Statistical characterization of piezoelectric coefficient d23 in cow bone

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					                                                  Journal of Biomechanics 32 (1999) 573}577




              Statistical characterization of piezoelectric coe$cient d
                                                                       
                                      in cow bone
                                           G. Aschero  , P. Gizdulich  *, F. Mango
                          Clinical Physiopathology Department, University of Florence, Viale Pieraccini 6, 50134 Firenze, Italy
                        INFM, Research Unit of Pisa, Physics Department, University of Pisa, Piazza Torricelli 2, 56126 Pisa, Italy
                                                            Received in "nal form 13 January 1999


Abstract

  In a newly developed, highly sensitive dilatometer we applied pulsatile electric "elds to "ve dry bone samples cut from mid-tibial
sections within a 903 angle from the rear to front axis. Samples of "ve cows were studied. We measured the piezoelectric coe$cient
d establishing its mean and con"dence interval for the "rst time. An analysis of variance detected a signi"cant di!erence of the
 
coe$cient between animals (P(0.01) but not between samples (P"0.5). Between animals the coe$cient ranged from 9.6;10\ to
27.1;10\ C/N. It can no longer be assumed that piezoelectricity is an inherent property of bone, constant between ani-
mals.     1999 Elsevier Science Ltd. All rights reserved.

Keywords: Piezoelectricity; Bones: Nanodilatometry; Statistics; Optical levers




1. Introduction                                                                       2. Materials and methods

   The electromechanical behavior of bones has been                                   2.1. Sample preparation
studied extensively, theoretically (Johnson et al., 1980;
Korosto!, 1979; Roesler, 1987) and experimentally                                        Tibia bones were extracted from "ve healthy, two-
(Aschero et al., 1996a; Bur, 1976; Fukada and Yasuda,                                 year-old cows of the &chianina' breed at a slaughter
1957; Otter et al., 1985). The piezoelectric coe$cients d                             house. Rings were cut at the mid-tibial position and "ve
                                                          GH
(Standard IEEE, 1988) of the standard linear theory of                                samples were cut from the rings at adjacent angular
piezoelectricity provide a useful tool to describe the phe-                           positions around the longitudinal axis within a 903 range,
nomenon, and are commonly used. In spite of this, pub-                                noting their orientation. The geometry was de"ned by
lished sets of d data are few. Moreover, published coe$-                              the reference system of Fig. 1. It shows the radial axis
                GH
cients d di!er so much between each other as to strongly                              r and the tangential axis t. The longitudinal axis z of the
        GH
reduce their utility (Martin, 1979), and may even lead to                             tibia is perpendicular to the plane of the paper, rising
wrong predictions in some cases (Williams and Breger,                                 from it. A typical sample measured l "19 mm, l "
                                                                                                                                 X            P
1975). Thus, although theory advanced considerably                                    0.8 mm, l "5 mm.
                                                                                                 R
since 1979, with several valuable papers published, ex-                                  In the central part of the compact bone cuts were made
perimentation did not.                                                                using a low-velocity ((2 cm/s) cutting machine. Using
   Having constructed a nanometer sensitivity dilatom-                                "ne grain (P 280) sand paper each sample was ground to
eter we decided to study possible causes of data variance                             a rectangular shaped block. During cutting and grinding
experimentally. In this paper, we present a set of repeated                           physiological saline solution or air jets were used to keep
measurements of coe$cient d on 25 cow bone samples                                    the bone temperature below 403C.
                               
aiming at the statistical evaluation of experimental error                               All samples were extracted and shaped within 24 h
and biological variance.                                                              after slaughtering and were allowed to dry under exposi-
                                                                                      tion to air at room temperature and 50% relative humid-
                                                                                      ity for a minimum of 10 days. The average moisture
  * Corresponding author. Tel.: 0039-055-422-2339; fax: 0039-055-412-                 content did not change more than 0.05% after the
396; e-mail: pagizd@cesitl.unift.it.                                                  "rst 10 h from sample preparation time, with a steady

0021-9290/99/$ - see front matter              1999 Elsevier Science Ltd. All rights reserved.
PII: S 0 0 2 1 - 9 2 9 0 ( 9 9 ) 0 0 0 2 1 - 4
574                                        G. Aschero et al. / Journal of Biomechanics 32 (1999) 573}577

                                                                            resolution is better than 10\ m in a single cycle. By
                                                                            synchronous averaging and "ltering a resolution of
                                                                            10\ m can be reached in 20 min. The present experi-
                                                                            ment usually required averaging over 20 cycles or 1 min.
                                                                            However, in a few cases the series averaging time had to
                                                                            be increased to a maximum of 30 min.
                                                                               All measurements were performed at room temper-
                                                                            ature, at ambient air pressure and humidity. An analog to
                                                                            digital conversion board (Analog Devices RTI-815) sam-
                                                                            pled the dilatometer's output every 10 ms, and stored the
                                                                            responses on hard disk for further elaboration. With the
                                                                            electrical "eld applied along the radial r-axis of the bone,
                                                                            the displacements were detected along its longitudinal
Fig. 1. The coordinate system used in a transverse sectioned ring of        axis z. Thus, we obtained the coe$cient d , or d ac-
a tibia. The positions of the "ve adjacent samples are also shown. Axes                                                   PX      
                                                                            cording to the IEEE convention (Standard IEEE, 1988),
r ant t are the radial and tangential direction, respectively. Axis z is
perpendicular to the paper, directed toward the reader, and is the
                                                                            by the equation
longitudinal axis of the tibia. With the animal standing, axis z directs
                                                                                     ;l
skywards. Axis r shown for site 1 directs from the rear to the front of
                                                                           d "        P ,                                         (1)
the animal.                                                                    Sl <
                                                                                     X
                                                                            with ; the voltage output of the dilatometer and S its
moisture content ranging from 5 to 7% between samples.                      sensitivity (in V/m) as calibrated. < is the potential
Thus we considered our samples &dry' and their biophysi-                    di!erence applied to the bone sample. It has negligible
cal characteristics proved &stable' (Gizdulich and As-                      error. For our dilatometer S has (0.5% error, and
chero, 1993).                                                               ; has a 1% error. The sample lengths l and l (Fig. 1) are
                                                                                                                   P      X
                                                                            measured to a 0.5% accuracy. Thus, the estimated rela-
2.2. Stimulation procedure                                                  tive error is (3%, as demonstrated elsewhere (Giz-
                                                                            dulich et al., 1999).
   Conductive silver paint (Agar Scienti"c Ltd.) was ap-                       A source of systematic absolute error is the hysteresis
plied to the two larger faces perpendicular to the radial                   of the Physik Instrument Model 249.20 piezoelectric
axis r. The silver paint not only has an excellent conduct-                 stack used to calibrate our dilatometer. Earlier (Aschero
ivity but also remains highly #exible. Silver wires were                    et al., 1996b), we estimated the maximum uncertainty
embedded in the wet silver paint to make electrical con-                    introduced by hysteresis during calibration at 15%. This
tact to the electrodes.                                                     problem does not a!ect the relative results presented in
   After placement in the dilatometer, an electrical "eld                   this paper, but may be important for future absolute
was applied, generated by a programmable voltage                            comparisons.
source (Keithley Model 236), controlled by a PC via an
IEEE-488 port. The potential di!erence between the elec-                    2.4. Statistics
trodes was initially zero. At time t the voltage was raised
                                                                              Measurement values di!er when repeated on the same
to the preprogrammed level in less than 1 ms, lasting
0.1 s, to be returned to zero at time t . The potential                     bone sample, between bone samples and between cows
                                                                           (further called subjects). To resolve the various sources of
di!erence applied was 220 V. The maximum electrical
"eld strength was 300 kV/m. We could "nd no statistical                     variance we analyzed the data with a &nested' analysis of
dependence d on the voltage applied. Field polarity was                     variance (ANOVA), also called &within subjects ANOVA'
               GH                                                           (Keppel, 1982). In this analysis, measurements are repeat-
such that a dilatation resulted. Measurement cycles were
repeated at 3 s intervals to allow for hysteresis e!ects to                 ed in the same subjects, and the ANOVA type is named
disappear. The several averaged measurement cycles, to                      &(AxS)'. A indicates the "ve adjacent mid-tibial anatom-
improve resolution, represent one series and yield one                      ical sites, S represents the "ve subjects.
measurement result.

2.3. Measurement of displacement                                            3. Results

  We expected displacements in the range from 10\ to                         Fig. 2 shows a typical dilatometer output response.
10\ m. They were measured using the dilatometer                           When the static electrical "eld to the bone sample is
described previously by Gizdulich et al. (1999), which                      suddenly switched on an immediate piezoelectric re-
was designed and constructed for the purpose. Its static                    sponse is observed, followed by a slow relaxation. The
                                          G. Aschero et al. / Journal of Biomechanics 32 (1999) 573}577                                          575

                                                                           Table 2
                                                                           Nested analysis of variance applied to the data in Table 1. The variance
                                                                           ratio, F, of 6.03 between subjects is signi"cant (P(0.01), the one
                                                                           between sites is not. DF are the degrees of freedom

                                                                           Source              Deviance         DF          Variance         F

                                                                           A: sites             132.61           4           33.15           0.83
                                                                           S: subjects          967.73           4          241.93           6.03
                                                                           A;S: error           641.67          16           40.10
                                                                           total:              1742.01          24           72.58
Fig. 2. Elongation in the longitudinal direction of a bone sample when
stimulated by a square wave electrical "eld with amplitude
E"300 kV/m in the radial direction. The "eld is applied at t and
                                                                 
removed at t .                                                             Table 3
             
                                                                           The d values pooled per subject and their standard deviation S.D.
                                                                                 
                                                                           N is the total number of measurements for that subject. The group
                                                                           average is shown in the last row
Table 1
Measurement results of piezoelectric coe$cient d on 25 dry bone
                                                                         Animal                  Mean                   S.D.             N
samples of "ve cows, expressed in 10\ C/N units
                                                                           1                       27.1                   5.7               27
Sample          Mean           S.D.         n            Range
                                                                           2                       12.5                   8.1               23
                                                                           3                       12.1                   3.2               17
1-1             18.77          0.32          4           17.84}19.70
                                                                           4                       16.3                   6.2               22
1-2             24.86          0.83         10           24.01}25.71
                                                                           5                        9.6                   4.4               19
1-3             28.80          1.12          5           26.49}31.11
1-4             27.26          0.66          3           23.48}31.04       All                     16.4                   8.8              108
1-5             36.45          3.18          5           29.90}43.00
2-1              6.31          0.17             5         5.96}6.66
2-2              9.15          0.49             4         7.72}10.58
2-3             13.66          1.29             5        11.00}16.32         Results of the (AxS) analysis of variance are given in
2-4              7.67          0.38             5         6.89}8.45        Table 2.
2-5             28.15          5.25             4        12.82}43.48         The di!erences between sites are not signi"cant but
3-1             12.46          0.28             5        11.88}13.04       they are between subjects, at P(0.01. Interaction be-
3-2             11.25          0.76             3         6.90}15.60       tween subjects and sites is not tested in this type of
3-3              9.36          0.14             3         8.56}10.16       ANOVA (Keppel, 1982). Because there was no statistical
3-4             17.64          2.94             3         0.79}34.49
3-5              9.33          1.18             3         2.57}16.09
                                                                           di!erence between sites, we pooled their data to obtain
                                                                           the subject means and standard deviations (Table 3). The
4-1             26.37          2.71             5        20.79}31.95
                                                                           coe$cient d appears to di!er over a three to one range
4-2              9.78          0.44             4         8.50}11.06                   
4-3             16.84          2.53             4         9.45}24.23       between animals.
4-4             12.49          0.24             5        12.00}12.98
4-5             14.72          0.72             4        12.62}16.82
5-1              4.37          0.23             3         3.05}5.69        4. Discussion
5-2              8.40          0.27             5         7.84}8.96
5-3              9.55          1.38             3         1.64}17.46         Using a highly sensitive dilatometer and a computer
5-4             16.84          2.87             4         8.47}25.22
5-5              7.84          0.64             4         5.97}9.71        controlled measurement rig, we presented for the "rst
                                                                           time values for the piezoelectric coe$cient d of tibia
                                                                                                                          
                                                                           bones of cow, including the within and the between
                                                                           variance of specimen and the variance between animals.
value used for ; in Eq. (1) is the amplitude of the                        This information is important because data reported up
immediate response. This type response is typical for                      to now show great and unexplained di!erences between
piezoelectric materials. The viscoelastic characteristics of               publications.
bone make the relaxation particularly apparent (Mango                        There are several explanations possible for the great
et al., 1997).                                                             di!erences between data reported in literature. First,
   Table 1 lists the individual d measurement results                      variance might arise from unreported experimental er-
                                  
of each of the "ve specimen of each of the "ve animals.                    rors. Second, variance might be introduced by the di!er-
Measurements were repeated n times on the same                             ent techniques for preparing the samples. A bone
bone sample. Mean, standard deviation S.D., total                          sample's physical properties may alter irreversibly due to
number of measurements, and 99% con"dence interval                         changes in moisture content, or to drying and re-wetting
are given.                                                                 (Bur, 1976; Currey, 1988; Reinesh and Nowick, 1975).
576                                   G. Aschero et al. / Journal of Biomechanics 32 (1999) 573}577

Third, repeated measurements on the same sample may                    easiest direction to establish potential di!erences by the
lead to di!erent values (Aschero et al., 1995). Fourth, due            body. In the longitudinal direction the body's principal
to the biological nature of the samples there is the normal            stress components are supported. Thus, a mechanical
physiological variability among animals. To distinguish                and an electrical axis are linked, working together to
between these various sources of variability only a statist-           generate the piezoelectric e!ect. As bio-piezoelectricity
ical analysis can help. However, in many pioneering                    can be considered a possible physiological mediator
studies the measurement's repetitions, the experimental                for Wol!'s law (Roesler, 1987), the radial and the
errors, and laboratory circumstances are often not de-                 longitudinal directions seemed an obvious measurement
scribed in su$cient detail to make such analyses post                  choice.
hoc.                                                                      This geometry was also chosen to obtain samples that
   Instead, research on bone piezoelectricity focused on               had been exposed to dissimilar stresses in vivo. We rea-
certain physical aspects, such as symmetry of the                      soned that the asymmetry in biomechanical function
piezoelectric tensor, dependency on frequency, humidity,               might have created similar asymmetries in the local
or temperature, and identi"cation of the microscopic                   piezoelectric behavior. Of course, samples extracted
sources of the e!ect. Therefore, only single samples were              along the radial or the longitudinal direction would have
often studied in the past and pooled measurements, or                  been subjected to dissimilar stresses too. The radial direc-
data statistics remained absent.                                       tion, however, poses considerable experimental problems
   Bone piezoelectricity does present several intriguing               since the thickness of the compact bone along the radial
physical aspects, some of them still unclear, and some of              axis is too small to harvest the many samples of accept-
them easily studied in single samples. On the other hand,              able thickness needed for statistical analysis. Thickness,
practical applications often require the knowledge of                  in particular, must be su$cient to prevent thermal and
data for a reference, normal or healthy population, for                mechanical #utter from Joule and environmental e!ects
example in physiology, prosthesis design, or fracture                  during the dilatometric measurements.
healing. However, for such applications even obvious
factors such as the in#uence of species, sex, age, and                 4.2. Discussion of results
health on d coe$cients are still unknown.
             GH
                                                                          Of the 99% con"dence intervals reported in Table 1 as
4.1. Discussion of methods                                             range, none includes or overlaps zero. This indicates that
                                                                       experimental error is less than the magnitude of the
   We used the converse piezoelectric e!ect and measured               quantities we attempted to measure. This fact is also
a bone specimen's motion under an applied electric "eld.               theoretically important in the identi"cation of a possible
This approach avoids the electrode response, which over-               symmetry in the piezoelectric tensor. Fukada and
whelms the piezoelectric response when electrodes are                  Yasuda (1964) suggested that the C hexagonal polar
                                                                                                                
mechanically compressed when attempting to measure                     class of symmetry should be a good candidate. In 1973,
the direct piezoelectric e!ect (Aschero et al., 1996a;                 however, Libo! and Shamos reconsidered previously
Romano et al., 1997).                                                  published measurements, including their own (Libo! et
   A similar approach was taken by Fukada and Yasuda                   al., 1971), to conclude that no proof of any symmetry in
(1957), and Reinesh (1974). Fukada and Yasuda's experi-                the piezoelectric matrix had as yet been given. For
mental specimen (Fukada, 1955) consisted of several                    example, Libo!'s d was 1.8;10\ C/N, but a non-
                                                                                             
piled disks tightly clamped together. Bone disks were                  zero d value is not compatible with C symmetry. This
                                                                                                                
alternated with metallic electrodes and piezoelectric crys-            argument is now strongly supported by the present
tals. In this setup the bone samples were subjected to high            measurements that also present non-zero results and
stresses mainly due to the thermal elongation induced by               which include an analysis of variance, con"dence inter-
the electrical stimulation. However, when measuring the                vals, and experimental error estimates, and should thus
converse e!ect the d should be observed at zero stress by              be reliable both from a physics and a biological point of
                       GH
de"nition (Standard IEEE, 1988). Even though the e!ect                 view.
of stress on dry bone piezoelectricity is probably negli-                 We found no evidence of di!erences among anatom-
gible, this is not a certain fact. We, therefore, considered it        ical sites in our tibia rings. This results is important for
unsafe to use this technique for our purpose.                          methodological and theoretical reasons. Methodologi-
   We conducted our study on bone samples from several                 cally, to obtain a better overall estimate, pooling is
adjacent sites positioned around the longitudinal axis                 often required of data obtained from di!erent samples.
(Fig. 1). Coe$cient d of the piezoelectric tensor links                This requires samples with the same behavior, an issue
                          
the radial direction with the longitudinal direction of the            that has not been determined until now. We believe we
bone. In the radial direction the medullary cavity is                  can now assert that a pooling of data, under the de-
connected to the periosteum, two sites with a great                    scribed experimental conditions, is a statistically safe
abundance of electrolytes and #uids, and probably the                  procedure.
                                        G. Aschero et al. / Journal of Biomechanics 32 (1999) 573}577                                          577

   The second reason is theoretical. In the past, Johnson                Aschero, G., Romano, S., Gizdulich, P., 1995. Evidence of electrical
et al. (1980) proposed that the d might not be constant                     hysteresis in bones. Electro- and Magnetobiology 14(3), 199}215.
                                   GH                                    Bur, A., 1976. Measurements of the dynamic piezoelectric properties of
inside a single bone along the radial axis, but rather
                                                                            bone as a function of temperature and humidity. Journal of Bi-
change in linear fashion. By this assumption several dis-                   omechanics 9, 495}507.
crepancies between the piezoelectric behavior of bones                   Currey, J., 1988. The e!ect of drying and re-wetting on some mechan-
and quartz could be easily explained. Perhaps even more                     ical properties of cortical bone. Journal of Biomechanics 21(5),
important, they thus implicitly pointed out that there was                  439}441.
no reason to assume the d spatially constant, a priori.                  Fukada, E., 1955. Journal of Applied Physics Japan 24, 299 (in Ja-
                             GH                                             panese).
Taking our samples in another direction, from a 903                      Fukada, E., Yasuda, I., 1957. On the piezoelectric e!ect of bone. Journal
segment around the longitudinal axis, and "nding no                         of Physics Society of Japan 12(10), 1158}1162.
signi"cant di!erence between samples, therefore, does                    Fukada, E., Yasuda, I., 1964. Piezoelectric e!ect in collagen. Japan
not disprove the theoretical argument of Johnson and                        Journal of Applied Physics 3(2), 117}121.
colleagues.                                                              Gizdulich, P., Aschero, G., 1993. Day-to-day trend of dielectric proper-
                                                                            ties of bones. In: Proceedings of the 15th Conference IEEE. S.
   The di!erences between subjects were tested (Table 2)                    Diego.
and found signi"cant (P(0.01), demonstrating that in-                    Gizdulich, P., Aschero, G., Mango, F., 1999. An optical dilatometer for
dividual physiological variability cannot be neglected.                     picometer displacements. Journal of Physics E: Measurement
Thus, although averages may probably be computed with-                      Science and Technology 10, 232}238.
in the same animal, future pooling of data should be                     IEEE, 1988. Standard on Piezoelectricity: ANSI-IEEE Std 176-1987.
                                                                         Johnson, M., Williams, W., Gross, D., 1980. Ceramic models for
restricted to single animals. Alternatively, pooling reliabi-               piezoelectricity in dry bone. Journal of Biomechanics 13,
lity should be proved under a suitable statistical protocol.                565}573.
   The di!erences among subjects suggest that the d are                  Keppel, G., 1982. Design and Analysis. Prentice-Hall, Englewood Cli!s,
                                                       GH                   NJ.
not as general a property as we perhaps thought. Until
proven otherwise, it is no longer safe to assume that all                Korosto!, E., 1979. A linear piezoelectric model for characterizing
                                                                            stress generated potentials in bone. Journal of Biomechanics 12,
bones share the same d just because they are bones. This
                        GH                                                  335}347.
fact poses severe limitations on our ability to compare                  Libo!, A., Shamos, M., 1973. Solid state physics of bone. In: Biological
data in the literature, and draw general conclusions                        Mineralization. Wiley, New York.
about the quantitative aspects of bio-piezoelectricity.                  Libo!, A., Shamos, M., DeVirgilio, W., 1971. Paper ThAm-F3. In:
                                                                            Proceedings of the 15th Annual Meeting of the Biophysical Society.
                                                                            New Orleans.
5. Conclusion                                                            Mango, F., Aschero, G., Romano, S., Gizdulich, P., 1997. Thermal
                                                                            dilatation coe$cients of cow bones. In: Proceedings of the World
                                                                            Congress on Medical Physics and Biomedical Engineering. Nice,
  By designing the experimentation to allow an analysis                     France.
of variance on the data we were able to show that the                    Martin, R., 1979. Theoretical analysis of the piezoelectric e!ect in bone.
piezoelectric coe$cient d is independent of the anato-                      Journal of Biomechanics 12, 55}63.
                                                                       Otter, M., Shoenung, J., Williams, W., 1985. Evidence for di!erent
mical site of extraction, given the sites chosen, but de-
pendent on the individual animal. It can no longer be                       sources of stress-generated potentials in wet and dry bone. Journal
                                                                            of Orthopedic Research 3, 321}324.
assumed that piezoelectricity is an inherent property of                 Reinesh, G., 1974. Dielectric and piezoelectric properties of bone as
bone constant between animals.                                              functions of moisture content. Ph.D. thesis, School of Engineering
                                                                            and Applied Science, Columbia University.
                                                                         Reinesh, G., Nowick, A., 1975. Piezoelectric properties of bone as
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