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The physiology of habitual bone strains
de Jong, W.C.
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Citation for published version (APA):de Jong, W. C. (2011). The physiology of habitual bone strains.
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Download date: 24 Aug 2020
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CHAPTER 6
REGIONAL VARIATIONS IN
BONE-MINERAL DENSITY
MIGHT SUPPRESS
LARGER STRAIN MAGNITUDES
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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.
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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.
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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.
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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
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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).
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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
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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
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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
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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
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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).
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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 %
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Mineral Density and Bone Strain
~ 123 ~
0 100 %
individual 5 individual 6
lateral mediallateral medial
mass
ptery
temp
all
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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
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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.
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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
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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.
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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.
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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.
![Page 21: UvA-DARE (Digital Academic Repository) The physiology of ... · density may vary regionally. Skedros et al. (1996) found caudal regions of the bone cortex of the equine third metacarpal](https://reader034.vdocuments.mx/reader034/viewer/2022050105/5f43b2f0c355c44a8468c780/html5/thumbnails/21.jpg)
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.
![Page 22: UvA-DARE (Digital Academic Repository) The physiology of ... · density may vary regionally. Skedros et al. (1996) found caudal regions of the bone cortex of the equine third metacarpal](https://reader034.vdocuments.mx/reader034/viewer/2022050105/5f43b2f0c355c44a8468c780/html5/thumbnails/22.jpg)
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.