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PIEZOELECTRIC PROPERTIES OF DRY HUMAN SKIN

PIEZOELECTRIC PROPERTIES OF DRY HUMAN SKIN

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IEEE Transactions on Electrical Insulation Vol. EI-21 No.3, June 1986<br />

<strong>PIEZOELECTRIC</strong> <strong>PROPERTIES</strong> <strong>OF</strong> <strong>DRY</strong> <strong>HUMAN</strong> <strong>SKIN</strong><br />

D. De Rossi, C. Domenici<br />

Centro "E. Piaggio"<br />

Universita di Pisa<br />

and<br />

Istituto di Fisiologia Clinica del C. N. R.<br />

Pisa, Italy<br />

and<br />

P. Pastacaldi<br />

Divisione di Chirurgia Plastica<br />

USL 12, Pisa, Italy<br />

ABSTRACT<br />

Mechanoelectrical conversion properties of dry human skin<br />

have been examined and their origin investigated in dermis,<br />

epidermis and horny layer. Shear stress piezoelectricity<br />

is observed in all three cutaneous sections. Piezoelectric<br />

properties of dermis can be ascribed to its collagen structural<br />

network, while the piezoelectric properties of epidermis<br />

appear to originate from partially oriented a-helical<br />

keratin-like tonofibrils. The highest piezoelectric coefficients<br />

have been found in horny layer samples. The values<br />

of thickness-compression piezoelectric coefficients were so<br />

low that they were not discernable from the intrinsic noise<br />

of the measuring system. Although thermally generated<br />

currents have been observed in the course of thermal pulse<br />

experiments, no evidence of relevant contributions from<br />

pyroelectric (polar) responses has been noticed in all<br />

cutaneous compartments.<br />

INTRODUCTION<br />

Different biological tissues show the ability to convert<br />

mechanical and thermal stimuli into electric signals<br />

[1]. Extensive studies are available [2], examining<br />

mechanoelectrical properties of bone both in the<br />

dry and in the moist, physiological state.<br />

The hypothesis ascribing bone mechanoelectric transduction<br />

to piezoelectric properties of the collagenous<br />

structure in the dry state and to electrokinetic phenomena<br />

(streaming potentials) in the moist state nowadays<br />

has a large consensus [3]. The eventual role of<br />

these phenomena on bone regrowth and healing is presently<br />

largely debated. However, the mechanoelectrical<br />

properties of human skin have been very little studied<br />

and their origin is largely unknown.<br />

Shamos and Lavine [41 have reported observations of<br />

direct piezoelectric effects in dry, whole human skin<br />

samples from the forearm and callus from the sole.<br />

These authors, by analogy with the behavior of bone<br />

and tendons, ascribe the piezoelectric properties of<br />

human skin to oriented collagen fibrils in dermis.<br />

Athenstaedt et al. [5] have examined fresh human<br />

0018-9367/86/0600-0511$01.00 @ 1986 IEEE<br />

skin samples both in vitro and in vivo, reaching the<br />

conclusion that the observed electrical signals obtained<br />

in response to mechanical or thermal stimuli are<br />

intrinsically of piezo- and pyroelectric nature. The<br />

same authors reported measurements performed on dry<br />

skin observing a reduced (20 to 60% less) mechanoelectrical<br />

activity compared to moist samples.<br />

It is worthwhile noting that, while Shamos and Lavine<br />

ascribe the piezoelectric properties of human skin to<br />

dermal collagen network, Athenstaedt et al. suggest<br />

that these properties originate-from uniaxially oriented<br />

polar keratin filaments in the basal cells layer of<br />

epidermis. To clarify the nature of mechanoelectrical<br />

transduction phenomena in human skin and to comprehend<br />

better their microscopic origin, a systematic study of<br />

these properties both in the dry and moist state has<br />

been undertaken. We report here results obtained on<br />

dry human skin samples.<br />

SAMPLE PREPARATION<br />

511<br />

Several samples of human skin from breast, thigh, pre-<br />

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5 I 2<br />

puce, and callus from sole have been obtained from patients<br />

undergoing plastic surgery. Prepuce samples<br />

were used because they are almost entirely composed of<br />

true epidermal tissue (the horny layer is virtually<br />

absent).<br />

The samples were rinsed in distilled water, cut into<br />

circular shape (2 cm diameter) and separated into their<br />

dermal, epidermal and horny layer components by microsurgical<br />

operations. The samples were dehydrated in<br />

vacuum for 12 h.<br />

Typical dehydrated sample thickness was 300 to 400<br />

vim for whole epidermis, 100 to 200 vm for horny layer<br />

and 300 to 500 vm for dermis. Electrodes made of conducting<br />

silver-loaded paint (Acheson Colloiden B.V.,<br />

Scheemda, Holland) were applied by brushing on the surfaces<br />

of the samples used in piezoelectric measurements.<br />

Colloidal graphite electrodes were sprayed on the samples<br />

used in thermal pulse experiments. After application<br />

of the electrodes the samples were again vacuum<br />

dried for two hours.<br />

EXPERIMENTAL METHODS<br />

Dry skin is an anisotropic material which contains<br />

oriented polar crystallites in an amorphous organic<br />

matter, and its piezoelectric characterization would in<br />

principle require determination of 18 components of the<br />

piezoelectric coefficient third-rank tensor d.. (the<br />

reduced matrix notation [6] has been used in iie present<br />

work). di are the proportionality constants between<br />

the applied mechanical stress T and the generated<br />

electrical polarization P:<br />

i<br />

6<br />

=1 i _j<br />

IEEE Transactions on Electrical Insulation Vol. EI-211 No3` June 1986<br />

i (l<br />

When studying piezoelectric properties of biopolymers<br />

it is customary [7] to define a cartesian coordinate<br />

system where the z-3 axis coincides with the assumed<br />

prevailing orientation of electric dipoles, which for<br />

a-helical proteins, is colinear with the helix long<br />

axis. The x_1 axis is assumed to be perpendicular to<br />

to the skin surface.<br />

Following these definitions, d14 represents the<br />

shear piezoelectric coefficient obtained by measuring<br />

the electrical charges on electrodes deposited on skin<br />

surfaces, generated by applying an uniaxial mechanical<br />

stress in the skin plane directed 450 from the preferential<br />

orientation of piezoelectric protein fibers.<br />

Because skin shows relaxational dispersion [8], the<br />

d coefficients are in fact complex quantities having<br />

an in-phase d' real part and an out-of phase d" complex<br />

part. A frequency dependence of the piezoelectric coefficients<br />

in this case has to be expected.<br />

Angular dependence in the plane of the samples (dermis,<br />

true epidermis and horny layer) of d' and of the<br />

real part of the elastic modulus c' have been measured<br />

at 25°C and at the frequencies of 1, 10, and 30 Hz using<br />

a Rheolograph Piezo (Toyo Seiki Seisaku-sho, Tokyo,<br />

Japan). The dependence of real d' and imaginary part<br />

d" of shear piezoelectric coefficient on temperature<br />

from -100°C to 1000C at 10 Hz have also been measured,<br />

using the same apparatus.<br />

Thickness-compression piezoelectric measurements<br />

have been performed by applying square wave stress<br />

pulses generated by a flat circular plastic pin, driven<br />

by an electromagnetic shaker. Load readings have been<br />

performed by means of a miniature load cell (Type 9201,<br />

Kistler Instrumente AG, Winterthur, Switzerland) mechanically<br />

in series with the sample, while charge generated<br />

by skin samples were detected by means of a<br />

charge amplifier (Type 5007, Kistler Instrumente AG,<br />

Winterthur, Switzerland). Two different methods have<br />

been used to determine the eventual pyroelectricity of<br />

skin samples. The first method, also called the static<br />

method [9], is the only one capable of giving absolute<br />

values of the pyroelectric coefficient. The measurements<br />

have been implemented using a Thermo Controller<br />

Unit (Toyo Seiki, Seisaku-sho, Tokyo, Japan) where the<br />

temperature has been raised at a rate of 2°C per minute.<br />

The voltage appearing at the electrodes was measured<br />

with a very high input impedance (1015 Q) voltmeter<br />

built around a FET-input electrometer operational amplifier<br />

(AD 515 J, Analog Devices, Norwood, MA, USA).<br />

This method, however, is known to be effected by errors<br />

related to voltages not of pyroelectric origin<br />

which are spontaneously generated by the sample and by<br />

voltages generated by any piezoelectric material when it<br />

is nonuniformly heated (tertiary pyroelectric effect).<br />

To provide an alternative measuring techniques, the<br />

rectangular pulse heating method [9] has been used,<br />

although this method is capable of providing only relative<br />

values of the pyroelectric coefficient.<br />

A sharply focused 50 W incandescent lamp was used as<br />

light source and light pulses of 1 s duration were delivered<br />

to the skin samples to change the temperature.<br />

However, both the static method and the classical<br />

rectangular pulse heating method are only capable of<br />

providing pyroelectric informations integrated over the<br />

sample thickness.<br />

To probe the spatial distribution of polarization<br />

across the thickness of the epidermis sample, as required<br />

to evaluate the hypotesis of a pyroelectric activity<br />

in the basal cell layer tonofibrils, the Collins'<br />

thermal pulse method [10] has been used.<br />

A very short (1 ms) duration light pulse, generated by<br />

an electronic flash lamp, was delivered to the sample<br />

located in a shielded, hermetic cell through a glass<br />

window; voltage at the electrodes was amplified with the<br />

Ad 515 J operational amplifier and recorded by means of<br />

a 7912AD Tektronix transient recorder.<br />

The physical basis of this method resides in producing,<br />

by means of thermal diffusion, a transient inhomogeneous<br />

strain across the sample, in order to measure<br />

its inho-moc,neous pyroelectric res-ponsc. Altlhough the<br />

information about the polarization distribution is convoluted<br />

with a time-dependent temperature distribution,<br />

a deconvolution process is typically applied to the experimental<br />

data to obtain the first few Fourier coefficients<br />

of the polarization distribution [11]. For<br />

the purpose of the present work, however, we were only<br />

interested to detect a limiting case of spatial distribution<br />

of polarization inside epidermis where the pyroelectric<br />

response may be eventually concentrated only<br />

at one very superficial layer of the sample.<br />

In this simple case, qualitative inspection of the<br />

volatage-time responses obtained by alternating the side<br />

of the sample in respect to the impinging light is sufficient<br />

to determine eventual strong asymmetry in the<br />

pyroelectricity spatial distribution [11].<br />

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De Rossi et al.: Piezoelectric properties of dry human skin<br />

Dermis<br />

RESULTS<br />

Typical recordings of the angular dependence of the<br />

real part of the piezoelectric shear coefficient and<br />

elastic modulus are shown in Fig. 1 for dermal samples.<br />

Fig. 1: In-pZane anguZar dependence of the reaZ part<br />

of eZastic modulus (c') and piezoeZectric shear coefficient<br />

(d') for a sanple of dermis from the<br />

breast.<br />

The values of d'(max) at room temperature have been<br />

found to be of the order of 0.05 to 0.1 pC/N.<br />

The presence of one or two maxima in the in-plane<br />

polar behavior of c' obtained for different samples<br />

from different anatomical sites indicates slight preferential<br />

uniaxial or biaxial orientation of collagen<br />

fibrils in the dermal three-dimensional structural network.<br />

The invariably observed bisinusoidal behavior of<br />

d' polar response is similar to the one observed in<br />

oriented collagen structures and uniaxially oriented<br />

synthetic polypeptides [7].<br />

This kind of anisotropy can be generally expressed<br />

through the relation [12]<br />

d' = 0.5 dl4sin(2e) (2)<br />

In the case of prevailing uniaxial anisotropy, such as<br />

shown in Fig. 1, for a composite piezoelectric material<br />

where the degree of orientation is low, the following<br />

expression can be used [12], assuming collagen to<br />

originate piezoelectric activity:<br />

d' = 0.5 d04 1cF sin[2(O -<br />

0 )] (3)<br />

where dC'4 is the shear piezoelectric coefficient for<br />

the single crystallite, b the volume fraction of the<br />

paracrystalline piezoelecYric component (collagen) in<br />

the sample, Fc the degree of orientation of collagen<br />

fibers, and 0c the angle of average direction of collagen<br />

crystallites orientation.<br />

Referring to Fig. 1, if we assume the angle of average<br />

direction of collagen crystallites orientation corresponds<br />

to the maximum of angular response of the real<br />

part of elastic modulus, 8c=90 '. The relationship d(e)<br />

should be hence represented by the function:<br />

d' = 0.5d1c v F sin[2(O - 2J] (4)<br />

As the maa itude of d 4 has been measured to be 6 pC/N<br />

(18.2xlO- cgsesu) [13], the volume fraction of collagen<br />

4v in dried dermis is approximately 0.75 [14] and the<br />

measured d'(O) for dermis has been found to be 3.3xlO09<br />

cgsesu, it follows from Eq. 4 that F..= 0.05. This low<br />

value of F.<br />

would indeed imply an almost random distri-<br />

bution of collagen fiber orientation in the plane of<br />

the dermis.<br />

This finding is indeed compatible with ultrastructural<br />

observations [15]. To obtain further evidence of<br />

collagen being at the origin of piezoelectric properties<br />

of dermis, the temperature dependence of the real<br />

and imaginary components of d of dried dermis have been<br />

measured and compared with the temperature dependence<br />

of df4 and d'c4 of pure, uniaxially oriented collagen<br />

at the relative humidity of 39% [16]. As shown in<br />

Fig. 2, the pattern of the two curves is very similar,<br />

although a shift is present along the temperature axis.<br />

It is known [17] that increasing water content shifts<br />

the d'(T) curve toward lower temperature, so we ascribe<br />

this discrepancy to the higher water content of the<br />

pure collagen sample.<br />

Epidermis<br />

Typical recording of c' and d' angular dependence<br />

are shown in Fig. 3 for samples of whole epidermis<br />

(horny layer was not removed).<br />

The value of d'(max) at room temperature has been<br />

found to be typically of the order of 0.01 to 0.03<br />

pC/N. As in the case of dermis, piezoelectric response<br />

can be described in terms of in plane shear<br />

stress piezoelectricity originating from slight preferential<br />

orientation (uniaxial or biaxial) of fibrous<br />

proteins in the tissue.<br />

In Fig. 4 the temperature dependences of d' and d"<br />

are reported for true epidermis and horny layer, together<br />

with rhinoceros horn samples. Close similarities<br />

can be observed. It appears that, in analogy<br />

with rhinoceros horn samples, the piezoelectric response<br />

of human epidermis can be ascribed to keratinlike<br />

a-helical fibers. True piezoelectric response<br />

(polar) to uniaxial thickness compression has not been<br />

observed in epidermal samples, although erratic stressgenerated<br />

potentials usually were observed.<br />

Thermal pulse experiments were performed on samples<br />

of epidermis to eventually verify the suggested hypothesis<br />

[5] of basal cell layer tonofibrils being responsible<br />

for the suggested piezo- and pyroelectric<br />

properties of epidermis. Thermally generated electric<br />

signals were not clearly pyroelectric in nautre, and<br />

sample reversal in respect to the radiant heat source<br />

did not show any marked asymmetry in charge response.<br />

Horny Layer<br />

513<br />

The characteristic features of piezoelectric response<br />

of the horny layer have been found to be very similar<br />

to those of true epidermis. However, d'(max) of the<br />

horny layer has been found to be of the order of 0.1<br />

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5;14<br />

i<br />

13<br />

z<br />

e1<br />

>1<br />

-Dermis<br />

-Oriented Collagen<br />

Fag. 2: Temrperature dependence of reaZ (dLf) and<br />

imaginary (d"' ) parts of shear stress piezoeZectric<br />

coefficient ot human dermis and pure coZZagen<br />

(coZZagen data from [13]).<br />

to 0.2 pC/N, a factor 5 to 10 times higher than the<br />

typical value of true epidermis. Neither pyroelectri c<br />

response nor thickness compression piezoelectricity<br />

were detected in the horny layer samples.<br />

A MODEL <strong>OF</strong> <strong>SKIN</strong> <strong>PIEZOELECTRIC</strong>ITY BASED ON<br />

MICROSTRUCTURAL ORGANIZATION<br />

<strong>OF</strong> FIBROUS PROTEINS<br />

Fibrous proteins constitute a major component of skin.<br />

IEEE Transactions on Electrical Insulation Vol. EI-21 No.3,<br />

/<br />

T(C)<br />

/<br />

June 1986<br />

They are, in the epidermal cells or in the form of fully<br />

developed keratin in the horny layer or finally as<br />

a three-dimensional network of collagen filaments in<br />

dermis (also containing elastin and reticulin) [15].<br />

M<br />

_-<br />

0.5<br />

0<br />

-0.5<br />

E<br />

4 z<br />

Fig. 3: In-pZane anguZar dependence of the reaZ<br />

part of elastic moduZus (c') and piezoeZectric coefficient<br />

(dT) for samples of epidermis from the<br />

thigh.<br />

The organization and orientation of fibrous proteins<br />

show distinctive features in the three cutaneous sections<br />

which may prove to be related strictly to the<br />

particular tensorial form assumed by the piezoelectric<br />

coefficients and to the eventual presence of local symmetry<br />

in the orientational arrangement, which may be<br />

compatible with pyroelectric activity.<br />

Fig. S shows a schematic drawing of skin, where the<br />

arrangement of fibrous proteins, as determined from<br />

X-ray analysis or ultrastructural observations [15], is<br />

clearly evident.<br />

The collagen network of dermis, as compared to the<br />

collagenous structural frame of other connective tissues<br />

such as bone and tendons, appears to be less ordered<br />

and oriented. Some degree of orientation, however,<br />

exists and it varies from one area to the next.<br />

For the sake of formulating a structural model of<br />

piezoelectricity in dermis, a loose, slightly oriented<br />

collagen network is compatible with shear piezoelectricity,<br />

but does not support any pyroelectric activity.<br />

These findings have been indeed observed in the<br />

present study as previously described.<br />

A more complex picture needs to be analyzed for what<br />

fibrous proteins arrangement is applicable to human<br />

epidermis. It appears that piezoelectric properties in<br />

epidermis originate from a-helical keratin-like tonofibrils,<br />

and their orientational arrangement is crucial<br />

to infer possible structures of their corresponding coefficient<br />

tensor. An almost uniaxial orientation of<br />

tonofibrils perpendicular to the plane of the epidermis<br />

is indeed found in the basal cells layer [18],<br />

these tonofibrils being seen as precursors of fully<br />

developed keratin. The uniaxial arrangements of tonofibrils<br />

in the basal cells is progressively lost in upwards<br />

epidermal areas to assume a more isotropic, star-<br />

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2<br />

o


De Rossi et al.: Piezoelectric properties of dry human skin<br />

0<br />

E<br />

10<br />

'N<br />

1<br />

E<br />

-<br />

.5<br />

-.5<br />

-1L<br />

- - - Rhinoceros horn<br />

14 _ - Skin horny layer<br />

o\\\ - - True epidermis<br />

-100 -50 0 50 T(C)<br />

d4 --- Rhinoceros horn<br />

- Skin horny layer<br />

- - True epidermis<br />

-100 -50 -\ 0 50 T(T)<br />

_. \E .<br />

'\, /''\ ~~~~~~I<br />

Fig. 4: Temperature dependence of real (df4) and<br />

imaginary (dr ) parts of shear stress piezoeZectric<br />

coefficient of human true epidermis and<br />

horny Zayer and rhinoceros horn (rhinoceros<br />

horn data from [13]).<br />

like arrangement in the spinous layer t15].<br />

In the horny layer the cells become fully cornified<br />

and flattened, and filaments account for almost half of<br />

the total protein content [15]. These keratin filaments<br />

are predominantly parallel to the plane of skin<br />

[19].<br />

In the case of uniaxially oriented tonofibrils in the<br />

basal cell layer, assuming isotropy in the plane perpendicular<br />

to the helical axis, the kind of symmetry<br />

Fig. 5: Schematic diagram showing the Layering of<br />

skin where the fibrous proteins organization is<br />

evident. ExtraceZZuZar coZZagenous mesh of dermis<br />

is shown in the bottom, while the intracelZular<br />

tonofibriZs in the epidermis are shown to progressiveZy<br />

change their orientation from an aZmost<br />

uniaxiaZ arrangement perpendicuZar to skin<br />

surface in the basaZ ceZZ Zayer to an horizontaZ,<br />

aZmost uniplanar arrangement in the horny Zayer.<br />

which can be hypothesized is C.co().<br />

This symmetry calls for the following form of the<br />

piezoelectric coefficient matrix [7]:<br />

II0 0 0 d14 dl 5 0<br />

d = O O d1 5 -d1 4 °<br />

d31 d31 d33 0<br />

This sort of symmetry would also support pyroelectric<br />

activity [9]. This reasoning is the basis of<br />

Athenstaedt's speculations on the origin of pyroelectric<br />

activity he claimed to exist in epidermis [5]. Except<br />

for a layer of one cell thickness (the basal layer)<br />

a more comples form of d should be postulated, were<br />

probably all the 18 d coefficients should be non-zero.<br />

The keratin organization in the horny layer allow to<br />

suggest a Dm (X22) form of symmetry and consequently [7]<br />

a very simple form of the d matrix.<br />

0 0 d14 0 0<br />

d - 0 0 0 0 -d14 0<br />

0 00 0 0<br />

This kind of symmetry supports neither pyroelectric nor<br />

thickness-compression piezoelectric properties.<br />

The higher degree of in-plane orientation and the<br />

larger fractional content of fibrous proteins in the<br />

horny layer in respect to true epidermis would suggest<br />

a higher piezoelectric activity in the horny layer.<br />

This fact has indeed been observed in the present study,<br />

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0<br />

(5)<br />

(6)<br />

515


516<br />

SYNTHETIC POLYMER ANALOGS <strong>OF</strong><br />

<strong>PIEZOELECTRIC</strong> <strong>DRY</strong> <strong>SKIN</strong><br />

In the process of investigating the microscopic origin<br />

of piezoelectric properties of biological materials,<br />

comparison with artificial piezoelectric material<br />

of inorganic and organic nature, has often been of<br />

valuable help [3]. To provide further insight into the<br />

nature of the piezoelectric activity of true epidermis,<br />

two synthetic polymer analogs have been prepared and<br />

characteri zed.<br />

The first physical model is made of a film of uniaxially<br />

oriented polyhydroxybutyrate (PHB), a semicrystalline<br />

biopolymer of bacterial origin which is known to<br />

assume a D (c22) symmetry upon mechanical drawing [20].<br />

PHB samples were supplied by Marlborough Ltd., Stocktonon-Tees,<br />

U.K. in the form of 200pm thick films, uniaxially<br />

stretched to 3.7 times.<br />

The second analog is made of a 120pm thick polyvinylidene<br />

fluoride (PVDF) film which has been purposely<br />

poled under a temperature gradient of 40%C and at a low<br />

electric field (0.5 MV/cm) following the method indicated<br />

by Marcus [211 to concentrate its piezo- and pyroelectric<br />

activity in a very thin layer close to one<br />

of the electrodes. This would in some aspect model the<br />

given picture of basal cell layer piezo- and pyroelectric<br />

properties. Comparative evaluation of the two<br />

polymers with true epidermis samples, performed by the<br />

experimental procedures used in the present work, has<br />

shown a very marked phenomenological analogy between<br />

PHB and epidermis piezoelectric properties.<br />

CONCLUSION<br />

Human dermis, true epidermis, and horny layer, all<br />

show piezoelectric activity. The preponderant contribution<br />

appears to originate from shear piezoelectricity<br />

of collagen network in dermis, and a-helical keratinlike<br />

fibrils in epidermis and horny layer. The horny<br />

layer typically shows the highest activity.<br />

No experimental evidence has been found for the suggested<br />

hypothesis [5] of pyroelectric response in the<br />

epidermis arising from uniaxially oriented tonofibrils<br />

in the basal cell layer being perpendicular to the dermal-epidermal<br />

junction. This hypothesis, however, cannot<br />

be totally discarded because more refined measuirement<br />

techniques are possibly needed to detect the very<br />

low level of pyroelectric activity and thickness compression<br />

piezoelectric response originating from a<br />

single cell layer. Strong contribution to electromechanical<br />

or thermomechanical response of human skin<br />

in the dry state has been found to arise from trapped<br />

charges, as is to be expected, because of the high ionic<br />

content of skin tissue. Finally, we observed piezoelectric<br />

decay with increasing moisture content. This<br />

fact does not corroborate the hypothesis [5] of piezoand<br />

pyroelectricity being a major effect in moist skin<br />

electromechanical properties.<br />

REFERENCES<br />

[1] A.J. Grodzinsky, "Electromechanical and physicochemical<br />

properties of connective tissue" CRC<br />

Crit. Rev. Biomed. Eng. Vol 9, pp. 133-197, 1983.<br />

IEEE Transactions on Electrical Insulation Vol. EI-21 No.3, June 1986<br />

[2] C.T. Brighton, J.Black and S.R. Pollack, Electrical<br />

properties of bone and cartilage: experimental<br />

effects and clinical applications,<br />

Grune & Stratton NY, 1979.<br />

[3] W.S. Williams, "Piezoelectric effects in biological<br />

materials", Ferroelectrics Vol 41, pp. 225-<br />

246, 1982.<br />

[4] M.H. Shamos and L.S. Lavine, "Piezoelcetricity as<br />

a fundamental porperty of biological tissues",<br />

Nature Vol 213, pp. 267-269, 1967.<br />

[5] H. Athenstaedt, H. Claussen and D. Schaper,<br />

"Epidermis of human skin: pyroelectric and piezoelectric<br />

sensor layer", Science Vol 216, pp.<br />

1018-1020, 1982.<br />

[6] J.F. Nye, Physical properties of crystals, The<br />

Clarendon Press, Oxford 1957, Chapter 7.<br />

[7] E. Fukada, "Piezoelectric properties of biological<br />

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Manuscript was received 4 November 1985.<br />

This paper was presented at the 5th InternationaZ<br />

Symposium on EZectrets, HeideZberg, Germany, 4-6<br />

September 1985.<br />

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