Effect of human trabecular bone composition on its electrical properties

Medical Engineering & Physics 29 (2007) 845–852

Effect of human trabecular bone composition on its electrical properties J. Sierpowska a,∗ , M.J. Lammi b , M.A. Hakulinen a , J.S. Jurvelin a,c , R. Lappalainen a , J. T¨oyr¨as d a Department of Physics, University of Kuopio, P.O. Box 1627, FIN-70211 Kuopio, Finland Institute of Biomedicine, Department of Anatomy, University of Kuopio, P.O. Box 1627, FIN-70211 Kuopio, Finland c Department of Clinical Physiology and Nuclear Medicine, Kuopio University Hospital, University of Kuopio, P.O. Box 1777, FIN-70211 Kuopio, Finland Department of Clinical Neurophysiology, Kuopio University Hospital, University of Kuopio, P.O. Box 1777, FIN-70211 Kuopio, Finland b

d

Received 23 March 2006; received in revised form 15 September 2006; accepted 19 September 2006

Abstract Mechanical properties of bone are determined not only by bone mineral density (BMD), but also by tissue trabecular structure and organic composition. Impedance spectroscopy has shown potential to diagnose trabecular bone BMD and strength, however, the relationships between organic composition and electrical and dielectric properties have not been systematically investigated. To investigate these issues organic composition of 26 human trabecular bone samples harvested from the distal femur and proximal tibia was determined and compared with relative permittivity, loss factor, conductivity, phase angle, specific impedance and dissipation factor measured at wide range (50 Hz to 5 MHz) of frequencies. A strong linear correlation was found between the relative permittivity at 1.2 MHz and trabecular bone fat content (r = −0.85, p < 0.01, n = 26). On the other hand, relative permittivity measured at 200 Hz served as a good predictor of water content (r = 0.83). Phase angle, specific impedance and especially conductivity were strongly related to the trabecular bone dry density and water content (|r| ≥ 0.69). Variation in bone tissue collagen content was strongly related to the relative permittivity measured at 1.2 MHz (r = 0.64), but only moderately to other parameters. Glycosaminoglycan content showed no significant relations with any investigated electrical parameters. The present study indicates that if the trabecular bone composition is known, the relationships presented in this study could facilitate calculation of current field distribution, e.g. during electrical stimulation of osteogenesis. On the other hand, our results suggest that permittivity measured at low (<1 kHz) or high (>100 kHz) frequencies could be used, e.g. during implant surgery, for prediction of trabecular bone water or fat contents, respectively. © 2006 IPEM. Published by Elsevier Ltd. All rights reserved. Keywords: Impedance spectroscopy; Bone; Electrical properties; Organic composition; Permittivity; Journal’s main topic area: biomaterials

1. Introduction Bone quality is determined not only by its structural and material properties including bone mass, geometry and architecture but also by its organic composition [1]. Indeed, some bone diseases are characterized by alterations in bone organic composition [2–4]. This raises a question whether some techniques, such as electrical measurements, sensitive to changes ∗

Corresponding author. Tel.: +358 17 162541; fax: +358 17 162585. E-mail address: [email protected] (J. Sierpowska). URL: http://www.luotain.uku.fi/.

in bone mineral density (BMD) would be also capable of detection of pathological changes in organic composition and would facilitate a more in-depth investigation of bone health. This knowledge could possibly be useful, e.g., when further developing impedance tomography methods. Trabecular bone is highly inhomogenous and anisotropic material. The bone matrix is a composite consisting of organic matrix and an inorganic mineralized phase. Type I collagen constitutes 90% of the organic phase. The cross-linked collagen fibrils are oriented along the trabeculae providing support for carbonated apatite crystals. Small amounts of proteoglycans, which consist of protein core with glycosaminoglycan

1350-4533/$ – see front matter © 2006 IPEM. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.medengphy.2006.09.007

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(GAG) side chains attached to it [5], are also present in the matrix. The mineral phase is the main determinant of bone fracture strength [6], while the organic matrix provides the elasticity and toughness of the tissue [7]. Interactions between the mineral and the organic phases determine the functional properties of bone [8]. Trabecular bone contains substantial amounts of water (∼20% of wet mass) necessary for the diffusion of nutritive molecules and waste products [9]. Yellow marrow occupies spaces of bony matrix of distal femur and proximal tibia in an adult human [5]. This kind of marrow is composed mostly of adipose cells and, as such, is often referred to as bone fat. Electrical properties of human trabecular bone and their relationships with bone composition, structure and mechanical properties are poorly understood. However, electrically stimulated osteogenesis is used in orthopaedic practice to increase bone production and to enhance repair and restoration of mechanical properties of the stimulated tissue [10]. The use of electrical stimulation has even been suggested for the prevention of osteoporosis [11–13]. Electrical impedance measurements, i.e. impedance spectroscopy, may provide a method to follow the bone status during corticotomy and distraction osteogenesis [14]. Thus understanding electrical properties of bone tissue and their relations to underlying physical and physiological phenomena is crucial for full comprehension and proper modeling of the mechanisms appearing in impedance spectroscopy, tomography or during stimulated osteogenesis [15]. Electrical properties of both compact [16–19] and trabecular bone [20–22] have been investigated. The trabecular bone has been reported to be electrically anisotropic [15,23] and the electrical properties to be different in dry [15] and wet [16,24,25] tissue. Furthermore, electrical properties are significantly related to bone mechanical properties [26,27], structure [19,28,29], as well as to dry and ash densities [30]. To our knowledge, the relationships between the organic composition of human trabecular bone and its electrical and dielectric properties have not been previously studied. Matrix proteins and proteoglycans may significantly affect the electrical properties of bone, owing to their negative charges. Moreover, the contribution of bone marrow to electrical and dielectric properties has not been fully investigated [26]. Consequently, the aim of the present study was to investigate the role of organic composition on bone electrical properties. For this aim the organic composition of human trabecular bone samples was investigated and related to their electrical and dielectric properties measured at wide range of frequencies.

2. Materials and methods 2.1. Sample preparation Cylindrical (diameter = 16 mm, height = 8 mm) human trabecular bone samples (number = 26) were prepared from

distal femur (femoral medial condyle, FMC, number = 10; femoral groove, FG, number = 10) and proximal tibia (tibial medial plateau, TMP, number = 6)). Specimens were collected from 13 human cadavers (age = 25–77 years, 1 female, 12 males) obtained from Jyv¨askyl¨a Central Hospital by permission of the Finnish National Authority for Medicolegal Affairs (TEO, 1781/32/200/01). The samples were machined using the Macro cutting system (Macro Exakt 310 CP, Exakt, Hamburg, Germany) so that the long axis of the sample was always oriented in the direction perpendicular to articular surface, i.e. along the loading axis. During the cutting process, the samples were moistened with phosphate-buffered saline (PBS) in order to prevent loss of moisture. After preparation the samples were frozen (−20 ◦ C) in sealed plastic tubes containing PBS and thawed just prior to measurements. The detailed preparation procedure has been described earlier [27]. 2.2. Measurements Electrical parameters (relative permittivity, conductivity, phase angle, loss factor, specific impedance and dissipation factor) were measured using the two-electrode method with an LCR meter (HIOKI 3531 Z HiTester, Koizumi, Japan) in a wide frequency range (50 Hz to 5 MHz). Humidity was kept constant during measurements to minimize the change in electrical parameters. The measurement procedure, experimental set-up and the details of the analysis have been described thoroughly in our previous publications [27,29]. After electrical measurements volumetric bone mineral density (BMDvol ) was determined using a dual energy Xray absorptiometry instrument (Lunar Prodigy, GE Medical, Wessling, Germany). The wet densities were determined by normalizing wet weights with sample volumes, as determined using the Archimedes principle. The samples were then freeze-dried and the dry weight was measured for determination of water content and dry density. Subsequently, acetone was used to remove fat from the samples. Acetone was then evaporated by drying the samples at 45 ◦ C for 18 h and the original fat content of the samples was calculated. Hydroxyproline and uronic acid assays were performed on fat-free bone powder. Approximately 20 mg of each sample was portioned for acid hydrolysis in 5 M HC1 at 108 ◦ C for 16 h, and hydroxyproline content in the hydrolysate was analyzed using a microplate assay [31]. Hydroxyproline content of collagen is approximately 14% of the collagen mass, therefore, estimates for the total collagen content were obtained by multiplying the analyzed hydroxyproline content by a factor 7 [32]. Proteoglycans were extracted from approximately 20 mg sample of the fat-free bone powder by using 4 M GuHCl including 0.2 M EDTA in 50 mM sodium acetate buffer, pH 6.0, for 70 h. Uronic acid content was determined with a spectrophotometric assay [33]. The determination of relative proportion of uronic acid in standard chondroitin sulfate (Sigma–Aldrich, St. Louis, MO) showed that 31% of chondroitin sulfate weight comes from uronic

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Table 1 Mean (±S.D.) values of compositional parameters and densities of human trabecular bone. No variations in trabecular bone composition between anatomical sites (FMC – femoral medial condyle; FG – femoral groove; TMP – tibial medial plateau) were found FMC Wet density (g/cm3 ) Dry density (g/cm3 ) BMDvol (g/cm3 ) Fat content (%) Water content (%) Collagen content (%) GAG content (%)

1.154 0.938 0.237 39.5 18.8 8.6 0.26

TMP ± ± ± ± ± ± ±

0.052 0.082 0.066 4.7 4.2 1.2 0.12

acid, therefore, the estimation of bone GAG content was obtained by multiplying the uronic acid content by a factor 3.2. Finally, water, fat, collagen and GAG contents were presented as normalized by individual wet masses of the samples. As the bone marrow was not removed from the samples before the compositional analysis, the measurements of fat content apply mainly to marrow whereas the measured water content is related to both marrow and mineralized bone

1.087 0.881 0.213 43.9 19.1 8.7 0.16

FG ± ± ± ± ± ± ±

0.060 0.074 0.069 6.0 3.0 1.8 0.06

1.158 0.941 0.260 37.6 18.9 9.8 0.22

± ± ± ± ± ± ±

0.040 0.067 0.051 2.3 3.8 1.2 00.08

matrix. However, collagen and GAG contents were determined for mineralized bone matrix only. 2.3. Statistical analysis Friedman-test was used to investigate the significance of site-dependent variation of the parameters. The linear correlation coefficients were determined by using the Pearson correlation analysis. Multiple stepwise linear regression anal-

Fig. 1. Linear correlation coefficients (r, number = 26) between the electrical and dielectric parameters and bone densities as a function of frequency: (a) permittivity, (b) conductivity, (c) phase angle and (d) dissipation factor. The correlation coefficients between the relative permittivity or dissipation factor and densities were dependent on frequency. The linear correlation coefficients between the density and other electrical parameters varied only slightly as a function of frequency.

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Fig. 2. Linear correlation coefficients (r, number = 26) between the electrical and dielectric parameters and compositional parameters of bone as a function of frequency: (a) permittivity, (b) conductivity, (c) phase angle and (d) dissipation factor. The correlation coefficients between the relative permittivity or dissipation factor and organic composition were dependent on frequency. The correlation coefficients between the organic composition and other electrical parameters were almost independent of frequency.

yses were used to find the best combination of electrical principal components for prediction of the variation in bone composition, as well as to investigate the contribution of organic composition to the electrical properties of trabecular bone. Principal component analysis (PCA) was used to reduce the number of electrical parameters into a lower number of independent variables [34]. Statistical analyses were conducted with SPSS 11.5 software (SPSS Inc., Chicago, IL, USA).

3. Results No site dependent differences in organic composition, mineral density or physical density among tests sites were seen (Table 1). The strength and sign (+/−) of linear correlations between the relative permittivity or dissipation factor and composition or density were dependent on frequency. The linear correlations between the composition or density and conductivity or phase angle varied only slightly as

Table 2 Linear correlation coefficients between compositional parameters and densities and electrical parameters of human trabecular bone at 1.2 MHz. Moderate or strong relationships between the bone composition and electrical properties were found. GAG content did not correlate with any electrical parameter Relative permittivity Wet density Dry density BMDvol Fat content Water content Collagen content GAG content * **

p < 0.05. p < 0.01.

0.60** 0.41* 0.67** −0.85** −0.07 0.64** 0.22

Phase angle

Conductivity

Dissipation factor

Specific impedance

−0.55**

−0.59**

−0.74**

0.48* 0.69** 0.49* −0.11 −0.76** 0.40* 0.31

−0.73** −0.43* 0.04 0.76** −0.36 −0.28

−0.77** −0.50* 0.10 0.79** −0.43* −0.25

−0.76** −0.61** 0.42* 0.59** −0.55* −0.24

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Table 3 Linear correlation coefficients between compositional parameters and densities and principal components of electrical parameters. The results suggest that fat and water contents of trabecular bone could be determined by the measurement of relative permittivity at two separate frequency bands (at high and low frequency, respectively)

Wet density Dry density BMDvol Fat content Water content Collagen content GAG content * **

Middle frequency permittivity

Low frequency permittivity

High frequency permittivity

Low frequency dissipation factor

High frequency dissipation factor

Energy component

Field propagation component

−0.07 −0.20 −0.15 −0.08 0.30 −0.01 0.09

−0.53** −0.72** −0.42* 0.04 0.78** −0.39* −0.19

0.56** 0.38 0.68** −0.85** −0.05 0.62** 0.20

0.10 0.24 0.19 0.11 −0.34 0.07 −0.02

−0.73** −0.75** −0.63** 0.45* 0.58** −0.59** −0.30

−0.50* −0.72** −0.41* −0.01 0.78** −0.33 −0.25

0.59** 0.38 0.62** −0.82** −0.02 0.60** 0.18

p < 0.05. p < 0.01.

a function of frequency or were independent of frequency (Figs. 1 and 2). The frequency dependence of the linear correlations between the loss factor or specific impedance and bone organic composition or densities were analogous to that seen with conductivity (data not shown). Furthermore, the linear correlations between the loss factor and the bone organic composition or densities were negative at all frequencies. Similarly, the corresponding correlations for specific impedance were systematically positive. The dissipation factor correlated significantly with composition and density only at high frequencies, while the relative permittivity was significantly related to these parameters at high and low frequencies (Figs. 1 and 2). Bone relative permittivity at 200 Hz served as a strong predictor of water content (r = 0.83) (data not shown) while at 1.2 MHz of fat content (r = −0.85, p < 0.01, number = 26, Table 2). Phase angle, conductivity and specific impedance at 1.2 MHz were significantly influenced by the dry density and water content (|r| ≥ 0.69, Table 2). The variation in collagen content was strongly related to the relative permittivity at 1.2 MHz (r = 0.64) but only moderately to other parameters (Table 2). Trabecular bone GAG content showed no or only minor impact on electrical parameters at all frequencies (Fig. 2). Electrical properties were measured at a wide range of frequencies. In order to reduce the vast amount of data, we grouped the frequencies into principal components (PCs). Relative permittivity displayed three significant PCs that explained altogether 97.9% of the variation in the data. The first component, referred to as “middle frequency permittivity,” represents relative permittivity mainly at frequencies

between 300 Hz and 500 kHz. “Low frequency permittivity” (the second component) and “high frequency permittivity” (the third component) account for frequencies at 50 Hz to 1.2 kHz and 300 kHz to 5 MHz, respectively. For dissipation factor, two significant PCs explaining 96.1% of the variation were extracted. The first component represents the dissipation factor mainly at low frequencies (50 Hz to 120 kHz) and the second component accounts mainly for high frequencies (50 kHz to 5 MHz). Only one PC representing all frequencies was obtained for other electrical parameters. In addition, the PCA was applied to group permittivity, conductivity, phase angle, dissipation factor and specific impedance measured at 1.2 MHz. The first PC, referred to as “field propagation component,” includes mainly phase angle, conductivity, specific impedance and dissipation factor and accounts for 68.2% of the variation in the data. The second PC, i.e. “energy component,” which explained 27% of the variation, consists mainly of the permittivity and dissipation factor. Principal components called middle frequency permittivity and the low frequency dissipation factor did not correlate with the organic composition or densities (Table 3). All compositional parameters, GAGs excluded, showed strong relations with some electrical principal components. For example, fat content was a strong determinant of variation in both high frequency permittivity and the field propagation component (|r| > 0.82). The linear combinations of electrical principal components were able to account for more than 50% of the variation in organic composition or densities. The high frequency permittivity was strong predictor of fat content

Table 4 Multiple stepwise linear regression model analysis. High frequency permittivity was a good predictor of trabecular bone fat content, while the linear combination of low and middle frequency permittivity was a good predictor of water content Predicted variable Fat content Water content Permittivity at 1.2 MHz Conductivity at 1.2 MHz **

p < 0.01.

Variables in the regression model

r2

High frequency permittivity Field propagation component Low frequency permittivity, Middle frequency permittivity Fat content Water content

0.72** 0.66** 0.66** 0.70** 0.60**

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(r2 = 0.72, Table 4). In contrast, a good predictor of variation in water content was the linear combination of low and middle frequency permittivity (r2 = 0.66).

4. Discussion This study investigated the relations between organic composition and electrical properties of trabecular bone. The motivation of the present study arises from the use of electrically stimulated osteogenesis in orthopaedic practice [35]. It is also related to potential of dielectric techniques to diagnose bone quality during open orthopaedic surgery [27]. Current knowledge on the relationships between the trabecular bone organic composition and dielectric properties is limited. However, the electrical environment of bone cells must be well characterized to understand rigorously the cellular mechanisms occurring during stimulated osteogenesis [35]. Thus, our study aims to provide a step towards a description of correlations between electrical properties and compositional, mechanical and structural measures, as well as to deepen the understanding of the characteristics of the bone-electrolyte interface and bone electrical conductivity. In the present study, several moderate or strong relationships between the trabecular bone composition and electrical properties were found. Linear correlations between the organic composition and relative permittivity or dissipation factor were dependent on frequency, while with conductivity and phase angle the relationships were frequencyindependent. A highly significant positive linear correlation between the permittivity and water content was found at low frequencies (<1 kHz), while for fat content the correlation was negative and highly significant at high frequencies (>100 kHz). Furthermore, permittivity at high frequencies correlated positively and significantly with the collagen content. These findings, along with our previous investigations on bone microstructure [28,29], supports the hypothesis that the trabecular bone structure with high density and collagen content as well as low fat content exhibits a high relative permittivity at frequencies above 100 kHz. Phase angle, loss factor and specific impedance correlated more strongly with water content and dry density than with either mechanical or structural parameters [27,29]. This suggests that the bone composition, especially ions free to move within the water phase and the bound electrical charges within organic bone matrix, significantly contributes to these electrical and dielectric parameters. The correlations between the electrical parameters and composition presented in this study can be utilized in two ways. First, during electrical impedance tomography (EIT), to determine bone composition based on measured electrical properties, relative permittivity in particular. Importantly, the results suggest that the fat and water content of trabecular bone could be predicted using a measurement of relative permittivity at two separate frequency bands. However, as the resolution of EIT is still relatively poor, this application

may not be not realistic at the moment. Certainly, electrical impedance spectroscopy could be applied to determine the quality of bone grafts or bone tissue during some special cases of open surgery. Second, provided that the composition of trabecular bone, e.g. bone mineral density, is known, the electrical properties of the tissue may be estimated. This knowledge could, for instance, facilitate calculations of the current filed distribution during electrical stimulation of osteogenesis. In this study conductivity was found to correlate strongly positively with the water content but negatively with the dry density and bone mineral content. Along with a former study [25], this negative correlation could suggest that the bony matrix exhibits a low intrinsic conductivity as compared to overall conductivity of bone and acts as a barrier for the current flow in the frequency range applied in the present study. Consequently, the linear regression analysis suggested that the water content primarily determined the trabecular bone conductivity. This result is in line with previous studies on electrical conductivity of compact bone [36]. Trabecular bone, however, includes a significant amount of bone marrow. In a previous study [20], the conductivity of marrow and human trabecular bone were found to be similar at frequencies 120 Hz to 10 MHz and the bone marrow was suggested to be the main determinant of trabecular bone conductivity. As the water content calculated in this study applies to both bone marrow and mineralized tissue, the results would suggest that water within marrow contributes significantly to overall conductivity of trabecular bone. The potential contribution of interstitial bone marrow water to the trabecular bone conductivity is hypothetical but consistent with the bioimpedance theory. Tissue conductivity is linked to permittivity and governed by Kramers–Kroning relation [37]. The progressive increase in conductivity along with the frequency originates from the Maxwell–Wagner effects, indicating an increase of available current pathways [38]. The cell membranes are considered to exhibit capasitive properties [38] and, for the alternating current below 100 kHz, i.e. below beta relaxation frequency, the cells are poorly conducting in comparison with the surrounding electrolyte [38]. Thus, at low frequencies only the extracellular fluid, or water in the present study, is available to the current flow. At frequencies above 100 kHz a high correlation between the trabecular bone conductivity and water content was observed, even though theoretically other structural or compositional constituents should contribute to the conductivity. This can be explained by two phenomena. The dispersion in bone is extensive making it dificult to judge unequivocally whether the cut-off for beta relaxation is at 100 kHz or higher. Moreover, the bone marrow shows alpha dispersion up to low radio frequencies while beta dispersion is almost absent [39]. Second, the bone tissue investigated in this study was dead and probably significant amount of cell membranes was destroyed during the freeze-thaw process. As such, the extracellular fluid, or water, would still act as the main determinant of tissue conductivity.

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The results demonstrated that the low frequency permittivity is strongly associated with the water content but not with the fat content. At high frequencies, the permittivity shows an opposite association with the fat-water content, and at middle frequencies, the permittivity exhibits no significant relation with the water or fat content. This frequency-dependent transition may be partially explained by the nature of alpha and beta dispersion in the tissue. At low frequencies (<100 kHz) the large values of permittivity are associated mostly with the ionic diffusion processes in the electrical double layers adjacent to the charged surfaces of micron size [37]. The mobile counter-ions originate in the extracellular fluid. Furthermore, previous studies have demonstrated a strong correlation between the permittivity and conductivity at low frequencies, suggesting that the permittivity could be determined by the amount and spatial distribution of water [36,25]. The correlation between the permittivity and conductivity has been reported to decrease with the increasing frequency [36]. Additionally, in this study a strong negative correlation was reported between the permittivity at low frequencies and the bone density. This may result from spatial distribution of liquid within the tissue and is further supported by a strong relation between the trabecular bone microstructure and its electrical properties [29]. The dense bone is known to possess a low bone marrow content [40]. As the density of the bone decreases, the marrow content and the values of relative permittivity at low frequency increase. Thus, the negative sign of the correlation between the permittivity and bone density may indicate that the diffusion processes take place mostly outside bony matrix, possibly in the bone marrow. Alternatively, it could be interpreted as a decrease in the amount of charged surfaces with increasing density. At frequencies above 100 kHz it is not water, but the interfacial processes between different dielectrics [38], such as mineralized and soft tissue, that determine the observed beta relaxation. For instance, a strong polarization of a thin membrane lining the trabeculae and thereby creating a natural border between bone and marrow may be observed. A dipolar orientation of proteins found in both tissues contribute to the observed beta dispersion as well [37]. Moreover, the dielectric behaviour of marrow and compact bone were reported to be similar at radio-frequencies [39], however, quite different from that of trabecular bone [20]. This further supports the idea that the interactions between the bone marrow and mineralized matrix strongly determine permittivity of the trabecular bone at frequencies above 100 kHz. However, due to very complex structure of trabecular bone it is difficult to explain the origin of the negative sign in the correlation between fat content and permittivity. The charged GAGs can be expected to contribute to permittivity, especially at frequencies above 100 kHz. However, no significant correlations were found between the GAG content and permittivity. The small amount of GAG chains present in the bone matrix [5] and the importance of interfacial processes could explain the lack of correlation.

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The correlation between the compositional and electrical parameters varies with frequency, whereas the correlation with the principal components is a single number. For example, the correlation between the fat content and permittivity at 300 kHz to 5 MHz varies between −0.70 and −0.85 (Fig. 2). The correlation with the principal component is −0.85 (Table 3). By conducting these two analyses the authors wish to point out that the correlation with the principal component falls into the range (−0.70 to 0.85) of correlations seen with individual frequencies. This implies that quite a wide range of frequencies may be used to predict bone fat content and the correlations presented in the Results-section for 200 Hz and 1.2 MHz should be interpreted as representatives of the frequency bands (50 Hz to 1.2 kHz) and (300 kHz to 5 MHz), respectively. No significant variations in trabecular bone composition among sample sites were found in this study. This is in line with our previous investigations on the same sample set, where no differences in mechanical or structural properties were observed between the groups [27,29]. Further, absolute values of electrical and compositional parameters are in good agreement with previous studies [20,41]. To conclude, trabecular bone composition has a significant impact on its electrical and dielectric properties. Water content and dry density associate significantly with all electrical parameters. Fat and collagen contents were strongly related with relative permittivity, while water content was significantly related with conductivity. Provided that the trabecular bone composition is known, the relationships presented in this study could facilitate, e.g. calculation of current field distribution during electrical stimulation of osteogenesis. On the other hand, the present results indicate that permittivity measured at low (<1 kHz) or high (>100 kHz) frequencies could be used for prediction of trabecular bone water or fat contents, respectively. This suggests that the impedance spectroscopy may provide a method for the evaluation of organic composition of trabecular bone in vitro or in situ. However, further experimental and theoretical approaches are warranted to further address the complex relationships between the bone composition and electrical properties. Acknowledgements Financial support from Biomaterial Graduate School, Finland, and Kuopio University Hospital (EVO 5213) is acknowledged. References [1] Einhorn TA. Bone strength: the bottom line. Calcif Tissue Int 1992;51:333–9. [2] Oz B, Olmez N, Memis A. Osteogenesis imperfecta: a case with hand deformities. Clin Rheumatol 2005;24:565–8. [3] Forin V, Arabi A, Guigonis V, Filipe G, Bensman A, Roux C. Benefits of pamidronate in children with osteogenesis imperfecta: an open prospective study. Joint Bone Spine 2005;72:313–8.

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