Tansey
Abstract
The skeletal system in starfish greatly influences behavior
and ecology. Locomotory behavior, especially aspects of flex¬
iblity, is dependent on the properties of the skeletal system.
Anatomical and mechanical properties are here examined to
determine the relationship of ossicle mass, material stiffness,
and flexibility. Flexibility behavior is also observed to
examine the range of degree and rate of bending among the3
subject species. It is concluded that a) The greater the
volume fraction of ossicles, the stiffer the tissue and b) The
greater the volume fraction of ossicles, the lesser the flex¬
ibility. It is also found that rate of flection varies more
among the species than does the degree of flexibility.
Introduction
Much of starfish behavior is influenced by the skeletal
system. This effect has been studied in feeding on bivalves
(Eylers '76) and in burrowing behavior (Heddle '67). The
effect of skeletal structure on flexibility, however, has not
been examined. The ability to survive on a complex 3-dimen¬
sional rocky coastline with wave action, predators, tides and
varying food sources is probably in part a function of flex¬
ibility. Sturdiness would benefit an intertidal starfish
that deals with constant compressive wave forces while good
flexibility allows movement in a greater variety of micro¬
habitats (crevices and open faces) giving greater access
to a greater number of prey and hiding places. This study
was undertaken to examine the effect of anatomical and
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and material properties of 3 species of intertidal starfish;
2ycnopodia helianthoides,Pisaster ochraceus, and Patiria
miniata,on their flexibility. These species were chosen
because of their differing habitats, morphologies and behaviors.
Materials and Methods
Ossicle Anatomy
Starfish of the above species were collected from
Monterey Bay, California and kept in seatable tanks at
Hopkins Marine Station, Pacific Grove, Ca. Patiria and
Pisaster of a typical size (130 and 170 g respectively)
and small to medium size Pycnopodia (260 g) were used for a
preliminary ossicle morphology examination. The animals
were first relaxed in a solution of 50% sea water and 50%
magnesium chloride solution (70 g Mgcl in 1 1. H,O)
(Heddle '67) then cleaned of soft tissue in a solution of
one-third household bleach (active ingredient 5.25% sodium
hypochlorite) and two-thirds sea water for 2-4 hours. An
examination was made of the individual ossicles and their
organization.
Flexibility
Flexibility experiments were performed on instarfish
of each species; the anus to arm tip lengths of which were
recorded. The starfish were relaxed in the Mgcl solution
for over 12 hours, then manually deformed around glass
tubing with radii ranging from 1.5 mm to 5.6 cm. Measure¬
ments of the minimum radius to which each could bend were
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taken for a lateral bend, an oral flection and an aboral
flection. The radius of curvature was then normalized to
the arm length.
An obstacle tank (fig. 1) was constructed to observe
natural bending behavior. 11 PVC pipes of radii ranging
from 1 cm to 5.5 cm were attached to the bottom and sides
of the concrete tank with marine epoxy. Natural bending
around the pipes was observed in 12 starfish; 6 Patiria
4 Pisaster, and 2 Pycnopodia. Bending was also induced
by manually setting the starfish on or against various
pipes. The starfish were also manually inverted so that
righting behavior could be observed.
Material Properties
The ratio of dry ossicle mass to total wet mass was
determined for a single arm of 1 individual of each species.
After the arms were removed from the animals and soaked
in 50% NaoH (Eylers '76) to remove soft tissue, the ossicles
were separated, dried with a heat lamp, and weighed.
The stress-strain relationships were determined for
patches of aboral skeleton (the more interspecifically
varied of the 2 sybsystems) for each species. These stress¬
strain curves were determined from the data yielded by the
starfish skeleton stretching machine (fig. 2) The test
sample was clamped between a clamp mounted on an anchored
double cantilever beam and a clamp mounted on a plate moved
by a lead screw. Force was sensed by deflection of the
double beam and was monitored by a linearly variable differ¬
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entiated transducer (LVDT) on the anchored plate. Deforma¬
tion of the sample was monitored by a LVDT mounted on the moving
plate. The voltage output of each LVDT was recorded on
a chart recorder. The machine could measure strain up to
40% and stress up to.85 N.
The 18 aboral patches (6 from each species) were removed
from starfish that had been relaxed in Mgcl and cut into
hourglass shapes with a rectangular center sections.
The volumes of the center sections were calculated from meas¬
ured length, width and thickness. For the sake of numerical
convenience, the length was kept at a constant 5 mm for all
tests. Volumes varied between 7 x 10"0 m2 and 3.6 x 10' m
for the 18 patches. Assuming the sample to be isovolumetric,
a new cross-sectional area was determined at each strain.
Stress (0) and strain (8) could then be calculated.
force
6  cross-sectional area
n LAL
where L is original length and LAL is the new stretched
length.
These stress-strain curves were determined at 2 different
strain rates (strain rate is £ - 8/unit time): £ - 3.5 x 10 "
(elapsed time = 96 sec) and £ = 2,8 x 10  sec
sec
(elapses time = 12 sec). 3 trials were run for each species
at each strain rate. Young's moduli were then calculated
from the slope of a plot averaged for the 3 trials. Young's
modulus is the stress at a natural strain divided by
that natural strain. The strains observed in nature
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were calculated using an average radius of curvature observed
from the starfish obstacle tank experiment
X -4L -
where X is extension, ris the distance from the neutral
axis (fig. 3) to the surface undergoing tension of compressive
stress, and R is the radius to which the arm is bent
(Wainwright et al '76)
Results
Ossicle Anatomy
The starfish skeletal system has been illustrated
elsewhere (Eylers '76, Heddle '67) for other species.
Both the ambulacral and aboral skeletal systems for the
3 species examined here are pictured in figure 4. The
ambulacral systems are similar in the species if the 2
rows of plate-like ossicles next to the ambulacral ossicles
in Pycnopodia are considered part of the aboral skeleton.
The aboral "lattice-work" structure in Patiria and Pisaster
differs greatly from the scattered spines in Pycnopodia,
but upon closer examination it is seen that even the 2
"lattice-work" structures are basically different. Patiria
has a flat, 2-dimensional shingle-like form; the anchored
ends of each ossicle being covered by the exposed portion
of the ossicles immediately below it (more oral).
Pisaster has a complex 3-dimensional lattice composed of
small irregularly shaped ossicles anchored together like
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a stone wall.
Flexibility
Pycnopodia is the most flexible of the 3 starfish
examined (table 1). Lateral flexibility in this species
is approximately half that of oral or aboral flixibility.
Pisaster shows approximately equal values of flexibility
in all directions. Patiria, the least flexible species,
is half as flexible as Pisaster in the lateral and oral
flections and one fourth as flexible in the aboral flection.
To check the values from this experiment, behavioral
observations were made of the 12 starfish in the obstacle
tank. If placed on the pipes manually, all three species
bend around the pipe to hold on with a majority of tube
feet. It is noted that if the radius of pipe is smaller,
the period of time of bending is longer. The best demon¬
strations of flexibility by all three species is obtained
by inverting the starfish and observing righting behavior,
The rate of flection seen in this experiment varies among
the species more than the degree of flexibility. Pycnopodia
was the fastest bender, and Patiria was the slowest.
Material Properties
The contribution of dry ossicle mass to total wet
mass is 4% in Pycnopodia, 15% in Pisaster, and 16% in
Patiria.
Stress-strain curves are determined for patches of the
aboral skeleton at 2 different strain rates (as described
in material and methods) and are shown in figures 5 and
6. Each outgoing curve (extension) and returning curve
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(relaxation) represents the average of 3 tests. At the
higher strain rate, considerable plastic flow is observed.
(20% in Pisaster, 40% in Patiria and 50% in Pycnopodia.)
At the lower strain rate, plastic flow is less (20% in Pisaster,
0% in Patiria, and 0% in Pycnopodia). Naturally occurring
strain is calculated (as described in materials and methods)
to be 0.28. Young's modulus was calculated for each extension
using this natural strain and the corresponding stress.
Patiria is stiffest at the higher & (3 times as stiff as
at the lower 6mp). Pisaster and Pycnopodia are stiffer
in the slower test than in the faster test (Pisaster 5
times as much).
Discussion
The comparative analysis of the 3 species in this
study revealed a relation between skeletal anatomy, mechani¬
cal properties and flexibility. Is there a mechanistic
basis for this relationship?
The differences in organization of ossicles among
species can be used to explain the results obtained from
the manual deformation of relaxed starfish. Pycnopodia
is only half as flexible in a lateral bend as in either an
oral or aboral direction. This fact can be explained by
the presence of the 2 lateral rows of ossicles on either
side of the ambulacral ossicles. When compressed, these
ossicles jam into each other to form a solid rigid unit
that resists further compression. Patiria's aboral flection
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is half that of other bends due to the greater height
of the arm (greater arm cross-sectional area) and the
large sturdy ossicles found on the proximal aboral surface.
The greater arm cross-sectional area would need a greater
stress to show the same strain. The may be responsible
for Patiria's general inflexibility. The aboral ossicles
are large enough to effect aboral flection in the same way
that the lateral ossicles in Pycnopodia effect lateral
bend in that species.
A rough prediction of flexibility can be computed
from the ratios of ossicle mass to total mass. Using the
relationship of density, mass and volume, these mass ratios
can be expressed as volume fraction ratios. If the density
of soft tissue is approximately 14 and the density of ossicles
is 2.6 g cm (Jones '70 as cited by Koehl 182), the
ratio of ossicle volume to total volume (the ossicle
volume fraction, Vpo) is
Vo  OM 1 2.6 q cm
Vro - Vr
2.6 g om total massl m
This equation yields values of ossicle volume fraction of
.016 for Pycnopodia, .064 for Pisaster, and .068 for Patiria.
(These values normalize to a 1:4:4.25 ratio for the 3
species). The Young's modulus of ossicle Caco, is approxi¬
mately 137 GN m (Wainwright et al '76) making it very
inextensible in comparison to the soft tissues likely to
be found in the arm, such as ligament, muscle, connective
tissue, and epidermis, which have Young's moduli between
10* and 102 N m (Wainwright '76). Thus as the volume
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fraction of ossicles increases the extensibility of the
tissue decreases. If the volume fraction of ossicles is
1, the total extensibility (Kay
will be essentially O.
If, however, the volume fraction of ossicles is O, the
will represent the extensibility of the soft tissues
max
(k). This linear function is illustrated in figure 7,
and can be expressed as
- -k Vpo t k
max
The extension experienced by the bending arm as a whole is
X-2L -
(fig. 3)
L
where X is extension of the aboral tissue, r is the distance
from the neutral axis, and R is the radius to which the arm
is bent (Wainwright et al '76). Therefore,
Vro tk
--kyptkor
where 1/R is equal to flexibility. This shows that the
greater the volume fraction of ossicles, the larger the
radius of bending and the smaller the flexibility. If
the k values are the same among the 3 species, the radii
of bending will have the same 1:4:4.25 ratio as the ossicle
volume fractions. This ratio is not experimentally observed
(table 3) implying that the k values differ. It should,
however, be noted that the experimental results are qualita¬
tively correct: the greater the ossicle volume fraction,
the less the flexibility. Using an average r value of 2.8
cm and the observed radius of curvature (oral flection)
the k values can be computed using the formula
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kRIIo
as 14.2 for Bycnopodia, 2.3 for Pisaster, and 1.4 for Patiria,
The results of relaxed starfish flexibility tests
conflict somewhat with observations of natural bending in
the obstacle tank. The degree of flexibility seems to
vary less among species at natural rates of flection.
The importance of such observations would be greatly strength¬
ened if more exhaustive statistically relevant examination
were made. Nevertheless, these results encouraged analysis
of material properties to explain the relation of material
stiffness and strain rate. Stiffness varies among species
and between rates of strain for each species. This variation
of stiffness can be related to ossicle mass (table 3).
For a composite material arranged serially (roughly the
situation in a starfish arm) the inverse of Young's modulus
is equal to the sum of the ratios of volume fraction to
stiffness of each component in the material (Wainwright
et al '76).
.
1 - Vro + Vro

FST
where Eg is the total stiffness, Eg is soft tissue stiffness,
E, is ossicle stiffness and Vy is ossicle volume fraction.
Again the ossicle stiffness is so much greater than the
stiffness of the soft tissue that the ratio of ossicle
volume fraction to ossicle stiffness is negligible. Therefore,
Esr
E
1-V
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The greater the ossicle volume fraction, the greater the
Young's modulus. If the Eg values are the same among the
species, the total stiffness will be directly proportional
to the ossicle volume fraction. An exact ratio is not
observed in the data implying different Eg values for
the species. It should again be noted that while the data
didn't perfectly conform to expectations, it still reflected
the general trend that the greater ossicle volume fraction, the
greater the stiffness. Using E values from the faster
strain test, approximate Eg values can be calculated using
the formula
Esr“ Er(1 - Vpo)
as 6.1 x 10° N m"4 for Pycnopodia, 1.6 x 10 Nm2 for
Pisaster, and 1.3 x 10° N m4 for Patiria.
Any relation between stiffness and flexibility in these
experiments is not clear. The major factor of confusion
is the change of stiffness with strain rate. Pycnopodia
is approximately equally stiff at both strain rates.
Patiria is 3 times stiffer at the faster strain rate;
Pisaster is 5 times stiffer at the slower strain rate,
Four possible explanations can be set forth.
1) Individual differences among members of the same
species may be reponsible. Different individual starfish
were used in Pisaster and Patiria for the 2 different strain
rates.
2) There may exist an optimal strain rate for each
species where the value of stiffness is lowest. If so,
the stiffnesses recorded here represent only 2 points on
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a curve, the minimum value of which is yet to be determined.
3) The amount of tissue damage done at the 2 strain rates
may have been different. The plastic flow, a measurement
of material destruction, is much greater at the faster
rate (up to 50%) than at the slower one (only 20%). Patiria
may have stretched at the fast rate while the other 2 species
may have just torn. Both the problems of individual dif¬
ference and breaking/stretching can only be fully examined
by statistically valid repetition.
The last explanation (4) may not only clarify the differ¬
ences in the stiffness at different strain rates but also
explain the lack of a direct parallel between ossicle mass
ratios, degree of flexibility and stiffness. Even if it
is assumed that the soft tissue components of each species
skeletal system are the same, the relative volume of any
1 type of soft tissue (e.g. ligament, muscle) to ossicle
volume and the organization of the soft tissue around the
ossicles differs greatly. An extensionin one species may be lim¬
ited by ligament while in another species muscle may be the
limiting factor. These differences may account for the
variety of k and Eg values calculated in previous equations.
Further experiments should be done to clarify this
situation. Both tensile and shear stress-strain curves
need to be determined at many more strain rates and percent
strains for a larger number of individuals. Further ana¬
tomical and histological examinations would be invaluable.
Nevertheless, these experiments do show that flexibility
and stiffness are related to ossicle mass. It is also
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found that rate of flection varies more among the species
than does degree of flexibility. Perhaps these results and
theoretical predictions will be considered in further ex¬
planations of starfish flexibility and locomotory behavior.
Acknowledgements
I am very grateful to M. Denny for his patient and
encouraging direction, consultation and inspiration. His
contribution of time and energy was limitless. I would
like to also thank S. Denny and K. Denny for their under-
standing. Thanks also go to M. Diab and Wm. Gilly for
critical discussion, K. Calhoun for showing pity and providing
typing skills, and F. Sommer for technical assistance and
humorous inspiration.
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Literature Cited
1) Eylers, John P. (1976) Aspects of Skeletal Mechanics
of the Starfish Asterias forbesii. J. Morph.,
149: 353-368.
2) Heddle, Duncan (1967) Versatility of Movement and the
Origin of the Asteroids. Symp. Zool. Soc. Lond.,
No. 20, 125-141.
3) Koehl, M.A.R. (1982)- Mechanical Design of Spicule¬
Reinforced Connective Tissue: Stiffness. J. Exp.
Biol. 98: 239-267.
4) Wainwright, S.A., Biggs, W.D., Currey, J.D., Gosline,
J.M. (1976) Mechanical Design in Organisms.
London: Edward Arnold.
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Figure Legend
Figure 1. Starfish obstacle tank. Eleven PVC pipes
with radii ranging from 1 cm to 5 cm. Used for
behavioral observations.
Figure 2. Starfish skeleton stretching machine. Force
and deformation were measured for aboral skeletal
patches to determine stress-strain curves,
Figure 3. Beam theory extension. Engineering model
to relate surface extension to radius of curvature.
Figure 4. Ossicle morphology. Ambulacral and aboral
skeletal systems are illustrated. P-proximal; D=
distal; AB=aboral; O-oral.
Figure 5. Stress-strain curves. Low plastic flow at
low strain rate. Pathway represents extension and relaxation.
Figure 6. Stress-strain curves. High plastic flow (502)
at high strain rate. Pathway represents extension
and relaxation.
Figure 7. Mathematical relation of extension and ossicle
volume fraction.
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STARFISH ARM FLEXABILITY
(MINIMUM BENDING RADIUS /ARM LENGTHJX IO
SPECIES
ABORAL
LATERAL ORAL
FLECTION
FLECTION
BEND
PYCNOPODIA
.55
.3
.23
PISASTER
2.4
2.4
.9
PATIRIA
4.3
8.9
4.3
Table 1
ABORAL SKELETAL STIFFNESS
YOUNGIS MODULUSX ION
SPECIES &2.8XIO 2SEC £3.5XO 9SEC
1.2
PYCNOPODIA
62
7.8
PISASTER
.7
4.9
4
PATIRIA
CALCULATED AT &=.28
Table 2
C
X
0
0
I
—

o u

LL
O

—

E
I
—
0
O
o
—

—

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O
1 —
L
—
STARFISH ÖBSTACLE TANK

Figure 1
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STARFISH SKELETON
STRETCHING MACHINE
LVDT
ANCHORED
LEVER PLATE



MOVING PLATE
LVDT
Figure 2
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DOUBLE
CANTILEVER
O
CLAMP
.........


G
0
CLAMPS
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BEAM THEORY EXTENSION


—

X = r/R
Figure: 3
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COMPRESION
NEUTRAL AXIS
TENSION
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OSSICLE MORPHOLOGY

ABORAL
PYCNOPODIA
A
Da

4
o
O
LATERAL
AMBULACRAL

PISASTER.




ABORAL
AMBULACRAL
PATIRIA
AB




O
E

S

ABORAL
AMBULACRAL
Figure 4
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C
50
45
40
35
X
N/m
25.
20
15
O.

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STRESS-STRAIN CURVES
EPYCNOPODIA
APISASTER
O PATIRIA
- 3.5XO SSEC
TIME 96 SEC

8


8


O



L



.3
.O5
15
.2
.25

Figure 5
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.35
50-
45
40
35
0
X1O
N/m
25
20
15
0
STRESS-STRAIN CURVES
H PYCNOPODIA
A PISASTER
O PATIRIA
-2.8XO 2SEC
TIME2 SEC







—

+




. 5
.25
2
.O5

6
Figure 6
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—2



—
3
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EXTENSION-OSSICLE VOLUME FRACTION
E QUATION


0
X-.-kVrok
Figure 7
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