PIEZOELECTRIC PROPERTIES OF DRY HUMAN SKIN
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 />
polymers", Quart. Rev. Biophys. Vol 16, pp.<br />
59-87, 1983.<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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