Microwave dielectrometer application to antibiotic concentration control in water solution

Subject and Purpose. Th is study focuses on the original waveguide-diff erential dielectrometer designed for complex permittivity measurements of high-loss liquids in the microwave range towards the determination of pharmaceutical ingredient concentrations in water solutions at room temperature. Th e suitability of the device and eff ectiveness of the dielectrometry method are tested on such pharmaceutical ingredients as lincomycin and levofl oxacin over a wide range of concentrations. Methods and Methodology. Th e main idea of the method consists in that the complex propagation coeffi cients of the HE 11 wave are obtained from the amplitude and phase shift diff erences acquired by the wave aft er it has passed through the two measuring cells of the waveguide-diff erential dielectrometer. Results. We have shown that the proposed dielectometry method allows a real-time determination of pharmaceutical ingredient concentrations in water solution by measuring the wave attenuation and phase shift diff erences. We have found that unless concentrations of pharmaceutical ingredients are low, few free water molecules in water solution are bound to the pharmaceutical ingredients. Th e number of free water molecules in solution decreases as the concentration of pharmaceutical ingredients rises. Conclusion. Th e current study confi rms that the dielectometry method and the device developed provide eff ective determination of pharmaceutical ingredient concentrations in water solutions. Fig. 9. Ref.: 18 items.

Development of robust physical methods for the detection of biologically active substances such as antibiotics or other medications in water solutions is one of urgent areas of the research [1,2]. Its importance for ecological monitoring of water environment and foodstuff control is reasoned by the wide and sometimes uncontrolled usage of antibiotics and other drugs in the agricultural industry involving growing crops, raising fi sh and animals [3][4][5], which is still more dramatized by a distinct lack of the appropriate control of pharmaceutical and food industry wastewater composition.
Various precise physical methods were developed to detect antibiotics and other organic pol-lutants in wastewater treatment processes, namely, high-performance liquid chromatography (HPLC), tandem mass spectroscopy (MS/MS), ultra-high performance liquid chromatography-tandem mass spectroscopy (UPLC-MS/MS) [2,6,7]. All these techniques are highly sensitive but depend on very costly equipment and consumables. Moreover, the measuring devices are mainly not portable. So, analysis at the site of sampling is beyond the power of analysts and can be made in laboratory conditions only. It takes a long period of time and requires highly skilled operators [2].
In comparison with the control methods mentioned above, modern radiophysical techniques of Microwave dielectrometer application to antibiotic concentration control in water solution organic compound detection in solutions, particularly dielectrometry, is a promising area of the research and is progressing rapidly. Compared with the traditional control technologies, the dielectrometry method has the advantages of instantaneousness, non-invasiveness, rejection of consumables, low energy consumption, safety, versatility, etc., which gives a signifi cant socio-economic eff ect. A series of studies [8,9] are devoted to accurate measurements of microwave dielectric properties of biologically active compound solutions.
Th e microwave dielectrometry method consists in measuring electromagnetic wave parameters during the wave propagation through a test liquid placed in the dielectrometer measuring cell [10][11][12][13][14]. Th e determined electromagnetic wave parameters allow the complex permittivity (CP) of the studied liquid to be calculated using the characteristic equation obtained from Maxwell's equations for a particular microwave waveguide or resonator structure.
We pursue our long-term research into microwave dielectrometric parameters of high-loss liquids including water solutions of organic compounds (see, e.g., our previous papers [15][16][17]) and set ourselves a task to develop a radiophysical non-invasive express method and translate it into a portable device intended for the dynamic control of the organic pollutant level in water samples and based on precision CP measurements of water solutions of organic substances of diff erent classes.
In the current study, a unique microwave dielectrometry devise that was designed, developed and equipped with appropriate soft ware in O.Ya. Usykov Institute of Radiophysics and Electronics of the National Academy of Sciences of Ukraine is examined. Th e subject of this study is the eff ectiveness of the device in determining concentrations of such antibiotics as levofl oxacin and lincomycin in water solutions.
Th e dielectrometric method. Th e proposed research methodology basically reduces to the measurements of the attenuation diff erence and the phase shift diff erence between the two cells in the diff erential measuring cavity of the dielectrometer aft er the electromagnetic wave has passed through them. One cell accommodates the reference liquid (distilled water in our case), the other contains the test liquid (water solution of a biologically active compound under study). Of use is the dependence of the complex wave propagation coeffi cient on the complex permittivity of the liquid in the measuring cell. Th e complex permittivity is computed based on the characteristic equation and using the measured data on the wave attenuation diff erence and the wave phase shift diff erence between the two measuring cells [17].
Structure of the measuring cavity of the waveguide-diff erential dielectrometer. Th e measuring cavity of our dielectrometer is a diff erential cavity consisting of two identical cells made of copper ( Fig. 1) [17]. One cell is for the reference liq- uid. Th e other is for the test liquid. In the middle of each cell, there is a quartz rod of radius a  0.25 cm and permittivity   3.8 + i 0.0001 oriented normal to the cell walls. Th e cell diameter b equals the cell length l  2 cm. Th e test liquid with 2 between the cell walls and the quartz rod. We work with the HE 11 wave excited in each quartz rod by the rectangular waveguide with the H 11 fundamental wave. Th e phase and attenuation coeffi cients of the wave passing through the cell correspond to the real h and imaginary h parts of the complex wave propagation coeffi cient h. Th e electromagnetic problem for the structure in Fig. 1 was solved [11,12] by the separation of variables in cylindrical coordinates ( , , ). r z  Th e fi eld along the rod radius r is represented by a combination of the Bessel ( ) is taken. Th e complex amplitudes of the electric and magnetic Hertz vectors in the dielectric rod and in the absorbing layer are, respectively, , e C and m C are the unknown coeffi cients. Satisfying the boundary conditions on the measurement cell surface yields the characteristic equation for complex propagation coeffi cient h as follows Th e primes stand for the derivatives with respect to the Bessel function arguments, i k is the transverse wave number in the rod ( 1) i  and in the surrounding liquid ( 2).
i  Th e electromagnetic energy loss in the metal walls of the measuring cells is negligible compared to the dielectric loss in the liquid. Th e complex roots of implicit characteristic Eq. (2) were calculated using a special computer program in Borland Builder 6.0 environment in the C++ language.
Measurement errors. Measurement error estimations for the reference liquid can be found in [11,12]. Here we suggest some remarks on the origin of the errors. Our dielectrometer based on the differential method off ers diff erential sensibility of the order ( )     0.025 deg/cm for the phase shift diff erence   measurements and of the order ( ) A    0.0005 dB/cm for the amplitude diff erence A  measurements in view of the root-meansquare random measurement errors. Th ese fi gures were attained through a series of measurements with water as the reference liquid and in stable ambient conditions. Taking them into our characteristic equation in the designed computer program yields the , h h and ,   errors reported in Table 1.
As seen, the relative errors caused by the complex permittivity measurements of the test liquid are 0.06% for the CP real part and 0.26% for the CP imaginary part.
Th e Bessel functions in our CP calculation algorithm are another source of errors as they are fast oscillating functions. Let us consider the inaccuracies arising in the CP calculation process. We take the real and imaginary parts of the water complex permittivity from, e.g., [18] and calculate the real and imaginary parts of the complex propagation coeffi cient, h  . Th en using the so obtained h  values we can solve the inverse problem, i.e. calculate   once more and fi nd the diff erence. Table 2 reports the results. Th e relative errors of the real (Eq. (3)) and imaginary (Eq. (4)) parts of the test liquid CP are found to be 0.15% and 0.52%, respectively.
Calculation procedure of the test liquid complex permittivity. In order to determine the CP of the test liquid in the course of the relative measurements, one needs to know the complex permittivity of the reference liquid to a high accuracy. When it comes to pharmaceutical ingredients, distilled (1)

Microwave dielectrometer application to antibiotic concentration control in water solution
Th e scheme of the CP measurement procedure is as follows: 1) Having solved characteristic Equation (2)    Th e real and imaginary parts of the test liquid CP become progressively smaller compared to the water CP as the antibiotic concentration in water increases. It means that the free water amount decays as the antibiotic concentration in water solution rises.
Th e following ideas about the molecular processes going in the water of medication solutions are proposed to explain the above given experimental results. Molecules of hydrophilic substances dissolved in water demonstrate propensity to form hydrated complexes with water molecules. Th ese are readily soluble compounds such as antibiotic salts -gentamicin sulfate, various proteins, etc. With the formation of hydrated complexes, the bounded water molecules are getting structured around the molecules of dissolved hydrophilic biologically active compounds, resulting in the microwave/dielectric constant decrease with the decreasing proportion of free water in the solution. As the dissolved compound concentration increases, the CP correspondingly decreases, as also does the proportion of free water in the solution.
Water 1000 2000 3000 4000 5000 Concentration, mkg/ml In our experiments, as long as the levofl oxacin or lincomycin concentration in water solution is low, not many free water molecules are bounded to antibiotic molecules (Figs. 7, 8). As the levofl oxacin or lincomycin concentration in water solution increases, more water molecules get bound to the newly coming antibiotic molecules in hydration processes. A number of free water molecules in water solution decays. Th e CP real and imaginary parts steadily decrease (Figs. 5 and 8).
It should be noted that the detection time in our experimental measurements of the reference (water) and test liquids was about 30 minutes within a fairly small temperature interval (Fig. 9). Th e infl uence of such temperature deviation on CP dependences is supposed rather small. We calculate the diff erences for the CP real and imaginary parts of water given the temperature of the liquids in the cells changes within 3 C and the detection time is about 30 minutes. Th ese diff erences are    0.04 and    0.3, and they are much smaller than the measured values for the CP real and imaginary parts of the test liquid. Th e liquids in the measuring cells heat up as the electromagnetic wave of a certain microwave power passes through the cells. Th e microwave signal source used in the circuit has output power of about 100 mW. Th is power value is justifi ed by the following considerations. Th e principle of the differential dielectrometer operation involves the output power division into two -reference and measuring -channels. With an E-tee junction, the inphase power is equally divided between the two channels. Th e point aft er which a change in the amplitude shift required to restore the balance disturbed by the replacement of the reference liquid with the test liquid starts with 10 dB attenuation. Th e reason for the starting attenuation as mentioned is the fact that at this point there is a minimal parasitic change in signal phase when the signal amplitude is changed by the measuring attenuator. In view of the signal absorption during the passage through the liquid in the cell, a high output power of the signal source is needed to ensure a good signal-to-noise ratio.
A number of circuit design and construction solutions, such as a suffi ciently high-power signal generator incorporation, have been introduced to the developed dielectrometer structure in order to reduce random measurement errors. Th e obtained results have shown that the developed microwave dielectrometry method is sensitive to the presence of antibiotics in water solutions and can determine antibiotic concentration changes. Also, the measurement results suggest potential employments of both the method and the microwave dielectrometry device developed from it and intended for lots of biomedical applications, including blood glucose monitoring, control over the spread of various biological contaminants in the environment and foodstuff s, clinical monitoring of gastrointestinal processes for the diagnosis of stomach and duodenum diseases (pH-value monitoring), characterization of biologically active substances in laboratory diagnostics in human and veterinary medicine. Conclusions. Th e performed experimental study of water solutions of levofl oxacin and lincomycin antibiotics by microwave dielectrometry has shown that the developed dielectometry method and the constructed from it device can perform a qualitative and quantitative real-time determination of pharmaceutical ingredients in water solutions through the measurements of wave attenuation and phase shift diff erences. It has been demonstrated that unless the pharmaceutical ingredient concentration in water solution is low, not many water molecules are bound to medication molecules. As concentrations of pharmaceutical ingredients in water solution increases, a number of free water molecules decreases and, consequently, the CP of the solution does the same. A serious advantage of the microwave dielectrometer developed by our scientifi c team is its ability to directly measure the concentration of a substance regardless of its structure. We emphasize that the real and imaginary parts of the test liquid CP behave monotonically (almost linearly) where the ingredient concentration is low. It gives us unambiguous dependences of the real and imaginary parts of the test liquid CP.
Th e measurement results described in the p aper indicate that our dielectrometry method can contribute to microwave biosensor technology and give rise to more advanced techniques of pharmaceutical ingredient control in water solutions.