Characterization of the mechanical properties of leptin ... · 2.3 Nanoindentation There are many measurement methods available to determine a variety of mechanical, material properties,

Characterization of the mechanical properties of leptinreceptor-deficient mice vertebrae, using nanoindentation testsCitation for published version (APA):Ruybalid, A. P., Dickinson, M., & Geers, M. G. D. (2012). Characterization of the mechanical properties of leptinreceptor-deficient mice vertebrae, using nanoindentation tests. TU/e.

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Characterization of the mechanical

properties of leptin receptor-deficient

mice vertebrae, using nanoindentation

tests.MT 12.03

Andre Ruybalid

Supervisor:dr. Michelle Dickinson

University of AucklandDepartment of Chemical and Materials Engineering

February 11, 2012

Abstract

In order to investigate the effects of leptin receptor-deficiency on the intrinsic mate-rial properties of vertebral mice bones, a total of twenty L4-vertebrae from the leptinreceptor-deficient (db/db) and wild-type (wt) mouse phenotype were tested, using thenanoindentation method. Each of the twenty samples was indented on cortical and tra-becular bone regions, allowing for comparison between these two bone types.

No significant differences were found in intrinsic material properties of vertebrae be-tween leptin receptor-deficient and wild-type mouse phenotypes, within cortical and tra-becular bone. The reduced elastic modulus of cortical bone was found to be 24.351 ±3.179 [GPa] versus 20.238± 2.364 [GPa] for trabecular bone. From this result, the formerbone type is regarded to be stiffer than the latter. The hardness parameters were foundto be: 1.055 ± 0.135 [GPa] and 0.997 ± 0.103 [GPa] for cortical and trabecular bone,respectively. From this result, the two bone types are not concluded to significantly differin hardness.

Since the intrinsic material properties of hormonal controlled (db/db) and wild-type(control group) mouse phenotypes are found to be equal, it is concluded that the bone-mineral density of both mouse species are equal as well, and therefore µCT-scan basedbone-mineral density (BMD) measurements become a quantitative measure of density,rather than a qualitative measure of relative bone volume.

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ii

Contents

1 Introduction 1

2 Background theory 1

2.1 Leptin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2.2 Bone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.3 Nanoindentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.4 In-situ SPM imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3 Experiment methodology and data processing 5

3.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.2 Nanoindentation experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.3 Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4 Experimental results 9

4.1 Cortical bone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4.2 Trabecular bone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.3 Trabecular versus cortical bone . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5 Discussion 18

5.1 Quantitative BMD measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.2 Cortical bone stiffer than trabecular bone . . . . . . . . . . . . . . . . . . . . . 18

6 Final conclusion 20

7 Future work 20

7.1 Influence of leptin receptor-deficiency on mechanical strength . . . . . . . . . . . 20

7.2 Modeling of vertebral bone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

References 23

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1 Introduction

Bone’s excellent ability for self-repair and adaptation is what makes it a unique, complex,and dynamic material, which’s structure is constantly being remodeled. This remodeling, andthe resulting bone structure, are affected by many factors, such as mechanical loading, priorfracture, loading history, and hormone activity. The strength and fracture risk of bone are notsolely determined by bone quantity,13 which is generally described by bone-mineral density(BMD), which is a volume measure rather than a density measure, but also by bone quality,which is described by the architectural characteristics of bone at multiple scales,19 and bythe intrinsic material properties of bone. There is evidence that the microarchitecture has asignificant influence on the mechanical strength and fracture risk of bone,2,4, 17,18 making itan important feature to study.

The effects of the leptin hormone on bone are not completely known, and contradictory resultsare found in literature, where research groups report increased bone mass and BMD in leptin(receptor-)deficient rodents,9 while others report results that conclude the opposite.5,15,22

This project extends the research done by Michelle Dickinson on the effects of leptin on thequality of bone.22 The goal of this research is to characterize the material properties oftrabecular and cortical bone, coming from leptin receptor-deficient and wild-type mouse phe-notypes, by performing nanoindentation measurements (extended with in-situ SPM imaging)on twenty L4-vertebrae, and conclude the effects of leptin receptor-deficiency, by comparingthe results from leptin receptor-deficient vertebrae with the results from wild-type vertebrae.

2 Background theory

In this section, basic theory is described regarding topics discussed in this report, such asleptin, bone, nanoindentation, and in-situ SPM imaging. For further, in-depth information(such as extensive derivations of equations), the referenced material found in the bibliographyof this report is suggested for reading.

2.1 Leptin

Leptin is an important hormone in controlling appetite and metabolism, and is secreted byadipocytes. It functions as a satiety signal in the hypothalamus to regulate food intake andenergy expenditure. When fat mass is low, leptin levels drop, causing appetite to increase.Reversely, appetitive satisfaction is induced by high leptin levels, resulting from plentifulenergy supplies.22 The db/db mouse phenotype used in this research are deficient of leptinreceptor signaling, which causes hyperphagia, and consequently obesity and diabetes.20

The hypothalamus is not the only active leptin signaling site, since receptors are also presentin skeletal cell types, e.g. osteoblasts.5 It has been shown that leptin is an important regulatorof bone formation, and that it influences bone quantity,5,9, 15,22 quality,15,22 and subsequently,fracture risk and mechanical strength.5,22

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2.2 Bone

Bone is the essential material of which the body’s load-bearing, protective framework; theskeleton, is made. Consisting of mainly three constituents; water (10 wt%), collagen (65 wt%),and mineral (25 wt%), bone is considered a natural composite material, which’s hierarchi-cally structured features consist of tropocollagen molecules surrounded by mineral crystals(hydroxyapatite) at the lower microscopic scale, forming stacked lamellar sheets at the highermicroscopic scale, which make up either compact or cancellous bone at the macroscopicscale.3,19

Compact, or cortical, bone contains no large cavities other than Haversian canals, which guideblood vessels and nerve cells through the bone, and is relatively dense compared to cancellous,or trabecular, bone.

Trabecular bone is much more porous than cortical bone, and makes up less than 30 vol% ofthe total bone volume. It consists of a network of interconnected rod- and plate-like structures,called trabeculae, that are some 100 µm thick and separated by 1 mm wide cavities.19 Thequality, and thereby the strength and fracture risk, of trabecular bone are predominatelygoverned by the microarchitecture in which the number of struts, their thickness, the spacebetween them, and their connectivity play important roles.2,10,17,18,22

There is evidence that the intrinsic material properties of trabecular and cortical bone differ,and that the latter is stiffer than the former. The exact reason for this difference is notfully understood. Possible reasons are that the mineral content of cancellous bone is lessthan that of compact bone,12 and that the alignment of lamellae is less well organized intrabecular bone.6 In this project, the material properties of both types of bone are analyzedand compared.

2.3 Nanoindentation

There are many measurement methods available to determine a variety of mechanical, materialproperties, such as the tensile test, bulge test, and indentation test. To determine the intrinsicmechanical properties of materials that are independent of the geometry and structure of thebulk, these tests need to be performed on a small scale. However, not all tests are easily scaleddown, and problems arise when attempting to approach the micro- and nanometer scale.

The conventional indentation test, which’s elastic contact theory was originally described byBoussinesq and Hertz in the late 19th century,1,11 has been modified, resulting in nanoin-dentation, which is now the most commonly used method to determine material propertieson the micro- and nanometer scale. The theoretical basis of this modern technique was laidby Sneddon in 1965,21 and has been further improved by, among others, Doerner and Nix,8

and Oliver and Pharr.16

In nanoindentation, local mechanical properties are acquired by impelling an indenter tip(with a radius of only a few hundreds of nanometers) into the material’s surface, using acertain force P , resulting in a penetration depth h. The forces used for indentation rangefrom several nano-newtons up to a few newtons, and the residual indent, after the indenter tiphas been retreated from the surface, is only a few micrometers in width. The recorded loading-

2

unloading P −h curve is analyzed to compute the wanted material properties. See Figure 2.1for a schematic of the indentation test and the load-depth curve. Many mechanical parameters

P

hmax

original surface

hc

(a) indentation

depth h

load P

P , hmax max

S =max

dP

dh

hc

(b) load-depth curve

Figure 2.1: Schematic of indentation and the resulting load-depth curve, where a load P is usedto drive an indenter tip into the surface of the material, resulting in an indentation depth h.Moreover, Smax is the slope of the initial part of the unloading curve, hc is the contact depth,and hmax is the maximum indentation depth.

are obtained from nanoindentation measurements, such as hardness, elastic modulus, yieldstrength, creep properties, viscoelastic properties, fracture toughness, and residual stress. Inthis research only the first two of these examples are of interest.

Linear elastic theory is used to determine the elastic modulus E and the hardness H, despitethe fact that the behavior of the material is never fully elastic, and permanent plastic defor-mation is always present. It is, however, safe to assume that during unloading, the materialrecovers in an elastic manner, so that application of this theory to the (initial) unloading partof the measurement cycle is justified. The expressions for the elastic modulus and hardnesstake the following form:16

Er =√π

2Smax√A

(2.1)

H =Pmax

A(2.2)

where Er is the reduced elastic modulus, which accounts for the effects of the indenter notbeing perfectly rigid:

1Er

=1− ν2

E+

1− ν2i

Ei(2.3)

where E and Ei are the elastic moduli of the indented surface and the indenter, respectively,and ν and νi are the Poisson’s ratios of the indented surface and the indenter, respectively.Furthermore, in equations 2.1 and 2.2, Smax is the slope of the unloading curve at the pointof maximum load Pmax, and A is the contact area between the indenter and the indentedsurface.

3

Difficulty arises in the determination of the contact area, which is needed for the calculationof the elastic modulus and the hardness. The contact area A is dependent on the contactdepth hc, which is defined as follows:16

hc = hmax − εPmax

Smax(2.4)

where ε is a geometric constant, which is determined by the geometry of the indenter tip. Fora Berkovich indenter, which is widely used, the contact area is now defined as:

A(hc) = 24.5h2c (2.5)

ε = 0.75 (2.6)

Equation 2.5 holds for a perfectly sharp indenter tip, which does not exist in reality. Therefore,as this equation gives an estimation of the area function, the actual contact area needs tobe determined for each individual indenter tip. A description of this procedure is given byOliver and Pharr,16 and is based on the assumption that the elastic modulus is independentof the indentation depth.

2.4 In-situ SPM imaging

The nanoindentation measurements performed in this research are extended with in-situ Scan-ning Probe Microscopy (SPM), with which an image of the to-be-indented and/or indentedarea is obtained. This technique makes it possible for accurately determining the positionswhere indentation measurements are to be performed, and analyzing the residual indents, af-ter indentation measurements are completed, which helps in the investigation and explanationof possible outliers in the indentation data.

In in-situ SPM, the same indenter tip used for nanoindentation also serves as the scanningprobe in the imaging procedure, which is illustrated in Figure 2.2. This type of imaging

scan direction

SPM image of indentindenter tipand probe

Figure 2.2: A schematic of an indenter tip functioning as an SPM probe to image the previouslyindented area. The arrow illustrates the scanning behavior of the probe when an SPM image isbeing produced.

resembles contact Atomic Force Microscopy (AFM). The SPM probe makes contact with thesurface of the material, using a very low, predefined set-force. This set-force is kept con-stant whilst the device scans the material surface, and any minor alteration in the measuredfeedback force is adjusted for, by moving the probe in the out-of-plane direction (closer to,or away from the surface, depending on the feedback force being smaller or larger than the

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set-force).7 The displacement caused by adjusting the probe’s vertical position is measured,and any height differences in the surface of the material are thereby captured. The result isa topographical surface-height image of the scanned area, in which positional differences inbrightness represent positional differences in height. The resolution of such an SPM measure-ment is limited by the probe’s radius of curvature, which is, in this research, of the order ofhundreds of nanometers.

Advantages of using the same tip for nanoindentation as well as to image the surface, includetime efficiency, positional accuracy, local data confirmation, and the feasibility of locallyperforming surface roughness measurements.7

3 Experiment methodology and data processing

This section explains all the methods used in preparing the samples, executing the experi-ments, and processing the experimental data. In addition, the devices and their specificationsused for the experiments are described.

3.1 Sample preparation

Twenty mice vertebrae; ten from leptin receptor-deficient (db/db) mice and ten from wild-type(wt) mice, were prepared for nanoindentation measurements in three steps.

The already trimmed and cleaned vertebrae, which had been stored in ethanol at a lowtemperature of 4◦C, were firstly mounted, using Loctite 401 glue, to an aluminum disk witha diameter of 30 mm, of which a photograph is shown in Figure 3.1 (a). Subsequently, the

(a) vertebrae on disk (b) vertebrae in epoxy

Figure 3.1: Photographs of the vertebrae glued to an aluminum disk (a), and of the vertebrae inthe epoxy stub (b). The aluminum disk was placed in a cast, which was filled with epoxy resin.After the resin had cured, it was taken out of the cast, after which the aluminum disk was removedby a grinding procedure.

aluminum disk was placed in a cast, which had the same diameter as the disk. The castwas then filled with Nuplex K36 epoxy resin, which has a curing temperature of 70◦C and a

5

curing time of 48 hours.

After the resin had hardened, the epoxy stub, with the vertebrae, was removed from the cast,and the aluminum disk was ground off, using silicon-carbide paper with a grit size of P80. Inorder to smoothen the relatively rough surface of the now exposed vertebrae, further grindingwas done in three subsequent stages, using silicon-carbide paper with progressively finer gritsizes: P220, P500, P1200.

After it was confirmed, by optical microscopy, that the vertebrae surfaces were smooth enough(no visible scratches), the final step of polishing was performed. This was done in threestages, using polishing cloths with progressively smaller diamond beads with diameters of3 µm, 2 µm, and 1 µm. After each stage, the diamond beads were rinsed off the samplesusing a mild detergent, which, in turn, was removed by pure ethanol. Finally, the ethanolwas evaporated by hot air from a blow dryer. A photograph of the epoxy stubs, containingthe vertebrae, is shown in Figure 3.1 (b).

3.2 Nanoindentation experiments

The nanoindentation tests were performed with a Hysitron TI950 Triboindenter, which isalso capable of imaging the sample surface (in-situ SPM), using the indenter tip as a probe.Information regarding the resolution, and other specifications of the used transducer of thisapparatus are listed in Table 3.1.14 As mentioned earlier, twenty vertebra samples were

z-axis x-axisMaximum force 10 mN 2 mNLoad resolution 1 nN 3 µNMaximum displacement 5 µm 15 µmDisplacement resolution 0.04 nm 4 nm

Table 3.1: Specifications regarding the transducer of the nanoindentation device.

tested; ten from each mouse phenotype (db/db and wt). The samples were tested blindly,meaning that at the moment of testing it was unknown from which mouse phenotype thesample originated. Each vertebra sample was tested in three different regions, and withineach region a total of sixteen indents were performed. The Triboindenter contains an opticalmicroscope, with which a region of interest (trabecular or cortical bone) was selected beforethe indentation procedure was initialized. An example of a microscopic image of a region ofinterest is shown in Figure 3.2.

After a region of interested had been selected, a 50 by 50 µm area of a bone was imaged,making use of the SPM imaging functionality of the Triboindenter, and the exact positionsof the sixteen indents were selected on this SPM image. This is also illustrated in Figure 3.2,where the green circles in the SPM image are the selected indentation positions.

The load frame compliance and the area function of the indenter tip had been calibratedusing the method of Oliver and Pharr16 on fused quartz of which the hardness and elasticmodulus are known. Additionally, a calibration between the tip and the optical systemwas performed, to ensure correct alignment, and air indents were carried out before each

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A

B C

microscopic imageSPM image

Figure 3.2: Illustration of the three regions (A, B, and C) of a sample in which indentationmeasurements were performed. These indentation regions were selected using optical microscopicimages, of which an example is seen in this figure. Such a microscopic image has a size of:781.5 x 608.2 µm. An SPM image of a 50 x 50 µm area was used to select the sixteen indentationpositions, which are seen as green circles.

measurement in order to weigh the tip, and account for any changes in mass, due to wear.The sixteen load controlled indentation measurements were hereafter automatically performedby the Triboindenter, using a diamond Berkovich tip with a radius of curvature of 150 nmand a pre-specified load function. The load function increased the load from 0 to 2000 µNin 5 seconds, subsequently held this maximum force for 3 seconds, and finally decreased theload back to 0 N in 5 seconds. A plot of the load function is shown in Figure 3.3.

0 1 2 3 4 5 6 7 8 9 10 11 12 130

500

1000

1500

2000

time [s]

forc

e [µ

N]

Figure 3.3: A plot of the load function used for the nanoindentation tests.

After an indentation measurement, consisting of sixteen indents, was completed, another SPMimage was made of the indented area (50 x 50 µm), which allowed for the investigation ofthe residual indents. The indents are best observed in an SPM gradient image, which showsthe gradient of the change in height in the surface. An example of such an image, in whichresidual indents are seen, is shown in Figure 3.4 of the next subsection (3.3).

Each vertebra sample was measured twice by the above described procedure, where trabecularbone and cortical bone were selected as the regions of interest. Hence, sixteen indents were

7

performed on three different regions within each of the twenty vertebra samples, and this wasdone twice (once for cortical and once for trabecular regions), resulting in a total number of1920 indentation tests.

3.3 Data processing

The load-displacement data, obtained by the Triboindenter, were analyzed using the Oliverand Pharr method,16 which was explained in section 2.3. Boxplots were used to analyze thevariation in the hardness and elastic modulus parameters between the different samples, andwill be presented in section 4. The boxes in the boxplots represent the interquartile range(IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1) ofthe data. Furthermore, the sixteen data points, the extreme outliers, the median, the meanvalue, and the standard deviation (σ) of each measurement’s data set are shown in theseplots. The standard deviation is calculated as follows:

σ =

(1

n− 1

n∑i=1

(xi − x)2) 1

2

(3.1)

where xi is the value of data point i, x represents the mean value of the data, and n is thetotal number of data points of each measurement.

Abnormal outliers in the data were analyzed using the load-displacement data and the SPMgradient images of the residual indents, of which an example is shown in Figure 3.4. Mea-surement results corresponding to abnormal indents are excluded from the data, and aretherefore not taken into account in the analyses of the statistical data (boxplots). Reasonsfor exclusion of data are: (1) indents performed on epoxy, (2) shift of the load-displacementcurve (increase of load not starting in the depth origin), (3) an indent performed on the edgeof a topographical peak or valley in the surface.

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Indents in epoxy

Figure 3.4: Image showing the load-displacement curves and the SPM micrographs of sixteenindents performed on a bone region. Data is excluded by analyzing abnormal load-displacementcurves and the corresponding indents. The indents marked by the red ellipse are performed inepoxy, which is softer than bone, and are represented by the curves with a higher maximum depth,and by the larger residual indents in the SPM gradient image (bottom right image). The meanvalues of the elastic modulus and the hardness over the sixteen indents are also shown in theload-displacement curves.

4 Experimental results

The experimental results from the nanoindentation measurements, performed on vertebraefrom leptin receptor-deficient and wild-type mice are presented for cortical and trabecularbone.

4.1 Cortical bone

In Figures 4.1 and 4.2, the elastic and hardness parameters of cortical bone from the twentyvertebra samples are shown by boxplots, where the mean ± Standard Error of the Mean(SEM) is shown in each plot.

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0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 3202468

10121416182022242628303234

measurement number

elas

tic m

odul

us [G

Pa]

dataσmeanextremesmedianQ1 ↔ Q3

mean elastic modulus: 24.6651 ± 2.7354 [GPa]

(a) db/db

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 3202468

10121416182022242628303234

measurement number

elas

tic m

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Pa]



(b) wt

Figure 4.1: Boxplots showing the elastic moduli of cortical bone from db/db (a) and wt (b)vertebra samples, where the mean ± SEM is shown.

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0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 320

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

measurement number

hard

ness

[GP

a]


mean hardness: 1.0294 ± 0.13497 [GPa]

(a) db/db

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 320

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

measurement number

hard

ness

[GP

a]



(b) wt

Figure 4.2: Boxplots showing the hardness parameters of cortical bone from db/db (a) and wt (b)vertebra samples, where the mean ± SEM is shown.

No significant differences in the material parameters, between the db/db and wt vertebrae,are observed from these results. These results are once more presented in Figure 4.3, byboxplotting the mean values of the elastic and hardness parameters of each measurement’sdata set from db/db and wt samples.

11

14

16

18

20

22

24

26

28

30

db/db wt

elas

tic m

odul

us [G

Pa]


(a) elastic modulus

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

db/db wt

hard

ness

[GP

a]


(b) hardness

Figure 4.3: Boxplots showing the mean elastic (a) and hardness (b) parameters of cortical bonefrom db/db and wt samples. These boxplots are acquired from the average values of eachmeasurement’s data set which consists of sixteen indentation results.

4.2 Trabecular bone

In Figures 4.4 and 4.5, the elastic and hardness parameters of trabecular bone from thetwenty vertebra samples are shown by boxplots, where the mean ± Standard Error of theMean (SEM) is shown in each plot.

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(a) db/db

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 3202468

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measurement number

elas

tic m

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Pa]



(b) wt

Figure 4.4: Boxplots showing the elastic moduli of trabecular bone from db/db (a) and wt (b)vertebra samples, where the mean ± SEM is shown.

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0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 320

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

measurement number

hard

ness

[GP

a]



(a) db/db

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 320

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

measurement number

hard

ness

[GP

a]



(b) wt

Figure 4.5: Boxplots showing the hardness parameters of trabecular bone from db/db (a)and wt (b) vertebra samples, where the mean ± SEM is shown.

Just as in the results for cortical bone, no significant differences in material parametersbetween the db/db and wt vertebrae are observed from these results. These results are oncemore presented in Figure 4.6, by boxplotting the mean values of the elastic and hardnessparameters of each measurement’s data set from db/db and wt samples.

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14

16

18

20

22

24

26

db/db wt

elas

tic m

odul

us [G

Pa]


(a) elastic modulus

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

db/db wt

hard

ness

[GP

a]


(b) hardness

Figure 4.6: Boxplots showing the mean elastic (a) and hardness (b) parameters of trabecularbone from db/db and wt samples. These boxplots are acquired from the average values of eachmeasurement’s data set which consists of sixteen indentation results.

4.3 Trabecular versus cortical bone

Since no significant differences in the material properties are observed between db/db and wtmice vertebrae, the elastic modulus and hardness data from db/db and wt vertebrae arealtogether plotted for trabecular and cortical bone regions in Figures 4.7 and 4.8, in order tocompare the material properties of these two types of bone. The mean ± Standard Error ofthe Mean (SEM) is shown in each plot.

15

0 5 10 15 20 25 30 35 40 45 50 55 6002468

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elas

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Pa]



(a) cortical

0 5 10 15 20 25 30 35 40 45 50 55 6002468

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measurement number

elas

tic m

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Pa]



(b) trabecular

Figure 4.7: Boxplots showing the elastic moduli of cortical (a) and trabecular (b) bone from db/dband wt vertebra samples, where the mean ± SEM is shown.

16

0 5 10 15 20 25 30 35 40 45 50 55 600

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

measurement number

hard

ness

[GP

a]



(a) cortical

0 5 10 15 20 25 30 35 40 45 50 55 600

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

measurement number

hard

ness

[GP

a]



(b) trabecular

Figure 4.8: Boxplots showing the hardness parameters of cortical (a) and trabecular (b) bonefrom db/db and wt vertebra samples, where the mean ± SEM is shown.

As is seen in these plots, the elastic modulus of cortical bone is higher than the elastic modulusof trabecular bone in vertebrae. There is, however, less difference in hardness between thetwo types of bone. This result is once more presented in Figure 4.9, by boxplotting the meanvalues of the elastic and hardness parameters of each measurement’s data set from trabecularand cortical bone.

17

14

16

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trabecular cortical

elas

tic m

odul

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Pa]


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0.8

0.9

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trabecular cortical

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Figure 4.9: Boxplots showing the mean elastic (a) and hardness (b) parameters of trabecular andcortical bone. These boxplots are acquired from the average values of each measurement’s dataset which consists of sixteen indentation results.

5 Discussion

5.1 Quantitative BMD measurements

When it is not established that, locally, the material density of bone mineral is equal for dif-ferent mouse or bone types, bone-mineral density (BMD) measurements do not quantitativelydisclose anything about bone density, but can merely be used to qualitatively compare relativebone volume. The results, shown in Figures 4.3 and 4.6, show that leptin receptor-deficiencyhas no effect on the local, intrinsic material properties of cortical and trabecular bone in micevertebrae. Therefrom it is deduced that the mineral density (e.g. hydroxyapatite) is equal forboth mouse phenotypes, and hence, that bone-mineral density (BMD) measurements, basedon µCT-scans of vertebral bones from db/db and wt mice, become quantitative measures forbone density, instead of qualitative measures for relative bone volume.

5.2 Cortical bone stiffer than trabecular bone

To investigate the difference in results between cortical and trabecular bone, EnvironmentalScanning Electron Micrographs (ESEM) and SPM images of both bone types from micevertebrae are shown in Figure 5.1.

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(a) ESEM: cortical (b) ESEM: trabecular

(c) SPM: cortical (d) SPM: trabecular

Figure 5.1: ESEM (a, b) and SPM (c, d) images showing cortical (a, c) and trabecular (b, d)bone regions from mice vertebrae. The horizontal field width is 45.07 µm in the ESEM imagesand 50 µm in the SPM images.

The ESEM images show no clear differences regarding homogeneity and structure. However,from the SPM images (in which indents are also seen) it is observed that the lamellae are, incortical bone, clearly oriented in a certain direction, while this is not observed in SPM imagesof trabecular bone. Despite the fact that the lamellae seen in the SPM image are organized inthe in-plane direction (direction within the viewed plane of the SPM images), while the loadingin the nanoindentation tests was performed in the out-of-plane direction (perpendicular to theimaged plane), this shows that cortical bone is more structurally organized than trabecularbone, and therefore it is reasonable to assume that also the out-of-plane stacking of lamellaeis better structured. This structural organization of bone material is a possible reason forcortical bone being stiffer than trabecular bone, and is in agreement with the findings madeby Currey.6

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6 Final conclusion

• Leptin receptor-deficiency affects neither cortical nor trabecular, vertebral bone in mice,since no significant difference in intrinsic material properties was found between verte-bral bone from leptin receptor-deficient (db/db) and wild-type (wt) mouse phenotypes.

• Cortical bone was found to be stiffer than trabecular bone in vertebrae from both leptinreceptor-deficient (db/db) and wild-type (wt) mouse phenotypes. The reduced elasticmodulus of cortical bone was found to be 24.351±3.179 [GPa] versus 20.238±2.364 [GPa]for trabecular bone.

• No significant difference in hardness was found between cortical and trabecular, verte-bral bone from both leptin receptor-deficient (db/db) and wild-type (wt) mouse pheno-types. The hardness parameters were found to be: 1.055 ± 0.135 [GPa] and 0.997 ±0.103 [GPa] for cortical and trabecular bone, respectively.

• µCT-scan based BMD measurements from mice vertebrae can be quantitatively an-alyzed, since it was found that there is no significant variance in intrinsic materialproperties, and therefore in bone mineral density, within mice species and betweenhormonal controlled mice species (db/db and wt). Cortical and trabecular, vertebralbone should be treated separately from one another, when using µCT-scan based BMDmeasurements, since it was found that these two bone types differ in intrinsic materialproperties, and therefore it cannot be assumed that their mineral densities are equal.

7 Future work

7.1 Influence of leptin receptor-deficiency on mechanical strength

Now that it is established that BMD measurements are useful to quantify bone density in micevertebrae, they can, together with (1) the investigation of vertebral microarchitecture fromdb/db and wt mice, and (2) other mechanical tests (e.g. whole vertebrae compression tests),conclude on the effects of leptin receptor-deficiency on vertebral bone quality and quantity,and on the consequent effects of these bone characteristics on mechanical bone strength.

7.2 Modeling of vertebral bone

Due to the complexity of bone material and its remodeling behavior, a realistic predictivefailure model of vertebral bone is difficult to realize, and requires knowledge of (1) the intrin-sic material properties of bone, (2) the geometry and architecture of the modeled vertebrae,(3) the BMD of the modeled vertebrae, (4) the constitutive behavior of bone, (5) the re-modeling behavior of bone, (6) the hormonal, environmental, and genetic effects on all ofthe formerly described features, and (7) the loading and boundary conditions which are (inreality) applied to the vertebrae.

By transforming µCT-scans from mice vertebrae into finite element (FE) models, which consistof a discrete number of elements, the geometry, architecture, and BMD of these bones are

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captured and taken into account in the model. Furthermore, the results obtained in thisresearch project, regarding the intrinsic material properties of vertebral bone from db/dband wt mice, can be used to contribute to an FE model that is able to capture the effects ofquality and quantity of vertebral bone on its failure behavior, in order to predict the loads atwhich failure occurs.

Optimization of such a model’s constitutive equations, and failure criteria, is possible bycomparing the model results to actual results from mechanical tests, such as compression testson whole vertebrae. It should be noted that, in order to compare a model to a mechanicaltest, the loading and boundary conditions of the model and the realistic situation must beequal.

Eventually, an adequate bone model that takes into account all bone features (quality andquantity), allows for non-invasive bone failure prediction, which is useful for the diagnosis ofbone diseases and the monitoring of treatment in e.g. osteopenia and osteoporosis. Currently,bone biopsies are performed for these purposes, which are traumatic and painful for thepatient.

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