Biomedical Applications of Biomaterials Functionalized with Magnetic Nanoparticles

3.1 The heat dissipation of magnetic nanoparticles

To understand the magnetization dynamic and the power losses of magnetic scaffolds, it is necessary to introduce the physical and mathematic descriptions of the response to a RF magnetic field of the MNPs embedded in it. If a population of magnetic nanoparticles in a solution is exposed to a harmonic RF magnetic field, they start to dissipate power due to the hysteresis loss but also to the magnetic dipole and to the Brownian relaxations [16]:

where μ0is the vacuum permeability; f is the frequency of the applied field, in Hz; H¯is the amplitude of the external magnetic field; and χ″is the imaginary part of the complex magnetic susceptibility of the particles. For ferrofluids, the magnetic susceptibility is known to be described by the Debye model [13, 16]:

The term χ0is the equilibrium susceptibility that is defined as [17]:

where ζis the ratio between the magnetic energy of the set of magnetic dipoles and the thermal energy. Mathematically speaking:

where Msis the saturation magnetization of the single MNPs, in Am−1; Vmnpis the particle volume in nm3; kBis the Boltzmann’s constant; and T is system temperature. In Eq. (3), χ0is the initial susceptibility, which is defined as [17]:

The term τin the Debye model (Eq. 2) is the effective relaxation time, in s, which can be evaluated as the parallel of the Néel and Brownian processes [17]:

The time required to the magnetic dipole moment to align with the direction of the external magnetic field is called the Néel relaxation time, τN[16, 17]:

The pre-exponential factor τ0is a time, and its value can range from 0.1 ps to 1 ns, but this term is a function of system temperature, i.e., τ0=τ0T[13]. The term Γis the ratio of the anisotropy energy of the nanoparticle to the thermal energy of the system, i.e.:

where Kais the magnetic anisotropy energy per unit volume in Jm−3and Vmis the MNP volume in nm3.

In a FF, the nanoparticles are allowed to rotate and move according to Brownian motion in the viscous medium where they are dispersed. When subject to a time-varying magnetic field, the particles rotate to orient with the direction of the external energy source, thus contributing to the relaxation process. The Brownian relaxation time can be evaluated as [16]:

being ηthe viscosity of the medium, in Pa⋅s, and Vhthe hydrodynamic radius of the particle in solution.

With Eqs. (1) to (9), it is possible to describe the frequency response and the power dissipation of a population of MNPs dispersed in a solution. This set of equations constitutes the theoretical basis for the understanding of magnetic scaffold behavior. However, since MagS are solid nanocomposites, the behavior of their magnetic phase is rather diverse than a FF. In the following, the experimental findings related to material characterizations and a new mathematical framework to account for their response are provided.

3.2 Hyperthermia response of magnetic scaffolds

Hyperthermia (HT) is a thermotherapy which aims at increasing the temperature of a target tissue between 41 and 46 C for about 60 min. For biological tissues, especially neoplasms and cancers, these temperatures are sufficient to damage the DNA of cells, altering its replication and also the repair pathways while determining cytotoxicity and activating the response of the host immune system [18, 19]. The rather chaotic vascular architecture of tumors is the reason of the thermo-sensibility of these pathologic tissues. The aforementioned biological effects can lead to the death of cancer cells, but, in the clinical practice, HT is exploited as a coadjuvant therapy combined with chemotherapy or/and radiotherapy rather than as a standalone therapy [19]. The hyperthermia can be induced using different types of energies, such as ultrasounds or electromagnetic (EM) field [14]. Currently different therapeutic modalities are available for HT induced by EM field. In particular, it is thoroughly investigated the local and in situ treatments using nanoparticles or magnetic scaffolds by exposing the target are with an external magnetic field.

Several magnetic scaffolds from Table 1 demonstrated to be capable of noticeable temperature increases when exposed to magnetic field working at the frequencies from 100 kHz to 1 MHz and with amplitude ranging from 8 to 25 kAm−1[5, 7]. Different biomaterials (e.g., hydroxyapatite, β-TCP, and PCL) loaded with magnetite or maghemite nanoparticle temperature increase, from room temperature, of 8–45∘C, were measured [5]. In particular, on one hand, a scaffold made with the intrinsic magnetic hydroxyapatite of Tampieri et al. [8] can increase the temperature of 40∘C in 60 s when exposed to a magnetic flux density with amplitude of 30 mT and frequency 293 kHz. On the other hand, in the same exposure conditions, a PCL scaffold loaded with magnetite nanoparticles can raise the temperature from 20 to 32∘C in 600 s [7, 8, 13].

These composite nanomaterials are identified as optimal candidates for local bone tumor hyperthermia [1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14]. However, their therapeutic potential must be investigated in a critique way. The understanding and the modeling of the heat dissipation of the MNPs embedded in the biomaterial are essential to allow an effective treatment planning.

3.3 The susceptibility spectra of magnetic scaffolds

The physical explanation of the relevant and significant temperature increases measured for MagS is not trivial. Moving from the theory explained in Section 3.1, the resonant Debye model cannot be applied to a system in which highly concentrated MNPs are fixed and embedded in a solid matrix and lattice or constrained in a highly viscous medium [13]. Indeed, the long-range interactions between the magnetic nanoparticles become relevant [20]. The following index ϒ, given in [20], can be considered to estimate the level of dipole–dipole interactions in the nanosystem under analysis:

where the cubic power of the particle diameter, dmnp3, is the lower limit of the volume packaging and of the steric hindrance in the system [5]. For example, for magnetite nanoparticles the particle diameter measured in dry condition with transmission electron microscope (TEM) is lower than the hydrodynamic radius assessed using dynamic light scattering (DLS), i.e., 10 nm against 25 nm. Therefore, at the body temperature of 37∘C, given the same dipole moment μmnp, the level of interaction of MNPs in solution is 2.5 times lower. It is demonstrated by the morphological and structural characterization of MagS that the MNPs in the biomaterial are often aggregated or very near, implying that small clusters of nanoparticles can be identified [5]. Moreover, this last evidence supports the theory for which the relaxation dynamic of clusters of MNPs is strongly modified due to the appearance of a distribution of anisotropy energies [20]. In other words, the Neel relaxation time in Eq. (7) will depend on the number and the dispersion of sizes of the nanoparticles. Another limitation of the applicability of the Debye model to the description of magnetic scaffolds is the influence of Brownian relaxation time on the heat dissipation mechanism. It has been demonstrated that the frequency response of the complex magnetic susceptibility χfof MNPs modifies if the particles are constrained in agarose gel or used as cross-linkers in hydrogels [21, 22]. This change in the susceptibility spectra is due to the fact that in a highly viscous matrix or in a solid, the Brownian mechanism is hindered or canceled. From Eq. (9), in mathematical terms:

Therefore, in MagS the only relaxation time is the Néel one.

The influence of long-range interactions between particles, the modified distribution of anisotropy energy, and the different Néel relaxation dynamic are the factors that contribute to enhance the power dissipation of magnetic scaffolds, and all of them can help to explain the hyperthermia behavior of MagS, such as for the magnetic hydroxyapatite and the Fe-doped PCL scaffolds [7]. Relying on the magnetic susceptibility spectra of MNPs in agarose gel measured by Hergt et al. [21], a Cole-Cole model for magnetic scaffolds [13]:

Equation (12) can fit the susceptibility data, with a 1.5% relative error, as shown in Figure 2, whereas the Debye model cannot (Eq. (2)). In Eq. (12)γis the broadening parameter, which is found to be equal to 0.75 [13]. The differences in the frequency response are depicted in Figure 2.

With Eqs. (1)–(8), but using Eq. (12) instead of Eq. (2), it is possible to evaluate and estimate the power losses of magnetic scaffolds. At this point it should be noted that the magnetic susceptibility χfis a function of the system temperature, which influences the initial susceptibility and the Néel relaxation time (Eqs. (5) and (7)). As the temperature increases, the therm τ0increases, whereas the time τNdecreases. The outcome is a decrease in the imaginary part of the magnetic susceptibility, χ″, which in turn lowers the power deposited by the magnetic scaffold. Therefore, since the goal of hyperthermia treatment is to increase the temperature of cancer tissues, it follows that the magnetic properties of and hence the power dissipated by MagS change during the treatment. The influence of temperature on the different physical quantities is shown in Figure 3. Since P=PT, planning a HT treatment which employs MagS as thermo-seeds against tumors is a multiphysics and highly nonlinear problem [14].

3.4 The hyperthermia treatment of bone tumors

Given the potential of magnetic scaffolds to be used as local heat source for setting the hyperthermia treatment of cancers, the most studied biological and clinical target of the nanosystems under investigation are bone cancers. Indeed, in clinical practice, currently available techniques such as chemotherapy, radiotherapy, and osteotomies presented a 15% probability of tumor recurrence, and therefore the hyperthermia treatment was proposed as adjuvant therapy [23]. Furthermore, since the surgical intervention causes a bone damage which calls for a graft or bone substitutes, magnetic scaffolds as theranostic, multifunctional, and magnetic-responsive biomaterials can be employed and can express their clinical potential [14].

Bone tumors are neoplasms mostly affecting subjects with age between 10 and 25 years old, causing impairment and pain, thus ruining the quality of life [24]. Malignant bone cancers such as osteosarcoma (OST) and fibrosarcomas (FIB) are known to affect long bone extremities [24]. OST and FIB are two different forms of bone cancer. The OST is big, aggressive and highly vascularized, whereas FIB is a poorly vascularized neoplasm. The survival rate for patients affected by OST and FIB may vary from 28–40% [14, 23, 24]. To overcome these clinical issues, oncologist investigated the use of immunotherapy or smart nanocarriers of drugs, but local hyperthermia stands out as a very promising therapy [14]. The rationale is to implant a MagS after the bone tumor resection or reduction and then perform a local and in situ hyperthermia treatment by applying an external RF magnetic field. The residual cancer cells would be killed or increase their sensibility to drugs or radiations. Finally, the scaffolds would serve as supporting architecture for healthy cells, favoring tissue repair [14].

3.4.1 The in silico scenario

With the knowledge of the mechanism of power dissipation of MNPs embedded in a scaffold, recently a numerical scenario, with layered geometry, was proposed to investigate using finite element methods (FEM) the effectiveness of magnetic scaffolds in treating the residual bone cells of OST and FIB tumors [14].

As shown in Figure 4, imagining a surgical intervention of a bone cancer in distal femur, a spherical magnetic scaffold, with radius rs= 5 mm, is implanted to fulfill the bone cavity [14]. A small gap or fracture (rf= 0.1 mm) separates the scaffold from an annular region where the residual cancer cells of OST or FIB are supposed to be found. The fracture gap is a heterogeneous region where blood and bone are present, and it is where the new bone forms. It was demonstrated that its presence and biological status, i.e., if it is inflamed or ischemic, can influence the HT outcome [14]. The tumor area has a radius rtwhich can vary from 0.1 to 0.5 mm. The goal of the HT treatment is to raise the temperature above 42∘C for 30 min [14, 17]. Finally, a healthy bone tissue region with radius rb=5 mm is included. The healthy bone should not be damaged by the treatment [5, 14]. It should be pointed out that muscle, fat, or skin tissues are not included in this analysis [25].

3.5 Results

The temperature pattern resulting from the exposure to the homogeneous RF field is uniform and radial, as shown in Figure 5a. This is a consequence of the homogeneous distribution of the MNPs in the biomaterials [7, 14]. After 60 min of treatment, it can be noticed that the temperature in the healthy bone can reach 47∘C, which is a potentially harming value. To assess the performance of the two types of MagS in treating OST and FIB, the average value of temperature in the tumor region vs. time was considered. From Figure 5b it can be noticed that both magnetic hydroxyapatite and Fe-doped PCL are able to treat the poorly vascularized FIS for any given dimension of the residual area rt. This can be explained considering that PEM≫∣ρbCp,bωbT−Ta∣, for H0=10–17 mT. However, the temperature rise is noticeable, and the external field should be modulated (or turned off) to keep the temperature closest to the target value of 42∘. In the case of OST, give the high value of blood perfusion (see Table 3); not all MagS are able to treat successfully the residual cancer cells. This is the most challenging tumor. Indeed, the Fe-doped PCL scaffold fails to reach the lethal HT temperature for an OST of 0.5 mm, even increasing the amplitude to 40 mT or the frequency to 409 kHz. The magnetic hydroxyapatite scaffold is more effective in treating the residual osteosarcoma cells, as can be observed in Figure 5c. These results demonstrate that the in HT treatment of residual bone tumor cells is feasible, and, with the knowledge of the physico-chemical properties of the nanomaterial, the treatment can be planned against different type of tumors.

4.1 Magnetic drug delivery

Magnetic scaffolds were conceived as a multifunctional platform for tissue engineering applications (see Figure 1) [1, 2, 3, 4, 5]. As presented in the Introduction, they are a platform for magnetically targeted drug delivery of growth factors to control and enhance tissue healing, such as in the case of bone tissue [1, 11]. The bio-nanotechnology research developed magnetic carriers of biomolecules such as VEGF or TGF-β[11, 27]; however, the problem of maximizing and controlling their delivery to the site of injury is still addressed in the literature [1, 2, 3, 4, 13]. This section will cover the use of MagS, implanted in a damaged bone, as an in situ magnet, i.e., as attraction site for external MNPs carrying GFs. The influence on the cellular response is assessed employing a multiphysics model [13]. The prediction of the magnetic force required to attract the MNPs, the velocity in the extracellular matrix (ECM) medium, and the final spatial distribution is fundamental to foresee a treatment planning procedure, while evaluating the influence parameters in the drug delivery and the cellular migration process.

4.2 Challenging the mathematical modeling of MDD

4.2.3 Results from the case study

The magnetic scaffolds exposed to the static magnetic flux density field B0respond in a way similar to a uniformly magnetized sphere, as shown in Figure 6a. As a matter of fact, the magnetic force and resulting velocity distribution are similar, implying that the MNP concentration is maximum at the poles of the scaffold, while it is minimum at the equator (Figure 6b). The generic GFs attached to the MNPs are sensed by the cells, which migrate toward the chemical stimulus. As shown by Figure 6, after only 24 h of migration, the MSCs invade the gap cavity and reach the biomaterial surface. This suggests that the cells can colonize the scaffold and boost the regenerative process. From the model and the results presented, the final cell density pattern can be predicted and controlled by tuning or acting on the scaffolds magnetic properties or geometry [13].