**3. The hyperthermia treatment of bone tumors**

#### **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]:

$$P\_m = \pi \mu\_0 f |\underline{H}|^2 \chi'' \tag{1}$$

where *μ*<sup>0</sup> is the vacuum permeability; f is the frequency of the applied field, in Hz; *H* is the amplitude of the external magnetic field; and *χ*<sup>00</sup> is the imaginary part of *Biomedical Applications of Biomaterials Functionalized with Magnetic Nanoparticles DOI: http://dx.doi.org/10.5772/intechopen.89199*

the complex magnetic susceptibility of the particles. For ferrofluids, the magnetic susceptibility is known to be described by the Debye model [13, 16]:

$$\chi(f) = \chi' - j\chi'' = \frac{\chi\_0}{1 + j2\pi f\tau} \tag{2}$$

The term *χ*<sup>0</sup> is the equilibrium susceptibility that is defined as [17]:

$$\chi\_0 = \chi\_i \frac{\mathfrak{Z}}{\zeta} \left( \coth \left( \zeta \right) - \frac{\mathfrak{1}}{\zeta} \right) \tag{3}$$

where *ζ* is the ratio between the magnetic energy of the set of magnetic dipoles and the thermal energy. Mathematically speaking:

$$\zeta(T) = \frac{\mu\_0 \phi \mathcal{M}\_s^2 V\_{mnp} |\overline{H}|}{\Im kBT} \tag{4}$$

where M*<sup>s</sup>* is the saturation magnetization of the single MNPs, in Am�1; V*mnp* is the particle volume in nm3; k*<sup>B</sup>* is the Boltzmann's constant; and T is system temperature. In Eq. (3), *χ*<sup>0</sup> is the initial susceptibility, which is defined as [17]:

$$\chi\_i(\overline{H}, T) = \frac{\mu\_0 \phi M\_s V\_m |H|}{\Re kBT} \tag{5}$$

The term *τ* in 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]:

$$\frac{1}{\tau} = \frac{1}{\tau\_N} + \frac{1}{\tau\_B} \tag{6}$$

The time required to the magnetic dipole moment to align with the direction of the external magnetic field is called the Néel relaxation time, *τ<sup>N</sup>* [16, 17]:

$$
\pi\_N = \frac{\sqrt{\pi}}{2} \pi\_0 \frac{e^{\Gamma}}{\Gamma} \tag{7}
$$

The pre-exponential factor *τ*<sup>0</sup> is 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., *τ*<sup>0</sup> ¼ *τ*0ð Þ *T* [13]. The term Γ is the ratio of the anisotropy energy of the nanoparticle to the thermal energy of the system, i.e.:

$$
\Gamma = \frac{K\_a V\_m}{k\_B T} \tag{8}
$$

where K*<sup>a</sup>* is the magnetic anisotropy energy per unit volume in Jm�<sup>3</sup> and V*<sup>m</sup>* is 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 timevarying 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]:

$$
\pi\_B(\eta, T) = \frac{3\eta V\_h}{k\_B T} \tag{9}
$$

being *η* the viscosity of the medium, in Pa�s, and V*<sup>h</sup>* the hydrodynamic radius of the particle in solution.

biomaterials with the magnetic drug delivery or the hyperthermia, in this chapter, two mathematical models for their use as hyperthermia agent and as a tool for

the stimulation of tissues, in particular bone tissues. In Section 3 the nonlinear chemico-physical properties of magnetic scaffolds are presented, described, and used to introduce a recent in silico model for the planning of bone tumor hyperthermia [14]. Finally, in Section 4 the use of MagS as tool for active magnetic drug delivery is discussed. Furthermore, a mathematical model able of providing insights into the parameters of influence of the phenomenon is presented and analyzed [13]. The complete description of magnetic scaffolds favors the assessment of their

Magnetic scaffolds have been tested both in vitro and in vivo, using animal models, demonstrating that they can transduce an external magnetic signal in mechanical stimulation to the cells attached to the biomaterial surface (**Figure 1**) [1–4]. MagS have been investigated for bone, cartilage, cardiovascular and neuronal regeneration, and repair [2]. The most studied tissue is bone. The injury of skeletal tissue by traumas and diseases, such as osteoporosis, or by a tumor resection calls for the need of a bone substitute or scaffold to guide cell adhesion, proliferation, and differentiation [15]. Moreover, the bone tissue requires a continuous mechanical stimulation. Therefore, the magneto-responsive biomaterials in **Table 1** can deliver a direct mechanical stimulation if exposed to SMF, to low-frequency magnetic field (strengths from to 18 *μ*T to 0.6 T, frequencies varying from 10 to 76.6 Hz), or to pulsed electromagnetic fields [4]. The mechanism of action is not fully understood yet. The presence of magnetic nanoparticles in the biomaterials determines an increased superficial roughness and favors the interaction at the cell membrane with the cell surface receptors. It has been demonstrated that the mesenchymal stem cells (MSCs) can differentiate into osteoblast thanks to the activation of the integrin signaling pathways, which upregulate the expression of the osteogenic GF bone morphogenetic protein 2 (BMP-2) [4]. The use of magnetic scaffolds permits the integration of the implant with the host tissue, accelerating the

defect healing and increasing the mineral density of newly formed bone.

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

*Pm* <sup>¼</sup> *πμ*<sup>0</sup> *<sup>f</sup>*j j *<sup>H</sup>* <sup>2</sup>

where *μ*<sup>0</sup> is the vacuum permeability; f is the frequency of the applied field, in Hz; *H* is the amplitude of the external magnetic field; and *χ*<sup>00</sup> is the imaginary part of

*χ*<sup>00</sup> (1)

**3. The hyperthermia treatment of bone tumors**

**3.1 The heat dissipation of magnetic nanoparticles**

dipole and to the Brownian relaxations [16]:

**4**

Section 2 briefly reviews the use of MagS as magneto-responsive biomaterials for

magnetic drug delivery are provided.

effectiveness and their potential clinical impact.

*Smart Nanosystems for Biomedicine, Optoelectronics and Catalysis*

**2. Magnetic scaffolds for tissue repair and regeneration**

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.

<sup>ϒ</sup> <sup>¼</sup> *<sup>μ</sup>*0*μ*<sup>2</sup>

*Biomedical Applications of Biomaterials Functionalized with Magnetic Nanoparticles*

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,

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 *χ*ð Þ*f* of 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),

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

Cole-Cole model for magnetic scaffolds [13]:

frequency response are depicted in **Figure 2**.

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

*χ ω*ð Þ¼ *<sup>χ</sup>*<sup>0</sup>

As the temperature increases, the therm *τ*<sup>0</sup> increases, whereas the time *τ<sup>N</sup>*

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) *γ* is the broadening parameter, which is found to be equal to 0.75 [13]. The differences in the

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 *χ*ð Þ*f* is a function of the system temperature, which influences the initial susceptibility and the Néel relaxation time (Eqs. (5) and (7)).

decreases. The outcome is a decrease in the imaginary part of the magnetic susceptibility, *χ*00, which in turn lowers the power deposited by the magnetic scaffold. Therefore, since the goal of hyperthermia treatment is to increase the temperature

where the cubic power of the particle diameter, *d*<sup>3</sup>

at the body temperature of 37<sup>∘</sup>

*DOI: http://dx.doi.org/10.5772/intechopen.89199*

in mathematical terms:

**7**

*mnp* 4*πkBTd*<sup>3</sup>

*mnp*

C, given the same dipole moment *μmnp*, the level of

lim*<sup>η</sup>*!∞*τB*ð Þ! *<sup>η</sup>*, *<sup>T</sup>* <sup>0</sup> (11)

<sup>1</sup> <sup>þ</sup> ð Þ <sup>2</sup>*π<sup>f</sup> <sup>τ</sup>* <sup>1</sup>�*<sup>α</sup>* (12)

(10)

*mnp*, is the lower limit of the

### **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<sup>1</sup> [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<sup>∘</sup> 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<sup>∘</sup> 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<sup>∘</sup> C in 600 s [7, 8, 13].

These composite nanomaterials are identified as optimal candidates for local bone tumor hyperthermia [1–9, 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:

*Biomedical Applications of Biomaterials Functionalized with Magnetic Nanoparticles DOI: http://dx.doi.org/10.5772/intechopen.89199*

$$\Upsilon = \frac{\mu\_0 \mu\_{mnp}^2}{4\pi k\_B T d\_{mnp}^3} \tag{10}$$

where the cubic power of the particle diameter, *d*<sup>3</sup> *mnp*, 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<sup>∘</sup> 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 *χ*ð Þ*f* of 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:

$$\lim\_{\eta \to \infty} \tau\_{\mathcal{B}}(\eta, T) \to \mathbf{0} \tag{11}$$

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]:

$$\chi(w) = \frac{\chi\_0}{1 + (2\pi f \tau)^{1-a}} \tag{12}$$

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) *γ* is 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 *χ*ð Þ*f* is 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 *τ*<sup>0</sup> increases, whereas the time *τ<sup>N</sup>* decreases. The outcome is a decrease in the imaginary part of the magnetic susceptibility, *χ*00, which in turn lowers the power deposited by the magnetic scaffold. Therefore, since the goal of hyperthermia treatment is to increase the temperature

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

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<sup>1</sup> [5, 7]. Different biomaterials (e.g., hydroxyapatite, *β*-TCP, and PCL) loaded with magnetite or maghemite nanoparticle temperature increase, from room temperature, of 8–

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 tempera-

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

These composite nanomaterials are identified as optimal candidates for local bone tumor hyperthermia [1–9, 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

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

C in 60 s when exposed to a magnetic flux density with amplitude of 30

account for their response are provided.

45<sup>∘</sup>

ture of 40<sup>∘</sup>

20 to 32<sup>∘</sup>

under analysis:

**6**

C in 600 s [7, 8, 13].

**3.3 The susceptibility spectra of magnetic scaffolds**

effective treatment planning.

**3.2 Hyperthermia response of magnetic scaffolds**

*Smart Nanosystems for Biomedicine, Optoelectronics and Catalysis*

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

*Biomedical Applications of Biomaterials Functionalized with Magnetic Nanoparticles*

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

As shown in **Figure 4**, imagining a surgical intervention of a bone cancer in distal femur, a spherical magnetic scaffold, with radius r*<sup>s</sup>* = 5 mm, is implanted to fulfill the bone cavity [14]. A small gap or fracture (r*<sup>f</sup>* = 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 r*<sup>t</sup>* which can vary from 0.1 to 0.5 mm. The goal of the HT treatment is to raise the temperature above 42<sup>∘</sup>

C for

scaffolds in treating the residual bone cells of OST and FIB tumors [14].

30 min [14, 17]. Finally, a healthy bone tissue region with radius r*b*=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

With respect to the geometry in **Figure 4**, the HT treatment using MagS is carried out applying an external RF magnetic field with strength H0, working frequency f (293 kHz or 409 kHz [14]), and a time envelope able to keep the target temperature above the therapeutic threshold. The magnetic field is supposed to be

*Simplified layered geometry for modeling the hyperthermia treatment of bone tumors using magnetic scaffolds. The MagS with radius r*<sup>s</sup> *= 5 mm is surrounded by a surgical fracture gap (r*<sup>f</sup> *= 0.1 mm), the area where residual cancer cells are present (r*<sup>t</sup> *= 0.1 mm–0.5 mm), and the healthy bone tissue (r*<sup>b</sup> *= 5 mm). Taken from [14].*

cells, favoring tissue repair [14].

*DOI: http://dx.doi.org/10.5772/intechopen.89199*

*3.4.1 The in silico scenario*

analysis [25].

**Figure 4.**

**9**

*3.4.2 The electromagnetic problem*

**Figure 2***.*

*Results of the fitting of the magnetic susceptibility spectra of MNPs embedded in agarose: a) real part (in-phase) and b) imaginary (out-of-phase) components are presented [21]. The Debye and Cole-Cole models are used and compared Taken from [13].*

**Figure 3.**

*Temperature variation of the pre-exponential term τ*<sup>0</sup> *and the Neel relaxation time τ*N*. The influence on the equilibrium and the complex magnetic susceptibility χ*<sup>0</sup> *and χ*ð Þ*f is represented. The curves are obtained for a magnetic scaffold filled with the 0.2% of magnetite nanoparticles (rmnp=10 nm, M*s*(0) = 2 emu*�*g*�<sup>1</sup>*,T*b*=150 K).*

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*=*P T*ð Þ, 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

## *Biomedical Applications of Biomaterials Functionalized with Magnetic Nanoparticles DOI: http://dx.doi.org/10.5772/intechopen.89199*

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 r*<sup>s</sup>* = 5 mm, is implanted to fulfill the bone cavity [14]. A small gap or fracture (r*<sup>f</sup>* = 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 r*<sup>t</sup>* which can vary from 0.1 to 0.5 mm. The goal of the HT treatment is to raise the temperature above 42<sup>∘</sup> C for 30 min [14, 17]. Finally, a healthy bone tissue region with radius r*b*=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].

### *3.4.2 The electromagnetic problem*

With respect to the geometry in **Figure 4**, the HT treatment using MagS is carried out applying an external RF magnetic field with strength H0, working frequency f (293 kHz or 409 kHz [14]), and a time envelope able to keep the target temperature above the therapeutic threshold. The magnetic field is supposed to be

#### **Figure 4.**

*Simplified layered geometry for modeling the hyperthermia treatment of bone tumors using magnetic scaffolds. The MagS with radius r*<sup>s</sup> *= 5 mm is surrounded by a surgical fracture gap (r*<sup>f</sup> *= 0.1 mm), the area where residual cancer cells are present (r*<sup>t</sup> *= 0.1 mm–0.5 mm), and the healthy bone tissue (r*<sup>b</sup> *= 5 mm). Taken from [14].*

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*=*P T*ð Þ, planning a HT treatment which employs MagS as thermo-seeds against tumors is a multiphysics

*Temperature variation of the pre-exponential term τ*<sup>0</sup> *and the Neel relaxation time τ*N*. The influence on the equilibrium and the complex magnetic susceptibility χ*<sup>0</sup> *and χ*ð Þ*f is represented. The curves are obtained for a magnetic scaffold filled with the 0.2% of magnetite nanoparticles (rmnp=10 nm, M*s*(0) = 2 emu*�*g*�<sup>1</sup>*,T*b*=150 K).*

*Results of the fitting of the magnetic susceptibility spectra of MNPs embedded in agarose: a) real part (in-phase) and b) imaginary (out-of-phase) components are presented [21]. The Debye and Cole-Cole models are used*

*Smart Nanosystems for Biomedicine, Optoelectronics and Catalysis*

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 there-

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

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

fore the hyperthermia treatment was proposed as adjuvant therapy [23].

and highly nonlinear problem [14].

potential [14].

**8**

**Figure 3.**

**Figure 2***.*

*and compared Taken from [13].*

**3.4 The hyperthermia treatment of bone tumors**

homogeneous in space [14]. At the initial time, the system is supposed to be in thermal equilibrium with a constant temperature distribution (T0=37<sup>∘</sup> C). Maxwell's equation in the frequency domain should be solved to calculate the power dissipated in the system [5]:

$$\begin{aligned} \nabla \times \overline{H} &= j\omega (\epsilon\_0 \overline{E} + \overline{f}) \\ -\nabla \times \overline{E} &= -j\omega \mu\_0 \overline{H} \end{aligned} \tag{13}$$

Eq. (14) was implemented in COMSOL using the *Bio-Heat transfer module*. The initial temperature T0 was set in all domains. The bone edges are assumed to be open boundaries. The temperature field is continuous at each tissue interface. The thermal properties of materials and tissues employed are reported in **Table 3**.

*Biomedical Applications of Biomaterials Functionalized with Magnetic Nanoparticles*

The solution of Eq. (14) is a new temperature field. As previously discussed, the different system temperature determines a change in the magnetic and heat dissipation properties of the scaffolds. Also the dielectric and thermal properties of tissues vary with temperature [14]. To account for the influence of these variations on the outcome of HT treatment, the solution of Eq. (14) should be used to evaluate the EM power solving Eq. (13) for the next time step; then the next temperature distribution can be calculated considering the changed physical properties. This solution scheme is justified by the rather different dynamic of the EM and thermal

C of the HT treatment, the following linear

¼ 1 þ *c*Δ*T* (15)

C�<sup>1</sup> and

C–47<sup>∘</sup>

Δ*p T*ð Þ *p T*ð Þ<sup>0</sup>

The thermal properties, C*<sup>p</sup>* and k, have been assumed to vary with c = 0.5%<sup>∘</sup>

In this condition the strength, frequency, and envelope of the external RF magnetic field required to treat both osteosarcoma and fibrosarcoma cells were

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

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

**Material or tissue k, Wm**�**1K**�**<sup>1</sup> C***p***, Jkg**�**1K**�**<sup>1</sup> Q** *<sup>m</sup>***, Wm**�**<sup>3</sup>** *ωb***, s**�**<sup>1</sup>** Magnetic hydroxyapatite 1.33 700 — **ϵ**-PCL 0.488 3359.2 — — Fracture gap–inflamed 0.558 <sup>2450</sup> 5262.5 <sup>6</sup>*:*<sup>95</sup> � <sup>10</sup>�<sup>3</sup> Fracture gap–ischemic 0.558 <sup>2450</sup> 5262.5 <sup>6</sup>*:*<sup>95</sup> � <sup>10</sup>�<sup>3</sup> Bone tumors: OST and FIB 0.32 <sup>1313</sup> 57,240 2.42�10�<sup>3</sup> ÷ 0.595 Bone 0.32 <sup>1313</sup> 286.2 0.262�10�<sup>3</sup>

magnetic hydroxyapatite and Fe-doped PCL are able to treat the poorly vascularized FIS for any given dimension of the residual area r*t*. This can be explained considering that *PEM* ≫ ∣*ρbCp*, *<sup>b</sup>ωb*ð Þ *T* � *Ta* ∣, for H0=10–17 mT. However,

relationship between the property p (ϵ, *σ*, C*p*, k) of each tissue and the system

The dielectric properties are assumed to increase linearly with c = 3% C�<sup>1</sup> [14].

C�1, respectively [14]. An exception was made for the heat capacity of blood,

C�<sup>1</sup> [14].

fields [14].

0.33%<sup>∘</sup>

investigated.

**3.5 Results**

47<sup>∘</sup>

**Table 3.**

**11**

*Heat transfer properties of scaffolds and tissues [14].*

In the temperature range 37<sup>∘</sup>

*DOI: http://dx.doi.org/10.5772/intechopen.89199*

which presents a negative coefficient of �1%<sup>∘</sup>

temperature [5, 14, 25]:

where *ω* is the angular frequency 2*π*f, ϵ<sup>0</sup> is the vacuum permittivity in Fm�1, *E* is the electric field vector in Vm�1, and, finally, *J* conduction current vector in the system, in A�m2. The total electromagnetic power dissipated is the sum of the power density dissipated by the scaffold and the tissues, i.e., P*EM* = P*<sup>m</sup>* + P*e*. The power deposited by the MagS, P*m*, requires Eq. (13) to be solved considering the set of Eqs. (1)–(8) but using Eq. (12) instead of (2). The power dissipated by the induced currents in tissues (P*e*) cannot be neglected, even though several mathematical models related to magnetic hyperthermia did not include it [26]. However, the dielectric losses in the system can have a significant contribution to the final temperature increase while causing the unwanted indirect heating of the nontarget tissues [5, 25].

The EM problem is solved employing the *RF module* of the commercial FEM software COMSOL Multiphysics (COMSOL Inc., Burlington, MA). The MagS studied are the intrinsic magnetic hydroxyapatite and the PCL loaded with magnetite [7], as in [14]. The dielectric properties of scaffold and tissues at T0 are reported in **Table 2**.

#### *3.4.3 The heat transfer problem*

The power deposited by the MagS and conducted to the tissues in the system of **Figure 4** modifies the temperature (*T* ¼ *T r*ð Þ , *z*, *t* ), whose spatiotemporal evolution can be evaluated using the Pennes' bioheat equation [14]:

$$
\rho C\_p \frac{\partial T}{\partial t} = \nabla \cdot (k \nabla T) + \rho\_b C\_{p,b} \alpha y\_b (T - T\_a) + Q\_{\text{met}} + P\_{\text{EM}} \tag{14}
$$

where *<sup>ρ</sup>* is the density in g�m�3, C*<sup>p</sup>* is the specific heat capacity in Jkg�1K�1, and k is the thermal conductivity in Wm�2K�1. The terms *ρ<sup>b</sup>* and C*<sup>b</sup>* are the density and heat capacity of blood, whereas the quantity *ω<sup>b</sup>* is the tissue perfusion, in s�1, i.e., the capillary contribution which acts to equilibrate the tissues with the blood temperature T*b*=37<sup>∘</sup> C. Q*<sup>M</sup>* is the metabolic heat rate generated by the tissues, in Wm�3.


#### **Table 2.**

*Electromagnetic properties of scaffolds and tissues [14].*

*Biomedical Applications of Biomaterials Functionalized with Magnetic Nanoparticles DOI: http://dx.doi.org/10.5772/intechopen.89199*

Eq. (14) was implemented in COMSOL using the *Bio-Heat transfer module*. The initial temperature T0 was set in all domains. The bone edges are assumed to be open boundaries. The temperature field is continuous at each tissue interface. The thermal properties of materials and tissues employed are reported in **Table 3**.

The solution of Eq. (14) is a new temperature field. As previously discussed, the different system temperature determines a change in the magnetic and heat dissipation properties of the scaffolds. Also the dielectric and thermal properties of tissues vary with temperature [14]. To account for the influence of these variations on the outcome of HT treatment, the solution of Eq. (14) should be used to evaluate the EM power solving Eq. (13) for the next time step; then the next temperature distribution can be calculated considering the changed physical properties. This solution scheme is justified by the rather different dynamic of the EM and thermal fields [14].

In the temperature range 37<sup>∘</sup> C–47<sup>∘</sup> C of the HT treatment, the following linear relationship between the property p (ϵ, *σ*, C*p*, k) of each tissue and the system temperature [5, 14, 25]:

$$\frac{\Delta p(T)}{p(T\_0)} = \mathbf{1} + c\Delta T \tag{15}$$

The dielectric properties are assumed to increase linearly with c = 3% C�<sup>1</sup> [14]. The thermal properties, C*<sup>p</sup>* and k, have been assumed to vary with c = 0.5%<sup>∘</sup> C�<sup>1</sup> and 0.33%<sup>∘</sup> C�1, respectively [14]. An exception was made for the heat capacity of blood, which presents a negative coefficient of �1%<sup>∘</sup> C�<sup>1</sup> [14].

In this condition the strength, frequency, and envelope of the external RF magnetic field required to treat both osteosarcoma and fibrosarcoma cells were investigated.

#### **3.5 Results**

homogeneous in space [14]. At the initial time, the system is supposed to be in

equation in the frequency domain should be solved to calculate the power dissipated

<sup>∇</sup> � *<sup>H</sup>* <sup>¼</sup> *<sup>j</sup><sup>ω</sup>* <sup>ϵ</sup>0*<sup>E</sup>* <sup>þ</sup> *<sup>J</sup>* �∇ � *E* ¼ �*jωμ*0*H*

where *ω* is the angular frequency 2*π*f, ϵ<sup>0</sup> is the vacuum permittivity in Fm�1, *E* is the electric field vector in Vm�1, and, finally, *J* conduction current vector in the system, in A�m2. The total electromagnetic power dissipated is the sum of the power density dissipated by the scaffold and the tissues, i.e., P*EM* = P*<sup>m</sup>* + P*e*. The power deposited by the MagS, P*m*, requires Eq. (13) to be solved considering the set of Eqs. (1)–(8) but using Eq. (12) instead of (2). The power dissipated by the induced currents in tissues (P*e*) cannot be neglected, even though several mathematical models related to magnetic hyperthermia did not include it [26]. However, the dielectric losses in the system can have a significant contribution to the final temperature increase while causing the unwanted indirect heating of the nontarget

The EM problem is solved employing the *RF module* of the commercial FEM software COMSOL Multiphysics (COMSOL Inc., Burlington, MA). The MagS studied are the intrinsic magnetic hydroxyapatite and the PCL loaded with magnetite [7], as in [14]. The dielectric properties of scaffold and tissues at T0 are reported

The power deposited by the MagS and conducted to the tissues in the system

where *<sup>ρ</sup>* is the density in g�m�3, C*<sup>p</sup>* is the specific heat capacity in Jkg�1K�1, and k is the thermal conductivity in Wm�2K�1. The terms *ρ<sup>b</sup>* and C*<sup>b</sup>* are the density and heat capacity of blood, whereas the quantity *ω<sup>b</sup>* is the tissue perfusion, in s�1, i.e., the capillary contribution which acts to equilibrate the tissues with the blood tem-

**Material or tissue Re[ϵ]** *σ***, Sm**�**<sup>1</sup>** Magnetic hydroxyapatite 12.5 2.1�10�<sup>3</sup> ϵ-PCL 2.20 10�<sup>4</sup> Fracture gap–inflamed 3580 0.545 Fracture gap–ischemic 1321 0.196 Bone tumors: OST and FIB 8000 0.280 Bone 192 0.0214

*<sup>∂</sup><sup>t</sup>* <sup>¼</sup> <sup>∇</sup> � ð Þþ *<sup>k</sup>*∇*<sup>T</sup> <sup>ρ</sup>bCp*, *<sup>b</sup>ωb*ð Þþ *<sup>T</sup>* � *Ta Qmet* <sup>þ</sup> *PEM* (14)

C. Q*<sup>M</sup>* is the metabolic heat rate generated by the tissues, in Wm�3.

of **Figure 4** modifies the temperature (*T* ¼ *T r*ð Þ , *z*, *t* ), whose spatiotemporal

evolution can be evaluated using the Pennes' bioheat equation [14]:

C). Maxwell's

(13)

thermal equilibrium with a constant temperature distribution (T0=37<sup>∘</sup>

*Smart Nanosystems for Biomedicine, Optoelectronics and Catalysis*

in the system [5]:

tissues [5, 25].

in **Table 2**.

perature T*b*=37<sup>∘</sup>

**Table 2.**

**10**

*3.4.3 The heat transfer problem*

*ρCp ∂T*

*Electromagnetic properties of scaffolds and tissues [14].*

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<sup>∘</sup> 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 r*t*. This can be explained considering that *PEM* ≫ ∣*ρbCp*, *<sup>b</sup>ωb*ð Þ *T* � *Ta* ∣, for H0=10–17 mT. However,


#### **Table 3.**

*Heat transfer properties of scaffolds and tissues [14].*

of 5 mm. An external uniform and static magnetic flux density field of strength B0 is supposed to be applied along the z-axis of the system. The magnetic composite nanomaterial will magnetize in a nonlinear way according to the following

*Biomedical Applications of Biomaterials Functionalized with Magnetic Nanoparticles*

*<sup>M</sup>* <sup>¼</sup> *Ms<sup>ϕ</sup> coth* ð Þ� *<sup>ζ</sup>* <sup>1</sup>

where all symbols have the previous definition. As presented in **Table 1**, the magnetization response of the scaffolds varies from a minimum of 0.4 emu�g�<sup>1</sup> to a maximum of 25 emu�g�1. Considering this nonlinear material property, the problem is the determination of the spatial distribution of the magnetic field, i.e., the solution of the following magnetostatic problem employing the scalar magnetic

> ∇ � *H* ¼ 0 *H* ¼ �∇*ψ <sup>m</sup>*

Due to the presence of the magnetic material, the magnetic field flux lines concentrate in the prosthetic implant, implying that the norm of the gradient of magnetic density field between the MagS and the diamagnetic tissues is relevant [6]. In the literature, it is reported that if the magnetic density field gradients are higher than 1.3 Tm�1, then the magnetic force exerted on a population of surrounding MNPs would be sufficient to overcome their weight force and set them in motion toward the scaffold [13, 28]. This is a very simplified view of the problem. Indeed, several relevant physical and biological factors took part to the transport phenomena of MNP attraction to the MagS in the presence of a static magnetic field. As defined by Grief and Richardson, the magnetic force vector *Fm* on an ensemble

*Fm* <sup>¼</sup> *Ms*2*Vm*<sup>2</sup>

<sup>6</sup>*kBT* <sup>∇</sup> *<sup>B</sup>* 

where M*<sup>s</sup>*<sup>2</sup> and V*<sup>m</sup>*<sup>2</sup> are the saturation magnetization, in Am�1, and the volume of the spherical magnetic nanoparticles, in nm�3, to be attracted, respectively. The nanoparticles conjugated with growth factors or drugs are hence set in motion with

> *vm* <sup>¼</sup> *Fm* 6*πηrm*<sup>2</sup>

where r*<sup>m</sup>*<sup>2</sup> is the radius of the magnetic carriers. The term *η* is the viscosity of the medium in which the nanoparticles move, in Pa�s. This medium is often assumed to be water (*ηw*=1�10�3Pa�s); however, actually the MNPs that move from the capillaries of bone tissues into the fracture gap are dragged in a solution of water, proteins (e.g., collagen, fibrin, and plasmin), and other macromolecules. Therefore, the extracellular matrix (ECM) can be assumed to be the medium in which the

After having solved Eq. (17) and calculated Eqs. (18) and (19), the spatiotemporal distribution of the concentration of MNPs (C*mnp*, mol�m3) functionalized with the drug can be obtained computing the following diffusion-convection equation [13]:

of MNPs in saturation regime can be evaluated as follows [12]:

*ζ*

(16)

<sup>2</sup> (18)

(17)

(19)

relationship [13]:

*DOI: http://dx.doi.org/10.5772/intechopen.89199*

potential *ψ <sup>m</sup>* [13]:

a velocity v*<sup>m</sup>* equal to [12, 13]:

**13**

MNPs move, implying that *<sup>η</sup>w*=1�103Pa�s [13].

**Figure 5.**

*(a) 2D temperature distribution after 60 min of treatment using a RF magnetic field of 30 mT and working at 293 kHz. A OST with r*t*=0.5 mm is considered. (b) Average temperature in the region with residual FIB cells. (c) Average temperature in the region with residual OST cells. (MHA = magnetic hydroxyapatite).*

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<sup>∘</sup> . 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.
