A kinematic model of swallowing in Aplysia californica based on radula/odontophore kinematics and in vivo magnetic resonance images
1 Department of Biomedical Engineering, Case Western Reserve University,
Cleveland, OH 44106-7080, USA
2 Department of Biology Case Western Reserve University, Cleveland, OH
44106-7080, USA
3 Department of Neurosciences, Case Western Reserve University, Cleveland,
OH 44106-7080, USA
4 MR Systems Department, G. E. Medical Systems Israel Ltd, Keren Hayesod
Street, PO Box 2071, Tirat Carmel 39120, Israel
* Author for correspondence at address 2 (e-mail: hjc{at}po.cwru.edu)
Accepted 3 July 2002
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Summary |
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Key words: feeding, behaviour, biomechanics, kinematics, mollusc, muscular hydrostat, Aplysia californica
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Introduction |
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Analysis of the radula and odontophore within the buccal mass is
complicated by the absence of hard skeletal elements and discrete joints that
make musculo-skeletal systems tractable to mechanical analysis. Molluscan
feeding structures are composed entirely of muscle and cartilage, and muscle
acts both to generate forces and to provide skeletal support. Thus, they are
examples of a broader class of structures, muscular hydrostats, that are
exemplified by tongues, trunks and tentacles
(Kier and Smith, 1985).
Because these structures have many degrees of freedom and are thus capable of
complex and flexible movements, understanding their biomechanical properties
is likely to be essential for a deeper understanding of their neural control.
Moreover, the great flexibility of these structures allows them to be utilized
for multiple different behavioral functions (e.g. the human tongue is used
both for feeding and for talking), and thus the neural architectures
controlling these devices are also of special interest for understanding the
dynamics of multifunctionality.
We have focused on analyzing the biomechanics and neural control of feeding
in the marine mollusc Aplysia californica. Aplysia is a generalist
herbivore that feeds on a variety of red, brown and green seaweeds whose
shapes, toughness and texture vary significantly
(Carefoot, 1967;
Howells, 1942
;
Pennings, 1990
). The feeding
behavior of Aplysia is under the control of motivational variables
(Kupfermann, 1974
) and is
subject to associative learning (Chiel and
Susswein, 1993
; Susswein et
al., 1986
). The neural control of the feeding apparatus in
Aplysia has been intensively studied. Sensory neurons responsive to
chemical or mechanical stimuli that induce consummatory feeding responses have
been identified (Miller et al.,
1994
; Rosen et al.,
1979
,
1982
,
2000a
,b
),
as have motor neurons for the major muscles of the feeding apparatus
(Church et al., 1991
;
Church and Lloyd, 1994
;
Gardner, 1993
). Neural
correlates that distinguish ingestion from rejection have been defined
(Cropper et al., 1990a
; Morton
and Chiel,
1993a
,b
)
and have been used to identify interneurons responsible for flexibly shifting
the timing and intensity of activation of motor neuronal pools so that
ingestive or egestive behavior can be generated under appropriate conditions
(Hurwitz et al., 1997
;
Jing and Weiss, 2001
).
Interneurons responsive to mechanical load have been shown to cause the switch
from biting to swallowing (Evans and
Cropper, 1998
).
The kinematics of the buccal mass of Aplysia have also begun to be
clarified. Earlier studies clarified the functional anatomy of the intrinsic
muscles (labelled `I' followed by a number) and extrinsic muscles (labelled
`E' followed by a number; Howells,
1942). In the present paper,
Fig. 21 provides a schematic
view of the buccal mass musculature, and
Fig. 19 provides a schematic
view of the muscles of the radula/odontophore proper. A series of kinematic
models of the entire buccal mass has been constructed (Drushel et al.,
1998
,
2002
). These models have
provided an increasingly accurate view of the inner workings of the buccal
mass, but may not have completely captured the three-dimensional shape of the
radula/odontophore. A previous attempt to capture the three-dimensional shapes
of the radula/odontophore throughout the feeding cycle
(Drushel et al., 2002
) used
two different approaches. In one approach, the radular halves could move
relative to one another and to the radular stalk, creating a three-dimensional
shape. This model was referred to as a radular-centric model. In the other
approach, the mid-sagittal shape of the odontophore was constrained to be
identical to that observed in mid-sagittal magnetic resonance images (MRIs),
and the remainder of the three-dimensional shape of the odontophore was
determined from the volume of the buccal mass and assumptions about its
medio-lateral width. This model was referred to as an odontophore-centric
model.
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If the full three-dimensional shapes of the buccal mass and its constituent
muscles could be simultaneously measured in intact, behaving animals, it would
be possible to develop a complete kinematic description of the musculature.
Since this is not currently technically feasible, we have developed a
technique for obtaining high-temporal- and spatial-resolution planar images of
feeding in intact animals using magnetic resonance imaging (MRI). In addition,
by inducing feeding-like movements in isolated odontophores in response to
pharmacological agents (Drushel et al.,
1998; Susswein et al.,
1996
), it was possible to analyze the kinematics of isolated
radula/odontophores in order to derive a set of kinematic relationships for
its three-dimensional deformations. By extracting parameters from mid-sagittal
MRIs of the radula/odontophore in intact, behaving animals and using them as
inputs to a kinematic model based on these kinematic relationships, it was
possible to reconstruct the three-dimensional shape of the radula/odontophore
throughout the feeding cycle. By combining these odontophore model shapes with
a kinematic model of the surrounding musculature, we generated a new
odontophore-centric three-dimensional kinematic model of the buccal mass.
After validating the overall model, we used it to describe the kinematics of
buccal muscles and buccal mass components during swallowing, and compared
these predictions with actual measurements. The model generated several
testable hypotheses about the context-dependent function of components of the
buccal mass that have significant implications for its neural control.
Portions of this work have appeared in preliminary form
(Neustadter et al., 2001
).
As adjuncts to the text, we provide digital movies (in QuickTime format) of the MRIs of swallowing in Aplysia californica used for the model presented in this paper, movies of the model construction and movies of the model output. The movie entitled `3_15_39highres.mov' shows interleaved sagittal, coronal and axial images of the buccal mass during swallowing from sequence 7732-S3, frames 15-39. The movies entitled `ModelProcess.mov', `ModelProcess2.mov', `ModelProcess3.mov', `ModelProcess4.mov' and `ModelProcess5.mov' illustrate the process by which the three-dimensional kinematic model of the odontophore and the buccal mass is constructed, and will clarify the Materials and methods section. The movies entitled `16-39ModelSideView', `16-39ModelTopView.mov' and `16-39ModelFrontView.mov' show side, top and front orthogonal projections of the kinematic model of the buccal mass for sequence 7732-S3, frames 16-39. These movies will clarify the Results section.
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Materials and methods |
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Measurements of the kinematics of the radula/odontophore
To create a complete three-dimensional model of the changing shapes of the
radula/odontophore during a feeding cycle, we needed to determine kinematic
relationships that would allow us to infer the overall shape of the structure
from planar mid-sagittal MRIs of the structure during feeding. We therefore
videotaped and analyzed the relationships between three-dimensional anatomical
features seen in multiple planar views of isolated, intact radula/odontophores
during spontaneous and drug-induced feeding-like movements. Aplysia
californica Cooper (160-303 g, obtained from Marinus, Long Beach, CA,
USA) (N=8) were anesthetized by gradually lowering their body
temperature to 4°C using a dissecting tray filled with ice and placing
them in a freezer for 30 min. For some studies, animals were anesthetized
using magnesium chloride (isotonic 333 mmol l-1 MgCl2
equal to half their body mass). The buccal mass was dissected out along with
the cerebral and buccal ganglia. The buccal mass was then placed in a dish
containing artificial seawater (Instant Ocean, Mentor, OH, USA) at room
temperature. The dorsal surface of the buccal mass was cut in an
antero-posterior direction along the mid-sagittal line back to the dorsal
surface of the esophagus. Much of the I1/I3 tissue on either side of the
ventral surface of the radula/odontophore was dissected away so that the base
of the radula/odontophore was exposed.
Multiple planar views of the radula/odontophore were obtained simultaneously by mounting two mirrors at 45° to the camera axis, providing three perpendicular views of the preparation that were captured in a single video image. The odontophore was mounted below the mirror that provided a top view and to the left of the mirror that provided a front view. The odontophore itself was oriented to provide the video camera with a side view. A light was shone onto the preparation from above, so that the odontophore's widest medio-lateral extent could be determined during movement by examining the line of shadow that it cast. In one preparation, the anterior edge of the radula/odontophore was mounted on a vertical pin using silk sutures so that the radula/odontophore would have a fixed frame of reference (Fig. 1). Digital NTSC video (Canon ZR10, Canon Inc., Jamesburg, NJ, USA; 30 frames s-1) was used to record the movements of the preparation.
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Feeding-like movements were obtained in several ways. As the buccal mass
recovered from anesthesia, vigorous spontaneous movements were observed.
Crystals of carbachol or dopamine hydrochloride (C-4382 or H-8502,
respectively; Sigma, St Louis, MO, USA) were placed on the cerebral ganglion,
inducing rhythmic movements (Drushel et
al., 1998; Susswein et al.,
1996
).
Kinematic measurements indicated that several features of the
radula/odontophore contributed significantly to the distribution of its volume
and should therefore be represented in the three-dimensional model. Moreover,
the planar views indicated that the positions and dimensions of these features
could be deduced from a mid-sagittal slice (see below). In particular, we
identified a wedge-shaped structure that appears to be filled with fluid and
is anterior to the I6 muscle, which we refer to as the prow of the odontophore
(Fig. 1) (see also
fig. 6 in
Neustadter et al., 2002). We
also recognized that the anterior surface of the radula does not curve
smoothly, but forms a ridge as a result of the upward protrusion of the I4
muscles (Fig. 1) (see also
fig. 6 in
Neustadter et al., 2002
). We
tracked the movements of these features, as well as monitoring the changing
position of the shadow, i.e. the line of widest medio-lateral extent, during
the feeding-like movements of the radula/odontophore (see Results for
measurements and below for a description of how the kinematic relationships
were used to deduce rules for the construction of the three-dimensional model
of the radula/odontophore).
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Measurements of the volume of the radula/odontophore
Given linear measurements from the mid-sagittal plane, and assuming that
the radula/odontophore is isovolumetric throughout the feeding cycle, it is
possible to use a scaled estimate of the volume to determine the medio-lateral
width of the radula/odontophore. We therefore measured the resting volume of
the odontophore. The apparatus used to make these measurements consisted of a
60 ml syringe clamped in an upright position and connected via a tube
to a 0.2 ml glass pipette, which was also clamped in an upright position to
approximately the same height. The pipette was used to provide a narrow water
column in which small changes in water level could be accurately recorded.
Changes in the water level were determined by measuring the height of the
meniscus of the fluid in the pipette through a microscope whose eyepiece was
equipped with a graduated reticle. To minimize surface tension, which
interfered with the free movement of the meniscus, the apparatus was soaked in
a solution containing soap (Alconox Detergent Powder; Alconox Inc., New York,
NY, USA) for at least 24 h prior to measurements, after which it was rinsed
and filled with artificial seawater. The apparatus was calibrated by adding
known volumes of water (using an Eppendorf pipette to deliver precise 0.5 ml
samples to the apparatus) and recording the changes in the height of the
meniscus. The precision of the measurements was ±0.05 ml, and the
volumes of the odontophores ranged from 0.4 to 1.5 ml, so that the largest
error in measurement of the smallest odontophore was approximately 12%.
As described in previous work (fig.
3 in Neustadter et al.,
2002), we have used the internal radular stalk width as a
reference length that normalizes lengths and volumes among animals so as to
combine measurements from isolated odontophores of different sizes and
mid-sagittal MRIs. The volume of the odontophore was therefore normalized to
units of (radular stalk width)3, which we refer to as
RSW3. From measurements performed on five animals ranging in mass
from 65 g to 335 g, the mean odontophore volume including the prow and the
stalk was computed to be 7.5±0.6 RSW3 (mean ± S.D.,
N=5).
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Kinematic model of the buccal mass
The kinematic model consists of the following components: (i) a model of
the radula/odontophore, whose three-dimensional shape is based on the
kinematic relationships deduced from the studies described above; (ii) a model
of the surrounding I3 musculature, based on a modified version of a previous
model of these structures (Drushel et al.,
1998,
2002
); and (iii) an iterative
algorithm that positions the radula/odontophore relative to the I3 model
muscles so as to best fit the mid-sagittal outline of the buccal mass. We will
describe each of these components in turn.
Radula/odontophore model
The three-dimensional shape of the radula/odontophore includes the prow and
the radular ridge. The `radular cleft', i.e. the space between the halves of
the radula when it is open, is not included in the model, because it was not
possible to identify a measurable parameter on the mid-sagittal MRI that could
be used to deduce its medio-lateral and dorso-ventral extents. Potential
errors that this introduces in the volume of the radula/odontophore are
considered in the Discussion. The model also does not include the narrow ridge
that the radular surface forms during and after the peak of retraction (which
we refer to as the radular `pinch'), again because of the absence of a
measurable parameter to indicate its extent on the mid-sagittal MRI.
Parameters
Fixed parameters for the model were measured from
high-spatial-resolution MRIs of anaesthetized animals and isolated buccal
masses, high-spatial-resolution photographs of isolated odontophores and
digital video recordings of radula/odontophore kinematics, as described above.
The fixed parameters are (i) the overall volume of the odontophore, (ii) the
volume of the radular stalk, (iii) the spline parameters describing the
vertical and horizontal cross sectional shapes of the odontophore, (iv) the
shape of the prow, (v) the volume of the prow and (vi) the parameters defining
the shape of the ridge (see Fig.
2; Table 1; see
also fig. 3C,D in
Neustadter et al., 2002). The
spline parameters are used to describe curves using two control points to
define a smooth curve between two endpoints
(Press et al., 1988
) (see
legend to Fig. 2).
Parameters for each model frame were measured from mid-sagittal
high-temporal-resolution MRIs. The parameters were (i) the outline of the
odontophore, including the prow, (ii) the line separating the prow from the
odontophore corresponding to the anterior margin of I6, (iii) the point above
which to search for the tip of the prow and (iv) the position and orientation
of the stalk. The shape of the stalk was based on an outline of the stalk from
high-spatial-resolution MRIs and was fixed (see
fig. 4 in
Neustadter et al., 2002). The
stalk outline was then scaled for each animal so that it fitted onto the stalk
in the image. The following measurements were also made: (v) the outline of
the entire buccal mass (including the radular stalk, odontophore and the I3
musculature, but excluding pharyngeal tissue); (vi) the `lateral groove' (the
most posterior part of the I3 musculature); (vii) the `hinge' (the point of
attachment of the ventral radula/odontophore and the most posterior part of
the I3 musculature); (viii) the `line of the jaws' (the location of the most
anterior part of the I3 musculature); (ix) an upper limit line that indicated
the inner border of the dorsal section of I3; and (x) a lower limit line that
indicated the inner border of the ventral section of I3. Extraction of
parameters i, ii, iv, v, vi and viii is illustrated in
fig. 4 of Neustadter et al.
(2002
).
Construction of the odontophore
The model creates a three-dimensional mesh that represents the shape of the
odontophore. If the odontophore were spherical, one could construct its shape
using vertices lying on a number of parallel circles. The diameter of the
central circle would be the diameter of the sphere, and the diameters of the
other circles would decrease as the circles were further from the center,
reaching zero at the front and back of the sphere. To provide an approximately
uniform distribution of the vertices on the surface of the sphere, the circles
should be spaced in an antero-posterior density corresponding to a cosine
function, i.e. more closely spaced at the front and back of the sphere than in
the middle.
Because the actual odontophore has a more complex shape, the curves used to define its vertices are not circles but more complex closed convex curves constructed of four spline quadrants. The spline parameters defining the shape of each quadrant are based on projections of radula/odontophores (Fig. 2B,E). The four spline quadrants that compose each curve connect at four anchor points (Fig. 3C). The dorsal and ventral anchor points are defined by the intersection of the plane of the curve with the outline of the odontophore extracted from the mid-sagittal high-temporal-resolution MRIs (Fig. 3A,C). The medio-lateral anchor points are defined by the intersection of the plane of the curve with a curve defining the medio-lateral width (described in the next section; Fig. 3B,C). The spacing between the curves in the antero-posterior direction is cosinusoidal (more closely spaced at the anterior and posterior edges, less closely spaced at the center) to provide approximately uniform coverage of the surface of the odontophore (Fig. 4C).
Determining the angles of the planes of the closed curves that define
the odontophore mesh
The maximum width of each of the closed curves is defined by its
intersection with a curve in a plane that cuts through the structure along its
widest medio-lateral extent (Fig.
3B). In the previous odontophore-centric model of the
radula/odontophore (Drushel et al.,
2002), this plane was assumed to be the plane that passed through
the anterior and posterior extremes of the mid-sagittal cross section of the
odontophore. As a consequence, a series of vertical closed curves could be
placed parallel to one another along the line from the anterior extreme to the
posterior extreme to include the entire volume of the odontophore
(Fig. 4A). Studies of the
shadow line on the isolated radula/odontophore during feeding-like movements
(see below; see also Fig. 7)
demonstrated that the line of widest medio-lateral extent did not necessarily
intersect the anterior and posterior extremes of the mid-sagittal cross
section of the odontophore. Consequently, if the closed curves were placed
parallel to one another and their width was defined by their intersections
with the line of widest extent, a portion of the volume of the odontophore
would extend past the ends of the line of widest extent and would, therefore,
have no defined width (Fig.
4B). To solve this problem, we computed the tangents to the
mid-sagittal outline at the posterior and anterior ends of the line of widest
extent and set the closed curves at angles that continuously changed from the
posterior tangent to the anterior tangent value. This guaranteed that the
entire volume was represented by curves that intersected the line of widest
extent (Fig. 4C).
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Determining the line of widest extent
The position and angle of the line of widest extent were derived using a
kinematic relationship based on observations of isolated, moving
radula/odontophores. The line of widest extent, which was observed as a shadow
line on the moving odontophores, was found to have a fixed angle (44°)
relative to the line connecting the top of the radular surface and the tip of
the prow and to pass through the tip of the prow (see below; see also
Fig. 7). This relationship
allowed us to deduce the angle of the line of widest extent, which cannot be
directly observed in the mid-sagittal MRIs, from the angle of the line
connecting the top of the radular surface and the tip of the prow, which can
be directly measured in the MRIs.
To calculate the angle of the line of widest extent in the model, the
location of the tip of the prow, the location of the top of the radular
surface and the angle of the line connecting them must be determined.
Anatomically, the tip of the prow is the anteriormost end of the radular
surface, and there is therefore a large change in curvature at that point
along the mid-sagittal outline of the prow
(Fig. 3D). To locate the tip of
the prow objectively, we therefore implemented an algorithm that identifies
the point of sharpest curvature along the top portion of the mid-sagittal
outline of the prow. The algorithm selected the point at which the sum of the
2 goodness-of-fit errors for linear fits to the portions of
the curve above and below the point was minimal. Because the tip and the
bottom of the prow were sutured to a vertical pin, this vertical line defined
the reference frame in which the top of the radular surface was measured in
the moving isolated odontophores. Consequently, before determining the
location of the top of the radular surface for the model, the mid-sagittal
cross section was rotated so that the line connecting the tip of the prow and
the bottom of the prow was vertical (Fig.
3E). After applying this rotation, we identified the topmost point
of the mid-sagittal cross section, which was the top of the radular surface.
We then defined the line of widest extent to be the line that passed through
the tip of the prow and was 44° counterclockwise from the line connecting
the top of the radular surface and the tip of the prow (relative to the
orientation shown in Fig.
3E).
Construction of the prow
Anatomical studies of the prow indicated that its volume could be treated
as constant, that its posterior margin formed a plane with the I6 muscle and
that the medio-lateral profile of its anterior edge could be approximated by a
Gaussian curve (see Fig. 6C in
Neustadter et al., 2002). The
Gaussian function used to determine the medio-lateral width x of the
prow in terms of its antero-posterior location was:
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Two parameters for the prow were extracted from each mid-sagittal MRI: (i)
the mid-sagittal anterior margin of the prow and (ii) the line along which it
meets I6, which we refer to as the `prow seam' (see
fig. 4B,C in
Neustadter et al., 2002; the
anterior margin of the odontophore corresponds to the prow seam). The
antero-posterior position of the prow seam is later iteratively adjusted to
achieve the correct prow volume, but its angle remains unchanged. The entire
three-dimensional mesh is constructed in the reference frame in which the prow
seam is vertical. To best approximate the actual anatomical shape of the prow
(see Fig. 6 in
Neustadter et al., 2002
), the
dorsal half of each curve defining the volume of the prow (i.e. the part of
the curve above the line of widest extent) was vertical (i.e. parallel to the
prow seam) and the ventral half (i.e. the part of the curve below the line of
widest extent) curved posteriorly to meet the other curves at the base of the
prow seam (Fig. 3F). The
curvature of the ventral half is such that its position is a fixed percentage
of the distance between the anterior margin of the prow and the prow seam. The
shapes of the dorsal and ventral parts of each curve were defined by the same
spline parameters used to define the curves of the rest of the odontophore,
and the maximum width at the intersection with the line of widest extent was
defined by the Gaussian approximation of the medio-lateral profile of the
prow. The width of the Gaussian curve at the prow seam was defined as 0.77
RSW, based on anatomical observations. To achieve the known fixed volume of
the prow, the mesh representing the prow was iteratively constructed with the
prow seam being moved anteriorly or posteriorly.
Construction of the ridge
Observations of the kinematics of isolated radula/odontophores indicated
that it was necessary to include a dorsal ridge. The spline curve used to
approximate the shape of the dorsal half of the odontophore does not
accurately represent the shape of the dorsal surface throughout the movements
of the isolated odontophore (in Fig.
2E, note the discrepancy between the location of the spline curve
and the dorsal surface of the odontophore). During a portion of the movement
cycle, a ridge projects above this shape. To determine the timing and extent
of ridge protrusion during a movement cycle in the isolated
radula/odontophore, we used the top view of the radula to locate the posterior
and anterior margins of the ridge, and identified these locations in the side
view (Fig. 5A). On the basis of
empirical measurements, we found that a circular arc (radius 1.23 RSW, arc
angle 100°) could be fitted to the dorsal radular surface anterior and
posterior to the ridge (Fig.
5B). This arc was therefore fitted to the anterior portion of the
odontophore outlines measured on the mid-sagittal MRIs and used to define the
ridge for the model. The arc was fitted to 0.25 times the distance between the
tip of the prow and the posterior of the odontophore. The arc was continued
posteriorly by a straight line tangential to the posterior end of the arc
(Fig. 5B), on the basis of
empirical observations. A protrusion above this arc indicated the presence of
a ridge. If a ridge was observed in the mid-sagittal section of the MRI, we
constructed the medio-lateral shape of the ridge (based on empirical
observations of the ridge in vitro) by constructing a trapezoid whose
ventral width was 0.46 RSW less than the maximum width of the odontophore, and
whose dorsal width was 0.4 times the ventral width. The radius of curvature of
the corner of the trapezoid in the medio-lateral dimension was 0.2 RSW
(Fig. 5C, top). For each curve
in the region of the protrusion, the dorso-ventral height of the ridge was
defined by the height of the protrusion, and the medio-lateral width of the
ridge was defined relative to the width of the odontophore at that location.
Since the planes of the curves are not necessarily vertical
(Fig. 4C), the medio-lateral
odontophore width used to determine the ridge width was the maximum of two
widths: (i) the width at the intersection of the curve with the line of widest
extent or (ii) the maximum odontophore width at the horizontal location of the
top of the curve. If the width of the odontophore was less than 1.0 RSW, no
ridge was constructed. Otherwise, a trapezoid representing the ridge was
constructed by relocating the vertices of the curve defining the dorsal edge
of the odontophore mesh (Fig.
5C, bottom).
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Total volume of the odontophore
Although it was possible to determine the location of the line of widest
extent from a mid-sagittal MRI using the kinematic relationships described
above, and the shape of the curve in the plane of widest extent was determined
by the spline parameters measured from the high-spatial-resolution MRIs of the
anesthetized buccal mass, the actual medio-lateral width of the
radula/odontophore could not be determined from a mid-sagittal image. Given
the assumption that the radula/odontophore is isovolumetric and given the
measured volume of the odontophore, the medio-lateral width of the
three-dimensional mesh was iteratively adjusted, and the odontophore mesh was
reconstructed until the correct volume was achieved. Determining the correct
volume required a measure of the volume of the radular stalk and the extent to
which it overlapped the volume of the odontophore. The volume of the radular
stalk was calculated from a measurement of the radular stalk width and a
three-dimensional reconstruction of the radular stalk from
high-spatial-resolution MRI (see fig.
3C in Neustadter et al.,
2002; the value is 0.69 RSW3). The volume of the
radular stalk was assumed to be approximately constant, on the basis of the
approximately constant area of its cross section in the mid-sagittal MRIs. The
position and angle of the radular stalk relative to the odontophore were
extracted from the mid-sagittal MRIs. If the radular stalk protruded through
the ventral side of the odontophore, as it does during retraction, the
protruding portion of the stalk was not included in the outline of the
odontophore. To calculate the total volume of the radula/odontophore, it was
therefore necessary for the model to calculate the sum of the volumes of the
odontophore and the radular stalk and then to subtract the overlapping volume.
If the total volume of the odontophore was incorrect, the model iteratively
adjusted the medio-lateral width at the line of widest extent and repeated the
construction of the three-dimensional odontophore mesh until the volume fell
within a pre-defined tolerance (±0.1 RSW3 of 7.5
RSW3).
Modifications to the kinematic model of the I3 musculature
Once the three-dimensional mesh of the odontophore had been constructed, a
model of the I3 musculature was constructed around it based on the previously
published kinematic model (Drushel et al.,
1998,
2002
), which approximates the
I3 muscle as a number of distinct rings
(Fig. 6A) whose parameters were
estimated by trial and error. Because the high-spatial resolution MRIs
provided more information about the actual shape of the I3 musculature than
had been previously observed, we extracted additional parameters and modified
the I3 model so that we could make use of these parameters to produce a better
match between the model and the in vivo data.
The shape and size of each model I3 ring are defined by five parameters (Fig. 6A): r, the radius of the half-circular cross section of the outer half-ring at the top and bottom and of the inner half-ring surrounding the lumen; the thickness of each model ring is 2r; a, half the maximum width of the lumen; q, the width added between the outer and inner half-rings so that the medio-lateral width of the model ring matches the medio-lateral width of the I3 muscle at that location; b1, the height of the lumen above its maximum width; and b2, the height of the lumen below its maximum width. In the model I3 rings, the lumen is centered relative to the dorso-ventral length of the ring, but the widest point of the lumen and of the I3 ring need not be at the midpoint of the dorso-ventral length (i.e. b1 and b2 could have different values). Each ring can have a unique set of parameter values.
High-spatial-resolution MRI of anesthetized buccal masses indicated that the lumen was not necessarily centered along the dorso-ventral length and that the maximum medio-lateral width of the lumen was not necessarily coincident with the maximum medio-lateral width of the muscle (Fig. 6B). As a consequence, the following procedure was used to extract the five model parameters: (i) parameter a was determined by measuring the maximum width of the lumen and dividing by two; (ii) parameters b1 and b2 were determined by measuring the height of the lumen above and below its maximum width, respectively; (iii) the maximum dorso-ventral height (h) of the muscle was measured, and r was calculated as (h-b1-b2)/4, since, in the model, the total dorso-ventral height h of the I3 ring medially is 4r+b1+b2 (Fig. 6A); (iv) the maximum medio-lateral width (w) of the muscle was measured, and q was calculated as (w-2a-4r)/2 since, in the model, the total medio-lateral width w of the I3 ring at its dorso-ventral midpoint is 4r+2q+2a.
The resting volume of the I3 rings served as a constraint for each ring so that, as a ring was placed around the odontophore during the feeding cycle, the ring's parameters were adjusted iteratively to maintain its constant volume. Parameter values for the model I3 rings, and their volume, were obtained from analysis of the resting anatomy of the I1/I3/jaw muscle. High-spatial resolution MRIs generated parameters for a series of 12 1.5 mm thick antero-posterior slices through the I3 muscle. Using the techniques described in the previous paragraph, a set of parameters was extracted for each of these 12 slices. This parameter set was then converted into resting parameters for an equivalent set of six model I3 rings using the following procedure. (i) Starting at the lateral groove, and starting with the r value of the slice closest to the lateral groove, all slices that were within a distance 2r of the lateral groove were analyzed and their parameters were averaged. (ii) Since, in general, this led to a new value of r, steps (i) and (ii) were repeated until the value of r stopped changing. (iii) Starting at the anterior end of the previous ring, steps (i) and (ii) were repeated for each additional ring until the r value estimated from the anatomy, multiplied by the number of remaining model rings, gave an antero-posterior distance that would not reach the jaws (in our measurements, this occurred for the fourth ring to be calculated, which is ring 3 in Table 1). For all remaining rings, a constant r value was then used so that the total thickness of the six model I3 rings would span the distance from the lateral groove to the jaws when the buccal mass was at rest. The parameters for the I3 rings with fixed r values were assigned by averaging the parameter values extracted from the equivalent MRI slices, based on the fixed r value. (iv) Finally, since the I3 and odontophore are anatomically attached by elastic tissue which stretches, and the six I3 rings are non-elastic, the calculated parameters were scaled (by 1.04) to model units such that the model I3 spanned the distance from the jaws to the lateral groove. The resulting parameter values are listed in Table 1.
Because both the high-spatial- and high-temporal-resolution MRIs showed that the inner margins of the I3 muscle were not straight lines, the I3 model was also modified to accept dorsal and ventral limit curves that could be arbitrary polynomials rather than straight lines. This made it possible to partially represent the ability of the I3 muscle to conform smoothly to the changing internal shape of the radula/odontophore, which was clearly visible in the mid-sagittal MRIs (e.g. see Fig. 9).
|
Iterative positioning algorithm
As demonstrated previously (Neustadter
et al., 2002), the midsagittal MRI provides detailed information
about the entire shape of the buccal mass during feeding. Instead of
attempting to match two idealized features of the shape, the ellipticity and
the eccentricity, as in previous models (Drushel et al.,
1998
,
2002
), the present model
attempted to match the entire irregular outline of the buccal mass. We
implemented an iterative placement algorithm for this purpose, which met two
constraints. First, the anterior I3 ring was required to meet the jaw line.
Second, the outer border of the I3 rings had to match the outline of the
buccal mass. The following degrees of freedom were modified if the I3 rings
did not contact the jaw line or fit within the outline of the buccal mass: (i)
the position of the hinge (i.e. the placement of the posterior I3 ring), which
primarily affected the ventral placement of the I3 rings; (ii) the angle of
the posterior ring relative to the odontophore, which primarily affected the
dorsal placement of the I3 rings; and (iii) the polynomial limit lines, which
primarily affected the match to the outline.
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Results |
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Kinematic relationships for the radula/odontophore
To measure the location of the maximum medio-lateral width of the
radula/odontophore throughout a feeding cycle, we examined the shadow cast by
a light above the isolated odontophore. We observed that the shadow formed a
line whose angle changed throughout the feeding-like movement cycle. We also
noted that the line connecting the tip of the prow and the top of the radula
had a fixed angle relative to the shadow line as it moved
(Fig. 7A,B; the angle between
the lines was 44±5°; mean ± S.D., N=15 measurements
from two cycles). It is therefore possible to deduce the angle of the line of
widest extent from the angle of the line connecting the tip of the prow to the
top of the radula, which can be measured in mid-sagittal MRIs.
How do the kinematics of the line connecting the tip of the prow and the top of the radula compare between isolated odontophores and odontophores within the buccal mass during an in vivo swallowing movement? We examined this question by measuring the same line on odontophores during swallowing sequences in vivo. We observed that the line connecting the tip of the prow and the top of the radula showed very similar changes in angle throughout the cycle [Fig. 7C; the timing of the different in vivo behavioral periods (t4, t1 and t2) used in this and subsequent figures is provided in the figure legend]. In turn, this suggests that inferences about the line of widest extent based on the experimentally defined kinematic relationship are likely to be valid throughout the feeding cycle in vivo.
We also characterized the kinematics of the large ridge that appears on the surface of the radula during feeding movements. After fitting a circular arc to the anterior portion of the radular surface (in a side view), the protrusion of the dorsal part of the odontophore above this arc correlated well with the ridge seen in a top view. Fig. 8A shows this relationship for several key frames for ridge protrusion in side and top views (r2=0.84, P<0.002). Thus, one can use this kinematic relationship to deduce the anterior and posterior borders of the ridge and its height from the mid-sagittal MRIs.
|
How do the kinematics of the ridge observed in isolated odontophores
compare with their kinematics in radula/odontophores within the buccal mass
during swallowing in vivo? We determined the extent to which the
ridge protruded above the radular surface in isolated odontophores as they
underwent distinctive shape changes and compared them with the ridge area of
odontophores during swallowing sequences in vivo
(Fig. 8). Our measurements
in vitro indicated that the ridge was most prominent from the time
that the radula closed and the odontophore elongated dorso-ventrally (event 4,
Fig. 8B) until the time that
the radular halves opened (event 6, Fig.
8B). On the basis of our previous analysis of the mid-sagittal
in vivo kinematics (fig.
12, right side, in Neustadter
et al., 2002), this corresponds to the early retraction phase of
swallowing. Interestingly, the ridge area measured from in vivo
mid-sagittal images reaches its maximum at the onset of retraction
(Fig. 8C, border of t4
and t1 periods). In turn, this suggests that inferences about the
ridge based on the experimentally defined kinematic relationship are likely to
be valid throughout the feeding cycle.
|
Model match to buccal mass kinematics
The kinematic model successfully matched the mid-sagittal outlines of the
buccal mass measured from the high-temporal-resolution MRIs
(Fig. 9). The only significant
mismatches occurred in the posterior rings of the I3 muscle, which often
extended beyond the outline of the buccal mass. This mismatch is due to an
inherent limitation of the current I3 model (see Discussion).
The most important assumption of the model was that kinematic relationships
derived from isolated radula/odontophores performing feeding-like movements
in vitro would generate valid predictions for the medio-lateral width
of the radula/odontophore throughout the feeding cycle in vivo. It
was possible to test this critical assumption because, during data
acquisition, mid-sagittal MRIs were interleaved with axial and coronal images
of the buccal mass (Neustadter et al.,
2002). By sectioning the three-dimensional model buccal mass at
the location of the corresponding coronal MR slice, it was possible to
generate coronal slices through the model that could be directly compared with
coronal MRIs (Fig. 10).
Because the coronal images were temporally interleaved between the
mid-sagittal images (see Neustadter et
al., 2002
), we compared each coronal image with the model frame
based on the mid-sagittal image preceding the coronal image, with the model
frame following the coronal image and with a combination of the preceding and
following model frames, and used the best match for the comparison. A
quantitative test of the validity of the model was performed by computing the
symmetric difference (Alt et al.,
1998
) between the outlines of the MR and model images as a
percentage, i.e. 100(union intersection)/union. Ten sets of images
that were correctly matched generated a mean error of 13±2% (mean
± S.D., N=10). In contrast, 10 pairs of randomly matched
images generated a mean error of 19±7% (mean ± S.D.,
N=10). A KolmogorovSmirnov test
(Sokal and Rohlf, 1981
)
comparing the error distributions in ordered versus randomized
comparisons suggested that they were different (P=0.014). A
qualitative test of the validity of the model was also performed by giving
seven human volunteers 11 MRI shapes and 11 model shapes (taken from sequence
7732, using every other frame from 18 to 38, inclusive) and asking each
volunteer to pair the images so that they matched (a subset of the shapes
presented is shown in Fig.
10). Errors were quantified by computing the difference between
the frame number of a given MRI shape and the frame number of the
corresponding model shape assigned by the human subject and summing this error
over all 11 possible matches. Thus, a subject who assigned all model shapes to
the correct MRI shapes would receive a score of 0, and a subject who
consistently missed all matches by one frame would receive a score of 11.
Actual error scores were 9.6±2.8 (N=7, mean ± S.D.),
suggesting that subjects could match model shapes to MRI shapes within one
frame or better, on average. No subject's match was off by more than two
frames. These results suggest that the model effectively captures changes in
the medio-lateral shape of the buccal mass throughout the feeding cycle.
Buccal mass kinematics
The mid-sagittal and coronal matches between the model and the MRIs suggest
that the overall three-dimensional shape of the buccal mass is captured well
by the model (Fig. 11). The
lateral views of the three-dimensional reconstruction
(Fig. 11A) are in the same
orientation as the original mid-sagittal images
(Fig. 9). The dorsal and
anterior views (Fig. 11B,C)
have been rotated so that the lateral groove (the posterior edge of the model
I3 musculature) is perpendicular to the plane of the page.
Fig. 11A and
Fig. 11B can be compared with
the outputs of the previous odontophore-centric model
(fig. 9G-I and
fig. 9J-L, respectively, in
Drushel et al., 2002). For the
purpose of the discussion of the dimensions of the odontophore, the reference
frame is such that the line defining the attachment of the prow to the I6
muscle is vertical. Thus, the ridge is dorsal, the radular sac is ventral and
the prow is anterior.
|
During transition (Fig. 11, left column), the odontophore is widest in the medio-lateral direction and narrowest in the dorso-ventral direction, compared with protraction and retraction, and the radular stalk is deep within the odontophore, suggesting that the radular halves are open. At peak protraction (Fig. 11, middle column), the odontophore is narrower medio-laterally than it is at transition, suggesting that the odontophore may be compressed by the I1/I3/jaw musculature. Shortly thereafter, the radular stalk moves out of the odontophore, suggesting that the radular halves are closing. At peak retraction (Fig. 11, right column), the radular stalk has moved out of the odontophore, which is now longer in the dorso-ventral direction and much narrower in the medio-lateral direction, suggesting that the radular halves are strongly closed together.
Kinematics of buccal muscles I2, I3 and I7
I2 kinematics
Another means of verifying the model of the buccal mass is to compare its
predictions about the changes in the length of a protractor muscle, the I2
muscle (Hurwitz et al., 1996),
with in vivo measurements during a swallowing cycle derived from
high-temporal-resolution MRIs (Neustadter
et al., 2002
). We compared these results with estimates of the I2
length derived from the model by measuring the arc length of the posterior
outline of a mid-sagittal cross section of the three-dimensional model from
the dorsal surface of the most posterior I3 ring to the ventral surface of the
most posterior I3 ring (Fig.
12; model results are shown in black, MRI data from the same
swallow are shown in grey). Qualitatively, the changes in length are very
similar, reaching a maximum near peak retraction and a minimum near peak
protraction. Quantitatively, the model measurements do not exactly match the
MRI measurements. The model predicts too long a length for peak protraction in
two swallows (Fig. 12C,D;
middle of t4 period), too short a length during retraction for two
swallows (Fig. 12A,B;
t1 period) and too short a length for peak retraction in one swallow
(Fig. 12B; onset of
t2 period). The average normalized values for the actual MRI data and
the model are close, except for a consistent overestimate of the length during
protraction (Fig. 12E;
t4 period) and an underestimate of the length predicted during
retraction (Fig. 12E;
t1 period). Despite these discrepancies, the overall shape of the I2
measurements are similar in the model, in the MRIs, and in estimates from
transilluminated juvenile animals (Fig.
7 in Neustadter et al.,
2002
).
I3 kinematics
The I3 muscle plays an important role in mediating retraction during
swallowing (Morton and Chiel,
1993a). Predictions of the model for the antero-posterior length
of I3 on the dorsal and ventral surfaces and for the dorso-ventral length of
I3 at the lateral groove and at the jaws can be compared with actual lengths
of I3 measured directly from the original MRIs
(Neustadter et al., 2002
). The
antero-posterior lengths of I3 along the ventral surface of the buccal mass
are reasonably well-matched to those measured from the MRIs
(Fig. 13, right-hand plots).
In contrast, the antero-posterior length of I3 on the dorsal surface is
consistently overestimated in three of the four swallows, especially late in
protraction and during much of retraction
(Fig. 13, left-hand plots;
only the third swallow, Fig.
13C, matches the in vivo data well throughout the cycle).
The dorso-ventral lengths of I3 at the lateral groove and at the jaw are
matched very well by the model throughout the swallowing cycle
(Fig. 14, left-hand and
right-hand plots).
|
|
In previous studies, we measured the medio-lateral width of the I3 jaw
musculature at several locations along its antero-posterior length from dorsal
views of transilluminated juvenile slugs
(Drushel et al., 2002).
Because the MRIs are cross sections of the buccal mass rather than projections
and do not necessarily cross through the widest plane of the buccal mass, it
is not possible to use the coronal MRIs to compare these results directly.
However, it is possible to measure these widths in the three-dimensional
kinematic model. Estimates of the widths of I3 from kinematic model runs of
four different swallows (Fig.
15A-D) are compared with measurements of the widths of I3 from
three successive swallows of a transilluminated juvenile Aplysia
californica (Fig. 15E,F).
Both methods of measuring the I3 widths suggest that there are significant
variations in the pattern of width changes in the muscle from swallow to
swallow. The model reproduces two important features of the in vivo
data: (i) the changes in the widths are smooth throughout the cycle, unlike
previous models that generated abrupt width changes when the odontophore
entered or left the I3 muscle; and (ii) the resting distribution of the widths
and their overall shape during the cycle are similar to the in vivo
data, which is also an improvement over previous models. One difference
between the data sets is that, in the data from the transilluminated animal,
the relative change in width is greatest for the most anterior part of I3
(near the jaws; lowest traces in Fig.
15E-G) and smallest for the most posterior part of I3 (near the
lateral groove; top traces in Fig.
15E-G). In contrast, in the data from the kinematic model, at
least for the first, third and fourth swallows, the relative change in width
is greatest for the region of I3 nearest the lateral groove and smallest for
the region of I3 nearest the jaws (Fig.
15A-D).
|
The second sequence of data generated by the model is different from the
other three sequences. During this swallow, the animal strongly protracted the
radula/odontophore (fig. 11B
in Neustadter et al., 2002;
note the prolonged and very strong forward translation and rotation of the
odontophore in the second swallow). At the same time, the estimated
mediolateral width of the odontophore is narrower than that observed during
other swallows throughout retraction (see
Fig. 17B; compare with
Fig. 17A,C,D). These
observations suggest that the animal strongly closed its radular halves after
its very strong protraction. These data suggest that measurements of I3 width
may be very sensitive to the shape of the radula/odontophore.
|
I7 kinematics
Previous studies in isolated buccal masses have demonstrated that the I7
muscle can act as a radular opener (Evans
et al., 1996). Using the model, we estimated the kinematics of the
I7 muscle throughout the swallowing cycle. On the basis of its anatomy, we
defined the I7 muscle in the model as extending from the anteriormost point on
the seam between the radular sac and the radular stalk to the top of the prow
seam, which is indicative of the dorsal anterior edge of the I6 muscle.
Because the position of the prow seam is iterated to obtain the correct volume
for the prow, the location of the anterior tip of I7 was set by the model,
although in general it was close to the location initially determined directly
from the mid-sagittal MRIs. The most significant changes in I7 are its
lengthening from the peak of protraction to the peak of retraction
(Fig. 16, t1 period),
and then its rapid shortening just after the peak of retraction, prior to the
onset of protraction (Fig. 16, t2 period). In all four sequences, there is a smaller lengthening and
shortening of I7 during the protraction phase
(Fig. 16A-D, t4
period).
|
Radula/odontophore kinematics during swallowing
By using the kinematic relationships and the kinematic model, it is
possible to infer the kinematics of the radula/odontophore in the
medio-lateral dimension. The maximum half-width of the odontophore in the
medio-lateral direction decreases steadily during protraction
(Fig. 17, t4 period),
is smallest after peak protraction and during the early retraction phase
(Fig. 17, t1 period)
and is largest after the collapse of the shape of the
radula/odontophore (Drushel et al.,
1997
) (Fig. 17;
end of t2 period). The ridge is largest during the late protraction
and early retraction phases and is not visible during middle to late
retraction (Fig. 8C shows data
for one swallow). The prow is largest in antero-posterior thickness during
protraction, decreases to a minimum during retraction and increases in
thickness during the collapse of the
shape (averaged data for four
swallows are shown in Fig. 18;
panel labelled `Prow size').
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Discussion |
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Limitations of the kinematic model
Examination of the detailed differences between the mid-sagittal MRIs and
the mid-sagittal model cross sections indicates that the most significant
discrepancies in this dimension are due to the limitations of the current I3
muscle model. In the comparison of the coronal MRIs and model coronal cross
sections, the lack of widening at the jaws during early protraction in the
model relative to that seen in the MRI is due primarily to the independence of
the I3 rings in the model. In the biological system, the stiffness of the
underlying cartilage, the tension provided by the overlying I1 muscle and the
large number of deforming I3 muscle bands act to move the musculature in a
more uniform way, inducing more uniform expansions or contractions of the
I1/I3/jaw musculature. In the model, the I3 rings represent the I3 muscle at
much lower spatial resolution and move independently and are, thus, much more
affected by the local cross section of the odontophore protruding through
them. In the model, the ring at the jaws will not expand significantly until
the odontophore protrudes through it, whereas in the biological system the
expansion of the more posterior regions of the musculature will cause the jaw
region to expand even if the odontophore is not protruding through it.
The I3 antero-posterior lengths on the dorsal side are consistently too long in the model compared with the MRIs (Fig. 13, left side). The errors are the result of two factors. First, the model does not provide independent control of the dorsal and ventral thicknesses of the I3 rings, which are clearly different, as seen in the high-spatial-resolution MRIs (Fig. 6). Second, the ventral length of I3 is constrained to fit between the line of the jaws and the antero-ventral surface of the odontophore, i.e. the hinge point. In the biological system, the ventral side of I3 is sometimes stretched and therefore becomes longer than the dorsal side, which cannot be reproduced by our model, leading to a significant error in the antero-posterior length of the dorsal side. The model's overestimate of the antero-posterior I3 length on the dorsal side is likely to account for the underestimate in I2 length during retraction (for example, for swallow 2, note the errors in Fig. 13B on the left side and in Fig. 12B near the t1/t2 transition). The inability of the ventral side of the I3 rings to stretch over the prow also causes the model to predict that I2 is longer than it actually is during the protraction phase. This suggests that we need to create a new model of the I1/I3 jaw musculature with higher spatial resolution and greater anatomical accuracy and to characterize the kinematic relationships between the midsagittal cross sections of the I3 muscle and its medio-lateral deformations in a study similar to that described in the present paper for the radula/odontophore.
Another limitation of the current radula/odontophore model is that it does not incorporate the radular cleft, i.e. the space between the radular halves. In the retraction phase of swallowing, during which the radular halves are in contact with one another and there is no cleft, this simplification is not inaccurate. However, as the odontophore protracts with its halves open into the I3 jaw musculature, the cleft is likely to be large (e.g. Fig. 1A, top view), and this limitation of the model is likely to be most significant. We approximated the size of this error by measuring the area of the cleft at its widest extent from a top view of the isolated odontophore and divided this area by the area of the top view of the entire odontophore. The resulting value was 8.5%, which is an overestimate of the cleft volume, since the cleft does not extend completely from the dorsal to the ventral surface of the odontophore. Since our symmetric difference error is approximately 13%, we believe that any errors introduced by the absence of the cleft volume would not be distinguishable because of the size of the measurement error.
A final limitation of the current model is its inability to provide
detailed kinematic descriptions of many of the individual muscles of the
odontophore. A full kinematic description of the buccal mass will require an
improved insideout model that explicitly represents the radular surface and
the I4, I5 and I6 muscles. With an explicit representation of the I4 muscles
and the base of the radular stalk, it will also be possible to describe the
kinematics of the I7, I8, I9 and I10 muscles
(Evans et al., 1996) and of
the leaflets of the I4 muscles that insert medially onto the radular stalk
(Evans and Cropper, 1998
). The
constraints provided by the current model of the kinematics of the odontophore
will be essential for defining the kinematics of these muscles.
Comparison with previous models
To understand the kinematics of the buccal mass, we have created a series
of increasingly complex models. By starting with simplified models and by
carefully comparing these models with biological data, it has been possible to
pinpoint those aspects of the models that corresponded accurately to the
biological system and to identify the assumptions and properties of the models
that caused them to fail to match the biological data.
Assuming that the radula/odontophore could be represented as a rigid sphere
generated a reasonable approximation to the shape of the buccal mass near the
peak of protraction, but failed to capture the overall shape of the buccal
mass during the remainder of the swallowing cycle
(Drushel et al., 1998).
Assuming that the radula/odontophore could be represented by fixed
radula/odontophore shapes obtained by passively deforming it into
protraction-like or retraction-like shapes provided a better match to the
shape of the buccal mass in specific parts of the feeding cycle, but did not
provide a continuous model of the shape of the buccal mass throughout
swallowing (Drushel et al.,
1998
). Assuming that the mid-sagittal shape of the modeled
odontophore should be constrained by the shape observed in mid-sagittal MRIs
and that the full range of shapes could be generated by rotating or pitching
the halves of a rigid-body radula relative to the radular stalk generated a
continuously changing odontophore shape that was convincing in mid-sagittal
view, but was excessively wide medio-laterally when the radular halves were
open (Drushel et al., 2002
).
Assuming that the odontophore was a smooth, globally convex shape (also
constrained by the shapes observed in mid-sagittal MRI), that its maximal
medio-lateral width corresponded to a line connecting the extremes of the
mid-sagittal cross section and that the ventral base of the radular stalk
corresponded to the ventral base of the mid-sagittal odontophore shape
generated better overall mid-sagittal shapes for the buccal mass, but was
still inaccurate medio-laterally (Drushel
et al., 2002
). Thus, each model provided guidance for the
development of an improved successor model and at the same time generated
specific, testable hypotheses for different aspects of the function of the
radula/odontophore.
The major differences between the model described in this paper and a
previous odontophore-centric model
(Drushel et al., 2002) are the
kinematically determined angle of the line of widest medio-lateral extent
(fixed in the previous model), the inclusion of the ridge and the prow (absent
in the previous model) and the ability of the current model to separate the
base of the radular stalk from the base of the odontophore (assumed to be the
same in the previous model). To test the importance of each of these
components, we performed `lesion' studies on the current model in which each
of the new features was removed. A fixed line of widest extent was used at the
average value observed, which was a line perpendicular to the vertical prow
line. The symmetric difference between the resulting coronal images and the MR
coronal images averaged 13%. Similarly, we ran the model without constructing
the ridge and found that the symmetric differences averaged 13%. We also
removed the prow and found that the symmetric difference averaged 12%.
Finally, we placed model odontophores created by the previous
odontophore-centric model within the modified I3 model using polynomial limit
lines rather than straight lines. Although the mid-sagittal fits were good,
there were very large discrepancies in the coronal fits (41%). These results
suggest that the most important of the changes made from the previous model
was separating the base of the radular stalk from the base of the odontophore.
An improved model of the I3 musculature would be likely to respond much more
accurately to the relatively small differences in the odontophore shape due to
the changing angle of the line of widest extent, to the prow and to the ridge.
Even if these features have little effect on the overall fit, they are clearly
important for making inferences about the internal kinematics of the
radula/odontophore.
Functional implications of the model for the buccal mass
At the outset, it is important to emphasize that a kinematic model can
provide only correlative information about the relative positions of system
components, not causal statements about the function of the system, since it
does not incorporate forces. However, preliminary work on a simplified kinetic
model suggests that inferences about muscle function based on a simpler
kinematic model were in fact valid (Chiel
et al., 2000; G. Sutton and H. J. Chiel, unpublished
observations), and hypotheses based on kinematics are therefore a useful
starting point for understanding function.
Functional implications of the prow
A significant improvement of the current kinematic model is that the rate
of change in the width of the I3 muscle is similar to that observed in the
in vivo data, unlike the previous kinematic models in which the
widths of the I3 muscle changed abruptly
(Fig. 15; compare figs
8,
10 and
12 in
Drushel et al., 2002).
Although the model cannot directly demonstrate the function of the prow, the
kinematics observed in the MRIs and in the model suggest two functional roles
for the prow. (i) The wedge-like shape of the prow and its position relative
to the most posterior I3 ring at the onset of protraction suggest that it may
serve to separate the apposed halves of the I3 jaw musculature as the
odontophore begins to protract through the jaw musculature's narrow lumen,
allowing opening to occur less abruptly. (ii) By increasing the arc-length of
the anterior edge of the odontophore, the prow may increase the amount of
translation for a given rotation (this is observed for a simple physical model
of the odontophore with and without the prow; D. M. Neustadter, unpublished
observations). In turn, an increase in translation for a given amount of
rotation may improve the efficiency of biting, swallowing and rejection.
Functional implications of muscle kinematics
Functional inferences about muscles I2, I7 and I4 can be drawn from the
data. The overall kinematics of the I2 muscle is similar to that described by
direct measurements from the MRIs
(Neustadter et al., 2002). The
I7 muscle lengthens by an average of 165±32% (mean±S.D.,
N=4) relative to its minimum length during the four swallows (range
203-124%). This predicted length change is less than that predicted by the
previous odontophore-centric model
(Drushel et al., 2002
) and is
within the physiological range of the muscle
(Evans et al., 1996
). The
kinematics of each of the two I4 muscles, lima-bean-shaped muscles that occupy
much of the volume of the odontophore and that are connected anteriorly by the
I6 muscle, can be inferred from the antero-posterior and dorso-ventral lengths
of the whole odontophore (Neustadter et
al., 2002
) and half the medio-lateral width of the odontophore
predicted by the model (Figs
17,
18). During the protraction
phase, I4 appears to lengthen both dorso-ventrally and antero-posteriorly as
it contracts medio-laterally, corresponding to the open radula being
compressed as it protracts through the I1/I3/jaw musculature. During
retraction, I4 remains contracted mediolaterally, lengthens dorso-ventrally
and contracts in its anteroposterior dimension, which may correspond to a
strong radular closure during retraction. During the loss of the
shape, I4 lengthens medio-laterally and contracts very significantly
dorso-ventrally and to a lesser extent antero-posteriorly, corresponding to
the opening of the radular halves.
Radular opening prior to protraction, and the I2 muscle
A striking feature of swallowing is the rapid reduction in the
dorso-ventral height of the odontophore after the peak of retraction. We first
noted this phenomenon in transilluminated animals and termed it `the loss of
the shape' (Drushel et al.,
1997
). The mid-sagittal MRIs clearly showed that the dorsoventral
shortening of the odontophore occurred as a result of the movement of the
radular stalk into the odontophore (see
Fig. 13, right traces,
t2 period, in Neustadter et al.,
2002
). As the dorso-ventral height of the odontophore rapidly
decreases, its medio-lateral width rapidly increases (see
fig. 12, right traces,
t2 period, in Neustadter et al.,
2002
) (see also Figs
17,
18). In two of the four
swallows, we also noted that the I2 muscle did not begin to shorten
significantly until after the medio-lateral width of the odontophore had
rapidly increased (see fig.
7C,D, t2 period, in
Neustadter et al., 2002
) (see
also Fig. 17C,D; t2
period). These observations, together with previous observations that the
translation of the radular stalk into the odontophore occurs near the end of
retraction (see fig. 13, right
panels, t1/t2 transition in
Neustadter et al., 2002
) and
the timing of I2 activation, suggest that the change in the shape of the
odontophore after the peak of retraction is not due to an active I2
contraction. Rather, it appears that forces internal to the odontophore, e.g.
the contraction of the I7 muscle, cause a rapid upward movement of the stalk
that pushes apart the two I4 muscles and opens the radular halves prior to
their protraction through the lumen of the I3 musculature. This is consistent
with in vitro observations of the function of I7
(Evans et al., 1996
). During
swallowing, active contraction of I2 may be primarily responsible for the
initial protraction of the opened radula/odontophore.
A context-dependent role for the radular stalk in opening and
closing
The observations of the changing position of the radular stalk within the
odontophore near the peak of retraction suggest that it plays a major role in
opening the radular halves. Other observations, however, suggest that, in a
different mechanical context, the positioning of the radular stalk may also
play a major role during radular closure
(Fig. 19). Near the peak of
protraction, we observed that the stalk remains between the two I4 muscles at
the same time that the ridge protrudes significantly dorsally (Figs
8C,
19B), at which time the
odontophore both increases in height dorso-ventrally and decreases in width
medio-laterally. Only after these changes have occurred does the stalk move
downwards and protrude out of the odontophore
(Fig. 19C). Although the model
does not represent the radular cleft, which defines the inner borders of the
I4 muscles, it is possible to infer the likely locations of the I4 muscles
using the borders of the radular stalk and the radular ridge. These suggest
that the radular stalk may be held firmly between the two I4 muscles so that,
when they contract, they will expand upwards and pinch together, allowing the
radula to grasp material somewhat further out than it could have if the
radular stalk immediately moved downwards as the I4 muscles contracted
(Fig. 19B). Thus, the
kinematics of the odontophore suggest that, in the mechanical context of
protraction, the radular stalk may contribute significantly to the process of
radular closing.
Muscle activations and functions throughout the swallowing cycle
It is possible to relate the kinematics that we have observed to the
activity of specific nerves and muscles within the buccal mass. Previous
studies have recorded the activity on the major nerves and muscles of the
buccal mass in intact, behaving animals during swallowing responses and in
isolated buccal masses during swallowing-like movements. In particular, in
vivo recordings of large extracellular units from buccal nerve 2 (which
primarily innervates the I1/I3/jaw musculature) and the radular nerve (which
primarily innervates the I4 muscles) have been used to distinguish
ingestion-like and rejection-like behaviors
(Morton and Chiel, 1993a),
in vivo recordings from the I2 muscle have been used to examine the
role of I2 during protraction in biting, swallowing and rejection
(Hurwitz et al., 1996
),
recordings from the I5 (ARC) muscle during a bite/swallow have been published
as part of the study of the modulation of this muscle by peptidergic
co-transmitters released by its motor neurons, B15 and B16 (Cropper et al.,
1990a
,b
)
and recordings from the I10 muscle (which are thought to be representative of
activity in I7, I8 and I9) in intact animals have been published during biting
and swallowing behaviors (Evans et al.,
1996
). Additional data on nerve and muscle activity have been
obtained from semi-intact preparations capable of generating feeding-like
motor patterns (Morton and Chiel,
1993b
; D. W. Morton and H. J. Chiel, unpublished observations). In
many cases, these data can be normalized to a single swallowing cycle by using
the time from the onset of I2 activity (i.e. the initiation of the protraction
phase) to the end of the inward movement of food (i.e. the end of the
retraction phase, prior to the initiation of the next protraction phase) or by
using the duration of the inward movement of food. These data must be regarded
as no more than an initial schematic view until it is possible to obtain
simultaneous recordings of nerve and muscle activity during swallowing in
intact animals.
We will analyze the cycle of swallowing from the initiation of protraction
through the return to the state in which the odontophore has shortened and the
radular stalk has moved within the odontophore because this appears to be the
sequence in which behaviors are initiated by the feeding pattern generator.
Observations of a sequence of swallows using MR imaging indicated that, once
protraction had been initiated, a complete cycle of activity was observed. We
also observed that pauses between successive responses occurred after the
dorsoventral shortening of the odontophore and the upward movement of the
radular stalk into the odontophore, and that the buccal mass would pause for
variable amounts of time before initiating another swallow. This observation
is consistent with our previous work showing that the initiation of all
feeding responses begins with protraction, because the interneurons that
initiate activity in the pattern generator, B31/B32, are also motor neurons
for the I2 muscle (Hurwitz et al.,
1996).
Phase 1: initiation of protraction. Activity in the I2 muscle and on buccal nerve 1 (BN1) is observed at the onset of protraction (Fig. 20). The I2 muscle shortens during the initial phase of protraction (Fig. 18, I2 length in t4 period). Since BN1 innervates the pharyngeal tissue posterior to the lateral groove and dorsal to the I2 muscle, simultaneous activity of BN1 and the I2 muscle may represent activation of motor neurons that induce all the tissue posterior to the lateral groove to contract, pushing the radula/odontophore anteriorly towards the jaws (Fig. 21, columns 1-3). At the same time, activity is observed on buccal nerve 3 (BN3). Since motor neurons that travel via BN3 innervate the `hinge' tissue, the interdigitation of ventral I4 fibers with the ventral posterior fibers of the I3 muscle (H. J. Chiel, unpublished observations), the activity on BN3 could represent motor neurons that cause contraction of the hinge tissue, inducing an anterior rotation of the radula/odontophore (Fig. 18, odontophore rotation in t4 period; Fig. 21B, columns 1-3). Note that the odontophore continues to translate and rotate anteriorly even after the I2 muscle has ceased to contract further (Fig. 18, t4 period).
|
Shortly after the onset of activity in the I2 muscle, a burst is observed in the I7 muscle. This could be responsible for the shortening observed in I7 during the protraction phase (Fig. 16, t4 period). In turn, this could have two effects. First, during protraction, the odontophore is pushed through the lumen of the jaws and, using the stalk to separate the two I4 muscles, may aid in keeping the radula open as it is compressed by the surrounding I1/I3/jaw musculature. Second, when the two I4 muscles begin to contract together medially, the presence of the radular stalk may force them to deform dorsally into a ridge. Thus, I7 may participate during the closure of the radular halves (Fig. 19B,E).
During the early phase of protraction, small units are active on buccal
nerve 2 (BN2) at a low frequency. It is possible that this could reflect the
activity of jaw opener motor neurons
(Church and Lloyd, 1994) that
could help relax the jaw musculature as the radula/odontophore protracts
through it. It could also reflect activity of motor neurons innervating I1,
which could act to shorten the dorsal surface of the jaw musculature
significantly and aid protraction (note the anteroposterior shortening of I3
on the dorsal surface during the protraction phase;
Fig. 18; t4
period).
Phase 2: protraction/retraction border. After a gap in activity
near the end of protraction, BN2 becomes active again, and these units
represent motor neurons (e.g. B10) that innervate the I1/I3/jaw musculature
and induce contractions (Morton and Chiel,
1993a,b
).
This corresponds to the time at which the odontophore stops rotating towards
the jaw and begins rotating away from the jaws
(Fig. 18, odontophore rotation
at t4/t1 border; Fig.
21B, columns 3 and 4), suggesting that compression of the
odontophore by the I1/I3/jaw musculature acts to initiate retraction. The
cessation of activity in I2 and BN1 should also cause the tissue posterior to
the lateral groove to relax, so that it will not resist as the odontophore
retracts into the I2 muscle and pharyngeal tissue.
At the same time, activity is observed in large units on the radular nerve,
and these units represent motor neurons (e.g. B8a and B8b) that innervate the
I4 muscles and induce radular closure (Morton and Chiel,
1993a,b
).
Closure of the radular halves at the protraction/retraction transition is
consistent with maximum protrusion of the ridge (Figs
8C,
18, ridge size at
t4/t1 border; Fig.
19B). The radular halves remain closed throughout retraction,
pulling food into the buccal cavity.
Activity is observed in large units on BN3 that are likely to represent the
activity of the B4/B5 multi-action neurons
(Warman and Chiel, 1995).
B4/B5 could inhibit the I2 motor neurons (H. Ye and H. J. Chiel, unpublished
observations), helping to terminate the protraction phase of swallowing and
also to delay the onset of firing of the jaw motor neurons (Gardner,
1977
,
1993
), allowing the
radula/odontophore to move posteriorly so that, when the jaw motor neurons do
begin to fire, the I1/I3/jaw muscle complex is positioned anterior to the
midline of the odontophore, allowing it to retract the odontophore
strongly.
At the onset of the inward movement of food, the I5 (ARC) muscle begins to
show electromyographic activity, reflecting activity in the B16 motor neuron
(Cropper et al., 1990b). If
the radular stalk is between the two I4 muscles
(Fig. 19B), and the I4 muscles
are stiff as a result of their own activation, contraction of the I5 muscles,
which insert both on the lateral margins of the I4 muscles and on the base of
the radular stalk, could aid in pulling the radular stalk out of the
odontophore. At the same time, compression of the I4 muscles resulting from
neural activation and compression of the odontophore by the surrounding
I1/I3/jaw musculature could aid in pushing the radular stalk out of the
odontophore. The wedge shape of the radular stalk and the smooth, inelastic
inner surfaces of the I4 muscles could aid in this process. All these
movements induce the radular surface to roll inwards, aiding it in pulling
food into the buccal cavity (Fig.
18, radular stalk translation at the t4/t1 border; Figs
19C,F,I,
21, columns 3-5).
Phase 3: mid-retraction. Midway through retraction, activity is
observed in large units on BN2 and facilitating activity is observed on I2.
This may correspond to the point at which the elongated odontophore is
rotating so that its tip is pushing on the dorsal surface of the I1/I3/jaw
musculature (see fig. 5 in
Neustadter et al., 2002, frame
16). A burst of activity in BN2 may represent an intensification of closing
forces, which cause the rapid retraction (`snap back') that is observed
kinematically (Neustadter et al.,
2002
). At the same time, the late facilitating activity in I2,
which may be due to the underlying I4 muscles, may act to brake the rapid
retraction (Hurwitz et al.,
1996
) since I2 is being activated at the same time that it is
being stretched. Passive forces in I2 may also act to brake the retraction
(Yu et al., 1999
).
Phase 4: end of retraction. After food has stopped moving inwards,
there is a burst of activity in the I10 muscle (and, presumably, in the 17-19
muscles; Evans et al., 1996)
and the I7 muscle shortens (Fig.
16, t2 period; Fig.
18, I7 length, t2 period;
Fig. 21B, columns 5 and 6).
Shortening of the I7 muscle could pull the radular stalk into the odontophore,
pushing the I4 muscles apart medio-laterally
(Fig. 19C,F shows the position
of the radular stalk before the I7 muscles contract;
Fig. 19A,D shows the position
of the radular stalk after the I7 muscles have contracted) and causing the
radular halves to open and release food into the esophagus. Interestingly,
during this time, it appears that the I5 muscle continues to be active,
showing facilitating activity that is likely to be due to the activity of
motor neuron B15 (Cropper et al.,
1990b
). When the radular stalk is held inside the I4 muscles by a
strong I7 contraction and the I4 muscles are relaxed, shortening of I5 may aid
in separating the I4 muscles, initiating radular opening, and the actions of
I5 may also therefore be context-dependent
(Fig. 19F shows the position
of the I5 muscles at the peak of retraction, when the I4 muscles are
lengthened and stiff; Fig. 19D
shows the position of the I5 muscles after the I4 muscles have relaxed,
although the I4 muscles would be further apart immediately after the loss of
the
shape). A previous study has shown that the mechanical advantage
of I5 may change with the position of the radular halves
(Orekhova et al., 2001
), but
these kinematic observations suggest that the function of the muscle could
change.
Once the odontophore has retracted posteriorly and the radular halves have
opened and released food into the esophagus, it is interesting to note a burst
in BN1. This may be part of the activation of the pharyngeal and esophageal
tissue that transports food by peristalsis from the most anterior portion of
the esophagus into the gut. Peristaltic movements that transport food into the
gut have been observed both in transilluminated juvenile slugs
(Drushel et al., 1997) and in
high-temporal-resolution mid-sagittal MRIs (D. M. Neustadter and H. J. Chiel,
unpublished observations).
Implications for neuromuscular control of movement
As described in the Introduction, several hypotheses have been proposed for
the functional mechanisms of the radula and the underlying adontophore. Some
investigators have proposed that it might act like a pulley, others have
suggested that it might act like a block and tackle (for a review, see
Smith, 1988). Our kinematic
studies suggest that it may be misleading to use a single mechanical metaphor
to describe the operation of the radula/odontophore throughout the entire
feeding cycle. Instead, it appears that small muscles (e.g. I7) act to change
the relative positions of larger muscles (e.g. the I4 muscles) and, by doing
so, create the appropriate mechanical context for the large muscles to effect
a particular behavior (e.g. opening or closing). By shifting among different
mechanical contexts, the same set of muscles can flexibly generate a much
larger repertoire of behaviors, such as biting, swallowing, rejection,
tearing, grazing and cutting (Hurwitz and
Susswein, 1992
; Kupfermann,
1974
; Rosen et al.,
2001
). The flexible mechanical architecture of this peripheral
structure lends itself to a reorganizing neural architecture in which
relatively small shifts in the phasing or timing of the activity of different
motor pools can generate a range of qualitatively different behaviors
(Hurwitz et al., 1997
;
Jing and Weiss, 2001
;
Morton and Chiel, 1994
).
The work described in this study is likely to contribute to our
understanding of neuromuscular control of movement in general. Recent attempts
to develop a theoretical understanding of the neuromuscular transform in
Aplysia californica, the non-linear transformation of neural inputs
to motor outputs (Brezina et al.,
2000a,b
),
have incorporated very simple biomechanical constraints
(Brezina and Weiss, 2000
) and
could be greatly improved by incorporating the more realistic relationships
between the muscles that are presented in the present paper. Moreover, recent
studies of the pattern generator in Aplysia californica have shown
that it is strongly modulated by proprioceptive feedback
(Borovikov et al., 2000
;
Evans and Cropper, 1998
), and
the natural kinematics of the musculature is essential for determining the
normal proprioceptive feedback that will occur during behavior. Finally,
studies of a form of operant conditioning in Aplysia californica, in
which freely moving animals (Chiel and
Susswein, 1993
; Susswein et
al., 1986
) or reduced preparations (Nargeot et al.,
1999a
,b
)
can associate specific tastes and textures with inedibility, may be understood
within a biomechanical context through the studies described here.
There are more general implications of the studies described in this paper.
These studies are an important step towards understanding the interactions
between biomechanics and neural control in a muscular hydrostat, i.e. a
structure in which muscle may have both force-generating and skeletal
functions (Kier and Smith,
1985), and in which forces exerted by the cross section of the
muscle as it lengthens or shortens may play important roles. Recent studies of
octopus tentacular extension have suggested that, for relatively stereotyped
extension movements, a peripheral program within the tentacles may be
sufficient (Matzner et al.,
2000
; Sumbre et al.,
2001
). Experimental and modeling studies of protrusible tongues
and tentacles have also begun to suggest several biomechanical principles for
the operation of these structures (van
Leeuwen et al., 2000
). Studies of the human tongue have suggested
that it may have muscular hydrostatic properties during normal speech and
swallowing (Nadapow et al.,
1999
) and that a linear combination of six directions of articular
motion involving the tongue, jaw and larynx may sum in a linear fashion to
generate speech (Sanguineti et al.,
1998
). Because of the tractability of the nervous system of
Aplysia californica to cellular and biophysical analysis, the studies
described here may provide the basis for understanding both detailed
biomechanics and detailed neural control of a muscular hydrostatic structure.
In particular, an understanding of the neural control of context-dependent
muscles in Aplysia californica may provide insights into the
principles of control of context-dependent muscles that have been described in
vertebrates. Finally, these studies are serving as the basis for the
development of soft-bodied robots whose biomechanics and neural control are
based on the biomechanics and neural control of animals such as leeches and
slugs (Mangan et al., 2002
;
Vaidyanathan et al.,
2000
).
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Acknowledgments |
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Footnotes |
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References |
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