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Biomaterials 26 (2005) 7350–7356

www.elsevier.com/locate/biomaterials

Corrosion behavior of titanium in the presence ofcalcium phosphate and serum proteins

Xiaoliang Cheng, Sharon G. Roscoe

Department of Chemistry, Acadia University, Wolfville, Nova Scotia, Canada, B4P 2R6

Available online 14 July 2005

Abstract

The effect of calcium phosphate surface deposit and the surface adsorption of the serum proteins, bovine serum albumin (BSA)

and fibrinogen, on the corrosion resistance and electrochemical behavior of (cp)titanium in phosphate buffer saline solution (pH 7.4)

was investigated at physiological temperature, 37 1C, using electrochemical impedance spectroscopy and dc electrochemical

polarization techniques. The formation of calcium phosphate deposit on the Ti surface decreased both the corrosion rate at the open

circuit potential (OCP) and the anodic reaction current in the high anodic potential range (42.6 V). Addition of BSA significantly

moved the OCP towards a more negative (cathodic) potential and inhibited the cathodic corrosion reaction, but did not significantly

change the corrosion resistance at the OCP. Addition of fibrinogen showed a similar, but less pronounced effect than BSA. The

possible mechanisms leading to these observed effects are discussed.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Titanium; Calcium phosphate; Bovine serum albumin; Fibrinogen; Corrosion; Biocompatibility; Electrochemistry

1. Introduction

Titanium and its alloys have been used in implants inthe human body for many years. Although they havebetter corrosion resistance and biocompatibility com-pared with other implant materials (e.g., stainless steels),their corrosion due to dissolution of Ti and alloyingelements (e.g., V, Zr, Al, etc.) is still a concern, becausethe metal ions released into the surrounding tissue mayinduce the release of potentially osteolytic cytokinesinvolved in implant loosening [1], cause discolourationof the tissue, and even more severe problems such asinflammatory reaction of the tissue [2]. As a result, manypublications have dealt with the corrosion resistance oftitanium implants under various conditions [3–11].

The human body contains fluid saturated in bothcalcium and phosphate ions. Similar concentrations ofthese ions in a simulated body fluid produced a calciumphosphate layer on the surface of titanium [12,13].

e front matter r 2005 Elsevier Ltd. All rights reserved.

omaterials.2005.05.047

ing author. Tel.: +902 585 1156; fax: +902 585 1114.

ess: sharon.roscoe@acadiau.ca (S.G. Roscoe).

Many investigations have been made on the effect ofcalcium phosphate or hydroxyapatite coatings on thecorrosion resistance of titanium and its alloys [14–17].Metikos-Hukovic et al. [14] found that well-crystallizedhydroxyapatite coatings derived from sol–gel exhibited abeneficial corrosion protection effect on the titaniumsubstrate during prolonged exposure to HBSS. Lavos-Valereto et al. [15] investigated the electrochemicalbehavior of Ti–6Al–7Nb alloy with and without plasma-sprayed hydroxyapatite coating in Hank’s solution, andfound that the corrosion rate of coated samples is morethan two times larger than that of uncoated ones.However, in both studies, calcium phosphate coatingswere prepared through high-temperature treatment. Theeffect of titanium oxide film formed in the heattreatment process on the corrosion resistance oftitanium materials was not considered. Sousa andBarbosa [17] investigated the influence of the additionof calcium ions and phosphate anions into the solutionon the passive current of chemically passivated titaniumand found that calcium phosphate did not change thepassive current at potentials lower than 1.5 V, but did

ARTICLE IN PRESSX. Cheng, S.G. Roscoe / Biomaterials 26 (2005) 7350–7356 7351

cause it to decrease between 1.5 and 3.0 V vs. SCE. Theelectrochemical impedance spectroscopy (EIS) measure-ments obtained at 1.0 V showed that calcium phosphatesignificantly decreased the charge transfer resistance(Rct) of the prepassivated titanium electrode [17].However, the influence of this calcium phosphatesurface deposition on the corrosion resistance of thetitanium implant around the open circuit potential(OCP) is still unknown.

Furthermore, titanium implants inserted into a humanbody are usually surrounded with blood-rich tissue, andthe serum proteins in blood may also influence thecorrosion of the implant materials. The influence of serumor serum proteins on the corrosion resistance of titaniumhas been studied under different experimental conditions.Different results (no influence, increase or decrease) havebeen reported [2,11,12,17–20]. Clark and William [20]investigated the corrosion of titanium powders in neutralsaline using atomic absorption spectrophotometry andfound no significant influence of serum proteins on thecorrosion of titanium. Okazaki et al. [11] investigated thepassivation behavior of several titanium alloys and foundno major variations between the passive current in salineand in calf serum. Sousa and Barbosa [17] found serumproteins brought no change to the anodic passivationcurrent of the calciumphosphate-coated titanium elec-trode which had been pre-passivated in HNO3. However,they also found that the presence of proteins significantlyincreased the Rct of the calcium phosphate-coatedtitanium at 1.0 V. More research therefore needs to bedone to determine why the polarization results differ fromthe impedance results. A number of investigations haveshown the corrosion resistance of titanium in a fluoridesolution to be improved in the presence of albumin[21–23]. Contu et al. [2] investigated the influence of fetalbovine serum on the corrosion of titanium at OCP withthe EIS technique and reported that the addition of serumincreased the corrosion resistance at OCP by 2–3 times.They attributed this result mainly to the ability of proteinsto bind free oxygen ions that move toward the metal/oxide interface. Williams et al. [24] investigated thecorrosion resistance (Rp) of titanium in 0.9% saline atOCP using the linear polarization technique. Theyreported that the presence of calf serum increased thecorrosion rate of the sanded commercially pure titanium,which they attributed to the ability of some proteins toform complexes with titanium ions. The similarity of theelectrodes and experimental conditions used in bothstudies [2,24] suggests more research needs to be done toclarify the contradictory results.

The acceleration effect of serum proteins on the anodicdissolution of various metals has already been reported[20,25–27]. Clark and Williams [20] found that thecorrosion of cobalt and copper was greatly increased bythe presence of two serum proteins: serum albumin andfibrinogen. Woodman et al. [27] reported that the

predominant corrosion products from 316 L stainlesssteel were organometallic complexes with serum pro-teins. Results obtained in our laboratory have shownthat the adsorption of serum albumin and b-lactoglobu-lin onto implant-grade stainless steel caused an increasedcorrosion rate, which was also attributed to the chelatingeffect of proteins with metal ions [25,28,29].

Up to now, only a few reports [12,17] have been foundabout the influence of a calcium phosphate surfacedeposit formed without high-temperature treatment onthe corrosion resistance and electrochemical polariza-tion behavior of titanium around the OCP. Althoughmany studies have been made on the influence of serumon the corrosion resistance of titanium, and the effectswere usually attributed to the presence of serumproteins, little work has been done with serum proteinsthemselves, especially the influence of serum proteins onthe cathodic and anodic polarization behavior of baretitanium around the OCP.

The major goal of this study was to investigate theinfluence of calcium phosphate surface deposits and theeffect of the two major serum proteins, bovine serumalbumin (BSA) and fibrinogen, on the corrosionresistance and electrochemical behavior of commerciallypure titanium in the potential range around the OCP. Inaddition, the influence of calcium phosphate depositsand serum proteins on the anodic current of titaniumover a wide potential range, extending beyond the rangenormally encountered for titanium in the body, wasused to obtain a comprehensive description of theseprocesses that may be encountered in industrial proces-sing of biological material.

2. Experimental

2.1. Reagents and solutions

The stock solutions of BSA (Sigma Chemical Co. Product

no. A-0281), were prepared by dissolving an appropriate

amount of solid reagents in a phosphate buffer saline solution

(PBS), pH 7.4 (0.05 mol L1 phosphate buffer+0.15 mol L1

NaCl). The phosphate buffer was made by dissolving an-

hydrous monobasic potassium phosphate (Sigma Chemical Co.

P-5379) and NaCl (Fisher Scientific Company, S-271) in

conductivity water (Nanopure, resistivity ¼ 18.0 MO cm) and

adding 0.10 mol L1 sodium hydroxide (made from 5 N solution,

ACP Chemical Inc. Product No. S-3732) to adjust the pH of the

solution. A solution with 0.05 mol L1 phosphate buffer (pH

7.4)+0.15 mol L1 NaCl+2 mmol L1 CaCl2 (ACP Chemicals

Inc. C-0360) was used as an electrolyte to study the corrosion

behavior of titanium in the presence of calcium phosphate [17].

2.2. Electrochemical equipment

A single compartment electrochemical cell (volume ca.

120 mL) was used. The working electrode was a commercially

ARTICLE IN PRESS

Table 1

Chemical composition of (cp)Ti electrode (mass%)

Material Ti C H Fe N O

(cp)Ti Bulk 0.10 0.015 0.5 0.05 0.40

Time / minutes0 20 40 60 80 100 120

E /

V v

s. S

CE

−0.8

−0.6

−0.4

−0.2

PBSPBS + Ca ionsPBS + FibrinogenPBS + BSA

Fig. 1. Dependence of the OCP of Ti with time in: PBS;

PBS+2 mmol L1 CaCl2; PBS+0.05 g L1 fibrinogen; PBS+0.05 g L1

BSA.

X. Cheng, S.G. Roscoe / Biomaterials 26 (2005) 7350–73567352

pure titanium rod, (cp)-Ti (99.7%, 6.4 mm diameter, alpha

structure, Johnson–Matthey), sealed with epoxy resin

(Torr Seal, Varian Vacuum Products) to produce a two-

dimensional surface. The chemical composition of the

working electrode used in the research is given in Table 1.

The counter electrode was a large-area platinum electrode

(mesh) of high purity (99.99%, Johnson–Matthey), which was

degreased by refluxing in acetone, sealed in soft glass,

electrochemically cleaned by potential cycling in 0.5 mol L1

sulfuric acid and stored in 98% sulfuric acid until use. A

saturated calomel electrode (SCE) was used as the reference

electrode, and all potentials in this paper are referred to

the SCE.

An EG&G PAR M273 potentiostat/galvanostat was used

for dc polarization measurements, and a Voltalab40 Dynamic

EIS and Voltammetry Electrochemical Laboratory (Radio-

meter) was used for EIS measurements.

2.3. Experimental methodology

All measurements were made in a PBS solution at 37 1C

without de-aerating. The level of dissolved oxygen was

assumed to be constant, since it was controlled by its partial

pressure in the atmosphere. The CaCl2 solution or protein

solution was prepared in a separate container using a PBS

solution pH 7.4, and was allowed to equilibrate for at least

30 min in the constant temperature bath, fitted with a Julabo P

temperature regulator, at the same temperature as the

electrochemical cell.

In order to obtain a reproducible surface, the electrode

was successively wet-polished down to 1500 gradation

using sand paper. After polishing, the electrode was thor-

oughly rinsed with Nanopure water, degreased in an ultra-

sonic bath containing ethanol for about 20 s, and then

again rinsed with Nanopure water. The electrode was then

immersed in a test solution at an OCP for 2 h in order to

reach a steady-state OCP value, followed by the EIS

measurement at the OCP and then the dc polarization

measurement in the cathodic direction. After the cathodic

polarization, the electrode was maintained at the open

circuit until the OCP value returned to that obtained

before the cathodic polarization. Polarization measure-

ments were then made in the anodic direction. After

the electrode was characterized by the electrochemical

techniques in the PBS solution, an aliquot of concentrated

CaCl2 solution or protein solution was then added to the

electrochemical cell and the electrochemical measurements

were repeated.

All measurements were made in triplicate, with fresh

solutions and newly polished electrodes. The data is presented

with the reported average of the results with error bars

showing the spread in the triplicate measurements.

3. Results and discussion

3.1. Open circuit potential measurements

The dependence of the OCP on electrode immersiontime is shown in Fig. 1. Initially, the OCP rose rapidlybut then gradually slowed reaching a stable value.Addition of BSA significantly moved the OCP tonegative values, while the calcium phosphate depositand fibrinogen showed only a slight influence on theOCP.

The OCP values for titanium in PBS (Fig. 1) isconsistent with previously reported results obtained insolutions without deaeration [30,31]. The passive oxidefilm of titanium has been investigated extensively[6,8,32–34]. When a freshly polished Ti surface isexposed to moist air, a thin Ti-oxide film is sponta-neously formed on its surface. XPS analysis has shownthat the amorphous oxide film, spontaneously formedon Ti during polishing, consists of three layers: the firstlayer adjacent to metallic Ti is a TiO film, on top ofwhich a Ti2O3 film is formed, and the third film is TiO2

which is in contact with the solution [35]. After thetitanium electrode was immersed into the electrolyte, atitanium oxide film began to grow on the electrodesurface. The protecting effect of the oxide film, andtherefore the corrosion resistance of the electrode,increased and eventually reached a relatively stablevalue. The increase of corrosion resistance caused thedecrease of the anodic dissolution current of titanium.As the OCP is determined by both the anodic andcathodic reaction, according to the electro-neutralitytheory, the decrease of the anodic current will movethe OCP gradually in the positive direction so that thecathodic current can be low enough to balance thedecreased anodic current. When the corrosion resistanceof the titanium oxide film reached a relatively stable

ARTICLE IN PRESS

Table 2

Rp and CPE of (cp)Ti electrode in different solutions

PBS PBS+Ca ions PBS+BSA PBS+

Fibrinogen

Rp (kO cm2) 201711 360715 18278 209712

CPE (mF cm2) 5574 3374 7776 7275

X. Cheng, S.G. Roscoe / Biomaterials 26 (2005) 7350–7356 7353

value, the anodic current, and therefore the OCP, alsoreached a stable value.

3.2. Electrochemical impedance spectroscopy

measurements

The EIS results at the OCP presented in Fig. 2ashowed only one time constant. Therefore, similar toother references for titanium electrodes [2,29], theRandles electrical-equivalent circuit (EEC) comprisedof only one time constant (Fig. 2b) was used to modelthe experimental spectra, and good agreement betweenexperimental data and fitted data was obtained.Electronic elements in the figure have the followingmeanings: Re is the resistance of the electrolyte betweenthe working and the reference electrode, Rp is thepolarization resistance related to the rate of corrosionreaction(s) at the OCP, and is inversely proportional tothe corrosion current, and CPE is the capacitancerepresented by the constant-phase element (CPE).Generally, the use of a CPE is required due to adistribution of the relaxation times as a result ofinhomogeneities present on the microscopic level underthe oxide phase and at the oxide–electrolyte interface.

The Rp and CPE obtained from the fits are shown inTable 2. Addition of calcium significantly increased theRp by about 80%, and decreased the CPE. BSA andfibrinogen brought no significant change to the Rp, butincreased the CPE. It is known that a calcium phosphatelayer will form on a titanium implant surface in neutralsolutions containing saturated calcium and phosphate[13]. Elemental calcium and phosphorus were also

Z' / kΩ0 20 40 60 80 100 120 140

Z''

/ kΩ

−140

−120

−100

−80

−60

−40

−20

0

PBSPBS + Ca ionsPBS + BSAPBS + Fibrinogen

Rp

Re

CPE

(a)

(b)

Fig. 2. EIS plot of Ti electrode recorded at the OCP in: PBS;

PBS+2 mmol L1 CaCl2; PBS+0.05 g L1 fibrinogen; PBS+

0.05 g L1 BSA.

detected on the rinsed and dried electrode surface byour EDX measurements. We therefore speculate that adeposited calcium phosphate layer existed on theelectrode surface, which inhibited the electrochemicalreaction and increased the Rp by covering the electrodesurface and blocking the mass transportation of oxygenand/or reaction products to and/or from the electrodesurface.

In Table 2, the presence of calcium phosphatedecreased the CPE while in contrast the presence ofproteins increased the CPE value compared with thatobtained in the PBS solution alone. As described byContu et al. [2], the CPE in Fig. 2b contains thecontribution of both the capacitance of the oxide film onthe titanium surface (Cf) and the double layer capaci-tance (Cdl). These capacitances are in series giving theequivalent capacitance as follows [2]:

CPE ¼ ½ðCf Þ1

þ ðCdlÞ11.

When protein molecules adsorb onto the electrodesurface, a new capacitor (Cad) needs to be consideredin the equivalent circuit. If the surface is not homo-geneously and compactly covered, the current will flowthrough two parallel paths: the first constituted by seriescombination of Cf and Cdl, the second through the seriescombination of Cf and Cad [2]. As a result, the CPEshould be given by:

CPE ¼ ½ðCf Þ1

þ ðCdlÞ11 þ ½ðCf Þ

1þ ðCadÞ

11.

In this case, the obtained CPE is possibly higher thanthat in PBS because of the second half of the aboveequation. However, if the coverage is homogenous andcompact, all three capacitors are in series and the CPEwill be given as:

CPE ¼ ½ðCf Þ1

þ ðCdlÞ1

þ ðCadÞ11.

In this case, the CPE will be lower than that in PBS.Since the proteins increased the CPE as shown in

Table 2, it is possible that the adsorbed proteins formeda porous rather than a compact film. On the other hand,the calcium phosphate deposit may be a more compactlayer giving the lower CPE reported in Table 2.

3.3. dc Polarization measurements

Quasi-steady-state linear polarization measurementswere made to investigate the effect of the addition ofcalcium ions on the electrochemical behavior of

ARTICLE IN PRESSX. Cheng, S.G. Roscoe / Biomaterials 26 (2005) 7350–73567354

titanium around the OCP (Fig. 3). As the PBSelectrolyte used in this experiment is an oxygen-contain-ing solution, the cathodic current recorded in thepresented potential region can be attributed to thereduction of oxygen dissolved in the solution [36,37]. Itis seen that addition of calcium resulted in a significantcurrent decrease in the cathodic range. Fig. 4 shows theanodic polarization curves recorded in a PBS solution inthe absence and presence of calcium ions. Both curvesshow similar behavior during the anodic polarization.However, in the PBS solution, the anodic current risesremarkably at about 2.6 V, while in the solution withcalcium, the anodic current begins to rise significantlyonly after about 3.1 V. Its current value is also lowerthan that in PBS at potentials greater than 2.6 V.

Fig. 3 and Table 2 show that the calcium phosphatedeposit decreased the cathodic current and increased thepolarization resistance at the OCP. This can be

E / V vs. SCE

−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2

log

(j /

A c

m−2

)

−7

−6

−5

PBSPBS + Ca ions

Fig. 3. Polarization curves of Ti in PBS solutions with and without

2 mmol L1 CaCl2 recorded at a scan rate of 0.5 mV s1.

E / V vs. SCE0 1 2 3 4

log

(j /

A c

m−2

)

−6

−5

−4 PBSPBS + Ca ions

Fig. 4. Anodic polarization curves of Ti in PBS solutions with and

without 2 mmol L1 CaCl2 recorded at a scan rate of 1 mV s1.

attributed to the covering and blocking effect of calciumphosphate deposit on the cathodic reaction. Since thedeposited calcium phosphate decreased the cathodiccurrent, it might be expected to decrease the anodiccurrent as well through its blocking effect, causing adecreased corrosion rate and increased polarizationresistance at the OCP as reported in Table 2.

Fig. 5 shows the dc polarization curves for titanium ina PBS solution with and without addition of BSA orfibrinogen. Both BSA and fibrinogen decreased thecathodic current and moved the OCP in the negative(cathodic) direction. The effect was most dramatic withthe addition of BSA (Fig. 5), which decreased thecathodic current, increased the anodic current betweenthe OCP and the passive region, and caused a significantnegative shift of the OCP. It is known that many organiccorrosion inhibitors prevent corrosion by forming anadsorbed film and blocking the mass transportation ofthe corrosion process. It is also well known that proteinshave a high affinity for adsorption onto solid surfaces[25,28,29]. The decreased cathodic current is thereforeinterpreted as being due to adsorbed BSA moleculescovering the reaction sites and/or blocking the trans-portation of dissolved oxygen to the electrode surface.

In order to examine the effect of protein concentra-tion on the cathodic current, the current was recorded at0.8 V after each incremental aliquot of BSA stocksolution (Fig. 6) and fibrinogen solution (Fig. 6, inset)were made to the PBS solution. The potential of 0.8 Vwas chosen since for all the polarization curves thispotential avoids the OCP and the diffusion controlpotential regions. The current decreased with theincrease in protein concentration and reached a plateauat 0.72 mM (0.05 g L1) for BSA and 0.037 mM

(0.01 g L1) for fibrinogen. The plateau threshold con-centration for fibrinogen was much lower than for BSA,i.e. fibrinogen required a lower equilibrium concentra-tion in the bulk solution to reach a saturated adsorption

E / V vs. SCE−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2

log

(j /

A c

m−2

)

−7

−6

−5

PBSPBS + FibrinogenPBS + BSA

Fig. 5. Polarization curves of Ti in: PBS; PBS+0.05 g L1 fibrinogen;

PBS+0.05 g L1 BSA recorded at a scan rate of 0.5 mV s1.

ARTICLE IN PRESS

Concentration of BSA / mM0.0 0.5 1.0 1.5 2.0 2.5 3.0

j / µ

A c

m−2

5

10

15

20

25

30

Concentration of Fibrinogen / mM0.00 0.05 0.10 0.15 0.20

j / µ

A c

m−2

10

12

14

16

18

20

22

24

Fig. 6. Dependence of cathodic current at 0.8 V on the concentration

of BSA and fibrinogen (inset).

E / V vs. SCE0 1 2 3 4

log

(j /

A c

m−2

)

−6

−5

−4

PBSPBS + FibrinogenPBS + BSA

Fig. 7. Anodic polarization curves of Ti in: PBS; PBS+0.05 g L1

fibrinogen; PBS+0.05 g L1 BSA recorded at a scan rate of 1 mV s1.

X. Cheng, S.G. Roscoe / Biomaterials 26 (2005) 7350–7356 7355

coverage, consistent with the relative size of themolecules considering the projected areas for adsorption(side-on orientation: BSA 46 nm2, fibrinogen 300 nm2).In addition, the lower inhibiting effect on the cathodiccurrent of a fibrinogen-containing solution may be dueto a more open structure or lower degree of ordering ofadsorbed fibrinogen molecules at the surface comparedto BSA, which is a consequence of the differencein protein structure. Fibrinogen is a fibrous moleculewith a long open structure, which fragments readily,whereas BSA has an oval compact globular structurethat packs well and is fairly resistant to denaturationduring the adsorption process. Therefore a layer of BSAis possibly more efficient in blocking the reaction sitesthan the more open structure formed by the fibrinogenlayer.

If we suppose BSA has no influence on the anodicreaction of titanium, then, since BSA decreased thecathodic current (i.e., reaction rate), the OCP should belower compared to that measured in the PBS solutionalone, and the corrosion resistance at the OCP should behigher than that in PBS as we saw from Table 2 for thesolution with calcium ions. However, Table 2 shows thatBSA did not increase the polarization resistance oftitanium, which suggests that BSA may have increasedthe anodic reaction around the OCP. It is known thatproteins can accelerate the dissolution of metals throughtheir chelation effects [20,25–27], and therefore BSAmay also be able to accelerate the anodic dissolution oftitanium at the OCP by a similar chelating process. Thecombination of the chelating effect on the anodicreaction and blocking effect on the cathodic reaction,results in a more negative OCP in the presence of BSAthan in PBS solution. Since titanium is a typical valvemetal, a lower OCP will cause a higher anodic current inthe potentiodynamic polarization curve between theOCP and the passive range. Similar to the presentobserved effect on the OCP by the adsorbed BSA,

Contu et al. [2] reported that the addition of serumsignificantly shifted the OCP of Ti in the negativedirection. This effect may be at least partially attributedto the presence of BSA in the serum.

Similar to the effect observed with the presence ofcalcium phosphate deposit in the high anodic range(42.6 V in Fig. 4), addition of BSA and fibrinogen alsodecreased the anodic current (Fig. 7) in the same highanodic region. The sharp rise of the anodic current inthis potential range may result from the development offractures in the passive film. The influence of calciumphosphate and proteins may be attributed to a blockingeffect on the crevices of the fractured passive film.

4. Conclusion

Both calcium phosphate deposition and proteinadsorption decreased the cathodic current and theanodic current in the high anodic potential range(42.6 V). This inhibiting effect can be attributed totheir covering and blocking effect. Calcium phosphatedeposition increased the corrosion resistance of titaniumat the OCP. Although BSA dramatically shifted theOCP in the negative direction, it did not significantlychange the corrosion resistance at OCP. This isattributed to the chelating effect by the protein on thedissolution process and the inhibiting effect on thecathodic reaction.

Acknowledgement

Grateful acknowledgment is made to the Nova ScotiaHealth Research Foundation and the Natural Scienceand Engineering Research Council of Canada forsupport of this research.

ARTICLE IN PRESSX. Cheng, S.G. Roscoe / Biomaterials 26 (2005) 7350–73567356

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