## 4 Applications of Fe\({}_{3}\)O\({}_{4}\) Nanoparticles
### Biomedical Applications (Therapeutic and Diagnostic Technologies)
#### 4.1.1 Contrast Agents for Magnetic Resonance Imaging (MRI)  
Magnetic contrast agents for MRI are some of the most promising applications of iron oxide nanoparticles. Several commercial iron oxide nanoparticles are used as MRI contrast agents, such as Feridex (dextran-coated Fe\({}_{3}\)O\({}_{4}\) and \(\gamma\)-Fe\({}_{2}\)O\({}_{3}\)), Resovist (carboxydextran-coated Fe\({}_{3}\)O\({}_{4}\)), and Combidex (dextran-coated Fe\({}_{3}\)O\({}_{4}\)) [97, 98, 99]. Contrast agents have been used to enhance the contrast and improve the resolution of diagnostic MRI by reducing either the longitudinal (T\({}_{1}\)) or transverse (T\({}_{2}\)) relaxation time of water protons. Consequently, two types of contrast agents, T\({}_{1}\) and T\({}_{2}\), enhance the positive (bright signal) or negative (dark signal) contrast, respectively. As presented in Equations (1) and (2), the inverse of the relaxation time (1/T\({}_{1}\) and 1/T\({}_{2}\)) is called the relaxation rate and is plotted as a function of the iron concentration to obtain linear lines. From those data, we are able to determine the slopes that are relaxivities r\({}_{1}\) and r\({}_{2}\), respectively. The higher the value for either r\({}_{1}\) or r\({}_{2}\), the better the contrast performance of T\({}_{1}\) or T\({}_{2}\) contrast agents, respectively. In addition, the ratio of relaxivities, r\({}_{2}\)/r\({}_{1}\), can be used to evaluate the potential of a contrast agent, with lower values preferred for T\({}_{1}\) agents and higher values for T\({}_{2}\) agents. Although Fe\({}_{3}\)O\({}_{4}\) nanoparticles have been extensively investigated as T\({}_{2}\) contrast agents [100, 101, 102, 103, 104], increasing efforts to use Fe\({}_{3}\)O\({}_{4}\) nanoparticles as T\({}_{1}\) contrast agents have been reported recently [98, 105]. In-depth mechanisms of T\({}_{1}\)-weighted and T\({}_{2}\)-weighted contrast agents in MRI and criteria for NPs as efficient MRI contrast agents were discussed in previous reviews [97, 98]. These investigations were conducted with both superparamagnetic and ferrimagnetic Fe\({}_{3}\)O\({}_{4}\) NPs, usually including functionalized NPs or core-shell architectures for better colloidal stability and biocompatibility. \[\frac{1}{\text{T}_{1}}=\frac{1}{\text{T}_{1}([\text{Fe}]=0)}+\text{r}_{1}[ \text{Fe}] \tag{1}\]  
\[\frac{1}{\text{T}_{2}}=\frac{1}{\text{T}_{2}([\text{Fe}]=0)}+\text{r}_{2}[ \text{Fe}] \tag{2}\]  
Different geometries, sizes, and nanostructures of Fe\({}_{3}\)O\({}_{4}\)-based nanoparticles have been investigated as MRI contrast agents. [PERSON] et al. prepared ferrimagnetic uniform-sized Fe\({}_{3}\)O\({}_{4}\) nanocubes with an edge length of 22 nm functionalized with PEG-phospholipids to provide excellent colloidal stability in aqueous media and great biocompatibility [106]. The colloid-containing functionalized 22 nm-sized Fe\({}_{3}\)O\({}_{4}\) nanocubes exhibit a very high r\({}_{2}\) relaxivity of 761 mM\({}^{-1}\) s\({}^{-1}\), which achieved the theoretically predicted maximum r\({}_{2}\) relaxivity. Figure 8a-d present the morphology of nanocubes, an image of a stable colloid, and in vivo images of tumors visualized with and without nanocube contrast agents. T\({}_{2}\)-weighted images produced with different sizes of nanocubes in various concentrations and their color-coded images are shown in Figure 8e,f. Separately, hyperbranched polyglycerol-grafted Fe\({}_{3}\)O\({}_{4}\) NPs (size from 6 to 9 nm) were successfully synthesized with excellent colloidal stability in water, phosphate-buffered saline (PBS), and cell culture medium [107]. These NPs exhibit a contrast enhancement effect on T\({}_{2}\)-weighted sequences. Moreover, highly crystalline 8 nm Fe\({}_{3}\)O\({}_{4}\) NPs were functionalized with an epoxy silane, (3-glycidyloxypropyl) trimethoxysilane, followed by the use of three-membered ring-opening chemistry to further graft polymers (e.g., polyetheramine and arginine) to the particle surface [108].