Characterization of bone materials as ultrasonic transducers

Characterization of bone materials as ultrasonic transducers

Characterizationof bone materials as ultrasonictransducers Surendra Singh Department of Biomedical Engineering, Rensselaer PolYtechnic Institute, Tro...

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Characterizationof bone materials as ultrasonictransducers Surendra Singh Department

of Biomedical Engineering, Rensselaer PolYtechnic Institute, Troy, New York 12 180, USA

Harcharan Singh Ranu Depaflment of Biomedical Engineering, Louisiana Technical University, Ruston, Louisiana 7 1272 (Received 23 October 1984; revised 27 November 1985)


Physical, dielectric, piezoelectric and electromechanical parameters have been reported for bone and its two major constituents i.e. collagen and apatite, for their characterization as ultrasonic transducer materials. Collagen and apatite have been extracted from full bone using well known methods. These materials have been used to prepare simple disc-shaped test pieces (dimensions: diameter 10 mm and thickness 1.0 f 0.01 mm). The variation of various electrical parameters with frequency in the region (l-108 MHz) is examined for these materials. These include impedance, phase angle, relative voltage output, quality factor ‘Q’, dielectric constant and resistivity. The data so obtained are compared with those for ceramic and quartz transducers. The observations on impedance, phase and relative voltage output for bone materials indicate that the first resonance peak falls around 58 MHz followed by second and third harmonics around 112 MHz and 168 MHz respectively. A low ‘Q’ value suggests a fairly wide band transducer, while other parameters compare favourably with ceramic and quartz materials. Bone material has also been used to obtain a transducer in the standard configuration and velocity dispersion in the frequency range l-108 MHz is examined. Keywords: Bone materials, collagen, apatite, ultrasonic transducers, piezoelectric behaviour

The physical processes associated with the control of bioelectric bone behaviour have received extensive investigation and electrical and mechanical properties of bone have been reported’-3. A study of the solid state properties of bone has been carried4, 5 out in order to gain an understanding of the physical properties of bone. It is still a major task to fit these data into a single framework, pertaining to an overall biological phenomenon. The piezoelectric behaviour of bone indicates that it may behave as an ultrasonic transducer and respond to dynamic loading. A systematic survey of piezoelectricity in bone was initiated by Fukada and Yasuda’wherein the value of electromechanical coupling coefficient ‘k’, charge constant (d) and voltage constant (g) were estimated under static and dynamic loading. As a corollary to this, electromechanical effects in viva’-’ and in vitro’“-‘2 have been identified and their relevance to bone electrical activity has been emphasized. In the megahertz (MHz) range of frequencies, ultrasound has found increasing use for diagnostic13 and therapeutic purposes’4,‘5. Transducers in the frequency Correspondence to Dr S. Singh. 6 1986 432


1986, Vol 7 November

range l-10 MHz are available, possessing wide power handling capacities. The small use of higher frequency ultrasound in the study of biological phenomenon may be due to the lack of appropriate transducers and because high frequency (> 10 MHz) ultrasound may not have much penetration on account of high absorption at these frequencies. A number of piezoelectric transducers are available for a frequency of 1 MHz, but in the vicinity of 10 MHz, their response declines. Firstly to bridge this gap and secondly to studythe possible role of still higherfrequency ultrasound in probing biological processes, an attempt was made to see whether bone materials were suitable as ultrasonic transducers. Attempts have been made” to obtain a wide band transducer for tissue characterization by using a RLC circuit in combination with a transducer in the l-10 MHz range and limited success has been obtained. More recently” high frequency response (permittivity and conductivity) have been scanned in fluid saturated bone. (For further information concerning this see Reference 18.) This suggests the need to consider the material properties of bone particularly as an ultrasonic transducer. The bone transducer has also been used to study velocity dispersion in the frequency range Butterworth & Co (Publishers) Ltd. 0142-961


Collagen and apatite as transducers: S. Singh and H.S. Ranu

l-l 08 MHz. It is hoped that these data will help to explain the mechanism of bone piezoelectric behaviour in the high frequency region.





Experiments were performed on 50 samples obtained from human and animal bones. Collagen and apatite were obtained from full bone using the methods described in Reference 19. Bone derivatives so obtained were used to prepare standard disc-shaped test pieces. The test pieces were washed in running tap water and then dried at room temperature. The dimensions of the test pieces were: diam. 10.00 mm and thickness 1 .O + 0.01 mm. Electrical contact was provided on either side by colloidal silver paste.

Poling Poling was done by applying a strong electric field to the electroded test pieces. To obtain the desired properties, electrical fields of 4.5, 4.0 and 3.5 kV/mm were applied for 45 min in the case of apatite, bone and collagen respectively, at an elevated temperature. Test pieces were immersed in a silicone oil-bath to sustain the high electric field strength applied across them20f21.

MEASUREMENTS Measurements for various physical, dielectric, piezoelectric and electromechanical properties of bone materials were carried out using standard techniques**. The variation of impedance, phase angle (,tan h) and relative voltage output with the frequency range 0.5-108 MHz were measured. Also the behaviour of quality factor ‘Q’, dielectric constant (KT), and resistivity (ohm cm), in the frequency range I-70 MHz for bone materials were observed on unpoled and poled test pieces. To ensure stabilization of the test pieces, measurements on poled pieces were conducted 1 wk after poling.


field measurements

Dielectric constant (KT), loss tangent (tan 6) and resistivity (ohm cm) measurements were performed on the unpoled and poled electroded sample test pieces of bone, collagen and apatite using a radio frequency bridge (B601, Wayne Kerr, England) at 1 kHz. Voltage constant (g) was measured by ‘drop-test’ method, i.e. a known mass was dropped from a definite height on the test piece which was connected to the electrometer (Keithley Digitial Electrometer 6 16) to measure the voltage generated. Voltage constant (g) was calculated by taking the ratio of the product of voltage and thickness of sample to the force at the time of striking. Charge constant (d) was calculated from the measured voltage constant and free dielectric constant using the following formula: d

where, Kc is the permittivity of the free space.




Variation of capacitance and loss tangent (tan6) with temperature was measured by immersing the mounted sample test pieces in silicone oil. The oil-bath was heated to

temperatures in the range 25-225X. The sample test piece was connected to the radio frequency bridge through the leads and the changes noted in capacitance and loss tangent at 1 kHz due to temperature change. The temperature corresponding to the maximum value of capacitance was noted separately for unpoled and poled pieces of bone, collagen and apatite and termed the Curie Temperature for these materials.

High frequency


High frequency measurements consist of two parts. Part 1 : Electrical properties of bone materials and PCB-6 (a piezoelectric ceramic transducer from Piezoelectric Ceramics, India) were measured in the frequency range I-70 MHz; Part II: The performance of standard bone transducer was observed in the frequency range l-l 08 MHz. Bone transducer was designed by taking into consideration its impedance at the resonance frequency. The choice of backing and loading media was governed by their characteristic impedances to express minimum reflection and maximum transmission. Par-f /. Measurements of variation of electrical properties i.e. quality factor, resistivity and dielectric constant for bone materials and the corresponding parameters for piezoelectric material (PCB-6) were performed on ‘Cl’ meter (Model 4342A, H.P.). Electroded test pieces were connected to ‘Q meter through wire contacts. The calculation of coupling coefficient ‘k’ was performed by finding the values of clamped dielectric constant (KS)and free dielectric constant (KT) with the help of the formula: KS = KT (1 - k*) Part Il. This deals with the operational assessment of bone transducer in the standard configuration in the frequency range l-l 08 MHz. A bone transducer was produced by mounting the sample in a shielded metal case with due consideration to its characteristic impedance, and quality factor ‘Q’ in the frequency range of operation. The transducer was connected to measuring apparatus through a standard 50 ohm coaxial wire having B and C connectors. Measurements of variation of electrical impedance (2) and phase angle (tan h) of bone transducer in frequency range 0.5108 MHz were made with the help of r-f vector impedance meter (48 1 5 A, H.P.). The apparatus displays both electrical impedance and phase angle, simultaneously. Frequency corresponding to minimum impedance and reversal in polarity was noted and termed as the resonant frequency. The product of the resonant frequency and thickness of the test pieces used in characterizing a standard transducer are referred to as the frequency constant of the bone materials. The determination of the frequency response of the bone transducer and piezoelectric ceramic transducer were carried out using a vector voltmeter (4805 A, H.P.) and signal generator (8601 A, H.P.). Two identical transducers acting as transmitting and receiving systems were coupled directly with the help of a coupling medium. The variation of relative voltage output was measured on the vector voltmeter (4805 A, H.P.), with change of frequency of the exciting signal obtained from the standard signal generator. The ratio of the direct signal to the one obtained through the transmitting and receiving system was measured for various frequencies in the range 0.5-l 08 MHz. It revealed that there were distinct peaks corresponding to frequencies of


1986, Vol 7 November


Collagen and apatiie as transducers: S. Sjngh and H.S. Ranu

56,112 and 168 MHz. An independent check on the peak positions was made by connecting the receiving transducer to the oscilloscope and to the spectrum analyser and the same peak distribution was observed. The experiments were repeated in an identical manner with a PCB6 transducer for comparison.


Velocity measurements

ovor 8taw


IR 78441

The measurements of the ultrasonic velocity in the frequency range l-l 08 MHz were based on the transmission technique using two identical transducers (as mentioned above) coupled to both sides of the samples of bone, collagen and apatite of various thicknesses. The t~nsmi~ing transducer was excited by a ‘tone burst’ signal, obtained by mixing r-f continuous wave signal generator and a pulsating signal of different frequencies N 25 kHz with pulse width l-l 0 us, pulse delay 1 O-l 00 ns and of voltage amplitude 20 Vfrom a double pulse generator (TF 2010 Marconi) in a mixer unit (ZAD-1, Double Balanced Mixer, Mini Circuit Laboratory, USA). Both the transmitting and receiving signals were fed to the two channels of the oscilloscope and the time delay was measured (Figure 1). The velocity of the ultrasound was found by taking the ratio of distance traversed in the medium to the time delay. This was repeated on samples of different thicknesses to minimize errors in measurements.

R,c*ner tran*d”c*r



band OmDlifi~r I"P46OAl

Figure 1

Block diagram for velocity me~orement

The variation of capacitance and loss factor with temperature (25-225X) are presented in figures 2 and 3 respectively. From Figure 2 it is clear that capacitance rises to a peak value of 440 pF corresponding to a temperature of 145°C and thereafter a sharp decline follows. Identical behaviour is observed for all three materials. The peak position moves towards the higher value in the order: collagen, bone and apatite. The highest value of capacitance was found for apatite. An identical pattern is observed for tan 6 versus temperature variation for the three materials (Figure 3). Maximum loss tangent has been found for apatite followed by bone and collagen (Table 1). Earlier investigations24, led to the conclusion that conductivity increases with the rise of temperature. An early increase in loss tangent with temperature may be interpreted as the increase in ‘c’ being faster than the decrease in ‘R’. At a temperature near 100°C the difference in their rate of variation is a maximum and thereafter ‘C’ decreases while ‘R’ becomes almost constant for the rise of temperature under investigation. As explained earlie?‘, a decrease in resistivity is due to an additional number of protons available for charge transport. It may be suggested that as the Curie Temperature reaches its optimum, the dipole layers formed in the process (of charge migration) begin to contribute to the increased capacitance. The maximum value of capacitance at the Curie Temperature for apatite follows from the fact that out of the three materials under investigations, its resistivity is highest. In terms of the molecular structure of the collagen, it may be stated that it has the lowest resistivity which accounts for its low value of dielectric constant and loss tangent for all the three materials (fable 7; Figures 2 and 3). To study the electrical behaviour of bone materials, in the high frequency range, the variation of resistivity,

RESULTS AND DISCUSSION Table 1 shows the data for bone and its two major constituents characterizing their solid state: density (kg/m31 resistivity (ohm cm), dielectric constant (KT), loss tangent (tan 6). charge constant (d), voltage constant (g), electromechanical coupling coefficient ‘k’, frequency constant (NJ and the Curie Temperature (“C) at a frequency of 1 kHz. These parameters were measured by the methods mentioned above. Table I gives the mean and standard error of the mean for 50 samples and these agree with the reported results3’ 6*23. This confirms that bone materials under study are similar to those of the materials used by other researchers. The behaviourof these materials was then probed in the high frequency region. The bone structure, and its density, varies with age, sex and species. However, these biological variations do not appear to influence the high frequency measurements presented in Figures Z-9. (Note that thedisc-shaped sample used has dimensions of, diameter 10 mm and thickness 1 .O mm in each case). Tab/e 1


So/id state characteristics of bone and its two major constituents Unpoled pieces at room temp. (25°C)

Poled pieces with conditions of poling

Parameters 9one



Bone (at 125°C. 4 kV/mm for 45 min)

Apatite (at 145X, 4.5 kV/mm for 45 min)

Collagen (at 95°C. 3.5 kV/mm for 45 min)


Density (kg/m3)


Resistivity (ohm cm) Loss tangent (tan 6) Charge constant d (C/N) 1 OVoltage constant g (V-m/N) 10’ 3 Dielectric constant (KT) Frequency constant (NJ

=z 108 0.042 j, 0.001 2.63 It 0.008 10.25 ?L:0.36 29 f 0.73 5 t 0.18

110s 0.052 + 0.001 3.36 + 0.1 1 1.88 f 0.42 32 + 0.8 4.5 rt 0.16

1851 f 46 = 107 0.033 ? 0.098 0.84 zb0.03 15.7 f 0.55 6 f 0.15 5 i 0.18

1897 f 47 z 10” 0.048 rt 0.00 1 3.45 rt 0.1 13.80 + 0.48 29 + 0.72 5 f 0.18

1867+46 .z 10’3 0.058 f 0.0015 3.79 * 0.11 13.38 f 0.46 32 f 0.8 4.5 rt 0.16

1872f48 2 10s 0.036 r 0.009 0.998 r 0.03 18.8 + 0.66 6 f 0.15 5t0.18

(Hz meter) 1 O4 Electrochemical coupling

0.42 +z 0.01

0.38 rt 0.01

0.53 + 0.01

0.43 rt 0.01

0.40 + 0.01

0.55 * 0.015

coefficient (k) Curie Temperature (“C)







f 45*

*Means and standard errors of the means for 50 samples in each case.



1986, Vol 7 November

Collagen and apatite as transducers: S. Singh and H.S. Ranu

a standard inductor yields C, > Cz. On the other hand, PCB-6 data reveals that its phase angle is always positive and hence behaves as an inductor in the region of its applicability. The frequency response curve for bone materials (Figure 8) shows that peak positions correspond to frequencies at 56, 112 and 168 MHz indicating first, second and third harmonics. Similar results have been observed in the variation of electrical impedance with frequency (Figure 7). In view of the reported values of the elastic constants25’26 using 5 MHz ultrasonic pulse, the phenomenon under observation may be related to the microscopic nature of the material, and the resonance peak positions of the crystal are the excited states of the molecules therein. Impedance minima correspond to 56, 1 12 and 168 MHz. Relaxation

---0one Figure 2 Capacitance versus temperature using disc-shaped test pieces.

for bone. apatite and collagen






1 :

Cotlog.” Apolila


-4 20








i i



A .


\\ I I \

I \

_. ^./

Figure 3 Loss factor (tan 6) versus temperature collagen using disc-shaped test pieces.






- --_

for bone, apatite and

capacitance, inductance and the quality factor ‘0’ have been examined (I-70 MHz). Figures 4 and 5 depict these observations for bone materials and ceramics (PBC-6). From Figure 5 it is clear that the slope for variation of dielectric constant with frequency is least for collagen while it is maximum for apatite and is intermediate for bone. This may be attributed to relatively larger symmetry in the structure at the molecular level in collagen resulting in the lesser number of free dipoles. In apatite, there are voids in it giving rise to the existence of ion pair vacancies and offering sites for impurities. This leads to higher dependence of dielectric constant on frequency for apatite. An intermediate state can be visualized as existing in bone. Variation of phase angle (tan h) with frequency in the range 0.5-l 08 MHz is depicted in Figure 6. It can be seen that phase angle is around - 90” over a frequency range 0.5-56 MHz. In the proximity of 56 MHz, there is a reversal in the polarity and thereafter, the phase angle rapidly approaches + 90”. From the observation of impedance (Z) and phase angle (tan h) (Figure 7). it may be concluded that the material is highly capacitive. An independent support of its capacitive nature is provided by ‘Q’ measurements. Capacitance of bone samples, obtained with ‘Q’ meter using

Figure 4 Resistivity versus frequency for apatite, bone and collagen and inductance versus frequency for PCB-6 using disc-shaped test pieces.


0 ;;



&& -




z 0


-Apotlte ---cone { -,----Collog8n



’ --Bon8









’ \

+ Y w : & : z



” ” z 0



/ !







\ .-’



” ;













. 0




,.._ I 10


_ ..

1 100

Figure 5 Dielectric constant andquality factor versus frequency for apatite, bone, collagen and PCB-6 using disc-shaped test pieces.


1986, Vol 7 November


Collagen and apatite as transducers: S. Singh and H.S. Ranu

9’o -


Sonpla [email protected]


also proposed earlie?g-3’ . This leads to higher scattering of ultrasound with the excited modes which probably result in velocity dispersion. These findings are consistent with the reported results26, wherein bone exhibits viscoelastic behaviour in the frequency range l-l 0 MHz. Furthermore, in the frequency region 41- 108 MHz, the curve for ultrasonic velocity in collagen versus frequency is almost linear. A similar trend is observed in the bone in the frequency region extending from 20-80 MHz. For apatite, the slope is small as compared to the other two materials. For bone, velocity increases from 4725 m/s at 1 MHz to 9235 m/s at 100 MHz ta 9873 m/s at 108 MHz. For apatite, the variation is small. This follows from the fact that bone and collagen are viscoelastic materials but apatite is not. In the bone, the stress is distributed non-uniformly over the entire medium due to a heterogeneous and anisotropic structure. Since collagen has a lower modulus of elasticity, the strain is more effective in this medium and the dispersion curve shows a higher slope. For the same reason in apatite the slope is less, while for bone it lies in between the two (Figure 9).

aPatite,cdlagcn) 0.


1‘ bOI’: 1 : z I







0.5 -

Figure 6 Phase angle (fan k) versus frequency for bone, apatite collagen and PCB-6 using disc-shaped test pieces.

and 0.4


-2 00





-41 b0



. i

.i 0.2',

! 1

I i




- 1,20:: ; j -B 03 : :

2 - .’

0 Figure 8 Relative amplitude versus frequency for bone, apatite, collagen and PCB-6 using disc-shaped test pieces.





Figure 7 Impedance versus frequency for bone, apatite, collagen and PCB-6 using disc-shaped test pieces.

---Bone -Apatlte

---Collagen 8000 -

processes in an in viva bone system fall in the MHz region 7V27z2s. In dry bone in addition to loss of water, formation of dipoles, existence of interstitial vacancies, combination, and impurities migration in response to ultrasonic field2’ may not be considered. These factors pertaining to the dry bone may be responsible for the movement in the resonance peak towards the high frequency side. Hence, it may be concluded that resonance peak positions of the crystal are related to the properties of the materials at the molecular level. An independent corollary of the above is contained in the velocity-dispersion curve (Figure 9). Apatite, being the stiffer of the three, shows least dispersion. For the collagen molecules, being the most elastic, there is a probability of the generation of acoustic modes of large amplitudes and hence the mutual coupling coefficient is maximum in this case as



1986, Vol 7 Nwember

7000 6000




/ _/ /

Frequency Figure 9 apetite.



velocity versus frequency

for bone, collagen end

Collagen and apatite as transducers: S. Singh and H.S. Ranu

The information regarding performance of transducer can also be obtained with the knowledge of C/Co and piezoelectric stress coefficient (e). The ratio C/C, is independent of crystal dimensions and modes of vibration and is related to electromechanical activity by the following relationship: C -=Co


8 k2 n2(1 - k2)

where, ‘k’ is the electromechanical coupling coefficient and its value is presented in Table 7. The values of ratio C/C0 for various materials are given below. These are the calculated values for 50 samples tested in this study and their mean and standard error of the mean are also shown: Quartz


= 0.008

f 0.0002;



11 12





= 0.756

+ 0.019;

= 0.494

+ 0.001.


C 14

co From this it may be inferred that the coupling coefficient for bone materials falls in between those of PCB-6 and quartz. The value of the piezoelactric stress coefficient (e) for various piezoelectric materials (PCB-6 = 24.39 + 0.7; quartz = 0.17 t 0.005; bone = 59.39 rf; 1.8 C rnp2 -the mean and standard error of the mean for 50 samples) provides an estimate regarding the input power required to produce the same acoustic output for different materials. From these values, it is clear the piezoeletric stress coefficient (e) for bone is higher as compared to quartz and is indicative of the fact that less input power will be needed in case of bone to produce the same output as for quartz. Therefore, it is cbncluded that bone materials offer promise for high frequency applications.

ACKNOWLEOGEMENTS The authors wish to thank Prof C.A.L. Bassett, Columbia University, for useful discussions and also CARE, I.I.T., Delhi for granting permission to use their laboratory facilities. A fellowship awarded to one of us (S.S.) by the University Grants Commission, New Delhi, India is fully acknowledged as is the assistance of Drs S.K. Jain and Harpal Kaur Ranu for this paper. We acknowledge the partial financial support of the National Institute of Dental Research (NIDR) and the encouragement of Professor J.L. Katz at R.P.I.


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Maeda, M.,Tsuda. K. and Fukada, E., The dependence of temperature and hydration of piezoelectric. dielectric and elastic constants of bone, Japanese J. ofdppl. Physics 1976.15, 2333-2336 Behari, J. and Singh. S., Bioelectric characterisncs of unstressed in viva

15 16 17 18

13 20 21


23 24 25




29 30 31

bone, Med. 8 &of Eng. B Cornput. 198 1,19,49-54 Behari, J., Rai, D.V. and Jha, R., On the solid state of bone. CaL Tiss. intl. 1979, 28. 33-36 Fukada. E. and Yasuda, I., On the piezoelectric effect of bone, J. Phys. Sot. Japan 1957, 12, 1158-1162 Behan, J. and Singh, S., Ultrasound propagation in in viva bone, Ultrasonics 198 1, 19, 87-90 Cochran. G.V.B.. A method for direct recording of electromechanical data from skeletal bone in living animals, J. Biomechanics 1974, 7. 563-565 Cochran, G.V.B., Pawluk, R.J. and Bassett, C.A.L., Electromechanical characteristics of bone under physiologic moisture conditions, C/in. Orthop. 1968,58,249-270 Johnson, M.W., Chakkal, D.A., Happer. B.A. and Katz, J.L., Comparison of the electrom~hanical effects in wet and dry bone, J. ffiomechanics 1980,13,437-442 Singh, S. and Saha. S., Frequency responses of SGP in wet bone, Proc. ?Oth Meeting on Biomateriak, Washington, DC, USA, 1984, p 22 1 Korostoff, E.. A linear piezoelectric model for characterizing stress generated potentials in bone, J. Biomechanics 1973.12, 335-347 Lutz, H. and Petzoldt. R.. Possibilities and lrmitations of ultrasonic diagnosis of space occupying lesions in internal medrcina, Ultrasonics 1976, 14, 156-l 60 Chainani, M.L., Effect of therapeutic ultrasonic on bona-growth, Intern. Conf. and Exhib. on Ultrasonics (ICEU-SO), National Physical LaboratorY, New Delhi, Indra, July, 1980 Greguss, P. and Berlenyi, A.. A critical analysrs of ultrasonic therapy, Ultrasonics 1976. 14. 81-82 Gammell. P.M. and Le Croissetts. D.H., Wide band transducer for tissue characterization, Ultrasonics 1978, 16, 233-234 Singh, S. and Saha. S., Electrical properties of bone: a revrew. C!in. Orthop. Rel. Res. 1384, 188. 249-271 Kosterich, J.D., Foster, K.R. and Pollock. S.R., Dielectric permittivity and electrical conductivrty of fluid saturated bone, IEEE Trans. Biomed. fng. 1983,30,8 l-86 Becker, R.O. and Brown, F.M.. Photoelectric effects In human bone, Nature (London) 1965, 206. 1325-l 328 Singh, S. and Behari, J., Physrcal characteristics of bone composite materials, J. Biol. Phys. 1984. 12, l-8 Singh. S., Behari. J. and Ranu. H.S., Piezoelectric properties of bone materials, Proc. 15th Internat. Conf on Med. Biol. Eng., Espoo, Finland, 1985 Zaffe, B.. Cook, W. and Zaffe. H.. IRE standards on piezoelectric crystals: Measurements of piezoelectric ceramics, 1961, in Piezo electric Ceramics, Academic Press, London & New York, 197 1j Appendix A, pp 281-300 Shamos, M.H. and Lavine, L.S., Physical basts for bioelectrical effects m mineralized tissues, C/in. &hop. 1964, 35, 177-l 78 Behari. J.. Guha, S.K. and Agarwal, P.N., Temperature dependence of the electrical conductivity of bone. Conn. 7%~. Res. 1974,2, 325-328 Lang, S.B., Ultrasonic method for measurmg elastic coefficients of bone and results on fresh and dried bovine bone, /EFF Trans. Biomed. Erlg. 1970,17,101-105 Yoon, S.H. and Katz, J.L., UltrasonIc properties and mrcrotexture of human cortical bone. Ultrasomc tissue characterization II, Ultrasonics 1979,525, 189-l 96 Coakley, W.T. and Dunn, F., Interaction of megahertz ultrasound and biologtcal polymer, in Interaction of Mtrasourtd and Biological T&sues, (Eds J.M. Reid and M.R. Sikov), Workshop Proc. US Dept. Health Et Welfare, 1972, pp 43-45 D. D’Brem, W. Jr. and Dunn, F., Ultrasonic absorption by biomacromolecules, in fnteraction of Ultrasound and Biological Tissues. (Eds J.M. Reid and M.R. Sikov). Workshop Proc. US Dept. Health Et Welfare, 1972, pp 13-l 9 Lakes, R.S. and Katz. J.L., Viscoelastic properties of wet corttcal bone. II. Relaxation mechanisms, J. Biomechanics 1979, 12, 679-687 Lakes, R.S., Harper, R.A. and Katz, J.L., Dielectric relaxation in cortical bone, J. Appl. Phys. 1977, 48, 808-8 1 1 Lakes, R.S., Katz, J.L. and Sternstein, S.S., Viscoelastic properties of wet cortical bone. I. Torsional and biaxial studies, J. Biomechanics 1979.12.657-678


1986, Vol 7 November