*3.4. Release Study*

Before we start to evaluate the quercetin-release kinetics from MNPs into PBS/EtOH (Vol. % 50:50), we want to emphasize that the results were obtained by applying external stationary and alternating magnetic fields. The underlying idea was to enable fine-tuned and controlled quercetin-release kinetics, which is certainly very important in a widespread, high-demand application of high-demand drug delivery via nanocarriers.

**Figure 7.** Volume size distributions of bare MNPs, PEG-coated MNPs and quercetin-loaded PEG\_MNPs.

The in vitro quercetin release profile from synthesized and carefully designed MNPs was studied in duration up to 8 h with a dialysis membrane and in the presence of external magnetic fields. The results are shown as the cumulative released mass of quercetin in Figure 8. Within 8 h, only up to 5% of quercetin has been released depending on the experimental conditions.

A similar sustained-release profile of quercetin from alginate NPs at pH 7.4 has been reported earlier [53], where only 10% of quercetin release was observed after 12 h, while after 9 days, only 50% of the quercetin got released. In another study, the quercetin release from the functionalized magnetite NPs was conducted in acidic and basic pH and cumulative release reached 3.7% after 6 h [14]. A similar prolonged release has also been found for quercetin release from polylactide NPs, which showed almost 60% quercetin released after 4 days [54]. The observed slow quercetin-release kinetics offers prolonged exposure to the drug and improves its efficiency compared with free drugs [55]. This is considered as an advantage because the burst release of drugs leads to a significant premature quantity of the drug that can result in toxicity [21]. For example, the quercetin at a concentration between 0 and 200 × <sup>10</sup>−<sup>6</sup> mol dm−<sup>3</sup> could decrease antioxidant activity while quercetin at a concentration of (0.2–1) × <sup>10</sup>−<sup>6</sup> mol dm−<sup>3</sup> possesses pro-oxidant activity [56]. In addition, quercetin release was affected by oxidative degradation process in PBS solution after continuously stirring for 6 h; this is yet another reason to employ nanocarriers for quercetin delivery [14,57,58]. Therefore, we prepared MNPs onto which quercetin easily adsorbs and has a prolonged stability and duration. The net result is quercetin release for a prolonged time. A first-order release profile of quercetin from Fe3O4-quercetin-copolymer NPs was revealed by Barreto et al. [3]. On the other hand, the release rate of quercetin from superparamagnetic magnetite NPs coated with chitosan, PEG and dextran was found to be of zero-order kinetics (linear with time) [41].

The assumptions in release kinetics experiments were as follows:

(i) The total amount of quercetin remained practically constant during the whole release experiment; (ii) both the quercetin solution within the membrane interior and in the membrane exterior were homogeneous due to the constant stirring and the fact that quercetin solution was never saturated; (iii) the thickness of the membrane provides the equal rate constants from the membrane interior to the membrane exterior, and vice versa; (iv) the volume within the membrane interior *V*<sup>i</sup> and the volume exterior to the membrane *V*<sup>o</sup> were constant during all performed release experiments. This is because *V*<sup>i</sup> = 1 mL and *V*<sup>o</sup> = 150 mL, *V*<sup>i</sup> < *V*o.

As a preliminary approach in working out the data, a simple model of single exponential decay was meant to be used in which the fraction of the released drug is Φ = 1 − *exp*(−*kt*), where *Φ* is a fraction of drug present in the outer volume *V*<sup>0</sup> (other fractions are in the inner volume *V*i. *Φ*i, and in the membrane, *Φ*m) [59]. The coefficient *k* is related to the apparent kinetics and, as such, cannot provide information about the actual release rate from the nanocarriers into the interior volume *V*i. However, the problem with this simple formula is the equilibrium value Φ<sup>o</sup> = 1 which is achieved when the elapsed

time is sufficiently large (*t* → +∞). In our release kinetics experiments, it is invariably between 0.04 and 0.10. Thus, the dialysis bag with its content has to be considered as a source of drug molecules. It is not possible to know the total mass of the drug that is amenable to be released, but it can be estimated from the value of *m*0, which occurs in another simple model:

$$m(t) = m\_0 \left(1 - e^{-kt}\right), \frac{m}{m\_0} = 1 - e^{-kt} \tag{2}$$

where *m*(*t*) is the released mass, not a fraction of, at time *t*, *m*<sup>0</sup> is the total released quercetin mass from the dialysis bag after infinite time, and *k* is the rate coefficient of actual release kinetics of the dialysis bag membrane. The problem is that *m*<sup>0</sup> is not experimentally well defined, i.e., it is only approximately constant across the series of experiments. Fitting the release experimental data obtained at various magnetic fields and at three different temperatures using this simple model (Table 2 and Figures 8 and 9) resulted as expected in a fairly narrow interval of *m*<sup>0</sup> values with average *m*<sup>0</sup> = (1.48 ± 0.34) mg.

Each experiment was done in duplicate. This was fully justified to avoid averaging the measurement results and use the mean values of the two fitting procedures because the product, *kt*, was always rather small (Table 2). This was the case because, if *<sup>m</sup>*<sup>1</sup> <sup>=</sup> *<sup>m</sup>*0,1- <sup>1</sup> − *<sup>e</sup>*−*k*1*<sup>t</sup>* , *<sup>m</sup>*<sup>2</sup> <sup>=</sup> *<sup>m</sup>*0,2- <sup>1</sup> − *<sup>e</sup>*−*k*2*<sup>t</sup>* and *m* = *m*<sup>0</sup> - <sup>1</sup> <sup>−</sup> *<sup>e</sup>*−*kt* where *m* = 1/2(*m*<sup>1</sup> + *m*2) and *m*<sup>0</sup> = 1/2(*m*0.1 + *m*0.2), the following is obtained:

$$
\varepsilon^{-kt} = \frac{m\_{0.1}}{m\_{0.1} + m\_{0.2}} \varepsilon^{-k\_1 t} + \frac{m\_{0.2}}{m\_{0.1} + m\_{0.2}} \varepsilon^{-k\_2 t} \tag{3}
$$

Since the product *kt* is always very small, it turns out that a simple formula,

$$k = \frac{m\_{0.1}}{m\_{0.1} + m\_{0.2}}k\_1 + \frac{m\_{0.2}}{m\_{0.1} + m\_{0.2}}k\_2\tag{4}$$

can be used. Furthermore, it is very often *<sup>m</sup>*0,1<sup>≈</sup> *<sup>m</sup>*0,2 which gives *<sup>k</sup>* <sup>≈</sup> <sup>1</sup> <sup>2</sup> (*k*1+ *k*2).

It is important to emphasize that the intent of this study was not only to estimate the time required for the complete quercetin release from nanocarriers, but also to investigate and demonstrate how the stationary and alternating field affect the rate of quercetin release. In our previous work [35], we have shown how the simultaneous application of stationary and alternating field can accelerate the release of drug from aggregates of MNPs. Being relatively unstable and dysfunctional, aggregates vigorously moved under the influence of the alternating field which resulted in drug release enhancement. MNPs that were additionally functionalized and stabilized by the PEG layer were used for this purpose in the present study. Figure 8 shows the release kinetics of quercetin at the temperature of 30 ◦C in the absence of the magnetic field and under an alternating field of 10 kHz, 50 kHz and 100 kHz at a constant stationary magnetic field *B* = 11 mT.

Since we used a dialysis membrane bag, the first step was to perform calibration experiments with free quercetin following the same protocol as in experiments with MNPs to get information about membrane permeation kinetics during the first several hours (*<sup>k</sup>* = 6.617 × <sup>10</sup>−<sup>3</sup> min<sup>−</sup>1; *<sup>k</sup>* = 9.637 × <sup>10</sup>−<sup>3</sup> min−<sup>1</sup> and *<sup>k</sup>* = 14.592 × <sup>10</sup>−<sup>3</sup> min−<sup>1</sup> at 25 ◦C, 30 ◦<sup>C</sup> and 37 ◦C, respectively). We selected the MWCO cellulose membrane (8 kD) membrane based on the porosity of the dialysis membrane as well as to avoid possible adverse interactions between quercetin and the membrane materials. The cellulose membrane has recently been used in the measurement of both, drug diffusion and drug release rates from varied formulations, such as creams and hydrogels [7].

The rate constant of the membrane when there was non-saturated quercetin solution in the membrane bag indicated the barrier effects of dialysis membrane and showed faster membrane permeation kinetics at higher temperatures (*k* = 0.0066 min−1, 0.0096 min−<sup>1</sup> and 0.0146 min−<sup>1</sup> at 25 ◦C, 30 ◦C and 37 ◦C, respectively), as expected. The rate constants obtained in our experiments are larger than those obtained in release kinetics of doxorubicin by Yu et al., where *<sup>k</sup>* = 0.019 ± 0.003 *<sup>h</sup>*−<sup>1</sup> = 0.0003 min−<sup>1</sup> [60].

With no magnetic field and at 30 ◦C, the rate constant is *<sup>k</sup>* = 0.0019 ± 0.0001 min−1. At 10 kHz, 50 kHz and 100 kHz and under *B* =11.0 mT the rate constant values were *<sup>k</sup>* = 0.0032 ± 0.0009 min−1, *<sup>k</sup>* = 0.0019 ± 0.0001 min−<sup>1</sup> and *<sup>k</sup>* = 0.0034 ± 0.0013 min−1, respectively. Thus, the release of the quercetin is the faster at the highest field frequency. It is evident that the alternating magnetic field can accelerate the quercetin release at a given stationary magnetic field.

**Table 2.** The experimental release kinetics under the permanent magnetic fields of 7.9 mT and 11.0 mT and three frequencies (10 kHz, 50 kHz and 100 kHz) at temperatures 25 ◦C, 30 ◦C and 37 ◦C.


**Figure 8.** The representative cumulative release profiles for the quercetin from MNPs through dialysis membrane under the stationary magnetic field *B* = 11 mT and alternating field with frequencies 10 kHz, 50 kHz and 100 kHz at 30 ◦C.

**Figure 9.** The representative cumulative release profiles for the quercetin from MNPs through dialysis membrane at 25 ◦C using two stationary magnetic fields and three different frequencies of alternating magnetic field (**A**) 100 kHz, (**B**) 50 kHz and (**C**) 10 kHz.

Our next task was to see the effect a stationary magnetic field on release kinetics. Figure 9 shows the dependence of quercetin-release kinetics at 25 ◦C under the alternating field frequency of 10 kHz and stationary magnetic field of *B* = 7.9 mT and 11 mT (Figure 9C). Under the stationary magnetic field of 7.9 mT, the membrane bag has released quercetin with a rate constant *<sup>k</sup>* = 0.0043 ± 0.0003 min−1. When a stronger stationary field of 11 mT is applied, the release kinetics becomes slower, *<sup>k</sup>* = 0.0024 ± 0.0012 min−1. The opposite effect on the release kinetics was observed at the highest 100 kHz frequency (Figure 9A), where an increase in the rate constant with increasing stationary field by almost 95% was observed (at *<sup>B</sup>* = 7.9 mT and *<sup>B</sup>* = 11 mT, *<sup>k</sup>* = 0.0015 ± 0.0002 min−1; *<sup>k</sup>* = 0.0029 ± 0.0004 min<sup>−</sup>1, respectively).

Since the opposite effects of the influence of a stationary magnetic field on the rate constant are obtained at different frequencies of the alternating field, our next analysis focuses on the measurements of the rate constants at the same stationary field and frequency, but at different temperatures. Comparing the constants of the apparent release rate of quercetin at a stationary field of 7.9 mT with an increase in temperature from 25 to 37 ◦C (*<sup>k</sup>* = 0.0022 ± 0.0004 min−1, *<sup>k</sup>* = 0.0022 ± 0.0008 min−<sup>1</sup> and *<sup>k</sup>* = 0.0025 ± 0.0002 min−<sup>1</sup> for 25 ◦C, 30 ◦C and 37 ◦C, respectively), it can be seen that the rate constant slightly increases with increasing temperature only above 30 ◦C. The same effect was observed under the stronger stationary field (*B* = 11 mT, see Table 2). At higher temperatures kinetic energy of quercetin molecules is larger or, putting differently, their diffusivity is larger and more quercetine is released and detected within the same time interval. If we compare the rate constants at the same temperature (e.g., 30 ◦C), the rate constant obtained at a stronger stationary field (*<sup>B</sup>* = 11 mT) and 50 KHz, is smaller (*<sup>k</sup>* = 0.0019 ± 0.0001 min−1) than at a weaker field of 7.9 mT (*<sup>k</sup>* = 0.0022 ± 0.0008 min−1). It is obvious that when overcoming stationary field, the thermal energy of the MNPs is large enough to increase the movement of the MNPs and increase quercetin release. The influence of the temperature under the constant stationary field and the frequency of the alternating field clearly shows that the amount of quercetin released increases with increasing temperature at almost all applied frequencies of the alternating fields except at *B* = 11 mT and frequencies *f* = 100 and 50 kHz and at *B* = 7.9 mT and *f* = 50 kHz, which is also reflected in the magnitudes of the quercetin release rate constants. For example, at *<sup>B</sup>* = 11 mT and *<sup>f</sup>* = 100 kHz, *<sup>k</sup>* = 0.0029 ± 0.0004 min<sup>−</sup>1; *<sup>k</sup>* = 0.0034 ± 0.0013 min−<sup>1</sup> and *<sup>k</sup>* = 0.0038 ± 0.0013 min−<sup>1</sup> for 25 ◦C, 30 ◦C and 37 ◦C, respectively.

Thus, it was shown here that by choosing the temperature, the quercetin release rates can cover a wide range of values. We have shown that the synthesized MNPs are suitable nanocarriers for quercetin, especially because the required drug dose can be delivered in a prolonged time. Since the average half-life of quercetin absorbed in the human body is 3.5 h [61], this study represents a significant improvement for flavonoid delivery, which, when loaded into MNPs, remains stable in a prolonged period of time.

## **4. Conclusions**

In summary, superparamagnetic magnetite nanoparticles (MNPs) were prepared by solvothermal method and stabilized by biocompatible poly (ethylene glycol) PEG-4000 Da. The X-ray powder diffraction patterns of the synthesized bare and PEG-coated MNPs confirmed the cubic inverse spinel structure of MNPs. The size and morphology of bare and PEG-coated MNPs have been obtained by SEM, TEM and AFM analysis. By AFM is showed that bare MNPs have cluster structure with a very rough surface and when bare MNPs is coated with PEG, the roughness of the MNPs surface has been increased by PEG coating, for almost 100%, from 5.58 ± 1.06 nm to 10.9 ± 2.1 nm, confirming the effective coverage of the bare MNPs by PEG. A size histogram of bare mesoporous MNPs obtained using SEM micrographs shows a broader size distribution than PEG-coated MNPs (*d*ave = 103.4 ± 0.7 nm and 101.0 ± 0.9 nm for bare and PEG-coated MNPs, respectively), indicating that PEG decreased the magnetic interaction among the particles and prevent their agglomeration. Nitrogen adsorption–desorption of bare MNPs and PEG-coated MNPs confirmed their mesoporosity. The PEG molecules were successfully coated on the surface of MNPs, as revealed by FTIR spectroscopy. The PEG-coated MNPs spectrum showed a strong C-O-C ether stretch at 1110 and 1381 cm−1. The results of the saturation magnetization confirmed the superparamagnetic properties of synthesized bare and PEG-coated MNPs. The stability of MNPs improved after PEG modification, indicated by the increase in zeta potential from (−30.6 ±0.7) mV to (−35.1 ± 1.5) mV.The loading of quercetin into MNPs was confirmed by FTIR spectroscopy and thermogravimetric analysis. The UV/VIS spectra of the supernatant revealed a loading efficiency of (20.2 ± 1.3%). The quercetin release studies in vitro followed by UV/VIS spectroscopy have shown the prolonged quercetin-release kinetics from MNPs that could be controlled

by using combined stationary and alternating magnetic fields. The prolonged quercetin release, as an important characteristic for targeted drug delivery, the study of the kinetic parameters of the quercetin release process and the increased response of quercetin release under both the lower stationary magnetic field (7.9 mT) and the higher frequency of alternating magnetic field (100 kHz) suggest that the fine tuning of the release as desired along with synergism of physicochemical and superparamagnetic properties enables the great potential of MNPs as a promising targeted flavonoid delivery system.

**Author Contributions:** S.Š. designed research; L.M., I.E. and A.S. performed research; L.M., G.B. and S.Š. analysed data and contributed to the discussion; L.M., S.Š. and G.B. wrote the paper; all authors approved the final version of the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Croatian Science Foundation under the project IP-2016-06- 8415. The funders had no role in the design and conduct of this study, collection and interpretation of the data, or preparation and approval of the manuscript.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data available on request due to restrictions e.g., privacy or ethical. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to extreme quality of data.

**Acknowledgments:** The authors thank T. Mrla for experimental setup and instrument development for controlling the electric current (*I* = 100 mA).

**Conflicts of Interest:** The authors declare no conflict of interest.
