Radula-centric and odontophore-centric kinematic models of swallowing in Aplysia californica
Richard F. Drushel1,
Greg P. Sutton2,
David M. Neustadter3,*,
Elizabeth V. Mangan2,
Benjamin W. Adams1,
Patrick E. Crago3 and
Hillel J. Chiel1,3,4,
1 Department of Biology, Case Western Reserve University, Cleveland, OH
44106, USA
2 Department of Mechanical Engineering, Case Western Reserve University,
Cleveland, OH 44106, USA
3 Department of Biomedical Engineering, Case Western Reserve University,
Cleveland, OH 44106, USA
4 Department of Neurosciences, Case Western Reserve University, Cleveland,
OH 44106, USA
* Present address: MR Systems Department, G. E. Medical Systems Israel Ltd,
Keren Hayesod Street, POB 2071, Tirat Carmel 39120, Israel.
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Fig. 1. The radula-centric kinematic model. (A—D) The physical construction
of the model. The model consists of two radular halves, a cylindrical radular
stalk with a rounded ventral dome and two cylindrical I7 muscles. The model is
constructed in a standard orientation such that the radular stalk is vertical.
(A) Medio-lateral view with radular halves fully closed. Mid-sagittally, the
radular halves are defined by an anterior ellipse quadrant a and a
posterior parabolic segment b. The posterior tip of the radular
halves is constrained to be level with the posterior edge of the radular
stalk. The radular halves can rotate about this posterior tip point (pitch,
 p). By convention, 0° is horizontal, anterior rotations
are positive and posterior rotations are negative. The I7 muscles run between
a point on the antero-ventral radular stalk and a defined point below the
radular halves (corresponding to an anterior radular `skirt' whose surface is
not explicitly represented, dotted line, ellipse segment c). I7
changes dimensions isovolumetrically as its anterior endpoint changes
position. (B) Dorso-ventral view showing radular yaw (y). In
this plane, the radular halves are defined by an anterior ellipse quadrant
d and a posterior parabolic segment e. As in A, the
posterior tip of the radula is constrained to be level with the posterior edge
of the radular stalk. By convention, both radular halves are closed at 0°,
and opening is a positive yaw. (C) Antero-posterior view showing radular roll
(r). In this plane, the radular halves are defined by an
ellipse quadrant f. Note that, as constructed, the dorsal endpoint of
the I7 muscle (arrowhead) is fixed relative to the radular half and thus moves
medially as the radular half rolls laterally. By convention, both radular
halves are closed at 0°, and opening is a positive roll. (D) Method of
odontophore volumetric database construction. All model components are
represented as isosurfaces composed of triangles. A completed odontophore
model is sliced in fixed steps along the antero-posterior axis, and ellipse
quadrants are used to fill in `missing' unmodeled space (presumed to contain
the I4 muscle and other structures) in the ventral half of each slice. The
resulting volumetric database, as well as a smoothed outline from the
mid-sagittal view, is used as input for the buccal mass model. (E—G)
In-vivo-derived model parameter inputs. All timebases have been
normalized to the mean t1, t2, t3 and t4 intervals (defined
in Materials and methods) of the constituent data sets (data not shown),
allowing data from multiple swallows to be combined. Each data point in E and
F represents the mean of a normalized time interval (0.2s). Values are mean
± S.E.M.; N=4 for each time interval in E;
N=2-9 (mean=4.7) for each time interval in F. E and F are from
mid-sagittal magnetic resonance images of an adult; smoothed curves from these
data were used as radula-centric model inputs. G represents a synthesis of all
available video and image data, including biting and swallowing in large
adults. (E) Radular stalk angle from four swallows. This is the angle formed
by the long axis of the radular stalk and a line perpendicular to the buccal
mass axis (the line from the jaws to the esophagus after external rotation of
the entire buccal mass has been removed, buccal mass angle 0°). By
convention, vertical is 0°, anterior rotations are positive and posterior
rotations are negative. (F) Radular pitch angle from nine swallows. (G)
Radular roll and yaw angles used as direct inputs to the model.
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Fig. 2. The odontophore-centric kinematic model. (A) Superellipse function, which
is used to create curved surfaces whose convexity or flatness varies with the
value of a single parameter, n. The behavior of the function at
several values of n is shown. (B) Extracting the midsagittal outline
of the radula/odontophore from magnetic resonance (MR) images. With the images
rotated such that the radular stalk is vertical, the anterior, posterior,
dorsal and ventral extrema of the radula/odontophore are determined
(horizontal and vertical lines). For each quadrant, four points on the surface
of the curve are selected (open circles, shown only for the antero-ventral
quadrant). Best-fit superellipse curves are found using these control points
(see Materials and methods). In the antero-dorsal quadrant, the point at which
the presumed long axis of the I7 muscle (diagonal line) intersects the radular
surface is determined (filled circle). (C—E) Three-dimensional
renderings (orthographic projection) of the resulting odontophore-centric
model with the right half of the odontophore cut away to reveal the radular
stalk (realistically reconstructed from high-spatial-resolution MR images) and
the I7 muscle. All structures are represented as isosurfaces composed of
triangles. (C) Mediolateral view with the four superellipse quadrants
a—d. (D) Antero-posterior view. Curves e and
f are ellipses (n=1.0) because there are no data available
to determine their true shape with high temporal resolution. (E) Dorso-ventral
view. Curves g and h are assumed to be ellipses
(n=1.0), as in D. Volumetric databases are created from each
radula/odontophore isosurface by stepwise slicing along the antero-posterior
axis, as in the radula-centric model (Fig.
1D).
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Fig. 3. Buccal mass shape space analysis (modified from Fig. 3 of
Drushel et al., 1998 ). (A)
Ellipse quadrant shape approximation for the mid-sagittal buccal mass outline,
showing the dimensions a, b, c and d used to compute the
ellipticity and eccentricity parameters (formulae given in the axis labels of
C). (B) Mean buccal mass shape changes from nine sequential swallows in a
transilluminated juvenile. Note that the ellipse approximation fails in the
antero-ventral quadrant around peak retraction (7-9, dotted lines). Images
1-3, 4-8, 9 and 10-11 correspond roughly to the intervals t4, t1, t2
and t3, respectively. Each image is 0.33 s (normalized). (C) Shape
space plot of ellipticity versus eccentricity parameters for the 11
images in B. Rest, peak protraction and peak retraction occupy distinctly
different points (dark gray geometric shapes) in the two-dimensional shape
space. The light gray region in the graph shows the approximate range of
responses in the nine individual swallows that were averaged. Individual
swallows show hysteresis (i.e. the path from protraction to retraction is
different from the path from retraction to protraction), which is removed by
averaging and timebase normalization. Each point is 0.33 s (normalized).
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Fig. 5. Comparison of transilluminated and mid-sagittal magnetic resonance (MR)
images of swallowing in Aplysia californica. (A-C) Mediolateral views
of a transilluminated juvenile, reproduced from
Fig. 3B, C and A (respectively)
of Drushel et al. (1997). (D-F)
Corresponding mid-sagittal MR images of an adult (sequence 5385-S1, frames
116, 122 and 128, respectively). (G-I) Schematic tracings of the anatomical
structures in D-F. The left-hand column is rest, the centre column is peak
protraction and the right-hand column is peak retraction. The characteristic
ovoid (shape 2), round (shape 1) and  (shape 3) buccal mass shapes
(first defined in transilluminated images) are apparent in the MR images, as
are the exact positions of internal anatomical structures. Note that some
structures that appear opaque to transillumination do not appear dark in the
MR images (D, dotted lines around elastic tissue joining the I1/I3 muscles to
the lips; G, tissue labelled et), whereas parasagittal structures that cast a
shadow in transillumination (e.g. the penis) are absent from the narrow
mid-sagittal plane of the MR images. ba, buccal artery; w, wall of container
holding the animal; e, esophagus; r, radula; rs, radular stalk.
Transilluminated NTSC video frames are 33.3 ms. MR image frames are 250
ms.
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Fig. 8. Quantitative results of the radula-centric kinematic model of swallowing.
(A) Shape space analysis of one of the magnetic resonance imaging (MRI)
swallowing sequences used to construct the radula-centric model (sequence
5385-S1, frames 116-133). Note that the entire plot is shifted to the right
along the ellipticity axis (i.e. less elongated along the antero-posterior
axis) compared with Fig. 3C
(mean transilluminated juvenile shape space plot) as a result of the presence
of elastic tissue around the jaws that is opaque to transillumination but is
distinctly different from the I1/I3 muscles (see
Fig. 5D). (B) Shape space
analysis of the radula-centric kinematic model, which is a composite of
several MRI swallowing sequences. There is only rough agreement with A,
probably because B is a composite of 4-9 different swallowing sequences. There
is a large hysteresis loop in frames 29-37. The gray symbols marking key
events of the feeding cycle in A and B are defined in
Fig. 3C. (C) Model I2 and I7
muscle lengths. I2 nearly triples and I7 quadruples its length during
t1. Intervals t1,t2,t3 and t4 are defined in
Materials and methods. (D) Model I1/I3 muscle antero-posterior length. (E)
Model I1/I3 muscle ring widths (medio-lateral). Ring 1 (posteriormost) is at
the lateral groove, and ring 5 (anteriormost) is at the opening of the jaws.
Note the rapid changes in the widths at mid-t4 (rings 3-4),
mid-t1 (rings 1-5) and t3 (rings 1-2). MRI frames are 250 ms
(real time). Model frames represent 66.7 ms (normalized).
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Fig. 10. Quantitative inputs and results of the odontophore-centric model of a
polyethylene tube swallow, magnetic resonance imaging (MRI) sequence 7732-S3,
frames 15-38. Each frame is 310ms (real time). (A) Radular stalk angle,
measured from each MRI frame. These values were direct inputs into the model.
(B) Shape space analysis of MRI frames 15-38. (C) Shape space analysis of the
corresponding odontophorecentric model frames. The four key landmarks of the
feeding cycle (start of protraction, peak protraction, peak retraction and
return to rest; gray symbols are defined in
Fig. 3C) and general progress
through shape space are in fair agreement, but the exact paths are not
identical. (D) Model I2 and I7 muscle lengths. I7 doubles and I2 more than
doubles its length during t1. Intervals t1, t2, t3 and
t4 are defined in Materials and methods. (E) Model I1/I3 muscle
antero-posterior length. (F) Model I1/I3 muscle ring widths (medio-lateral).
The rate of width changes is less than in the radula-centric model (see
Fig. 8E).
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Fig. 12. Quantitative inputs and results of the odontophore-centric model of a
seaweed noodle swallow, magnetic resonance imaging (MRI) sequence 7725-S2,
frames 44-66. Each frame is 310ms (real time). (A) Radular stalk angle,
measured from each MRI frame. These values were direct inputs into the model.
(B) Shape space analysis of MRI frames 44-66. (C) Shape space analysis of the
corresponding odontophore-centric model frames. Peak protraction and peak
retraction are in good agreement with B, but frames near rest do not match.
The gray symbols marking key events of the feeding cycle in A and B are
defined in Fig. 3C. (D) Model
I2 and I7 muscle lengths. I7 doubles and I2 more than doubles its length
during t1. Intervals t1, t2, t3 and t4 are defined
in Materials and methods. (E) Model I1/I3 muscle antero-posterior length. (F)
Model I1/I3 muscle ring widths (medio-lateral). Ring 1 (posteriormost) is at
the lateral groove, and ring 6 (anteriormost) is at the opening of the jaws.
There are some sharp changes in width (rings 3-6 during mid-t4 and
the end of t1).
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Fig. 7. Three-dimensional renderings (orthographic projection) of the
radula-centric kinematic model of swallowing. (A—C) Latero-medial views;
(D—F) dorso-ventral views; (G—I) antero-posterior views. The
left-hand column is rest (model frame 1), the centre column is peak
protraction (model frames 24 and 25) and the right-hand column is peak
retraction (model frame 51). The right or left halves of the I1/I3 rings have
been cut away to reveal internal details. Note the gaps in the rings in G and
H (arrows) where the radula/odontophore has large changes in medio-lateral
width and also the kinematic interference between the radular stalk and I7
volumes in C and I (arrowheads). Each frame represents 66.7 ms
(normalized).
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Fig. 6. In vivo measurements of I1/I3 muscle dimensions in three
consecutive swallows from a two-axis video recording of a transilluminated
juvenile. All timebases have been normalized as in
Fig. 1E-G. Each data point is
the mean of a 0.2 s (normalized) interval. Values are means ± S.E.M.
Intervals t1, t2, t3 and t4 are defined in Materials and
methods. (A) Estimated I1/I3 muscle antero-posterior length computed as 45% of
the total buccal mass antero-posterior length
(Drushel et al., 1998).
N=2-6 (mean=4.3). Lengths were measured in medio-lateral view. (B)
Estimated I1/I3 muscle mediolateral width computed by dividing the
dorso-ventral views of the I1/I3 muscle into six rings of equal
antero-posterior thickness (see Fig.
4). N=4-27 (mean=20.8). Ring 1 (posteriormost) is at the
lateral groove, and ring 6 (anteriormost) is at the opening of the jaws.
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Fig. 9. Odontophore-centric model of a polyethylene tube swallow, magnetic
resonance imaging (MRI) sequence 7732-S3, frames 15-38. (A—C)
Mid-sagittal MR images; (D—F) schematic tracings of the anatomical
structures in A—C; (G—L) corresponding odontophore-centric model
representations (orthographic projection). G—I are latero-medial views
and J—L are dorso-ventral views. The left-hand column is rest (MRI frame
15), the centre column is peak protraction (MRI frame 26) and the right-hand
column is peak retraction (MRI frame 35). Buccal mass rotation has been
removed from the MR images (buccal mass angle 0°). Note the apparent
stretching of the ventral I1/I3 muscle at the hinge region between rest and
peak protraction (dotted line, A and B). The plane of the lateral groove tilts
anteriorly at peak protraction (arrowheads, B), but in the model
representation, the plane of the first I1/I3 muscle ring remains vertical (H;
arrowheads indicate the in vivo lateral groove plane). The right or
left halves of the I1/I3 rings have been cut away in G—L to reveal
internal details. e, esophagus; r, radula; rs, radular stalk; rt, radular tip.
Each frame is 310 ms (real time).
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Fig. 11. Odontophore-centric model of a seaweed noodle swallow, magnetic resonance
imaging (MRI) sequence 7725-S2, frames 44-66. (A-C) Mid-sagittal MR images;
(D-F) schematic tracings of the anatomical structures in A-C; (G-L)
corresponding odontophore-centric model representations (orthographic
projection). (G-I) Latero-medial views; (J-L) dorso-ventral views. The
left-hand column is rest (MRI frame 44), the centre column is peak protraction
(MRI frame 52) and the right-hand column is peak retraction (MRI frame 63).
Note the more tortuous outline of the dorsal I1/I3 muscle (A, solid lines) and
the more pronounced shape of peak retraction (C) compared with the
7732-S3/15-38 sequence (see Fig.
9A,C, respectively). The greatly different cross-sectional radii
of the six I1/I3 rings are an attempt to capture these anatomical details in
the model. As in Fig. 9B, there
is also a large apparent stretch of the ventral I1/I3 muscle at peak
protraction (B, dotted line) as well as an anterior rotation of the lateral
groove plane in vivo that is not duplicated by the model (arrowheads,
B and H). The right or left halves of the I1/I3 rings have been cut away in
G-L to reveal internal details. e, esophagus; rs, radular stalk. Each frame is
310 ms (real time).
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© The Company of Biologists Ltd 2002
