*4.2.2 Including the cells and the biological elements*

Now, we assume that the MDD system is constituted by an active GF with concentration C*chemo* present at the MNP surface. The presence of such specific biomolecule is supposed to represent a direct chemotactic stimulus for the human mesenchymal stem cells (MSCs) present in the surrounding host bone tissue [13]. Chemotaxis is the phenomenon of cellular migration directed toward a chemical stimulus. This means that the osteoprogenitor cells can respond to the chemical signaling stimulus carried by the MNPs. The magnitude of the chemotactic stimulus can be assumed to be equal to [13]:

$$K\_{chemo} = \frac{D\_c}{\mathcal{C}\_{chemo}}\tag{21}$$

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

*Biomedical Applications of Biomaterials Functionalized with Magnetic Nanoparticles*

*(a) Normalized magnetic field distribution (H=H*0*). (b) Normalized MNP concentration profile after 48 h*

acting on the scaffolds magnetic properties or geometry [13].

*(Cmnp=C*m, <sup>0</sup>*). (c) MSC density after 24 h (Cc=C*c, <sup>0</sup>*).*

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

allows the manufacturing of a magnetic-responsive biomaterial with

MSCs in a way dependent on the geometrical and material properties.

The authors would like to sincerely thank Prof. G. Mazzarella for the helpful

**5. Conclusions**

**Figure 6.**

**Acknowledgements**

**Conflict of interest**

**15**

discussions and suggestions to this work.

The authors declare no conflict of interest.

presented, the final cell density pattern can be predicted and controlled by tuning or

This chapter presented an innovative family of nanocomposite magnetic biomaterials and their biomedical applications. Mixing magnetic nanoparticles with traditional biomaterials, e.g., polymer or ceramics, or chemically doping them

multifunctional properties. The so-called magnetic scaffolds have been studied for their ability to transduce an external magnetic signal into mechanical and biological outcome, thus proving to be a powerful platform for cell and tissue stimulation [1–4]. Exploiting the ability of the MNPs embedded in the biomaterial to dissipate power when exposed to a radio-frequency magnetic field makes MagS a valid candidate to perform local hyperthermia treatment on residual cancer cells. In this chapter the physical properties and the magnetic susceptibility of these novel composite nanosystems are investigated. Then an in silico model to study the feasibility of employing MagS in the treatment of bone cancers, such as osteosarcomas and fibrosarcomas, is presented [14]. The results indicate that further research on the nanomaterial is required to develop an effective and tailored magnetic scaffold. Finally, the potential of MagS to serve as an in vivo attraction site to enhance the magnetic drug delivery of growth factors is faced. To predict the final concentration pattern, a mathematical model which relates the nonlinear magnetic problem and the mass transport issue is presented. Furthermore, the link between these two aspects and the biological influence on cellular migration is challenged [13]. The results indicate that MagS are able to attract MNPs and exert an indirect action on

Given C*mnp* from Eq. (20), the spatial pattern of the MSCs exposed to the biological signal carried by the MNPs is the solution of the mass balance for the cell population C*c*:

$$\frac{\partial \mathbf{C}\_{\mathbf{c}}}{\partial t} = \nabla \cdot \left[ D\_{\mathbf{c}} \nabla \mathbf{C}\_{\mathbf{c}} - \mathbf{C}\_{\mathbf{c}} K\_{chemo} \nabla \mathbf{C}\_{mnp} \right] \tag{22}$$

Similar to Eq. (20), Eq. (22) is subject to Dirichlet and Neumann boundary conditions, i.e., the diffusive flux of cell population should be null at the scaffold surface, and the cell concentration at host bone is set to a constant value of C*c*, 0. Moreover, the cell concentration in the fracture gap is assumed to be null at the initial time.

With this set of equations, it is possible to model the role of magnetic scaffolds as part of a MDD system studying the influence on the cellular migration and the scaffold colonization, providing valuable insight into the use of MagS as a tool in tissue engineering.

#### *4.2.3 Results from the case study*

The magnetic scaffolds exposed to the static magnetic flux density field B0 respond 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 *Biomedical Applications of Biomaterials Functionalized with Magnetic Nanoparticles DOI: http://dx.doi.org/10.5772/intechopen.89199*

#### **Figure 6.**

*∂Cmnp*

*Smart Nanosystems for Biomedicine, Optoelectronics and Catalysis*

C*mnp*ð Þ¼ *r*, *z*, *t* ¼ 0 0 as initial condition.

can be assumed to be equal to [13]:

population C*c*:

initial time.

**14**

tissue engineering.

*4.2.3 Results from the case study*

*4.2.2 Including the cells and the biological elements*

*∂Cc*

*<sup>∂</sup><sup>t</sup>* <sup>¼</sup> <sup>∇</sup> � *Dmnp*∇*Cmnp*

*vm* is inserted in the *Transport of Dilute Species* interface to solve Eq. (20).

Now, we assume that the MDD system is constituted by an active GF with concentration C*chemo* present at the MNP surface. The presence of such specific biomolecule is supposed to represent a direct chemotactic stimulus for the human mesenchymal stem cells (MSCs) present in the surrounding host bone tissue [13]. Chemotaxis is the phenomenon of cellular migration directed toward a chemical stimulus. This means that the osteoprogenitor cells can respond to the chemical signaling stimulus carried by the MNPs. The magnitude of the chemotactic stimulus

*Kchemo* <sup>¼</sup> *Dc*

Given C*mnp* from Eq. (20), the spatial pattern of the MSCs exposed to the biological signal carried by the MNPs is the solution of the mass balance for the cell

*<sup>∂</sup><sup>t</sup>* <sup>¼</sup> <sup>∇</sup> � *Dc*∇*Cc* � *CcKchemo*∇*Cmnp*

Similar to Eq. (20), Eq. (22) is subject to Dirichlet and Neumann boundary conditions, i.e., the diffusive flux of cell population should be null at the scaffold surface, and the cell concentration at host bone is set to a constant value of C*c*, 0. Moreover, the cell concentration in the fracture gap is assumed to be null at the

With this set of equations, it is possible to model the role of magnetic scaffolds as

part of a MDD system studying the influence on the cellular migration and the scaffold colonization, providing valuable insight into the use of MagS as a tool in

The magnetic scaffolds exposed to the static magnetic flux density field B0 respond 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

*Cchemo*

(22)

(21)

at the host bone interface. In the fracture gap, it is assumed that

D*mnp* is the diffusion coefficient of MNPs in the medium, assumed to be equal to 10�9ms�2. The analytical mass balance is subject to the outflow condition at the scaffold surface, while a constant initial concentration of MNPs (C*m*, 0) is assumed

The magnetic field distribution (Eq. (17)) is derived by solving numerically the magnetostatic problem for the geometry depicted in **Figure 4** using the *Magnetic Fields No Currents* package from the *AC/DC module* of COMSOL Multiphysics. Then

� *vm*∇*Cmnp* (20)

*(a) Normalized magnetic field distribution (H=H*0*). (b) Normalized MNP concentration profile after 48 h (Cmnp=C*m, <sup>0</sup>*). (c) MSC density after 24 h (Cc=C*c, <sup>0</sup>*).*

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].
