Solid state bone behaviour.

Proo. Biophys. molec. Biol., Vol. 56, pp. 1~.1, 1991. Printed in Great Britain.All rightsreserved.

0079-6107/91 $0.00+ .50 © 1991 PergamonPress pie

S O L I D STATE B O N E B E H A V I O U R J. BEHARI Bioelectromagnetics Laboratory, School of Environmental Sciences, Jawaharlal Nehru University, New Delhi-110067, India

CONTENTS I. INTRODUCTION II. CHEMICALCOMPOSITION OF BONE

1. Collagen 2. The Inorganic Phase of Bone (a) Macromolecular organization of apatite (i) Wide angle X-ray diffraction profiles (ii) Low angle diffraction, scatter and electron microscopy III. TYPE OF BONES

1. Cortical Bone 2. Cancellous Bone IV. BONE AS A COMPOSITEMATERIAL

1. Bone as Two Phase Material V. ELECTRICALPROPERTIES OF BONE

9 9 9 10 11

1. Electrical Conduction in Bone (a) DC conductivity (b) AC conduction 2. Mechanism of Charge Transport in Bone

11

VI. DIELECTRICCONSTANT VII. HIGH FREQUENCY DIELECTRIC RELAXATIONIN BONE

13 15

VIII. THERMODYNAMICALBONE BEHAVIOUR

15 16

IX. SOLID STATE OF BONE

1. Hall Effect

17 17 17

X. PHOTO-ELECTRIC EFFECTS

1. Optical Spectra 2. Bone Photovoltaic Cell XI. LIFE TIME AND DRIFT MOBILITY OF CHARGE CARRIERS

1. Drift Mobility XII. PN JUNCTION AND PHOTO-ELEcTROMAGNETIC EFFECTS

1. Photo-Electromagnetic Effect (PEM)

19 19 19 21

XIII. ELECTRET

21

XIV. PIEZOELECTRICITY

22 22 25 26 27 28

1. 2. 3. 4.

Experimental Measurement Physical Concept of Piezoelectricity Piezoelectric Theory Equivalent Single.Crystal Structure of Bone 5. In Vivo Applications of Bone Piezoelectricity

28 29

XV. ELECTRONPARAMAOr~nC Rr=SONANCE(EPR)

1. Bone Mineral Powder

30

XVI. TRACE ELEMENTS OF BONE JPB

56

: I-A

1

2

J.

XVlI. STREAMING POTENTIALS XVIII. MECHANISM OFBONESURFACE REMODELLING REFERENCES

BEHARI 31 34 36

I. I N T R O D U C T I O N Since about the last two decades, great strides have been made in understanding of bioelectric phenomena in skeletal systems, particularly in bone (Behari, 1991; Bassett, 1971, 1989; Kosterich et al., 1983; Ray and Behari, 1986; Singh and Katz, 1986). Bone is a remarkable tissue, combining such striking features as plasticity and regeneration capacity. Some soft tissues, e.g. liver and skin, regenerate; rarely do they reduplicate the precise structure of the pre-existing tissue. Bone provides us with structural support, levers for locomotion and undergoes growth and remodelling throughout the subject's life. Bone is a compositionally and structurally complex material capable of remodelling itself in response to mechanical loads. The understanding of processes which relates load bearing and growth has become an area of considerable interest. It has also been reported that dead bone also has many interesting mechanical, electrical and acoustic properties (Becker and Brown, 1965; Behari et al., 1975; Singh and Behari, 1984; Saha and Williams, 1989). Bone growth, maintenance, destruction and remodelling is governed by the behaviour of three related cell types (Bassett, 1971): the osteoblasts, the osteoclasts and the osteocytes. Long branching processes (osteocytes), contained in bone, are encased in calcified cavities (lacunae). These are connected together to capillaries (in haversian canals) by narrow channels (canaliculi) permeating in a solid bone matrix (Hancox, 1972). The matrix consists of bundles of collagenous fibres in an amorphous ground substance (cement) impregnated with calcium phosphate complexes deposited in the osteoid (Frost, 1986). The osteoblasts formed within the matrix are converted into osteocytes. Osteocytes surrounded by nearly solid bone receive nourishment and excrete waste products through diffusion and fluid transport. These physiological processes are dependent upon the existence of an adequate blood supply (Hancox, 1972). Bone is produced and resorbed, guided along orientation patterns corresponding to the functional type of stress. Mechanical influences upon bone are the sum total of a variety of intrinsic and extrinsic effects: viz. ballastics of cardio-vascular action, gravity muscle tones, voluntary muscle activities, and the impact between skeletal systems and the environment. Old bone tissue is first resorbed by cells called osteoclasts and new un-mineralized tissue is then deposited by cells called osteoblasts. The new tissue is then gradually mineralized to synthesize new bone. In adults, the remodelling process is usually in a state of dynamic equilibrium, with the amount of new bone removed being balanced by the newly deposited bone. Disturbances of this balance can be triggered by several types of stimuli (e.g. genetic, hormonal and metabolic). Significant amounts of data have been generated since the pioneering work of Becker and Brown (1965) and Fukada Yasuda (1957), defining and quantifying bone electrical state. It therefore appears imperative to review the existing data and analyse this in the light of two aspects: examining its solid state behaviour for its relevance to the in vivo situation, and to extrapolate these data to a clinical situation. The structure of bone is well known, almost down to a molecular level, and demonstrates an organization permitting it to be viewed as quasi-crystalline in nature (Glimcher, 1959; Glimcher and Krane, 1968). The water content of mature cortical bone is low, and the major component of the structure is non-cellular. The tissue can therefore be subjected to various controlling mechanisms (physical and chemical) and still retain significant elements of organization for study. The physical nature of the bone permits the application of solid state physical methods of experimentation to the problem of understanding biophysical phenomena in bone. Though bone remodelling induced by mechanical stress is of considerable physiological importance the mechanism at work still remains a matter of conjecture. It appears that both osteoblastic and osteoclastic activities are regulated by cells. Since bone responds to mechanical stress by differential growth so as to undo the effect of the former, it satisfies the requirements of a stimulus-response adaptive system. Therefore, its behaviour can be

Solid state bone behaviour

3

analysed by the control system theory of cybernetics. Mechanically, induced bone remodelling can be thought of as being regulated by a closed loop negative feedback system, an approach in which the response feeds back to the original signal and tends to cancel it out. In the language of a system approach this can be written comprising the following steps: (1) an external mechanical stimulus applied to bone, (2) biotransduction to convert it into a biological response, (3) the response triggers osteoblastic and/or osteoclastic activity, and finally (4) the bone structural changes take place appropriately to resist the stress. In general, the simplest control system is a closed loop feedback in which the response feeds back to the original signal and tends to annul it. This also satisfies Wolff's law. Examples of such hypothetical mechanisms are: (1) relative motion between the lamella causing impingement on osteocyte processes, (2) stress-induced fluid motion resulting in improved nutrition of osteocytes, (3) stimulation of bone cells by piezoelectrically or stress generated potentials (Bassett and Becker, 1962; Korostoff, 1979; Cochran et al., 1968; Behari et al., 1987; Jha and Behari, 1991). Keeping this in mind, it is planned to undertake a survey of various properties of bone: e.g. electrical properties, solid state behaviour and electrokinetic phenomena. This requires an understanding of various parameters: viz. the nature of bonding, mechanism of carrier transport, conductivity, thermodynamical behaviour, etc. This then will characterize the bone behaviour. Establishing a link between mechanical and electrical properties is important, for this provides an insight into physiological behaviour of bone under cross stress adaptation. II. C H E M I C A L C O M P O S I T I O N OF BONE Bone is a highly organized material from the gross macroscopic to the molecular level. At the former level, bone has an overall linear arrangement with collagen fibres lying parallel to each other and effectively in line with the original long axis of bone (Herring, 1972). At the molecular level, the apatite crystals (about 500 A axis dimensions) are applied to the surface of the collagen fibres in precise relationship to the 640 A. Schmidt (1956) proposed that the major 640 A periodicity arose through an overlap of the tropocollagen molecule with respect to the nearest neighbours by about one quarter of its length. Three helices are wound into a super helix, 3000 tk long, 15 A~diam, and a molecular weight of 300,000 Da (Ramachandran, 1963). The basic collagen unit is defined as tropocollagen (Hodge and Schmitt, 1961). Analytically on a dry weight basis, bone consists roughly 65-70% of the inorganic crystals of the calcium phosphate salt, apatite, and 30--35% of organic matrix of which collagen makes up the major fraction (95-99%) (Glimcher, 1959). The collagen in bone appears to be structurally similar to that in other tissues, although it is highly cross linked. In a loose analogy, bone structure can be considered similar to that of fibre glass because fibreglass is constructed by impregnating a resin matrix with a quasi-mineral phase (Katz, 1971; Kitsugi et al., 1989; Liu et al., 1987). 1. Collagen

From an X-ray diffraction point of view, bone collagen does not differ markedly from collagen obtained from other sources. Also no marked differences have been reported by electron microscopic studies (Herring, 1972). Collagen is a macromolecule consisting of polypeptides organized in the form of a triple helix. The triple helix is stabilized by hydrogen bonds formed between amino groups of polypeptide chains and carboxyl groups of adjoining polypeptide chains (Ramachandran and Kartha, 1955). The peptide groups forming the intramolecular hydrogen bonds have a permanent electric dipole moment, which may primarily contribute to the piezoelectric polarization. It has been established that the piezoelectric polarization in helical polypeptides is produced by the internal rotation of the dipole moment of peptide groups under an applied shearing (Namiki et al., 1978). The structure of collagen is related to the investigations of vibrational and other motions of the molecular assembly in collagen. The force constants of hydrogen bonds in some polypeptides have been estimated on the basis of models but it lacks experimental confirmation. A number of spectroscopic studies have focused on the structural aspects of

4

J. BEHARI

collagen to elucidate the relationship between its molecular structure and function (Diem et al., 1984; Lazarev et al., 1985). Harney et al. (1977) have described measurements of the inelastic light scattering (Brillouin) spectra of collagen from rat tail tendon from which they obtained the elastic modulus of the tropocollagen molecule and an estimate of hydrogen bond force constants. It may be pointed out that the value of the force constants so obtained compares well with such data obtained for other solids on the basis of neutron inelastic scattering, thereby suggesting that the classical central force constant model can be applied in such cases. In synthetic macromolecules the modulus decreases strongly with the degree of coiling because bond twisting rather than bond stretching or angle opening strains accommodate the stress. A low frequency Raman study of collagen in the region 200-600 cm- 1 was reported by Renugopalakrishnan et al. (1985). Phonon dispersion curves have been calculated for helical polyglycine II (Small et al., 1970) and an incoherent inelastic neutron scattering study of polyglycine I and II has been reported by Gupta et al. (1968). Berney et al. (1987) have reported results of an elastic neutron scattering study of collagen at ambient and low temperatures. They reported four peaks (17, 27, 40 and 57 cm - 1), each representing a normal mode of the collagen chain. Five peaks (22, 31, 40, 68 and 101 c m - l ) were discerned in the spectrum of the cooled sample. These authors have suggested the possibility of significant structural changes accompanying the cooling.

2. The Inorganic Phase of Bone Bone is a living tissue which exists in dynamic equilibrium with the body fluids. Its chemical composition varies not only from one bone to another but also within the microscopic structure of the same bone. From X-ray diffraction studies it was realized that most basic calcium phosphates belonged to the apatite group. It was found (Naray-Szabo, 1930; Mehmel, 1930) that the hexagonal fluorapatite unit cell contains Calo (PO4)6F2. It belongs to the space group C2h (Pra/m) and the size of the unit cell is a=9.37_+0.01 A, c = 6.88 _+0.01/~, and a = 9.36_+ 0.02 A and c = 6.85 __0,02 ,~, respectively, which is in good agreement with the results of other investigators. Studies on synthetic fluorapatite (Engstrom, 1972) gave a=9.371 ,~ and c=6.884 A. The unit cell has two equal edges, a inclined at 120° to one another and a third, c, perpendicular to these. The inorganic fraction of bone, hydroxyapatite, has atomic contents of the crystallographic unit cells given by the formula Calo(PO4) 6 (OH)2. The hydroxy group lies at the edge of the rhombic unit cell and occurs at the equidistant interval one half the height of the unit cell (3.44 A) parallel to the c axis. In fluorapatite (which can be considered as the prototype of the apatites), the ions can be fully substituted by other ions of close physico-chemical relationship. Calcium can be replaced by strontium, barium and lead, the PO4 group by ASO4 or VO 4, and fluorine by C1 or OH, forming a wide range of intermediates (Naray-Szabo, 1930; Beevers and McIntyre, 1946). (a) Macromolecular organization of apatite (i) Wide angle X-ray diffraction profiles. There is a marked meridional orientation of the 00.2 reflection from apatite. On the basis of this it is concluded that the apatite crystals are elongated in the c direction and that they are located parallel to the fibre axis of the collagen fibrils. Attempts have been made to estimate the dimensions of the apatite crystals from the broadening of the wide angle diffraction lines. Since there are a number of factors besides size that influence the profile of the diffraction lines, it is necessary to measure several orders. (ii) Low angle diffraction, scatter and electron microscopy. In the low angle region bone specimens give both discrete reflections and a particle scatter (Finean and Engstrom, 1953; Carlstrom and Finean, 1954). Qualitatively the continuous particle scatter gives the information that the particles or particle aggregates (hydroxyapatite) are rod shaped (21 mm long and 7.5 mm wide) and that their c axis is parallel to the collagen fibres. Hydroxyapatite is the most important component of bone salt. Another striking feature of


5

the powder pattern of bone is the continuous background scatter. Eanes and Posner (1970) measured the background scatter to assess the relation between crystalline and amorphous portions of apatite. They found a particle length of 330-350/~ in agreement with the experimental results. Caglioti et al. (1956) using a combination of low-angle scattering and electron microscopy, suggested that the mineral phase was continuous and not composed of totally discrete particles. Carlstrom and Glas (1959) using line broadening of wide angle X-ray reflections of oriented fish bone, concluded that the mineral was in the form of rods estimated to be 60-70 nm long and 4-4.5 nm wide. However, Harper and Posner (1966), by comparison with X-ray diffraction from 100% crystalline standards, suggested that bone mineral from mature humans, cow and wistar rats contained a non-crystalline calcium phosphate in addition to the well-known apatite phase. The non-crystalline component is 40% of the mineral. Termine and Posner (1966) have also interpreted infrared spectra of rat bone as resulting from the presence of amorphous calcium phosphate. Posner and Betts (1975) using X-ray radial distribution analysis, found 10% of amorphous phase in mature rabbit cortical bone. Wheeler and Lewis (1977) interpreted the broadening of wide-angle X-ray patterns of bovine bone mineral in terms of a paracrystalline structure. Their paracrystalline dimensions of 22 nm and 7 nm for the basal and prism planes are similar to the crystalline size as obtained in earlier studies. Miller et al.'s (1981) experiments on adult rat femur revealed a poorly crystalline hydroxyapatite, similar to a mature amorphous calcium phosphate. These authors have suggested that bone mineral is intermediate in structure between an amorphous solid and a perfect crystal. Transmission electron microscopy of thinly sectioned bone also reveals a variety of shapes and dimensions for the hydroxyapatite crystals (Cameron, 1972; Jackson et al., 1978; BocciareUi, 1970), ranging from needle to rod and plate shapes. Scanning electron microscopy has suggested spheroidal shaped particles 100 nm in diam which aggregate to form the mineral component of macroscopic bone (Boyde, 1972; Boyde and Sela, 1978; Sela, 1977; Pautard, 1978). Green et al. (1985, 1987) used biochemical etching techniques to demonstrate that the mineral phase in bovine bone is largely independent of the collagen. Structural order was revealed at three levels, namely crystalline (20 nm diam), which aggregate to form larger continuous spheroidal particles (100 nm diam) which in turn form granules (500 nm diam). These authors (Green et al., 1988) have further worked on fish bone microstructure and reported its mineral organization and spatial relationship of the collagen and mineral phases. Using the technique of collagenase etching by electron micrographs these authors have concluded that a preferred orientation of the collagen fibres along the fish bone axis exist. III. TYPES OF BONES Material properties of bone have been measured in vitro and in vivo using a continuous wave ultrasound technique (Ashman et al., 1984; Behari and Singh, 1980). Bone is described as a connective tissue. A tissue is an aggregation of similarly specialized cells--combined to perform a particular function. At the macroscopic level there are two major forms of bone tissue called compact or cortical bone and cancellous or trabecular bone (Engstrom, 1972). 1. Cortical Bone

Cortical bone can respond in two ways to a change in loading environment: (1) the change in the local mechanical material properties by means of a change in the porosity of the cortical bone tissue, called internal remodelling; (ii) the change in the shape of the bone by the deposition or resorption of bone on the external bone surface, called surface remodelling. Cortical or compact surface of bone is a dense material with a specific gravity of about two (Singh and Behari, 1980). The external surface of bone is smooth and is called the periosteal surface. The interior surface is called the endosteal surface (Fig. 1). From a microscopic viewpoint there are three types of cortical bone: woven, lamellar and haversian (Lacroix, 1971 ). Woven bone is found typically in both cortical and cancellous

6

J. BEHARI

.ate is

:avity

Cancellous bone

FIG. 1. Diagrammatic representation of the parts of a long bone.

bone of young growing animals and in adults after some bone injury. However, during normal maturation, it is gradually replaced by lamellar bone so that, in man for example, there is normally no woven bone present after the age of 14 or 16 years. An additional distinguishing feature of woven bone is the relationship of mineral to collagen. In lamellar and harversian bone, these elements are closely related and it seems impossible for lamellar bone to become hypermineralized. However, the mineral density of woven bone varies enormously: the mineral appears to be less closely related to the organic matrix, mineralization occurs in an irregular manner, and hypermineralization is often observed. When it occurs in the mid-shaft of a long bone, lamellar bone consists of a number of concentrically arranged laminae. The thickness of the laminae is about 200 #m. Between each lamina and the next there is a net-like system of blood vessels. Each lamina is divided into the three zones as shown in Fig. 2 (Kraus, 1972). The first zone, which extends from the

Osteone

Central canal contoining

Long axis of osteone

blood vessels

Bone cell osteocyte

Outer Larnell o ~ Collagen f ibets 450sPiraL and 90° to

_I

Adjacent LameLto-----~ / I

ColLagenJ fibers

FIG. 2. Microscopic structure of compact bone.


7

surface of the blood network to about one-third of the way across the lamina, is of highly organized bone which is dense. The second zone, which also extends for about one-third of the distance, is a poorly organized tissue. This zone is interrupted in the middle by a line that, in ordinary light, appears to be bright. 2. Cancellous Bone

Cancellous bone exists only in the metaphyseal region of long bones and within the confines of the cortical bone covering in the smaller flat and short bones. Cancellous bone is also called trabeculae. The connected trabeculae give cancellous bone a spongy appearance and it is often called spongy bone. There are no blood vessels within the trabeculae, but there are vessels immediately adjacent to the tissue and they weave in and out of the large spaces between the individual trabeculae. Cancellous bone has a vast surface area as would be suggested by its spongy appearance. Cancellous bone is distinguished from cortical bone by its highly porous structure, with porosity greater than 30% (Gibson, 1985). The rigid open cell foam nature of cancellous bone has been discussed in detail by several authors (Cowin, 1983; Carter and Hayes, 1977). The anisotropic nature of bone demands mechanical properties to be measured in several different directions to completely characterize the anisotropy. Cancellous bone can be considered linearly elastic and anisotropic (Carter and Hayes, 1977). Several modes of wave propagation are possible depending on overall specimen geometry, the internal structure of the specimen geometry, the internal structure of the specimen, and the type of acoustic excitation. Measured structural densities and modulus reported by Ashman et al. (1987) using an ultrasonic technique are similar in value to those of Carter and Hayes (1977) and Bensusan et al. (1983). There are some anatomical sites in which the architecture of cancellous bone is fairly isotropic with modulus relating to apparent density squared. The modulus of highly oriented cancellous bone however, has been shown to exhibit a cubed relation to density (Gibson, 1985). In general cancellous bone is anisotropic, requiring different correlations with density for different material directions. Further, the degree of anisotropy varies significantly throughout most cancellous structures. The cancellous structure does not appear as a continuum to waves of such short wavelength. At high frequencies (> 2 MHz) propagation of elastic waves seem to be through individual trabeculae rather than through the structure. Velocities are much closer to those seen in cortical bone (approximately 2000-3000 m/see) (Ashman et al., 1987). IV. BONE AS A C O M P O S I T E MATERIAL Understanding of calcified tissues as composite materials is an important area of research. By far the strongest and the most efficient materials created by nature are two phase materials. Under this category falls bone, wood and fibre glass to name a few (Katz, 1970, 1971). These are made up of two different substances with contrasting properties of strength and elasticity. The knowledge of orientation of the HAP crystallites with respect to the collagen fibres play an important role in predicting the orientation of the principal axis of stress in bone tissue. In fact Cowin and Hart (1990) have estimated that assuming elastic isotropy maximum error turns out to be 45% and the typical error is significant. This confirms anisotropic nature of bone. Three hypotheses have been advanced to explain the mechanical properties of bone. These are: (i) compound bar, (ii) pre-stressed material, and (iii) a two phase material. On the basis of the compound bar model, the load borne by each component (collagen and hydroxyapatite) in response to any given force on the whole bone, is given by Currey (1964): PAcEc W C -- E A A A q- E c A c '

PAAEA W A -- E A A A q- E c A C '

where P is the total load borne by the whole bone, E c and E A are the Young's modulus of

8

J. BEHARI

elasticity, and Ac and ,4A are the cross sectional areas (assumed to be proportional to their fractional volumes, Vc and VA) of collagen and hydroxyapatite, respectively. An analysis of the calculation (Currey, 1964) shows that the collagen's contribution to the modulus of elasticity of bone (EB = 1.6 x 101~ dyn/cm 2) is practically negligible (Ec Vc = 0.06 x 10 ~1 dyn/cm2). Hence, the total contribution can be considered to be due to hydroxyapatite alone (EA VA= 2.6 X 101 ~dyn/cm2). This model leads one to conclude that presence of coUagen may be neglected to explain the modulus of elasticity of bone. A close relationship exists between degrees of mineralization and its microhardness. It is observed that increasing amounts of calcium salts in single osteons cause an increase in their modulus of elasticity. For the purpose of modelling, osteons have been identifed as porous tubes with cross wrapped mineralized collagen fibres. Therefore, it is hypothesized that the strain in the mineralized phase of bone would initiate remodelling to the bone cells in regions subjected to increased or decreased mechanical stress. In view of this assumption and of the high sensitivity of cells to environmental calcium, it seems possible that a mechanochemical effect may exist in the hydroxyapatite crystal which would provide the trigger. 1. Bone as Two Phase Material

Currey (1969a) proposed that calcified tissue was a two phase composite consisting of hydroxyapatite (HAP) and collagen. The tissue has been studied in more detail by Bonfield and Li (1965, 1967), Welch (1970) and Katz (1971). In this hypothesis the crystallites of hydroxyapatite are distributed throughout the collagen matrix. In the simplest model the HAP is uniformly dispersed without order, but to account for the observed anisotropy a more complex model have been suggested which includes the orderly distribution of the microcrystallites in the collagen fibrils of bone and dentine, or the prisms of dental enamel. Lees and Davidson (1977, 1979) pointed out that boney tissues be considered as two phase composite systems of hydroxyapatite and collagen. Bone becomes stiffer as the hard filler (HAP) is added until a maximum elastic modulus is reached. It is postulated that increased density of crosslinking is associated with increased HAP content and HAP crystallites provide rigid bases for shortened links to stiffen the composite by reversible enzyme-directed processes. Several models have been employed to explain the mechanical properties of hard tissues. The oldest are the Voigt (uniform strain model) and the Reuss (uniform stress model). Katz (1971 ) discussed other models which provide closer upper and lower bounds, particularly the Hashin-Shtrikman (1963) bounds based on variational principles applied to the strain energy of the composite. These bounds are useful when the properties of the constituents are close together in value, which permits some kind of averaging to be employed by which to estimate experimentally-determined elastic constants. However, the density and elastic moduli of collagen and HAP are very different and the bounds are far apart. Most authors are concerned with improving the law of mixtures to account for the observed elastic properties. Currey (1969b) has suggested that the microcrystallites are fused together to make the hard material more fibrous contrary to the findings of other workers (Ascenzi et al., 1965; Glimcher and Krane, 1968). The longitudinal and shear moduli are sufficient to define the elastic properties of isotropic homogenous media and these are most convenient for sonic measurements, since the moduli are directly calculable from measurements. Other elastic moduli can be obtained from these two (Lees, 1975; Katz, 1971). The Voigt and Reuss models for composites expressed in terms of the longitudinal modulus are given by the equations: Kv = vlkx +/92k2 KR=

or

1

KR

-

klk2 /)1 k2 d-/32kl

v~

V2

kl

k2

(Voigt model)

(Reuss model)


9

where vl=volume fraction of constituent No. 1, v 2 = l - v 1, and k 1, k2=longitudinal modulus of constituent No. 1, 2. In these equations the longitudinal modulus is used, where other authors use bulk and shear modulus. The Voigt model yields the same expression no matter which modulus is calculated, but the Reuss model will not. In calculating bounds, first the longitudinal modulus is found for the particular volume fraction, vl, as well as the density given by

P=vlpl + v 2 P

2•

The longitudinal sonic velocity is then found from C~ = K / V , there being two values, one for the Voigt and the other for the Reuss model. The Reuss calculation was shown by Hill (1952, 1963) to provide a rigorous lower bound to the elastic modulus of a mixture. Solving for one of the component moduli will then yield an upper bound for that modulus. When the moduli of the components are almost equal, there is very little difference between the models in predicting the correct behaviour and the average of the two may be a reasonably good approximation. V. ELECTRICAL P R O P E R T I E S OF BONE 1. Electrical Conduction in Bone

(a) D C conductivity An analysis of the direct and the induced current flow in the bone requires accurate information on the electrical properties of bone. Such data is also important for understanding the mechanism of bone growth and regeneration. The key to these is to understand the mechanism of charge transport. Electrical conductivity is found to be dependent upon (i) humidity, (ii) temperature, (iii) magnitude of applied electric field, and (iv) exposure to radiation (Becker et al., 1964; Behari et al., 1974, 1975). Humidity and temperature are two important parameters which are found to control conductivity. The former is important as it accounts for the water content of the samples. Bone behaves as a semiconductor whose resistivity varies over a range (107-1012 ohm/cm) depending upon the method of sample preparation and its thermodynamical history. Correspondingly the activation energy falls in the range 1-5 eV and is temperaturedependent (Becker et al., 1964; Behari et al., 1974; Andrabi, 1978). Reinish and Nowick (1974) measured the dielectric properties of bone which was initially dried and then equilibrated at 98% relative humidity level. They found almost an order of magnitude increase in conductivity per percentage change in moisture content. The DC resistivity of bone is reported to be in the range of 2-5 x 105 ohm/cm (Liboffet al., 1975; Stefan et al., 1976). However, these values are highly dependent on the chemical reactions of the electrode. In freshly excised sheep metatarsal a resistivity of 7-12 x 103 ohm/cm was reported which was four to eight times the value found for the bone marrow (Durand et al., 1978). A different resistivity value (10-100 ohm/era) was reported using a four point method. This method minimized polarization and electrode interactions with tissues (Sansen et al., 1978). The difference in resistivity values was attributed not to bone itself but to the tissues surrounding it. In addition, it was noted that there was a large capacitance between the tissue and the electrodes which influenced conduction. Chakkalkal et al. (1980) investigated the dielectric relaxation behaviour of bovine, compact bone, saturated with 0.9% NaC1 solution. The resistivity in the radial direction was found to be two orders of magnitude smaller than that reported by Reinish and Nowick (1979) at 98% relative humidity. Based on this, these authors have suggested that, at 98% relative humidity, the larger pores in bones are not filled with fluid, and that Reinish and Nowick (1979) were measuring the dielectric properties of the solid phase and perhaps a thin layer of absorbed water on the phase. Liboff et al. (1975) studied the electrical conduction in rabbit femur and human tibia in vivo. They reported a resistance value of 2-5 x 10s ohm/cm for rabbit femur and 0.7-1 x l05 ohm/cm for human tibia. Durand et al. (1978) examined the electrical impedance characteristics of whole bones in vitro by utilizing a four-point measurement technique

10

J. BEHARI

(Sansen et al., 1978). They measured a resistance of 2-3 k ohm per unit length (cm) of the whole bone and also observed a linear variation of the bone impedance as a function of the interelectrode distance. These results are similar to the results of Durand et al. (1978). Experimenting with full bone, Reddy and Saha (1984) found that the resistance of the bone cortex was several times higher than that of marrow space. Behari and Singh (1981) characterized the bioelectrical properties of in vivo bone. Bone is being treated as a source of bioelectric power. Passing a dc constant current through the bone resulted in increased polarization and a consequent higher charge retention. Electrical activity of bone is also enhanced by direct current which seems to suggest that dc electrical current may be ionic gradients and ionic transport across membranes to the inhomogenous structures of tissues that give rise to polarized molecules of dipoles. This is in agreement with the reported results (Behari et al., 1974, 1975, 1979), wherein it has been described that the source of electrical activities are dipoles, ionic spaces and the phenomena of proton conduction (H + vacancy migration). Friedenberg et al. (1973) recorded bioelectric potentials from unstressed tibia using silver/silver chloride electrodes. Potentials recorded from the anterior medial and lateral surfaces indicated that the surface voltage was constant around the transverse axis of a bone but varied in relation to its long axis. In order to explain the origin of these potentials, Becker (1961 ) has suggested that dc potentials are related to the axoplasm of the nervous system. Harlow et al. (1971) demonstrated that the source of potential is dependent on cell viability and its cytotoxic perfusion and physical destruction causes a significant voltage fall. In an attempt to measure the resistance of growing bone, a titanium coil was used as the cathode and was placed in a negatively created defect in dog tibia (Collins et al., 1981). A platinum anode and an Ag/AgC1 chloride reference electrode were placed in the thigh. It was reported that the resistance did not change over the current measurement period, with values ranging from several hundred ohms to 1000 ohms. This tends to contrast with an earlier report that a stainless steel cathode level in the marrow cavity would be encased in bone with subsequent decrease in resistance that correlated with bone formation around the cathode (Friedenberg and Brighton, 1966). (b) A C conduction Reinish and Nowick (1979) measured ac (1 k Hz) electrical conductivity of human cortical bone at various relative humidities. They also measured the conductivity and the capacitance of bone as a function of temperature and frequency (50 Hz-20 kHz). Based on this data, they developed a model of bone as a multiphase, beterogenous dielectric. Behari and Singh (1981) measured the impedance, loss factor and Q parameter of in vivo bone in the frequency range (0.5-100 kHz). The bone is characterized by a low Q (< 3) and impedance (,~ kf~) which decreases with increasing frequency. Reddy and Saha (1984) also performed experiments on fluid-saturated bone in the frequency range (1 kHz-1 MHz) and found that electrical parameters under measurement, namely the specific resistance, dielectric constant and loss factors, are frequency-dependent. These authors measured the value of dissipation factor as 50, which is much higher than that reported by Reinish and Nowick (1979), and Marino et al. (1967) (< 1). This is probably because of the fact that the results of Reddy and Saha (1984) are on fully wet bone and that of other workers are for partially wet bone. However, their results are in agreement with those of Kosterich et al. (1983) who measured the dielectric properties of bone under near normal physiological conditions. Reddy and Saha (1984) have further reported that the specific resistance in the radial direction is approximately two times higher than in the axial direction. This is in confirmation with the findings of Chakkalkal et al. (1980) who also found the ratio of resistivities in the radial to axial direction to be 3-4. The anisotropic behaviour of bone electrical characteristics stems from the fact that the bone structure is different in the longitudinal direction, compared to the transverse or radial directions. Bone is more porous in the longitudinal direction due to the presence of haversian canals, therefore it is expected that resistance in the longitudinal direction will be smaller. Due to its porous structure, the


11

electrical behaviour of wet bone, where the pores are filled with conducting fluid will be significantly different from that of dry or partially wet bone. In a recent study, Saha and Williams (1989) studied the electric and dielectric properties of wet human cancellous bone from distal tibiae as a function of frequency (120 Hz-10 MHz) and direction. The resistance and capacitance of the cancellous bone specimens were measured at near 100% relative humidity and measurements made in all the three orthogonal directions. They found that at a frequency of 100 kHz, the mean resistivity and specific capacitance were (500 ohm cm and 8.64 PF/cm), (613 ohm cm and 15.25 PF/cm) and (609 ohm cm and 14.64 PF/cm) in the longitudinal anterior posterior and in the lateral, medial direction respectively. These authors have reported that except for resistivity and the impedance, all other electrical and dielectric properties were highly frequency-dependent. All electrical and dielectric properties were transversely isotropic as the values for the longitudinal direction were different from values obtained for the two transverse directions and properties in the two transverse directions were approximately similar. The specific capacitance showed a highly significant correlation with wet density at 100 kHz and at 1 MHz. Available results on bone are summarized in Table 1. 2. Mechanism of Charge Transport in Bone

A fundamental understanding of bone conduction requires consideration of several divergent parameters. First, the conduction properties of cortical bone and its medullary cavity. Second, more than two distances should be compared in order that one may test the uniformity of conduction. Thirdly, It appears that more results devoted specifically to long term chronic and in vivo conduction of both cortical and medullary bone are needed. An aspect which is important in understanding the mechanism of charge transport is to examine the effect of temperature and radiation on conductivity. The effect of a particular type of radiation depends upon the energy of the photon relative to the bond energy. Radiation studies provide valuable information concerning molecular structure and energy transfer within bone tissue. Since the energy of the ultraviolet light is of the same order of magnitude as the energy of the hydrogen bonds, the effect of the former on the latter may be significantly perceptible in conductivity measurements. It has been found that ultraviolet light produces a decrease in conductivity of bone and its two major constituents, the decrement being maximum for apatite, intermediate for bone and least for collagen (Behari et al., 1975; Ray and Behari, 1986). An increase in conductivity with temperature of bone (Behari et al., 1974) cannot be explained on the basis of a simple band model. In order to explain the mechanism involved it may be worthwhile to look into their structure at the molecular level. Bone consists of collagen and apatite, both of which are hydrogen-bonded solids (Ramachandran and Kartha, 1955; Hamilton, 1968). According to this scheme the hydrogen bonds involved in activation can be disrupted by energies of thermal magnitude. The breaking of hydrogen bonds can impede both the electronic and the protonic conduction. Due to UV exposure some free radicals may be produced leading to aggregation of collagen molecules and increased crosslinking by stronger bonds. The mechanism of electronic conduction in polypeptides has been discussed by Cardew and Eley (1959) and they have proposed that it involves the transfer of activated electrons along a polypeptide chain (collagen and apatite both). The mode of charge transfer (intra- and extramolecular) is affected by the breaking of hydrogen bonds. Water also enters the structure of organic and inorganic components of bone, thereby leading to the formation of hydrogen bonds. In water, proton transfer takes place through the migration of an HgO ~ structure while in intra-peptide chains proton transfer through the hydrogen bonds takes place by means of a quantum mechanical tunnelling process (Eigen, 1957). VI. D I E L E C T R I C CONSTANT A parameter related to the conductivity is the dielectric constant. The first semiquantitative survey of dielectric measurements as a function of sample water content in bone

Bovine femur (wet)

Goat femur (wet) Wet cancellous bone (Human) (RH = 100%)

9

10 11

4lgl-1300 MHz 120 H ~ 1 0 M H z

AC (1 kHz)Impedance analyser, vector impedance meter AC 10 kHz

Rabbit femur (in vivo) Bovine femur (fluid saturated)

Rat femur

Sheep bone (fresh without periosteum)

5

8

AC (500 Hz) DC step function

Rabbit femur (in vivo)

Rabbit tibia (in vivo)

3

4

Rabbit femur Human TibiaJ in vivo

2

V vs 1 curve (DC)

Range of measurement

V vs / curve (DC) V vs 1 curve AC 0.01-1 kHz V vs I curve (DC) V vs I curve AC (0.01-1 kHz) V vs I curve AC (100 Hz-5 kHz)

Human femur

Specimen and source

1

Sr. No.

(kf~ cm) (P~ f/cm) P, = 54 Csp,r = 21.4 Pc = 36 Csp,c= 24.74 Pl=17 Csp,l = 60.87 150-240 (ms/m) Mean resistivity (ohm cm) at 100 kHz = 500 (longitudinal direction) = 613 (anterior posterior direction) = 609 (lateral-medial direction)

P1 = 12.9+2.7 (Q cm)-~ fresh P~ =4.8 +0.1 (f~ cm)- 1 fixed

R = 2 - 3 kf~/cm for whole bone Z = 8 kf~/cm "°1 = 4.54.8 kf~/cm

R = 2-5 • 105 f~/cm R = 3.5 M ~ for cortical bone C = 2 0 + 8 #F R = 20kf~/cm C = 5 pF/mm z R b = 2-3 kf~/cm

Sample resistance increases with the exposure of ultraviolet light, but decreases with the rise of temperature

Results

TABLE 1. ELECTRIC PROPERTIES OF WHOLE BONE

Reddy and Saha (1984)

Ray and Behari (1986) Saha and Williams (1989) Network analyser LCR meter

Behari and Singh (1981) Chakkalakal and Johnson (1981) Kosterich et al. (1983)

Durand et al. (1978)

Sansen et al. (1978)

Stan et al. (1976)

Liboffet al. (1975)

Behari et al. (1974, 1975)

Reference

Differential technique

Cell suitable for radial direction only

Two point method Direction-dependent

Two point method Two point method Four point method Four point method

Two point method Two point method

Two point method

Technique

rr >


13

was undertaken by Marino et al. (1967). It was found that at a critical level of sample water content (approximately 40% by weight), the dielectric constant was found to change sharply. The critical value of water content was interpreted as the amount of water necessary to occupy the primary absorption sites in bone, i.e. the bound water of the system. When water is absorbed by the system above the critical level, the dielectric constant is found to change sharply. This critical value of the water content was interpreted as the amount of water necessary to occupy the primary absorption sites in bone, i.e. the bound water of the system. When water is absorbed by the system above the critical level, the dielectric constant showed a characteristic conductivity dispersion at the low frequencies suggesting an increase in ionic mobility as secondary layers of water are absorbed. An extensive survey of cortical bone dielectric properties at low frequencies as a function of time and humidity was carried out by Lakes et al. (1977). These authors used a direct-coupled low frequency bridge containing active circuits to study the response below 50 Hz. Experiments were carried out in four terminal probe mode in which the voltage across two high impedance probes embedded in the specimen was measured. Their findings are: (i) The permittivity of bone is large and increases with increasing humidity or decreasing frequency. The maximum exceeds 105 and maximum tan 6 exceeds unity. If the electric field is parallel to the bone axis, both tr and tan 6 are larger than if the electric field is perpendicular to the bone axis. (ii) The transient resistivity is greater for the case of electric field perpendicular to the bone axis and approaches an asymptote at a time approximately 10 times larger than in the case in which the electric field is parallel to the bone axis. (iii) At high humidity the transient resistivity exhibits no asymptote indicating that charge continues to be stored in the specimen for long times. At lower humidity, an asymptotic resistivity is reached in a reasonable length of time. (iv) The loss tangent does not exhibit sharp peaks which can be associated with single relaxation time (Debye peaks). The experiments carried out by Marino et al. (1967) were performed at 21°C and therefore cannot be directly compared with those of Lakes et al. (1977). Reinish (1974) performed a series of experiments at 25, 30 and 35°C, and noted as much as a two-fold increase in tr with a 10°C increase in temperature, for a relative humidity of 75%. The results of Lakes et al. (1977) agree qualitatively with those of Reinish (1974) obtained at 35°C and 75% room humidity level. However his data are lower by a factor of 4. This may be attributed to the difference in the species examined (bovine vs human) and the water content of bones. A linear dielectric arbitrary curve of RC and tan 6 can be modelled by sufficiently complex RC networks corresponding to a distribution of relaxation times. However, since the exact mechanisms responsible for dielectric relaxation in bone over a wide frequency range are not as yet well defined, the validity of such modelling is questionable. Levy (1971) has suggested that biologically important energy transfer processes may occur in bone at a frequency of a few hertz, corresponding to the rate at which bone is stressed in walking. However, a pronounced peak in tan 6 near 1 Hz is not reported by these authors. The conductivity resulting from ionic mobility in this material will contribute to the overall dielectric response of bone. The presence of inhomogeneity is a well known mechanism for dielectric relaxation (yon Beck, 1967). Behari et al. (1982) measured the dielectric parameters of bone and its two constituents at 9.2 GHz by the cavity perturbation method. The results obtained are in good agreement with those of Swicord (1977), obtained by broadband dielectric measurement technique. A decrease in e' and 8" value due to ultraviolet light exposure was observed (Table 2). VII. HIGH FREQUENCY DIELECTRIC RELAXATION IN BONE The electrical behaviour of living bone resembles a parallel combination of resistance and capacitance (Lakes et al., 1977; Schwan, 1968; Singh, 1982; Reinish, 1974). For an analysis of the roles of the various modes of electrical stimulations, it is important to characterize the electrical and the elect romechanical properties of bone as a function of frequency (Singh and Saha, 1984). Kosterich et al. (1983) reported that conductivity was nearly independent of

8

Bone samples from several species (rat, rabbits, goat and humans)

5

Wet cancellous bone (Human) (RH = 100%)

4.5 GHz Bone in Microstip line configuration using time domain technique LCR meter (120 H ~ 1 0 MHz)

Human bone (60% RH)

4

1 kHz, impedance bridge method Direct coupled low frequency bridge At 9.2 GHz, by cavity perturbation method

Goat femur (dry)

Bovine hone (78% RH)

3

1 kHz bridge method

Network analyser (400-1300 MHz)

Human bone (62% RH)

2

Capacitance bridge

Technique

Goat femur (RH = 72%, temperature 17°C)

Fresh femur (cow)

Specimen and source

1

St. No.

At 100 kHz specific capacitance (PF/cm) = 8.64 (longitudinal direction) = 15.25 (anterior posterior direction) = 14.64 (lateral-medial direction)

d=22.1 (wet bone) e'= 24.0 (dry bone) e'= 19.8 (UV irradiated) e' = 11.56 e" = 3.63

d=16, e" = 2.8 e'= 100 tan 3 "~ 1 e'=30 (1 kHz) e"= 18 e' =4.96+0.37 e" = 1.72 __+0.20

Results

TABLE 2. DIELECTRIC PROPERTIES OF BONE SPECIMENS

et al.

(1967) (1977)

et al.

Reinish and Nowick (1976)

Lakes

Marino

Freeman (1967)

Reference

e' and e" are much higher in transverse as compared to longitudinal direction

Saha and Williams (1989)

Ray and Behari (1988)

Behari et al. (1982) Reduction in e' and d' due to ultraviolet light exposure of the samples, though e"/d ratio remains constant Ray and Behari (1986)

Electric field perpendicular to the bone axis Four point method

Only normalized values were reported

Comments

>

X


15

frequency below 100 kHz, and above it increased with increasing frequency. This was found to be true for both fresh and fixed bone specimens. A decrease in dielectric parameters with increasing frequency was also found. In a similar study, others reported that the impedance was almost independent of frequency up to 70 kHz, and that above this frequency it decreased rapidly with increasing frequency (Reddy and Saha, 1984). Singh and Behari (1984) measured impedance and phase angle of bone specimens in the frequency range 0.5-108.0 MHz using a vector impedance voltmeter. Their investigations reveal relaxation phenomena at 36.0 MHz, 72.0 MHz and 108.0 MHz. These frequencies seem to indicate the role of such frequencies in bone growth and possibly in life processes. Ray and Behari (1986) examined the conductivity and dielectric permittivity in the range 400-1200 MHz using a network analyser. They have analysed the electrical properties of bone in different states: viz. dry, wet and UV-irradiated bone. The specific resistance was found to be frequency-dependent and suggests the possibility of a relaxation process. Also the specific resistivity of UV-irradiated bone is larger than the dry bone. This may be attributed to the rupture of hydrogen bonds due to UV-irradiation and thereby causing an increase in its resistivity. A higher wet bone conductivity as compared to the dry bone is attributed to the presence of ions through the fluid-filled portion of the bone including the haversian canals, canaliculi and porous fractions. The conductivity decrease due to the UV exposure is caused by the rupture of disulphide bonds and hydrogen bonds of protein. UV exposure may also lead to generation of free radicals which causes aggregation of collagen molecules and increased cross-linking. VIII. T H E R M O D Y N A M I C A L BONE BEHAVIOUR Behari et al. (1974) have reported the effect of temperature on conductivity as a function of electrical field strength. A uniform increase in conductivity was observed in the range (3~60°C). Also Vvs/curves were linear only in a limited region, thereafter a break occurs in the vicinity of 300 V/cm. At a given field strength if conductivity is studied as a function of temperature (log vs I/T) their slope yields the activation energy. If activation energy is plotted as a function of temperature, a decrease is observed with an increase of temperature (Andrabi, 1978). A related phenomenon is the estimation of thermal conductivity and phonon free path. Since the size of the apatite crystal is of the same order of magnitude as that of the thermal phonon at low temperatures (70K), phonons will be scattered strongly by crystallites (Chu, 1972). It was found that mean free path of phonon decreases rapidly with temperature and seems to approach a constant value as the temperature is raised. It has been proposed (Kittel, 1974) that the constancy of the phonon mean free path is a result of phonon reflection at the interfaces between crystal grains. These reflections are the dominant resistive process when the wavelength of phonons becomes smaller than the grain size and the phonons are propagated by a diffusion-type mechanism. Under such conditions the phonon mean free path should be of the order of the grain diameter (40 A)---a value close to the average diameter of the HAP crystallites. The rapid increase of free path at low temperatures can be explained by the fact that the dominant phonon wavelength increases with decreasing temperature and eventually becomes several times larger than the grain size. Hence the propagation of phonons is more or less uniform over the grain and the scattering at the boundaries will modify the waves only slightly. At these temperatures, the observed mean free path changes roughly as T 2. It is concluded that the low temperature thermal conductivity of bone is governed by the size and arrangement of the crystallites. The mean free path of phonons above 40K is directly related to the size of individual crystallites. At low temperature the phonon mean free path is related to their arrangement. IX. SOLID STATE OF BONE The solid state properties of bone have been the subject of constant survey for a variety of reasons. One such factor has been the interest that has steadily grown in understanding the mechanism of charge transport in such solids. The photoelectric effect, Hall effect and photo

16

J. BEHARI

electromagnetic effects are some of the important phenomena besides electrets that have been reported so far. Some of these data though qualitative in nature reveal apparent interrelationship and their possible role in controlling bone processes remains a point of investigation.

1. Hall Effect The generation of Hall voltage has been reported in bone, collagen and apatite in samples having resistivity in the region of 107-109 f~ cm (Behari and Andrabi, 1978). Samples carrying a current of a few microamperes in a magnetic field of 10K gauss were found to generate a voltage of the order of tens of millivolts (Fig. 3). The Hall coefficient (Rn) has been evaluated using the expression:

v,x, Rn-IxxHz,

tI

++++

++

+++

.

.

.

+++

.

.

(1)

++TF~+ ÷ + +~-

.

HZ"

FIG. 3. Hall effect experiment.

where Vy is the Hall voltage generated in the y direction, when the magnetic field (Hz) is applied in the z direction and Ix refers to the direction of the current I and t is the thickness of the sample. A related parameter is the mobility of charge carriers. While the Hall mobility (un) relates to the motion of the current carriers within the limits of a single crystallite, the drift mobility (up) is determined by the concentration and energy levels of the carrier traps. The conductivity (~r) is related to the Hall mobility (uH) through the relationship: uH= RHa.

(2)

R n is dependent on resistivity and the thermodynamical history of the sample. The small value of u H ( < 1 cm2/volt see) suggests the inapplicability of the sample band model. It has also been reported that there is a diminution of the Hall voltage in the same specimen after exposure to ultraviolet light, because of increase in the resistivity of the sample (Behari et al., 1975). The low value of mobility suggests that the carriers can move only within the limits of the regions of continuous configuration. On application of the electric field, the medium becomes polarized with the formation of dipoles. The dipoles are aligned along the direction of the electric field. The dipoles extract extra energy from the magnetic field thereby contributing to the generation of the Hall voltage. On reversing the direction of the magnetic field, there is no reversal in the sign of the voltage generated. This confirms the symmetry of the matrix element d14. From the biological point of view the significant parameter is the charge carrier mobility. The drift mobility values for bone (0.000052 cm2/volt see) are field-dependent and much smaller than the corresponding Hall mobility value (0.13 cm2/volt sec). Pething and Cross (1980) have reported a value of 0.3 cm2/volt see for dry collagen and polyglycine from Hall effect measurements. Several authors have determined the mobility from the transit times of charge fronts moving through compressed bovine serum albumin (Lewis and Toomer, 1981; Lederer et al., 1981). It has been found that while for dry material the mobility was very low (10 -7 cm 2 v -1 s -1) it increased exponentially with degree of hydration reaching about 1 cm 2 v- 1 s- 1 at a hydration level of 35% by weight of water. The data reported by Behari and Andrabi (1978) on bone, collagen and apatite are roughly in agreement with these results. Although these absolute values of mobility, for compressed


17

samples, can be greatly affected by inter-molecular transfer processes, the values obtained are significant. In a field of, say, 107 v/cm, existing in a membrane and electron mobilities of 10 -.1 to 10 -5 cm 2 v -1 s -1, the transit time along a 50 A chain would be between 5 x 10 -5 and 5 x 10- ~* s. If only one electron passes along this pathway at a time, the rate is between 104 and 101° s-1, an adequate range to account for turnover numbers in enzyme activity. Thus even very low dry state mobilities are compatible with biological processes. Moreover, since according to the hopping model, a low mobility is a consequence of strong localization, there can be a positive biological advantage in low mobility systems. X. P H O T O - E L E C T R I C EFFECTS 1. Optical Spectra

Becker and Brown (1965) have reported that whole bone consistently demonstrated three major spectral peaks: 4100 A, 4800 A in the visible range and a broad response between 8500 and 10500 A with a peak approximately at 9500 A in the near infrared. They also observed a minor peak in the vicinity of 5700 A. Liquid nitrogen temperatures increased the amplitude of the response approximately ten-fold in the two visible ranges and 50-fold in the infrared regions. Samples of highly purified bone apatite demonstrated a single peak in 4800 A region. Demineralized samples, however, demonstrated spectra quite similar to that for whole bone except that the response in the 4800 A and 9500 A regions were diminished and the 5700 A response was frequently missing. Behari et al. (1977) have also reported absorption peaks at 4950 A and at 5700 A in broad agreement with the above results. The peaks in collagen (2600 A) and apatite (3000 A) are not present in the full bone. This may be due to the cementing of these two dissimilar materials through polymucopolysaccharides. On exposing these samples to ultraviolet radiations, these peak positions undergo minor displacements. Becker and Brown (1965) have reported that specimens prepared with surface electrodes placement and diode configuration demonstrated definite photoconductivity in the range of biasing voltages (0.05-1.35 V). In the case of surface electrode placement, rise times were averaged around 2.6 sec for a maximum response. These results were interpreted as indicating a charge storage or polarization type of phenomenon (Kallman and Rosenberg, 1955). They further concluded that changing the direction of the applied field has no effect on the amplitude or the type of the photocurrent obtained. The diode electrode configuration also demonstrated photoconductivity phenomena but differed sufficiently from the surface electrode configuration. Reverse bias was indicative of a greater photoconductive response than the forward bias (with the same range of bias voltage). Cooling the specimens to 77K with liquid nitrogen results in approximately 40-fold increase in the magnitude of the response, but with some prolongation in the rise time. Generation of photo voltage in the bone and its two major constituents (collagen and apatite) was also examined by Behari et al. (1979). This offers additional information regarding the mechanism of charge generation and transport. These authors have reported that after a few minutes of exposure the magnitude of photo voltage becomes constant and then starts falling, and attains a base line value. The sample responses to IRL and visible light decreases after exposure to UVL. It is suggested that UVL exposure produces morphological changes on bone surface as confirmed by electron microscopic studies (Rai and Behari, 1988) (Fig. 4). Fuller et al. (1976) studied photo conductivity in bone and tendon in response to ultraviolet light (450W xenon lamp focused through a 200 Hz chopper). These authors have further reported that photocurrent parallel to the fibrils is greater than the photocurrent perpendicular to it. In bone the longitudinal photocurrent is less than the transverse photocurrent. 2. Bone Photovoltaic Cell

Bone, collagen and apatite show photovoltaic effects when mounted in Hall configuration (Andrabi and Behari, 1981). Compared to standard Hall geometry the direction of the JPB

56:1-B

18

J. BEHARI

F1c. 4. (Top) Scanning electrom micrograph of normal bone sample ( x 7000). (Bottom) Scanning electron micrograph after UV exposure of normal bone sample ( × 7950).


19

application of electric field is substituted by the incident light. The magnetic field and axis of output voltage are mutually at right angles to each other. A voltage (Hall voltage) of the order of tens of microvolts is observed for an applied field (~ k gauss). The effect is found to be reversible. XI. LIFE TIME AND DRIFT MOBILITY OF CHARGE CARRIERS Quantitative measurements on the life time of carriers were performed using the pulse technique (Andrabi et al., 1980). Life time is obtained by estimating the time taken for the pulse to decay to 36.8% of its peak value (Shive, 1959). The life time turns out to be 0.2, 0.25 and 0.2 #sec for bone, collagen and apatite, respectively. It may be seen that these are an order of magnitude less than those obtained for a typical P-type germanium indicating a higher concentration of recombination sites at the surface and the existence of shallow traps. This data further supports the view that in bone H ÷ plays an important part in the charge transport processes. 1. Drift Mobility In order to estimate the order of magnitude of the drift mobility (up), the I vs V2 plot is obtained for the samples in the sandwich form. A plane parallel capacitor having a capacitance C (cm -z) is given by ~3

C = 4n---d"

(3)

The transit time can be expressed in terms of the field F = V/d, and the carrier drift mobility

(up): dz uo = ~--~.

(4)

The mobility (up) calculated from I vs V2 curves turns out to be 0.0014, 0.00049 and 0.0142 cm2/volt sec in the case of bone, collagen and apatite, respectively. It thus becomes apparent that the charges are localized on particular lattice sites (Gutman and Lyons, 1967; Kepler, 1962). The value of up is higher for lower values of the field, which can be attributed to the decreased frequency of collisions at these field values. The transit times in the three cases are 5.5, 14.0 and 0.42 msec respectively. It is known that mature cortical bone contains a small, but significant amount of water in vivo. This bound or structured water is associated with the collagen fibres. Bone may acquire excess water through hygroscopic action. The presence of such free water would presumably tend to decrease the photo-electric response. Although dry collagen is piezoelectric (a member of the o o point group), wet collagen is not because of the bound water presence. Fukada and Yasuda (1964) reported that piezoelectric voltages in tendon collagen decrease with increased water content, and that at approximately 40% H20 content by weight, no voltage is generated. Free water only exists above a hydration level of about 300 mm H zO/g dry collagen at which point the dry collagen is rendered completely non-piezoelectric by absorbed structured water. This finding is consistent with the existence of free water in the collagen and the production of stressinduced streaming voltages (Fukada and Yasuda, 1964; Korostoff, 1977; Behari et al., 1987). XII. PN JUNCTION AND P H O T O - E L E C T R O M A G N E T I C EFFECTS Bone behaves as a semiconductor in a variety of ways and also shows properties pertaining to an insulator. This seemingly uncommon behaviour stems from the fact that bone consists of two dissimilar materials--collagen and apatite (having widely differing resistivities), put together in such a way that the collagen-apatite relationship exhibits multiple PN junction characteristics throughout the osseous structure. In analogy with the inorganic PN junction diodes the collagen-apatite junction is taken to behave as a diode with the former behaving as N type material and the latter as a P type (Fig. 5). However, this classification cannot be

20

J. BEHARI ATTRACTION

REPULSION

LL

P

DIPO ®®

AYER

M

%®®®

SPACE CHARGE LAYER N

® @ ® E) MUCOPOLY SACCHARIDES

APATITE

e

®e® ® @ ® E) C) COLLAGEN

UNBIASED CONDITION

FIG. 5. Model for PMN junction in the bone.

taken too far. This is because the mechanism of charge transport and the nature of charge carriers in the two major constituents does not seem to be identical. Also as has been pointed out above, in bone, transport of protons, ions and impurities is predominantly controlled by a hopping mechanism. The collagen and apatite are assumed to be cemented together by mucopolysaccharides which are electrically negative (Glimcher, 1959). The crystalline collagen tends to have an abundance of electrons, crystals of apatite, a lack of them and as such the interface between collagen and apatite is a semiconductor junction of P - N type. Further, tropocollagen which makes up the native collagen fibril is polar and there is a permanent electric moment in the direction of the longitudinal tropocollagen axis (Athenstaedt, 1974). Negative charges on tropocollagen molecules are sites for calcification and the introduction of negatively-charged mucopolysaccharide molecules is introduced between collagen and apatite during the processes. Hence, it may be suggested that the negative charge on M faces the negative charge on N during the formation of bone (Fig. 6). The P

M

N

I,

+

Forward Bias condition. P

M

N

,f Reverse Bias condition.

FIG. 6. (Top) Forward bias condition. (Bottom) Reverse bias condition.

mucopolysaccharides form two different electrically-charged layers, namely dipole layer (attraction) on the apatite side and unipolar or space charge layer (repulsion) on the collagen side. There will be no charge transfer or conduction taking place in the junction PM or PN because there may be formation of a space charge layer in the vicinity of the PM junction as the negative charges from M will be attracted towards P which will then produce a negative layer on the P side facing M; there is no possibility of conduction between M and N. The extent of this space charge layer between the two materials is called a 'depletion layer'. The behaviour of the PN junction under reverse and forward conditions with different applied biases when subjected to infrared radiations reveals that current increased and remained constant for a brief time and then started decreasing. A faster decrease is observed when the light is put offat constant current value. The observations were again repeated after subjecting bone to UVL. The magnitude of the current with IRL exposure was more


21

compared to that observed after UVL exposure indicates a change in structure at the molecular level introduced due to irradiation. The PN junction characteristics of such samples are lost. The energy of UVL is sufficient to bring the structural changes (by disruption of hydrogen bonds) whereas IRL does so to a lesser extent.

1. Photo-Electromaonetic Effect (PEM) The PN junction of bone, when subjected to IRL and UVL, shows an increase in the currents which are further increased with the application of the magnetic field. On exposure of junctions (PM, PN) to light they absorb photons that result in excitation and migration of charge carriers and some impurities. Consequently, number of charge carriers exceeds the value that it has in the absence of radiations and hence an increase of current is observed which shows a steady state after some time. At this steady state value the magnetic field (16K gauss) produces an enhancement in the photocurrent. It was also observed that the reversal in the direction of the magnetic field does not change the direction of enhanced current. It is suggestive that the application of the field merely reverses the alignment of charge carriers. Since the mobility of carriers is much less than unity the hopping type conduction model may be operative in such solids. XIII.

ELECTRET

Biomedical investigators have been looking to relate electrical energy storage as an important parameter at the physiologic level and specifically at the level of macroscopic gross behaviour of tissues. It is found to be present in collagen, gelatin, artificial polypeptides, etc. The presence of charge storage has been reported for bone, blood vessel, walled materials, keratin cellulose, DNA, etc. (Mascarenhas, 1974). Yasuda (1977) observed callus formation by placing a teflon electret over bone surface. Although it is difficult in practice to measure such effects in physiologically moist bone with a high water content, the effect has been demonstrated to occur in rive (Behari and Singh, 1981). Andrabi and Behari (1981) examined electret formation in bone and its two major composites by taking the specimen in sandwich configuration. Thermoelectret, electroelectret and magnetoelectret made out of bone were examined and charge decay characteristics obtained in the field intensity range of 1-5 kV/m polarized at the temperature of 35, 45 and 65°C. Once the electric field is withdrawn the fall of charge with time is fastest in thermoelectret, intermediate in electroelectret and least in magnetoelectret. The initial rate of fall ceases after about thirty minutes and thereafter it becomes much slower. All the three materials, viz. bone, collagen and apatite, show the electret state and are able to store large amounts of polarization (10 -6 col/cm2-10 - a col/cm 2) in the region of fields under study. The value is comparable to the polarization storage obtained with a good electret. A comparison of the data reveals that electroelectret is most efficient in terms of storage of charge. The electrets prepared in this way were found to retain charge even after a lapse of 7 days and current would immediately increase manifold once the temperature is increased. Electret state was observed even after a period of three months, though the magnitude of charge was diminished by one or two orders of magnitude. The bone electret which was put in position for about 24 hr at freezing temperature, was found to have lost the electret effect but immediately recovered it once the temperature was increased. This is suggestive of the fact that at lower temperatures the mobile charges are in a state of freeze so that they produce no net electric field but at higher temperature the packed arrangement is broken resulting in a net polarization charge. The role of bound water in such processes is quite evident. Sources of electric fields in bone are dipoles, ionic space charge and the phenomena of protonic conduction (H +--vacancy migration) (Mascarenhas, 1974). On the switching off the electric field change in alignment takes place and that accounts for the decay of charge with time. The effect in bone is due to the collagen component and is linked to a space charge type of storage mechanism. Bound water in bone may also be responsible for electrical energy storage via the electret effect (Mascarenhas, 1974). A similar mechanism may be assumed to

22

J. BEHARI

be present in collagen and apatite. The behaviour observed here is similar to that reported for other dielectrics. Results on apatite are at variance with the findings of other workers in the sense that electret state is observed in apatite too. The effect is as predominant as it is in full bone, though it is less than that in collagen. Similarity in behaviour of bone and its two major constituents has also been found to be present in other solid state properties. The electret behaviour of apatite may be partly attributed to the asymmetry in the crystal structure produced during its extraction from full bone and inherent lattice defects. XIV. P I E Z O E L E C T R I C I T Y In a piezoelectric material such as bone, the application of an electric field causes a change in physical dimensions. The electrical charges bound within the lattice of the material contract with the frequency of the applied field to produce a mechanical stress. The converse effect leads to a potential difference across the end faces of the transducer in response to an applied stress. Piezoelectricity is thus a cross effect between elasticity and dielectricity (Nye, 1960), dielectricity being the relation between electric field and polarization. Piezoelectricity in bone has long been established (Fukada and Yasuda, 1957; Shamos et al., 1963) and the contemporary investigations have revealed the bioelectric potential as the possible stimulus for bone formation (Bassett, 1989). For composite materials, the macroscopic piezoelectric constant is a function of the piezoelectric moduli, elastic moduli, dielectric constants and geometry of the different phases (Date, 1972). It is generally believed that protein collagen is responsible for the piezoelectric effects in bone. It is also apparent that the dielectric effects in bone (including the conductivity) have a strong influence on the piezoelectric effect, especially in composites, and the presence of a finite conductivity introduces a frequency (or time) dependence into the measured voltages. A simple system is represented by a dielectric (a capacitor) in parallel with a resistance, where the ratio e'/tr is just the RC time constant. In this case e(og)can be a complex quantity; the real part, e', represents the dielectric constant, and the imaginary part, (e"= tr/o~) represents the conductivity divided by the frequency co. Then 8=e'-i

ff

--. 09

The resistance and the capacitance depend on the frequency so e' is frequency-dependent (Reinish and Nowick, 1979; Lakes et al., 1977) (Fig. 7).

I I

j I

FIG. 7. The dependence of resistance and capacitance combination on frequency, e' is thus frequencydependent.

Since the discovery that dry bone and collagen have piezoelectric properties, interests have arisen in understanding the mechanism controlling osteogenesis. The work on electrical stimulation of bone growth has emphasized the need to study both electrical and piezoelectric properties of bone under varying degrees of moisture content so as to bridge the gap between the well characterized behaviour of dry bone and the not too well understood behaviour of living bone. 1. E x p e r i m e n t a l M e a s u r e m e n t

The first quantitative measurement of the piezoelectric constant of bone by means of both direct and converse piezoelectric effect was performed by Fukada and Yasuda (1957). The


23

direct effect was studied by a static method. In this method the pressure was applied on the side plane of the specimen by a lever mechanism and the electric charge appeared on the square plane which was detected by galvanometer deflection. The converse piezoelectric effect was measured by a method of comparison. When the electric field is applied in the direction of electric polarization the mechanical strain is produced in the direction of applied force. Due to converse piezoelectric effect the oscillatory force is transmitted to the piezoelectric crystal. In the direct and converse effect both the relationship between stress and applied electric field turns out to be a straight line. These authors (Fukada and Yasuda, 1957) have also studied the variation of complex dielectric constant (e' and e") at 1 kHz, with temperature and humidity. They found that these parameters increase sharply with increasing hydration (Table 3). Marino et al. (1967) measured the dielectric constant (e', e") of human cortical bone at frequencies 1-102 kHz and found that these parameters alter sharply at a critical hydration level which ranges from 0.037 to 0.048 g/g. Tomaselli et al. (1973) working in the frequency range of 0.1-100 kHz at room temperature found the critical hydration of bovine Achilles tendon to be 0.054-0.115 g/g. Reinish and Nowick (1976) investigated collagen hydration with X-ray diffraction and reported that absorption of water by the helical structure of the collagen molecule becomes saturated at a moisture content of 26% wt (RH = 60% ). Above this moisture content, water is adsorbed within the intermolecular space. Further data with different moisture content shows difference in temperature dependence. For collagen with 10% weight moisture content, there exist two kinds of relaxations which depend upon moisture content and the frequency. It is concluded that the relaxations at 0°C result from reoverietal motion of the collagen molecules side chains, whereas relaxation around - 8 0 ° C is caused by low frequency oscillation of the collagen's main chain. This seems to be correlated with the amount of the adsorbed water. From the above it is evident that there is a sonic contribution to the piezoelectric response in bone. A converse piezoelectric effect for collagen has been similarly measured (Fukada and Yasuda, 1964). The absolute value of the piezoelectric constant of specimen is determined by the ratio of two output voltages when the alternating voltage is applied to specimen and quartz crystal respectively. When the shearing force is applied in the direction of fibre axes, the upper end becomes polarized negatively and the lower end is polarized positively. When the pressure is applied in a perpendicular direction to the fibre axis, similar polarization takes place. If the direction of force is reversed, the sign of electric polarization is also reversed. The converse piezoelectric effects are also observed when the electric field is applied in the direction of electric polarization. Dielectric relaxations and mechanical properties of collagen and bone have been examined by Meda and Fukada (1982). These authors determined the piezoelectric elastic and dielectric constants of collagen at selected hydration and temperature range ( - 150-50°C) at a frequency of 10 Hz. For collagen e' and e" increased with increasing hydration, d' at - 150°C increased below hc but decreased above hc with increasing hydration. For bone the dependence of piezoelectric constants on hydration and temperature reflects a two phase structure consisting of collagen and mineral hydroxyapatite. The critical hydration for bone was 0.04 g/g. The piezoelectric constant ( d = d ' - j d") of this study gives the ratio of polarization to stress at 45°C to the direction of fibrillar orientation in the collagen (= -d14/2). Pfeiffer (1977) described a method to measure the frequency response of piezoelectric coefficients of the mineralized collagen fibril, including the ground substance of adult human cortical bone. Reinish and Nowick (1974) found out that the piezoelectric polarization at 100% humidity decreased to 30% of the value obtained for the dried bone. Assumptions in the model used are: (i) mechanical isotropy but piezoelectric anistotropy, (ii) validity of symmetry C~ for the mineralized fibril, (iii) distances between the canals and the sample surface.

Human femur (dry and wet)

Bovine bone (hydrated)

Bovine femur (dry and wet) Bovine tibia (fresh) and human femur Bovine tibia Bovine Powdered bone components mixed to form pellets Dry and wet femora bone samples (human)

4

5

6 7 8 9 t0

11

In compression mode In compression mode

Beef bone (dried and wet) Human tibia and calf femur

2 3

Impact loading in longitudinal direction

In compression mode Four point bending In compression mode Cantilever mode Compression mode

Uniaxial compression mode

In compression mode

In compression mode

Method of measurement

Human and ox femur (dried)

Specimen and Source

1

Sr. No.

At 1 kHz, g=0.04 (dry) V crn/N 0.30 (wet) At 6.25 kHz, g=0.10 (dry) 0.80 (wet)

Human d14=2.0 Ox d14=2.2 Dried bone d33 = 0.45 Human d14 = 5.9+0.5 Bovine d14 = 2.57 + 5.67 Dry bone (5600 Hz) d14= 5.4, d14 =0.2 Piezoelectric parameters are frequency and hydrationdependent Wet bone has higher signal content Properties dependent upon bathing medium g = 19.2 GuY cm)/N Wet and dry bone has different set of mechanisms g = 0.93 (V cm/N )

Results/observations

TABLE 3. PmZOELECTRIC PROPERTIES OF BONE SPECIMEN

Saha et al. (1987)

Gross and Williams (1982) Pienkowski and Pollack (1983) Singh and Saha (1984) Johnson et al. (1980) Singh and Behari (1984)

Burr (1976)

Reinish and Nowick (1976)

Anderson and Ericksson (1970) Marino and Beeker (1975)

Fukada and Yasuda (1957)

Reference

tO


25

The material-data piezoelectric tensor d ijk and the dielectric tensor eik join the dielectric constant. Elastic compliance and the piezoelectric tensor join them to the strain. Following Sedlin and Sonnerup (1966) and McElhancy (1966), cortical bone is a viscoelastic material, with a stress strain relation approximated by a Poyniting Thomson model. This way material data become time-dependent. This implicates that the piezoelectric coefficients for direct and inverse effect must not be identical. If the stress is applied periodically, the material parameters become frequency-dependent. Magnitude of the piezoelectric constants increase with increasing molecular orientation for bone tendon and extracted collagen films (Fukada, 1974). The single crystal equivalent parameters as reported by Gundjian and Chen (1974) show a greater increase as compared to the averaged data for bone, reported by Fukada (1968), though the results of Pfeiffer (1977) are still greater. The difference can be explained best by the increase at low frequencies and on the other hand, by different organization of the lamellae in bovine and human femur samples.

2. Physical Concept of Piezoelectricity A necessary condition for the occurrence of piezoelectricity in a crystal structure is the absence of a centre of symmetry. Piezoelectric media are intrinsically anisotropic. Piezoelectricity provides a coupling between elastic and dielectric phenomena. Since bone is an anisotropic material containing oriented crystallites, the piezoelectric data are expressed in terms of the piezoelectric matrix: 6

P, =

d,:j

(5)

j=l

where d is the constant of proportionality between the applied mechanical stress T and the generated electric polarization P. (Fig. 8). The d matrix contains 18 coefficients relating to ×

~

y

I

z/

I I I t

l Flo. 8. Relationship between applied mechanical stress T a n d the generated electric polarization in an anisotropic crystal.

the piezoelectric polarization in different directions with the applied tensile and shear stress in different directions, i=1, 2, 3 corresponds to x, y, z, coordinates and where the macroscopic field E across the sample is zero. The six j indices correspond to three tensile stresses and three shear stresses. In general the d coefficients are complex quantities d * = d ' - j d " where the real part is proportional to the charge generated in phase with the applied stress and the imaginary part is proportional to the charge generated out of phase with the applied stress. When d" is non-zero, a relaxation dispersion is present and measurements as a function of frequency become a necessity. The equations for the piezoelectric relations in a crystal producing a single mode of motion can be written in the form:

Sz=S~z " T2 +d21E1 D1 = d21 T2 + ~rE1

(6)

26

J. 8EHARI

where $2 and T2 are the extensional strain and stress respectively; s2E2 = a l l , the elastic compliance (i.e. inverse of Young's modulus) along the length measured at constant electric field, d 2i, the piezoelectric constant relating the strain with applied field Ex:D I the electric displacement and e r the dielectric constant measured at constant stress. These equations are sufficient to determine the static and low frequency behaviour of piezoelectric crystals. The constant strain dielectric constant (es) is related to the constant stress dielectric constant by the relation: es =e~(1 -k2), where k is the electromechanical coupling factor. The square of the coupling factor is written as

d21

k2 -

E T

(7)

S2zel

By solving eqn (6), it is readily shown that the clamped dielectric constant es, obtained by setting $2 =0, and elastic compliance of constant displacement S °, obtained by setting D 1 = 0, are related to the constant stress dielectric constant er and the elastic compliance at constant field, $2e2 by the equation es - S2°2 = 1 - k 2. ~ S~

(8)

3. Piezoelectric Theory

The phenomenon of stress generated potential (SGP) in bone has been interpreted as piezoelectric and originates in its organic component (Marino and Becker, 1971). However, the correlation between the observed sign of potential in bending and the sign fixed by specimen orientation has not been established. Obviously there is some aspect of bone that decouples the sign of the strain gradient potential (SGP) in the PZE matrix from the macroscopic specimen coordinates. The problem was eventually solved by Korostoff (1979). In order to solve these problems there has been growing interest in the study of the electromechanical properties of bone, the stiffness constant and the piezoelectricity. Bone has a microscopic polycrystalline structure with a certain degree of ordering that varies substantially from one point to the other in a given sample. Gundjian and Chen (1974) assumed the microscopic unit of the crystalline structure of bone consisting of collagen molecules and hydroxyapatite crystals intervened with their crystallites c-axes parallel to each other. Bone crystallite units are thus a composite of these two having an equivalent c-axis of infinite rotational symmetry (T(~)). This structure results in a physical behaviour corresponding to that of the single crystal of point group symmetry (Lang, 1966, 1970). In conformity with this it is suggested an idealized parallel plate lamella for a specimen in bending, in which the prevailing collagen orientations in a local region are alternatively at approximate right angle to each other. Each of these lamellar regions is composed to be described by the same PZE matrix. Acting upon these crossed (90 °) orientations of collagen are the tensile stresses parallel to the plane but at some angle to the collagen axes. From the equation below Pi

anddij=

=

dijkajk

o

o

o

d14

0

0

0

0

0

0

0

0

o

o

-d14

o

0

O,

(9)

it can be seen that the resulting polarizations are perpendicular to the lameilar plane and that they are antiparallel for adjacent planes. An antiparallel arrangement would result in


27

cancellation of polarization to give a zero net polarization perpendicular to the lamellar plane, while experimentally one observes a net unidirectional polarization. The apparent disagreement between this theoretical postulate and experimental finding was averted by the suggestion of a possible mechanism for the reorientation on the antiparallel polarization configuration to a parallel configuration. These energies are estimated to be + 36 J/m 2 and - 36 J/m 2 for a polarization strength of 2 x 10-6 C/m 2 (Korostoff, 1979). The higher energy for antiparallel configuration derives from the interactions of the electric field due to the polarization in a given lamella with the oppositely directed polarization of the adjacent lamella. The concurrent energy increase for strain and demagnetizing field which accompany the change from antiparallel to parallel alignment are very small. Thus, the antiparallel state predicted by the PZE tensor is unstable, and yields to the equilibrium configuration in which the polarization is parallel. In this theory the process of redisection of polarization from the unstable antiparallel configuration thus decouples the macroscopic bone specimen from the rigid polarity imposed by the PZE matrix. It is further postulated that the trigger is based upon the net molecular surface charge of bone which is normally negative (Nieders et al., 1970; Eriksson, 1976). The bone has been idealized as being composed of surfaces with net negative charge. In a bent configuration polarization vector can be thought of as adding vectorially to the antiparallel piezoelectric polarization to enhance that direction. It is seen that the trigger polarization is about 0.1% of the PZE polarization. 4. Equivalent Single-Crystal Structure of Bone Gundjian and Chen (1974) further suggested that the equivalent c-axis of the composite collagen-hydroxyapatite crystallite is not oriented perfectly throughout a macroscopic bone sample but is distributed around a distribution symmetry axis with a finite angular dispersion around this axis. The 'standard equivalent single-crystal structure' (SESCS) of bone is a hypothetical structure in which the bone crystallites are all perfectly oriented in the direction of the distribution symmetry axis. It is to be noted that, since the measured values of the physical properties of natural bone correspond, clearly to an average over a large aggregate of differently oriented bone crystallites, they are expected to be sensitively dependent on the actual crystallite orientation distribution function of the sample. Consequently, natural variations for different samples will produce corresponding variations in the measured values of the physical properties, thus making impossible the identification and the interpretation of the more fundamental intrinsic changes in the values of these properties. It is apparent that the standardized value of the physical properties will correspond directly to those of the individual crystallites. This will, therefore exhibit only changes resulting from actual physical changes in these crystallites. It is also clear that the angular position of the crystallite distribution asymmetry axis, as well as the distribution function vary slightly with position in a given bovine femur sample. In the measured samples, the width is found to be of the order of 30 ° . Measurements of the piezoelectric properties of bone (Holt et al., 1977; Liboff and Frost, 1974; Bur, 1976; Fukada, 1974) indicate that: (a) Although the piezoelectric element of bone (the collagen molecule) has a hexagonally symmetric crystal structure, bone itself exhibits no apparent symmetry in its matrix of piezoelectric coefficients. (b) Inhomogeneities in bone composition and/or structure results in considerable variations in the piezoelectric matrices, measured in different specimens, even though the specimens may come from neighbouring sites in the same bone. Conclusions. (i) The SESCS (Gundjian and Chan, 1974), Korostoff (1979) and Bazenov (1961) theories produce approximately the same results when supplied with the given constituent crystal and its spatial arrangement. (ii) There seems to be a fundamental inconsistency regarding the sign of d 123 in the maze of experimental data. The sign of d 123 for collagen is theoretically inconsistent with most of the bone data, and important discrepancies exist within the data for bone and other collagenous tissues, some investigators finding d123 positive, others negative. (iii) In fluid-saturated bone, strain-related piezoelectric polariza-

28

J. BEHARI

tions are concealed by ohmic charge leakage (Gross and Williams, 1982; Johnsen et al., 1980; Pollack et al., 1984). Thus, the solid matrix of bone may retain its piezoelectric properties even in the completely hydrated state (Johnsen et al., 1980; Korostoff, 1979). 5. In Vivo Applications of Bone Piezoelectricity If electrical signals mediate the bone morphology, then their generation should take place only as required by physiological need. The signal in bone should occur only when the stress applied to it is excessive or unbalanced. This suggests a fundamental criteria for the mechanical design of intraosseous implants, i.e. that the functioning implants shall not produce in the bone significant tensile stress associated with stress gradients. Here the maintenance of bone in the absence of macroscopic potential can be explained by suggesting that microscopic potentials continue to exist within each osteon. For zero gravity or bed rest, these microscopic potentials will decrease or disappear, and the loss of bone mass (osteoporosis) may be related to that decline. It has been shown that the SGP magnitude is a function of the age of bone during animal maturation (rat femur: Pollack et al., 1977) and that extrapolation indicates zero SGP at 5 weeks or younger. This has been attributed to the development of intermolecular collagen cross-linking with age, and it is suggested here that an additional influence may be the concurrent continuing development oflamellar bone from the immature woven bone. The woven bone with its random collagen orientations is at a distinct energy disadvantage under stress, since the statistical net angle among the collagen polarizations leads to a system energy above the equilibrium energy for parallel polarizations. Developing muscular and functional use results in mechanical stress in bone, the interaction energy may provide the impetus for reorientation of a liable woven structure also into the mature lamellar one. The external field may be seen as a trigger for determining the directionality of antiparallel polarizations due to existing stress. The piezoelectric properties of bone have attracted several efforts to apply them to accelerate healing of fracture (Ficat et al., 1984). XV. E L E C T R O N PARAMAGNETIC RESONANCE (EPR) The electron spin resonance technique allows quantitative and qualitative analysis of all kinds of paramagnetic materials. The paramagnetic entities possess one or more unpaired electrons. Because of their spins the paramagnetic molecules produce a magnetic field which can be detected and measured, When a sample containing paramagnetic species is placed in a strong external magnetic field the random orientation of unpaired electron is changed (Fig. 9). The electrons start precessing around the directions of the magnetic field. They

HO

\x

!

/

I

FIG. 9. A particle possessing a ma~-letic moment placed in a magnetic field of strength H o . A weak magnetic field H, is applied perpendicular to H o and rotates above H o.

become segregated into two subpopulations differing in energy levels. This difference is caused by, and depends on, parallel and antiparallel orientation of electrons in respect of the lines of the external magnetic field. One can induce energy transition of the electrons from one level to another by the application of an additional quantum of energy in the range of microwave radiation (Ho). The effect of energy transition is observed only if the energy quantum of electromagnetic radiation fulfils the equation:


29

E=hv

where Eis the difference in energy level, h is Planck's constant and v the frequency. The shape of the absorption curves derived from the first derivatives, called the EPR signal, may differ for different paramagnetic species because of hyperfine splitting, which is associated with the interaction between the spin magnetic moments of the unpaired electrons and the atomic nucleus. Differences in the shape of the EPR spectra may sometimes be helpful, though not decisive in the qualitative identification of the paramagnetic species. The hyperfine splitting phenomenon allows us to draw conclusions as to the structure of the EPR active centres. Search for an EPR signal in bone has been a continuing exercise over a period of time. Slager and Zucker (1962) found no resonances in bone prepared for the use in bone banks. On the other hand Becker (1963) reported the detection of EPR signals in non-radiated human and amphibian bone. Commoner (1964) suggested that the resonances in whole bone was most likely due to the apatite. Vinokurov and Zaripov (1961) also discovered the presence of EPR signals in geological apatite. To avoid the anisotropic nature of EPR signals as obtained from the whole bone, Becker and Marino (1966) performed investigations on powdered samples of human bone, collagen and mineral. Dehydrated samples of all materials were prepared by vacuum drying at a pressure of 10 # of mercury for a minimum of 2 weeks. It was found that at room temperature all samples showed a clearly defined signal resonance at g 2.001 (10.005) with a line width of 10+ 1 gauss. The total signal amplitude decreased very slowly with storage under dark conditions. A decline of 30% of the original value was apparent even after 90 days, leaving other signal parameters unchanged. Also vacuum drying results in about four-fold increase in signal amplitude without affecting other parameters. The amplitude of both hydrated and dehydrated samples is found to have the same temperature dependence in the interval - 150°C to +20°C. The curves in this range are also found to be reproducible on heating. Hydrated bone showed a discrete shift to a smaller amplitude in the vicinity of + 65°C, while dehydrated bone showed a more gradual transition to smaller amplitudes over the range + 20°C to + 95°C. The decrease in signal amplitude at + 65°C appears to be irreversible. Each sample demonstrated this phenomenon one time only, provided the sample was kept below + 100°C. Heating to +200°C caused the hydrated sample signal to increase in magnitude while the dehydrated sample signal remained essentially constant. Heating of a hydrated sample in a + 800°C flame for 3 min caused the signal to increase by a factor of 100. In all heating experiments including the burning in a + 800°C, the g value and line-width of the observed resonance remained constant. 1. Bone Mineral Powder

In hydrated mineral powder a complex resonance curve is obtained (composed of several unresolved resonances) with the largest to the low field side of gl. In addition three equally spaced, low amplitude resonances have been found toward the low field side. The low amplitude resonances are relatively independent of temperature, and disappear when the apatite is heated above + 150°C. Storage in the dark for 90 days did not result in any appreciable decline in signal amplitude. Cole and Silver (1963) analysed electron paramagnetic resonance spectra of a mineralized portion of tooth after X-ray irradiation. The analysis was performed immediately after irradiation and again 2½ days later at room temperature. They identified three kinds of paramagnetic species including one as hydrogen atom. Swartz (1965) analysed the site of the stable, radiation-induced EPR signals in organic and inorganic phases of bone. The dose-dependent relationship of EPR signal intensity was studied in vitro and in vivo though their results remained inconclusive. Termine et al. (1967) studied low-temperature EPR spectra of irradiated bone tissue by comparing them with artificial mixtures of irradiated organic bone matrix and synthetic calcium phosphates. These authors have concluded that an intimate interaction, probably through chemical bonding between organic and mineral phases, takes place in bone tissue. Stachowicz et al. (1970) examined the EPR spectra of paramagnetic species in mineralized

30

J. BEHAR1

tissues irradiated and measured at room temperature. Their observations extended on demineralized and decollagenized bone as well as on synthesized samples. Samples were analysed at room temperature and after heating to 423K. Under these conditions two long lived paramagnetic species are observed. One, derived from bone collagen possesses the nature of the true free radicals which combine with air at room temperature in about 6 weeks, the second is attributed to the structural defects in crystalline hydroxyapatite. The influence of several parameters, e.g. the Ca: P ratio, degree of crystallinity and impurities, on the yield and stability of radiation-induced paramagnetic species in collagen and apatite was studied by Houben (1971). He found that the yield of apatite like paramagnetic species depended on the density of bone. Fisher et al. (1971) examined the low temperature ESR spectra of 7-irradiated samples of bone. They found that the damage is concentrated randomly along the main peptide chains of collagen, with relatively few radicals formed in the side chains of amino acids residues. It was concluded that ESR spectra in calcium phosphate is similar in structure and composition to the mineral components of bone and teeth. XVI. TRACE ELEMENTS OF BONE Another important aspect which has largely remained unexplored and their importance poorly understood is the trace element of bone. Several workers (Tipton et al., 1964; Schroeder, 1967) have investigated the presence of many elements in the body. It is obvious that physical and electrical properties of bone will be drastically affected by the presence or absence of some or all of the ions. The material aspect of bone is rather neglected. This is probably because of the fact that the degradation of material is thought to drastically effect its behaviour. However, the recent experimentation suggests that dead bone also possesses a variety of physical properties (Singh and Behari, 1984). Therefore it seems quite pertinent to explore and correlate the presence of trace elements to the overall bone behaviour. The data reported are on the powdered bone and its components. Bones were ashed for 24 hr in a muffle furnace at 450°C. Their weight loss was monitored: (i) after equilibrium for 18 hr under room conditions; (ii) during drying at 110°C for 24 hr; (iii) after ashing at 450°C for 48 hr; and (iv) again after equilibrium at room conditions. A general method of semiquantitative spectrographic analysis with structure d.c. arc excitation was employed for analysis and found very satisfactory for bone, where low sensitivity and high content are inherent. Semiquantitative standards were made, using tribasic calcium phosphate reagent grade, the composition of which is much like bone ash, as well as lithium carbonate and specially prepared standard mixtures of known amounts of elements. The calcium phosphate was mixed with equal parts of the lithium carbonate-graphite mixtures, with enough of the standard powders substituting within for the graphite to make standards of 5, 25, 50, 125 and 250 parts per million. The methods of analysis chosen for the work was that of arc emission spectroscopy chiefly because of its fairly high sensitivity (one part per million less) and its easy accessibility to a wide range of elements (60 or more in one arcing). Furthermore, since the sample preparation for the technique is minimum, involving only ashing powdering mixing, and loading into electrodes the possibility of concentration is reduced. Another method to detect trace elements of human bone is atomic absorption spectroscopy. Trace metals are thought to play an important role in the synthesis, cross-linking, calcification and diseases of connective tissues (O'Dell et al., 1966; Schiffmann et al., 1966; Chvapil and Hurych, 1968). Several investigators (Becker et al., 1968; Ellis et al., 1969) observed a regularity in the appearance of certain metals, Cu, Fe and Zn. These and possibly other ions may be structurally incorporated in the collagenous matrices. These are not merely passive cellular products, but are themselves active substrates for initiating the growth and repair of connective tissues (Friedman et al., 1968; Urist et al., 1968). Spadaro and Becker (1970) found that Pb, Si, Sr and V are found in relatively reduced concentrations in bone mineral, and seemed to be absent from demineralized bone to relatively low limits. Therefore, part of the content of these metals in bone is bound to the mineral, either as substituted or interstitial ions. In contrast, part of the Cu and most of the Fe remained with


31

the decalcified organic matrix, with little or none remaining with the bone mineral. This indicates that these ions are relatively strongly bound to the bone collagen and may therefore be functionally important to it. The actual average concentrations of Cu and Fe in the organic matrix in terms of dry mineralized bone were found to be 2.7 +0.4 ppm and 8.4 + 3.7 ppm respectively. Zn was also detected in bone samples. More recently Rai and Behari (1986) detected Mg, Pb, Cu and Fe as trace elements in rat bones. They found the presence of Cu in the range of 5-50 ppm and Fe, Mg and Pb in the range of 50--500 ppm. The results on Cu seem to be in good agreement with the results of Spadaro and Becker (1970) confirming thereby that these ions are functionally important. XVII. S T R E A M I N G P O T E N T I A L S Streaming potential--an electrokinetic phenomenon--takes place in the porous portion of the bone which contains electrolytes in the fluid phase. Due to amphoteric behaviour, the bone becomes charged at the fluid/bone interface, by exchanging chargs with the electrolyte. Bone is negatively charged at the physiological pH level. Therefore, free charges in the fluid phase screen the charged portion of the bone phase. This causes the double layer formation in the bone. Streaming potential theory describes the electrical interactions of polar fluids with charged substrates. This can be measured in capillaries and capillary porous materials which have a mobile electrolyte phase surrounded by an immobile electrical double layer. A pressure difference between two ends of the capillary displaces the mobile electrolyte phase relative to the electrical double layer thereby generating a current (convection). A conduction current opposite and equal to the convection current is established and a steady potential difference, termed as the streaming potential, is maintained. The difference in potential so generated gives rise to the electrokinetic phenomena of electrophoresis, electrocosmosis, and streaming potentials (Pohl, 1980; Gross and Williams, 1982; Guzelsu, 1982; Berretta and Pollack, 1986; Otter et al., 1988). This electrostatic double layer may be regarded as a parallel plate capacitance (Fig. 10).

SoLid- Liquid interface g/Shear slip plane

®

t

,

fLui~ flow

i

T

i

SoLid

C C Diffuse Layer Zeta 4 - potentia~ D'" FIG. 10. Schematic representation of an electric double layer at a solid-liquid interface.

Ions and water molecules in the fluid phase adjacent to the electrically charged bone matrix remain stationary with respect to the fluid flow away from the surface, and constitute an imaginary surface called the surface of shear. In addition, a diffuse and weakly held layer of ions extend away from the interface into the bulk of the liquid. This diffuse layer contains unequal numbers of positive and negative ions and therefore is electrostatistically charged. When the liquid is forced to move against such a surface, the region of the diffuse layer

32

J. BEHARI

outside the shear slip plane is carried along with the rest of the liquid. Such a movement of charged liquid constitutes an electric current, thereby causing a difference in potential between two electrodes placed in the path of the streaming liquid. These potentials are called Streaming potentials. The potential difference between the bulk of the liquid and that at the surface of shear is termed as zeta potential. The nature of electrokinetic phenomena and hence the magnitude of the zeta potential then characterize a particular solid-liquid interface. For laminar flow of a liquid under pressure P through a capillary, the streaming potential E s across the ends of the capillary is given by (Bockriss and Reddy, 1970):

~-

eZ

ap

4rc~/xo where Z is the zeta potential, e represents the dielectric constant of the liquid, Ap equals the pressure difference across the capillary, ~/ designates the viscocity and x o is the specific conductance of the liquid. Within the limits of laminar flow, the faster the movement of the liquid the greater the value of E,. The above relationship does not contain all the possible variables. The magnitude of the zeta potential is also a function of pH and in living bone this may also depend on the calcium level in the extra-cellular fluid. Since the movement of the liquid in bone capillaries gives rise to electrical current it is therefore directly responsible for measured streaming potential. The observed dependence of stress-induced voltages in bone with strain and rate of strain are also found to be consistent with the nature of streaming potentials. Piekarski and Munro (1977) studied stress-induced fluid flow in an osteon by testing a model constructed of concentric porous cylinders separated by regions of liquid. By axially loading these cylinders, they were able to generate a radial pressure gradient caused by Poisson's strain, that produced the radial fluid flow. Streaming potentials have been shown to occur in collagen, bone or cartilage (Anderson and Eriksson, 1968). Convex surfaces in deformed bone are positively charged with reference to concave surfaces. The stress distribution in living bone is thus time-dependent. When living bones such as a femur, are functionally deformed so as to produce bending, even the smallest transverse canaliculi are differentially strained. On the convex surfaces they are subjected to tensile stress, whereas on the concave side, they will be compressed. Midway between these two surfaces is a neutral plane, where the canaliculi are unstressed. Since the extracellular fluid in bone carries a positive charge, the convex surface will become positively charged with respect to the concave surface. It is thus speculated that streaming potentials may therefore have a direct role in stress-induced bone remodelling. Lack of stress-generated flow may contribute to osteoporosis and bone resorption in regions of low stress, where the osteocytes may be metabolically deficient (Kufahl and Saha, 1986, 1987). Guzelsu and Walsh (1990) measured streaming potentials on control and chemically treated intact wet bone plugs in phosphate and phosphate buffers. Their data indicate that the organic constituents of bone dominate streaming potentials. Guzelsu and Regimbal (1990) have further pointed out that bone mineral lies within the organic phase and is not exposed to the fluid phase. In fact bone tissue has a negative Z while hydroxyapatite has a positive potential. A model for streaming potentials in the osteons based on structural considerations, principles of electrokinetic theory and continuum mechanisms was proposed by Pollack et al. (1984). Their findings seem to confirm that an electrokinetic theory effect was the origin of the observed SGP. Several groups of workers (Neiders et al., 1970; Elwood and Smith, 1984a,b) have investigated the charge carried by enamel dentine, cementum and synthetic hydroxy particles in Hank's balanced physiologic saline solution at pH 7.2 and at 30°C. A typical zeta potential evaluated for enamel and dentine is found to be -10.32 mV and -6.23 mV respectively. Because dentine and bone are similar it is expected that these results are also valid for bone. Since streaming potentials are directly proportional to zeta potential, with all other variables constant, local stress-induced streaming voltages will be greater in areas of high mineralization than in areas of low mineralization. They will also increase in value as the calcium content of the local extracellular fluid decreases. In both the cases of osteogenesis and osteoclasis, the extracellular fluid is positively charged. However, the magnitude of the


33

surface charge density and hence of any resultant streaming potentials, will depend on the local degree of mineralization and calcium content of the extracellular fluid. It has been reported that storage of bones in saline at deep freeze temperatures ( - 80°C) results in a significant decrease in streaming potentials. However, storage in Waymouth's medium under similar conditions resulted in a significant increase (Elwood and Smith, 1984a). These authors have also investigated the effect of the refrigeration or deep freeze storage of bones in buffered HEPES. Their results showed that in N-2-hydroxyethylpiperazine-N'-2-ethanesulphonic acid (HEPES), pH 7.4 produced no significant change in potentials. However, refrigerator storage of bones overnight in pH 7.4 HEPES or storage in a deep freeze in 0.9% NaCI caused a significant change in electrokinetic characteristics. However, storage of bones immediately in a deep freeze in HEPES, pH 7.4 produced no significant change in potentials. The electrical polarizations observed by Anderson and Eriksson (1968, 1970) were two orders of magnitude greater than those observed by Reinish (1974). Johnsen et al. (1980) have also predicted such an observation. Cignitti et al. (1970), Eriksson (1974) and Eriksson and Jones (1977) have also demonstrated streaming potentials in wet bone. Gross and Williams (1982) demonstrated: (i) the consistency of the sign of the electrical potentials in fluid saturated bone, and (ii) the reciprocal dependence of the electrical potential on electrolyte viscosity and conductivity, as predicted by streaming potential theory. A similar conclusion was also arrived at by Pienkowski (1982). Pollack et al. (1984) and Chen and Saha (1985) investigated the streaming potentials in bone by modelling stress-induced transport between a single lacuna and a haversian canal through a single canaliculus. Measurements on dielectric properties of fluid-saturated bone (Chakkalakal et al., 1980) imply that the electromechanical effect observed in wet bone is several orders of magnitude larger than one would expect from a piezoelectric effect (Johnsen et al., 1980). The electromechanical effects in wet bone are attributed to the streaming potential (Anderson and Ericksen, 1970). When bone is saturated with fluid, one would not be able to measure an appreciable voltage due to a piezoelectric effect at low frequencies because the conductivity of the fluid will 'short' the voltage produced by the piezoelectric effect. The decay times for the mechanically generated potentials in the wet bone are of the order of several tenths of a second to a couple of seconds (Cochran et al., 1968). This time is much longer than the predicted decay time for flow in the haversian systems. A possible suggestion is that the decay time is due to decay of fluid flow in other pore systems, e.g. the lacunar-canalicular systems (Fig. 11). This is because the canaliculae are very small and

FIG. 11. Modelof the haversian canal-lacunae-canaliculi system. could be clogged by the cell processes, thereby decreasing the effective radius of the canalicula and therefore increasing the time constant which is inversely proportional to the fourth power of the radius. This is also in agreement with the measurements of Starkebaum et al. (1979) who found that the electromechanical effect in wet bone produced large electric fields between the edge of an osteon and its haversian canal. In vivo, the effective size of the haversian systems will be smaller, because of the presence of blood vessels and cells. The fluid in the haversian systems will be more viscous than water. These will act to increase the time constant for the relaxation of the fluid pressure in vivo. This may be important because it is believed that bone remodels in response to the stresses it bears. Petrov et al. (1989) investigated the contribution of the microstresses on the azimuthal distribution of the streaming potentials in the osteon. These authors have assumed that: JPB

56ti-C

34

J. BEHARI

(i) the haversian canals of the osteon are considered as a cylindrical hole in a continuous isotropic medium; and (ii) the fluid pressure influence on the equilibrium deformation state of the matrix is small. The fluid flux at the cement line of the osteon and the fluid pressure in the haversian canal is taken to be zero. Scott and Korostoff (1990) examined oscillatory and step response electromechanical phenomena in bone in the range 0.05-100 Hz. They concluded electrokinetic origin for the observed electrical potentials and microporosity of bone as the location where this phenomenon occurs. Both piezoelectric and streaming potential mechanisms have been proposed to account for the generation of electrical potentials in bone (Guzelsu, 1982). Salzstein et al. (1987) proposed a model to describe streaming potential generation of strain-related potentials. The model was formulated by coupling biphasic poroelastic theory with electrokinetic theory. The model successfully predicts the strain-related potential magnitude and phase spectra observed over the range of 0.05-1.5 Hz for cortical bone samples subjected to four-point bending (Salzstein and Pollack, 1987). Compared with soft tissues, little is known about bone microcirculation. Although some information is available about the size and distribution of the canalicular network carrying nutrients to the osteocyte in the lacunae, there has been no experimental quantification of the flow rate in these minute (1 #m diam) vascular networks (Arlet et al., 1984; Frost, 1986). Almost no quantitative information exists regarding the intraosseous circulation in the canaliculi-lacunae network. XVIII. MECHANISM OF BONE SURFACE R E M O D E L L I N G Justees and Luft (1970) proposed a mechanochemical hypothesis for bone remodelling to explain mechanical stress applied to bone in terms of osteoblastic and osteoclastic activity. According to this hypothesis, a change in loading of bone results in an altered straining of the hydroxyapatite crystals in bone. This effects the solubility of the crystals, providing the required negative feedback message to the bone cells in the form of a mechanically-induced chemical change. The cells then respond to the altered calcium activity by building up bone to redistribute an increased stress, or by removing the bone which is surplus to the structural needs imposed by a reduced stress. Osteocytes are most sensitive to the distribution, rate of change, and magnitude of strain within the bone matrix. Osteocytes are distributed throughout the load-bearing matrix and they also have a wide network of processes by which they communicate with one another, and with cells on the surface of the bone (Menton et al., 1984; Doty, 1981). The network would then also facilitate the passage of information, particularly relating to the mechanical loading of their surrounding matrix. These cells influence the behaviour of cell populations at the bone surfaces which in turn are responsible for modelling and remodelling. These remodelling cells adjust bone architecture in response to the strain-related influences from the strain-sensitive cells until functional strains match those which are genetically determined (Lanyon, 1987). It is conceivable that the adaptive response could be a reparative one in relation to an unacceptable rate of accumulated microdamage. There is evidence that microdamage does not influence internal or surface remodelling (Burr et al., 1985). Functional adaptation involving changes in bone form can be induced by strain magnitudes and membranes of strain cycles, too low to induce appreciable microdamage (Lanyon et al., 1982; Rubin and Lanyon, 1984). One of the consequences of long bones having a longitudinal curvature is that this curvature determines the manner in which the bones deform in response to loading through their articular surfaces. The advantage of an agreement of high but predictable strains may be that it is easier to control adjustment of bone form in response to a progressively increasing stimulus. The response of osteocytes to strain provides a sensory input, which influences the adaptive response. The requirement is primarily a biological one. Rubin and Lanyon (1985) have shown experimentally the increasing osteogenetic response to increased loading. This confirms bone remodelling in response to dynamic


35

strains. It has been suggested (Currey, 1968) that the bone's assessment of its strain situation is built up from the gradients of strain-related stimulation between cells in the osteocyte surface osteoblast network. If the strain distribution to which the bone is subjected is appropriate then the gradients in strain related-stimulation will not endanger any adaptive remodelling response. If the strain-related distribution to which bone is subjected is appropriate then the gradients in strain-related stimulation will differ from that to which the bone cells are accustomed. It is this mismatch which defines the nature of the remodelling stimulus. Lanyon (1987) has reported that strains of up to 0.003 can be applied without engendering an adaptive response. The nature of the strain-related stimulus is defined by the strain distribution and its strength by the characteristics of the strain waveform. This has led to suggest (Frost, 1986) that there is a minimum effective strain which is the strain magnitude necessary to maintain balanced remodelling. This pressure keeps bone mass at a consant level. It is further reported (O'Commor et al., 1982) that the osteoregulatory effect of a strain regime may be affected by the rate at which strain changes, at least by the peak strain magnitude. Summarizing a series of experiments, Unthoff (1982) concluded that large increase in bone stress, or a sudden increase in mechanical usage, may lead to woven bone formation, while smaller increase in bone stress, or a gradual increase in usage may result in normal primary lamellar bone formation. Unthoffet al. (1986) observed a new woven bone formation on the periosteal surface of dogs when they were remobilized after 60 weeks of immobilization. It is suggested that bones were severely compromised by the long period of immobilization and resumption of normal loading consequently caused high levels of strains in a bone with low mass. Burr et al. (1989) have concluded that woven bone can be a normal response to an intense mechanical challenge. As such, this tissue may represent a common final pathway to any situation in which bone must be produced rapidly. Burr et al. (1989b) have also studied the alteration in bone tissue kinetics responsible for adaptive remodelling in response to altered strain environments. Using histomorphometric analysis these authors have concluded that the increased bone mass in response to elevated strain results from increased frequency of modelling with more sites undergoing formation processes than resorption processes on periosteal and endocortical surfaces. Increased remodelling activation did not lead to increased bone mass. The effectiveness of the stimulus in terms of remodelling it depends upon the nature and strength of non-mechanical stimuli with which it normally interacts. These stimuli are principally derived from the hormones concerned with calcium metabolism. Lanyon et al. (1986) have shown that during periods of extensive hormonally-based resorption, functional load bearing modulates bone loss. Nevertheless, the reverse is also true. A strain-related stimulus which under circumstances of calcium sufficiency produces an osteogenic effect, will under conditions of calcium insufficiency modify hormonally-based resorption. A mismatch in strain distribution is responsible for the existence of an adaptive remodelling stimulus suggesting that regardless of peak strain magnitude, no adaptive response will be affected, provided the strain distribution is normal. The dependence of functional bone mass on a continuing load-related stimulus is evidenced by the hormonally mediated resorption which consistently follows the withdrawal of functional activity in immobilization (Jaworski and Uhthoff, 1986) and bed rest (Krolner and Toft, 1983). Strain change to which these cells need be exposed may be extremely short (1 min/day) (Rubin and Lanyon, 1984). Lanyon (1987) has shown that exposure of the avian isolated ulna preparation to a single period of strain shows osteogenic response in a period of 4 days by conversion of a quiescent periosteum to an active periosteum, indicating thereby the production of new bone tissue. The process ceases when the bone's new architecture is such that there is no mismatch between the strains within the tissue and the strains genetically determined to be appropriate for that location. The transient nature of the strains necessary to produce an adaptive response indicates that bone cells can assess the strain situation in the short time during which the strain changes occur. There is evidence to suggest that osteoclasts which cause bone resorption are substantially

36

J. BEHARI

controlled by osteoblasts (Chambers, 1985). Osteoblasts in t u r n c o m m u n i c a t e with osteocytes (Doty, 198 i; M e n t o n e t al., 1984). The osteoblasts/osteocytes n e t w o r k provides a structural basis for c o n t r o l l i n g b o t h aspects of remodelling (formation a n d resorption) in relation to the prevailing strain s i t u a t i o n which they then translate in b o n e architecture. T o u n d e r s t a n d the m e c h a n i s m of cell response to strain, L a n y o n (1987) has considered the possible influences of p r o t e o g l y c a n o r i e n t a t i o n o n b o n e cell b e h a v i o u r . T h e core proteins of p r o t o g l y c a n are attached to receptors o n the cell m e m b r a n e completely a n d attach directly to the cells cytoskeleton. It is possible that the o r i e n t a t i o n of these p r o t e o g l y c a n molecules within the b o n e tissue could influence b o n e cell b e h a v i o u r . This m e c h a n i s m could then serve as a physical basis for a 'strain m e m o r y ' in b o n e tissue. This m e m o r y could provide the m e a n s for b o t h recognizing strain transients a n d for presenting the b o n e cells with a stimulusrelated average strain pattern. However, this theory needs experimental support.

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