1. Introduction

The study of causes and development of oxidative stress (OS) in the human skin, its association with skin diseases and other types of diseases has been conducted by scientists in different fields: medicine, chemistry, biology[1–3]. Oxidative stress contributes (or appears) significantly to the development of some nervous, lung, eye, and blood diseases as well as aging, coronary deficiency, strokes; take part in progressive damage in cardio-surgery, transplantation of tissues and organs and lungs surgery. Oxidative stress contributes to adverse effects on the skin, expressed as erythema, edema, wrinkling, photoaging[4], inflammation, autoimmune manifestation, hypersensitivity, keratinization abnormalities, preneoplastic lesions and skin cancer[5], psoriasis[2,6,7], vitiligo[8,9] seborrheic dermatitis[10].

The negative role of free radicals in human health is described in[2,11,12]. On the other hand, reactive oxygen (ROS) and reactive nitrogen (RNS) substances play a crucial role in the body, ensuring good metabolism and performance of vital functions in cells. Previous studies in this field[13-16] allow thinking that AOA/OA (antioxidant/oxidant activity) of the skin can provide information on AOA/OA of the whole body. Thus, developing a method of evaluating this parameter will enable to create a noninvasive method of assessing human health.

Antioxidant determination methods are widely reported in the literature[17-19]. Actually, proposed methods are invasive: they require blood taking or homogenate preparations of the analyzed tissue. The data about non-invasive methods used for determining antioxidant activity of biological objects are limited[19–21].

Because of inductor of oxidative stress is an overall deficit of electrons accessible to cells, AOA/OA body balance has the electrochemical nature that is why electrochemical methods of evaluating this parameter are naturally should be considered as fully corresponding with the nature of the phenomenon.

In[22] we described a potentiometric method of skin AOA/OA measurement. Advantages of the proposed approach are as follows: skin AOA/OA can be measured as integrated parameter by a direct, highly sensitive, user friendly and selective method. However, the following problem arises: the investigated ‘skin-gel-electrode’ system is complicated in comparison with the ‘water solution- electrode’ system used in the early described method[15–16] and it is not obvious, that the same approach and calculations can be used in applying a new method.

To justify the correctness of approach and conformity assessment of the measured value of AOA/OA to actually existing in the sample, it is essential to provide theoretical background to the processes occurring in the system, to create a mathematical model that takes into account a range of parameters such as the thickness of the the gel containing the mediator system; the rate of the chemical reaction between skin antioxidants/oxidants and compounds of the mediator system in the gel.

2. Theoretical Considerations

The method proposed in[22] is based on the interaction between antioxidants/oxidants diffusing from the skin epidermis into the gel and the mediator system introduced into the gel which is applied on the skin. The information source with regard to AOA/OA is the electrode potential shift in the mediator system K₃[Fe(CN)₆/K₄[Fe(CN)₆], which is observed when the gel comes into contact with the skin as a result of changing concentration of oxidized or reduced forms of the mediator system in the gel. These changes in the concentration result from reaction (1) for antioxidants and reaction (2) for oxidants:

(1)

(2)

where AO – antioxidant; AO_Ox – antioxidant oxidation product; OA – oxidant; OA_Red – oxidant reduction product.

The initial potential of the system E is determined by the following equation (3):

(3)

where E₀ – standard potential of mediator system, C_Ox – concentration of oxidized form of mediator system, M; C_Red – concentration of reduced form of mediator system, M, b=2.3RT/nF.

The signal measured at any times depends on the concentration ratio of Fe(III)/Fe(II) at the electrode surface, wherein the change in Fe(II) concentration equals to the concentration of antioxidants, and the change in Fe(III) concentration equals to the concentration of oxidants.

After the sample containing antioxidants, is introduced in the system, the potential of the mediator system is described by applying Equation (4):

(4)

where E₁ – end potential, V; X – concentration of antioxidants, that come to the gel from skin, M.

After the sample containing oxidants is introduced in the system, the potential of the mediator system is described by Equation (5)

(5)

where Y -concentration of oxidants, that come to the gel from skin, M,

AOA=X and OA=Y are expressed in mole-eq/l (M-eq), if mentioned mediator system is used. Because in this case one electron participates in reaction Fe(III)+e= Fe(II). AOA and OA are calculated applying Equations 6 and 7:

(6)

(7)

Proposed a physical model of the process is shown in Fig 1.

Figure 1. Physical model of the process: C0skin – initial concentration of antioxidants/oxidants in epidermis; Cskin – current concentration of antioxidants/oxidants in epidermis; CA – concentration of antioxidants/oxidants in gel, CR concentration of reagent (reduced form of mediator system Fe(II) or oxidized form of mediator system Fe(III) in gel

A mathematical model of the process is as follows: concentrations of antioxidants in epidermis (AOA=C_skin), reduced form of the mediator Fe(II) – C_R, resulting from Reaction (1) taking place in the space between skin surface and electrode, are determined by the solution of respective one-dimensional diffusion problems where the spatial coordinate x counts from the electrode surface (x=0) through gel layer to skin surface (x=δ_gel). The coefficients of substances diffusion in the gel D[cm²∙s^-1] is taken as a first approximation equal. Reactions 1 and 2 are considered first-order reactions with rate constant k. Antioxidant or oxidant penetrates from the epidermis into the gel through the skin surface. where its concentration is the desired time function with an initial value equal C⁰_skin. For simplicity sake, we consider in calculations given below changes in the concentration of Fe(II) in Reaction (1) or Fe(III) in Reaction (2), as its concentrations. The electrode surface is impenetrable to substances AO and R, δ in equations below is equal to δ_gel.

The diffusion problems for calculating concentration distribution of substances AO and R in the gel layer are as follows:

(8)

(9)

The mathematical model is added by the equation of the material balance of substance AO in the skin. The similar behavior is observed in the case of oxidants. The only difference is that the change in concentration of Fe(III) is considered instead of Fe(II).

(10)

δ_skin – epidermis layer thickness,

An approximate solution of the problem was found by Laplace integral transformation along with Bubnov - Galerkin orthogonal method[23,24]. As a result, relative concentrations of antioxidant C_skin/C⁰_skin in the skin and C_R(el)/C⁰_skin at the electrode surface were determined as a function of three dimensionless complexes:

(11)

This representation allows us to analyze the effect of diffusion, the chemical reaction rate and the thickness of the gel layer on the dynamics of the processes.

(12)

(13)

(14)

(15)

The solution enables to obtain the key correlation between the parameters which define characteristics of the processes occurring in this system, namely, to find the functions C_skin/C⁰_skin and C_R(el)/C⁰_skin depending on the arguments δ_skin-epidermal thickness, δ_gel-thickness of the gel layer and t-time.

In this case C_R reflects C_AOA, as substance R (Fe(II)-reduced form of the mediator system) results from Reaction (1) which is running in the gel. In case of oxidants C_R will reflect C_OA as substance R (Fe(III)-oxidized form of the mediator system) results from Reaction (2) Let us once again focus on a very important fact: C_R is an increment (rather than an absolute value) of the concentration of reduced (Eq. 1) or oxidized (Eq. 2) forms of the mediator system.

C_R(el) – increment (rather than an absolute value) of concentration at the electrode surface determines a measuring signal that is recorded as a shift of the electrode potential in the mediator system, initially introduced into gel.

Ideally, C_R(el)/C⁰_skin should approach to 1.

Since the mathematical model and calculations in the cases described by Equations (1) and (2) do not differ, the value of C_R(el) will be used for further considerations.

The general profile of dependence of C_skin/C⁰_skin and C_R(el)/C⁰_skin on non-dimensional parameters, including the above given arguments, is shown in Figure 2.

Figure 2. Dependence of CR(el)/C0skin on non-dimensional parameters Bi and Fo

Consequently, the values of C_skin/C⁰_skin and C_R(el)/C⁰_skin that reflect the change in the concentration of the original substance (antioxidants) and reagent (the product of reaction (1)) at the interface of skin-gel and gel-electrode, are determined by the initial concentration of C⁰_skin in skin; by the rate of AO diffusion and by the rate of chemical interaction of AO with the component of the mediator system (reaction 1) in the gel.

The aim of further research is to find the conditions when a recorded signal has a maximum correct reflection of C⁰_skin.

For clarity and ease of comparison of the calculated and experimental data, C_skin/C⁰_skin and C_R(el)/C⁰_skin are given as functions of t at different combinations of δ_skin, δ_gel, k and D.

It is apparent that C_skin/C⁰_skin decreases whereas C_R(el)/C⁰_skin increases with time (Fig. 3). Moreover, at a given moment, the higher reaction rate constant, the lower C_skin/C⁰_skin; but the bigger C_R(el)/C⁰_skin. The diffusion coefficient affects neither C_skin/C⁰_skin nor C_R(el)/C⁰_skin.

Figure 3. Calculated value of Cskin/C0skin (a, c) and CR(el) /C0skin (b,d) as functions of t for different D and k: D=10-4 cm2s-1 (a, b); D=2x106 cm2s-1 (c, d) k =0.01 (1), 0.001 (2) and 0.001 (3) s-1, δskin=0.1 mm; δgel=0.1 mm

Fig. 4 shows dependence of C_skin/C⁰_skin and C_R(el)/C⁰_skin on the thickness of the gel and epidermal layers. It is also apparent that increasing duration of measurement and thinner gel layer lead to lower C_skin/C⁰_skin but higher C_R(el)/C⁰_skin. This relation is understandable since these parameters have an impact on exit of antioxidants from the skin and delivery of potential-determining substance R to the electrode surface. It is important to take into account the ratio of δ_skin/δ_gel, since the smaller δ_skin, the smaller the amount of antioxidants and, therefore, a potential-determining substance in gel, the smaller. The thicker the gel layer the lower the concentration of AO and R in it.

The calculations allow making an important practical conclusion: measurements should be long enough to ensure maximum exit of antioxidants from the skin into the gel; thickness of a gel layer should be minimum and close to thickness of epidermis. It should be reproducible in different experiments. The lower the rate constant of antioxidant/oxidant interaction with a corresponding component of the mediator system, the lower its contribution to the detected signal is.

Figure 4. Calculated dependence of Cskin/C0skin (a,c) and CR(el)/C0skin (b,d) on thickness of gel layer (a,b) and skin (epidermis) layer (c,d). D = 10-6 cm2∙s-1; k=0.001 s-1; δskin=0.1 mm (a,b), δgel =0.1 mm (c,d)

3. Experimental Section

3.1. Materials

• K₄[Fe(CN)₆], K₃[Fe(CN₆)], KH₂PO₄, Na₂HPO₄·12H₂O, ascorbic and uric acids, cysteine and glutathione of high purity grade or chemically pure were obtained from Reachim, Russia.

• Mixture of K₃[Fe(CN₆)] and K₄[Fe(CN)₆] served as mediator system.

• Unimax, highly conducting gel (Geltek-Medica, Russia) and adhesive plaster Silkofix PE 2500 were bought in Pharmacy store.

3.2. Investigated Subject

The surface of human skin in the wrist area served as the subject of investigation. The investigated area of skin was washed with deionized water.

Gel, containing ascorbic acid, cysteine or glutathione served as model systems.

3.3. Instruments

Potentiometric measurements were performed using potentiometric analyser Taion (Tomanalyt Ltd, Tomsk, Russia) with a two-electrode electrochemical cell. Platinum screen-printed electrode (IVA, Ekaterinburg, Russia) and ecg electrodes H92SG Ag|AgCl, KCl (Arbo, Kendal, USA served as working and reference electrodes. Silver/silver chloride electrode (Ag/AgCl/3 M KCl), EVL -1M type (Gomel Measuring Equipment Plant, Gomel, Republic of Belarus) was used as reference electrode in kinetics experiments.

3.4. Methods

Measurements of chemical reactions rate using model systems

Four ml of the gel and 0.2 ml of an aqueous solution of the mediator system containing a mixture of 10^-3 M K₃[Fe(CN)₆]) + 10^-5 M K₄[Fe(CN)₆] were placed in a glass cell. Electrodes were immersed in the mixture and the potential (E) was measured after 60 s. Then the electrodes were removed from the cell and 0.2 ml of an aqueous solution of an antioxidant was added. The concentrations of the solutions in the cell were 2∙10^-5 M ascorbic acid or 4∙10^-5 M glutathione. The electrodes then were again immersed in the cell and the change in the potential was recorded until its value stabilized. Concentration of antioxidants in gel was calculated using Equation 6 and assuming ΔE=E-E₁, where E was the electrode potential in the gel containing the mediator system; E₁ was the potential in the gel containing the mediator system and antioxidant at a given time t. Value of found antioxidant concentrations at the end of the measuring process and at a half-time of that were used to calculate constants of chemical reaction rate. Form of the curves is shown on the Fig.6.

Skin investigation

In order to study the effect of thickness of a gel layer on potentiometric measurements two plates were placed on the tested skin area at a distance of 1cm from each other (Fig.5). The gel containing mediator system, platinum screen-printed and ECG H92SG electrodes were placed in the space between the plates, as shown in Fig. 5. The layer thickness was controlled by the number of pieces of hypoallergenic adhesive plaster (from 1 to 5) located on each other. The thickness of plates were measured with a micrometer.

Figure 5. Design of a unit for measuring skin АОА: 1 – reference electrode; 2 – gel, containing mediator system (10-3 М K3[Fe(CN)6]+ 10-5 М K4[Fe(CN)6]), 3 – plates; 4 – platinum screen-printed electrode; 5 – skin

4. Results and Discussion

Fig. 6 presents the dependence of E-t, obtained experimentally and AOA-t, calculated applying Eq. 6. All experimental results given below were obtained in this way. Sudden changes in the potential and AOA were observed in the range 0–500 s, which is consistent with the results of the calculations (Fig. 3). After 600 s measurements the potential change in time was slow. For example, the difference between the experimental values of AOA (Fig.6) during 600 s and 783 s was 0.3∙10^-6 M-eq, or 0.8%. Further measurements were carried out during 600 s.

Figure 6. Time dependence of potential (1) and antioxidant activity (2) measured on human skin

Standard deviation of measurements on different areas of skin of the same person was within 5–6% The value C_R(el)/C⁰_skin required for the comparison of the experimental and calculated data was found as the ratio of AOA concentration at a given moment to concentration found after 600s measurements.

The search of the literature allowed to find the values only for water solutions in the range from 1.52∙10^-5 cm²∙s^-1 (in the presence of 0.1 mM potassium ferricyanide in 0.1 M Na₂HPO₄)[25] to 7∙10^-6 cm²∙s^-1[26].

The value of the diffusion coefficient of ferri/ferrocyanides in the gel was calculated using the relation D_gel=D_water∙η. Gel viscosity (η) was taken close to 8-9 Pa∙c[27] and density range equaled 1.02–1.05 g∙cm^-3. Further, D_gel was taken as 2∙10^-6 cm²∙s^-1.

The rate constants of Reaction 1, determined by the above mentioned method, were 10^-2 s^-1 for ascorbic acid and 5∙10^-4 s^-1 for glutathione

Fig. 7 shows the calculated and experimental dependence of C_R(el)/C⁰_skin on the thickness of a gel layer. A thicker gel layer led to lower C_R(el)/C⁰_skin. Two important conclusions are apparent from Fig. 7: (i) theory and experiment are in good agreement and (ii) thickness of a gel layer should be minimum and close to thickness of epidermis as follows from the theoretical calculations. It should be reproducible in different experiments.

Figure 7. Calculated and experimental dependence of CR(el)/C0skin on thickness of gel layer; k=0.01 s-1, δskin=0.1mm

Time dependence of (а) C_R(el) (experimental measurements, volunteers 1-7); and (b) C_R(el)/C⁰_skin: averaged experimental (Curve 1) and calculated curves (Curve 2, k =0.01 s^-1 and Curve 3, k=0.0005 s^-1) are presented on Fig. 8.

Big differences in the values of AOA are due to a variety of volunteers’ levels of health and nutrition/diets. For example, Curve 7 was obtained by taking measurements on the volunteer’s skin who suffers from atopic dermatitis.

It is apparent that the expression of data as dependences C_R(el)/C⁰_skin lead to confluence of the curves: Figure 8b demonstrates averaged Curve 1 and a small scatter of the experimental data around it. The average curve is very close to the curve that was theoretically calculated for the case when a constant rate of the chemical reaction (1) between antioxidant and an oxidized form of the mediator system in the gel equaled 0.01s^-1. As mentioned above, that was the rate of the reaction of ascorbic acid with[Fe(CN)₆]^3-. Glutathione reacts with[Fe(CN)₆]^3- much slower (k=0.0005 s^-1). The result seems to be a less significant contribution of glutathione than of ascorbic acid to the formation of potential- determining substance and, therefore, to the signal. This would give significant errors in AOA determination if content of these antioxidants in the skin would be the same. Fortunately, ascorbic acid (70%) and uric acid (20%). prevail in epidermis. Cysteine and glutathione are present at low concentration (9%). The quantity of other antioxidants (including liposoluble antioxidants) does not exceed 1 – 2%[28]. Taking into account these data, the analysis results of the proposed method can be considered as reflecting the real situation and the calculated and experimental results demonstrate good correlation.

Figure 8. Time dependence of (а) AOA=CR(el) (experimental measurements, volunteers 1 – 7); and (b) CR(el)/C0skin: averaged experimental (1) and calculated curves (2 – k =0.01 s-1 and 3 – k=0.0005 s-1)

Due to complexity of the mathematical models and calculations, lack of accurate data related to thickness of epidermis, AO diffusion in the skin, AO and R in the gel, and the rate constants of chemical reactions, it should be accepted that there is quite a good agreement between theory and experiment. This gives grounds to use the results of calculations as a source of information regarding selection of experimental conditions, evaluation and interpretation of the results.

5. Conclusions

The existing relationship between the internal state of a human body and skin pathology suggests that skin AOA/OA can be a source of information regarding common health problems. Skin AOA/OA can also constitute the basis for developing new methods of analytical chemistry that can be used for monitoring levels of human health and population screening in order to identify, in particular, groups of risk, and detect diseases in an early stage. Decreasing antioxidant content in the skin reflects the emergence of imbalances in the body's antioxidant defense system, i.e. oxidative stress. Oxidative stress has an electrochemical nature that is why electrochemical methods of evaluating this parameter may be considered as fully corresponding with the nature of the phenomenon.

Potentiometry is one of the most easily implemented electrochemical method. Moreover, it is widely used in sensors for medical diagnostics. The article elaborates upon the theory of non-invasive method of potentiometric determination of antioxidants and oxidants in the skin. The method is based on measuring an electromotive force produced when electrodes are placed in the gel applied to skin. A good agreement between theoretical and experimental results allows using the calculated results as a source of information regarding selection of experimental conditions, evaluation and interpretation of the results.

The advantages of the method are as follows: skin AOA/OA is measured as an integral parameter by direct method; results can be obtained quickly; the method is non-invasive and painless. The measurements are highly sensitive and show good selectivity. Hardware design is simple and accessible and provides possibility to work in the field, in the hospital or at the bedside.

ACKNOWLEDGEMENTS

Authors express their deep gratitude to the financial support of the RFBR (Projects # 12-00-14037_Ir and 13-08-96-050).