# Dielectric properties of animal bone.

INTRODUCTION

The study of dielectric properties of macromolecules, cells and tissues of biological interest become part of the inter-disciplinary armoury of the biological sciences. Advances in such studies certainly be of benefit to some branches of medicine. Although the dielectric properties of matter are primarily of interest to the physicists and electrical engineers, they have also proved to be of importance and use in the understanding and development of other fields of knowledge including chemical and biological sciences.

In everyday life, bones are under constant remodeling i.e. apposition and resorption occur depending on the degree and type of functional stress. Based on electrical nature of mechanical stimulation of bone, dielectric and electrical properties are closely linked. Obviously , more detailed information on the basic electrical and dielectrical properties of bones could result in the development of tools for diagnostic and therapeutic applications (Saha and Williams, 1989). Detailed knowledge of electrical and dielectrical properties is also necessary to determine electrical field and current distribution during electrical stimulation of bone fracture. (William and Saha 1996).

The physiological effects of electric currents had drawn the attention of the researchers in the 19th century. "Electrotherapy" came to be widely practiced by physians. The early theories of Cole (Cole 1972), Frickle and Danzer (1934) for the dielectric properties of cell suspensions were further simplified and extended by Schwan and co-workers (Schewan 1957). Studies of dielectric properties of biological materials remain an active area of research. With the introduction of modern network analyzer and time domain measurement systems, the determination of dielectric properties of the biological samples is easier and this should encourage increased efforts in this field. Many opportunities exist and fundamental problems remain to be solved.

Today, work on dielectric properties of biological systems and their response to electric fields is being conducted at an increasing number of places. This work will surely provide new insights into how electrical fields can act on cells and tissues and will lead to beneficial applications of electric fields and currents.

However, to get a deeper insight into the dielectric nature of the material, additional parameters like dielectric loss ([epsilon]"), dissipation factor (tan [delta]), dielectric constant ([epsilon]'), electrical resistivity ([rho]) and conductance (K) are needed.

Bovine trabecular bone is known to be denser and less porous than the human trabecular bone. (Jiang et.al 1988, Keaveng et al 2001, Toyras et al 2002). Micro damage does not affect other parameters to such an extent, e.g. conductivity is not as sensitive for interface processes as the dielectric constant is (Seirpowska et.al 2005). In the present study we investigated relationships between electrical and dielectric properties of animal bones. This paper constitutes a step towards the application of electrical measurements for in vivo bone diagnostics.

MATERIALS AND METHOD

Fresh bovine bones such as femur, tibia, humerus, radius/ ulna (fore arm), metacarpus, metatarsus, scapula, skull, pelvis, rib and backbone were collected from slaughterhouse for present investigations. Fleshly material present on the bone is removed. Specimens (pellets or discs) were cut from mid region of the bone.

[FIGURE 1 OMITTED]

For the dielectric measurements, a two terminal cell was constructed in Biophysics Laboratory, Nizam College, Hyderabad. The cell consists of two parallel circular plates made up of copper. The diameter and thickness of the plates are 1.2 cms and 0.5 cms respectively. The lower circular plate electrode plugs directly into the live terminal of the capacitance measuring bridge while the upper one, at earth potential is moved by means of a micrometer having least count 0.001 cm. This serves two purposes. One is to apply a slight pressure on the specimen placed between them and the other is to measure the separation of the plates or the thickness of the sample. To eliminate capacitance due to leads, the capacitance (Ca) of the cell for different inter-electrode spacing (d) was measured. A plot is drawn between air capacitance on y-axis and 1/d on x-axis. The plot is linear and the capacitance [C.sub.a] at infinite distance of the plates (i.e. 1 /d = 0) gives the value of lead capacitance ([C.sub.L]) of the cell. This value is to be subtracted from the measured value of capacitance with the sample [C'.sub.s] and with air [C'.sub.a] to have an exact value of the capacitance with sample (Cs) and with air (Ca).

i.e Cs = C 's- [C.sub.L] and Ca = C 'a- [C.sub.L]

[FIGURE 2 OMITTED]

Capacitance

A commercial digital LCR meter (Pacific, PLCR 8C) was used to measure the capacitance and dissipation factor (tan [delta]). To have a comparative study of dielectric behaviour of bovine femur, tibia, radius / ulna (fore arm), metacarpus, metatarsus, scapula, skull, pelvis, rib, and backbone in the applied alternating filed of frequency 1 KHz capacitance and dissipation factor were measured with and without the sample in the cell. All the measurements were taken at room temperature.

The dielectric constant ([epsilon]') of the sample is given by [epsilon]' = CS / Ca = [C'.sub.S] - [C.sub.L] / C'a - [C.sub.L]

Where Cs = actual capacitance of the cell with the sample.

Ca = actual capacitance of the cell with air

C's = measured capacitance of the cell with sample

C'a = measured capacitance of the cell with air.

[C.sub.L] = lead capacitance.

[FIGURE 3 OMITTED]

The electrical and dielectric properties were investigated by applying electrical current to samples through dielectric cell using commercial LCR meter (Pacific, PLCR 8C).

Knowing the value of [epsilon]' and tan [delta], the dielectric loss was calculated by using the formula [epsilon]" = tan [delta]. [epsilon]'. The specific alternating current conductance K was calculated from the relation [epsilon]" = 1.8 X [10.sup.12] K/v where v is the frequency of the applied electric field in Hertzs.

The dielectric constant and dielectric loss of bone specimen were measured along its z-direction. But it was not possible to measure along x and y--directions due to the limitations in the dimensions of the specimens.

RESULTS

The tables below present the data on the electrical parameters such as dielectric constant ([epsilon]'), dielectric loss ([epsilon]"), resistivity ([rgo]) and conductivity (K) of bovine femur, tibia, humerus, radius /ulna (fore arm), metacarpus, metatarsus, scapula, skull, pelvis, rib, and backbone taking 10 samples of each in wet / normal condition (table 1) and oven dried condition (table 2). The parameters were determined at 1 KHz frequency at room temperature. Here the standard deviation values of the parameters reveal the variation among the different bone specimens of above- mentioned, but not the uncertainity of the measurement. It is evident from the data that there exists a considerable variation in the observed parameters. The absolute values of electric and dielectric parameters determined in this study were in agreement with earlier studies (Saha and Williams 1989, Gabriel et al 1996a).

DISCUSSION

Results on electrical parameters of bovine femur, tibia, humerus, radius /ulna (fore arm), metacarpus, metatarsus, scapula, skull, pelvis, rib and backbone reveal the considerable variation in different bone samples and also in different specimens of the same bone, obtained from the various parts of the bone. This may be attributed to the inhomogeneous deposition of calcium phosphate and water content of the bones. Bone density and investigated electrical parameters were significantly interrelated, as reported earlier (Saha and Williams 1989, Seirpowska et.al 2003). The sharp fractional change in dielectric constant and resistivity with the water content suggest that the electrical parameters are very sensitive to free water present in bones. Influence of water on electrical behaviour is specific to bone because of the fact that mineral content of the bone is found to be in different proportion which also effect the electrical make up of the bone. Here it is the water content which causes lot of variation in dielectric parameters. The three parameters namely water content, mineral content (calcium phosphate) and orientation of the collagen fibers with respect to the applied electric field play an important role in influencing the electrical parameters such as dielectric constant, dielectric loss, and conductivity of the bone tissues when measured at the bulk level.

REFERENCES

[1.] Cole, K. S. 1972. "Membranes, Ions and Impulses", University of California press, Berkely.

[2.] Danzer, H. 1934. Ann.Phys. (N. Y), Vol 21(5) :463.

[3.] Gabriel, C., Gabriel, S. and Corthout, E. 1996a. "The dielectric properties of biological tissues: I. Literature survey.", Phys.Med.Biol.,Vol.41: 2231-49.

[4.] Jiang, Y., Zhao, J., Augat, P., Ouyang, X., Lu, Y., Majumdar, S. and Gehant, H.K. 1998. "Trabecular bone mineral and calculated structure of human bone specimens scanned by peripheral quantitative computed tomography; relation to biomechanical properties", J. Bone Miner., Res., 13: 1783-90.

[5.] Keaveny, T.M., Morgan, E.F., Neibur, G.L., and Yeh, O.C., 2001. "Biomechanics of trabecular bone". Annu. Rev. Biomed. Engg., Vol.3 : 307-33.

[6.] Saha, S. and Williams, P.A. 1989 "Electric and dielectric properties of wet human cancellous bone as a function of frequency", Ann. Biomed. Eng, Vol 17: 143-158.

[7.] Schewan, H. P. 1957. "Advances in Biological and Medical Physics", Vol.5 ,Academic Press, New York : 147.

[8.] Sierpowska, M.A., Hakulinen, J. ,Toyras, J., Day, S., Weinans, H., Jurvelin , J.S. and Lappalainen, R.2005. "Prediction of mechanical properties of human trabecular bone by electrical measurements", Physiol.Meas., Vol.26 : S 119-S131.

[9.] Sierpowska, J., Toyras, J. , Hakulinen, M.A., Saarakkala, S., Jurvelin, J.S. and Lappalainen, R.2003. "Electrical and dielectric properties of bovine trabecular bone--relationships with mechanical properties and mineral density.", Phys.Med. Biol.,Vol.48 : 775-786.

[10.] Toyras, J., Nieminen, M.T., Kroger, H., and Juvelin, J.S., 2002, "Bone mineral density, ultrasound velocity and broadband attenuation predict mechanical properties of trabecular bone differently", Bone, Vol.31: 503-7.

[11.] William, P. A. and Saha, S. 1996. "the electrical and dielectric properties of human bone tissue and their relationship with density and bone mineral content." Ann. Biomed. Eng., Vol 24: 222-33.

R. Jeevan Kumar, S.Md. Shoaib, Kaleem Ahmad Jaleeli * and Adeel Ahmad *

Molecular Biophysics Laboratories, Dept of Physics, S. K. University, Anantapur-515003, India.

* Biophysics Unit, Department of Physics, Nizam College (Autonomous),Osmania University, Hyderabad, A. P India.

The study of dielectric properties of macromolecules, cells and tissues of biological interest become part of the inter-disciplinary armoury of the biological sciences. Advances in such studies certainly be of benefit to some branches of medicine. Although the dielectric properties of matter are primarily of interest to the physicists and electrical engineers, they have also proved to be of importance and use in the understanding and development of other fields of knowledge including chemical and biological sciences.

In everyday life, bones are under constant remodeling i.e. apposition and resorption occur depending on the degree and type of functional stress. Based on electrical nature of mechanical stimulation of bone, dielectric and electrical properties are closely linked. Obviously , more detailed information on the basic electrical and dielectrical properties of bones could result in the development of tools for diagnostic and therapeutic applications (Saha and Williams, 1989). Detailed knowledge of electrical and dielectrical properties is also necessary to determine electrical field and current distribution during electrical stimulation of bone fracture. (William and Saha 1996).

The physiological effects of electric currents had drawn the attention of the researchers in the 19th century. "Electrotherapy" came to be widely practiced by physians. The early theories of Cole (Cole 1972), Frickle and Danzer (1934) for the dielectric properties of cell suspensions were further simplified and extended by Schwan and co-workers (Schewan 1957). Studies of dielectric properties of biological materials remain an active area of research. With the introduction of modern network analyzer and time domain measurement systems, the determination of dielectric properties of the biological samples is easier and this should encourage increased efforts in this field. Many opportunities exist and fundamental problems remain to be solved.

Today, work on dielectric properties of biological systems and their response to electric fields is being conducted at an increasing number of places. This work will surely provide new insights into how electrical fields can act on cells and tissues and will lead to beneficial applications of electric fields and currents.

However, to get a deeper insight into the dielectric nature of the material, additional parameters like dielectric loss ([epsilon]"), dissipation factor (tan [delta]), dielectric constant ([epsilon]'), electrical resistivity ([rho]) and conductance (K) are needed.

Bovine trabecular bone is known to be denser and less porous than the human trabecular bone. (Jiang et.al 1988, Keaveng et al 2001, Toyras et al 2002). Micro damage does not affect other parameters to such an extent, e.g. conductivity is not as sensitive for interface processes as the dielectric constant is (Seirpowska et.al 2005). In the present study we investigated relationships between electrical and dielectric properties of animal bones. This paper constitutes a step towards the application of electrical measurements for in vivo bone diagnostics.

MATERIALS AND METHOD

Fresh bovine bones such as femur, tibia, humerus, radius/ ulna (fore arm), metacarpus, metatarsus, scapula, skull, pelvis, rib and backbone were collected from slaughterhouse for present investigations. Fleshly material present on the bone is removed. Specimens (pellets or discs) were cut from mid region of the bone.

[FIGURE 1 OMITTED]

For the dielectric measurements, a two terminal cell was constructed in Biophysics Laboratory, Nizam College, Hyderabad. The cell consists of two parallel circular plates made up of copper. The diameter and thickness of the plates are 1.2 cms and 0.5 cms respectively. The lower circular plate electrode plugs directly into the live terminal of the capacitance measuring bridge while the upper one, at earth potential is moved by means of a micrometer having least count 0.001 cm. This serves two purposes. One is to apply a slight pressure on the specimen placed between them and the other is to measure the separation of the plates or the thickness of the sample. To eliminate capacitance due to leads, the capacitance (Ca) of the cell for different inter-electrode spacing (d) was measured. A plot is drawn between air capacitance on y-axis and 1/d on x-axis. The plot is linear and the capacitance [C.sub.a] at infinite distance of the plates (i.e. 1 /d = 0) gives the value of lead capacitance ([C.sub.L]) of the cell. This value is to be subtracted from the measured value of capacitance with the sample [C'.sub.s] and with air [C'.sub.a] to have an exact value of the capacitance with sample (Cs) and with air (Ca).

i.e Cs = C 's- [C.sub.L] and Ca = C 'a- [C.sub.L]

[FIGURE 2 OMITTED]

Capacitance

A commercial digital LCR meter (Pacific, PLCR 8C) was used to measure the capacitance and dissipation factor (tan [delta]). To have a comparative study of dielectric behaviour of bovine femur, tibia, radius / ulna (fore arm), metacarpus, metatarsus, scapula, skull, pelvis, rib, and backbone in the applied alternating filed of frequency 1 KHz capacitance and dissipation factor were measured with and without the sample in the cell. All the measurements were taken at room temperature.

The dielectric constant ([epsilon]') of the sample is given by [epsilon]' = CS / Ca = [C'.sub.S] - [C.sub.L] / C'a - [C.sub.L]

Where Cs = actual capacitance of the cell with the sample.

Ca = actual capacitance of the cell with air

C's = measured capacitance of the cell with sample

C'a = measured capacitance of the cell with air.

[C.sub.L] = lead capacitance.

[FIGURE 3 OMITTED]

The electrical and dielectric properties were investigated by applying electrical current to samples through dielectric cell using commercial LCR meter (Pacific, PLCR 8C).

Knowing the value of [epsilon]' and tan [delta], the dielectric loss was calculated by using the formula [epsilon]" = tan [delta]. [epsilon]'. The specific alternating current conductance K was calculated from the relation [epsilon]" = 1.8 X [10.sup.12] K/v where v is the frequency of the applied electric field in Hertzs.

The dielectric constant and dielectric loss of bone specimen were measured along its z-direction. But it was not possible to measure along x and y--directions due to the limitations in the dimensions of the specimens.

RESULTS

The tables below present the data on the electrical parameters such as dielectric constant ([epsilon]'), dielectric loss ([epsilon]"), resistivity ([rgo]) and conductivity (K) of bovine femur, tibia, humerus, radius /ulna (fore arm), metacarpus, metatarsus, scapula, skull, pelvis, rib, and backbone taking 10 samples of each in wet / normal condition (table 1) and oven dried condition (table 2). The parameters were determined at 1 KHz frequency at room temperature. Here the standard deviation values of the parameters reveal the variation among the different bone specimens of above- mentioned, but not the uncertainity of the measurement. It is evident from the data that there exists a considerable variation in the observed parameters. The absolute values of electric and dielectric parameters determined in this study were in agreement with earlier studies (Saha and Williams 1989, Gabriel et al 1996a).

DISCUSSION

Results on electrical parameters of bovine femur, tibia, humerus, radius /ulna (fore arm), metacarpus, metatarsus, scapula, skull, pelvis, rib and backbone reveal the considerable variation in different bone samples and also in different specimens of the same bone, obtained from the various parts of the bone. This may be attributed to the inhomogeneous deposition of calcium phosphate and water content of the bones. Bone density and investigated electrical parameters were significantly interrelated, as reported earlier (Saha and Williams 1989, Seirpowska et.al 2003). The sharp fractional change in dielectric constant and resistivity with the water content suggest that the electrical parameters are very sensitive to free water present in bones. Influence of water on electrical behaviour is specific to bone because of the fact that mineral content of the bone is found to be in different proportion which also effect the electrical make up of the bone. Here it is the water content which causes lot of variation in dielectric parameters. The three parameters namely water content, mineral content (calcium phosphate) and orientation of the collagen fibers with respect to the applied electric field play an important role in influencing the electrical parameters such as dielectric constant, dielectric loss, and conductivity of the bone tissues when measured at the bulk level.

REFERENCES

[1.] Cole, K. S. 1972. "Membranes, Ions and Impulses", University of California press, Berkely.

[2.] Danzer, H. 1934. Ann.Phys. (N. Y), Vol 21(5) :463.

[3.] Gabriel, C., Gabriel, S. and Corthout, E. 1996a. "The dielectric properties of biological tissues: I. Literature survey.", Phys.Med.Biol.,Vol.41: 2231-49.

[4.] Jiang, Y., Zhao, J., Augat, P., Ouyang, X., Lu, Y., Majumdar, S. and Gehant, H.K. 1998. "Trabecular bone mineral and calculated structure of human bone specimens scanned by peripheral quantitative computed tomography; relation to biomechanical properties", J. Bone Miner., Res., 13: 1783-90.

[5.] Keaveny, T.M., Morgan, E.F., Neibur, G.L., and Yeh, O.C., 2001. "Biomechanics of trabecular bone". Annu. Rev. Biomed. Engg., Vol.3 : 307-33.

[6.] Saha, S. and Williams, P.A. 1989 "Electric and dielectric properties of wet human cancellous bone as a function of frequency", Ann. Biomed. Eng, Vol 17: 143-158.

[7.] Schewan, H. P. 1957. "Advances in Biological and Medical Physics", Vol.5 ,Academic Press, New York : 147.

[8.] Sierpowska, M.A., Hakulinen, J. ,Toyras, J., Day, S., Weinans, H., Jurvelin , J.S. and Lappalainen, R.2005. "Prediction of mechanical properties of human trabecular bone by electrical measurements", Physiol.Meas., Vol.26 : S 119-S131.

[9.] Sierpowska, J., Toyras, J. , Hakulinen, M.A., Saarakkala, S., Jurvelin, J.S. and Lappalainen, R.2003. "Electrical and dielectric properties of bovine trabecular bone--relationships with mechanical properties and mineral density.", Phys.Med. Biol.,Vol.48 : 775-786.

[10.] Toyras, J., Nieminen, M.T., Kroger, H., and Juvelin, J.S., 2002, "Bone mineral density, ultrasound velocity and broadband attenuation predict mechanical properties of trabecular bone differently", Bone, Vol.31: 503-7.

[11.] William, P. A. and Saha, S. 1996. "the electrical and dielectric properties of human bone tissue and their relationship with density and bone mineral content." Ann. Biomed. Eng., Vol 24: 222-33.

R. Jeevan Kumar, S.Md. Shoaib, Kaleem Ahmad Jaleeli * and Adeel Ahmad *

Molecular Biophysics Laboratories, Dept of Physics, S. K. University, Anantapur-515003, India.

* Biophysics Unit, Department of Physics, Nizam College (Autonomous),Osmania University, Hyderabad, A. P India.

Table. 1 : Data on electrical parameters of bones in normal / wet condition Identification Dielectric Dielectric loss Constant ([epsilon]") ([epsilon]') Femur 8.423 [+ or -] 0.94 1.499 [+ or -] 0.38 Tibia 10.353 [+ or -] 1.52 2.285 [+ or -] 0.66 Humerus 8.012 [+ or -] 1.08 1.461 [+ or -] 0.37 Radius /ulna 9.786 [+ or -] 0.99 2.487 [+ or -] 0.71 (Fore arm) Metacarpus 7.773 [+ or -] 1.32 1.606 [+ or -] 0.56 Metatarsus 10.36 [+ or -] 0.84 2.663 [+ or -] 0.52 Scapula 7.980 [+ or -] 1.48 2.144 [+ or -] 0.72 Skull 6.464 [+ or -] 2.57 1.342 [+ or -] 0.91 Pelvis 9.00 [+ or -] 3.24 3.411 [+ or -] 2.01 Rib 9.133 [+ or -] 1.91 3.640 [+ or -] 1.40 Backbone 5.413 [+ or -] 2.03 1.220 [+ or -] 0.93 Identification Conductivity (K) Resistivity [rho] K=[epsilon]" v/1.8 x (X [10.sup.9]ohm.cm) [10.sup.12] (K X [10.sub.-9] mho.[cm.sup.-1]) Femur 0.832 [+ or -] 0.21 1.275 [+ or -] 0.33 Tibia 1.269 [+ or -] 0.37 0.846 [+ or -] 0.24 Humerus 0.811 [+ or -] 0.20 1.305 [+ or -] 0.33 Radius /ulna 1.381 [+ or -] 0.39 0.779 [+ or -] 0.22 (Fore arm) Metacarpus 0.892 [+ or -] 0.31 1.320 [+ or -] 0.65 Metatarsus 1.479 [+ or -] 0.29 0.704 [+ or -] 0.16 Scapula 1.190 [+ or -] 0.40 0.938 [+ or -] 0.37 Skull 0.745 [+ or -] 0.51 2.052 [+ or -] 1.30 Pelvis 1.894 [+ or -] 1.12 0.840 [+ or -] 0.85 Rib 2.022 [+ or -] 0.78 0.586 [+ or -] 0.31 Backbone 0.677 [+ or -] 0.52 2.402 [+ or -] 1.54 Table. 2 :Data on electrical parameters of bones in oven dried condition Identification Dielectric Dielectric Constant loss ([epsilon]") ([epsilon]') Femur 5.760 [+ or -] 0.58 0.335 [+ or -] 0.13 Tibia 7.636 [+ or -] 0.61 0.840 [+ or -] 0.24 Humerus 5.834 [+ or -] 0.76 0.395 [+ or -] 0.18 Radius /ulna 6.509 [+ or -] 1.12 0.667 [+ or -] 0.24 (Fore arm) Metacarpus 5.711 [+ or -] 0.91 0.394 [+ or -] 0.22 Metatarsus 7.141 [+ or -] 1.26 0.761 [+ or -] 0.34 Scapula 3.995 [+ or -] 1.23 0.196 [+ or -] 0.16 Skull 3.325 [+ or -] 1.06 0.106 [+ or -] 0.06 Pelvis 4.528 [+ or -] 1.55 0.493 [+ or -] 0.37 Rib 7.049 [+ or -] 3.4 1.116 [+ or -] 0.72 Backbone 2.853 [+ or -] 0.41 0.205 [+ or -] 0.08 Identification Conductivity (K) Resistivity [rho] K=[epsilon]"v/1.8 (X [10.sup.9]ohm.cm) x [10.sup.12] (K X [10.sup.-9] mho.[cm.sup.-1]) Femur 0.186 [+ or -] 0.07 6.465 [+ or -] 3.34 Tibia 0.466 [+ or -] 0.13 2.286 [+ or -] 0.58 Humerus 0.219 [+ or -] 0.10 8.233 [+ or -] 11.30 Radius /ulna 0.370 [+ or -] 0.13 3.095 [+ or -] 1.26 (Fore arm) Metacarpus 0.218 [+ or -] 0.12 7.145 [+ or -] 5.46 Metatarsus 0.422 [+ or -] 0.18 2.704 [+ or -] 0.90 Scapula 0.109 [+ or -] 0.09 18.140 [+ or -] 16.35 Skull 0.593 [+ or -] 0.03 22.082 [+ or -] 12.18 Pelvis 0.273 [+ or -] 0.20 7.416 [+ or -] 6.99 Rib 0.620 [+ or -] 0.40 3.408 [+ or -] 4.66 Backbone 1.138 [+ or -] 0.04 10.236 [+ or -] 4.03