Exploring the Effects of Hypermineralisation in Bone Tissue by Using an Extreme Biological Example

Connrcnw Tissue Kesronlr. Val Jl l i ) . pp 229-248 Reprints available directly from the publisher Photocopying permilled by license only

0 2001) OPA tO\errce\ Publicherb Association) N V Published by license under

the Gordon and Breach Science Publishers imprint. Printed in Malaysia

Exploring the Effects of Hypermineralisation in Bone Tissue by Using an Extreme Biological Example

PETER ZIOUPOS”*. JOHN D. CURREYb and ADRIA CASINOS‘

‘Dept cfMaterials & Medical Sciences, Cranfeld Universih, Shrivenham SN6 801, United Kingdom, “Dept oj‘ Biology, Universi@ of York, PO. Box 373, York YO10 5YW United Kingdom and ‘Dept de Biologia Animal Vertebrats. Universih oj Barcelona. Aving. Diagonal 645,

08028 Barcelona, S p i n

(Received 28 Februun 2000: Revised 24 April 2000; Accepted 27 April 2000)

The properties of bone tissue with very high or very low mineral levels attract attention because they allow researchers to comprehend more fully the mechanics, interaction and effects of mineral on collagen through a greater range of compositions than that found in the “ordinary”. The bone tissue of the rostrum of the whale Mesoplodon densirostris is the dens- est bone known. We examined the composition, static and fatigue strength, hardness and toughness of this tissue and compared them to those of other less mineralised analogues. The rostrum bone has remarkably little organic matter and retains very little water in its native state, but its basic mineral stoichiometry is very similar to that of other bones. We present here updated versions of the microhardness vs. modulus and microhardness vs. mineral f rac- tion relationships, which thanks to the rostrum have been produced for a considerably wider range than in the past. We found the rostrum to be extremely brittle with a toughness ratio in two perpendicular directions (along and across its length) similar to that of tissue of other “ordinary” long bones and we discuss the possible significance of our findings.

Keyv0rd.s: Mesoplodon rostrum: bone; mineral; microhardness; fatigue; toughness: constitution

1. INTRODUCTION

Bone tissue comes in a combination of forms and constitutions to perform a great variety of functional needs and duties. The mechanical and physicochemi- cal properties of bone tissue are related to the relative fractions of its components (water, organic, mineral) quite often in a straightforward way. Currey[1,21, for instance, has shown that some mechanical properties of bone show a monotonic increase (e.g. Young’s

modulus) with the amount of mineralisation (in this case the weight of Ca++/dry weight of bone), while others show a monotonic decrease (e.g. strain at failure). However, some properties, like the bending strength and the area under the load-deformation curve, show a maximum and then a catastrophic decline. For other properties, such as fatigue and some fracture mechanics properties, the situation is unknown. Needless to say the study of bone would benefit significantly if a complete knowledge of the

* Corresponding Author: Dr Peter Zioupos, Dept of Materials & Medical Sciences, Cranfield University, Shrivenham SN6 8LA, UK; Tel: +44(0) 1793-785932: Fax: +44(0) 1793-785772: E-mail: [email protected]

229

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230 PETER ZIOUPOS er d

remaining mechanical properties were to be derived for the complete range of mineralisation found in nature.

Valuable information quite often is provided by some biological extreme^[^,^], which serve as limiting cases for the sought-after behaviour. Zioupos et investigated some mechanical properties and the possible biological use of the extremely dense bone of the rostrum of the toothed whale Mesoplodon densirostris. Some families of toothed whales have nar- row rostra and this feature is most notable in Ziphiidae. Within Ziphiidae the species of the genus Mesoplodon show rostra with bone tissue of high compactness and density, which in the males of Meso- plodon densirostris, in particular, is taken to an extreme['] (densities of 2.6-2.7 g cmP3). In recent studies of its h i ~ t o l o g y [ ~ , ~ ] , ultrastructure[61 and mineral phaseL7] the rostrum has been shown to consist of intensely remodelled bone, and almost entirely of secondary osteons (Haversian systems). The rostrum was found to be stiffer, harder and more minerali~ed[~] than even the tympanic bulla of a whale (Buelunop- tera physalus), a tissue which has set the standard for extremes of fragility and brittleness of very mineralised bone in studies of the pastL3].

However, unlike cetacean tympanic bulla, whose structure architecture and orientational layout of whose various elements (collagen, mineral, osteons) is somewhat ill defined and/or characterised, the Mes- oplodon rostrum has the orderly unidirectional architecture and anisotropic preference of a mammalian long bone, albeit with much more There- fore, whereas tympanic bulla is perhaps adequate for providing an analogue for studies of composition and isotropic physical properties, it is not appropriate for comparisons on the anisotropic related characteristics of hypermineralised tissues and for drawing conclu- sions on the detrimental effects of extreme mineralisation on some specific bone mechanical properties including its toughness (which in most cases is also linked to anisotropy). In this article we report on the composition, strength, hardness, fatigue, and toughness properties of this remarkable rostrum bone material, and also make comparisons with those of other less mineralised tissues.

2. MATERIALS AND METHODS

A short section of the rostrum of a male Mesoplodon densirostris was given to us by colleagues in the MusCum National d'Histoire Naturelle, Paris, France. This rostrum was used to give the samples used in all the recent s tud ie~[~-~Ion this extraordinary piece of tissue (Fig. 1). Our present data therefore are directly related to all other information on the rostrum, but we don't know how exactly it changes with age in the animal. The reason for this is that the Mesoplodon densirostris rostrum specimens are a rare find.

2.1 The primary composition of Mesoplodon rostrum and other bones

For a wide comparison on composition we prepared specimens from the following species and anatomical sites: Galapagos tortoise (Geochelone midus) femur (GTF); Red deer (Cervus eluphus) antler base (FE) and middle-stem (FC); Nile crocodile (Crocodilus niloticus) nasal bone (CR); Blackfoot penguin (Sphe- niscus dernersus) radius (BP); Alligator (Alligator rnississipiensis) femur (AF); Wallaby (Protemnodon rufogriseus) femur (NWF) and tibia (NWT); Bovine (Bos) femur (BF, 9 yrs old); Fin whale (Buluenopteru physalus) tympanic bulla (TB), and Mesoplodon densirostris rostrum (Ml, M12).

Bone tissue has three main components: mineral, organic material and water['], the organic material being mainly collagen[91. In order to demonstrate where the rostrum lies in respect to its mineralisation and comparatively to other tissues we used the compositional examination method of Lees"] to produce a ternary diagram of the interrelationships of the weight fractions of the three major components in a variety of mineralised tissues. Small samples were cut from each species and were centrifuged briefly (3 mins in a MSE MISTRAL 1000 unit, at 300 rpm) while wrapped in damp cloth to remove excess amounts of water from their major pores. Their wet weight (WW) was determined with a METTLER TOLEDO College B 154 balance to a 0.1 mg accuracy. The samples were then dried in an oven for at least 3 days at -40°C over calcium sulphate crystals and their dry mineralised

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HYPERMINERALISATION EFFECTS IN BONE TISSUE 23 1

10cm

Dorsal

VL FIGURE 1 Schematic representation of the rostrum, its principal planes of anatomical symmetry and the part of the tissue which we had available for preparing specimens. Orientations: Longitudinal (L), Vertical (V), Horizontal (H), Transverse (T), Sagittal (S) and possible specimen orientations with their designatory letters

weight (DMW) was measured with the balance. The difference between the WW and DMW was taken to be the weight of the water in the specimen. The mineral was then removed with EDTA[1'-'21 (ethylenedi- aminetetra-acetic acid disodium salt, OSM, pH=7.4). The solution of EDTA was changed every day; the process was considered to be complete when the calcium present in the EDTA solution became undetecta- ble by a spectrophotometric method for calcium content['31. The specimens (which always kept a coherent shape, like the original samples) were then dried out in an oven at -40°C for 2 days. The weight of the demineralised matrix was measured and this was the dry demineralised weight (DDW), which is

the weight of the organic component. (A little organic material["] may have gone into solution in the EDTA, but for comparative purposes we consider this method to be sufficiently accurate.) By this method 3 values for each sample were produced"':

Mm-f = mineral fraction = DRIIV-DDW / IVIV (1)

Wat-f = water fraction = IV\V-DMIT f WW ( 2 )

Org-f = organic frartiori = DDIV / IVW ( 3 )

The sum of the 3 weight fractions equals I .

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232 PETER ZIOUPOS et a/ .

TABLE 1 The Young’s modulus of elasticity of whole specimens (a single measurement in 3 point bending of beama), the Vickers mean (kS.D.) microhardness values (n=10), and the relative weight fractions (each measured 3 times and averaged) of minerals, organic and water per wet bone matrix weight of the 12 types of bone examined. The data are presented in descending order of the Young’s modulus values and this is followed closely by the Vickers hardness values in most cases

YouiigS modulus Vickers Hardness Min-f (weighfhvet Org-f (weight/wet War-f (weight/wel (GPO) (kg rnm-2) weight) weight) weight) Soinrw of bone

Mesoplodon rostrum (M 12) 44.1 229.5 (28.4) 95.8 1 .0 3.2

Mesoplodon rostrum (M 1 ) 38.2 225.0 (43.2) 96.2 0.8 3.0

Bovine femur (9yrs old) (BFJ 24.2 82.6 (8.27) 67.1 24.9 8.0

Wallaby tibia (NWT) 21.4 64.5 (2.68) 64.Y 24.8 10.3

Wallaby femur (NWF) 19.5 74.4 (13.3) 69.0 22.2 8.8

Blackfoot Penguin radius (BP) 17.0 47.7 (6.30) 60.3 27.9 11.8

Galapagos Tortoise femur (GTF) 1 1 . 1 33.5 (4.21) 44.3 34.6 21.1

Red-deer Antler base (FE) 7.5 22.4 (3.58) 50.4 31.7 17.9

Fin whale tympanic bulla (TB) 33.5 170.8 (21.6) 83.4 11.5 5.1

Alligator femur (AFJ 14.9 48.1 (4.12) 61.4 27.2 11.4

Crocodile nasal bone (CR) 6.5 26.4 (3.62) 51.5 33.0 15.5

Red-deer Antler middle (FC) 5.4 13.5 (1.40) 44.3 36.0 19.7

2.2. Chemical constitution of Mesoplodon rostrum and some bones

The chemical composition of the rostrum and samples from a bovine femur and a cetacean tympanic bulla were analysed. To these tissues we added two other less mineralised biological bone tissue examples, which have demonstrated remarkable toughness characteristics: a sample from the antler of a red deerC3], and a sample of dentine from the tusk of a Narwhal Monodon r n o n o ~ e r n s ~ ~ ~ ~ . The content of Ca, Mg, Na and P was quantified (after samples were hydrolysed with HCI) using Atomic Spectroscopy by Inductively Coupled Plasma. C and N contents were determined by means of an elemental analyser NA 1500 (C.E. Instruments).

2.3. Hardness & elasticity measurements

We examined the relationships between Young’s modulus ( E ) , microhardness (VHN) and mineral content (Min- f ) of the specimens whose compositions we discuss in section 2.1. Ten samples were chosen from a collection of specimens from a previous study on

stiffness, hardness and mineral content[15”61. These specimens had been mechanically characterised for modulus of elasticity, the yield stress, yield strain and the strain at failure‘’] all tested in the longitudi- navstiffest direction of the bone. Results had been produced for tension and bending[” by use of an INSTRON 1122 materials testing machine (INSTRON, High Wycombe, UK) at an estimated strain rate of lop3 s-I. To these we added two Meso- plodon specimens. The values for Young’ modulus for the rostrum material came from tests in 3-point bending only from a previous report of oursL4]. Because of its very brittle nature it was impossible to machine tensile samples from the rostrum and, therefore, we confined ourselves to testing beams (40 x 5 x 2.5 mm) cut under continuous water irrigation by the use of an EXAKT (Exakt, Otto Herrmann, Denmark) metallurgical saw. Two rostrum specimens were cut, one from a mid-transverse, one from the sagittal plane on the rostrum (fig. 1).

Microhardness was determined using a LEITZ WETZLAR “miniload’ microhardness tester (060- 366.002; Ernst Leitz Gmbh, Wetzlar, Germany). Specimens were smoothed to a final polish using fine

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HYPERMINERALISATION EFFECTS IN BONE TISSUE 233

grades of carborundum paper, finishing with BUEH- LER Micropolish 0.05 pm gamma alumina powder and were cast into resin tto secure them for microhardness testing. A load of 50 g for 10 s was used as rec- ommended previously[15-'s1 and this produced approximately square irnpressions whose diagonals ranged from 18 pm (rostrum bone) to 80 pm (antler bone). Ten readings were taken from widely spaced areas on the flat surfaces (40 mm long by 5 mm wide) of the beams (in a direction normal to the long stiff axis of the bones). The size of the diagonals was measured at ~ 4 0 0 magnification and Vickers hardness was calculated as: V H N = 1 8 5 4 . 4 x P ~ 6 ~ , where P is the applied load in g and d the mean of the two diagonals in pm. The data were produced on dry specimens at room temperature.

2.4. Fatigue testing

The fatigue properties of highly mineralised bone have not been examined previously. However, as we have already mentioned it proved impossible to test Mesoplodon specimens in either tension or compres- sion. They were so brittle: that they failed at any inad- vertent slight overloading during preparation and during gripping. We were, however, able to conduct a successful series of 3-point bending fatigue tests, in which we compared Mesoplodon specimens with bovine specimens, and 'constructed stress-cycles to failure (S-N) diagrams for these two tissues.

Beam shaped specimens, 50 mm long x 5 mm wide x 2 mm deep, were prepared from Mesoplodon rostrum and from the femur of a relatively young cow (18 months old). In eachi case the orientation of the specimen was in the longitudinalktiffest direction on the bone. The specimens were fatigued in a three-point bending rig; (E-399-83 and D-790- 86 ASTM standards) mounted on an INSTRON 85 11 servohydraulic machine, in Ringer's solution (BDH Lab. Suppl., Poole, UK). at -20°C under load con- trol. A sinusoidal waveform of a frequency of 2 Hz and a load range AF (the minimum load being zero, the maximum load varied between samples between 2 5 4 2 N) was applied though the indentor and the estimated resulting maximum tensile stress at the

outer layers of the beam was taken to be: As=l S x A F x L ~ b - ~ x h - ~ , where L=span between the two supports (this was set at 40 mm), h=specimen breadth and h=specimen thickness. We know that during fatigue of bone there is some change in the compliance of the specimens due to damage with the cycle number. However no information was gained about changes in compliance here; we simply recorded the applied stress range and the numbers of cycles to failure.

Before the fatigue tests the modulus of elasticity of each specimen (rostrum or bovine) was obtained by cycling a few times at a very low stress range. This measure of stiffness was used to determine the stress at which the specimens would be tested in fatigue. We arranged the specimens so that there was an even dis- tribution of stiffer and less stiff specimens at the various imposed fatigue stresses. Because of the great difference in stiffness between the two tissues some pilot tests were also performed to find the appropriate machine PID settings (gain, time, mass) for testing. Twenty-two Mesopladon and eleven bovine bone specimens were finally successfully fatigue tested.

Post-testing analysis included a normalisation by adjusting the stress values As by use of the particular modulus of elasticity of each specimen:

_Is(E) = AS x E,/E, (4) where: E, is the modulus of elasticity of each specimen and E, is the mean elastic modulus value of all Meso- plodon or bovine specimens. This adjustment performs a normalisation to equivalent strain values as it has been shown that damage and onset of microfractures in bones["] depend on the macroscopic strain.

2.5. Toughness measurements

Fracture toughness (Frir, specimens had dimensions (thickness/width/length) that were prepared according to ASTM E399-83 standards (width equals twice the thickness, length between supports equals eight times thickness). All faces of the samples were polished by use of progressively finer grades of carborundum paper in a direction along the long axis of the specimens and finally brought to a mirror finish by use of

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234 PETER ZIOUPOS el ul

100% organic

0.0 /f 1.0

Crocodile nasal bone ,

Blackfoot Penguin radius \,

Bovine femur

Wallaby femur .

Mesoplodon rostrum

loo% 0 0 0 1 0 2 0.3 0 4 0.5 06 0 7 08 09 1 0 100% mineral water

FIGURE 2 Ternary diagram showing the mineral, collagen and water fractions of the current 12 bone specimens from 1 0 species (we have also included data for the human femur for comparison)

BUEHLER Micropolish powder. The final dimensions were prepared to a 0.01 mm accuracy. The whole preparation was under water at room temperature.

FrT was assessed using the critical stress intensity factor (Kc) at the initiation of a macrocrack. A notch was cut in the Kcspecimens by the use of the finest EXAKT band saw blade. The notch cut across the full thickness of the specimens and its length was approximately half the width of the specimens as to provide a notch lengthlwidth ratio u/W=0.5 according to standards. The length of the notch was measured by both a travelling microscope and vernier callipers to an accuracy of 0.01 mm. The width of the notch was roughly 100 pm and its tip was semi-circular with a minimum radius just under 50 pm. By stereo-micro-

scopic observation (at ~ 2 0 ) we were able to establish that in all samples (bovine and Mesoplodon) the point where the notch started growing was coincident with the overall maximum load point on the trace, after which the rapid decrease in load was caused by the rapid growth of the crack.

The Kc values we report here come from the following formulae (ASTM E399-83):

K p = 0.031623 x f ( a / l l ~ ) P p S ~ - ' ~ ~ - - ~ ~ ' ~ ( 5 )

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FIGURE 3 3-D plot on logarithmic scales of modulus of elasticity, Vickers hardness and mineral content

where: B is the specimen breadth (thickness), W the specimen depth (width), S the span between the supports (length), and a the notch length, all measured in mm. P , was the critical load for crack growth in newtons. The result in (5) is expressed in MPa m'12.

The displacement rate was 2 mm min-' and was chosen so as to give a rate of increase of stress intensity in the range of [OX-2.751 MPa ,'I2 s-'.

Work of fracture (wf) tests were carried out on square cross section specimens cawing a chevron

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236 PETER ZIOUPOS et ul.

notch (a triangular ligament area remained intact) prepared by use of the diamond band saw. The ligament tip was facing so that the crack would travel transversely across the structural elements. Bending was applied at a cross head speed of 0.1 mm min-’. The span of supports was 32 mm for all Wftests. In these tests fracture starts at the tip of the triangular chevron ligament and advances towards the base of the trian- gle. The fracture progresses in a stabilised manner assisted by the ever-increasing width of the fracture front. The work done to complete the fracture process is divided by twice the ligament area to yield the work needed to create a unit of new fracture surface.

We tested in total: (i) for FrT: 17 Mpwplodon and I3 bovine specimens with the notch oriented transversely across the osteons (LH & LV geometries in Fig. 1): 6 Mesoplodon with a longitudinal notch (3 notches were driven in the longitudinal direction TL, and 3 in the radial direction TV, Fig. 1); three bovine specimens with a longitudinal notch driving radially between the osteons on a longitudinal radial plane; these were complemented by four specimens from human femoral bone from a 56yr old female; (ii) for W f in the transverse direction: six Mesoplodon (taken from a sagittal plane) and six bovine (3 radial and 3 cir- cumferential) specimens. FrT specimens were prepared of various thicknesses as the relative magnitude of the yield stress. the fracture toughness value and the thickness determine whether the dominant conditions in fracture are those of plain stress or plain strain.

3. RESULTS

3.1 Primary composition

Our results (Figure 2, table I) are very similar to those of a previous study”]. However, our whale tympanic bulla specimen was not as highly mineralised as the bulla and petrosal specimens reported by Leesc8]. Our rostrum specimen had an extremely small organic component. The organic remnant looked like a ghostly but sharp-edged version of the original sani- pie when wet. although it dried to a thin smudge on the filter paper. It is very interesting to note that in this

ternary diagram there is a clear trajectory for increased mineralisation in tissues and by using the Mesoplodon rostrum extreme we have now high- lighted a possible target end point for this process. It seems that in mammalian tissues, whenever collagen and mineral combine to form bone, the relative contents of the 3 components lie on a well defined route as shown in fig. 2, where collagen and its loosely bound water are substituted by mineral. There is also a slight indication in our results that from the least mineralised bone (Antler mid-stem and Galapagos tortoise femur) to the “ordinary” bones (Wallaby femur) water was lost more readily than the organic fraction (the organic fraction declined from 35% to 22% by weight, a loss of 3796, whereas the water declined from 20% to 9%, a loss of 55%). Suffice it to say that in the Mesoplodon rostrum there was extremely little water and organic material.

3.2. Chemical constitution of Mesoplodon rostrum and some bones

The chemical analysis ofjust 5 bone tissues (table 11) showed some interesting features: Calcium (Ca) reduced in concentration (down the table) as the ovcr- all mineral decreased and so did the phosphorus (P) content. The CdP weight ratio is nearly the same for all the tissues (except dentine) and corresponds to a poorly stoichiometric hydroxyapatite (perfect HAP has a C d P weight ratio of 2.16 corresponding to an atomic ratio of 1.67). Magnesium (Mg) followed a similar pattern for all bones except dentine (high Mg contents are a feature normal in teeth, in general). The ratio of P to N increased rapidly the more mineralised the tissue was (P/N column table 11). Moreover the P/N ratio, which has been studied in a detailed manner in studies of in-situ mineralising osteons120] appeared to continue the pattern observed in this previous studyL2’’, starting from the level of osteoid tissue. to immature non-fully mineralised osteons to the fully mineralised osteons as seen in the last 3 rows of table 11. It appears, therefore, that the patterns that other workers have observed in mineralisation processes in a specific species, may also apply in between species.

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237 HYPERMINERALISATION EFFECTS IN BONE TISSUE

TABLE I1 Mean percentages by dry weight (number of samples in parenthesis) of various basic elements in five different tissues (including Narwhal tooth dentine) laid out in reducing order of overall mineral content (section 2.1). The varying proportions of the different components accord with what one would expect to find in “bone” tissue in general. The table shows that there exists a gradual transition of all elements with a certain regularity from the most mineralised (rostrum) to the least (antler)

Nu P/N C/N C d P %mineral C N Ca P Mg

Mesupludon 2.21 (3) 0.23 (3 ) 33.78 (3) 15.48 (3) 0.43 (3) 1.24 (3) 67.30 9.61 2.18 83.6

Tynzp. Bulla 4.58 ( 1 ) 0.85 (1) 31.71 (3) 14.83 (3) 0.40(3) 0.98 (3) 17.45 5.39 2.14 80.1

Bovine F. 13.09 (3) 4.05 (3) 26.08 (3) 12.43 (3) 0.39 (3) 0.59 (3) 3.06 3.23 2.10 67.1

Dentine 13.86(1) 4.52(1) 23.23(1) 12.21 ( I ) 1.06(1) 2.70 3.06 1.90 66.1 -

Antler 17.09 ( 3 ) 5.52 (3) 22.37 (2) 10.47 (2) 0.37 (2) 0.60 (2) 1.89 3.09 2.14 56.5

10.11 2.28 ~ 54.6 ‘MFM osteons ~ 4.42 -

7.27 1.16 - 39.3 VNFM osteons 6.29 -

‘Osteoid 7.71 - 2.05 - 0.27 ~ - 1 1 . I b

- - - - - - -

- -

a. The last 3 entries are from the study of mineralising osteons by Pugliarello e t a / . (1970). They studied the variation in Nitrogen levels and Phosphorus content in gradually mineralising osteons (MFM: mature fully mineralised osteons: INFM: immature not fully mineralised osteons: and osteoid). Note how hoth P, N and their weight ratio follow in osteons the same patterns we see here across species. The last column %mineral =mineral/dry weight = 5.4 x (the phosphorus content), and corresponds to perfect hydroxyapatite. Note that because of the non-stoichiometric CaP ratios this is just an indication of the level of mineralisation from the osteoid tissue to the rostrum. (-) missing value. b. Probably inaccurate value since the osteoid is not mineralised.

3.3. Relationship between modulus, mineral content and hardness

We investigated the relationships between Young’s modulus, hardness and mineral content of the same specimens whose compositions we discussed in section 3.1. Microhardness was chosen because it is non-destructive and allows for the examination of small and awkward structures[’5-’8]. Microhardness can also be made to provide data on the anisotropy of the its spatialhegional heterogene- ity[222231, its and material properties near interface^^^^^^^^].

One would expect to see an increase in both E and VHN as the Min-f increases, and this was indeed found in two previous studies[‘5,161, which used specimens from the same collection of samples and species as here. The additional element here is that: 1) we have included the rostrum material, which extends considerably the range of mineralisation we are considering and 2) we have consistently kept the indentation for all species and in all samples normal to the longktiff axis of the bone (the stiff direction being on the plane of the indentations) so as to avoid small errors[4321,221 that may be caused by the anisotropy of

the bone tissue. Figure 3 shows the raw data of E, VHN and Min-f on 3-D logarithmic scales. Changes in all 3 variables followed each other closely.

Table I11 outlines some predictive relationships by use of the 3 variables. The linear relationships, although showing values for proportion of the total var- iance explained (R2) as high as those for the logged relationships, are clearly unrealistic because for instance (eqs.7, 10) a VHN of zero give a minimum value for the Young’s modulus of 6.52 GPa, and a minimum Mineral weight fraction of 0.463 (46.3%). Table I11 contains linear least squares regressions (eqs. 7,lO) and log-log least square regressions (eqs. 8 , l l ) for read- ers who may wish to use microhardness as a tool to obtain prediction of either the Young’s modulus or the Mineral fraction of bone. Fig. 4 shows log-log least squares relationships of E and Min-f by using the VHN values for predictions. Equations 9 and 12 are Model-I1 regressions (reduced major axis) and have been included here as these may be perhaps less biased (no assump- tions for the error variances of either VHN, E, or Min-f) estimates of the functional relationships between the two variables in each case. In fact, equations 8 and 9 are similar to each other, as are 11 and 12, as would be expected given the high R2 values.

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PETER ZIOUPOS et al. 238

TABLE I11 VHN: Vickers Hardness (kg mm-2), M i n - f : mineral (weighvwet weight of bone), and E : modulus of elasticity (GPa) relationships allowing predictions between the variables

VHN R2 = 94.0% (7) E = + 6.52 + 0.159

(8)

(model-11) (9)

( 1 1 )

(model-I I ) (12)

(13)

(14)

+ 0.513 VHd).747 + 18.7 M i n - f R’ = 96.6% (15)

Log E = - 0.251 + 0.147 Log VHN R’ = 95.5%

Log E = - 0.321 + 0.764 Log VHN

M i n - f = + 0.463 + 0.0023 VHN R’ = 94. I % (10) LogMin:f =-I620 + 0.284 Log VHN R2 = 93.5%

Log M i n - f = - 1.656 + 0.294 Log VHN E =- 10.68 + 0.075 VHN + 37.2 M i n - f R2 = 9S.77~

E = + 2.13 + 0.901 vHfl.’51 - 13.6 M i w f 2 . 4 3 R’ = 96.5%

E = - 5.47

120 100 80

60

h 40

30 m

v

- 5 20

E

P

3 m

10 0, c 3

5

2 - I I I 1 I 1 1 1 1

10 20 30 50 70 100 140 200 280

VHN (kg rnrn-’)

1 0.9 0.8 0.7 0.6

0.5

0.4

0.3

0.2

0.1

FIGURE 4 Modulus of elasticity and Mineral content log-log relationships by using the Vickers microhardness values as a predictive tool Least squares regression lines and their 95% confidence intervals (dotted) and the 95% prediction intervals (solid lines)

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The last three predictive relationship use values for both VHN and Min-f. Assuming that one can acquire non-invasively and non-destructively (i) an estimate of the mineral content (by for instance, back scattered SEM, or even acoustic microscopy) and (ii) the in-situ microhardness, then the best estimate we can produce here for the modulus of elasticity of any bone tissue is given in eqs.13-15. Eq.13 is a linear regression by using both VHN and Min-f with an R2=95.7%. In Eq. 14 the regression is performed after raising the two variables to the power of 0.747 and 2.43 respec- tively, since these were the exponents produced as best estimates in log-log relationships between E on one hand and VHN and Min-f on the other. However, since E is to a first qualitative approximation a linear function of Min-f and a power law function of VHN we have also produced the last eq. 15, which has an R2=96.6%. The predicted values of eq.15 are compared to the experimentally acquired data in fig. 5.

3.4. Fatigue strength of Mesoplodon and bovine bone

The capacity of the rostrum material to withstand fatigue (the repetitive cyclic application of stress) was compared to that of the “ordinary” bone from a bovine femur. The general perception we have formed of the rostrum is that is very brittle and as such we have already suggested in a previous paper[41 that it is unlikely to have any serious mechanical demands placed upon it in-vivo. However, because of the very high mineral content the rostrum is essentially a biological ceramic and very little is known about fatigu- ing this kind of material. In metals and polymers mechanical fatigue leads LO failure, at cyclic stress amplitudes well below the static strength, starting from cumulative irreversibility at sites where plasticity occurs. Ceramics are in general immune to crack tip plasticity and other modes of microstructural shielding, but they may also be susceptible to mechanical degradation caused by processes of other origin[271. What we are seeking to establish here is whether the fully mineralised rostrum is also susceptible to progressive processes leading to fatigue failure.

The results are shown in figure 6. For each specimen two values of stress are shown, (i) the calculated maximum stress, and (ii) the maximum stress normalised by the Young’s modulus of elasticity of the specimen as we described in methods. (The normalisation quite often considerably reduces the variability/scat- ter of the results.) Table IV gives the regression equations for the fatigue data. In each case the equations are of the form log stress as a function of log cycles to failure (N). This is an illogical way of depicting the data, because the cycles to failure are a function of the applied stress, rather than vice versa. However, this way of doing things is unfortunately deeply embed- ded in the fatigue literature.

There two important aspects in fatigue: the fatigue strength (also fatigue life) and the fatigue resistance of a material. As expected the fatigue strength of bovine bone is much higher than that of the rostrum reflecting the great difference in static strengths (intercept values on the stress axis). There is a very large difference in the heights of the two curves, so that the stress resulting in a particular number of cycles to failure being about 3.7 times greater in the bovine bone than in the Mesoplodon. Another way of putting this, more strikingly, is that at the rostrum’s static strength level of 60 MPa bovine bone will take -3~10” cycles to break!

However, the rostrum possesses a better fatigue resistance than bovine bone (table IV). This is judged by the slope of the two curves. The two slopes are significantly different (F1 ,,,=6.46, p<0.05) and that for the rostrum is almost flat (although still significantly different from zero p=0.002). It is obvious that the rostrum is relatively immune to fatigue and within a very small stress range 40-60 MPa it may take just one or 10,000 cycles to failure! One may argue that like in other ceramic materials failure is stochastic and it occurs overall at stresses not far from the static strength level. (Whether, for instance, at a stress of 50 MPa failure will occur or not, is not an entirely deter- ministic process. If the same stress is applied a great number of times it will be only more likely for failure to occur as opposed to when it is applied only once.)

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'3 40 a (3 W

50 r

-

PETER ZIOUPOS el < I / .

4 / I l l 1 I I 1 I

4 6 810 14 18 24 30 40 50

Predicted Young's modulus (GPa)

FIGURE 5 Comparison between measured modulus of elasticity values and predicted modulus values (eq. 15) using both Mineral content ( M i n - f ) and Vickers microhardness (VHfl.747) as predictive tools. Least squares regression line and its 95% confidence intervals (dotted) and the 9510 prediction interval (solid lines). On average the error in the estimate values is 4.8% of the experimental values over the full range of stiffnesses and 6.7% in the range 14-30 GPa

Both the rostrum tissue and ordinary bone comply with our expectations for the kind of material they are. Because in fundamental terms fatigue is caused by irreversible processes, the extent of fatigue is determined by the stress level at which irreversible damage occurs relative to the stress for complete failure. Materials that show a fully elastic and perfectly

brittle behaviour (like the rostrum here) have S-N curves that are flat and these materials are insensitive to alternating stresses possessing good fatigue resistance. Materials that undergo plastic or viscoelastic flow prior to failure (like ordinary bone tissue) start deforming at low stresses and develop fatigue damage in a progressive manner.

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24 1 HYPERMINERALISATION EFFECTS IN BONE TISSUE

TABLE IV Log-log S-N relationships for rostrum tissue and bovine bone. (For comparisons on fatigue strength note the intercepts on the stress axis and for fatigue resistance the relative values for the slope.)

Equation Stundard deviation I P R2

Un-normalised stress values

Mesoplodon

Bos

,Stress = 1.78 - 0.0304 cycles

:Stress = 2.35 - 0.0627 cycles

0.007 I 4.26 0.001 50.29”

0.0112 5.62 <0.001 75.3%

Normalised stress values

Mesoplodon !$tress = 1.76 - 0.0240 cycles 0.0065 3.67 0.002 42.3%

Bos Stress = 2.33 - 0.0528 cycles 0.0062 8.52 <0.001 87.7%

TABLE V Fracture toughness results for different bones and orientations: I transversely across the grain, 1 longitudinally along the grain. Mean (SD) and sample number in)

K c ( l ) (MPa m’”) Kc(:) (MPa m’”) W f ( l ) (kJ 6’)

Mesoplodon rostrum 1 .50 (0.39) 0.74 (0.22) 0.09 (0.02)

(n=17) (n=6) (n=6)

Bovine femur

Human femurd

6.02 ( I .46)

(n=13)

4.79 (1.07)

(n=13) lref.281

2.23 (0.48)

(n=3) -

3.22 (0.7 I )

(n=6)

2.41 (0.58)

(n=9) [ref.28]

a. Human femur from 56-90 yrs males. (For completeness of comparison the anisotropy ratios in two normal directions (I, 1) i n elastic modulus are for bovine bone: 18, 12 GPa, for human: 16, 9 GPa: for rostmm: 42, 25 GPa; and in microhardness for bovine bone: 80, 60 kg mm-*, human 60.50 kg mm-*, and rostrum 230,200 kg mm-2)

3.5. Toughness

In Mesoplodon rostrum specimens the FrT curves were initially linear and ended at a load peak after which rapid failure commenced (Fig. 7). By comparison in bovine bone FrT traces there was a noticeable deviation from linearity in the loaddisplacement curves and this was coincident with the appearance of disperse microcracking near the notch. The loaddisplacement traces for the ICOW bone did not comply strictly with the ASTM set of standards for measurement of plane strain fracture toughness KIc and our observations were indicative of significant “plastic” deformations being presenl. as a result of the pre-initiation microcracking seen in the vicinity of the notch. The measurements for Kc fracture toughness for bovine bone can, therefore, only be estimates and not Klc ASTM standard values. In Mesoplodon however, there were no thickness restrains and the actual traces ended in an abrupt point fcdlowed by fast brittle frac-

ture and we are confident that these values do quan- tify sufficiently the KIc fracture toughness of this brittle solid.

The results are summarised in table V. Our results showed that (especially when the influence of specimen thickness is allowed for, fig. 8) ordinary bone tissue is between 3 to 5 times tougher than the hypermineralised rostrum. Admittedly what we are considering here is only one aspect of tissue toughness and this is the necessary stress intensity factor to initiate the growth of a major crack. However, simi- larly to the 3-point bending results in quasistatic load-

where stress was much less concentrated, the rostrum exhibited a profoundly brittle behaviour. This is exclusively due to its inability to create/generate damage (a form of “plasticity”) around major cracks and thereby deter complete fracture. This confirms the already expressed view that there is a threshold mineralisation level beyond which bone matrix

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PETER ZIOUPOS et a1

220 200 180 160 140

120 n CU 3 100 W

v ) 80

60

40

bovine bone

0

0

Mesoplodon rostrum

Cycles to failure, N, FIGURE 6 S-N fatigue diagram in 3-point bending for Bovine bone and Mesoplodon rostrum tissue. Open symbols are the original data values (dotted: the least square regression line); solid symbols are the adjusted values by using eq.4 and the modulus of elasticity for each sample (also shown in solid lines the regression relationships and their 95% confidence intervals)

becomes very brittle. That threshold level is in fact much lower than the rostrum’s since extreme brittleness has already been seen in the whale tympanic

More importantly the rostrum is anisotropic in its toughness in two mutually perpendicular directions (along and across its grain) with a -2:l ratio. Ordi- nary bone has a ratio varying between 2-311, but

bu11a[3!

because of its internal architecture and significant collagen content one can not possibly infer what proportion of this anisotropy is due to the mineral and what to other features. The rostrum on the other hand is mostly mineral and, therefore, the present results suggest that bone tissue toughness anisotropy, very much like its general anisotropy in stiffness[291 may be due to a great extent to its mineral phase. Figure 9a shows

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30 N

F

70 N

F

A

P


C

MR

FIGURE 7 Force/displacement (F/F) traces for FrT(A & B) and Wf (C) tests on specimens (MR:Mesoplodon, BF:Bovine femur) of compa- rable dimensions. (A) The Mt.sop/,odon traces showed a linear-elastic region and a rapid decline in load as brittle fracture commenced. (B) The bovine traces showed an elast(n-plastic behdviour with the sustained load increasing between point PQ where there was a 5% deviation from linearity and P , the max load. (C) The relative size of the Wf curves for bovine femur and Mesoplodon rostrum

that the tissues clustered in two groups: one containing ordinary bones (including bovine and human femur) and one for the rostrum itself. However, the toughness to stiffness ratio was nearly the same and constant in

rostrum and in the other bones. The only difference being that the rostrum is overall more brittle.

Figure 9b shows that when placed on an A~hby '~ ' ] material chart the performance of the rostrum is

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244 PETER ZlOUPOS et a1

10 7 5

3

I 0.7 0.5

0.3

0.1

2

---- V - K P .- c

/- V Y _--- V

Bovine femur transverse V

Bovine femur longitudinal BL v /-

M .rostrum transverse

M.rostrum longitudinal v

TL

3 4 5 6 7

Specimen thickness (mm) FIGURE X K c 1's. specimen thickness. Regression line\: bovine-dashed. rostrum-solid, with their 95% confidence intervals

within the "porous ceramics" group and that all bone tissues showed the same positive stiffnessltoughness relationship as this seen in other man-made engineering composites. This is not the case for metals and polymers and shows the beneficial effect of the composite structure of bones, in so far as they are able to increase simultaneously their stiffness and toughness and irrespective of the species. One other aspect is the anisotropy in mineral orientation, which is responsi- ble for the steeper slope of the bones' stiffnesskough- ness curve. This means that for an increase in stiffness

the critical strain energy release rate will increase accordingly (further anisotropy in toughness), which is not always the case in other engineering cortipos- ites. This is a further advantage of the bone composite design.

4. DISCUSSION

The bone material of the rostrum of Mesoplodon densirostris is unique in a number of' respects including

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HY-PERMINERALISATION EFFECTS IN BONE TISSUE

B F f ,

5000 I- I I I

10

1. -

0.1

0.01 -

10000 22000 40000 60000 Young’s Modulus (MPa)

G,,= 1 000(kJ/m2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

/

/ ,

245

B Young‘s Modulus (MPa)

FIGURE 9 (A) K c vs. specimen Yclung’s modulus. Regression lines with their 95% confidence intervals in two groups: dashed for “ordinary” bones and solid for the rostrum. Symbols: rostrum I solid triangles, I open triangles; bovine femur I BT, I BL; and H: human femur I (4 samples tested here and 9 aged 56-90yrs from ref.[281). (B) the previous plot inserted in an Ashby material chart of srifiess LJS. toughness. The rostrum “falls” on the porous ceramics group

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PETER ZIOUPOS el al. 246

its very combination of structure, architecture, constitution and histology. We have in the past examined some hypotheses relating to its intended specific physiological and biological function[41 in life, but without much success. Its purpose remains a mystery. In the present article we focus exclusively on the rostrum tissue as a material and draw comparisons with other tissues of similar make. We believe that our results are of specific value for the material aspects of hypermineralised and mineralising tissues and for that reason of use to at least two modern scientific domains: biomimetics and tissue engineering.

The rostrum is well placed at the most extreme end of the biological analogues where collagen and bone mineral mix. It has a primary composition in which collagen and water are replaced by an ever-increasing mineral content. There were of course some odd findings here like the very high Sodium (Na) content of the rostrum, which can not be easily accounted for. We have in the past observed in the SEMr4] large scale of mineral depositions in this material. These were extensive to the point that blood channels and canaliculi were almost occluded with some kind of solid matter as yet unidentified and maybe these deposits can account for the extra Na content. One other way of having high Na in the structure is by ionic substitutions. Aged and diseased bone tissue shows higher carbonate substitutions and when this happens the bone mineral needs to readdress the charge balance perhaps by incorporating more Na. From the 4 recent studies on the we know that rostrum showed some odd histological features and signs of accelerated ageing. This may explain the high Na content through the route we have just outlined. Independent support for this pathway could possibly be offered by the high carbon content (C). As seen in table I1 the C/N ratio in rostrum is nearly three times that found in other bones. How- ever, it is also true that higher carbonate contents restrict the overall size of mineral crystallites and in the most recent of our studiesr7] we have also found the rostrum crystallites to be much larger than in normal bone. The various data features, therefore, cannot be reconciled easily. Overall, the mineral constitution results (and especially CaP) show sufficiently that

this “odd” Mesoplodon tissue is basically bone that has been taken to the most extreme limits of mineralisation, as opposed to some organic structure that has inadvertently mineralised. It seems, therefore, that it is a good model for examining the more general con- sequences of processes that lead to cases of hypermineralisation.

In general terms, the mineral itself is not dissimilar to “ordinary” bone mineral in elemental composition, but it does differ in the shape and size and perhaps the registration of crystallites along the major axis of the rostrum. Both Zylberberg et a1.[61 and Rogers and Z i o ~ p o s [ ~ ] have shown that the crystallites of the rostrum are much larger than normal and very well aligned. They also have very regular plate-like shapes and seem to displace the sparse collagen fibres around them. In fact the ultrastructural study of the rostrum[61 has shown that the mineral assumes the central role in the rostrum with collagen being sparse and laid out in a residual quasi-hexagonal pattern around long mineral columnar formations. This reversal of roles between collagen and mineral in providing a mineral backbone for the inner structure of rostrum does probably explain why the rostrum is so brittle - in effect it comprises a nearly homogenous ceramic mass with no interconnecting cohesive matrix. The presence of a significant amount of organic matrix would presuma- bly have helped the toughness of the tissue.

There may be other reasons, besides extreme niin- eralisation, for the reduced toughness of the rostrum material. It has been r e p o ~ ~ e d ~ ’ , ~ ] that the secondary osteons, which comprise the majority of the rostrum volume, are more mineralised than the surrounding matrix. This is the opposite of what is found in normal bone. If combined with a much-reduced elastic mismatch between matrix and osteons with both being much more mineralised than usual; this observation may explain some of the observed brittleness. In addi- tion to this, the rostrum osteons are not obviously lamellar in their construction. This rules out the extra toughening trick of an osteon pulling out and dissipat- ing energy within the layers of its walls a feature of normal bone and a very effective mechanism in extremely tough bone tis~ue’’~’. More importantly the secondary osteons appear to have other smaller “sat-

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ellite” osteons around them. This is unusual but has been noticed in some pathophysiologies of bone where it has been called “clustering”. The metabolic and histological changes that happen at the neck of the human femur with age[311, which have a very detrimental effect for its structural integrity and mechanical capacity, are of a :similar nature. Clusters of osteons have been reported in those areas of the femoral neck cortex that are more prone to fracture in humans[321, and up to now their existence has not been satisfactorily explained. We suggest here that there may be a link between these two biological examples. The “satellite” osteons of the rostrum may result from the attempt of the bone to repair perioste- onal cracks that open readily because of the very brittle nature and the mismatch of properties between osteons and interstitial matrix. The same may be true for the neck of the ageing femur. Local hypermineralisation, which has been observed in ageing bone, may localise damage and this may attract further remodelling. The peppered cluster osteonal effect is then probably a result of an overstimulated response, which tries to alleviate the danger by locally repairing the bone.

Some of the phenomena and the extreme mineralisation found in the rostrum may be produced by processes which, in other species, would be considered pathological, and therefore may not be representative of the true physiological extreme of hypermineralisation we are seeking to find. But then, maybe the only way of achieving such a hypermineralised tissue in-vivo is by quasi-pathological mechanisms, where normal conditions and rules break down. These aspects warrant further investigation and perhaps the more valuable ones would be provided by biochemical analysis of the rostrum growth in ontogeny, could specimens be found.

Acknowledgements The authors acknowledge the financial support provided for collaboration between Britain and Spain by an “Acciones Integradas” program. Adria Casinos was supported by a PB95-0113-C02-02 grant. Ira Laketid carried out the compositional analysis and the microhardnesb measurements of this study; Jorge

Cubo conducted the chemical composition analysis. Thanks are due to Dr Vivian De BuffrCnil of the MusCum National d’Histoire Naturelle, Paris for sup- plying the rostrum material and to Dr Keith Rogers for advising us on the mineral phase of bone.

References [ I 1 Currey, J.D. (1988). The effect of porosity and mineral con-

tent on the Young’s modulus of elasticity of compact bone. ./. Biomech., 21, 131-139.

[21 Currey, J.D. (1990). Physical characteristics affecting the tensile failure properties of compact hone. J. Biomech., 23, 8 37-844.

[3] Currey, J.D. (1979). Mechanical properties of bone with greatly differing functions. J. Biomech., 12, 3 13-3 19.

[41 Zioupos, P.. Currey, J.D., Casinos, A. and Buffrenil, V. De. (1997). Mechanical properties of the rostrum of the whale Mesoplodow densirostris, a remarkably dense bony tissue. J . Zool., Lond., 241, 725-737.

[51 BuffrCnil, V. De and Casinos, A. (1995). Observations his- tologiques sur le rostre de Mesoplodon densirosrris (Mam- malia Cetacea, Ziphiidae): le tissu osseux le plus dense connu. Ann. Sci. Nat. Zool. Biol. Anim., 16, 21-32.

[6] Zylberberg, L.. Trauh, W., Buffrknil, V. De., Allizard, F., Arad, T. and Weiner, S. (1998). Rostrum of a toothed whale: Ultrastructural study of a very dense hone. Bone, 23, 241- 247.

171 Rogers, K.D. and Zioupos, P. ( 1999). The bone tissue of the rostrum of a Mesoplodon densimsfriswhale: a mammalian hiomineral demonstrating extreme texture. J Mare,: Sci. k t t s . , 18, 651-654.

[8] Lees, S. (1987). Considerations regarding the structure of the mammalian mineralized osteoid from the viewpoint of the generalized packing model. Cnnn. Tiss. Rex., 16, 28 1-302.

[9] Olsen, B.R. and Ninomiya, Y. (1993). “Collagens” In: Guide- book to the extracellrrlar matrix and adhesion proteins, edited by Kreis, T & Vale. R., pp 32-48. Oxford University Press, Oxford.

101 Aerssens, J.. Dequeker, J . and Mhuyi-Muamba, J:M. (1994). Bone tissue composition: biochemical anatomy of hone. Clin. Rheumat., 13, S54-62.

1 I ] Broz, J.J., Simske, S.J. and Greenberg, A.R. (1995). Material and compositional properties of selectively demineralized cortical bone. J . Biomecli., 28, 1357-1368.

121 Bowman, S.M., Zeind, J., Gibson. L.J.. Hayes, W.C. and McMahon. T.A. (1996). The tensile behavior of demineralized bovine cortical bone. J . Biornech., 29, 1497-1501.

131 Sarkhar, B.C. and Chauhan, U.P.S. (1967). A new’ method for determining micro quantities of calcium in biological materials. Ancrl. Bioch. 20, 155-156.

141 Zioupos, P. and Currey, J.D. (1996). Pre-failure toughening mechanisms in the dentine of the Narwhal tusk: microscopic examination of stredstrain induced microcracking. J . Mot. Sci. Letts, 15. 991-994.

[IS] Evans, G.P., Behiri, J.C., Currey, J.D. and Bonfield, W. ( 1990). Microhardness and Young’s modulus in cortical bone exhibiting a wide range of mineral volume fractions. and in a bone analogue. J Materids Sci: Mate,: Medicine, 1, 38-43.

[ 161 Currey, J.D. and Brear. K. (1990). Hardness, Young’s modulus. and yield stress in mammalian inineralised tissues. .I Moterids Sc.i: Mote,: Medicine. 1. 14-20,

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