Dorsal and anal fin function in bluegill sunfish Lepomis macrochirus: three-dimensional kinematics during propulsion and maneuvering
Museum of Comparative Zoology, Harvard University, 26 Oxford Street, Cambridge, MA 02138, USA
* Author for correspondence (e-mail: standen{at}fas.harvard.edu)
Accepted 24 May 2005
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Summary |
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Key words: swimming, maneuvering, locomotion, dorsal fin, anal fin, kinematics, stability, bluegill sunfish, Lepomis macrochirus
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Introduction |
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Fin use is an important issue for understanding fish locomotor biomechanics
because fish are statically unstable
(Eidietis et al., 2003;
Harris, 1936
,
1937
; Webb,
2002
,
2004b
;
Weihs, 1993
). The size and
position of fins relative to an animal's centre of mass (COM) will greatly
affect how dynamic stability is achieved during locomotion. Perturbations in
fish body position are caused by external environmental forces such as water
currents, or by forces produced by their own fins, which may result in roll,
pitch and yaw body movements (Fig.
1A). Fish use their fins to control body posture, and the relative
position of fins to the centre of mass and centre of buoyancy (COB) is
important in determining the forces and torques a fish experiences and
produces during swimming. For example, Fig.
1B depicts dorsal and anal fin positions relative to the COM and
COB of a typical fish. In this case, as is found in most fishes (Webb,
2004a
,b
),
the COB is below the COM, causing rolling instability. The greater the
distance of the fins from the midpoint between the COM and COB, the larger the
moment arm for that fin. Assuming fins of similar size, one may predict that
the anal fin in Fig. 1B would
require less force to produce the same torque as the dorsal fin due to the
length of its moment arm. Similarly, longitudinal and mediolateral position of
fins on the fish's body will also affect pitch and yaw instabilities around
the COM.
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Lauder and Drucker (2004)
discuss the active role of dorsal fins during propulsion and maneuvering, as
well as the absence of equivalent information available on the role of anal
fins. Dorsal fin musculature is active during steady swimming and maneuvers,
which suggests the soft-rayed portion of the fin acts as a control surface
independent of the body (Jayne et al.,
1996
). Hydrodynamic studies of soft dorsal fins show that they
produce lateral and posterolateral jets during swimming, suggesting that
dorsal fins produce significant locomotory forces (Drucker and Lauder,
2001a
,b
).
In many actinopterygian fishes the dorsal fin is often divided into two parts,
spiny and soft-rayed portions. The anterior spiny dorsal fin in bluegill
sunfish does not oscillate laterally during locomotion and is depressed during
higher speed swimming. These observations suggest that the soft-rayed portion
of the dorsal fin is responsible for the hydrodynamic forces recorded by
Drucker and Lauder
(2001a
,b
).
Also, due to the relative position of fish fins, we hypothesize that soft
dorsal fin hydrodynamic forces are, in large part, balanced by corresponding
movements of the anal fin.
Currently no studies address the hypothesis that anal fin movement balances forces produced by dorsal fin motion. A quantitative three-dimensional kinematic analysis of anal fins simultaneous with dorsal fins is important to understand the existing dorsal fin hydrodynamic data. Subtleties in fin movement are determined by fin shape; therefore, the movement and positions of individual fin rays should also be studied because rays represent the fundamental mechanical support within fish fins. Fin rays appear to be intricately involved in fin surface control, but the motions of individual fin rays have not been quantified previously during fin movement in fishes.
In this paper, we present a three-dimensional kinematic analysis of the function of dorsal and anal fins during locomotion. We used three calibrated and synchronized video cameras to capture the three-dimensional movement of both dorsal and anal fins in bluegill sunfish Lepomis macrochirus Rafinesque 1819 during locomotion. We quantify dorsal and anal fin excursions, curvature of individual fin rays, and phase lags between fins during both steady and unsteady locomotion. Our goal is to use these kinematic data to describe patterns of coordinated movement between the dorsal and anal fins, compare and contrast fin ray motion within and between the two fins, and formulate hypotheses of anal fin hydrodynamic function for comparison to previous dorsal fin data.
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Materials and methods |
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Behavioral observations
Bluegill swam in the centre of the working area (28 cm wide, 28 cm deep, 80
cm long) of a variable speed flow tank under conditions similar to those
described in previous kinematic work on both Lepomis and
Oncorhynchus (Drucker and Lauder,
2001a,
2003
). Steady linear swimming
was elicited from bluegill swimming at five speeds: 0.5 TL
s1, 1.0 TL s1, 1.5 TL
s1, 2.0 TL s1 and 2.5 TL
s1. Fish also performed yawing turns while swimming at 0.5
TL s1. As in previous research
(Drucker and Lauder, 2001b
),
turns were elicited using visual stimulus: a small-diameter wooden dowel was
dropped into the tank along the flow tank wall lateral to the fish's head. The
swimming behaviours induced in this study are directly comparable to those
studied on the same species in the hydrodynamic analysis of Drucker and Lauder
(2001a
,b
).
To characterize the simultaneous movement of dorsal and anal fins during all
behaviours we filmed fish using three synchronized high-speed video cameras
(Photron Fastcam 1280x1024 pixels, HiDCam II 1280x1024 pixels, and
a Photron APX system, 1024x1024 pixels) operating at 500 frames
s1 (1/500 s shutter speed). The three camera system gave us
a clear view of the dorsal fin, the anal fin and the lateral view of both
fins, enabling us to make a simultaneous comparison of dorsal and anal fin
kinematics (Fig. 2A).
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Camera calibration
To quantify the simultaneous spatial and temporal kinematics of the dorsal
and anal fin, video sequences were analyzed using a custom digitizing program
written using Matlab (version 6.5.1, Mathworks, Natick, MA, USA). The three
temporally synchronized camera images were calibrated to view the same
three-dimensional volume using a three-step process, detailed below.
First, a calibration cube with known location points was used to image the
field of view of each pair of cameras: once for the dorsallateral
camera pair and again for the ventrallateral camera pair
(Hsieh, 2003). These two
separate calibration images were necessary because the dorsal and ventral
cameras were located directly above one another
(Fig. 2A) and therefore saw
opposite sides of the calibration cube. To share enough points with the
lateral view the calibration cube was rotated to face the dorsallateral
camera pair and then the ventrallateral camera pair, resulting in two
separate calibration images. For each camera pair, the calibration cube filled
the entire field of view in the X, Y and Z directions, and
had no less than 23 points visible in both camera views simultaneously.
Second, a direct linear transformation (DLT) algorithm
(Reinschmidt and van den Bogert,
1997) implemented in Matlab used the above calibration images to
calculate and quantify the volume of the field of view for each of the camera
pairs (dorsallateral and ventrallateral). The DLT method uses 11
calculated coefficients to determine the positions of the cameras relative to
each other and to a calibration coordinate system (our calibration cube). This
removes linear image distortion. The calibration coordinate system must have a
minimum of 15 non-coplanar points that maximally fill the field of view of the
cameras to work successfully (Reinschmidt
and van den Bogert, 1997
). This volume calibration allowed
accurate calculation of real world coordinates for any point digitized in both
cameras of a given pair.
Third, to compare the dorsallateral image with the ventrallateral image in three-dimensional space, we had to ensure that both volumes created by the DLT method had the same origin and three-dimensional coordinate axes. To do this we used a separate image with points of known location where a minimum of five points were visible in all three camera images (dorsal, ventral and lateral cameras). This image allowed us to apply a custom Matlab matrix rotation and translation program to align the dorsallateral volume and the ventrallateral volume to the same three-dimensional coordinate axes.
Kinematic measurements
A total of 112 swimming events performed by six fish were reviewed to
establish general patterns of fin movement. Detailed kinematic analysis was
restricted to videos sampled from four fish during periods when they swam at
constant speeds (N=1113 fin beats per behaviour) or during
turning maneuvers (N=7). Each sequence contained, at minimum, three
consecutive tail-beats, and 20 points equally spaced in time per tail-beat
were digitized. Kinematic analysis was completed on the portions of the fins
that were actively moving during locomotion. The stiff, non-oscillating spiny
portion of the fins was not included in the analysis. Although the spiny
portions of the median fins may provide resistance to rolling caused by
imbalance in the fishes body position, it appears that the role it plays in
producing lateral forces that may be counteracted by the anal fin are
negligible, particularly when considering the depression of the fin at higher
speeds.
Calibration and fish images were digitized using a custom Matlab program. When a point was digitized in one camera image the DLT calibration coefficients were used to calculate a line in the second, corresponding image, along which this point could lie. This reference line, in combination with the second image, allowed precise location and digitization of a desired object in both images, and reduced digitizing error.
Excursion of dorsal and anal fins (mm) was calculated by digitizing the tip
of the fin ray at the trailing edge of each fin. Body excursion (mm) was
calculated by digitizing the posterior attachment point of the dorsal fin to
the body (Fig. 2B). Observed
phase lag (% of cycle) was calculated by analyzing excursion over time, and is
the temporal difference in oscillation between the dorsal and anal fin and
between each fin and the body. Expected phase lag (% of cycle) was calculated
assuming the fins track the body, by measuring the longitudinal distance
between the points used to depict the fins and body and representing these
distances as a percent of the full oscillation cycle. Curvature (1/mm) and fin
area (mm2) were calculated when the posterior edge of each fin was
at the point of greatest lateral excursion. Four evenly spaced points along
every other fin ray were digitized to capture fin ray curvature and fin
surface area (Fig. 2B). The
equation of the line that describes the arc of the fin ray was calculated
using a cubic spline in Matlab. The spanwise curvature at 20 points equally
spaced along the fin ray line was calculated using the equation:
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Centre of mass was calculated by hanging preserved individuals on a string, first by a point posteriorly located on the dorsal side and again from a point anteriorly on the dorsal side. By superimposing the image of one fish exactly overtop of the other, the point at which the two lines of string would intersect represents the COM. Calculating the dorsoventral COM location for a series of fish allow estimation of the COM of the study individuals. Rolling axis was drawn on images of the study species as the horizontal axis, which ran longitudinally through the COM. Moment arm for each fin was the distance from rolling axis to the anterior/posterior midpoint of the fin base.
Statistics
Maximum fin excursion was analyzed using a three-way ANOVA with steady
swimming speed and fin as fixed effects and fish as a random effect
(Table 1). Area and maximum
curvature of the fin were analyzed using two-way ANOVAs with swimming speed
and fin as fixed effects, ensuring enough degrees of freedom (d.f.) to test
the entire model (Quinn and Keough,
2002; Zar, 1999
)
(Tables 2,
3). Maximum curvature was
log-transformed to normalize the data. Multiple comparisons within effects
were made using least-square means (LSM) with a Bonferroni correction. Where
missing values prohibited the use of LSM as a multiple comparison, individual
t-tests were used and are noted as such in the results to enable
conservative interpretation. For steady swimming speeds, during which the fish
exhibited regular oscillatory swimming, expected phase lag due to fin and body
position differences was compared with observed phase lag using three
t-tests (DorsalBody, DorsalAnal and AnalBody
comparisons). P-values of the t-test were subject to
Bonferroni correction. Significance levels for all tests were based on initial
P-values of <0.05 and all statistical tests were completed using
SAS (version 9.1 TS Level 1M2 XP_Pro Platform). Measurements noted in the text
are expressed as mean ± S.E.M.
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Results |
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Both dorsal and anal fins are used during maneuvers but their motions become far more variable than during steady swimming. Both median fins move to the same side of the fish during maneuvers, and the excursion of the trailing edge of the fins can be greater than that of steady swimming (Figs 3F, 4, 5). On average maximum excursion of the anal fin during maneuvers is greater than that of the dorsal fin (t-test, N=6, P=0.058; Fig. 4). Kinematic variation is large during maneuvers. Fig. 5 shows the dorsal and anal fin positions at the point of maximum excursion during a maneuver. The large displacement of the trailing edge of both fins is evident from the dorsal and ventral camera views; however, the lateral view shows that actual deformation of the dorsal fin exceeds that of the anal fin in this particular example.
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Discussion |
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Coordinated dorsal and anal fin function in bluegill sunfish
Most studies involving the locomotory function of fish fins have focused on
paired fins (Drucker and Jensen,
1996a,b
;
Drucker and Lauder, 2003
), the
caudal fin (Blake, 1983a
;
Lauder, 2000
;
Lauder et al., 2003
) or
represent theoretical, mathematical hypotheses of paired and median fin use
(Blake, 1976
,
1977
,
1980
,
1983b
;
Lighthill and Blake,
1990
).
The few papers that have looked at dorsal and anal fins during locomotion
focus on boxfish (ostraciiform swimmers with rigid trapezoid-shaped bodies)
and burrfish (tetraodontiform swimmers;
Arreola and Westneat, 1996;
Gordon et al., 2000
;
Hove et al., 2001
). These
fishes are known to use their dorsal and anal fins differently in different
gaits (Gordon et al., 2000
;
Hove et al., 2001
). At
swimming speeds below 1 TL s1 boxfish swim with a
pectoral/anal fin dominant gait, where both pectoral and anal fins provide
thrust for the animal and the dorsal fin is rarely used
(Hove et al., 2001
). At speeds
above 1 TL s1 boxfish use dorsal/anal fin swimming,
where synchronous oscillations of the dorsal and anal fin produce thrust and
become the principle propulsors (Hove et
al., 2001
). Bluegill sunfish also exhibit different gaits while
swimming but use their dorsal and anal fins only during body caudal fin steady
swimming and during maneuvers. When swimming at speeds above 1.5 TL
s1, bluegill sunfish use both dorsal and anal fins
synchronously, with similar lateral excursions. Unlike the ostraciiform
swimmers, there are no speeds at which bluegill use only the anal fin. At
swimming speeds below 1.5 TL s1 most bluegill hold
both dorsal and anal median fins motionless, and rely entirely on the pectoral
fins and tail for propulsion.
When bluegill use their median fins for propulsion the dorsal and anal fins
oscillate synchronously, showing no significant phase shift relative to each
other (Table 1). The forces
produced by fins and the symmetry of the fins in the sagittal plane of the
animal may explain the synchronous movement of dorsal and anal fins. For
example, the amount of torque a fin produces on the body of a fish depends on
the moment arm of the fin (the distance the fin is from the COM), the surface
area of the fin (how much water the fin is pushing) and fin velocity.
Different methods can be used to calculate fin area, velocity, moment arm and
resultant torque. Fins can be divided into strips, each having a moment arm,
area, velocity and resultant torque. These values can be summed to calculate
torque for the entire fin surface. This method provides good precision but,
like all calculations, depends upon measurement accuracy to be useful. For the
purposes of this study we do not divide the fins into strips to calculate
torque; we use average fin areas, average velocity and a single moment arm for
each fin. We do this because we are interested in the relative difference in
torque production between the dorsal and anal fins and are limited by the
accuracy with which the COM and fin moment arms can be calculated. Both the
dorsal and anal fins attach to the body over a relatively broad area (about 1
cm), and the precise location where fin forces are transmitted to the body is
not known. Using our method we find that although there are differences
between dorsal and anal fins in the bluegill, the relative differences in
moment arm (anal=23.7±0.65 mm, dorsal=21.4±0.48 mm), surface
area (anal=529±32.09 mm2, dorsal=601±34.79
mm2) and excursion (steady swimming, anal=4.4±0.34 mm,
dorsal=5.06±0.25 mm) between these fins suggests anal fins are
producing similar torques on the body as those produced by dorsal fins. Fin
forces that are synchronous and symmetrical will balance each other and create
minimal net pitch, roll or yaw moments. Relative phases of dorsal and anal fin
movement have been studied in needlefish, which have symmetric dorsal and anal
fins, and needlefish show no phase lag between dorsal and anal fin oscillation
(Liao, 2002).
Though dorsal and anal fins move together, oscillation of each fin relative to the body does show some phase shift. Both dorsal and anal fin oscillations vary inconsistently in timing from that of the body. The lack of phase matching between the dorsal and anal fins and the body suggests median fins have a more complex role than simply following the oscillation of the body during locomotion. The variation in timing of the anal fin also suggests it does more than balance the lateral thrust produced by the dorsal fin.
Both Harris (1936) and
Breder (1926
) suggest that the
function of the anal fin is to act as a bilge keel (a high aspect ratio, rigid
fin attached to the bottom or side of boats to attenuate rolling
instabilities) straightening and balancing the body position of the animal as
it produces forward thrust. Two major factors contribute to forces that cause
possible perturbations for fish: the external environment and the fish's body
and fin morphology. Environmental forces, such as turbulence, may not be
predictable and, as long as they are the proper scale
(Webb, in press
), can perturb
fish body position. Fish must react to these perturbations by using fins such
as the anal fin to maintain an effective body position. The body shape and
paired fin positioning of bluegill may also produce destabilizing forces,
which must be balanced by the anal fin. Although the median fins and body
shape of bluegill are relatively symmetrical around the long axis of the fish,
the ventral paired pelvic fins make the fish dorso-ventrally asymmetrical, as
there are no comparable fins on the dorsal edge of the body. The phase lag
between anal fin and body may be the result of the anal fin acting not just as
an oscillating foil to compliment the movement of the dorsal fin, but as a
complex flexible foil, not a bilge keel, which provides a variety of movements
required to stabilize the fish's body by counteracting forces encountered due
to environmental turbulence and pelvic fin asymmetry.
Implications for stability
Studying the kinematic performance of dorsal and anal fins allows one to
make inferences about force production by these fins. Hydrodynamic studies
using bluegill have shown that dorsal fins produce lateral jets of fluid
during oscillation (Drucker and Lauder,
2001a,b
;
Lauder and Drucker, 2004
).
Because the kinematics of the anal fin are similar to those of the dorsal fin
we hypothesize that the anal fin is also producing lateral fluid jets. Any jet
produced lateral to the fish's longitudinal axis and above or below the COM
will induce a rolling moment away from the direction of the jet (see roll,
Fig. 1A). Dorsal and anal fins
oscillate synchronously to the same side of the fish, one fin above the COM
and one below at roughly the same longitudinal position on the fish. As a
result, the lateral jets produced by each fin induce roll in opposite
directions, balancing their rolling torque. By producing two strong lateral
forces to the same side of the fish one might expect a lateral shift in body
position or yawing, but this is not seen in steady swimming. Experimental work
using flow visualization has shown that the wake of the dorsal fin may add
momentum to the caudal fin wake (Drucker
and Lauder, 2001a
), increasing thrust for the animal. The extent
to which the lateral forces produced by both the dorsal and anal fin are
incorporated into axial and caudal fin movement is unknown; further flow
visualization experiments would clarify the validity of this hypothesis.
Theoretical work has also suggested benefits of the dorsal and anal fin acting
as a `double-tail', the thrust produced by dorsal and anal fins being out of
phase with that of the caudal fin to maximize uniform thrust during locomotion
(Webb and Weihs, 1983
;
Weihs, 1973
).
As speed increases we see a decrease in both dorsal and anal fin area. The
reduction of fin surface area may let fish control the magnitude of lateral
jet production, while reducing surface area drag, which can be costly at
higher swimming speeds. The ability of the fish to change its fin area gives
it control over the force each fin produces. Force, be it lift or drag, is
proportional to the velocity of the fin squared
(FU2). Therefore, as swimming speed
increases, velocity of water moving over the fin (velocity of the fin relative
to the water) increases and a smaller fin area can produce the same force with
a given movement.
During maneuvers, dorsal and anal fin motion results in yawing of the body,
suggesting the fins are producing a larger jet to the side away from the turn.
These fin movements and the resulting changes in body position are consistent
with the understanding that median fins are capable of producing torques,
which cause moments of yaw and roll
(Drucker and Lauder, 2001b;
Webb, 2004a
). How fish are
moving dorsal and anal fins relative to each other to produce these forces is
unknown at present. During steady swimming the dorsal fin has a larger surface
area and produces a larger magnitude lateral excursion compared to the anal
fin. If this difference equates to the dorsal fin producing larger lateral
forces than the anal fin, why then is there no visible rolling? This may be
because the rolling moment arm of the anal fin is longer than that of the
dorsal fin (anal=23.7±0.65 mm, dorsal=21.4±0.48 mm;
Fig. 1B). A fin with a longer
moment arm requires less force to produce the same amount of torque, compared
to a fin with a shorter moment arm. The slightly longer moment arm found in
the anal fin may explain why it generally shows smaller area and excursions in
steady swimming than the dorsal fin (Figs
4,
5). The large amplitude motion
of the anal fin during maneuvering suggests that the anal fin may be critical
in initiating a large rolling moment, unbalanced by the dorsal fin, which
leads into the visible lateral yawing of the fish's body, accompanied by some
roll. Calculation of actual values for forces generated by dorsal and anal
fins, and hence torques, awaits future flow visualization analysis.
Fin ray function
Overall fin shape is the result of the position of individual fin rays. Fin
rays show different curvatures from base to tip and different positions
relative to their base depending on swimming speed and maneuver (Figs
7,
8). Curvature between adjacent
fin rays can also be very different. A clear example of this can be seen in
the dorsal fin plot of swimming speed 2.5 TL s1 in
Fig. 8; rays 1, 2 and 3 all
display different maximum curvatures, suggesting they have some independence
from one another. The ability of fish to adjust the curvature of individual
rays suggests a greater control over fin surface shape than if all rays were
confined to the same curvature at a given point in time; fish fins can have
different spanwise curvatures depending on the longitudinal position along the
fin surface. In addition, the shape of the whole fin surface can be
dramatically bent without extreme curvature of individual rays. This bending
of the fin surface appears to be mostly achieved by a rotation of individual
fin rays at their base. As can be seen in
Fig. 5, both dorsal and anal
fins are bent nearly 90°. Despite this large deformation of the fin
surface, the individual rays are only modestly curved, as can be seen visually
in Fig. 5. The position of the
ray and its curvature appear to be independent control mechanisms, allowing
the fish multiple degrees of freedom in fin ray and thus fin surface control.
The diversity of possible curvatures within individual rays and the multitude
of angles that a ray can occupy during a fin stroke allow considerable
diversity of fin surface shape and position.
Ray curvature during maneuvers is larger relative to steady swimming (Fig. 7) but still remains small. Consider the units of curvature, 1/R, where R is the radius of the circle around which the fin ray would curve if it held that maximum curvature along its entire length. Because the length of the rays are generally <3 cm it would take a very small circle to produce a large curve in the ray. The maximum curvature measured during a maneuver is <0.1 mm1, which corresponds to a circle with a radius of 10 mm and therefore a relatively modest curvature for a ray at its most curved point.
The curvature seen during maneuvers involving large whole fin surface
displacements (see Fig. 5), may
be due to a combination of fin ray mechanics and fluid pressure forces (normal
to the fin) as the fin pushes against water. Each fin ray is composed of two
hemitrichia (together termed a lepidotrich;
Geerlink and Videler, 1987;
Haas, 1962
;
Lanzing, 1976
), and each
hemitrich is made of a series of bony elements, which form a semi-circular
rod-like structure. The hemitrichia are attached to one another along their
concave sides by elastic fibers; these fibers allow the hemitrichia to slide
slightly relative to one another. The base of each hemitrich is wide and
supports a large area for the attachment of erector, depressor and inclinator
muscles (Winterbottom, 1974
),
which permit rotation of each fin ray as well as motion of hemitrichia
relative to each other.
Muscles that pull on one hemitrich while the other is held in position
cause curvature of the whole fin ray
(Geerlink and Videler, 1987).
Hemitrichia are of fixed length and cannot shorten; if fin muscles pull on one
hemitrich while the other remains anchored at its base, both hemitrichia slide
and bend relative to each other, resulting in the curvature of the fin ray
towards the direction of the pulled hemitrich
(Geerlink and Videler, 1987
).
One might hypothesize that equal contraction of musculature attaching to both
hemitrichia would not cause curvature. But, depending on the combination of
muscles used, the entire fin ray may rotate around its base, changing the
position of the entire ray without changing its curvature. Because ray
position contributes to fin surface shape, this hypothesis would explain the
ability of the fish to change the surface shape of fins without large
curvature occurring in individual fin rays.
Fin ray curvature may also be reduced by normal pressures on the fin caused by water flow. For example, in Fig. 5, dorsal fin surface is deformed to lie 90° to the direction of the water flow. The normal pressure of the water on the surface of the fin may push with enough force to straighten rays that would otherwise curve forward into the flow.
The mechanisms of base rotation and fin ray curvature combined would allow fish to change the whole fin surface shape with far more control than if it had only one or the other mechanism. Confirming the hypothesis that fin ray base rotation and hemitrich sliding are the mechanisms that account for the observable fin surface control we see during locomotion will require measuring the activation patterns and force outputs of the muscles attached to the fin rays in future experiments.
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Acknowledgments |
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References |
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