nonderivatized nanodisks.⁴⁷ Silica has been also used to improve dispersion capability and facilitate further surface modification of disks.³⁶ However, it should be noted that the use of nonmagnetic materials for coating magnetic particles may result in a decrease in saturation magnetization.^48,49 Therefore, it is necessary to search for a compromise between surface modification and conservation of magnetic properties to optimize the performance of the disk-shaped particles.

The other cornerstone of disk-shaped particles is the torque generated by the external field, for it defines the force they will exert and, thus, their capability to damage cancer cells. As explained above, an external magnetic field induces a net magnetization on the disk, which is assumed to be aligned with its easy axis (in-plane for SAF and vortex disks, and an out-of-plane for P-SAF disks). As a result, the disk suffers a torque driven by the tendency of the magnetization to align with the field direction.

The torque exerted by an external magnetic field H on a magnetic moment m is given by $τ →= μ 0 m →× H →$⁠. For a given amplitude of the external field, whether this torque can be used by the disk-shaped magnetic particles to damage cells or not depends mainly on two factors: the magnitude of the magnetic moment and the strength of the magnetic anisotropy, which determines the ability of the torque on the magnetic moment to be transmitted to the disk.

Regarding the magnitude of the magnetic moment, since the three types of disks ideally have no remanence, that is, present null magnetization at zero field (which is useful to avoid agglomeration as it has been already said), the magnetic moment must be induced by the same external magnetic field responsible for the torque. If V is the volume of the disk, and M the achieved magnetization, the magnetic moment of the particle is $m=MV$⁠. Therefore, according to their basic magnetization processes, illustrated in Table I, the torque generation mechanism is different for SAF and vortex disks than that for P-SAF. SAF and vortex disks develop a magnetic moment even at low fields, according to their magnetic susceptibility (m = χ H V), whereas P-SAF particles need that the applied field is greater than a threshold value before developing a magnetic moment, which then acquires a fixed value, corresponding to the saturation magnetization $m= M SV$⁠.

On the other hand, the magnetic anisotropy must be strong enough to guarantee that the torque on the magnetic moment is transmitted to the structure and does not simply produce a rotation of the magnetization inside the disk. In SAF and vortex particles, the strong shape anisotropy makes that the magnetization remains always in the disk plane, if the disks are free to rotate. Even with the eventual application of large fields, the magnetization never goes out of the plane, since a finite magnetic moment is induced for any value of the in-plane component of the applied field, and the torque will make the disk to rotate toward the direction of the field. For these particles, we can estimate the magnitude of the torque by the expression (see Fig. 9)

that depends on the angle α, and gives a maximum value for α = 45° of

The susceptibility of the vortex disks can be estimated from experimental hysteresis loops, like those presented in Fig. 10 for Ni₈₀Fe₂₀ disks.¹⁹ The nanodisks with 140 nm in diameter present a nearly canonical vortex hysteresis loop. Assuming that the saturation magnetization corresponds to pure permalloy Ni₈₀Fe₂₀ (M_s = 8  $×$ 10⁵ A/m), the susceptibility has a constant value of about χ = 10. Similarly, the measured hysteresis loop of vortex disks with a diameter of 2 μm allows estimating a value of the susceptibility (at low fields) of about χ = 50.

Alternatively, for the case of vortex disks, the susceptibility can be calculated using the expression proposed by Guslienko et al.⁵⁰ 

provided that β, thickness (t) to radius (R) aspect ratio of the disk, is β ≪ 1. For a nanodisk with β = 0.71 (t = 50 nm, R = 70 nm), the calculated susceptibility is χ = 4.6, whereas for a microdisk with β = 0.06 (t = 60 nm, R = 1 μm), χ = 23.8. In both cases, the theoretical value underestimates the measured susceptibility by a factor of two, but provides a reasonable agreement considering the condition β ≪ 1 is not fulfilled, especially in the case of nanodisks.

Therefore, for an applied magnetic field of amplitude H = 8 × 10³ A/m (μ₀H = 10 mT), the maximum torques generated for vortex nano- and microdisks are τ_max = 3.1 × 10⁻¹⁷ N m and τ_max = 3.8 × 10⁻¹⁴ N m, which are translated into 440 pN and 38 nN force values, respectively (Table III).

For the case of SAF disks with a structure of (M/i)_n/M (M = magnetic layer, such as CoFeB or NiFe, i = nonmagnetic coupling layer, such as Ru), the susceptibility can be estimated from the theoretical relation between H and M derived by minimizing the magnetic energy⁴⁰ 

where t_M is the thickness of each magnetic layer and J₁ and J₂ are the bilinear and biquadratic coupling constants, respectively.

For low fields, the susceptibility can be approximated by

Using the same total magnetic thickness as the vortex microdisks, (n + 1)t_M = 60 nm, n = 10 and the values of the coupling constants provided by Joisten et al.⁴⁰ for (NiFe/Ru)_n/NiFe structures and Ru layer thickness of 0.6 nm (J₁ = 6.6 × 10⁻⁵ and J₂ = 2.2 × 10⁻⁵ J/m²) the susceptibility results χ = 50. Accordingly, the maximum generated torque of SAF particles is similar to that of the microdisks provided that they have the same volume of the magnetic material.

In the case of P-SAF, a magnetic field with a certain magnitude H_threshold must be applied to generate the out-of-plane magnetic moment. The disk becomes magnetized to saturation with a m = M_sV. If the direction of the field is not perpendicular to the plane of the disk, depending on the strength of the anisotropy K_u, the applied magnetic field H > H_threshold produces a deviation of the magnetization from the perpendicular easy axis. Using a Stoner–Wohlfarth model,²⁶ the equilibrium position of the magnetization is determined by the minimization of the magnetic energy (per unit volume)

with the angle definitions of Fig. 11.

The angle θ that minimizes the energy satisfies

The magnitude of the torque τ = μ₀M_sVHsin(α - θ) is then

The maximum torque τ_max = K_uV is produced at θ = 45°.

Note that, in contrast to the case of vortex and SAF disks, this angle is not the angle of the field with respect to the disk α. In fact, according to Eq. (9), α must be greater than 45°

and the maximum torque can only be achieved for H ≥ μ₀M_sK_u. In terms of the anisotropy field H^k = 2 K_u/μ₀M_s, this implies H ≥ H^k/2.

Using the data from Ref. 26, disks of (CoFeB/Pt/Ru/Pt/CoFeB)₁₂ with a total magnetic thickness of t = 21.6 nm, radius R = 1 μm, M_s = 1.1 × 10⁶ A/m, and H^k = 7.9 × 10⁵ A/m are able to produce a maximum torque of τ_max = 3.7 × 10⁻¹⁴ N m (force of 37 nN), when the applied field is larger than H = 3.95 × 10⁵ A/m (Table III).

The initial torque of a certain disk will be the same regardless of whether the applied magnetic field is rotational or not. Further application of the field, however, changes the response of the disk-shaped particles.

According to Mansell et al.,²⁶ under a rotating magnetic field, generated by a Halbach array rotating around the cell well-plate, the easy-axis of the P-SAF disks will align with the field direction and will follow it, leading to a continuous torque [Fig. 12(a)]. In the case of the vortex disks, once the easy plane of the disk aligns with the plane of the field rotation, the magnetization will rotate without exerting further torque on the particle [Fig. 12(b)]. The same would happen with SAF disks.

The process under a uniaxial magnetic field is completely different. The AC field generated by a pair of helmholtz coils has typically an amplitude of few tens of mT, sufficient to saturate Ni₈₀Fe₂₀ vortex and SAF microdisks,^19,31 but insufficient in the case of the P-SAF particles.¹⁴ For the first two types of disks, the magnetization will align with the field direction [as illustrated in Figs. 2(a) and 2(b)]; however, as the field goes to zero, the disks will demagnetize and relax in the fluid going back to a random orientation. Again, when the magnetic field reaches the maximum, a net magnetization will be induced in the disk, which will tend to align with the field direction. If the viscosity of the medium permits the relaxation of the disks, the repetition of this process, i.e., the application of an AC field, would lead to a continuous oscillation of the disks.

It is clear that each type of disk requires a specific magnetic field setup to maximize its magnetomechanical actuation. However, the RMF seems to be a more versatile technique, reaching larger magnetic field amplitudes (above the saturation fields of the three types of disks) and leading to a large cell viability reduction for both P-SAF disks and vortex disks, provided the magnetic stimulus is applied for a longer period of time^24,25 (see Table II). The reason why applying the magnetic field for a longer time leads to a more effective killing for vortex disks may be the formation of particle chains/agglomerates, with an effective net anisotropy, which then can be rotated under the field. Furthermore, although the UMF setup is effective when the disks are outside the cell (larger freedom of motion), in the case of the disks being inside the cell (larger viscosity), once they are aligned with the field, they might get blocked and not exert further torque. This would explain the much lower cell death percentage observed in Ref. 19 compared to Ref. 16 (%15 against 90%), with very similar experimental conditions, but with intracellular and extracellular actuation, respectively. The RMF, thus, guarantees a continuous rotation of any disk or assembly of disks with an effective net anisotropy.

Although disk-shaped magnetic particles have proved to hold great potential for cancer therapy in vitro, real cancer treatments entail another level of complexity that needs to be addressed. In order to evaluate the clinical translation possibilities of disk-shaped magnetic particles, we consider necessary to do it by discussing the achievements and limitations of iron oxide nanoparticles in cancer therapy since they are the most clinically tested inorganic nanoparticles. As explained in the introduction, SPIONs have been extensively studied as magnetic hyperthermia agents. In the last 20 years, a full spectrum of SPION-based cancer treatment research has been systematically carried out, modeling magnetic nanoparticle distribution and heat dissipation, or evaluating nanotoxicity, in vitro cytotoxicity, in vivo antitumoral effects, etc.⁵¹ Regardless of the thousands of publications in nanoparticle synthesis and the improvements achieved, these formulations have generally failed to translate into real commercial products as hyperthermia agents. Until now, only Nano-Therm (MagForce, Berlin), a ferrofluid constituted by aminosilane-coated spherical SPIONs of 15 nm size, has been granted approval for clinical magnetic hyperthermia.^52,53 Ferumoxytol is another successful clinically approved iron oxide nanoparticle showing promising magnetic hyperthermia properties after a preclinical validation step, though it is originally formulated and tested as a contrast agent for magnetic resonance imaging (MRI).⁵⁴ The major problems encountered during translation of iron oxide magnetic nanoparticles into real commercial products as magnetic hyperthermia agents are three: (i) insufficient heating of the tumor, (ii) low targeting efficiency, and (iii) cytotoxic effects.

The first issue is about the SAR value of the magnetic nanoparticles. It has been argued that in order to heat a 3 mm cluster of cells, the SAR of the magnetic nanoparticles must be unrealistically high, several orders of magnitude greater than is currently reported.³⁵ Consequently, the limited SAR values require a very high injected dose of magnetic nanoparticles to achieve sufficient thermal enhancement. Moreover, the high concentration and the confined nanoparticle distribution at the site of injection lead to nonhomogeneous treatment of the tumor and damage of surrounding healthy tissue. An alternative approach to enhance the inductive heat is by increasing the strength and frequency of the alternating magnetic field. However, these conditions are limited in a clinical setting due to safety restrictions. Indeed, high-frequency magnetic fields can generate nonspecific heating due to eddy currents,⁵⁵ which potentially lead to damage of peripheral nerves. Therefore, the product of the field strength and frequency should be below 5  $×$ 10⁹ A m⁻¹ s⁻¹,³⁵ although there is still an ongoing discussion about the validity of this limit since the final value depends on the area of the tissue treated. In any case, it is proposed that it should not exceed 10¹⁰ A m⁻¹ s⁻¹.⁵⁶ In contrast, the magnetomechanical actuation of disk-shaped magnetic nanoparticles requires very low magnetic fields, as small as a few tens of millitesla and hertz, which constitutes a $H×f$ value at least 10 000 times smaller than that used in hyperthermia with magnetic nanoparticles. More importantly, in the magnetomechanical treatment there is no heat generation, as demonstrated by Kim et al. by monitoring the temperature of the cell-particle solution with an infrared camera,¹⁶ which would exclude the aforementioned side effects attributed to heating approaches. In turn, the motion of disk-shaped magnetic particles strongly depends on the viscosity of the biological medium and the magnetic field setup. Therefore, these two aspects ought to be thoroughly studied under in vivo conditions, which have remained barely explored.^25,39

Another challenge that needs to be addressed is targeting of tumor sites. The fact is that according to a recent meta-analysis study,⁵⁷ less than 1% of injected nanoparticles reach tumor sites due to the rapid removal of most nanoparticles from blood circulation by the reticuloendothelial system. In short, adsorption of plasma proteins on particles leads to their recognition by macrophages in liver and spleen, followed by phagocytosis and elimination. Thereupon, the ability of particles to remain in circulation turns out to be one of the most important determinants of their therapeutic potential, longer circulation ensuring longer contact time of the particle with the target tissue.⁵⁸ Interestingly, shape is now recognized as a crucial parameter in determining the behavior of the particles in various processes including blood circulation, cellular uptake, and intracellular trafficking.⁵⁹ Promisingly, recent investigations have unveiled the higher resistance of discoidal particles, compared to spherical SPION, to be taken up by phagocytic cells, which inhibits their clearance and prolongs their circulation time.⁶⁰ Yet another determinant of the therapeutic potential of nanoparticles is their ability to transmigrate from the blood vessel into the diseased tissue. After the particle successfully evades phagocytosis via macrophages and reaches its target site, it must be able to escape the blood flow and drift toward the wall of the blood vessel. Spherical nanoparticles tend to follow the streamlines of the flow they are traveling in, whereas discoidal particles are subjected to torques in a highly oscillatory trajectory that leads to increased interactions with the vessel walls (the drift velocity increases as the particles aspect ratio deviates further away from one).⁶¹ All this indicates that disk-shaped magnetic particles could achieve more success in overcoming some of the most important biobarriers than their spherical counterparts, enhancing the targeting and therapeutic efficiencies.

However, tumor targeting remains a major limitation in cancer nanotechnology and novel strategies are greatly needed to improve therapeutic efficiency in tumors. In this line, bioinspired cell-based approaches have recently attracted more attention to mediate the transport of nanoparticles.⁶² These approaches exploit the ability of certain cell types to home or migrate to tumors, such as leukocytes⁶³ and mesenchymal stem cells (MSCs).⁶⁴ Recently, Kalber et al. combined MSCs and magnetic nanoparticles (SPIONs) for the first time.⁶⁵ MRI results evidenced the enhanced tumor-targeting of nanoparticles when carried by MSCs. However, no significant reduction of the tumor size or growth was noted after magnetic hyperthermia treatment. According to authors, the initial heating was effective enough to induce destruction of the MSC population and subsequent clearance of both SPIONs and necrotic MSCs, but not widespread enough to retard the proliferation of cancer cells. This result brings to light once more that the role of magnetic particles in cancer treatment should not be based on thermoablation and cellular necrosis, but rather on induction of individual cell-apoptosis and instigation of the immune response. In this scenario, we envision a tumor-tropic cell-based system that increases the accumulation of disk-shaped magnetic particles, which have proved to be able to induce such apoptotic response in in vitro tests.

Third, SPIONs have been shown to carry a risk of oxidative stress and consequent immunotoxicity.⁶⁶ Indeed, a variety of nanoparticles have long been known to induce reactive oxygen species (ROS), which is considered one of the principal mechanisms of nanotoxicity. ROS are generated by activated macrophages in a phenomenon called “oxidative burst,” which helps the killing of ingested microbes. Macrophages scavenge for dead cells, as well as any foreign particles, promptly engulfing them. Interestingly, the nature of the material phagocytosed would determine whether the macrophage would become activated or not. A key factor in nanoparticle-induced activation of macrophages is the presence of pro-oxidant functional groups on the reactive surface of nanoparticles, i.e., the presence of oxygen and/or transition metals.⁶⁷ Therefore, transition-metal-oxide nanoparticles, and iron oxide nanoparticles in particular, play a key role in the activation of ROS generation.⁶⁸ The compositions of the most widely used disk-shaped particles in the literature, presented in this review, are also based on transition metals such as Fe, Ni, and Co. Fe is involved in ROS generation via mechanisms such as Haber–Weiss and Fenton reactions,⁶⁹ where Co can act as a catalyzer.⁷⁰ Furthermore, Co and Ni promote the activation of intercellular radical-inducing system.⁷¹ Promisingly, as explained above, particles with a high aspect ratio like disks possess higher resistance to be taken up by macrophages in contrast to spherical particles. Moreover, the gold coating would significantly reduce the generation of free radicals. Although these two factors may help reduce the risk of oxidative stress, very few works in the literature have actually studied cytotoxic effects of disk-shaped particles,^34,47,72 and none of them are specific to oxidative stress and immunotoxicity, which are factors that must be certainly considered and overcome in future translational research.

Taking all of the above together, it appears that disk-shaped particles could potentially face the main challenges encountered by magnetic nanoparticles in cancer therapy. However, this will only be possible if in-depth in vitro and in vivo experiments are carried out in order to answer several questions that remain unresolved, e.g., what is the composition, size, and surface coating that leads to the lowest cytotoxicity? Can the targeting efficiency be enhanced by harnessing the tumor-tropism of certain types of cells? What is the dose of disk-shaped particles and magnetic stimulus duration needed to induce a therapeutic effect?

Magnetic vortex disks and perpendicularly magnetized synthetic antiferromagnetic (P-SAF) disks have proven to be excellent magnetomechanical actuators to induce self-destruction of cancer cells via apoptosis. A similar capability to that of vortex disks could be attributed to in-plane synthetic antiferromagnetic (SAF) disks too, since the easy axis lies in the plane of the disk. Nevertheless, vortex disks seem to hold the greatest potential to be implemented in a real cancer therapy. First, the simple fabrication process, compared to the thickness-sensitive preparation of SAF and P-SAF multilayered structures, makes it easily scalable to produce large amounts of particles required for biomedicine. Second, in terms of dispersion capability, vortex disks always reach a complete dispersion if enough time is left to the system after magnetic field removal with a negligible relaxation time for diameters below 200 nm. This is a crucial property not only for a good intravenous transport and a homogeneous distribution of the particles in the tumor tissue, but also for facilitating the removal of the particles from the body after the treatment. Third, the magnetic softness of Ni₈₀Fe₂₀ disks requires external magnetic fields as small as a few tens of millitesla for their manipulation, avoiding necrotic cellular death and the consequent tissue inflammation. This magnetic field can be applied by a rotational setup, which would ensure a continuous torque on the particles and an effective killing of cancer cells provided the sufficient stimulus duration. Finally, the forces that vortex disks exert can be tuned from hundreds of piconewtons to tens of nanonewtons just by increasing the radius. Interestingly, hundreds of piconewtons have been found to be sufficient to break the cell membrane, whereas only a few piconewtons can induce stretch-activated channels and increase the levels of intracellular calcium ions, which are involved in a number of key mechanisms implicated in cell death. It is then necessary to search for a compromise between the dispersion capability and the force magnitude when designing the dimensions of the disk.

Looking forward, we hope that the promising in vitro experiments, along with the potential of disk-shaped magnetic particles to face the clinical challenges in cancer therapy and the physical considerations presented in this review, will inspire researchers to carry out in vivo studies in order to progress in this emerging research field.

This work was supported by the NSF Nanosystems Engineering Research Center for Translational Applications of the Nanoscale Multiferroic Systems (TANMS) under the Cooperative Agreement Award (No. EEC-1160504) and the Spanish Government Project No. MAT2017-83631-C3. M. Goiriena-Goikoetxea acknowledges the support of the Basque Government for the Postdoctoral Fellowship.