fulltext

In vivo human-skin electrical conduction and pain sensations

(1_{) Dipartimento di Fisiopatologia, Divisione di Fisica Medica}

Università di Firenze - Firenze, Italy

(2_{) Istituto della I Clinica Medica, Università di Firenze - Firenze, Italy}

(ricevuto il 4 Settembre 1995; approvato il 27 Gennaio 1997)

Summary. — In vivo human skin is stimulated by direct current the intensity of

which ranges from 1 mA to 1 mA. We have detected the voltage/current plot and the temporal trend of potential difference (for different values of current intensity/cm2₎

between two electrodes placed in a suitable cutaneous region of stimulation, in a group of healthy subjects. We have elaborated a non-linear functional equivalent model to describe the system behaviour. The electrical stimulation can induce painful sensation, over a critical value of the current intensity, and we believe that this sensation is due to thermal dissipation into the inner layers of the skin. In fact, subjects begin to feel pain when the electric power dissipated in the stimulated region for unit time is within the range of 235–260 mcal/cm2_{Q s, that corresponds to}

the thermal threshold required to evoke pain.

PACS 87.90 – Other topics in biophisics and medical physics. PACS 66.10.Ed – Ionic conduction.

PACS 02.60.Ed – Interpolation; curve fitting.

PACS 07.50 – Electrical and electronic components, instruments and techniques.

1. – Introduction

Living organisms, or their parts, can interact with an incident electric field absorbing energy. From this point of view, the matter can be described as an atomic or molecular aggregate in ionic form, i.e. a set of electric charge carriers. Electric field interacts with these free charge carriers through suitable forces, and so electric current and ionic conduction is produced.

When total current I and potential difference V detected across the ends of the conducting medium are related in a linear form, Ohm’s law holds. This is equivalent to assume a linear law between current density J and electric field E:

J 4sE ,

where s is the conductivity of the conducting medium.

On the other hand, there are many important examples of conductors for which 835

Ohm’s law does not hold, and these are known as non-linear conductors. This fact implies that either the number of free charge carriers or their mobility is influenced by the applied electric field.

In a conductor through which a current is flowing, the energy E transferred from the electric field to the moving charges (i.e. the mechanical work done from the field to the charge carriers against electrostatic forces) is converted into heat for the collisions between charges and other particles in the conductor (Joule effect). The energy lost per unit time, i.e. the power P, is given by

P 4IQV

(1)

and the total energy is

E 4



(2)

When a potential difference V is maintained between two terminals of a given conductor, electrical energy is transformed into heat at the rate I P V and this effect increases the temperature of the conductor and changes the istantaneous conductivity

s 4 ( dV/dI). Thus the measured ratio (V/I) will not be constant and the system under

these conditions is essentially a non-linear conductor, in which J is not proportional to E.

Skin shows some complex and non-linear electrical properties and in vivo results are influenced by some factors as:

a) relative humidity and environmental temperature; b) cutaneous region chosen for stimulation;

c) pathologic conditions;

d) mechanical strain of the system (for instance, a couple of electrodes applied on

the skin can exert a pressure that produce a misurable change of potential difference between electrodes [1]);

e) types of electrodes.

Moreover, water and soap or suitable solvents are used to remove grease from skin surface to minimize its influence [1]. Some authors remove horny layer (where the higher skin resistive component keratine [1, 2] seems to be localized) by abrasion. This technique, we believe, modifies experimental conditions and hardly perturbs the system. We must keep in mind that biological tissues are open thermodynamical systems and in vivo measurements must be carried out with extreme caution, well-defined external conditions and non-invasive methods.

Several authors, some of them of the past century, have studied the passive electrical properties of the human skin [3-7], in which the electric conduction and the cutaneous sensibility induced by electrical stimulation (in particular pain sensation) were investigated. These works have emphasized skin resistance or impedance changes with d.c. or a.c. stimulation [8-10], but it was very difficult to evaluate the results with objectivity and reproducibility, as explained above. Experimental works, indeed, have given very different values of skin resistance that range from about 500V to 600 kV [3-11], and some authors have emphasized a non-ohmic behaviour of tissue current-voltage characteristics also for low current densities (about 100 nA/cm2_{) [12].}

In our study, the skin was considered a black box in which a current with variable intensity can flow. In this way, we can detect the voltage/current plot and the temporal

trend of potential difference (for different values of current intensity/cm2_{) between two} electrodes placed in a suitable cutaneous region of stimulation. In vivo measurements are carried out on healthy subjects to elaborate a functional equivalent model describing the system behaviour.

We have used square wave stimuli for the possibility of programming and exactly varying the parameters of the impulses, and assuming that the skin shows non-ohmic electrical properties, we must use a d.c. unit, because it would be incorrect to use a.c. stimulation in a non-linear system as the results would be hard to evaluate.

2. – Ionic conduction mechanisms

Typically, ionic conduction is observed in electrolytic solutions (in water or other substances) in which molecular splitting can occur for electrolytic dissociation. When an electric field is applied through suitable electrodes, the motion of ions produces a matter transfer (electrolysis). This process is caused by the formation of new chemical substances in the proximity of the electrodes. On the surface of electrodes prevails a charge, positive at the anode and negative at the cathode, while on the skin immediately under the electrodes an opposite electrolityc charge is distributed. Electrolytic gel, with 0.9% of NaCl, is commonly used to improve electrode-skin contact. A charge gradient is consequently formed at the electrode-skin interface, the spatial distribution of which is called the electrical double layer.

Moreover, in a general way the surface of a solid electrode is not homogeneous and, on the other hand, skin itself is not homogeneous. This fact favours the presence of cutaneous regions for which the contact with the electrode is better than in others, inside the stimulated area. For this reason, the useful contact area is less than the electrode physical area and also the electrolytic cream does not form a uniform layer at the interface, but it spreads itself in a heterogeneous way when the electrode is applied on the skin.

Electrodes tipically used in electrical-stimulation measurements are Ag/AgCl, because they have been found to give acceptable standards.

We hypothesize that skin electrical behaviour is characterized by ionic conduction mechanisms, which are due to

1) ions present in extra-cellular fluids;

2) temperature increase due to thermal dissipation within the system; 3) charge carriers increase, due to

a) hydrogen bond alteration in free water and in intermolecular sites (that are

responsible for the stabilization of proteic structures), in consequence of energy dissipation in the cutaneous tissue, with induction of H1_{and OH}2_flow;

b) activation of a new way of conduction, in consequence of perspiration and

sweating induced by electrical stimulation, probably due to point 2).

Point 2), we believe, is very important because when temperature increases, resistivity of skin decreases and, obviously, ion mobility increases. In fact, when temperature goes up, viscosity of water and biological materials decrease, according to [13]

h24 h1Q exp [2cQDT] , (3)

where h2 is the viscosity at temperature T2, h1 is the viscosity at T1, DT 4 (T22 T1) and c is a constant. This effect increases the ion conductivity s , because s is influenced by viscosity h . In conformity with Stockes’ Law, the motion of an ion in a viscous medium, under the action of a constant force F, is uniform with velocity v 4F/(6phr), when the ion can be approximated to a spherical shape with radius r. If F is produced by the application of an electric field and v is related to the current density j by equation j 4nqv (n is the ion number per cm3), conductivity is determined by the relation

s 4 n Q q

2 6 phr (4)

and so, thermal dissipation produces an increasing of charge carriers mobility.

When the current intensity is over a given value, we assume that the system is not ohmic, because we believe that conducting mechanisms 2) and 3) are activated by a threshold mechanism and are negligible for low values of the electrical stimulation.

3. – The model

We propose a non-linear model with time-varying parameters to quantify the assumptions stated above. This model is also structural, because we can explain its parameters physically. The model (fig. 1) is constituted by three blocks in series: the first is a parallel R(I) Q C and represents the electrode-skin interface, the second and the third are the elements R1(I) and R2(I), where I is the current intensity. We have assumed that

i) the capacity C is due to the formation of a charge gradient (double layer) at the interface;

ii) the resistance R(I) is the “charge-transfer resistance” across the double layer (the passage from electronic to ionic conduction) [14], and it depends on I;

iii) R1(I) and R2(I) are electrolyte resistances and exponentially depend on the charge I Q Dt ; this derives from the assumption that:

a) electrical energy is transformed into heat (Joule effect) with energy

dissipation into the system given by (2); this is a valuation of the resistance of the conductor to the current flow;

b) perspiration and hydrogen bond alterations produce charge carriers

increase and, consequentely, a resistivity decrease of the system.

The potential difference V(t) between the non-polarizable electrodes is given by

V(t) 4IQ [R1(I) 1R2(I) ] 1IQR(I)Q

[

]

where the time constant R(I) Q C is responsible for the starting transient during the low-current injection.

4. – Materials and methods

For the measurements, we have used a d.c. unit composed of an insulated voltage/current converter that can supply up to 20 mA on a load of 1 kV. The unit is connected through an analogic-digital interface RTI815 to a PC386 IBM compatible. The computer sends, through an original software, a square wave signal to the interface and then to the d.c. unit, and so the electrical stimulation is applied from t0 (“firing” time) to t1 (“quenching” time). The signal length and the intensity are chosen by the PC operator [15].

The unit output is connected by two circular Ag/AgCl electrodes of 1 cm, that are placed on the volar surface of the right forearm, at a 1.5 cm reciprocal distance. A divider is placed in parallel with the d.c. output, and it is connected to the interface for the measurement of the voltage between the electrodes (fig. 2).

The measurements were carried out on 5 healthy subjects, 3 males and 2 females ranging in age from 30 to 50 years, and were repeated two-three times on the same day and also on different days with constant environmental temperature and relative humidity (T 423–247C, RH 450–55%). Surface grease was removed from skin with water and suitable soaps which did not change the local cutaneous pH. We have used a thin film of electrolytic gel to improve electrode-skin contact.

A 1.5 kV resistance was placed in series with the load represented by the subject’s cutaneous impedance. The ends of this resistance are connected to the RTI815

interface for measuring the current intensity which passes through the skin. The subjects were stimulated by currents whose intensities ranged from 1 mA to 1 mA. The measurements were controlled by a program which permitted the choice of the signal characteristics, and the acquisition of the voltage and current values with a sampling interval determined by the program (minimum 0.5 ms). In an experimental session the subjects were stimulated N following times.

Electrical stimulation parameters (pulse intensity, width, rate) can produce tactile or painful sensations (priking pain). When stimulation time lasted over 5 s, we observe red spots or even tissue damage under the cathode. These red spots have not a homogeneous distribution. In a preliminary analysis we have observed that for direct currents inducing pain, if the stimulation time is over 0.5 s, the system changes its electrical characteristics and, immediately repeating the measurement for currents not inducing pain (less than 20 mA), the resistance results markedly lowered. For this reason we have chosen a 0.25 s d.c. stimulating time. During this time, voltage and current values are acquired with a 0.5 ms sampling interval. We have observed, in the subjects, a resistance average decrease of about 30%.

The voltage temporal trend and the voltage/current behaviour are represented on the monitor and the values are memorized on a hard-disk file. The induced sensations (touch and pain) are recorded.

5. – Results

The resistance values in different subjects during different measurements ranged from 80 kV to 1500 kV.

For current intensities from 1 mA up to 20 mA we have observed in all subjects that:

a) the voltage trend, and therefore the resistance trend, was constant after a

starting exponential transient (due to double-layer formation);

b) the voltage values were proportional to the corresponding current intensity

values; we assumed that the system, in this range of I values, was linear and than Ohm’s law held;

Increasing the current up to 1 mA, we have observed an increase of the potential difference between the electrodes, and its trend changed during time. A critical value

Ith, typical for each subject, was found; when the current intensity was over Ith, the potential difference V decreased during time, with very quick initial trend and a slower final trend. The resistance decreased during time, according to the voltage decrease, because the stimulating current was maintained constant by the converter. We have assumed that this effect could be bound to the tactile or painful sensation in all subjects. In fact, these sensations can activate, with reflex mechanisms, sweat production. The experimental data were fitted from the proposed model

(

)

Subjects did not feel sensations up to an average current value of about 150 mA (this value changes very much from each subject), but when current intensity increased they

Fig. 3. – Voltage temporal trend between the electrodes applied on a subject for different values of the current; full dots, experimental data; continuous line, theoretical trend (see text).

Fig. 4. – Voltage temporal trend for fixed steps of the current intensity; a) pure resistance;

Fig. 5. – Skin response, in one subject, before and after the induced painful sensation.

Fig. 7. – Current/voltage curve for the subject shown in fig. 3 (see text).

started to feel tactile and later painful pricking sensations. Subjects that showed skin resistance lower to 200 kV distinguished these two sensorial modalities with great precision, while subjects that had higher values of skin resistance did not distinguish them, and so they felt painful sensation only.

Voltage trend vs. current intensity increased with fixed arbitrary step are showed in fig. 4 and 5; these plots show, in a single representation, the two modalities of the system behaviour that are described in fig. 3. Figure 4 shows the difference between a pure resistance and the data from the subject shown in fig. 3, while fig. 5 shows, in one subject, the skin response before and after the induced painful sensation.

The non-linear voltage/current behaviour in three subjects is shown in fig. 6, where current intensity rises with fixed step. Figure 7 shows the voltage/current plot for one subject; experimental data are obtained choosing the voltage mean value in the measurement range, in volts, and the corresponding current intensity value, in mA. The voltage trend is reversible (no hysteresis loop) if the subject does not feel pain. When the subject feels a pricking sensation, the system behaviour is not reversible, because skin resistance has a lower value for the same current values, decreasing the current.

6. – Discussion

Our data confirm that the skin is not a linear system from the electrical point of view, and the results are in agreement with the hypothesis introduced a priori.

When the current is over Ith, we believe that the multiexponential behaviour of the voltage trend during time is due to thermal alteration of the system and sweat glands activation (also for reflex mechanisms) [16].

When a subject feels pain induced by electrical stimulation, we believe that the sensation can be induced from thermal dissipation into the inner layers of the skin, when the energy dissipated into the system reaches a value E0 that can be determinated, in first approximation, with the experimental equation

E04 E(td) 2 [kQtd] , (6)

where k is the thermal flow from the stimulated region to the surrounding medium and

td is the pulse length.

Energy dissipation into the skin for a particular value of td, E(td), is determined by eq. (2). We hypothesize that the red spots, that are localized in the region under the cathode when stimulation time is long, are an index of the useful contact area. In this way, we can determine the regions of a good contact between the skin and the electrode. In our measurements, we have estimated that an average value of this area is about 2 Q 1023_cm2_.

The intensity of thermal radiation required to evoke pain, on the volar surface of the forearm, is about 250 mcal/cm2

Q s [17] and, if we compare this value with our data, we observe that a subject begins to feel pain when the electric power dissipated in the stimulated region of the skin for unit time is within the range of 235 –260 mcal/cm2Q s . We know that thermal radiation is absorbed almost completely in the first 20 mm [18] and, if we hypothesize that also electrical energy is dissipated across this thickness (corresponding to the horny layer), we obtain an increase DT of local temperature of about 19 7C/cm2_{Q s on a volume of about 0.013 cm}3_{, in the first approximation that} energy dissipated into the skin is absorbed by tissue water. This value of DT increases the subcutaneous skin temperature up to the pain threshold temperature (about 45 7C) [19], so it seems reasonable that the pain sensation induced by electrical stimulation is due to the dissipation of electrical energy in the skin.

We have excluded, analysing voltage-current plots and published data [20], that painful sensation can be determined by a “dielectric breakdown” [2-4] of the horny layer. In fact, if we assume that the electric field is totally across the horny layer, pain appears when the electric field is 2 Q 106V/cm or less, while the measured breakdown field is over 4 Q 107_{V/cm [20].}

R E F E R E N C E S

[1] MILLINGTONP. F. and WILKINSONR., Skin (Cambridge) 1983, pp. 127-132. [2] SHAEFERH., Elektrophysiologie (Wien) 1940.

[3] ROSENDALT., Acta Physiol. Scand., 5 (1943) 130. [4] ROSENDALT., Acta Physiol. Scand., 8 (1944) 183.

[5] GIBSON R. H., Electrical stimulation of pain and touch, in The Skin Senses, edited by KENSHALOD. R. (Charles C. Thomas, Springfield) 1968, pp. 223-261.

[6] EDELBERG R., in Biophysical Properties of the Skin, edited by H. R. ELDEN (Wiley-Interscience, New York) 1971, pp. 513-550.

[7] GALLETTIR., PROCACCIP., ROCCHIP. and BUZZELLIG., Arch. Fisiol., 61 (1961) 346. [8] PROCACCIP., DELLACORTEM., ZOPPIM., ROMANOS., MARESCAM. and VOEGELINM. R., in

Recent Advances on Pain. Pathophysiology and Clinical Aspects, edited by J. J. BONICA, P. PROCACCIand C. A. PAGNI(Charles C. Thomas, Springfield) 1974, p. 105.

[9] ROSELL J., COLOMINAS I., RIU P., PALLAS ARENY R. and WEBSTER J. G., IEEE Trans.

Biomed. Eng., 35 (1988) 649.

[10] WOOE. J., HUAP., WEBSTERJ. G., TOMPKINSW. J. and PALLASARENYR., Med. Biol. Eng.

Comput., 30 (1992) 97.

[11] SALTERD. C., in Bioengineering and the Skin, edited by R. MARKSand P. A. PAYNE(MTP Press, Lancaster) 1981, p. 267.

[12] RUSSELDAVISD. and KENNARDD. W., Nature, 193 (1962) 1186.

[13] TAREEVB., Physics of Dielectric Materials (Mir Publishers, Moscow) 1979. [14] DYMONDA. M., IEEE Trans. Biomed. Eng., 23 (1976) 274.

[15] VOEGELINM. R., PAOLIG. and ZOPPIM., Physica Medica, IX (Suppl. 1) (1993) 22.

[16] STEINMETZM. A. and ADAMST., in Bioengineering and the Skin, edited by R. MARKSand P. A. PAYNE(MTP Press, Lancaster) 1981, p. 197.

[17] HARDYJ. D., WOLFFH. G. and GOODELLH., Pain Sensations and Reactions (The Williams and Wilkins Co., Baltimore) 1952.

[18] WELCHA. J., PEARCEJ. A., DILLERK. R., YOONG. and CHEONGW. F., J. Biomech. Eng., 111 (1989) 62.

[19] GUYTONA. C., Structure and Function of the Nervous System (Philadelphia) 1972, p. 100. [20] MASONJ. L. and MACKAYA. M., IEEE Trans. Biomed. Eng., 23 (1976) 405.