ZooL J. Linn. Soc., 58: 237-254. With 9 figures
April 1976
The development, function, and design of
amphicoelous vertebrae in teleost fishes'
JOSHUA LAERM
Department o f Ecology, Ethology, and Evolution, University of Illinois,
Urbana, Illinois 61801, U.S.A.2
and
Division o f Vertebrate Paleontology, Smithsonian Institution, Washington, D. C.
20560, U.S.A.
Accepted for publication May 1975
The vertebral centra of teleost fishes are amphicoelous. They resemble biconid hour-glass
shaped cylinders, the ends of which are concave.
The development, function, and design of the biconid amphicoelous shape of teleost centra
are discussed in view of: the role of morphogenesis in the development of centra shape;
function of the precaudal portion of the vertebral column in teleost locomotion; design of the
centra as an adaptive response t o functional problems.
The biconid portion of the centrum is formed in compact bone by ossification within the
cylindrically arranged sclerotome. The characteristic biconid shape is controlled by alternating
dilation and constriction of the developing anlage, a result of differential growth of the
sclerotome and notochordal sheaths. The shape of the biconid compactum is not correlated
with stress distributions resulting from locomotion.
Much spongy bone is present in teleost centra; it surrounds the compact biconid and forms
longitudinal bars of bone along the lateral margin of the centra. Spongy bone is derived from
sclerotomal mesemchyme. The time for formation, its position, and alignment of bony
trabeculae within the spongy bone suggests it to be deposited in response t o mechanical
stresses.
CONTENTS
Introduction
. . . . . . . . .
Discussion
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Morphogenesis of teleost centra
.
Biomechanics of fish vertebral columns
Form and function in amphicoely
Conclusion
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Acknowledgements
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References
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'From the Laboratory of T. H. Frazzetta.
'Present address.
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238
J. LAERM
INTRODUCTION
The vertebral centra of teleost fishes are amphicoelous. Generally, they are
well-ossified and monospondylous. Typical amphicoelous centra resemble
biconid hour-glass shaped cylinders, the ends of which are concave (see Fig. 1).
Sections through a typical teleost centra indicate the biconid is formed in
compact bone. On the lateral surface longitudinal bars of bone can be observed.
These extend the length of the centrum. The dorso-lateral and ventro-lateral
surfaces of the centra may similarly exhibit longitudinal bars of bone. These are
invariably continuous with the neural and haemal arches respectively. In
sectioned centra these lateral longitudinal bony bars are seen to be composed
of cancellous or spongy bone (see Fig. 1B).
Although characteristic of teleosts, amphicoely is not limited to this group.
It occurs in other non-teleost osteichthyan groups, including lower levels of
actinopterygian organization. Also, amphicoelous centrum design may be
observed in the calcified cartilage of the vertebrae of numerous
chondrichthyans (Ridewood, 1921), is well known in Paleozoic and Mesozoic
tetrapods (Romer, 1966), and is present in a few known modern tetrapods
(Camp, 1923).
The mechanics of fish locomotion and the relationship of the propagation of
flexures of the body to propulsive forces has been analyzed and discussed in
great detail (see Breder, 1926; Bainbridge, 1958a, 1960, 1961; Gadd, 1963;
Hertel, 1966; and Gray, 1968 for varied general review and extensive
references). Much attention has also been given the relationship between
muscular anatomy and function in locomotion (Nursall, 1956;Willemse, 1959,
1966; Jarmin, 1961; Szarski, 1964; Gutmann, 1966; Lund, 1967), but until
recently (Alexander, 1969; Willemse, 1972) had suffered from much confusion
and disagreement. The role of the vertebral column in fish locomotion, on the
other hand, has been discussed only summarily (Rockwel1,et al., 1938), and the
design and function of vertebral centra has been virtually neglected (see,
however, Borkhvardt, 1970). Since amphicoely is such a widely occurring and
constant feature in teleosts, it should be examined. This paper will, therefore,
discuss the adaptation of amphicoely in the precaudal vertebrae of teleost
fishes, in view of: (1) the role of morphogenesis in the development of centra
shape; (2) function of the precaudal portion of the vertebral column in
locomotion; and ( 3 ) design of the centra as an adaptive response to functional
problems.
DISCUSSION
Morphogenesis of teleost centra
Descriptions of the development of the vertebral column of
actinopterygians, in general, and teleosts, in particular, are numerous (Gadow &
Abbott, 1895; Hay, 1895; Schauinsland, 1906; Schneider, 1913; Ramanujan,
1929; Goodrich, 1930; Gadow, 1933; Faruqi, 1935; Mokerjee, 1936; Gwyn,
1940; Mookerjee et al., 1940; Gabriel, 1944; Blanc, 1953; Devillers, 1954;
Francois, 1958, 1966, 1968; Ganguly & Mitra, 1962; Reinbold, 1966;
Schaeffer, 1967).
AMPHICOELOUS VERTEBRAE IN TELEOSTS
239
Figure 1. Typical amphicoelous centrum from a Jew Fish (Epinephelus). A. Fronto-lateral view;
arrow indicates longitudinal bony bar. B. Horizontal section through same centrum at level of
longitudinal bar showing longitudinal alignment of spongy bone. Bony compactum not
stippled. C. Shape of compact bony biconid with longitudinal bar, neural and haemal arches,
and spines removed.
Despite considerable attention to descriptive accounts of the development of
the vertebral column in fishes, there have been only limited attempts t o
elucidate the epigenesis of the functional form of the vertebral bodies, i.e.,
amphicoely. While some of the differences in the development of teleost centra
have been pointed out (Ganguly & Mitra, 1962; Schaeffer, 1967; Francois,
1966) there is considerable similarity in the dynamics of the morphogenetic
processes which result in the characteristic amphicoelous shape.
J . LAERM
240
A
s
Ce
-v
C
D
Figure 2. Development of amphicoelous centrum. See text for details. Ce, Centrum deposition;
EE, elastica externa; FS, fibrous sheath; Nc, notochord; Ne, notochordal epithelium; S,
notochordal septum; Sc, sclerotome; V. vacuoles.
The following description of the epigenesis of amphicoelous centra is
characteristic of teleosts and has been abstracted from the work of the authors
cited above. Where exceptions or differences in the morphogenetic processes
occur, they will be discussed.
Shortly after the notochord differentiates as a cylindrical tube it becomes
characteristically vacuolated by the outer notochordal cells migrating to the
periphery, thereby forming a notochordal epithelium. The notochordal
epithelium is then believed to induce the formation of a membranous elastica
externa which surrounds the notochord and its epithelium.
In oviparous teleosts myotomal rudiments are developing about the time the
elastica externa is formed and contractile muscle fibers are present. Shortly
thereafter the larvae are free-living and capable of locomotor activity. As the
somites differentiate, sclerotomal cells migrate, accumulate, and invest the
notochord and the elastica externa within a continuous cylindrical perichordal
tube. A fibrous sheath forms between the elastica externa and the notochordal
epithelium. Before this time, no segmentation of the developing vertebral
column is evident. (See Fig. 2.)
Shortly after the formation of the elastica externa, differential thickening of
the two sheaths (i.e., externa and fibrous) and the notochordal epithelium
AMPHICOELOUS VERTEBRAE IN TELEOSTS
24 1
occurs in prospective intervertebral regions (Fig. 2B). This thickening is the
first indication of segmentation of the developing column typical of not only
teleosts but other actinopterygians as well (Hay, 1895; Schaunisland, 1906).
After this initial segmentation is evidenced, ossification begins intravertebrally.
The mechanisms for the induction of centra formation from skeletal
mesenchyme although considered in some detail in tetrapods (Holtzer, 1951,
1952, 1956; Holtzer & Detwiler, 1953; Grobstein & Holtzer, 1955; Detwiler &
Holtzer, 1954; Fowler & Watterson, 1953) have not been considered in fish.
Williams’ (1959) and Schaeffer’s (1967) reviews, however, suggest fundamental
differences between the developmental mechanisms in fish and tetrapods.
Borkhvardt’s (1969) study of the cartilaginous and osseous origins of centra in
fishes and tetrapods, on the other hand, suggests similar inductive mechanisms.
From available descriptions there appear to be two sites involved in the
initiation of centra formation. Francois (1958, 1966, 1968) has discussed
centrum formation in several species in which it forms as a double ring. In
Clupea, Esox, and Salmo, for example, an internal chordacentrum is formed by
calcification of the fibrous sheath. Later, a second outer ring (the autocentrum)
is formed by ossification in the sclerotomally derived perichordal tube.
Francois notes, however, that in the species studied, the internal
chordacentrum degenerates and the definitive centrum is formed by the
contributions made by the outer perichordal ring. In these species, Francois
describes a differential thickening and growth of the chordacentrum in which
constrictions of the notochordal tissues occur intravertebrally, while lack of
chordacentrum growth intervertebrally results in characteristic dilations of the
notochord in these regions. This initial differential constriction and dilation
provides, in addition to the segmentation of the column, the first indication of
the future hour-glass or cone shape of the developing centrum (Fig. 2B).
Francois remarks, however, that in those fish in which the thickening of the
chordacentrum occurs, it does not increase in later stages and actually becomes
incorporated into the ossifying perichordal autocentrum. He further suggests
that since the chordacentrum does not grow appreciably, the thickness of the
vertebral body is accomplished exclusively by the deposition of bony layers on
the whole surface of the primitive autocentrum (i.e., from perichordal
sclerotome). In all forms of teleosts described it is believed that the vertebrae
develop from both chordal and perichordal elements. While arches generally
form by perichordal ossification from cartilaginous anlage, the centrum itself
always forms by direct ossification.
Francois (1966) suggests that although other authors do not describe a
chordacentrum it is because the fibrous sheath in which it forms degenerates
early in these forms and that a chordacentrum, although formed, is of
diminished size and becomes incorporated into the definitive autocentrum
earlier. Ramanujan (1929), Mookerjee et al. (1940) and Kame1 (1953) similarly
report the chordacentrum to be a transitory formation. In the fish described by
these workers the complete chordacentrum does not appear. However, some
calcified vestiges may be observed (Reinbold, 1966). In the most advanced
teleosts the fibrous sheath degenerates very early being represented only by the
intervertebral ligaments.
In species in which degeneration of the fibrous sheath occurs, it does so
17
242
J . LAERM
intravertebrally while thickening of the fibrous sheath and notochordal
epithelium occurs intervertebrally. Simultaneously, a differential growth of the
perichordal tube may be observed intravertebrally. The lack of perichordal
growth intervertebrally apparently allows for the swelling of the fibrous sheath
and notochordal epithelium in that region (Fig. 2B).
In either case, at the onset of ossification (Fig. 2C) the developing vertebral
column is characterized by a series of intravertebral constrictions alternating
with intervertebral dilations. At this time, the notochord becomes
characteristically more vacuolated with, in most cases, only an intervertebral
septum of notochordal tissue remaining.
Centrum formation continues by ossification. It is initiated in the
intravertebral region of the sclerotome at the center of the centrum and
proceeds caudad and cephalad (Fig. 2D) toward adjacent centra forming a
Figure 3. Horizontal section through representative teleost centra: A, Grouper; B, Perch; C,
Bass;D, E, F, anterior, mid, and caudal centra of Sea Trout. See text for discussion.
AMPHICOELOUS VERTEBRAE IN TELEOSTS
243
cylindrical tube constricted at its center, i.e., a cone. At the same time the
notochord, its epithelium, and the remainder of the fibrous sheath tissues
become further expanded in the intervertebral regions. As centrum ossification
proceeds, it extends to the regions of the intervertebral swellings. Even as it is
first developing, this intervertebral thickening of tissue resembles a ring
(perichondral ring) and its presence would appear to have a very definite
physical effect on the shape of the centrum as its morphogenesis proceeds. For,
as the ossified centrum elongates (Fig. 2D), the mass of notochordal tissue
present as the perichondral rings requires the developing bony centrum to grow
outward and around it contributing further to the biconid shape.
Thus, the cylindrical shape of the developing centrum results from the
cylindrical arrangement of perichordal sclerotome and subsequent ossification
within it. The attainment of the characteristic amphicoelous (or cone) shape,
on the other hand, is controlled by the alternating dilation and constriction
associated with differential growth of the sclerotome and notochordal sheaths.
The underlying morphogenetic mechanisms which control the epigenesis of
the teleost biconid are unknown. However, it is axiomatic that the shape
described by a finite cone is a function of its length and basal diameter. I t
would, therefore, appear that developmental limitations on the length and
diameter of the centrum anlage might be expected to control the differences in
the shape of the amphicoelous biconid observed not only in different groups of
teleosts, but also perhaps between regions along the vertebral column of a
single fish (see Fig. 3).
Sections in the frontal plane through the centra in Figs 1 B and 3 show
considerable spongy bone-deposition lateral to the compact biconid. As noted
earlier, this spongy bone occurs as longitudinal bars of bone on the lateral
surface of almost all teleost centra. This portion of the centrum develops from
undifferentiated mesenchyme derived from the sclerotome (Fig. 2D). The
timing of the onset of ossification of the spongy bone corresponds to that of
the compact biconid. However, spongy bone deposition continues after the
biconid has been completed. The morphogenetic mechanisms which control
spongy bone deposition and which control the shape and orientation of the
lateral longitudinal bars will be discussed below.
Biomechanics of fish vertebral columns
In many considerations of vertebral mechanics the axial skeleton is suggested
to be a relatively homogeneous elastic beam to which may be applied beam
deformation mechanics and Euler’s Theory of Buckling (i.e., Badoux, 1967).
Although the vertebral column in fish functions to resist buckling, the
application of beam mechanics to the basic design of vertebral elements may
not be strictly applicable. For while the analogy to mechanical engineering
phenomena may permit generalized description of biological function, the
problems of failure in a solid rod or beam and failure in a column composed of
separate elements are different and, therefore, require different strategies of
design in their structure.
Consider a column or beam that is subject to compression as a result of two
forces applied to the ends of the beam (Fig. 4). As the load increases failure
J. LAERM
244
A
6
C
4
Stressed Fracture
Member Failure
L
Stressed
Member
Buckle
Failure
Stressed
Member
Buckle
Failure
Figure 4. The effect of axial loads on various columns. See text for details.
may result occurring either by fracture, general yielding, or excessive
deformation (Smith & Sidebottom, 1969). If the column is sufficiently long it
will buckle (Fig. 4A) and the column will fail by bending at approximately the
middle (Den Hartog, 1949). If, however, the column is sufficiently short (or in
the case of most brittle materials) failure by fracture occurs. The force required
to initiate buckling in a long member is considerably less than that required to
initiate fracture failure; therefore, buckling generally occurs first. However,
whether a structure of given material properties will tend to fail by buckling or
by fracture is largely a function of the length of the member relative to its
cross-sectional area. In a short member the force required for buckle failure is
greater than that for fracture. As a result, short members with large
cross-sectional areas generally fail by fracture before bending occurs.
If a long column composed of separate short elements (Fig. 4C) is subjected
to axial loading it can be shown that buckling of the column will most
probably be due to failure “between” the separate elements. For example, as
bending deformation occurs under axial loading it can be shown that bending
moments will be created between at least two elements that will result in
flexion between them (Fig. 4C).If the load increases, further flexion will occur
between elements and the column will fail. In such a case it is highly unlikely
that fracture failure in the separate elements would occur before bending
failure between them. Clearly, a long column composed of separate elements
and subjected to axial loading must possess design modifications that limit
AMPHICOELOUS VERTEBRAE IN TELEOSTS
245
B
Figure 5 . Horizontal section through typical teleost showing relationship of a muscle fiber
trajectory to the vertebral column. When muscle fibers between X and Y contract, the vertebral
column bends. View is dorsal.
flexion between elements.
The axial skeleton of teleosts is analogous to a long column. I t is composed
of short separate elements, the centra, that are subjected to axial loading. The
nature of the intervertebral articulations between teleost centra may best be
described as an amphiarthrosis. Successive bony centra are separated by a thin,
notochordally derived, intervertebral fibrocartilage ring. The articulations are
maintained by intervertebral ligaments (derived from the notochord and its
sheaths) as well as dorsal and ventral longitudinal ligaments (Ramanujan, 1929;
Mookerjee, 1934). The movement between successive centra is limited to
lateral flexion in the frontal plane by structural adaptations which limit torsion
and dorso-ventral flexion (see Fierstein & Walters, 1968 for example).
Although the lateral musculature of many representative teleosts has been
well described (Cole, 1907; Greene & Greene, 1913; Emelianov, 1935; Nishi,
1936; Nursall, 1956), the relationship of the arrangement and folding of fish
myomeres to body flexion has not. The lateral musculature of fish are
segmentally arranged. The muscle fibers, grouped into myomeres, are
interrupted by segmental myosepta, sheets of connective tissue each of which
has attachment to a vertebra (see above references for excellent general
descriptions of muscular anatomy in various groups).
Alexander (1 969) has shown that the muscle fibers in successive myomeres
are arranged in functional units which he terms “muscle fiber trajectories”
which operate over several vertebral segments (Fig. 5 ) . More recently, Willemse
246
J . LAERM
i ntervertebral I igaments
A
Figure 6. Simplified mechanical model analogous to generalized teleost vertebral column of Fig.
7 . View is dorsal.
(1972) discussed the arrangement of connective tissue fibers in view of
Alexander's (1969) trajectorial model and has provided further evidence of the
relationship between muscle fiber trajectories and the axial skeleton. Although
these authors provide an excellent model for the function of the lateral
musculature, neither discusses vertebral function in response to the bending
created by the muscles.
The effect of muscle fiber trajectories in bending the vertebral column may
be seen in Fig. 5 . Serial contraction of the fibers in successive myomeres
between the endpoints (X and Y)of a muscle fiber trajectory results in bending
loads applied to the vertebral column at those points.
Flexion between vertebral elements is resisted first, by the flat articular
surfaces of adjacent centra and, second, by the tension in the intervertebral
ligaments. However, while flexion is resisted, the elasticity of intervertebral
ligaments and the plasticity of intervertebral fibrocartilage may permit flexion
if sufficient bending forces are applied. As bending forces are applied by the
muscle trajectory this (as shown in Fig. 5 ) results in flexion between successive
vertebrae.
Form and function in amphicoely
Figure 6 represents a simplified mechanical model analogous to a generalized
teleost vertebral column. The bending forces created by fibers of the
muscle-trajectory system are represented by force vectors F , and F 2 . The
intervertebral ligaments are analogized to a single spring which reflect the
tension forces encountered by the ligaments during flexion between adjacent
AMPHICOELOUS VERTEBRAE IN TELEOSTS
247
Figure 7 . Graphic model of mechanics of vertebral flexion. See text for details.
centra. When bending forces are exerted on the column, flexion between
adjacent centra results.
A simplified graphic model of the relative magnitude and line of action of
the reaction forces (compressive) which result in stress within individual centra
may be shown for the above.
Figure 7 represents, greatly exaggerated, the three middle bodies or centra
taken from Fig. 6. In Fig. 7 bodies A and C are being flexed on body B about
points P and Q, respectively. The tensions developed in the intervertebral
ligaments as a result of flexion between A and B, and B and C are analogized to
springs. In the free body diagram of body B (Fig. 7) these forces are
represented by vectors Rr and Sr at points R and S, respectively. The reaction
forces of bodies A and C act on B at points P and Q, respectively. Equilibrium
equations may be determined and it can be shown that reaction forces at points
P and Q have components Px and Py, and Qx and Qy which permit these forces
to be resolved into single resultant forces whose lines of action are indicated by
Pr and Qr at those points respectively.
In an unbent vertebral column compressive stresses are distributed in each
centra normal to their end surface. This compressive stress is the force per unit
area acting on the entire surface of contact between two adjacent centra. As
the vertebral column undergoes bending in response to loads due to the
unilateral contraction of the muscle-fiber trajectories, successive centra are
flexed upon one another. The line of action of the distributed stress is altered
and its magnitude increases. First, it can be seen that as flexion occurs the line
of action of the stress acting on any centrum is, in part, a function of the angle
J. LAERM
248
of flexion between adjacent centra, Also, as flexion between adjacent centra
occurs the area of their surface of contact decreases, theoretically, at least, t o a
point. Therefore, for any given force exerted between them, the stress acting
upon them, being a function of the area, will increase. Furthermore, as flexion
between adjacent centra occurs, there is an increase in the resistance to it by
the intravertebral ligamentous connections. This results in greater reaction
forces and thus greater stress distributed on those surfaces in contact. In the
models discussed above, it can easily be shown that the angle the resultant
reaction force has to the lateral margin of a centra is a function of the lines of
action of the forces applied to the body, in turn, a function of the angle of
flexion between centra.
I t was Borkhvardt (1970) who first suggested the possibility that the
amphicoelous or biconid shape in teleost centra was correlated with stress.
Borkhvardt inferred that differences in the deposition of compact bone and
hence, shape of the biconid compactum seen in different teleosts should reflect
differences in the line of action of stress distribution due to differing degrees of
lateral bending during locomotion. While intuitively satisfying, quantitative
comparisons suggest otherwise.
The angle of flexion between adjacent centra for a number of fish can be
measured. This angle can provide an indirect measure of the angle at which the
greatest compressive stress distribution is occurring in adjacent centra during
flexion. I t is then possible to compare the angle of stress distribution to the
angle formed by the mass of compact bone in the biconid.
Table 1. Measurement of the angle of flexion between
adjacent centra and angle at which bone deposition
occurs in the biconid and longitudinal bony bar
~
Name
~~
Mean
angle of
flexion
Perca flavescens (Perch)
8.8
Gadus morhua (Codfish)
8.4
Roccus saxatilis (Striped Bass)
8.6
Micropterus salmoides (Largemouth Bass) 8.7
Centropristis philidelphica (Rock Bass)
8.8
10.1
Anguilla rostrata (Eel)
ESOXlucius (Pike)
8.1
Pomoxis annularis (Crappie)
8.3
Epinephelus (Grouper)
8.0
Lutjanus campeehanus (Snapper)
7.8
Thunnus (Tuna)
5.9
Mudl (Mullet)
8.0
Salvelinus fontinalis (Brooknout)
9.4
a p r i n u s carpi0 (Carp)
9.0
Pomatomus saltatrix (Bluefish)
7.9
Scomber scornbrus (Mckerel)
6.2
Moxostoma macrolepidotum (Redhorse)
8.5
Ictalurus melas (Catfish)
8.7
~
a'
P'
4s
28
53
40
52
47
42
38
38
41
28
42
39
3s
39
32
37
46
1s
14
14
15
1s
22
13
14
14
12
10
12
20
14
11
12
15
12
'a,Angle of the compact biconid measured from sectioned centra
(see Fig. 8).
*p. Angle formed by the alignment of spongy bone with respect to the
lateral surface (see Figs 1 B and 8).
AMPHICOELOUS VERTEBRAE IN TELEOSTS
2 49
Figure 8. Tracing of horizontal section of centra shown in Fig. 1B. a is the angle of the biconid
compactum with respect to lateral margin of the centrum. p is the angle formed b y the mass of
spongy bone deposition and approximate line of deposition of bony trabeculae. Compare with
Fig. 1B for details.
The angle of flexion between adjacent centra was measured for several
groups of fish. Specimens were obtained from a fresh-fish market. Lateral
musculature was removed on both sides of the body and the vertebral columns
manipulated manually to determine the degree of bending between adjacent
centra. The angle of flexion was determined by bending a segment of the
column and measuring the total angular displacement between the two centra
at either end of the segment. The angle obtained was divided by the number of
articulations giving the mean angular flexion between individual centra. These
data are shown in Table 1.
Centra were removed from the mid-portion of the vertebral column (which
corresponded to those measured above) and sectioned in the horizontal plane.
The angle between the lateral margin of the centrum and the compactum of the
biconid (Fig. 8) were measured under a dissecting microscope with a template
protractor calibrated to the nearest degree. These measurements also are shown
in Table 1 .
The bending angles between adjacent centra occur at fairly low angles. This
would suggest that the actual line of action of greatest stress distribution would
occur at angles very much lower than those exhibited by the biconid.
Application of a Wilcoxon Two-Sample Rank Test to these data indicates that
the angle of flexion between centra and angle formed by the biconid are not
significantly correlated.
The reaction forces that result from flexion between adjacent cone shaped
centra are exerted on the lateral margin of the anterior and posterior surfaces as
shown in Fig. 9A. Since the lines of action of the two reaction forces are lateral
to the central longitudinal axis of the centrum, two opposite and assumedly
equal moments will be acting about the central constricted portion of the
centrum. The bending moments about this area will result in a load distribution
such that deformation due to compression would occur on the side under
250
J. LAERM
Figure 9 . Amphicoelous centrum under bending loads. A. Biconid centrum as suggested in Fig.
1C. Arrows indicate bending loads due to flexion between adjacent centra. B. Diagrammatic
dorsal view of same biconid. C. Compressive struts resist stresses due to bending loads. D.
Suggested design modification of amphicoelous biconid with longitudinal struts, compare with
Fig. 1A.
compression (shown by dark arrows in the figure) while tensile deformation
would occur on the other side. The cone shape, under such asymmetrical
loading conditions, is unsound. For, if sufficient loads were applied, failure due
to local crushing on the side under compression or tensile failure on the
opposite side might result. In such a case, design modification of the cone
shape is required to reduce or eliminate the possibility of failure. Such a
modification is possible by the placement of a compressive strut between the
points on the lateral margins of the centralwhere loading occurs (Fig. 9C and
D).
It had been noted earlier that fracture failure of a single element in a column
composed of elements is much less likely to occur than buckling of the column
due to failure between elements. It can be suggested, however, that bone design
of a single centrum need not only reflect selection for resistance to failure but
rather that bone design reflects a modeling response to stress.
Bone is likened to a mechanical engineering structural material (Alexander,
1968; Frost, 1964) which, like other structural materials, deforms under stress.
Bone, however, unlike other structural materials, is capable of modeling and
remodeling its shape or form in response to changes in the distribution of
stresses applied to it. This phenomenon has been long recognized and'
popularized by morphologists (Wolff, 1892; Koch, 1917; Murray, 1936;
Thompson, 1942; Bell, 1956; Enlow, 1963; Frost, 1964). It is only recently
that the biophysical basis for the relationship of stress to bone development has
AMPHICOELOUS VERTEBRAE IN TELEOSTS
25 1
been understood (see Bassett, 1972, for a review of the biophysical principles
affecting bone structure and extensive bibliography).
The modeling process is analogized to a feedback mechanism (Warburton,
1955; Frost, 1967; Bassett, 1972) in which activation of undifferentiated
mesenchymal progenitor cells, osteoblasts, and osteoclasts is thought to be due
to an electrophysical response of tissue to mechanical loading. The application
of a force to bone or bone forming tissue results in plastic deformation. The
plastic deformation apparently functions as a transducer in which the
mechanical signal (the load) is transduced into piezoelectrical signals which
control site-specific and orientation-specific osteoclastic and osteoblastic
activity. Adaptively, the electrophysical response of bone to different
functional stresses results in architectural arrangement of both the shape and
mass of bone structure appropriate to resist the applied loads.
Bone deposition in response to stress is known to occur fairly early in the
ontogeny of fishes. For example, Weisel (1967) has shown that the first formed
bony structures in several teleosts are those that must meet the functional
demands associated with locomotion, feeding and respiration. In particular,
Weisel has shown that the timing of the onset of ossification and the location
of ossification along the vertebral column is controlled by mechanical stresses
associated with locomotor activity of the larvae and fry.
Although the timing and location of the initiation of ossification of teleost
centra is controlled by stress, the compact bone of the biconid is not correlated
with particular stress distributions as pointed out above. However, the
remaining bone of the centrum, the longitudinal bars of spongy bone deposited
around the compactum of the biconid, is subject to modeling in response to
stress.
The distribution of the mass of spongy bone in longitudinal bars of a
representative centrum can be seen in Fig. 1. The angular alignment of the
bony trabeculae in sectioned centra can be measured and compared statistically
to the suggested angles at which bending stresses are distributed; it was
suggested above that the angle at which stresses are distributed is a function of
the bending angles between centra.
The measured angle (see Fig. 8) at which spongy bone is deposited relative to
the lateral longitudinal axis of the centrum for several groups of fishes is given
in Table 1. A Wilcoxon Two Sample Rank Test indicates the distribution of the
mass of bone tissue and the alignment of bony trabeculae in the longitudinal
bar is correlated with bending angles. Therefore, the presence of such a bony
bar (whose function is clearly analogous to a compressive strut) with
longitudinal alignment of trabeculae indicates an adaptive modeling of centra
shape in response to mechanical stresses during locomotion.
CONCLUSION
From developmental and functional considerations, the shape of the
compact biconid portion of amphicoelous teleost centra does not appear to be
correlated with functional stress. The biconid forms in response to cylindrically
arranged sclerotomal mesenchyme and subsequent ossification within it. The
particular shape of the cone is determined apparently by length and diameter
252
J . LAERM
constraints imposed upon the developing centrum anlage by morphogenetic
mechanisms not presently known.
The attainment of the characteristic shape of the compact biconid is
controlled by alternating dilation and constriction associated with differential
growth of the sclerotome and notochordal sheaths.
The spongy bone present in the centrum lies lateral to the compact biconid
and makes up much of the bony centrum. It is present as a horizontal bar and
serves also as support for neural and haemal arches. I t is derived from
sclerotomal mesenchyme. The time of formation of this portion of the
centrum, its position, and the alignment of bony trabeculae within it suggest it
to be deposited in response to mechanical stress.
ACKNOWLEDGEMENTS
This manuscript was read and commented upon by R. McN. Alexander, N.
Hotton, R. Lund, B. Schaeffer, and G. Zug. Special thanks goes to T. H.
Frazzetta whose discussion and criticism of earlier drafts improved the quality
of this report.
C. Arian and A. Prickett prepared the illustrations.
Funds were provided by the Provisional Department of Ecology, Ethology,
and Evolution, University of Illinois, and by a Smithsonian Institution
Predoctoral Fellowship.
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