isation of the electric properties of bone tissue because of the importance of ... KAL et al., 1980; CHAKKALAKAL and JOHNSON, 1981; KOS-. TERICH et al.
1 Introduction THERE [S a continuously growing interest in the characterisation of the electric properties of bone tissue because of the importance of electrically stimulated osteogenesis in orthopaedic therapy of nonunions and congenital pseudoarthrosis, and because the mechanism of electrical action is still unknown. Several investigators have measured these properties in cortical bone (LAKESet al., 1977; CHAKKALAKAL et al., 1980; CHAKKALAKALand JOHNSON,1981; KOSTERICH et al., 1983; REDDY and SAHA, 1984; SINGH and SAHA, 1984), in cancellous bone (SAng and WILLIAMS, 1986a; b; c; 1989; DE MERCATO and GARCJA-S.~NCHEZ, 1988) and as a function of the immersion fluid (KoSTERICH et al., 1984), the measuring method (SAHA et al., 1984) and the storage method (SAHAand WILLIAMS,1988). Some of the reports present results for three orthogonal measuring directions, defined either as longitudinal, anterior-posterior and lateral-medial or as axial, tangential and radial directions. The measurements performed on the cortical and cancellous portions of bone illustrate the significant differences between the electrical properties in these two structurally dissimilar types of bone tissue. However, this knowledge alone does not give enough Correspondence should be addressed to Dr De Mercato at the address shown above. First received 2nd January and in final form 20th July 1990
9 IFMBE: 1991 Medical & Biological Engineering & Computing
information about the variability of the electrical properties along the bone and particularly within the diaphysis. Such information is needed to understand the locationdependent bone structure and its resulting electric properties. For this reason we have began to study the longitudinal variability of the conductivity and the permittivity, in the three orthogonal directions, along the diaphysis of a femoral bovine bone. The objective of the present paper is to report the initial results of the study.
2 Experiment
2.1 Specimen choice and preparation In this study we wished to measure the electrical properties at several positions along the diaphysis, with the three orthogonal directions being measured at exactly the same position to avoid the problem of local biological variation. For this purpose, a bovine femur, measuring 37 cm in length from its outmost points, was removed soon after the sacrifice of a two-year-old animal. A zero reference location was set at the centre of the measured distance. Eight other locations on both sides of zero, four towards the proximal epiphysis and four towards the distal epiphysis, were marked at 2 cm increments along a centre line on the medial side, within the cortical region of the femur, as shown in Fig. 1. These locations were given the designations of - 8 , - 6 , - 4 , - 2 , 0, 2, 4, 6 and 8. In this nota-
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tion the digit corresponds to the distance in centimetres from the zero position and the negative sign corresponds to the side of the diaphysis nearer the proximal epiphysis. From the point of view of the electrical measurement arrangement, it would be desirable to use samples in slice form, with large areas and small thicknesses. However, we have yet to find a way to prepare separate orthogonally oriented samples with such a geometry, in large enough practical sizes and still small enough as to allow us to neglect a priori the fact that they are really at different positions. We thus concluded that it was necessary to be able to measure the electric properties using the same sample for the three directions and consequently adopted a cubic sample geometry. The size of these cubes has to be small compared with their separation along the diaphysis, but large enough for practical cutting, handling and placement between the measuring electrodes. A size of 4mm was chosen after some experimentation.
Fig. 1
Positions of the nine samples cut from a medial centre line in the diaphysis showin9 the location of the zero reference
Because of the mentioned requirements and limitations, using more than one such cubic sample at each axial position was discarded for this first study. We decided that, in the absence of previous knowledge about the positional variability of the electric properties, it was preferable to use only one cubic sample from each of the nine positions along the diaphysis, rather than using multiple samples positionally displaced from each other. The shape and final dimensions of these samples were obtained by first sawing bone sections, about 2 cm thick, centred on the nine previously marked positions. From these sections, the cubic samples were machined with a low-speed mill, keeping the bone continually wet during the process. The result is a quasi-cubic geometry with sides parallel to the three orthogonal directions and approximately 4 + 0.2 mm in length. The location of the samples along the diaphysis was established by setting the centre of each cube directly below (-t- 1 mm) the medial centre line at each of the nine marked positions. The location of the sample along the bone radius within each section was such that the outermost face of the cube, normal to the radial direction, was at 3 +_ 1 mm from the periostial surface. After milling, the samples were cleaned for 2min in deionised water in an ultrasonic cleaner to remove debris. They were then placed in individual glass containers, immersed in saline solution (0.9 weight per cent NaCI in H20, pH = 6.10), and stored in a refrigerator at about 3-4~ until needed for measurement. 2.2 Measurement system and procedure At least 20 sets of measurements of the electric properties were carried out on the nine cubic samples for each of the three orthogonal directions: axial, tangential and radial. The samples were kept in the saline solution under refrigeration during the approximately three months that 442
the presently reported measurements lasted. No antibacterial agents were used to preserve the samples. However, before each measurement each sample was rinsed, placed in fresh saline solution and left to equilibrate to room temperature. As a consequence, the saline solution in the individual glass containers was frequently renewed, about once every three days. Neither immersion in physiological solution nor other external means, such as those reported in our previous work (DE MERCAa'O and GARCiA-S/~NCHEZ, 1988), were used in the present study to assure complete bone saturation throughout the measurement. The capillary system previously used by us to keep saturated the slice-type samples used in that study allowed longer measurement times, but does not perform well with the larger cubic geometries of the present samples. Instead, in this case we quickly extracted each sample from the fresh saline solution, excess liquid was removed from its surfaces and it was immediately placed between wormscrew-driven silver chloride electrodes. To minimise fluid loss during measurement, the electrodes were enclosed in a small plastic chamber containing a supersaturated saline solution on its base and away from the electrodes. The time that elapsed between sample removal from the solution and the end of the measurement for each location and direction was kept approximately constant and was always less than 1 rain. During this time the change of the measured electric properties due to fluid loss was estimated to be negligible compared with the total measurement error. Prior to the measurement, a thin layer of conductive jelly was applied to the silver chloride electrodes to improve the contact to the samples. The electrodes are mounted through small gimbals and springs to their screw-driven shafts in such a way that they are free to move, adapting to the various quasicubic samples having slight deviations in parallelism between facing sides. More than 20 measurement sessions were completed during the time of the experiment. The three directions of each of the nine samples was measured during the same measurement session using a 5Hz-13MHz, HP4192A automatic impedance analyser. The instrument provides the capacity for open- and short-circuit calibration, which was performed before the measurements to compensate for interconnection parasitics. All measurements were taken at about 23~ using a 500mV signal at three frequencies: 100Hz, 10kHz and 1 MHz. The samples were also measured once continuously from 10 Hz to 13 MHz to observe the behaviour of the electrical properties as a function of frequency. After having taken all the electrical measurements, the samples were weighed in wet and dry conditions on an analytic electronic balance. Drying was accomplished by subjecting the samples to a vacuum of less than 10-3 tort at room temperature. 3 Results Each sample's electrical impedance was measured as a capacitance and a conductance representing a parallel equivalent circuit model. From these, the relative permittivity and conductivity were calculated using the measured dimensions of each cubic sample. The variation of the conductivity in the axial, tangential and radial directions along the diaphysis is presented in Figs. 2, 3 and 4 for the frequencies of 100Hz, 10kHz and 1MHz, respectively. Figs. 5, 6 and 7 show the relative permittivity at these same frequencies for the axial, tangential and radial directions, respectively. The dependencies of conductivity and relative permittivity as a function of frequency, presented in Figs. 8 and 9 for location - 6 , illustrate the typical
Medical & Biological Engineering & Computing
July 1991
Because the large number of measurements taken had to be carried out during a long span of time, it is more meaningful to indicate these m a x i m u m and minimum values than to present standard deviation bars. The curves drawn in the figures are not intended as rigorous fits of the data points, but are shown for the sole purpose of visualising the general variation tendency, as the results refer to only one sample per position in a single bone and therefore no statistics are possible.
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behaviour of the rest of the samples. The total fluid content of the samples was calculated using known values of the fluid's relative density, the dimensions and the results from the wet and dry weight measurements. The variation of this total fluid volumetric percentage content along the bone diaphysis is shown in Fig. 10. The error bars shown in the figures indicate the m a x i m u m positive and negative variation about the mean, taking into consideration the errors in measuring the size of the samples, the experimental electric and gravimetric measurement errors, and the dispersion of the results obtained from the more than 20 sets of measurements performed on each sample at 100Hz, 10kHz and 1MHz. Medical
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4 Discussion Figs. 2-4 reflect that the conductivity is greater in the axial than in the other two directions at all locations, for 444
the range of frequencies considered here. This feature agrees with all previous observations and is in general consistent with the bone structure, because fluid content in the axial Haversian systems is clearly larger than that of the channels in the radial and tangential directions. It is also evident that the behaviour of the conductivity as a function of position indicates that there is a general tendency of increased fluid content as the epiphyses are approached and that this holds true irrespective of the measurement direction. The conductivity presents maximum variations as a function of position of 47 per cent, 53 per cent and 59 per cent, for the axial, tangential and radial directions, respectively, which are significantly larger than any deviation attributable to local biological variability. As Fig. 10 shows, the total fluid volumetric fraction, measured by gravimetry, ranges from 17 to 22 per cent. These values are below those reported in some earlier studies (GONG et al. 1964), but are in agreement with the 15-20 per cent reported by more recent work (KosTERICH et al. 1983; 1984) and with the unpublished results of 17.4 per cent obtained from our own measurements of other bovine femoral bones used for our previous study (DE MERCATOand GARCiA-SANCHEZ, 1988). Based on the work previously published by other investigators and on our own about the comparison between the properties in the diaphysis and the epiphyses (DE MERCATO and GARCiA-SANCHEZ, 1988), indicating larger conductivity and permittivity in the epiphyses, we originally hypothesised that there must exist a minimum value of conductivity somewhere along the diaphysis. This minimum value would be located in a region where the 'compactness' of the bone was greatest, and it would probably correspond to the position of maximum mechanical stress. Consequently the amount of fluid, or the relative density of microchannels, in the three directions would be minimum at or near this point. However, the present results indicate that, although the conductivities are certainly larger towards the epiphyses and all three directions present minima within the measurement interval ( - 8 to 8 cm from the geometric centre of the bone); there is no evident correlation between the conductivity minima in the three measurement directions, as these minima do not seem to coincide in position along the bone. Furthermore, Fig. 10 shows that the total fluid volume fraction, as measured by gravimetry, also does not clearly present a single minimum near the centre of the bone, although it does increase towards the epiphyses, and more steeply towards the distal one. It must be concluded then that the rate, direction and location at which mechanical stresses resulting from physical activity during bone growth, among other factors such as histology of the bone, age and state of health of the animal, determine the anisotropic and position-dependent microstructure by acting upon the bone in ways that produce dissimilar effects at different locations and directions. This structural anisotropy has also been evidenced mechanically by the different elastic properties observed (LIPSON and KATZ, 1984) in the axial, tangential and radial directions of compact bone, although this difference is small between the last two. The low-frequency axial conductivity measured in the cubic samples of this study ranges from 66 +_ 7-3/iS cm-1 at location - 4 to 107 _+ 2.5#Scm -1 at location +8. These results are comparable to those of a previous study that reports values of about 60#Scm -1, although measured in larger thickness samples and using Ringer's solution (REDDY and SAHA, 1984). Another study reports larger axial conductivity values of about 2!5#S cm-~, using thin
Medical & Biological Engineering & Computing
July 1991
(1-1.5mm) slice samples immersed in 0.9 per cent NaCI solution (CrIAKKALAKAL et al., 1980). Our own previous measurements of the axial conductivity produced values of about 200/~S c m - 1 using thin (2-4-2-8 mm) slice samples from other bovine femoral bones that were kept saturated by a capillary system (DE MERCATO and GARCtA-S,~NCHEZ, 1988). The ratio of axial to radial low-frequency conductivity in the present study ranges from 1:75 _-t-0.15 at location - 6 to 3.23-t-0.28 at location +4, and compares favourably to those of previous studies that report values of about 3.2 (REDDY and SAHA, 1984) and 2.97-3.66 (CHAKKALAKALet al., 1980). The most significant electrical manifestation of the anisotropy is the different amounts of fluid intervening in low-frequency conduction in the three directions. The results show that the conductivities in the tangential and radial directions, in addition to exhibiting lower values than in the axial direction, present forms of variation along the length of the diaphysis which are in general more similar to each other than to the variation in the axial direction. This greater similarity of the conductivity's magnitude and variation form between the two transverse directions with respect to the axial direction is a consequence of the fact that the conductivities in these two directions constitute a structural representation of the relative density of conducting fluid in planes normal to the bone's longitudinal axis. This density is determined principally by the same type of oblique and transverse channels, whereas the axial conductivity is a consequence of the relative density of conducting fluid in the axial direction determined mainly by the longitudinal channels. The contribution of the dielectric loss factor to the total conductivity can be visualised comparing the values of measured conductivity at low frequencies (100Hz and 10kHz) presented in Figs. 2 and 3 with those of Fig. 4 (1 MHz). This effect can be seen more clearly in Fig. 8 for the sample from position - 6 and is consistent with the rise of total conductivity at high frequencies observed in all previous studies. The variation of permittivity along the diaphysis follows the general form of the conductivity variation, within the range of frequencies considered here, although this fact is not apparent from Figs. 5-7 due to the logarithmic scale used. This implies that the low-frequency permittivity is partially determined by the amount of liquid intervening in conduction as well as by the total amount of fluid in the bone, which includes a significant proportion of fluid that does not directly intervene in low-frequency conduction. However, the magnitude of the low-frequency permittivity cannot be attributed exclusively to the amount of liquid intervening in conduction. Fig. 9 clearly shows the similar and rapid decrease of the permittivity with increasing frequency for the three directions of measurement. In this figure the permittivities are approximately 52130, 40540 and 37650 at 10 Hz, and 870, 730 and 780 at 1 kHz, for the axial, tangential and radial directions, respectively. Although these values indicate that the low-frequency permittivity is anisotropic, the ratios between the axial permittivity and either the tangential or radial permittivity obtained from these values reveal a greater tendency towards dielectric isotropy at low frequency than has been previously reported (REDDYand SAHA,1984). We cannot propose, at this time, a satisfactory explanation for this discrepancy. 5 Conclusions The results confirm the orthotropic nature of the electric properties and evidence a significant tendency towards axis Medical & Biological Engineering & Computing
symmetry, which varies along the length of the bone, as can be seen by comparing the tangential and radial curves in Fig. 2. This agrees with the structural composition of long compact bone tissue, which is a complex composite material that presents particulate, porous and fibrous features, and which contains fluid-filled lacunae, transverse canaliculi and Haversian systems, the last two running approximately parallel to each other and to the bone longitudinal axis. The measured values do not reflect an unequivocal relationship between the total amount of fluid in the bone and its low-frequency electrical properties. Instead, these properties seem to be more a consequence of the dissimilar anisotropic microstructure along the bone. The results also show that the electric properties of femoral bovine bone vary significantly along the diaphysis and that the variations are different for each of the three directions of measurement and do not follow the variation of the total amount of fluid. It should be kept in mind that only the variation along the medial side of one bone and at a single radial location was examined. Because femoral microstructure, and therefore its electrical properties, are to a great extent a consequence of stress-induced bone modelling, it is reasonable to expect different behaviour at the anterior, posterior and lateral sides, and at other radial locations. Furthermore, as only one bovine femur was studied, the particular results presented here cannot be directly extrapolated, except in a very general way, to bones from other animals with different physical activity histories, ages, breeds or states of health, and much less can they be extended to human bones. Nevertheless, it is not unreasonable to expect that the general variability of the electric properties in the three directions along the bone hold true for any femoral bone and possibly for other compact long bones, although the specific local behaviour will depend on the particular bone considered. Further analysis of the relationship between the conductivity, permittivity, total amount of fluid and the connectivity of channels and their fluid content should be carried out using a sufficient number of bones, samples and locations to make a statistical analysis meaningful.
References CHAKKALAKAL,D. A., JOHNSON,M. W., HARPER,R. A. and KATZ, J. L. (1980) Dielectric properties of fluid-saturated bone. IEEE Trans., BME-27, 95-100. CHAKKALAKAL,D. A. and JOHNSON, M. W. (1981) Electrical properties of compact bone. Clin. Orthop., Rel. Res., 161, 133145. DE MERCATO,G., and GARCiA-SANCHEZ,F. J. (1988) Dielectric properties of fluid-saturated bone: a comparison between diaphysis and epiphysis. Med. & Biol. Eng. & Comput., 26, 313-316. GONG, J. K., ARNOLD,J. S. and COHN, S. H, (1964) Composition of trabecular and cortical bone. Anat. Rec., 149, 325-332. KOSTERICH,J. D., FOSTER,K. R. and POLLAC,S. R. (1983) Dielectric permittivity and electrical conductivity of fluid saturated bone. IEEE Trans., BME-30, 81-86. KOSTERICH,J. D., FOSTER,K. R. and POLLAC,S. R. (1984) Dielectric properties of fluid saturated bone--the effect of variation in conductivity of immersion fluid. Ibid., BME-31, 369-373. LAKES, R. S., HARPER, R. A. and KATZ, J. L. (1977) Dielectric relaxation in cortical bone. J. Appl. Phys., 48, 808-811. LIPSON, S. F. and KATZ, J. L. (1984) The relationship between the elastic properties and microstructure of bovine cortical bone. J. Biomech., 17, 231-240. REDDY, G. N. and SAHA, S. (1984) Electrical and dielectric properties of wet bone as a function of frequency. IEEE Trans., BME-31,296-302.
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SAHA, S., REDDY, G. N. and ALBRIGHT,J. A. (1984) Factors affecting the measurement of bone impedance. Med.& Biol. Eng. & Comput., 22, 123-129. SAHA, S. and WILLIAMS,P. A. (1986a) Electrical properties of cancellous bone. Fed. Proc., 45, 172, SARA, S. and WILLIAMS, P. A. (1986b) Electrical properties of human cancellous bone from distal femur. Trans. 12th Ann. Meet. Soc. Biomat., 9, 80. SARA, S. and WILLIAMS,P. A. (1986c) Electrical and dielectric properties of wet human cancellous bone as a function of fre-
quency. In Biomedical engineering V: Recent developments. SAHA, S. (Ed.), Pergamon Press, New York, 217-220. SARA, S. and WILLIAMS,P. A. (1988) Effect of various storage methods on the dielectric properties of compact bone. Med. & Biol. Eng. & Comput., 26, 199-202. SARA, S. and WILLIAMS, P. A. (1989) Electric and dielectric properties of wet human cancellous bone as a function of frequency. Ann. Biomed. Eng., 17, 143-158. SINGR, S. and SARA, S. (1984) Electrical properties of bone: a review. Clin. Orthop. Rel. Res., 186, 249-271.
Authors" biographies Giovanni De Mercato received the degree of Dottore in Ingegneria from the University of Naples, Italy, and the Magister en Ingenieria Electr6nica degree from Sim6n Bolivar University, Caracas, Venezuela. He is presently a member of the Bioengineering & Biophysics Group and an Associate Professor in the Electronics Department at Simbn Bolivar University. His current research interests include electrotherapy, clinical engineering and electrical characterisation of tissues.
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Francisco J. Garcia S~inchez received the BEE, MEE and Ph.D. degrees from the Catholic University of America, Washington DC. He is presently a member of the Solid State Electronics Group and a Full Professor of the Electronics Department at Simbn Bolivar University, Caracas, Venezuela. His current research interests include fabrication and electrical characterisation of composite dielectrics and semiconductors, modelling of solid-state electronic devices and development of thin-film solar cells.
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