Adaptive bone formation in acellular vertebrae of sea bass (Dicentrarchus labrax L.)
1 Experimental Zoology Group, Wageningen University, Marijkeweg 40, 6709 PG
Wageningen, The Netherlands
2 Division of Biomechanics and Engineering Design, K.U. Leuven,
Celestijnenlaan 200A, 3001 Leuven, Belgium
* Author for correspondence (e-mail: sander.kranenbarg{at}wur.nl)
Accepted 18 July 2005
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Summary |
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The effects of lordosis on the strain distribution in sea bass (Dicentrarchus labrax L.) vertebrae are assessed using finite element modelling. The response of the local tissue is analyzed spatially and ontogenetically in terms of bone volume.
Lordotic vertebrae show a significantly increased strain energy due to the increased load compared with normal vertebrae when loaded in compression. High strain regions are found in the vertebral centrum and parasagittal ridges. The increase in strain energy is attenuated by a change in architecture due to the increased bone formation. The increased bone formation is seen mainly at the articular surfaces of the vertebrae, although some extra bone is formed in the vertebral centrum.
Regions in which the highest strains are found do not spatially correlate with regions in which the most extensive bone apposition occurs in lordotic vertebrae of sea bass. Mammalian-like strain-regulated bone modelling is probably not the guiding mechanism in adaptive bone modelling of acellular sea bass vertebrae. Chondroidal ossification is found at the articular surfaces where it mediates a rapid adaptive response, potentially attenuating high stresses on the dorsal zygapophyses.
Key words: acellular bone, sea bass, Dicentrarchus labrax, vertebra, adaptive modelling, lordosis
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Introduction |
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Bone tissue in the Actinopterygii can be divided into two types
(Fig. 1): cellular bone and
acellular bone. Cellular bone contains osteocytes in its matrix and is found
in the lower taxa of the Actinopterygii. The bone of higher Actinopterygii,
especially the neoteleosts, is devoid of osteocytes, as osteoblasts recede
from the mineralization front and never become entrapped
(Parenti, 1986). Although the
phylogenetic dichotomy is clear, exceptions to the rule do occur. Notably
within the Protacanthopterygii, the Salmonidae have cellular bone, as do the
Thunnini within the Acanthopterygii
(Kölliker, 1859
; Moss,
1961
,
1965
). Furthermore, within the
Ostariophysi, which normally have cellular bone, larval bone is reported to be
acellular (Fleming et al.,
2004
).
|
Despite the lack of strain-sensing osteocytes, acellular bone is capable of
showing conformational changes under increased loading
(Kihara et al., 2002;
Kranenbarg et al., 2005
).
Strenuous exercise [evoked by, for example, high current velocity
(Backiel et al., 1984
) or
caudal fin removal (Kihara et al.,
2002
)] is known to induce lordosis in several teleosts. Lordosis
is characterized by extra-mineralized vertebrae, accompanied by an abnormal
ventrad curvature of the vertebral column
(Chatain, 1994
;
Divanach et al., 1997
;
Paperna, 1978
). Similar
deformities have been reported in elasmobranchs
(Heupel et al., 1999
). The
conformation of the affected vertebrae is probably a response of the local
tissue to a change in loading (Kranenbarg
et al., 2005
).
The response of bone to physical stimuli can be classified as a modelling
response (growth-related changes in the gross shape of the bone) or a
remodelling response (change of architecture rather than total volume of the
bone) (Currey, 2002). The
mechanisms governing the growth-related modelling process in the acellular
vertebrae of lordotic European sea bass (Dicentrarchus labrax L.) are
unknown (Kranenbarg et al.,
2005
).
Adult teleost vertebrae are composed of a vertebral centrum, a dorsal
neural arch and a ventral haemal arch. The centra develop through membranous
ossification (Bertin, 1958;
Liem et al., 2001
). The
central part of the vertebral centrum is formed by ossification of the
perinotochordal sheaths. Rostral and caudal parts are added to the centrum by
sklerotomal membranous ossification
(Grotmol et al., 2003
).
Both the neural and the haemal arch generally develop through cartilage
intermediates (see Bird and Mabee,
2003), collectively called the arcualia
(Liem et al., 2001
). The
cartilaginous precursor of the arches is maintained for a longer period of
time in the lower orders of the teleosts, while ossification proceeds more
rapidly in the higher orders
(François, 1966
). The
zygapophyses and bony ridges connecting pre- and postzygapophyses develop
through membranous ossification (Mookerjee
et al., 1940
).
The combination of acellular bone and membranous ossification seems to preclude adaptive modelling in the classical sense for vertebral centra of the neoteleosts.
We present a numerical analysis of the strain energy density distribution in normal and lordotic vertebrae under compression. Subsequently, we present an analysis of the spatial distribution of bone formation in adaptively modelled vertebrae. We discuss the potentials for strain-regulated modelling in acellular bone and provide new insights into the mechanism governing bone modelling in a species without osteocytes to act as strain gauges.
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Materials and methods |
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Finite element analysis
Column under compression
To determine the loading pattern on the vertebrae, we assumed the vertebral
column to be simply a column under compression
(Fig. 2). We recognize the
importance of lateral bending in fish swimming, yet this paper analyzes the
effects of the overall compressive force due to alternated lateral bending.
The dynamic effects of undulatory swimming will be analyzed in future work and
we will limit ourselves to a static application of force in the current
manuscript. The total compressive stress distribution, t,
over the cross-sectional area, A, of the column with dorsoventral
eccentricity, e, under compression with force, F, is given
by the following equation (Nash,
1977
):
![]() | (1) |
|
where d is the direct compressive stress,
i is the induced compressive stress due to the eccentricity,
M is the induced bending moment, y is the distance from the
neutral axis, I is the second moment of area in the dorsoventral
direction, and A is perpendicular to the direction of the load
(Fig. 2). Division by
d, introduction of the radius of gyration in the
dorsoventral direction as
and
definition of the dimensionless spatial variable
=y/r gives the
dimensionless stress distribution
.
![]() | (2) |
The range of is given in
Table 1.
|
|
The eccentricity, e, was measured for each specimen, and the mean radius of gyration in the dorsoventral direction, r, was calculated in Matlab 7.0® (MathWorks, Inc., Natick, MA, USA) for vertebra number 15 of each specimen. The stack of bitmaps was hand-edited before the calculation to remove part of the neural and haemal spines where they did not connect to the vertebral body in cross section. Table 1 gives the parameter values.
Single vertebra under compression
The selected sea bass specimens were scanned with a Skyscan® 1072
micro-CT system (Antwerp, Belgium) at 80 kV and 100 µA and with a cubic
voxel size of 6.08 µm. Vertebra number 15 (centre of lordosis) was scanned
for each specimen. The scans were subsequently reconstructed, segmented and
edited according to Kranenbarg et al.
(2005) to obtain a stack of
bitmaps representing a single vertebra.
The stack of bitmaps from the micro-CT analysis was resampled with a cubic interpolation algorithm to a resolution of 14 µm. Each voxel was converted to a an eight-node hexahedral element (type 7 in MSC.Marc2005; MSC Software Benelux BV, Gouda, The Netherlands) and the resulting surface was smoothed. Mesh generation was performed in Matlab 7.0®. The resulting output file was imported into MSC.Patran2005 for further pre-processing.
The centre of mass (COM) was calculated in MSC.Patran®, and a
new coordinate frame was defined with the origin in the COM and the
axes along the principal axes of the vertebra. Subsequently, the dimensionless
stress distribution, , was
applied perpendicular to the free face of each element on the frontal surface
of the vertebra (rim of the vertebral centrum and prezygapophyses). This
procedure ensures the component of the compressive force parallel to the long
axis of the vertebra to be equal to F, as defined in the previous
section. It was not feasible to incorporate full biological complexity (e.g.
exact positions of tendons and muscle fibres) in our current model and
therefore our mode of application of the loads is necessarily simplified.
Nevertheless, Saint-Venant's principle attenuates the effects of possible
inaccuracies in our mode of application by stating that the stress
distribution may be assumed independent of the actual mode of application of
the loads (except in the immediate vicinity of the points of their
application) (Beer and Johnston,
1992
).
As the range of is comparable
for all vertebrae in the present study (see
Table 1), the applied
dimensionless stress is determined primarily by the lordosis ratio
e/r. The mean lordosis ratio of the normal vertebrae is 2.29
and of the lordotic vertebrae is 4.17 (see
Table 1).
Fig. 3 shows the applied
dimensionless stress distributions for a normal (blue line) and a lordotic
(red line) vertebra.
|
To analyze the effect of increased loading on normal vertebrae, we doubled the eccentricity for the normal vertebrae, thereby simulating a lordotic configuration for the normal vertebrae.
The problem was solved in MSC.Marc® using a linear solver to obtain the
dimensionless strain energy density distribution, :
![]() | (3) |
where ut is the total strain energy density and ud is the strain energy density due to direct compression. The results were post-processed in MSC.Patran.
Bone volume distribution
No lordosis was observed in any specimen under 30 mm TL. The distribution
of bone volume over the anterior-posterior axis of each vertebral centrum was
resampled to 300 data points to obtain the bone volume as a function of
position (%) along the vertebral centrum. Subsequently, the bone volume at
each position was regressed on total length of the animal with a quadratic
function. This procedure was performed for lordotic and non-lordotic animals
separately, yielding two surfaces showing differences in bone volume over the
length of the vertebral centrum. A 95% confidence interval was calculated for
both surfaces. All calculations were performed in Matlab 7.0®.
Histological analysis
The specimens were post-fixed for 1 week in Bouin's fixative
(Romeis, 1968) (modified to 17
vol. % glacial acetic acid). The specimens were embedded in paraffin,
sectioned parasagittally at 5 µm and stained according to Crossmon's
protocol (Romeis, 1968
).
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Results |
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Fig. 5 shows the
distribution of over the centra of the vertebrae (vertebral
body). Normal vertebrae of both the 35 mm TL stage and the 45 mm
TL stage show only limited regions of high
(Fig. 5A,D). The same vertebrae
show extensive regions of high
when the eccentricity is
doubled (Fig. 5B,E). Both
stages show high
values in the struts connecting the neural
arch with the parasagittal ridges, and the parasagittal ridges themselves. In
addition, the 35 mm TL stage shows high
values in
the dorsal and ventral part of the vertebral centrum sensu stricto.
Effect of high eccentricity and change in architecture
A comparison of the average between normal vertebrae
(with normal eccentricity) and lordotic vertebrae (with a characteristically
large eccentricity) shows a significantly increased value in the lordotic
vertebrae (Fig. 4C), although
the difference is less pronounced than in
Fig. 4A. This is illustrated
again in Fig. 4D, which shows a
significantly larger proportion of elements in the lordotic vertebrae with a
high
, although the proportion of elements with a low
only tends to be smaller in lordotic than in normal
vertebrae.
The distribution of over the vertebrae shows clear
differences in magnitude between normal and lordotic vertebrae
(Fig. 5A,C,D,F), with the
parasagittal ridges being the high
regions. These
quantitative differences between normal and lordotic vertebrae are present at
both the 35 mm TL stage and the 45 mm TL stage.
Effect of change in architecture
By comparing the normal vertebrae with double eccentricity with the
lordotic vertebrae, we analyzed the effect of architectural changes on the
distribution. The eccentricity is similar in both groups,
only the architecture of the vertebrae differs
(Kranenbarg et al., 2005
). A
comparison of average
shows no significant differences,
although the
in lordotic vertebrae tends to be smaller
(Fig. 4E). The same trend is
observed in the histogram analysis of Fig.
4F.
The distribution of does show clear differences between
the lordotic vertebrae and normal vertebrae with double eccentricity,
especially in the 35 mm TL stage
(Fig. 5B,C,E,F). Although the
parasagittal ridges show high
values in both groups, the
regions of high
in the vertebral centrum sensu stricto in
the normal vertebrae with double eccentricity
(Fig. 5B,E) have disappeared in
the lordotic vertebrae (Fig.
5C,F).
The absolute value of the distribution reaches peak
values of well over 2000 and is nearly 200 on average in the normal vertebrae
with normal eccentricity. This reveals that even the relatively small
eccentricity of a normal vertebral column
(Table 1) causes strain energy
densities many times larger than those in a compressed, perfectly straight
column.
Spatial distribution of bone volume
Fig. 6A shows the
distribution of bone over the length of the vertebral centrum in lordotic
(red) and normal (blue) vertebrae during growth. The amount of bone increases
with TL in both groups. The difference in bone volume between the
normal and lordotic vertebrae is shown in
Fig. 6B. The dark green region
indicates where the 95% confidence intervals of the surfaces of
Fig. 6A do not overlap.
Although some additional bone is deposited in the central part of lordotic
vertebrae, most of the extra bone material in lordotic vertebrae is deposited
at about 20% and 80% vertebral centrum length, which are the articular areas
of the vertebrae.
|
Histology
Fig. 7 shows a parasagittal
section through a normal (A) and a lordotic vertebra (B). The intervertebral
ligament connects the two consecutive normal vertebral centra. These vertebral
centra, as well as the projecting zygapophyses, consist of acellular bone
(Fig. 7A). The intervertebral
ligament is similarly present in the lordotic vertebra, and the vertebral
centrum also consists of acellular bone
(Fig. 7B). The zygapophyses of
the lordotic vertebrae, however, are highly proliferated and the tissue in
between the postzygapophysis of one vertebra and the prezygapophysis of the
next ranges from densely fibrous to chondroid tissue. Chondroid tissue was not
observed in the normal specimen.
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Discussion |
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Biomechanical effects of lordosis
Lordosis can be characterized as a ventrad curvature (double eccentricity
when compared with the normal situation; see
Table 1) of the vertebral
column with an accompanying local response of the tissue. The effect of the
ventrad curvature is an extensive increase in strain energy stored in the
vertebrae (due to the excessive induced bending moment), if the architecture
of the vertebrae would not change (Fig.
5A,B,D,E).
The local response of the tissue to the increased loading regime effectively removes the high strain regions from the vertebral centrum sensu stricto, possibly preventing the strains from exceeding the yield point. High strain regions remain, however, in the parasagittal ridges (Fig. 5C,F). This effect is especially clear in the 35 mm TL stage, as in the older stage, the normal development of the vertebrae already accomplishes a similar effect of redirecting the high strain regions to the parasagittal ridges.
Fig. 6 shows that the
articular surface areas are the main sites of bone apposition in lordotic
vertebrae. Kranenbarg et al.
(2005) and
Fig. 5 show that the apposition
results in large articular areas in lordotic vertebrae. This effectively
reduces the pressure on the zygapophyses.
Although a similar phenomenon is seen in dogs, where the articular surfaces
of caudal vertebrae are disproportionately larger in large breed dogs
(Breit, 2002), articular
surface areas are generally found to be not phenotypically plastic in mammals
on an individual basis (Lieberman et al.,
2001
).
Fig. 6 also shows a limited
amount of extra bone being formed in the central region of lordotic vertebrae.
Fig. 5(arguably) shows that in
lordotic vertebrae more struts are formed that connect the neural arch with
the dorsal postzygapophysis. The extra bone in the central region does
increase the second moment of area in this region
(Kranenbarg et al., 2005) and
thus helps strengthen the entire vertebra. Nevertheless, the extra struts
cannot prevent regions of high strain occurring in the parasagittal ridges of
lordotic vertebrae, and the mean
remains significantly
larger than in normal vertebrae with normal eccentricity.
The adaptive modelling of the articular surfaces of lordotic vertebrae is only partially effective in counteracting the overall strain-increasing effect of the ventrad curvature. This incomplete compensatory response is further illustrated by the larger value of the lordosis ratio in lordotic vertebrae (Table 1), which signifies the lordosis severity, as explained in the Materials and methods.
Mechanism of adaptive modelling
Adaptive modelling of bone is well documented in mammals
(Cowin, 2001;
Currey, 2002
), yet (acellular)
teleost bone is also capable of an adaptive response
(Glowacki et al., 1986
;
Witten and Villwock, 1997
;
Huysseune, 2000
).
Strain-related stimuli are known to induce adaptive (re)modelling in bone
(Cowin, 2001
;
Currey, 2002
). In mammals,
osteocytes are considered strain gauges that recruit osteoblasts to form bone
(Burger and Klein-Nulend,
1999
).
Frost (1983) introduced the
`minimum effective strain (MES)' principle, stating that `strains smaller
than the MES would not evoke bone architectural adaptations, but those larger
than the MES would'. The MES was found to be around 1000
µ
(Cowin, 2001
). It
should be noted that the MES principle is under much debate
(Currey, 2002
) and has been
modified over the years. Lanyon
(1987
) proposed to generalize
the principle to the `minimum effective strain-related stimulus (MESS)' to
include strain distribution and strain rate in the stimulus.
Despite the lack of consensus, a generalized comparison of the MES with our
results is useful. Assuming linear elasticity in our model and a direct
compressive stress component of 22 kPa
(Cheng et al., 1998
), we can
recalculate the MES to a minimum effective
of approximately
2000. Fig. 5 shows that,
especially in the normal vertebrae with doubled eccentricity
(Fig. 5B,E) and the lordotic
vertebrae (Fig. 5C,F),
extensive regions occur with a
higher than the minimum
effective
(red regions). As the value of 22 kPa for the
direct compressive stress component is not experimentally tested, we note
that, although variations in the actual value may either reduce or expand the
potential modelling area, our conclusion that extensive regions with a
higher than the minimum effective
occur
remains valid.
For a stimulus to be effective, however, a sensor should be present. As sea bass bone is acellular, no osteocytes are present and the bone matrix lacks a strain gauge as is present in mammalian bone. A comparison of Figs 5 and 6 reveals that regions in which the highest strain energy densities are found (especially the parasagittal ridges) do not correlate spatially with the regions in which the highest amount of extra bone is deposited (especially the articular surfaces). A strain (related) stimulus is therefore unlikely to be the sole explanatory variable for adaptive modelling in the sea bass vertebral articulations.
The articular surfaces show extensive formation of extra bone, although the
zygapophyses develop as extensions from the acellular vertebral centrum.
Histology reveals that this articular surface modelling is mediated by
chondroid tissue (cf. Beresford,
1981). Chondroid tissue is also found in articular surfaces of
other joints (Beresford, 1981
)
and is hypothesized to be especially suited to fulfil a fast reconstruction
demand (Huysseune and Verraes,
1986
; Huysseune et al.,
1986
; Huysseune,
2000
). Apparently, in the central part of the vertebrae,
conditions are not met to develop chondroid, while compression of the
intervertebral disk causes chondroid tissue to develop. The chondroidal
ossification subsequently results in a fast adaptive modelling of the
articular surfaces.
Experiments on mammals have shown that bone material deposited in a
modelling response is very similar to the original bone
(Currey, 2002). We assumed all
bone material detected by the CT scanner had equal material properties. The
actual mechanical properties of chondroid bone are unknown, although Meunier
and Huysseune (1992
) suggest
mechanical excellence to be inferior to speed of reconstruction. Further
testing is needed to assess the material properties of lordotic sea bass
vertebrae.
Despite the lack of osteocytes, a limited modelling response is found in
the high-strained central part of lordotic sea bass vertebrae. Osteoblasts and
fibroblasts are also known to be strain sensitive
(Buckley et al., 1988;
Chiquet et al., 2003
) and
might induce the extra bone deposition that does occur in the central part of
lordotic vertebrae.
While the central part of lordotic vertebrae shows possibly strain-mediated
modelling, the volumetrically most important modelling response at the
articular surfaces does not correlate spatially with a high strain energy
density. Chondroid tissue appears to meet the demand for an accelerated growth
rate and the demand for a shear-resistant support
(Huysseune, 2000;
Meunier and Huysseune, 1992
).
Cartilage growth and ossification is known to be promoted by shear stresses
(Carter and Wong, 2003
).
Cartilage mechanobiology might therefore provide interesting new insights into
the mechanisms of chondroidal ossification and modelling in acellular
bone.
Conclusions
Our dimensionless analysis enabled us to define the load on a `typically
normal' and a `typically lordotic' vertebra, as illustrated in
Fig. 3. Furthermore, the
analysis prompted the introduction of a lordosis ratio as a dimensionless
factor describing the severity of the lordosis irrespective of body size.
The present paper further shows that, although some extra bone is formed in the central part, the articular surface areas are the main modelling sites in lordotic vertebrae. The highest strain energy densities are found in the central part of the vertebrae. Mammalian-like strain-regulated bone modelling is therefore unlikely to be the sole mechanism guiding sea bass bone modelling. The adaptive response at the articular surfaces is mediated by chondroidal ossification, possibly induced by other physical stimuli (shear stresses). The increased articular surface area will effectively reduce the pressure on the dorsal zygapophyses.
Despite the adaptations, the overall strain energy of lordotic vertebrae remains higher than that of normal vertebrae in our numerical analyses. Apparently, the morphological adaptations cannot fully compensate for the effect of an increased eccentricity in terms of strain energy.
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Acknowledgments |
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