The associations between mineral crystallinity and the mechanical properties of human cortical bone.pdf

Bone 42 (2008) 476

–

482

www.elsevier.com/locate/bone

The associations between mineral crystallinity and the mechanical

properties of human cortical bone

Janardhan S. Yerramshetty a , Ozan Akkus b,

⁎

a Bone and Joint Center, Henry Ford Health System, Detroit, MI, USA

b Weldon School of Biomedical Engineering, 206 S. Martin Jischke Drive, Purdue University, West Lafayette, IN 47907-2032, USA

Received 31 July 2007; revised 19 October 2007; accepted 2 December 2007

Available online 14 December 2007

Abstract

It is well known that the amount of mineralization renders bone its stiffness. However, besides the mere amount of the mineral phase, size and

shape of carbonated apatite crystals are postulated to affect the mechanical properties of bone tissue as predicted by composite mechanics models.

Despite this predictive evidence, there is little experimental insight on the relation between the characteristics of mineral crystals and hard tissue

mechanics. In this study, Raman spectroscopy was used to provide information on the crystallinity of bone's mineral phase, a parameter which is

an overall indicator of mineral crystal size and stoichiometric perfection. Raman scans and mechanical tests (monotonic and fatigue; n=64 each)

were performed on the anterior, medial, lateral and posterior quadrant sections of 16 human cadaveric femurs (52 y.o. – 85 y.o.). The reported

coefficient of determination values (R 2 ) were adjusted for the effects of age to bring out the unbiased contribution of crystallinity. Crystallinity was

able to explain 6.7% to 48.3% of the variation in monotonic mechanical properties. Results indicated that the tissue-level strength and stiffness

increased with increasing crystallinity while the ductility reduced. Crystallinity explained 11.3% to 63.5% of the variation in fatigue properties.

Moduli of specimens with greater crystallinity degraded at a slower rate and, also, they had longer fatigue lives. However, not every anatomical

quadrant displayed these relationships. In conclusion, these results acknowledge crystal properties as an important bone quality factor and raise the

possibility that aberrations in these properties may contribute to senile osteoporotic fractures.

Keywords: Osteoporosis; Strength; Fatigue life; Spectroscopy; Mineralization

Introduction

tissue, yet, excessive mineralization has a negative effect on

tissue ductility when observed using various species [10] or

human bones [5] .

Much less investigated is the relation of the shape and

stoichiometry of mineral crystals on the mechanics of bone

tissue [16] . Changes in the crystal size [17] and/or lattice

perfection are reflected in the crystallinity measure obtained by

using infrared or Raman spectroscopy [14,18

Mineral crystals of bone form within the collagen template

after a fast primary and a protracted secondary mineralization

stages [1,2] . The longer c-axes of crystals are aligned along the

longer axis of collagen fibers [3] . Mineral crystals are reported

to be plate- [3] or needle-shaped [4] and they are relatively

poorly crystalline due to the presence of impurities. The average

dimensions of crystals are small, around 5×5×20 nm, render-

ing non-stoichiometric substitutions of ions like carbonate,

fluoride, chloride easier [4] . Contribution of the mineral phase

to the mechanics of bone is investigated in great detail in terms

of its amount, i.e. the so called degree of mineralization [5

27] . Specifically

for Raman spectroscopy, we have demonstrated that c-axis

length of crystallites is correlated with the crystallinity measure

[17] . Also reported is the broadening of the phosphate sym-

metric stretch peak (i.e. reducing crystallinity) with increasing

carbonate content [17,19] . Increasing crystal dimensions may

affect bone mechanics by inducing residual stresses in their

vicinities [3,14] . Non-stoichiometric substitutions are known to

modify crystal size, resulting in microstrains within and around

the crystal lattice [22,24,28,29] . Composite mechanics models

of collagen/mineral phases predict that the aspect ratio of crystal

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16] .

These studies have repeatedly demonstrated that increased

degree of mineralization imparts strength and stiffness to bone

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⁎ Corresponding author. Fax: +1 765 496 1912.

E-mail address: ozan@purdue.edu (O. Akkus).

doi: 10.1016/j.bone.2007.12.001

J.S. Yerramshetty, O. Akkus / Bone 42 (2008) 476 – 482

477

32] . However,

there is not much experimental evidence on the relation between

tissue mechanics and crystallite size, geometry and perfection.

Earlier Akkus et al. reported that crystallinity of bone's apatite is

a correlate of elastic properties of rat cortical bone. Apart from

this limited knowledge on rat bone, the role of crystallinity in

bone tissue mechanics is poorly understood for human bone.

This study aims to increase the current understanding by as-

sessing the relation between monotonic and fatigue properties of

human cortical bone and its crystallinity. The substantial overlap

of bone mineral density (BMD) scores between healthy indi-

viduals and patients who experience fractures [33] calls for novel

diagnosable measures to supplement BMD information for

refined estimation of the fracture risk. Therefore, verification of

crystallinity as a correlate of bone's ductility would be valuable.

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from the load – strain data by converting load to stress, using the cross-sectional

area of gage regions. Modulus, yield stress, yield strain, fracture stress, fracture

strain, resilience and toughness (i.e. energy absorbed to fracture) were calculated

using a custom written Matlab code (The Mathworks, Inc, Natick, MA). Yield

point was identified from the intersection of the stress – strain curve and a line

constructed parallel to the initial linear region with the slope of modulus value at

0.2% of the strain data.

The other set of sixty four specimens were fatigued in tension sinusoidally at

2 Hz. Fatigue loading was conducted until failure. Strain was measured using a

clip-on strain gage extensometer (Epsilon Tech. Corp., WY, USA). Fatigue tests

were conducted using load-controlled feedback at a load level that created an

initial strain of 0.4% for all specimens, thereby, creating similar initial loading

conditions for bones of varying stiffnesses. Samples were kept wet during the

entire test using a customized water irrigation system. Maxima and minima of

load and strain data were acquired at each cycle and these loads were later

converted to stresses using cross-sectional areas of gage regions. Secant

modulus (E) was calculated as the ratio of stress amplitude ( σ max – σ min ) to strain

amplitude ( ɛ max – ɛ min ). The percentage of modulus degradation (D n =E n / E i ×

100, n: nth cycle, i: 1st loading cycle) was calculated as a function of loading

cycles. Similar to earlier studies [36,37] , degradation curves displayed three

regions: I

Materials and methods

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initial modulus loss, II

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a protracted modulus degradation, and

rapid modulus degradation before failure. Slopes of degradation curves

(% degradation per cycle) were calculated within region I (S1), region II (S2)

and the number of cycles to failure (C3) was recorded for each specimen ( Fig. 1 ).

Crystallinity obtained from the gage region of each specimen allowed

establishing relationships between monotonic/fatigue properties and crystal-

linity. Pearson's correlations (r, linear correlation) were established to assess the

significance of relationships between mechanical properties and the crystallinity.

Fatigue properties were analyzed in logarithmic form. Along with regressions

between crystallinity and mechanical properties for individual quadrants,

regressions were also conducted after data were pooled over the four quadrants

(i.e. 64 specimens from four quadrants were included in the regression). The

relations were reported as significant at the level of P ≤ 0.05 and as marginally

significant at the level of 0.05 b P b 0.1. Outliers were diagnosed by using

Cook's distance value. The observations with a Cook's distance value greater

than 0.5 were excluded from regression analysis. Cook's distance combines

leverage and standardized residual into one overall measure of how unusual an

observation is [38] . Leverage indicates if an observation has unusual predictors

(x variable), and standardized residual indicates if an observation has an unusual

response (y variable). As the age range in this study was broad, significant

relationships between crystallinity and mechanical properties could be

confounded, indirectly, by other parameters related with age (such as the degree

of mineralization, collagen orientation, porosity, osteonal density, etc.).

Accordingly, the reported correlations were adjusted for age using partial

correlation analysis (The Minitab Inc., State college, PA, USA). Partial

correlation coefficient is computed by regressing two variables while controlling

for the effects of age. Therefore, the relations reflect the effects of predictors on

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Sixteen cadaveric human femurs from male donors (52 – 85 y.o.) were

collected from the following institutes, the Musculoskeletal Tissue Foundation

(Edison, NJ), the National Disease Research Interchange (Philadelphia, PA), the

International Institute for the Advancement of Medicine (Jessup, PA) and the

Department of Health and Mental Hygiene (Baltimore, MD). Donors had no

recorded history of musculoskeletal diseases. Sixty millimeter long segments of

the diaphyseal shaft were cut distal to the lower trochanter using a high-speed

saw with a diamond-coated wafer blade (MK Diamond Products Inc., Torrance,

CA, USA). These rings were first divided into anterior, posterior, medial and

lateral quadrants, and each quadrant was machined into two beams using a low-

speed saw (Model 660, South Bay Technology Inc., San Clemente, CA, USA),

resulting in a total of 128 specimens. These beams were further machined to

coupon-shaped tensile specimens using a table-top mini milling machine

(Sherline Products Inc., Vista, CA, USA) with a reduced gage region of

5×2×1mm [17] . Two tensile specimens were obtained from each quadrant, one

of which was assigned for tensile-monotonic tests and the other for tensile-

fatigue tests. The tensile stress was applied along the longer axis of the

diaphyseal shaft.

Physicochemical analysis

1700 cm − 1 ) were obtained from both

sides of gage regions of all tensile specimens. Scans were conducted while the

sample was immersed in calcium supplemented saline solution using water

immersion objective. In Raman analysis, photons interact with the material and

the energy of some scattered photons differs from the incident ones. The extent

of the difference between the energies of incident and scattered photons is a

function of the particular chemical bond with which the photon interacts.

Therefore, the Raman spectrum [17] includes information on the types, amounts

and status of chemical bonds in the volume investigated. In Raman spectrum of

bone, phosphate symmetric stretch peak (at ∼ 960 cm − 1 ) was used to assess the

crystallinity of mineral, which was calculated as the inverse of the width of the

phosphate band at half the maximum intensity value (FWHM). Earlier, it was

shown that stoichiometrically more perfect mineral crystals yield greater

Raman-based crystallinity value [34,35] . Our earlier investigation revealed that

crystallinity measure is also positively correlated with the length of crystallites

along the c-axis [17] .

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Mechanical tests

As Raman analysis is non-destructive, the same specimens were subjected to

monotonic tests. Sixty four specimens were monotonically tested to failure in

tension at the rate of 1%/s using an electromagnetic testing machine (ELF 3200,

Enduratec, Minnetonka MN). Strain was measured with a clip-on strain gage

extensometer (Epsilon, Tech. Corp., WY). Stress – strain curves were established

Fig. 1. A typical modulus degradation curve with respect to normalized cycles.

Three regions (I, II and III) were identified for most of the specimens. S1 and S2

indicate the slopes (modulus degradation rate) of region I and II, respectively

and C3 indicates the number of cycles at failure.

length to width and the spacing between mineral crystals affect

the anisotropic elastic properties of bone [30

III

Arrays of 11×30 Raman spectra (800

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J.S. Yerramshetty, O. Akkus / Bone 42 (2008) 476 – 482

response without the interference of age as a factor. Fatigue properties were also

adjusted for stress amplitude, along with age, as other studies reported the

influence of initial stress on fatigue life [39 – 42] .

crystallinity indicating that the modulus of bone tissue with

longer crystals degraded more slowly. In addition, the positive

correlation between fatigue lifetime (C3) and crystallinity in-

dicates that samples with greater crystallinity had longer fatigue

lives. It was observed that the modulus degradation rate in-

creased with age while fatigue lifetime decreased with age.

Results

Correlations of crystallinity with monotonic properties

indicated significant relationships for some of the anatomical

quadrants ( Figs. 2 and 3 ). The yield strength (medial, pooled),

fracture strength (medial, pooled) and moduli (lateral, posterior,

and pooled) increased with increasing crystallinity, indicating

that increasing crystal length along c-axis benefits tissue-level

strength and stiffness. However, deformability of bone suffered

a decline with increasing crystallinity as reflected by decreasing

yield strain and fracture strain in the lateral quadrant. As these

correlations are adjusted for age, reported relations are specific

to the crystallinity parameter. Crystallinity did not change with

age, while yield and fracture strength reduced with age.

Correlations between crystallinity and several of the fatigue

properties were also significant for certain quadrants ( Fig. 4 ).

Modulus degradation rate (S2) related inversely with mean

Discussion

32] , there is a lack of experimental insight in this regard. This

study was able to demonstrate significant relationships between

crystallinity of the mineral phase and both monotonic and fatigue

properties of cortical bone tissue. Earlier composite mechanics

model [31] predicted that crystals with greater aspect ratios

(length/width ratio) should have greater modulus which is

corroborated by the current experimental result that samples

with more crystalline mineral phase had greater moduli. There are

certain limitations and assumptions that need to be set forth.

Specimens were prepared from femoral proximal diaphysis and

Fig. 2. Significant relationships between crystallinity and monotonic properties for individual quadrants. Regression coefficients indicated on the figures are R 2 values

adjusted for age.

Although composite mechanics models predict associations

between crystal size/geometry and bone's mechanical properties

[30

–

J.S. Yerramshetty, O. Akkus / Bone 42 (2008) 476 – 482

479

Fig. 3. Significant relationships between crystallinity and monotonic properties for pooled data. Regression coefficients are R 2 values adjusted for age.

whether these results apply to cortices of other bones or to the

trabecular bone remains to be investigated. Additionally, the

results are applicable to tensile loading mode only. The results

were reported after adjusting for the effects of age, therefore,

potential confounding effects due to age-related changes in

modulus, degree of mineralization or porosity should be minimal.

Crystallinity versus monotonic properties

Collagen provides bone with flexibility and tensile strength

while mineral crystals render bone its rigidity and compressive

strength [2,8,14,43,44] . To date, amount of mineralization, histo-

logical variables (porosity, osteonal density etc.) [7,13,45,46] ,

Fig. 4. Significant relationships between crystallinity and fatigue properties for individual and pooled data. Regression coefficients are R 2 values adjusted for age and

stress.

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J.S. Yerramshetty, O. Akkus / Bone 42 (2008) 476 – 482

collagen quality (cross linking, orientation etc.) [13,47,48]

have been reported as correlates of bone's material properties.

The current results bring the quality of mineral crystallites

into this picture where the stoichiometric perfection and size

of crystallites correlated with elastic as well as post-yield

mechanical properties of bone tissue. Correlation of crystal-

linity with post-yield mechanical properties of bone is

particularly interesting as the current thought assumes the

mechanics of the post-yield region to be predominantly

governed by the collagen. To the best of our knowledge, there

have not been other reports on the involvement of any mineral

related parameter with post-yield properties.

The growth pattern of carbonated apatite crystals over

decades occurs in an anisotropic fashion and crystals become

more elongated as they mature [3,16,21,24] . The mechanical

outcome of this growth pattern is estimated as bone becoming

the stiffest along the direction of longer axis of the crystal [31] .

Mineral crystals accumulate, grow [1,2,21] and may fuse with

adjacent crystallites, which may be providing the additional

tensile strength and stability to the collagen structure. In attes-

tation of this prediction, we observed that the modulus increased

with increasing crystallinity which indicates a more mature and

elongated crystal status [24] . Rho et al. observed the same trend

along the long axis of collagen fibers in herring bones [16] . Our

results also indicated that crystallinity benefited fracture strength

but decreased the ability to deform as per reduced fracture strain.

The predictive power of the regression has ranged from low to

moderate (R 2 (adj) =15%

predictors are also correlated amongst each other and it is a major

challenge to design an experiment (in vivo or in vitro) to control

single parameter without changing the other. The current study

alleviated the possibility that the observed correlations between

crystallinity and mechanical parameters result from an implicit

dependence on age-related factors by way of adjusting the age

effect via partial correlation analysis.

A recent study by Kazanci et al. [49] , indicated that the

intensity of the phosphate and amide I peaks is strongly affected

by the orientation of specimens with respect to the polarization

direction of incident laser, while amide III was not affected. If

orientation had a confounding effect on our results then amide I

and amide III intensities should not correlate as the former

depends on orientation whereas the latter does not. Our analysis

reported a significant correlation between the two, suggesting

that Raman data may not have been affected by the orientation

factor. This outcome likely depends on the following differ-

ences between this study and the study by Kazanci et al.: 1)

current study had much smaller magnification (10

48%). The net mechanical function of

bone is the combined outcome of many variables such as mineral

content, osteonal density, collagen fiber orientation, collagen

crosslinks, non-collagenous matrix proteins and other factors.

Given the hierarchical nature and the complexity of bone, there

is no single parameter which would predict mechanical function

of bone adequately by itself. Therefore, the level of correlation

reported for crystallinity in the current study should be inter-

preted in this context. Another level of complexity is that the

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Fig. 5. A proposed mechanism by which the crystal length can affect deformability of bone tissue. Left schema shows collagen molecules with smaller crystallites and

consequently greater number of unreinforced interdigital regions with greater extension under load whereas the schema on the right side shows larger crystallites with

consequently fewer unreinforced regions.

m spot size)

than the study by Kazanci et al. in which spectral data sourced

from individual lamella. Therefore, in our case the data were

averaged out over several lamellae. 2) The confocal option was

fully enforced in the study by Kazanci et al., therefore, the

sampling depth in the z-axis was very limited. In our case our

confocal aperture was fully open to maximize the sampling

depth, again, resulting in volume averaging effects countering

the orientation effects. However, we cannot rule out the fact

that the bandwidth of the phosphate peak may be orientation

dependent.

The mechanism(s) by which a longer or more mature mineral

crystal increases modulus or decreases failure strain is un-

known. These effects may function directly, or indirectly by

way of affecting collagen [14,25] . Longer crystals may present a

greater surface area over which the chemical attractions [50]

between collagen mineral phases may tether the mobility of

collagen molecules [51] more efficiently; thereby, reducing

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