UvA-DARE is a service provided by the library of the University of Amsterdam (http://dare.uva.nl)

UvA-DARE (Digital Academic Repository)

The physiology of habitual bone strains

de Jong, W.C.

Link to publication

Citation for published version (APA):de Jong, W. C. (2011). The physiology of habitual bone strains.

General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s),other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons).

Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, statingyour reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Askthe Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam,The Netherlands. You will be contacted as soon as possible.

Download date: 24 Aug 2020

CHAPTER 6

REGIONAL VARIATIONS IN

BONE-MINERAL DENSITY

MIGHT SUPPRESS

LARGER STRAIN MAGNITUDES

Chapter 6

~ 112 ~

§ 6.1 Abstract

Regional within-bone variations in mineral density are possibly related to function.

Although bone-mineral density can be influenced by mechanical loading, a heterogeneous

mineral-density distribution might primarily serve to maintain strain amplitudes under

habitual loading within a specific range. Bone regions that would be deformed the most on

the basis of architecture alone might have a higher mineral density to make them more stiff

and resistant to deformation.

We hypothesised that the cortical bone of the rabbit mandible contains a functional

distribution of the mineral density, and therefore expected similar mineral-density patterns

in different individuals due to the overall similar masticatory function. Secondly, we

hypothesised that higher mineral densities will be found in regions predicted to be exposed

to larger amplitudes of strain. Mineral-density maps of the cortical bone of rabbit mandibles

were obtained using micro-computed tomography (µCT). These µCT scans were converted

into finite-element models (FEMs) with a homogeneous stiffness to calculate the strain

amplitudes when influenced by bone architecture alone. The models were virtually loaded

by muscle forces and by reaction forces, on the condyles and on either the incisal or molar

bite point, to predict mandibular deformation during biting.

We found the cortical bone-mineral density to have a similar pattern in all six

mandibles. The mineral density of the corpus was higher than that of the ramus. One

consistent feature of the mandibular mineral-density distribution was that the medial ridge

of the temporal-muscle insertion groove contained more mineral than the surrounding

regions. The strains calculated with the FEMs were variable and did not feature clear corpo-

ramal differences. However, mandibular regions exposed to the largest amplitudes of strain,

including the medial ridge of the temporal-muscle insertion groove, corresponded with

high-mineral-density regions. Thus, in the rabbit mandible, the heterogeneous mineral

density might serve to suppress larger strain amplitudes under habitual loading.

Mineral Density and Bone Strain

~ 113 ~

§ 6.2 Introduction

Mineral density co-determines the stiffness, or Young’s modulus, of bone tissue (Ji and Gao,

2004). It is suggested that variations in bone-mineral density are related more to function

than to other factors, such as species (Currey, 1987). Bone-mineral density varies between

and within bones. Cancellous bone of human mandibular condyles, e.g., has a lower mineral

density than cortical bone (Renders et al., 2006). But also within cortical bone the mineral

density may vary regionally. Skedros et al. (1996) found caudal regions of the bone cortex of

the equine third metacarpal to contain consistently less mineral than other regions, although

the difference was subtle. Much larger regional intracortical variations in mineral density

were found in human mandibles, ranging from 300 to 1300 mg/cm3 (Maki et al., 2000).

Unlike the shape and micro-architecture of a bone, which have an obvious relation to

function (Roux, 1881; Wolff, 1891), the possible functional aspects of mineral-density

variations within bones are still being explored.

The mineral density of bone tissue depends on the speed at which the mineral

density of newly deposited osteoid (and later, bone) increases and on the rate of bone

renewal (Boivin et al., 2009). Bone renewal, or bone turnover, is a homeostatic process and

comprises the replacement of older bone by new young bone which has yet to mineralise.

Bone growth, modelling, and renewal are controlled by hereditary as well as non-hereditary

factors, the latter including mechanical loading. Loads deform bone tissue and thereby

influence osteocyte viability (Noble et al., 1997, 2003; Bakker et al., 2004; Aguirre et al., 2006)

as well as the accumulation of microdamage. Osteocyte death and microdamage may

subsequently trigger bone turnover (Burr et al., 1985; Verborgt et al., 2000; Cardoso et al.,

2009). If there are regions within a bone that are consistently deformed with larger

amplitudes under habitual loading, then bone turnover might have higher rates in those

regions, thereby lowering locally the mineral density. A predominant deformation pattern

under habitual loading of the bone as a whole would maintain such regional variations in

turnover rates and, therefore, mineral density. Conversely, a heterogeneous mineral density

might function to resist too large amplitudes of deformation under habitual loading, in

which case hereditary factors are likely more in control. A higher mineral density in regions

that would be strained too much on the basis of architecture alone could prevent

microdamage by locally increasing the stiffness of the bone tissue.

Chapter 6

~ 114 ~

The rabbit mandible is a bone exposed to intense repetitive and static loads (De Jong et al.,

2010). Hence, not to fail during function, the bone as a whole must be both tough and stiff.

Strong masticatory muscles almost continuously load the mandible whilst the dental

elements and the temporomandibular-joint contact surfaces supply reaction forces. All of

these loads deform and strain the bony tissue of the mandible. Although the functions and

activities of the masticatory apparatus are numerous, a predominant habitual strain pattern

of the mandible comparable in different individuals might exist—like there are predominant

deformation patterns of the human mandible (Van Eijden, 2000) and of certain long bones

(Lanyon and Baggott, 1976; Lieberman et al., 2004). The mineral-density distribution within

the mandible may be related to regional differences in the amplitudes of these strains.

Subsequently, the consistency of the mineral-density distributions within the mandibles of

different individuals may illustrate this predominant strain-amplitude pattern.

In this paper, two questions are addressed. Firstly, what is the interindividual

variation in the mineral-density distribution in the cortical bone of the rabbit mandible?

And, secondly, if there is a heterogeneous mineral density, is it related to habitual

amplitudes of strain in the cortical bone of the rabbit mandible? We hypothesised that

regional variations in the mandibular mineral density might exist to prevent strain

amplitudes from becoming too large. Through the use of micro-computed tomography

mineral-density maps of the cortical bone of the mandibles of six adult rabbits were

obtained for interindividual comparison. The second research question was tested for two

rabbits only. To this end, finite-element models (FEMs) of their mandibles were created and

assigned a homogeneous Young’s modulus. Although taking into account regional

variations in the stiffness due to regional variations in the mineral density would make the

FEMs more realistic (Strait et al., 2005; Renders et al., 2011), we aimed to simulate a situation

in which only bone architecture influences mandibular deformation. The strain amplitudes

predicted with these ‘homogeneous’ FEMs might then clarify why in specific mandibular

regions bone-mineral density is lower or higher. FEM-predicted strain-amplitude maps of

the rabbit mandible were then compared to the mineral-density maps of the cortical bone of

the corresponding individual.

Mineral Density and Bone Strain

~ 115 ~

§ 6.3 Materials and methods

Bones and scans

The mandibles of six adult New Zealand white rabbits had been dissected previously and

stored at -20 °C until use for this study. High-resolution X-ray scans of the rabbit mandibles

were made with a desktop cone-beam micro-computed-tomography scanner (µCT 80,

SCANCO Medical AG, Brüttisellen, Switzerland). The mandibles were submerged in water

whilst being scanned. The scan peak voltage was 70 kV, the electric current 114 µA, the

spatial resolution 30 µm, and the scan integration time 1.0 s for each cross section. An

aluminium filter in the micro-CT scanner and a correction algorithm in its software reduced

beam hardening artefacts (Mulder et al., 2004, 2006). A threshold of 490 mg

hydroxyapatite/cm3 was applied to separate bone from background. From the X-ray

attenuation maps, which contain the computed linear attenuation coefficients of each

volume element (voxel) of the scan, the mineral density of each voxel of the 3D

reconstruction of the mandible was determined. From the 3D reconstructions of the six

rabbit mandibles the outer two voxel layers were peeled off. The mineral densities of the

voxels in a 0.288-mm thick layer below the removed voxels were used to make the mineral-

density maps of the mandibles.

Finite-Element Model construction

Finite-element models were made of the right hemimandibles of two of the six rabbits. The

mandibles were assumed symmetrical so that only half of the mandible needed to be

modelled, thereby enabling a better resolution of that hemimandible. The meshes of the two

finite-element hemimandibles were identical to the geometry of the scanned bones by using

a voxel-conversion technique (Van Rietbergen et al., 1995). The number of finite elements

per model was approximately 12 million. The Young’s modulus of the elements

representing bone in the FEMs was given the value of 20 GPa. Within the ramal attachment

sites of the masseter and medial pterygoid the bone-mineral density was much lower than

the previously mentioned threshold. This resulted in loosely connected bone ends within

the ramus that made the FEMs unsolvable. Therefore, these regions were segmented with a

lower threshold, and combined with the meshes from the original segmentation. The thus

Chapter 6

~ 116 ~

obtained extra finite elements were given a Young’s modulus of 2 GPa. To simulate the

presence of periodontal ligaments, the space around the dental elements within the sockets

was filled with finite elements with an arbitrary Young’s modulus of 2 GPa. The dental

elements themselves were considered non-deformable.

Boundary conditions of the FEM

The FEM of the rabbit mandible was loaded with the forces of maximally six different

masticatory muscles: the left and right superficial masseter, medial pterygoid, and temporal

muscles. Also included in the finite-element analyses were the reaction forces on the

mandibular condyles and on the incisal or molar bite points. Symmetry was assumed

regarding the muscles forces on the left and right sides of the mandible. Nodi in the

symphyseal plane were fixed in the midsagittal plane.

The insertion areas of the masticatory muscles, as well as the application areas of

the reaction forces in the temporomandibular joints, the incisal and molar bite points, and

the symphyseal connection were marked manually on the surface of the FEMs (Figure 6.1).

All forces were applied to the centroids of the selected areas of loading, which were

calculated with custom software. The directions and amplitudes of the muscle-force vectors

were based on the working-line vectors and physiological cross-sectional areas published by

Weijs and Dantuma (1981). A method was developed to calculate the reaction forces on the

molar or incisal bite points and the condyles. The surface normal of the contact area in the

joints was also calculated and it was assumed that the reaction force in the joint was

perpendicular to this surface, i.e., we assumed an absence of friction in the joint. Since the

rabbit mandibular condyles in vivo cannot move in the mediolateral direction, a mediolateral

force through the condyles was included. Finally, the bite force was given three, unknown,

components. Assuming static equilibrium—the sum of all moments and the sum of all

forces equal zero—it was possible to calculate all unknown forces.

Static incisal and molar biting were simulated using four different muscle-activity

patterns: contraction of either the superficial masseter muscles, the medial pterygoid

muscles, or the temporal muscles, or contraction of all six muscles. A Dutch national

supercomputer (SARA Computing and Networking Services, Amsterdam, the Netherlands)

was made available to solve the large-scale finite-element simulations and calculated the

equivalent strain amplitudes throughout the hemimandibles (Van Rietbergen et al., 1995).

Mineral Density and Bone Strain

~ 117 ~

The equivalent strain amplitudes were normalised in each of the simulations. For an optimal

display of the regional differences, the colour bar of every strain map was adjusted.

Comparisons were made between the equivalent-strain-amplitude maps and the mineral-

density maps of the rabbit mandible.

Figure 6.1 Diagrams showing lateral, medial, and superior views of a finite-element model of a rabbit

hemimandible. The dark grey areas are the mandibular regions onto which boundary conditions were

imposed. The blue arrows represent muscle and reaction forces in no particular combination per view.

Arrow directions are approximate. The thickness of the arrows does not indicate force amplitude. The

reaction force on the condyle, which was included in the static equilibrium during simulations of incisal

or molar biting, is not shown—its insertion area is, in the superior view. Symphyseal nodi were fixed in

the midsagittal plane, i.e., strains in the mediolateral direction were not allowed.

lateral

medial

superior

Chapter 6

~ 118 ~

§ 6.4 Results

Mandibular mineral-density maps

The mandibles of the six rabbits had remarkably similar distribution patterns of mineral

density (Figure 6.2). On the lateral side of the corpus, in the incisal and molar regions, the

mineral density was fairly homogeneous and higher than in all other regions (Figure 6.3).

The ventral side of the molar region of the corpus had the highest mineral density of the

mandibular bone. Through the mental foramen and the porous region postero-inferior of it

the lower mineral density of the cancellous bone was visible. The incisal region at the medial

side featured a homogeneous mineral density, albeit one colour lower (± 200 mg HA/cm3)

than at the lateral side. The medial side of the corpus surrounding the molars featured a

horizontally aligned mineral-density pattern. A strip of lower mineral density roughly

followed the trajectory of the inferior alveolar nerve. Above and below this strip the mineral

density resembled the density at the lateral side of the corpus. The lower horizontal strip

continued posteriorly into the ventral ridge of the ramus, crossing the medial side of the

impressio vasculosa mandibulae. The high mineral density delineating the upper strip extended

posteriorly into the bar that forms the medial side of the insertion groove of the temporal

muscle. Just below the molars, the upper strip was topped off superiorly by a region of

heterogeneous mineral density.

The lowest mineral densities were found in the ramus. The inferior (or ventral), the

supero-anterior, and the posterior borders of the ramus, as well as the crested insertion line

of the anterior deep masseter muscle contained more mineral than the ramal parts they

surround, but less mineral than the lateral aspect of the corpus. The angular process of the

mandible—in the posterior border of the ramus—had a mineral density as low as the

surrounded ramal parts. The mineral density at the medial side of the ramus followed the

same patterns as on the lateral side. This was partly due to the rami being very thin in some

regions, which caused overlapping of the lateral and medial 0.288 mm thick analysed

surface layers. The insertion fossae of the medial and lateral pterygoid muscles contained

less mineral than the surrounding parts of the ramus.

The two premolars and three molars were as highly mineralised as the corpus.

Their protruding lateral and medial vertical ridges contained the highest mineral density of

Mineral Density and Bone Strain

~ 119 ~

Figure 6.2 Lateral (left column) and medial (right column) views of the cortical bone-mineral density in

six rabbit hemimandibles. The colours red, yellow, green, blue, and purple indicate the mineral-density

ranges 500-700, 700-900, 900-1100, 1100-1300, and 1300-1500 mg HA/cm3, respectively. Note that the

grey areas in the ramus are regions of extremely thin bone tissue.

500 mg/cm³ 1500 mg/cm³

1

2

3

4

5

6

Chapter 6

~ 120 ~

Figure 6.3 Representative lateral (left) and medial (right) views of the mineral density in the cortical

bone of the rabbit mandible. 1. Incisor. 2. Mental foramen. 3. Ventral side of the corpus inferior of the

molars. 4. Crested insertion line of the anterior deep masseter muscle. 5. Angular process. 6. Higher-

density strip extending posteriorly. 7. Lower-density strip. 8. Higher-density strip extending into

ventral border of ramus. 9. Impressio vasculosa mandibulae. 10. Insertion fossa of the lateral pterygoid

muscle. 11. Bar forming the medial side of the insertion groove of the temporal muscle. 12. Insertion

fossa of the medial pterygoid muscle. The colours delineate mineral-density ranges similarly as in

Figure 6.2.

all structures of the mandible. In several individuals (no. 4 and 6, Figure 6.2) the cortical

bone surrounding the incisor seemed highly mineralised. This, however, was likely an

artefact caused by the peeling away of the two superficial voxel layers and the subsequent

exposure of the highly mineralised incisor itself.

Finite-element predictions of strain

The strain-amplitude maps of the finite-element predictions featured complex patterns. The

largest amplitudes of deformation were repeatedly found in the following mandibular

regions: the lateral side of the premolar corpus, the anteroventral border of the ramus (just

posteriorly of the impressio vasculosa mandibulae), and the retromolar region either or not

combined with the medial bar of the temporal-muscle insertion groove (Figure 6.4). In

addition, maximum strain amplitudes were also repeatedly found in the medial side of the

corpus directly posterior of the symphysis. However, we excluded this region from further

analysis as we considered it too close to the symphyseal plane onto which boundary

conditions were imposed.

500 mg/cm³ 1500 mg/cm³

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

Mineral Density and Bone Strain

~ 121 ~

The lateral side of the corpus anterior of the molars featured strain-amplitude maxima

under masseter loading during both incisal and molar biting, under pterygoid loading

especially during molar biting, to a lesser extent under temporal loading during incisal

biting only, and under loading by all three muscles in both incisal and molar bite

simulations. Maximum corpus strains were either centred on the mental foramen or, when

only the pterygoid was ‘active’, in the entire lateral aspect of this part of the corpus.

The ventral border of the mandibular ramus featured a strain-amplitude maximum

under masseter loading, under pterygoid loading, and under loading of the masseter,

pterygoid, and temporal muscles, always in both biting simulations. The largest strains in

the ventral ramal border were located within the short anteroventral part of this border, just

posterior of the impressio vasculosa mandibulae.

The retromolar region and the bar forming the medial side of the temporal-muscle

insertion groove featured strain-amplitude maxima under masseter loading in both biting

simulations, under pterygoid loading especially during incisal biting, to a lesser extent

under temporal loading, and when all three muscles were ‘active’ in both biting simulations.

There were no clear relations between the mineral-density maps and the strain-

amplitude maps of the modelled rabbit mandibles. A clear corpo-ramal gradient on the

lateral side of the mandible, such as present in the mineral-density maps, was absent in the

FEM predictions under all loading conditions. However, various cortical bone regions

predicted to be exposed to the largest equivalent strain amplitudes under incisal and molar

biting corresponded with regions having higher mineral densities. These included: the

lateral side of the premolar corpus, the bar forming the medial side of the temporal-muscle

insertion groove, and the short antero-ventral border of the ramus (Figure 6.5).

Chapter 6

~ 122 ~

Figure 6.4 Equivalent strains in the finite-element models of the mandibles of two rabbits (individuals 5

and 6 from Figure 6.2). Strain amplitudes are normalised and indicated with a colour scale. The loading

conditions differ per row and are from top to bottom: contraction of the superficial masseter (‘mass’),

the medial pterygoid (‘ptery’), or temporal muscle (‘temp’), or all three muscles (‘all’) during incisal

biting (this page) or molar biting (opposite page). Note that the largest amplitudes of strain are found in

the premolar corpus, the short anteroventral border of the ramus, and the retromolar region—which

extends into the medial side of the temporal muscle-insertion groove.

mass

ptery

temp

all

lateral mediallateral medial

individual 5 individual 6

0 100 %

Mineral Density and Bone Strain

~ 123 ~

0 100 %

individual 5 individual 6

lateral mediallateral medial

mass

ptery

temp

all

Chapter 6

~ 124 ~

Figure 6.5 Representative FEM prediction of strain during incisal biting with simultaneously

contracting masseter, medial pterygoid, and temporal muscles (upper row) shown together with the

mineral-density map of that individual (bottom row). The lateral side of the premolar corpus, the bar

forming the medial side of the temporal-muscle insertion groove, and the short antero-ventral border of

the ramus feature maximum strain amplitudes, but also have higher mineral densities.

§ 6.5 Discussion

We hypothesised that a heterogeneous mineral density within a bone might exist to

suppress larger strain amplitudes. To test this, we compared mineral-density maps of the

cortical bone of rabbit mandibles to strain-amplitude maps of those mandibles as predicted

with finite-element modelling. The FEMs featured a homogeneous material stiffness to

calculate the strain amplitudes throughout the mandible when only architecture was of

influence to bone deformation. Mandibular regions predicted to be exposed to the largest

amplitudes of strain during simulated biting appeared to correspond with regions having

higher mineral densities in the micro-CT-derived mineral-density maps. This implies that if

0 100 %

0 1500 mg/cm³

FEM, lateral FEM, medial

mineral density, lateral mineral density, medial

Mineral Density and Bone Strain

~ 125 ~

we had incorporated the heterogeneous mineral density in the Young’s modulus of the

FEMs, the strain amplitudes would have been less different between mandibular regions.

Therefore, a regionally higher mineral density may serve to better resist deformation under

loading. Such a biological ‘strategy’ is in line with the hypothesis that bone adapts its

morphology and composition to the habitual loads in order to keep habitual strains within a

specific amplitude band (Rubin, 1984).

The described patterns of the mandibular mineral density were very consistent

between the six rabbits. The bar at the medial side of the temporal-muscle insertion groove,

e.g., had a higher mineral density than the surrounding parts of the ascending ramus in all

six mandibles. The lateral corpo-ramal mineral-density gradient was present in all six

mandibles also. If there were no mineral-density pattern, the chance to find one of the

described interregional density gradients in all six rabbits would be 0.56 = 1.6 %. We found

several interregional density gradients in the six rabbits, rendering the described patterns

significant. This reinforces the notion that the heterogeneous mineral-density distribution

has a function and is advantageous over a homogeneous mineral density.

The mineral-density map of the mandible of the adult rabbit might be the result of

heritable information. This would mean that after attaining adult dimensions mandibular

bone turnover and mineralisation are tightly controlled by genetic factors to have different

intensities regionally. Although ossification patterns during embryonic growth have been

studied in several species, not much is known about spatial within-bone variations in the

genetic control of bone-mineral density. Bang and Enlow (1967) described the consistency of

postnatal patterns of depository and resorptive surfaces in the mandible of rabbits in the age

range of 2 to 6 months—our rabbits were about 4 months old. Amongst others, they

described a resorptive surface covering most of the lateral side of the ramus and extending

onto the supero-anterior border of the ramus (the lateral side of the temporal-muscle

insertion groove). In our mineral-density maps this and other ramal borders have a higher

mineral density than the ramal surfaces they surround, which does not correspond well

with Bang and Enlow’s findings. It might be that despite resorption at the bone surface the

mineral density of the deeper cortical bone layers is kept intact. The posterior border of the

angle of the mandible has a consistently low mineral density in all of our specimens, which

corresponds well with Bang and Enlow’s finding that this is an area of bone deposition, i.e.,

young bone.

Chapter 6

~ 126 ~

In contrast to our data, a positive relation was found between habitual strain amplitudes

and the intensity of bone turnover in the zygomatic arch of immature macaques (Bouvier

and Hylander, 1996). This finding supports the rationale that bone regions habitually

undergoing larger amplitudes of deformation accumulate more microdamage and osteocyte

apoptosis, which in turn triggers osteoclasts to remove bone. Subsequently, mineral-density

lowering Haversian remodelling starts in those regions (Burr et al., 1985; Bentolila et al.,

1998; Verborgt et al., 2000; Cardoso et al., 2009). Because we did not incorporate the

heterogeneous mandibular stiffness into the model we do not know the in-vivo strain

amplitude distribution within the rabbit mandible during loading. However, it appears that

bone turnover is the fastest in the masseter and pterygoid insertion areas and in the condyle,

as these regions have the lowest mineral densities. If bone turnover were to be strongly

influenced by microdamage, in-vivo strain amplitudes should be the largest in those regions.

Long-term in-vivo bone-strain recordings revealed that the lateral side of the rabbit

mandibular corpus is habitually exposed to maximum strain amplitudes of ~300 µε in

tension and ~500 µε in compression. Within this range thousands of strain events take place

per day with amplitudes smaller than 100 µε, of which about one thousand events per hour

fall below the level of 10 µε (De Jong et al., 2010). Although this strain history was not

recorded at the aforementioned ramal regions it nevertheless seems that the habitual rabbit

mandibular strain history is less burdening than the 10,000 cycles of 1500 or 2500 µε at

which measurable microdamage is elicited in dog long bones in in-vivo loading studies (Burr

et al., 1985; Mori and Burr, 1993). Possibly, microdamage is not an important determinant of

turnover rates in rabbit mandibular bone.

There is a strong corpo-ramal division in the mandibular cortical bone-mineral

density; the lateral side of the corpus consistently featured a higher mineral density than the

ramus. Except for the digastric muscles, all masticatory muscles insert on and directly load

the rami of the mandible. The dental elements will supply the corpus of the mandible with

reaction loads through the periodontal ligament. If loads of a muscular origin strain the

bone up to frequencies higher compared to the reaction loads, then the corpus receives

much less high-frequency loads compared to the ramus. The mechanosensitivity of bone is

known to increase with loading frequency (Rubin et al., 2001). It could be that the bone-

turnover rate of the ramus is higher than that of the corpus due to the persistent presence of

low-amplitude, high-frequency muscle activity. However, this implies that bone-mineral

Mineral Density and Bone Strain

~ 127 ~

density is influenced by mechanical loading—a premise that, again, is the opposite of the

idea that mineral-density variations exist to counteract strain-amplitude variations.

The ramus of the rabbit mandible is very thin within its borders and has a low

mineral density compared to the corpus. Considering the facts that rabbits chew unilaterally

(Ardran et al., 1958) and that the masseter and medial pterygoid muscle forces working on

the lateral and medial ramal surfaces are directed upward and forward, large internal

stresses in the ascending ramus may be expected should the condyle experience joint-

reaction loads. However, the mineral density of the ramus indicates that this part of the

mandible is not very strong at all. It could therefore be that the working-side condyle hardly

experiences loads during the power stroke of a chewing cycle. This would support an early

hypothesis by Weijs and Dantuma (1981) who found negligible loads on the working-side

condyle after calculating the forces and torques in the rabbit masticatory apparatus under a

static masticatory power-stroke condition.

We could not compare our results to those of other researchers as, to the best of our

knowledge, this was the first time a FEM of the rabbit mandible was made. In interpreting

our results one must consider that several assumptions were made in our finite-element

analyses. Firstly, the Young’s modulus of bone was set on 20 GPa, which is fairly high and

exceeds the value of ~16 GPa found for the rabbit middle-ear ossicles (Soons et al., 2010)—

bones known to be very stiff (Currey, 2003). A high modulus will lower the amplitude of

deformation under a given load. In the finite-element work presented here, however, we did

not aim to approximate in-vivo strain magnitudes, but the strain-amplitude distribution

considering architecture only. Secondly, the Young’s modulus of the periodontal ligament

was set on the arbitrary value of 2 GPa. This choice was made on the basis of usefulness. The

actual Young’s modulus of the periodontal ligament will differ greatly between tension and

compression, which complicates the assignment of accurate in-silico material properties. In-

vitro mechanical testing of periodontal ligaments has generated low moduli of elasticity,

ranging from ~1 MPa (Komatsu et al., 1998) to ~19 MPa (Sanctuary et al., 2005). A lower

Young’s modulus for the finite-element ligament would have caused greater compressive

stresses in the inferior regions of the molar and incisor sockets due to tooth-bone contact.

We assumed that such stresses do not occur in vivo and, therefore, chose not to use a

Young’s modulus lower than 2 GPa. A future approach to this problem might be to remove

all periodontal finite elements with a first principal strain that is negative, i.e., compressive.

The remainder of the periodontal ligament might then better simulate the in-vivo situation.

Chapter 6

~ 128 ~

Thirdly, our set of forces loading the mandible was limited to six active muscles maximally,

to which were added the reaction forces on the mandibular condyles and incisal or molar

bite points. Loads of other origins will exist, but were assumed to have negligible influence

on the deformation of the mandible for the sake of feasibility. In addition, the superficial

masseter, medial pterygoid, and temporal muscles are known to be very active during

biting activities in the rabbit, but they reach their maximal force outputs at different time

points during a chewing cycle (Weijs and Dantuma, 1981). Fourthly, symphyseal nodi were

fixed in the midsagittal plane. We, therefore, neglected the prediction in the FEMs of large

strain amplitudes on the medial side of the mandible just posterior of the symphysis, an area

too close to the fixed nodi. However, further applications of node fixation, e.g., in the

mandibular condyles, were avoided by calculating the reaction forces in a static equilibrium.

To summarise, the mineral density of the rabbit mandible is strongly heterogeneous and

features a very consistent gradient pattern amongst different individuals. Simulations of

incisal or molar biting with a finite-element model that has a homogeneous tissue stiffness

revealed that the largest strains occur in regions of the mandible that have higher mineral

densities. This hints at a functional mineral-density distribution; the regional differences in

mineral density might cause more homogeneous strain amplitudes across the entire bone

structure to better endure habitual loading. Heritable information might play an important

role in maintaining the heterogeneous bone mineral-density pattern.

Acknowledgements

We are grateful to the Netherlands National Computing Facilities Foundation (NCF, The

Hague, the Netherlands) for funding of the finite-element-model research (grant no. SH-138-

09), and to SARA Computing and Networking Services (Amsterdam, the Netherlands) for

providing the necessary supercomputer hardware. We also wholeheartedly thank Bert van

Rietbergen for putting the SCANCO µCT 80 scanner at our disposal and Lars Mulder for

making the micro-computed tomographs of the rabbit mandibles.

Mineral Density and Bone Strain

~ 129 ~

§ 6.6 References

Aguirre JI, Plotkin LI, Stewart SA, Weinstein RS, Parfitt AM, Manolagas SC, Bellido T (2006).

Osteocyte apoptosis is induced by weightlessness in mice and precedes osteoclast

recruitment and bone loss. Journal of Bone and Mineral Research 21: 605-615.

Ardran GM, Kemp FH, Ride WDL (1958). A radiographic analysis of mastication and

swallowing in the domestic rabbit: Oryctolagus cuniculus (L). Proceedings of the

Zoological Society of London 130: 257-274.

Bakker A, Klein-Nulend J, Burger E (2004). Shear stress inhibits while disuse promotes

osteocyte apoptosis. Biochemical and Biophysical Research Communications 320:

1163-1168.

Bang S, Enlow DH (1967). Postnatal growth of the rabbit mandible. Archives of Oral

Biology 12: 993-998.

Boivin G, Farlay D, Bala Y, Doublier A, Meunier PJ, Delmas PD (2009). Influence of

remodeling on the mineralization of bone tissue. Osteoporosis International 20:

1023-1026.

Bouvier M, Hylander WL (1996). The mechanical or metabolic function of secondary

osteonal bone in the monkey Macaca fascicularis. Archives of Oral Biology 41: 941-

950.

Burr DB, Martin RB, Schaffler MB, Radin EL (1985). Bone remodeling in response to in vivo

fatigue microdamage. Journal of Biomechanics 18: 189-200.

Cardoso L, Herman BC, Verborgt O, Laudier D, Majeska RJ, Schaffler MB (2009). Osteocyte

apoptosis controls activation of intracortical resorption in response to bone fatigue.

Journal of Bone and Mineral Research 24: 597-605.

Currey JD (1987). The evolution of the mechanical properties of amniote bone. Journal of

Biomechanics 20: 1035-1044.

Currey JD (2003). The many adaptations of bone. Journal of Biomechanics 36: 1487-1495.

de Jong WC, Koolstra JH, Korfage JAM, van Ruijven LJ, Langenbach GEJ (2010). The daily

habitual in vivo strain history of a non-weight-bearing bone. Bone 46: 196-202.

Ji B, Gao H (2004). Mechanical properties of nanostructure of biological materials. Journal of

the Mechanics and Physics of Solids 52: 1963-1990.

Chapter 6

~ 130 ~

Komatsu K, Yamazaki Y, Yamaguchi S, Chiba M (1998). Comparison of biomechanical

properties of the incisor periodontal ligament among different species. Anatomical

Record 250: 408-417.

Lanyon LE, Baggott DG (1976). Mechanical function as an influence on the structure and

form of bone. Journal of Bone and Joint Surgery 58-B: 436-443.

Lieberman DE, Polk JD, Demes B (2004). Predicting long bone loading from cross-sectional

geometry. American Journal of Physical Anthropology 123: 156-171.

Maki K, Miller A, Okano T, Shibasaki Y (2000). Changes in cortical bone mineralization in

the developing mandible: a three-dimensional quantitative computed tomography

study. Journal of Bone and Mineral Research 15: 700-709.

Mori S, Burr DB (1993). Increased intracortical remodeling following fatigue damage. Bone

14: 103-109.

Mulder L, Koolstra JH, van Eijden TMGJ (2004). Accuracy of microCT in the quantitative

determination of the degree and distribution of mineralization in developing bone.

Acta Radiologica 45: 769-777.

Mulder L, Koolstra JH, van Eijden TMGJ (2006). Accuracy of microCT in the quantitative

determination of the degree and distribution of mineralization in developing bone.

Acta Radiologica 47: 882-883.

Noble BS, Peet N, Stevens HY, Brabbs A, Mosley JR, Reilly GC, Reeve J, Skerry TM, Lanyon

LE (2003). Mechanical loading: biphasic osteocyte survival and targeting of

osteoclasts for bone destruction in rat cortical bone. American Journal of

Physiology. Cell Physiology 284: C934-C943.

Noble BS, Stevens H, Loveridge N, Reeve J (1997). Identification of apoptotic changes in

osteocytes in normal and pathological human bone. Bone 20: 2273-282.

Renders GAP, Mulder L, van Ruijven LJ, Langenbach GEJ, van Eijden TMGJ (2011). Mineral

heterogeneity affects predictions of intratrabecular stress and strain. Journal of

Biomechanics 44: 402-407.

Renders GAP, Mulder L, van Ruijven LJ, van Eijden TMGJ (2006). Degree and distribution

of mineralization in the human mandibular condyle. Calcified Tissue

International 79: 190-196.

Rubin CT (1984). Skeletal strain and the functional significance of bone architecture.

Calcified Tissue International 36: S11-S18.

Mineral Density and Bone Strain

~ 131 ~

Rubin CT, Sommerfeldt DW, Judex S, Qin YX (2001). Inhibition of osteopenia by low

magnitude, high-frequency mechanical stimuli. Drug Discovery Today 6: 848-858.

Roux W (1881). Der Kampf der Teile im Organismus. Engelmann, Leipzig.

Sanctuary CS, Anselm Wiskott HW, Justiz J, Botsis J, Belser UC (2005). In vitro time-

dependent response of periodontal ligament to mechanical loading. Journal of

Applied Physiology 99: 2369-2378.

Skedros JG, Mason MW, Nelson MC, Bloebaum RD (1996). Evidence of structural and

material adaptation to specific strain features in cortical bone. Anatomical Record

246: 47-63.

Soons JAM, Aernouts J, Dirckx JJJ (2010). Elasticity modulus of rabbit middle ear ossicles

determined by a novel micro-indentation technique. Hearing Research 263: 33-37.

Strait DS, Wang Q, Dechow PC, Ross CF, Richmond BG, Spencer MA, Patel BA (2005).

Modeling elastic properties in finite-element analysis: how much precision is

needed to produce an accurate model? Anatomical Record Part A 283A: 275-287.

van Eijden TMGJ (2000). Biomechanics of the mandible. Critical Reviews in Oral Biology

and Medicine 11: 123-136.

van Rietbergen B, Weinans H, Huiskes R, Odgaard A (1995). A new method to determine

trabecular bone elastic properties and loading using micromechanical finite-

element models. Journal of Biomechanics 28: 69-81.

Verborgt O, Gibson GJ, Schaffler MB (2000). Loss of osteocyte integrity in association with

microdamage and bone remodeling after fatigue in vivo. Journal of Bone and

Mineral Research 15: 60-67.

Weijs WA, Dantuma R (1981). Functional anatomy of the masticatory apparatus in the rabbit

(Oryctolagus cuniculus L.). Netherlands Journal of Zoology 31: 99-147.

Wolff J (1892). Das Gesetz der Transformation der Knochen. Hirschwald, Berlin.