The currently observed increased interest in metal nanoparticles (NPs) is caused by discovering their unique physical and chemical properties features of biological action, which often differ from the properties of this substance in a macrodispersed form. Good prospects are for metal NPs in medicine, particularly dermatology. A new direction of developing nano preparation is forming a complex between known drugs and NPs, which gives the possibility of a deeper penetration of such complex drugs into the pathological process. To maximize the benefits of nanoscale materials, accurate control of their concentration is a necessary condition. In particular, this is necessary regarding magnetic drug targeting to maximize the efficacy and minimize the toxicity of the nanomaterials. Towards this significant yet chronic problem, various strategies are currently under development1.

Some of the concentration determination methods apply to the ensemble of physical properties of dispersions of NPs (for example, light absorption), while others, such as microscopy and sensors, directly count individual particles. The UV-Vis spectroscopy2, turbidimetry3, and dynamic light scattering (DLS)4 are three optical methods that measure the intensity of light upon absorption or scattering by nanoparticles. The turbidimetry method measures a decrease in the intensity of the incident light caused by light scattering of nanoparticle suspensions. The values measured by these methods are ensemble properties of nanoparticle suspensions, which can reflect averaged concentrations with statistical significance. The limitations of these three methods lie in the complexity of measuring extinction/scattering coefficient or employing a reference sample with a known concentration.

Laser-induced breakdown detection (LIBD) is another method measuring the plasma generation from nanoparticles irradiated by an intense, focused laser in a suspension. It has a wide application in various particles of different sizes, but a special laser system is required to ensure the breakdown of nanoparticles. Unlike measuring ensemble quantities of nanoparticle dispersions, several techniques enable counting individual nanoparticles under direct visualization5.

Resistive-pulsed sensing, inductively coupled plasma mass spectrometry (ICPMS), and light scattering particle counter are three methods that can count particles. They provide concentration information based on the signal pulses from a sensor, and a standard reference sample is usually required for calibration. The ICPMS is a highly sensitive and rapid analytical technique for elemental analysis at ultra-low concentrations. The samples in traditional ICPMS are usually metal ions dissolved in solution, and the concentration of total metal can be calculated based on the averaged intensity of the ion peak over a measuring period6.

Mössbauer spectroscopy is widely used to determine magnetic NPs (MNPs). The methods based on the analysis of X-ray diffraction data have a reasonably wide range of determined parameters (phase composition, structure, average size, and morphological characteristics of nanocrystals. However, using this method can lead to significant errors due to the influence of various factors on the effect of broadening of diffraction maxima and others. When the Mössbauer spectroscopy method is used for measurements at 4.2 K, the nanoparticles typically exhibit well-defined but complicated hyperfine spectra that may present some evaluation problems but eventually yield reliable results. The different situation was when nanoparticles of Fe3O4 (magnetite) and gamma-Fe2O3 (maghemite) had been studied by Mössbauer spectroscopy at room temperature when they are superparamagnetic. The magnetic hyperfine fields were averaged to zero, making Mössbauer spectroscopy useless for the characterization of superparamagnetic NPs7.

Among the magnetic NPs suitable for use in medicine, particles of iron oxide Fe3O4 can be distinguished due to their biological compatibility with biological objects. These particles are superparamagnetic and cannot be studied by the Mössbauer spectroscopy method at room temperature. The characterization of magnetic iron oxide NPs is important for their use as contrast agents in magnetic resonance imaging, as carriers for magnetic drug targeting, for local hyperthermia. Magnetic resonance imaging (MRI) can be used for magnetic particles concentration determination8.

Magnetic nanoparticles change the electromagnetic excitation spectra of organic molecules of the human body. Registration of these spectra by MRI provides information on the distribution of particles in space and, consequently, the concentration of drugs coupled with them. The special features of the MRI method are the high cost and the associated with it less availability and give information about NPs distribution. Analysis of existing methods shows no universal method for determining the concentration of NPs of various types9. Each of the listed methods has both certain advantages over others and limitations. In particular, developing a more straightforward method applicable to in vivo and in vitro use for superparamagnetic nanostructures at room temperature is important. This study aims to describes a simplified acoustomagnetic method (AMM) of detecting magnetic particles concentration10 and experimental procedure for determining the concentration of MNPs in a colloidal solution that is the model of the cosmetic products with MNPs both in vivo and in vitro that is important in dermatology as the possibility of penetration through the skin, in particular through the sebaceous glands and hair follicles. Such carriers provide long-term drug release and protect it from degradation.

Materials

The object of study was a colloidal solution of nanoparticles based on Fe3O4 in a mixture of oleic acid and kerosene, a model sample of a cosmetic product colloidal solution. The average particle size with magnetite was 50-150 nm, size of Fe3O4 was much less. Oleic acid prevents powder particles from sticking together in solution, and kerosene provides the necessary viscosity. For biophysical applications, it is recommended to use a solution with a concentration of nanoparticles not more than 5%. In our experiments, the weight concentration of the actual magnetite was no more than 0.15%. The viscosity of the suspension was chosen close to the viscosity of the blood (5 x 10-3 poise).

Methods

The experimental verification of the applicability of the AMM method was carried out using the setup shown in Figure 1. The scheme consists of three component blocks (A, B, and C), allowing to determine the concentration of nanoparticles in a vessel with a studied medium. Block A is a conditional image of a plot of a model studied medium with nanoparticles affected by a constant magnetic field Hd and ultrasonic radiation (US). The result of these actions is the generation under the action of US on magnetic particles of an alternating magnetic field Ha, depending on the concentration of the nanoparticles in the indicated studied medium. Block B is a sensitive device for measuring the field Ha. Block C is a recorder of the value Ha. Ultrasonic radiation has induced excitation of vibrations of magnetic nanoparticles in the target area of ​​the sample, located in the external uniform constant magnetic field Hd. Oscillations of the particle ensemble oriented (polarized) by Hd field caused the appearance in the surrounding space of the alternating magnetic field Ha with a frequency of US. The magnetic flux of this field depends on the concentration of nanoparticles in the studied region and can be measured by a sensitive detector located outside this region. As such a detector, it can be used a superconducting quantum magnetometer, which, as is known, has the highest sensitivity and dynamic measurement range among the known types of magnetometers11. In the experiments with a model of a cosmetic product due to the higher permissible content of magnetite nanoparticles, which themselves do not belong to highly toxic additives, a highly sensitive voltmeter was used. In addition, in practice, the possibility to use a sensor with a lower sensitivity compared to the superconducting quantum magnetometer will make the AMM technique available for practical use in the future.

Figure1. Block diagram of a measuring system

Voltage (U) on the induction coil of unit B resulted from the excitation of oscillations of magnetic nanoparticles in the target area of ​​the medium under the action of ultrasonic radiation. Accordingly to the Faraday’s law on electromagnetic induction, the resulting U should be proportional to the magnitude of the nanoparticles' total magnetic field at the detector's location and their speed relative to the detector12. In turn, field Ha and U are proportional to the concentration (K) of the nanoparticles in the moving solution. In the specific case of the described experimental installation, the solution with the nanoparticles was moved using an ultrasonic wave, and the magnetic moments of the nanoparticles were oriented along the required direction by constant magnetic field Hd. In this case, the speed of movement of the nanoparticles is proportional to the power of the ultrasound. The magnitude of the U is proportional to the concentration of nanoparticles in the field of action of US and magnetic field Hd and the US intensity (I). Dependence of the U at the induction coil on the I of ultrasound can be described by the Equation [1]:

[1]

In which the parameter k characterizes the magnetic field properties in the coil area, the N number of the magnetic nanoparticles creates a magnetic field when all nanoparticles are oriented in the direction perpendicular to the plane of the coil by uniform constant magnetic field Hd. The value of K of the magnetic nanoparticles is equal to as described in Equation [2]:

[2]

In which V, ρ, and m are the volume of one nanoparticle, its specific weight, and the total mass of the solution, respectively. The increase of the voltage on the induction coil proportionally to the I of the ultrasound confirmed the possibility of the magnetic particles registration using an acoustomagnetic method to measure the quantitative value of the concentration of the magnetic particles (Figure 2).

Figure2. Dependence of the effective value of the alternating voltage U on the US intensity I

It is proposed to use a simplified method for determining the concentration of the cosmetic preparations when superconducting magnetometer usage is replaced by the highly sensitive voltmeter, which makes it possible to exclude the use of cryogenic liquid and makes the proposed method more accessible in practice for quality control of cosmetic preparations. Also, it has been experimentally shown that the sensitivity of detecting the response of an ensemble of MNPs using the selected measurement scheme is sufficient at the therapeutic dose with nanoparticles, which may be contained in a cosmetic product. The chosen method has several advantages over Mössbauer spectroscopy since it allows the concentration of superparamagnetic MNPs to be measured at room temperature, as Mössbauer spectroscopy is useless at this condition. Compared to MRI, the chosen technique is a direct method for determining the magnetic field's concentration and magnitude is significantly lower than it is used for MRI. Unlike most techniques, the chosen method allows its use not only for in vitro measurements but also for in vivo measurements at the penetration of MNPs through the skin in dermatology.

None.

All authors have an equal contribution in carrying out this study.

None.

The authors have declared no conflict of interest.

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