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1 This rticle ppered in journl published by Elsevier. The ttched copy is furnished to the uthor for internl non-commercil reserch nd eduction use, including for instruction t the uthors institution nd shring with collegues. Other uses, including reproduction nd distribution, or selling or licensing copies, or posting to personl, institutionl or third prty websites re prohibited. In most cses uthors re permitted to post their version of the rticle (e.g. in Word or Tex form) to their personl website or institutionl repository. Authors requiring further informtion regrding Elsevier s rchiving nd mnuscript policies re encourged to visit:

2 Interntionl Journl of Ftigue 32 (2010) Contents lists vilble t ScienceDirect Interntionl Journl of Ftigue journl homepge: Ftigue of biomterils: Hrd tissues D. Arol,b, *, D. Bjj, J. Ivncik, H. Mjd, D. Zhng c Deprtment of Mechnicl Engineering, University of Mrylnd Bltimore County, Bltimore, MD 21250, USA b Deprtment of Endodontics, Prosthodontics, nd Opertive Dentistry, Bltimore College of Dentl Surgery, University of Mrylnd, Bltimore, MD 21201, USA c Deprtment of Mechnics, Shnghi University, Shnghi , Chin rticle info bstrct Article history: Received 23 June 2009 Accepted 26 August 2009 Avilble online 4 September 2009 Keywords: Bone Cementum Dentin Enmel Ftigue crck growth Frcture toughness The ftigue nd frcture behvior of hrd tissues re topics of considerble interest tody. This specil group of orgnic mterils comprises the minerlized (roughly 50% minerl by volume or greter) nd lod-bering tissues of the humn body; it includes bone, cementum, dentin nd enmel. An understnding of their ftigue behvior nd the influence of loding conditions nd physiologicl fctors (e.g. ging nd disese) on the mechnisms of degrdtion re essentil for chieving lifelong helth. But there is much more to this topic thn the immedite medicl issues. There re mny chllenges to chrcterizing the ftigue behvior of hrd tissues, much of which is ttributed to size constrints nd the complexity of their microstructure. The reltive importnce of the constituents on the type nd distribution of defects, rte of colescence, nd their contributions to the initition nd growth of crcks, re formidble topics tht hve not reched mturity. Hrd tissues lso provide medium for lerning nd source of inspirtion in the design of new microstructures for engineering mterils. This rticle briefly reviews ftigue of hrd tissues with shred emphsis on current understnding, the chllenges nd the unnswered questions. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction Within the lst decde there hs been n increse in the number of studies imed t understnding ftigue of hrd tissues. This is not new subject s studies reporting on ftigue of bone ppered in the literture over 50 yers go [1]. The rise in interest is for good reson nd cn be ttributed to number of fctors. Hrd tissues represent those tht re minerlized (sometimes considered highly minerlized in comprtive sense to soft tissues, nd generlly ner 50% minerl by volume or greter) nd re principlly lod-bering. Bsed on the cyclic nture of lods trnsmitted in the orl environment nd throughout the skeletl system, progressive degrdtion of these mterils through ftigue is relevnt concern. In ddition, there hs been n increse in the verge lifespn of both men nd women, nd most of these individuls seek to mintin n ctive life, n essentil element of longevity [2,3]. Tht plces greter physicl demnds on the humn body, nd over n extended period of time. Simply put, these relities equte to greter number of cycles tht the skeletl system must endure, nd ftigue hs become incresingly relevnt. Some of the developing interest in ftigue of hrd tissues ppers to come from the new understnding itself, nd the promise of improved dignostic technologies. For exmple, there is now * Corresponding uthor. Address: Deprtment of Mechnicl Engineering, University of Mrylnd Bltimore County, 1000 Hilltop Circle, Bltimore, MD 21250, USA. Tel.: ; fx: E-mil ddress: drol@umbc.edu (D. Arol). greter interest in development of methods/models for predicting nd/or preventing filures tht originte from dmge identified within hrd tissues (e.g. identifiction of flws using imging techniques nd prescribing interventions) [4]. Some of this new understnding is leding to greter wreness tht there re certin physiologicl conditions tht increse the frgility nd/or susceptibility of these tissues to ftigue [5 10]. While much of the interest in this topic is focused on the development of knowledge to ddress obstcles to lifelong helth, there is expnding interest in the opportunities for pplying this knowledge towrds the development of bio-inspired mterils nd structures [11,12]. And despite ll the immedite nd tngible pplictions of knowledge from studies on ftigue of hrd tissues, there re some less obvious, but eqully vluble rewrds. These nturl composites possess fscinting microstructures tht re delight to study nd lern from. 2. Microstructure There re totl of four hrd tissues in the humn body tht includes bone, cementum, dentin nd enmel. Interestingly, ll four of these tissues re locted in the orl environment nd only one is locted both within nd externl to this environment (i.e. bone). Bone, cementum nd dentin re very similr in tht ll three re connective tissues, ech is comprised of the sme principle constituents, nd re roughly blnce of orgnic nd inorgnic mteril by volume. The structure of these mterils plys n importnt role on their ftigue behvior nd is n essentil topic for this review. A /$ - see front mtter Ó 2009 Elsevier Ltd. All rights reserved. doi: /j.ijftigue

3 D. Arol et l. / Interntionl Journl of Ftigue 32 (2010) comprison of the density nd some selected mechnicl properties of the hrd tissues is provided in Tble Bone Corticl bone comprises the outer shell of bones of the skeletl system nd is comprtively dense with regrds to the more porous interior cncellous (trbeculr) bone (Fig. 1). Bsed on its rchitecture nd composition, corticl bone is often described s complex hierrchicl composite [13,14] s it exhibits importnt structurl elements operting from the nnoscle to the mesoscle. By volume it is comprised of pproximtely 50% minerl, with the reminder comprised of orgnic mteril (35%) nd wter (15%); by weight it is pproximtely 70% minerl nd 24% orgnic mteril nd 6% wter. Corticl bone is comprised of type I collgen fibrils (pproximtely nm dimeter nd few micrometers in length) tht re bound nd supported by n rrngement of crbonted ptite nnocrystls (of roughly 2 3 nm thickness, nm width nd up to 100 nm length) [13]. The collgen fibrils nd ptite crystls combine to form minerlized fibrils (or bundles, much less thn micrometer in dimeter), which re then orgnized into lmellr structure with djcent lmelle oriented orthogonlly, nd with thickness between 3 nd 7 lm [14]. On microscopic scle corticl bone is trversed by sprse distribution of cnls, i.e. the Hversin cnls (50 90 lm in dimeter), which re ligned long the long xis of bone. Ech of the cnls is surrounded by the lmelle in concentric fshion, which form the osteon, i.e. the bsic metbolic unit [15,16]. In dults the individul osteons re secondry osteons (not originl) nd re bounded by the cement sheths or cement lines s they pper when viewed in cross-section (Fig. 1). While the composition is still under evlution, there is evidence tht the cement line exhibits lower collgen content [17,18] nd slightly different minerl composition [19] thn the osteons. Unique from the other hrd tissues, bone hs the cpcity to undergo self-repir, coordinted process of resorption nd remodeling controlled t the cellulr level [20]. There is strong evidence tht micro-dmge rising from ftigue triggers the remodeling process, or t lest plys role in its initition [21,22]. Remodeling is importnt to this topic s dmged bone is replced by the deposition of new bone; secondry osteons develop nd replce existing primry or secondry osteons. As such, there is n increse in the number nd density of cement lines, s well s reduction in the osteon size nd increse in number of Hversin Cnls over the course of one s life [19,23]. Trbeculr bone is viewed s cellulr solid nd is differentited from corticl bone by its lrge porosity nd mosic structure (Fig. 1). Morphologicl evlutions hve shown tht the bone volume frction vries widely with ntomic site, rnging from 5% to up to 60% [24]. The bsic structurl element is the trbecule, which re both rods nd pltes of boney tissue. Like corticl bone, the trbecule re comprised of lmelle tht re derived from n ssembly of the sme primry constituents. But the lmelle in trbeculr bone re rrnged longitudinlly long the trbecule nd not in Hversin system. The pores of trbeculr bone re compromised sttes, which originlly contined dipose tissue (i.e. bone mrrow) nd blood vessels; these smll reservoirs contin nutrients nd progenitor cells tht ply n importnt role in remodeling ctivity. Due to the site specific cellulr rchitecture, the mechnicl behvior is often described with regrds to the density. There re excellent reviews covering this topic [24,25] Cementum The cementum serves s one of the primry connective tissues nd exists between the root dentin nd periodontl ligment (Fig. 1b). It occupies region tht is comprtively thin ner the junction with enmel (<100 lm), but rnges from roughly lm thick ner the root pex [26]. Cementum is roughly 45 50% hydroxyptite, with the reminder comprised of the orgnic components, including collgen nd non-collgenous mtrix proteins, nd wter [26,27]. But it is worth noting tht the composition of cementum vries considerbly with the type, its loction bout the root surfce nd function. A detiled description of the microstructure tht supports n understnding of the mechnicl behvior of this tissue ppers to be developing. In simplistic sense, the cementum is chrcterized ccording to whether it contins cells or not. Primry cementum (lrgely cellulr) is locted most djcent to the dentin, comprises the mjority of tissue in the upper two thirds of the root nd is chrged with tooth ttchment. In generl, secondry cementum (i.e. cellulr cementum) occupies the lower third of the root region [26] nd is considered responsible for bsorbing occlusl lods. Due to differences in structure nd chemicl composition, the primry nd secondry cementum exhibit differences in mechnicl behvior. There re sptil vritions in this distribution, nd regions in which the cellulr nd cellulr regions lternte. There is further subdivision of the cellulr cementum into intrinsic (i.e. fibrillr) nd extrinsic fiber structures. The ltter is comprised of collgen fibril bundles tht re of lower minerliztion nd extend orthogonl or oblique to the tooth root; it lso contins extensions of the collgenous Shrpey s fibers from the periodontl ligment. The former is locted closest to the tooth surfce nd comprised of more highly minerlized fibrils tht run essentilly prllel to the root surfce nd orthogonl to the extrinsic fibers. Cellulr cementum is comprised of both intrinsic fibrillr nd extrinsic fiber structures tht pper to be oriented mostly norml to the root surfce. Cellulr cementum lso contins cementoblsts, which contribute to the deposition of cementum in phses throughout life. But unlike bone, the cementum is not cpble of remodeling Dentin Like bone, dentin exhibits complex hierrchicl structure [28] nd is comprised of both orgnic nd inorgnic components. Den- Tble 1 Typicl rnge of some physicl nd mechnicl properties of the hrd tissues. Property Bone Cementum Dentin Enmel Ti6Al4V Density (g/cm 3 ) Elstic modulus (GP) Tensile strength (MP) N/A Frcture toughness (MP m 0.5 ) 2 8 N/A Endurnce strength (MP) 23 b N/A b N/A 300 c m (power lw exponent) 4 10 N/A DK th (MP m 0.5 ) 0.5 N/A Stress mplitude reported or pprent t b Zero to tension (flexure). c Fully reversed.

4 1402 D. Arol et l. / Interntionl Journl of Ftigue 32 (2010) Corticl bone Trbeculr bone Bone Mrrow Blood Vessel b R IR R IR Enmel Dentin Pulp Cementum Bone I P I P Blood Vessel Nerve Fig. 1. Microstructure of the hrd tissues. () Microgrphs of trbeculr bone (upper right) nd corticl bone (lower right). These two microgrphs re from Poole nd Compston [76] nd Zioupos et l. [10], respectively. (b) The tooth nd microgrphs of the enmel (top right), dentin (middle right) nd cementum (bottom right). For enmel, I nd IR represent selected rod nd interrod regions, nd for dentin, P nd I represent selected peritubulr cuffs nd intertubulr dentin. The microgrph of cementum ws grciously provided by Prof. Ho of UCSF. tin is comprised of pproximtely 45% minerl, 33% orgnic mteril (primry type I collgen) nd 22% wter by volume [26]; by weight the distribution is pproximtely 70% minerl, 20% orgnic mteril nd 10% wter. On microscopic scle the most distinct fetures re the dentin tubules (Fig. 1b), which re network of microscopic chnnels tht extend rdilly outwrd from the pulp

5 D. Arol et l. / Interntionl Journl of Ftigue 32 (2010) towrds the dentin enmel junction (DEJ) nd cementum with density rnge from 20,000 to 60,000 per mm 2 [29]. The tubules decrese in dimeter from pproximtely 2.5 lm (ner the pulp) to less thn 1 lm (t the DEJ). Ech tubule is bounded by highly minerlized cuff of peritubulr dentin consisting of ptite crystls [26]. The region between the tubules is regrded s the intertubulr dentin nd consists of collgen fibril mesh oriented essentilly perpendiculr to the tubules nd bound by ptite crystllites [28,30]. The collgen fibrils hve dimeter of between 50 nd 100 nm, wheres the ptite crystls hve pproximtely 5 nm thickness nd remining dimensions dependent on distnce from the pulp (needle-like t pulp nd plte-like t DEJ) [31]. Dentin is incpble of remodeling, which rises the importnce of dmge introduced within this tissue nd the potentil for degrdtion of the structurl behvior with cyclic loding Enmel Enmel, the outermost tissue of the humn tooth, serves s protective enclosure for the dentin nd the vitl pulp (Fig. 1). Comprised of pproximtely 87% minerl, 11% wter nd only 2% orgnic proteins by volume, enmel is the most highly minerlized tissue of the humn body [26,32]; by weight the enmel is nerly 96% minerl, the smller reminder comprised of orgnic mteril (1%) nd wter (3%). The inorgnic portion is lrgely comprised of crbonted hydroxyptite crystls in the form of nnoscle rods (25 30 nm thick, nm width nd considerbly greter length) tht systemticlly combine to form long keyhole shped rods (4 8 lm in dimeter) [26,32]. These micro-scle rods re the enmel prisms nd rrnged in columnr fshion, extending from the dentin enmel junction (DEJ) to the occlusl surfce. The rods re prtilly surrounded by sheth (t 1 lm) of noncollgenous orgnic mtrix, the composition of which differentites it from the other hrd tissues. As evident from the descriptions of chemicl composition nd microstructure, wter is n importnt component of ech of these mterils. And consistent with ll mechnicl testing, studies imed t chrcterizing the mechnicl behvior of these tissues will require the preprtion of specimens from bones or teeth with suitble geometry. It is essentil tht the methods of hrvesting the tissue nd specimen preprtion do not disturb the composition or wter content. Mintennce of the moisture nd lso the minerl concentrtion re criticl requirements in this re of evlution, but re not discussed in detil in this review. 3. Ftigue behvior The ftigue properties of corticl bone nd dentin were recently reviewed by Kruzic nd Ritchie [33]. Tht detiled tretment ddresses the ftigue behvior from mechnistic perspective nd includes work on humn tissues s well s tht of other nimls (bovine, elephnt, equine, etc.). It is n informtive review. Here, in the interest of brevity, the effort is primrily focused on studies on humn tissues nd presenttion of importnt highlights. It lso extends the discussion to trbeculr bone, cementum nd enmel. There is lso more emphsis on the importnce of ging nd other fctors on the ftigue behvior Bone Corticl bone Of the four hrd tissues, the ftigue behvior of corticl bone hs received the most ttention nd over the longest period. Much of the interest is ssocited with the development of stress frctures tht rise with intense ctivity nd result in the development Fig. 2. A comprison of experimentl results for ftigue of humn corticl bone obtined from zero tension nd tension compression cyclic loding with model prediction ccounting for creep-ftigue. Figure reproduced with permission from Crter nd Cler [36]. of loclized dmged tissue consisting of high density of microcrcks [34]. Of equl concern nd relevnce is the incidence of frgility frctures in the elderly [34]. Erly work showed tht humn bone exhibits trditionl ftigue life response (nlogous to engineered metls), but tht bone undergoes considerble time-dependent deformtion. Of importnce, Crter nd Cler [35] noted tht tissue from young individuls exhibited superior ftigue strength nd life, n erly forecst tht ging is importnt to the ftigue behvior. A relted study by this tem showed tht the time to filure of bone is function of the cumultive creep nd ftigue dmge [36]. A trnsition in behvior ws identified where creep dominted the responses for cyclic stress rnge (Dr) exceeding 60 MP s shown in Fig. 2. At lower stresses the life ws primrily function of the ccumultion of ftigue dmge. Ftigue tests performed t different frequencies hve demonstrted tht stress-bsed models predict time to filure of humn corticl bone better thn cycles to filure [37,38]. Moreover, the permnent strin tht evolves with ftigue of bone cn be estimted by models developed for creep [39]. The creep deformtion in bone hs been ttributed to dissocition of the hydroxyptite crystls from the orgnic mtrix, cusing increse in lod trnsfer to the collgen nd viscoplstic deformtion of the fibrils [40]. The nture of degrdtion in bone with cyclic loding is lso dependent on the stress rtio. For exmple, zero to tension ftigue of humn femorl bone promoted time-dependent degrdtion (i.e. creep), wheres zero to compression loding promoted cyclic dmge only [37]. A frctogrphic nlysis showed tht cyclic tension resulted in filure t the cement lines nd promoted osteonl pullout, wheres cyclic compression cused filure on n oblique plne consistent with the mximum sher stress, which is consistent with the erlier work of Crter nd Hyes [41] with bovine bone. Due to the difficulties in working with humn tissues, experimentl studies in this re re often conducted with niml tissues. But subtle differences in microstructure cn be of tremendous importnce. A comprison of bovine femorl bone (lmellr bone) nd red deer ntler (osteonl bone with slightly lower minerliztion) under zero to tension loding showed tht bone exhibited the highest ftigue strength [42]. However, the ntler ws fr more dmge tolernt nd underwent reduction in

6 1404 D. Arol et l. / Interntionl Journl of Ftigue 32 (2010) modulus prior to filure lmost three times greter thn tht of bone. Besides the contribution of microstructure, differences in the ftigue strength of bones cross species [43] hve lso been ttributed to the stressed volume nd popultion of intrinsic defects [44]. Chnges in the microstructure of bone tht result from remodeling re lso importnt here. An evlution of stress-life ftigue in cyclic tension, compression nd sher found tht heterogeneity in the hrdness between the osteons nd interstitil res ( by-product of remodeling) ws the most importnt fctor to the ftigue response [10]; the ftigue strength decresed with incresing heterogeneity. Tht observtion is unique from the notion tht remodeling increses the ftigue strength s new secondry osteons re significntly more effective t rresting ftigue crcks thn old osteons [45]. Yet, remodeling ppers to ply n essentil role in preventing frgility filures s there is reduction in the frcture toughness of bone with incresing degree of microcrcking [46]. After the colescence of dmge hs progressed to the initition of well-defined flw, ftigue crck propgtion ensues in this tissue. Few studies hve exmined ftigue crck growth of corticl bone. The erliest were conducted with bovine [47] nd equine [48] bone. Recent work hs provided mechnistic understnding of ftigue crck growth in humn bone [49,50] for cyclic extension prllel to the osteons. Overll, cyclic crck extension in these studies occurred over stress intensity rnge (DK) of DK MP m 0.5 with growth rtes rnging from to mm/cycle. Utilizing the conventionl power lw [51] for modeling the stedy stte region of response the growth exponents rnged from 4.4 to 9.5 (Tble 1). The ftigue crck growth behvior of compct humn bone is influenced by the mgnitude of stress nd the contributing mechnisms (cyclic nd time-dependent). At low cyclic driving forces (DK 6 1 MP m 0.5 ) crck growth ppers to be enbled by lternting blunting nd reshrpening of the crck tip, i.e. true ftigue. Yet, t higher driving forces the crck extends primrily by sttic processes (i.e. creep) with only minor ssistnce from cyclic loding. This behvior is similr to the contributions of creep to the S N response noted by Crter nd Cler [36] nd discussed by Tylor [34]. Cyclic extension occurred primrily long the cement lines [49]. Also, the crck pth ws littered with so-clled uncrcked ligment bridges, which ct to bridge Fig. 3. A comprison of ftigue crck growth rtes in corticl bone for short nd long crcks. The short crck dt is from Akkus nd Rimnc [55] nd Kruzic et l. [50] nd the long crck dt is from Nll et l. [54]. Figure reproduced with permission from Kruzic et l. [50]. the crck nd increse the resistnce to frcture through the reduction in the locl stress intensity. This extrinsic mechnism of toughening is the primry component [52] responsible for the rising R-curve behvior of humn bone [53,54]. And in evlutions on the propgtion of smll surfce crcks ( 6 1 mm) in bone [50,55] the formtion of these ligments promote decelertion nd rrest of ftigue crcks (Fig. 3), consistent with short-crck behvior of more common extrinsic toughening mterils [56] Trbeculr bone In contrst to the lrge number of studies on corticl bone, very few studies hve exmined ftigue of humn trbeculr bone [9,57 61]. This is rther surprising since loosening of implnts is often relted to ftigue of trbeculr bone [62]. Due to the difficulties of gripping the rther porous nd delicte rchitecture, experimentl studies of trbeculr bone re commonly performed under cyclic compression. A clever study performed by Choi nd Goldstein [57] compred ftigue of trbeculr nd corticl humn bone using miniture bem specimens (pproximtely mm) tested in 4-point loding. The bems were prepred from single trbecule or corticl bone, thereby minimizing the influence of bone volume frction (or porosity). The ftigue strength of trbeculr bone ws 20 40% lower thn the corticl bone, the degree of difference incresing with life. The difference in ftigue behvior ws rtionlized by the unique microstructure; the specimens of corticl bone contined single or no cement lines, wheres the plte-like ssembly of lmelle in trbeculr bone resulted in mny cement lines. Those orientted norml to the mximum principl stress served s potent defects for crck initition. The ftigue behvior of trbeculr bone follows the trditionl S N behvior. Moreover, the tissue undergoes reduction in modulus with cyclic loding nd there is substntil evidence of creep. A comprison of the ftigue responses for bovine nd humn trbeculr bone showed tht they re consistent nd cn be modeled using single power lw reltion if the yield strin is included in the ssessment [58]. The conformity in responses suggests tht while the monotonic behviors re site specific (due to density vritions), the dominnt cyclic processes regulting ftigue re occurring t the ultrstructurl level. Indeed, the current opinion concerning mechnicl degrdtion induced by ftigue ppers to be tht the dmge initition nd propgtion is regulted by the trbecule [61]. Orienttion of the trbecule contributes to nisotropy in the ftigue behvior (Fig. 4). Nevertheless, detiled mechnistic evlution of ftigue nd frcture in trbeculr bone, like tht developing for corticl bone [63,64], hs not been presented Aging of bone Experimentl studies hve reported tht the elstic modulus, strength nd toughness of humn bone decrese with individul ge [65 67]. There re lso notble vritions in the R-curve behvior with ge including reduction in both the initition toughness nd growth toughness [64,68]. Despite evidence tht ging is importnt to the ftigue behvior [69], this topic hs received limited ttention nd remins n importnt re of reserch. There hs been some effort in understnding the formtion nd ccumultion of microcrcks in ged corticl bone [70,71]. This work suggests tht both the rte of ccumultion nd severity of microcrcks increse with individul ge. Microcrcking in bone is discussed in more detil in erlier reviews [33,34]. It is cler tht there is reduction in the ftigue strength of corticl [10,69] nd trbeculr [9] bone with ge. But the most recent evlution of corticl bone showed tht the ftigue behvior ws more highly correlted with heterogeneity between the osteon nd interstitil res thn with donor ge [10]. The degrd-

7 D. Arol et l. / Interntionl Journl of Ftigue 32 (2010) Fig. 4. Cycles to filure s function of r/e 0 (rtio of mximum stress nd verge modulus) for bovine nd humn trbeculr bone. Smples were obtined from vertebre nd femurs nd for two different orienttions s described by the inset. In order to enhnce clrity of the representtion, dt points re only provided for the bounding groups. An dditionl curve from Hddock et l. [58] is plotted for comprison in this figure. Figure reproduced with permission from Dendorfer et l. [61]. tion is potentilly ttributed to the incresing cement line density, nd properties of the collgen mtrix [72 75], both of which could reduce the dmge initition resistnce nd the extent of intrinsic mechnisms of crck growth toughening. It is importnt to recognize tht ge is not physicl prmeter, but simply serves s n indice for the pprent microstructurl chnges. There is n increse in microcrck density of bone with ge [70] tht triggers remodeling, but there is lso n increse in porosity with repeted bone turnover, s well s with the incidence of osteoporosis [76]. Age-relted frgility frctures re generlly ttributed to reduction in bone mss nd/or reduction in bone minerl density (BMD). An lterntive to this belief contends tht the degrdtion is due to high rtes of remodeling [77]. Tht would promote n increse in number of secondry osteons nd cement line density, thereby reducing the degree of extrinsic toughening vilble for promoting crck growth resistnce. Studies imed t chrcterizing ftigue response in terms of the remodeling rtes, nd secondry osteon size could provide new insight, but will require improved methods for studying remodeling in quntittive mnner. Of equl importnce, there re differences in the ge-dependent remodeling rtes between individuls of specific ethnic bckgrounds [77], which could contribute to the rte of degrdtion in ftigue behvior with ge. These issues re of substntil importnce nd offer opportunities for interesting reserch Cementum The cementum hs two primry mechnicl functions, nmely to fcilitte nchoring the tooth to the lveolr bone nd to serve s prtil dshpot with the periodontl ligment in bsorbing trnsmitted lods from the tooth. Of the four hrd tissues considered, evlutions on the mechnicl properties of the cementum re comprtively rre. Ho nd collegues [27,78,79] hve performed some recent investigtions nd reported some new informtion on structure nd mechnicl behvior. These mechnicl ssessments hve focused on hrdness nd elstic modulus using microindenttion nd nnoindenttion methods. Similr to the structure, the mechnicl behvior exhibits substntil heterogeneity s evident from the lrge rnge in elstic modulus (Tble 1). No studies hve been reported on the ftigue behvior of this tissue. There is limited cementum vilble for such studies nd, undoubtedly, number of consequent difficulties. Nevertheless, there ppers to be welth of vluble informtion here regrding the design of ftigue resistnt dhesive systems nd joints tht require both stiffness nd energy dissiption to fcilitte function. The cementum promises to be n interesting mteril to lern from nd one tht will likely receive considerble ttention in the future Dentin Interest in the ftigue properties of dentin emerged only decde go [80]. Tht is surprising considering tht cyclic stresses cused by therml ftigue were reported to induce crcks in teeth much erlier [81] nd tht tooth frcture hs been significnt problem in restortive dentistry [82,83]. Studies on ftigue of humn dentin hve distinguished tht dentin exhibits the trditionl S N response [5,6,68,84,85]. Collectively these studies hve estblished tht dentin exhibits n pprent endurnce limit tht rnges from pproximtely MP, nd tht it is dependent on the frequency of loding [84], the men stress [68] nd the tubule orienttion [85]. Orienttion of loding reltive to the tubules is importnt due to the rnge of loding conditions posed by cyclic contct nd the chnges cused by introduction of restortive mteril [86]. The pprent endurnce strength of dentin (defined t 10 7 cycles nd t stress rtio of 0.1) is 24 nd 44 MP for tissue with tubules ligned prllel nd perpendiculr to the mximum norml stress (Fig. 5) [85]. The difference is ttributed to the collgen fibrils, which re oriented roughly perpendiculr to the tubules [31]. Note tht the microstructure of dentin is misleding s the peritubulr cuffs look like reinforcing fibers in fibrous composite (e.g. Fig. 1(b)). However, the minerlized collgen fibrils, which re generlly not visible in microscopic ssessment, re primry contributors to nisotropy in the ftigue behvior. Similr to bone, dentin exhibits greter ftigue life nd lrger pprent endurnce strength t higher lod frequencies [84]. An nlysis of the responses in terms of time to filure reveled time dependence nd rised some question s to whether the cyclic response is true cyclic ftigue. But further work by this group using elephnt dentin hs estblished tht the cyclic responses re true cyclic ftigue tht is ssisted by time-dependent degrdtion [87]. A relted study considering men stress effects distinguished tht there is reduction in the ftigue life of dentin with incresing tensile men stress nd incresing stress rtio [53]. Tht study lso found tht the lifetime dt were bounded by the Gerber prbol [88] t lower lives nd by the Goodmn line [89] t longer lives, qulity tht is consistent with the behvior of most engineering metls [56].

8 1406 D. Arol et l. / Interntionl Journl of Ftigue 32 (2010) P Stress Amplitude, σ (MP) = 0 = 45 = Cycles to Filure, N b 100 FAILURE Stress Rnge, Δσ (MP) 10 0 o 45 o 90 o crck length (μm) Fig. 5. Ftigue behvior of humn dentin. () Stress-life responses for coronl dentin from comprtively young individuls (17 < ge < 35). Dt points with rrows indicte specimens tht did not fil. (b) A Kitgw Tkhshi digrm describing the trnsition from stress-life ftigue to ftigue crck growth in humn dentin for three tubule orienttions. The orienttion is described by the ngle between the dentin tubules nd the plne of mximum norml stress. Figures reproduced with permission from Arol et l. [95]. Ftigue crck growth in dentin ws initilly studied using tissue of bovine teeth [90,91]. The first study performed with humn dentin utilized complince pproch [84]. Cyclic extension followed power lw form with growth exponent of 8.76 nd stress intensity threshold of DK th = 1.06 MP m 0.5. Cyclic growth chrcterized using the direct crck mesurement pproch [7] provided considerbly higher growth exponent (13.3 ± 1.3) nd lower DK th (0.7 MP m 0.5 ), quntities indicting tht dentin is highly susceptible to ftigue crck growth. Interestingly, ftigue crck growth surfces in dentin exhibit stritions (Fig. 6). A comprison of strition ptterns from lbortory specimens nd crck surfces in restored teeth hs been used to estimte the cyclic stresses contributing to ftigue crck growth in vivo [8]. Flws introduced during restortive prctices my ply n importnt role in the incidence of tooth frctures. Indeed, crcks exceeding 100 lm in length hve been identified in preprtion of dentin using lsers for hrd tissue bltion [92]. Surprisingly, no study hs distinguished contributions from the surfce integrity on the ftigue life of dentin. Though the chrcteristics of intrinsic flws in dentin re not well understood, quntittive ssessment of the criticl flw size Fig. 6. Ftigue stritions resulting from ftigue crck growth in humn dentin nd evidence of microcrcking long djcent peritubulr cuffs. Arrows in (b) indicte ridge/step (bifurction of crck) formed becuse of microcrcking (crck growth is from left to right). Note tht the stritions do not develop ech cycle, but rther form fter period of cycles. Figure reproduced with permission from Bjj et l. [8]. nd cyclic stress envelope promoting ftigue filure hs been performed. Kruzic nd Ritchie [4] dopted the Kitgw Tkhshi [93] nd El Hdd [94] methods, which enble mrrige of the stress-life nd dmge tolernt pproches. A Kitgw Tkhshi digrm ws constructed for stress rtio (R) of 0.1 nd conditions where the tubules were oriented prllel to the mximum cyclic stress. The informtion detiled by Kitgw Tkhshi digrm for dentin (or ny tissue) my provide clinicins mens of ssessing the risk of frctures, provided tht the flws cn be imged prior to reching instbility. But tht digrm hs lso been used to describe the reltive nisotropy of dentin s ftigue behvior in terms of flw size for flws oriented prllel (0 ), oblique (45 ) nd perpendiculr (90 ) to the tubules (Fig. 5b) [95]. Evident here, humn dentin undergoes trnsition from ftigue to ftigue crck growth t the lowest cyclic stress rnge when the tubules re ligned with the direction of cyclic stress. Using the rtio of criticl stress rnge (Dr c ) to quntify the degree of nisotropy (r = Dr c (mx)/dr c (min)), r = 2 within the stress-life regime nd reduces to pproximtely 1.2 under ftigue crck growth. Thus, humn dentin exhibits the lrgest degree of nisotropy within the stress-life regime (i.e. short crck regime), indicting tht structurl nisotropy plys the lrgest role on the ccumultion of dmge nd crck initition Aging of dentin A review of ging of dentin, including the chnges in microstructure nd its importnce on the mechnicl behvior of this tissue ws recently presented [96]. Aging of dentin is ccompnied

9 D. Arol et l. / Interntionl Journl of Ftigue 32 (2010) b 80 Young Old Stress Amplitude, σ (MP) P Cycles to Filure, N c young old old (Asi) d/dn (mm/cycle) ΔK (MP*m 0.5 ) Fig. 7. Influence of ging on the microstructure nd ftigue behvior of humn coronl dentin. () Chnge in the microstructure with individul ge s evident from microgrphs of coronl dentin from 20 yer old femle (left) nd 50 yer old mle (right). (b) The reduction in ftigue strength of dentin with individul ge bsed on comprison of young (17 6 ge 6 30, men ± std. dev. = 25 ± 5 yers) nd old (506 ge, men ± std. dev. = 64 ± 9 yers) tissue [5]. (c) A comprison of the ftigue crck growth resistnce of humn dentin from young nd old individuls from the US nd Asi. Figure reproduced with permission from Bjj et l. [103]. by reduction in the tubule dimeter due to the deposition of minerl within the lumens (Fig. 7). This process begins in the third decde of life nd results in n increse in minerliztion [6,97]. After n dequte degree of minerl is deposited within the tubules the tissue ppers trnsprent. There re lso some chnges in the minerlized collgen mtrix with ging, but this is less well understood [98,99]. Independent studies of the R-curve behvior for crck extension prllel (in plne) [100,101] nd perpendiculr [102] to the dentin tubules report significnt reductions in the crck growth resistnce of dentin with ge. Yet, studies of the ftigue behvior hve reported slightly conflicting responses. Kinney et l. [6] found tht trnsprent dentin (from old individuls) exhibited lower pprent ftigue strength for lives from 10 3 to 10 5 cycles, but negligible difference for 10 6 cycles. In contrst, Arol nd Reprogel [5] showed tht old dentin exhibits significntly lower ftigue life thn tht of young dentin, throughout the

10 1408 D. Arol et l. / Interntionl Journl of Ftigue 32 (2010) stress-life rnge (Fig. 7b). The rtio of endurnce strength (t 10 7 ) to ultimte strength for young nd old dentin is pproximtely 0.5 nd 0.38, respectively. These rtios re well within the rnge reported for engineering metls [56]. The smller rtio for old dentin emphsizes the incresed sensitivity to ftigue, nd contributions from the chnge in microstructure. Age is lso importnt to the ftigue crck growth resistnce of dentin. The Region II crck growth responses for young nd old (506 individul ge) dentin re shown in Fig. 7c. Though the verge ftigue crck growth exponent for the old dentin (m = 21.6 ± 5.2) is significntly greter thn tht of the young dentin, differences re most evident in the verge rte of ftigue crck growth [7]. The verge rte of ftigue crck growth in the old tissue is more thn 100 times greter thn tht in young dentin. Thus, crcks introduced within dentin during routine restortive procedures re fr more likely to cuse tooth frcture in senior ptients. Note tht the comprison of ftigue crck growth responses (Fig. 7c) lso includes dt for senior individuls from Asi with comprble ge distribution. Results from this preliminry study indicte tht there re significnt differences in the ftigue properties between the dentin of these two different ethnic groups [103]. Further work is presently underwy to estblish how ethnic bckground nd/or diet contribute to the ging process nd the ftigue properties of this hrd tissue. Unique from bone, the reduction in ftigue resistnce of dentin with ge is ssocited with n increse in density, not reduction, nd through decrese in number of nturl stress concentrtions by filling of the dentin tubules. Though flws hve been distinguished to be n importnt contributor to the structurl behvior of dentin [6], no study hs chrcterized these flws, nd whether there re intrinsic flws in this tissue. One spect of the ftigue behvior of dentin tht hs not been ddressed is the sptil dependence. Evlutions reported thus fr hve been primrily limited to coronl dentin. The tubule density is greter within the tooth root nd the ge-relted microstructurl chnges begin in the tooth root nd progress coronlly [104]. There would be some vlue in estblishing if there re differences in the ftigue properties of root nd coronl dentin nd if the degrdtion in ftigue properties of root dentin begins t n erlier ge, or re more severe Enmel Due to its high minerl content, the enmel of teeth would be expected to exhibit limited resistnce to ftigue nd ftigue crck growth. Indeed, crcks or crze lines re commonly viewed on the surfce of teeth, but these seldom led to tooth frcture. They re potentilly rrested t the dentin enmel junction (DEJ) [105], or immeditely beneth the enmel within the mntle dentin [106]. Nevertheless, the ftigue properties of enmel hve received limited ttention. To the uthor s knowledge no study hs been reported on the stress-life ftigue behvior of enmel. The ftigue crck growth resistnce of enmel hs been recently studied using novel pproch tht embodies smll piece of enmel within miniture CT specimen [107,108]. Mesures of cyclic extension prllel to the prisms hve shown tht enmel exhibits prominent shortcrck behvior [56] nd then trnsitions to long-crck response (Fig. 8). Ftigue crck growth initites t reltively low stress intensity rnge (DK 0 = 0.39 ± 0.09 MP m 0.5 ) nd continues to instbility t DK of 0.65 ± 0.14 MP m 0.5, much less thn hlf the reported frcture toughness [108,109]. Using Pris model to chrcterize the stedy-stte responses, the exponent rnges from 5.6 to 9.2 [107]. These vlues re not substntilly different from those of some common monolithic engineering cermics. But in compring the ftigue crck growth responses with tht of sintered d/dn (mm/cycle) b d/dn (mm/cycle) Short crck K ΔK(MP*m 0.5 ) HAp Nll et l., ΔK(MP*m 0.5 ) t hydroxyptite (HAp) hving nerly identicl crystllinity, chemistry nd density, the HAp required significntly lower driving forces for initition of cyclic extension (DKth 0.13 MP m 0.5 ) nd throughout the growth rnge. A 4% increse in orgnic content (over tht of HAp) nd tilored distribution contributes to 3-fold increse in required cyclic driving force. Surprisingly, the ftigue crck growth resistnce of enmel is not substntilly lower thn tht of humn bone nd dentin (Fig. 8b), despite the high minerl content. Hence, the microstructure of enmel is extremely effective in resisting cyclic crck growth in this comprtively hrd nd brittle mteril. Extrinsic mechnisms of toughening re clerly ctive in the crck wke (Fig. 9) during both cyclic nd monotonic crck growth in enmel. Nerest the ntomic tooth surfce (i.e. in the outer enmel) crck extension occurs between nd prllel to the prisms (Fig. 9b), resulting in crck growth extending directly towrds the vitl pulp. This would pper reckless design by nture s crcks reching the pulp would require tooth extrction. However, this chrcteristic is ctully ingenious s the guided crck is prevented from curving bck towrds the tooth s surfce nd fcilitting chipping; the crck is rrested before reching the den- E Long crck B D Bjj et l., 2006 Fig. 8. Chrcteristics of ftigue crck growth in humn enmel. () A typicl ftigue crck growth response for humn enmel nd evidence of both short nd long crck behviors. (b) A comprison of the verge ftigue crck growth behvior of bone (B), dentin (D) nd enmel (E) with hydroxyptite (HAp). Figure reproduced with permission from Bjj et l. [107].

11 D. Arol et l. / Interntionl Journl of Ftigue 32 (2010) OE b c d e IE 100 µm b c d e Fig. 9. Observtions of crck growth in the forwrd direction. Direction of crck growth is from left to right indicted by white rrow. () Opticl microgrph of crck extension showing trnsition in behvior from outer enmel (OE) to inner enmel (IE). Growth in the inner enmel ws ccompnied by vrious mechnisms of toughening. (b) Stright crck pth in the outer enmel is ttributed to the reltively stright prism orienttion. (c) Crck bifurction occurred while trnsitioning from the outer to the inner enmel. (d) Crck extension though the decussted zone resulted in formtion of unbroken ligments tht bridge the crck. (e) Crck growth in the proximity of the DEJ underwent deflection nd stll due to chnge in prism orienttion. Figure reproduced with permission from Bjj nd Arol [109]. tin. Almost midwy through the enmel thickness the prisms undergo crossing, n rchitecture regrded s decusstion. Upon reching this region the crck undergoes bifurction (e.g. Fig. 9c) nd number of toughening mechnisms develop including bridging induced by unbroken ligments of tissue (Fig. 9d) nd crck curving nd twisting (Fig. 9e). Microcrcking bout the primry crck nd secondry bridging induced by ligments of orgnic mtter provide further resistnce [108]. This concert of mechnisms is extremely effective in promoting retrdtion nd crck rrest. In fct, recent evlutions of the R-curve behvior indicte tht these mechnisms result in toughness exceeding 2.0 MP m 0.5 [109]. Teeth subjected to lrge occlusl lods my develop crcks bout the DEJ t nturl fissures [110]. Tht would enble crcks to initite nd extend from the inner enmel outwrds (i.e. the reverse direction). Mesures of cyclic crck extension in the reverse direction show tht rtes rnge from to mm/ cycle, but tht totl growth history extends over less thn 0.7 mm (fr less thn the forwrd direction) [108]. Cyclic extension in the reverse direction occurred lmost exclusively in the short crck regime with miniml stedy stte behvior. The pprent DK th for this orienttion (0.53 MP m 0.5 ) is nerly 40% greter thn tht for the outer enmel nd nerly equivlent to tht t instbility (DK c = 0.68 MP m 0.5 ). The crck growth resistnce ws ttributed to the sme extrinsic mechnisms identified in forwrd crck growth. However, the mechnisms evolved for growth within the inner enmel only nd the crck reched instbility prior to escping the decussted zone. The grded microstructure of enmel chieves n increse in crck growth resistnce with cyclic extension nd it is optimized for crcks inititing from the tooth s surfce nd propgting inwrd. Tht rises questions to prticiption of the DEJ to crck growth resistnce. A study of cyclic crck extension from enmel towrds the DEJ indicted tht the crcks were deflected to grow long the interfce [105]. It is unknown whether the DEJ works in the sme cpcity for crcks growing from dentin into enmel. There re number of remining components of the ftigue behvior of enmel tht remin unknown. For exmple, the studies conducted thus fr hve been limited to n exmintion of ftigue crck growth. The stress-life ftigue response is of interest, especilly considering the potentil for dmge to develop s result of cyclic contct between enmel nd engineered cermics used for crown replcement. And of equl relevnce, the influence of microstructurl chnges induced by chemicl tretments on the ftigue properties is timely concern, but one tht hs not been ddressed. There re lso issues relted to sptil vritions in the ftigue response nd whether the properties re consistent throughout the crown of the tooth, or whether there re differences in properties between nterior nd posterior teeth. The studies conducted thus fr hve been limited to n exmintion of enmel from extrcted 3rd molrs, teeth tht will rrely be enrolled in chewing. There ppers to be something to lern from the microstructure of enmel in the design of hrd nd ftigue resistnt brittle systems. A quntittive evlution of the nisotropy nd mechnistic evlution of the response could nurture the development of new microstructures nd/or engineered behvior.

12 1410 D. Arol et l. / Interntionl Journl of Ftigue 32 (2010) Chllenges nd opportunities In review of the ftigue behvior of hrd tissues there re number of chllenges nd remining questions. Some of these items were presented in the context of the individul tissues. It should be evident from the review tht there is significnt extent of degrdtion in the stress-life nd ftigue crck growth properties of bone nd dentin with ging. These chnges re primry contributors to the increse in frgility frctures nd tooth frctures in senior individuls. But the mjority of existing knowledge ddresses wht hppens, nd there re mny remining questions tht involve why nd when. For bone, the declining ftigue resistnce nd frcture toughness ppers to be complicted function of chnges in bone mss, rte of remodeling nd potentil chnges in the collgen. In dentin, the reduction in ftigue crck growth resistnce cn be ttributed to the diminished contribution of extrinsic toughening; cuse for the reduction in dmge initition resistnce nd its onset re less well understood. Thus, dditionl knowledge of contributions from the individul constituents on the mechnisms of ftigue nd frcture behvior in the hrd tissues is criticl. Furthermore, the evlutions conducted thus fr hve bounded the behvior by extremes (young nd old), with less emphsis on the ge t which the reduction in ftigue resistnce begins, nd how it progresses with mturtion. This is where the issues relted to ethnic bckground nd nutrition my become relevnt, mking such studies not only interesting, but lso worthwhile. Bone dentin nd enmel exhibit substntil nisotropy in their microstructure. In bone, cement lines hve been identified s comprtively wek interfces tht ply n importnt role in cyclic crck growth, especilly in crck deflection [75]. And in enmel, cyclic crck growth occurs lmost exclusively long the interprismtic regions nd prllel to the rods [109]. In contrst, dentin exhibits the most nisotropy during the initition of crck, nd pprently less during cyclic crck extension, despite the structurl similrity to bone. Little effort hs been spent exploring the nture of this nisotropy nd if it cn be dopted or ptterned in engineered systems. Also of interest, to the uthor s knowledge no experimentl study hs quntified the role of remodeling on the ftigue response of bone, or pursued studies on the bility for dentin nd enmel to self-repir in the presence of evolving ftigue dmge. These re importnt concepts nd hve tremendous merit. Much of the work on ftigue of hrd tissues hs focused on those occupying the lrgest volume. Both the enmel nd cementum ply unique functionl roles tht re quite different from those of bone nd dentin, but hve received little ttention. The interfces between these two tissues nd dentin re regions tht exhibit unique dmge tolernce; mechnistic understnding of their ftigue properties could provide new models for the development of ftigue resistnt interfces. Indeed, biomimetic principles re now being used in the development of tough hybrid mterils with hierrchicl microstructures tht re ble to chieve toughness in excess of 300 times their constituents [12,111]. But these studies re often directed towrds mximizing crck growth resistnce through biomimetic nlogs tht chieve extrinsic mechnisms of toughening. There ppers to be tremendous opportunities for using these mterils to inspire new concepts for resistnce to dmge initition, nd then the cpcity for invoking self-repir. 5. Closing remrks The pursuit of lifelong helth nd interest in extending the current definitions of n ctive nd high qulity of life hve rised the level of interest in the ftigue properties of hrd tissues. There hs been some progress towrds understnding the importnce of the microstructure of these mterils on their ftigue properties, nd contributions from chnges relted to ging nd disese, prticulrly with bone nd dentin. But this re of reserch hs not reched mturity nd there re number of fundmentl topics remining to be ddressed. There is still tremendous distnce between the knowledge obtined from lbortory studies nd the ppliction of this knowledge in medicl prctice. Due to the complexity of their microstructures, dvncements in this re will require better understnding of the microstructure of these mterils nd distinction of contributions from the constituents, cting lone nd in concert, on the primry mechnisms of dmge initition nd crck growth resistnce. These pursuits will undoubtedly fuel investigtions in this re for decdes to come. Acknowledgement The uthor grtefully cknowledges support from the Ntionl Institute of Helth through NIDCR R01 DE nd NIDCR R01 DE The uthors lso thnk Professor Sunit Ho of the University of Cliforni Sn Frncisco for her comments regrding the structure nd properties of cementum. References [1] Evns FG, Lebow M. Strength of humn compct bone under repetitive loding. J Appl Physiol 1957;10: [2] Shephrd RJ. Aging, physicl ctivity, nd helth. Chmpign, IL: Humn Kinetics Pub Inc.; 1997 [illustrted ed.]. [3] Westendorp RG. Wht is helthy ging in the 21st century? Am J Clin Nutr 2006;83:404S 9S. [4] Kruzic JJ, Ritchie RO. Kitgw Tkhshi digrms define the limiting conditions for cyclic ftigue filure in humn dentin. J Biomed Mter Res A 2006;79: [5] Arol D, Reprogel RK. Effects of ging on the mechnicl behvior of humn dentin. Biomterils 2005;26: [6] Kinney JH, Nll RK, Pople JA, Breunig TM, Ritchie RO. Age-relted trnsprent root dentin: minerl concentrtion, crystllite size, nd mechnicl properties. 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Remodeling nd the repir of ftigue dmge. Clcified Tissue Int 1993;53(Suppl. 1):S75 80 [discussion S80-1]. [23] Thompson DD. Age chnges in bone minerliztion, corticl thickness, nd Hversin cnl re. Clcified Tissue Int 1980;31:5 11.