A kinematic model of swallowing in Aplysia californica based on radula/odontophore kinematics and in vivo magnetic resonance images
David M. Neustadter1,4,
Richard F. Drushel2,
Patrick E. Crago1,
Benjamin W. Adams2 and
Hillel J. Chiel1,2,3,*
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
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Fig. 21. Schematic summary of the movements of the entire buccal mass during a
swallowing cycle. This summary, which supersedes
fig. 10 of Drushel et al.
(1997 ), is based on the data
presented in the present paper and in Neustadter et al.
(2002) and incorporates
observations from in vivo high-temporal-resolution MRIs taken in
intact, behaving animals as well as high-spatial-resolution MRIs of
anesthetized buccal masses. Details not visible in the MRIs are based on
observations of buccal masses or isolated odontophores undergoing
pharmacologically induced feeding-like movements and on dissections of fresh
and fixed buccal masses. All illustrations are in orthographic projection. (A)
A superficial lateral view of the outer buccal mass. (B) A mid-sagittal view.
(C) A dorsal view. In C, the upper half of each diagram depicts a superficial
dorsal view, whereas the lower half depicts a view in which the radular
surface and the I4 muscles are transparent, showing the ventral structures
beneath them. Columns 1-6 correspond to frames 15, 19, 25, 30, 35 and 37,
respectively, of sequence 7732-S3. The circumferential muscle shown in C4 was
designated as such by Starmühlner
(1956). The nomenclature for
the other intrinsic muscles follows Howells
(1942) and Evans et al.
(1996), and the nomenclature
for the extrinsic muscles follows Chiel et al.
(1986) and Howells
(1942).
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Fig. 19. Inferences about the context-dependent function of the radular stalk, 17
and 15 from odontophore kinematics. All illustrations are in orthographic
projection, with the radula/odontophore rotated such that the radular stalk is
vertical. The top row (A—C) shows transparent antero-posterior views of
the model from fully open to just after radular closure. The middle row
(D—F) shows antero-posterior views (i.e. through the jaws) of the
radula/odontophore with the inferred locations of its constituent muscles
indicated schematically. The bottom row (G—I) shows postero-anterior
views (i.e. through the esophagus) of the radula/odontophore with the inferred
locations of its constituent muscles indicated schematically. The first column
shows the radula/odontophore before peak protraction (t4 period) from
frame 22 of sequence 7732-S3. The inferred borders of the I4 muscles are drawn
using thick black lines. Note that the radular stalk is entirely within the
odontophore (A,D) and that the radula is open (G). The second column shows the
radula/odontophore at the onset of retraction (start of t1) from
frame 26 of sequence 7732-S3. The radular stalk is still entirely within the
odontophore. We hypothesize that the presence of the stalk between the I4
muscles as they begin to compress together induces the I4 muscles to deform
upwards and form a ridge (B,H), enhancing their ability to grasp food as they
close. Note the shortening of the I7 muscles (E) relative to early protraction
(D). If the I7 muscles contribute to holding the radular stalk between the I4
muscles, they could enhance the early phase of closing in this configuration.
The third column shows the radula/odontophore during retraction (end of
t1 period) from frame 34 of sequence 7732-S3. The radular stalk has
moved maximally out of the odontophore, allowing the I4 muscles to close on
one another as the radular surface rolls downwards. This induces the formation
of the radular `pinch' (I), and also lengthens the I7 muscles (F), so that
their contraction can pull the radular stalk upwards and separate the I4
muscles (i.e. the I7 muscles and the radular stalk can open the radular halves
by changing their configuration from column 3 to column 1). Contraction of the
I5 muscles can contribute to closing (E) by pulling the radular stalk out of
the I4 muscles, and contraction of the I4 muscles can further push the radular
stalk downwards, causing the radular halves to close as the odontophore
changes from its column 2 to its column 3 configuration. However, relaxation
of the I4 muscles and movement of the radular stalk into the odontophore,
separating the I4 muscles and lengthening the I5 muscles, could allow a
contraction of the I5 muscles to cause the I4 muscles to rotate outwards, so
that I5 may enhance opening (changing the odontophore from its column 3
configuration to an open configuration; column 1 shows the odontophore after
the peak opening of the radular halves).
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Fig. 1. Measurement of in vitro radula/odontophore kinematics. Two frames
are shown from a digital video recording of an isolated radula/odontophore
induced to perform feeding-like movements in response to carbachol. The line
of shadow indicating the region of widest medio-lateral extent is indicated in
the side views, and the ridge, prow and cerebral ganglion are indicated in the
top views. (A) Multiple views of the open radula and odontophore. (B) Multiple
views of the closed radula and odontophore. Scale bars, 10 mm.
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Fig. 6. Model I3 rings and parameter extraction from high-spatial-resolution MRIs.
(A) Model I3 rings. The maximum width of the lumen is 2a, the height
of the lumen above the maximum width is b1, and the height of the
lumen below the maximum width is b2. The radius of the semi-circular
cross section of the outer half-ring at the top and bottom and of the inner
half-ring surrounding the lumen is r. The width added between the
outer and inner half-rings so that the medio-lateral width matches that of the
muscle at its widest extent, is q. The total height h of the
model ring is equal to 4r+b1+b2, and its total
width w is equal to 4r+2q+2a. (B)
High-spatial-resolution MRI of the I3 muscle in axial section from an isolated
buccal mass. The maximum lumen width, a, and of the heights below and
above this maximum width (b1 and b2, respectively), are
shown on the image. In addition, the measurement of the maximum width,
w, and maximum height, h, is illustrated. The parameter
r is calculated from (h-b1-b2)/4, and the parameter
q is calculated from (w-2a-4r)/2. The top
and bottom borders of the lumen used in measuring b1 and b2
are measured from the dorsal and ventral extremes of the cartilage of the
lumen, which appears black in the MRI because the lumen is partially closed.
Measurements were made in pixels and then scaled to arbitrary model units.
Note that, although lumen width 2a and muscle width w are
not measured at the same dorso-ventral height, the calculation of q
is performed as if they were at the same height. This follows from the model
approximation (A), which assumes that the maximum lumen width and the maximum
I3 ring width are at the same dorso-ventral height. Magnetic resonance
acquisition parameters for the slice shown: fast spin echo, TE (time to
echo)=120 ms, TR (time to repeat)=3000 ms, ETL (echo train length)=16, FOV
(field of view)=5 cmx5 cm, SW (slice width)=1.5 mm, AM (acquisition
matrix)=512x512, NEX (number of excitations)=4.
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Fig. 3. Constructing the odontophore and the prow. (A) Perspective view of a square
containing a mid-sagittal outline of the odontophore and prow extracted from
high-temporal-resolution magnetic resonance imaging (MRI). The prow seam and
the line of widest extent (see D and E and text for definition) are indicated.
A, anterior; D, dorsal; P, posterior; V,
ventral. (B) Curve defining the medio-lateral dimension. The curve lies in the
plane that contains the line of widest extent and is perpendicular to the
mid-sagittal plane. The curve is constructed of four spline quadrants whose
spline parameters are based on high-spatial-resolution MRIs of an anesthetized
odontophore (see Fig. 2C,D and
Table 1). The four anchor
points for this curve at which the spline quadrants meet are defined as
follows (each is indicated by a small circle): the posterior anchor point is
the intersection of the line of widest extent with the mid-sagittal
odontophore outline; the anterior anchor point lies along the line of widest
extent, and its position is defined such that the width of the curve at the
prow seam is equal to the fixed maximum prow width (see
Table 1). The other two anchor
points are midway between the prow seam and the posterior anchor point in the
antero-posterior direction, and their medio-lateral position is iterated until
the correct odontophore volume is achieved. (C) Example of one of the closed
curves used in the construction of the odontophore mesh. The antero-posterior
intersections of the planes of these curves are illustrated in
Fig. 4C. Anchor points are
indicated using circles. The dorsal and ventral anchor points are defined by
the intersection of the plane of the curve with the mid-sagittal outline of
the odontophore (A). The medio-lateral anchor points are defined by the
intersection of the plane of the curve with a curve defining the medio-lateral
width (B). (D) The tip of the prow is indicated by a grey circle. See
Materials and methods for the algorithm that locates it along the anterior
margin of the prow. (E) The line of widest extent passes through the tip of
the prow. In the orientation shown, its angle is 44° counterclockwise from
the line connecting the top of the radular surface and the tip of the prow.
The top of the radular surface is defined in the reference frame in which the
line connecting the tip of the prow and the bottom of the prow seam is
vertical (represented by the vertical dashed line). (F) Construction of the
prow. Each line indicated here represents a side view of a closed curve
similar to that described in C. The portion of the curve above the line of
widest extent is parallel to the prow seam. The portion of the curve below the
line of widest extent is bent such that its antero-posterior position remains
at the same percentage of the distance between the anterior margin of the prow
and the prow seam as it had when it intersected the line of widest extent.
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Fig. 2. Extraction of spline parameters from three-dimensional reconstructions
based on high-spatial-resolution magnetic resonance imaging (MRI). (A)
Definition of spline parameters. The Bezier equations define the x
and y positions of the points along the curve with respect to a
parameter t, which ranges from 0 to 1 along the length of the curve
given the endpoints (x1,y1) and
(x4,y4), and the corresponding control
points (x2,y2) and
(x3,y3), which define the curve. In
our implementation, the endpoints lie on the perpendicular axes
(y1=x4=0) and the control points are
perpendicular to the endpoints (x2=x1
and y3=y4), forcing the tangents to
the curve at its endpoint to be perpendicular to the axes. As a consequence,
the Bezier equations for the curves become
x(t)=(2x1-3x3)t3+3(x3-x1)t2+x1
and
y(t)=(3y2-2y4)t3+(3y4-6y2)t2=3y2t.
The spline parameters given in Table
1 are y2/y4 and
x3/x1, given as fractions to make them
independent of scale. When the curve is actually constructed, the two
endpoints provide y4 and x1; once
these endpoints are given, all parameters for the curve are defined. See
Table 1 for spline parameter
values used in the model that define the lines illustrated in B-E. (B)
Extraction of ventral spline parameters. A three-dimensional reconstruction of
the odontophore as viewed through the jaws (i.e. with the prow seam vertical)
is shown. The spline curve is shown as a dark line at the lower right. Only
one side is shown here and in C-E since the structure is bilaterally
symmetrical. The white spots at the base of the reconstruction and in the
anterior parts of C and D are due to cross sections of the I5 muscle. (C)
Extraction of anterior spline parameters. A three-dimensional reconstruction
of the odontophore as viewed from its ventral surface (i.e. with the prow seam
perpendicular to the plane of the figure) is shown. The spline curve is shown
as a dark line at the lower right. (D) Extraction of the posterior spline
parameters. Same view as C. The spline curve is shown as a dark line at the
upper right. (E) Extraction of dorsal spline parameters excluding the ridge
from a video recording of the front view of an isolated odontophore. Since the
ridge is not discernible in an anaesthetized buccal mass, these parameters
could not be extracted from the high-spatial-resolution MRI data. The spline
curve is shown as a dark line at the upper right.
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Fig. 4. Selecting curves that define the vertices of the odontophore mesh when the
line of widest extent does not pass through the anterior and posterior
extremes of the mid-sagittal cross section. In all parts of this figure, note
the cosinusoidal spacing of the curves to provide approximately uniform
coverage of the odontophore surface. (A) A mid-sigittal shape can be
extrapolated into a three-dimensional mesh using vertices that lie along
parallel curves and whose widths are defined by their intersection with a line
of widest extent, if the line of widest extent passes through the anterior and
posterior extremes of the mid-sagittal shape. (B) If the line of widest extent
does not pass through the anterior and posterior extremes, then parallel
curves whose widths are defined by their intersection with the line of widest
extent cannot encompass the entire volume. (C) This problem can be overcome by
angling the planes of the curves such that they are tangential to the
mid-sagittal shape at both ends of the line of widest extent.
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Fig. 7. Kinematics of the line of widest extent. (A) The line of widest extent is
measured on the moving isolated odontophore as the line of dark shadow
produced from a light source directly above the odontophore (shadow line). In
addition, the line joining the tip of the prow and the top of the radula is
measured (top line). The angles of the lines are measured relative to the line
of the pin, which is the line connecting the tip of the prow with the bottom
of the prow. (B) Comparison of the angle of the line of widest extent (shadow
line) with the line connecting the tip of the prow and the top of the radula
(top line) (measured in the side view). The two lines consistently differ by
44±5° (mean ± S.D., N=15). The left and right parts
show data measured from an isolated odontophore induced to perform movements
by application of dopamine or carbachol crystals (respectively) to the
cerebral ganglion. Event 1, rest, closed radula; event 2, widest radular
opening; event 3, immediately prior to radular closure; event 4, radular
closure; event 5, odontophore elongation; event 6, maximum elongation; event
7, elongation relaxed. (C) Averaged and normalized changes in angle of the
line connecting the top of the radula and the tip of the prow during four
in vivo swallows. The feeding cycle was normalized on the basis of
definitions of the components of the swallowing cycle from our previous work
(Drushel et al., 1997,
1998;
Neustadter et al., 2002). The
time intervals for this and all subsequent figures are defined as follows,
using the nomenclature adopted in our original papers for consistency:
t4, start of anterior buccal mass movement to peak protraction;
t1, peak protraction to peak retraction; t2, peak retraction
to the loss of the  shape, i.e. the shape in which the base of the
elongated radula/odontophore extends ventral to the long axis of the buccal
mass (see fig. 3A of
Drushel et al., 1997). Cycle
times are normalized to the sum of the times
t4+t1+t2. Lengths l were normalized to
100(l—lmin)/(lmax—lmin),
so that lengths range from 0 at lmin to 100 at
lmax. After normalization and averaging, the data were
smoothed using an interpolation function that fitted cubic polynomials between
successive data points. The average function is displayed as a solid line. A
function representing ± 1 S.D. was calculated from the individual
functions of the data and is displayed using dashed lines. The overall pattern
of angular changes is similar to that observed in vitro.
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Fig. 5. Measurement and construction of the ridge. (A) Simultaneous top, side,
front and oblique views are shown. Lines drawn on the different views indicate
the extent of the ridge in these different views. In the front view, the lower
line (yellow) indicates the spline curve defining the top of the odontophore
not including the ridge, and the upper line (green) indicates the protrusion
of the ridge above this curve. (B) A 100° arc of a circle whose radius is
1.23 radula stalk widths (RSW) (shown in grey) is a good fit to the radular
surface below the region where the ridge occurs and is superimposed on the
mid-sagittal outline of the odontophore extracted from the MRI to estimate the
extent of the ridge. This curve is drawn in yellow on the side view of the
radula in (A). The arc is continued posteriorly by a line tangential to the
posterior end of the arc. (C) Implementation of the ridge. See Materials and
methods for details.
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Fig. 9. Comparison of mid-sagittal magnetic resonance images (MRIs) (left) and
superimposed mid-sagittal outputs (right) from the model. The frames shown are
from sequence 7732-S3, frame 17 (A), sequence 7732-S3, frame 24 (B), and
sequence 7732-S3, frame 35 (C). The outline of the odontophore, the outline of
the radular stalk and the overall outline of the buccal mass were initially
extracted from the MRIs shown on the left. The dorsal and ventral cross
sections of the model I3 rings were placed by the model.
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Fig. 8. Kinematics of the ridge. (A) Plot of the antero-posterior length of the
ridge as seen in a top view versus the antero-posterior length of the
protrusion of the ridge above a circular arc fitted to the odontophore in a
side view (r2=0.84, P<0.002).
Fig. 5 shows one frame of these
data and how they were analyzed. Lengths are measured in radular stalk width
units (RSW). (B) Area of the ridge recorded in vitro during a
dopamine-induced series of movements. See
Fig. 7B for definitions of
events labelled on the x axis. Area is reported in units of
RSW2. (C) Area of the ridge recorded in vivo from
mid-sagittal frames (sequence 7732-S3, frames 16-39). Note the large ridge
area at the end of protraction and at the onset of retraction, which
corresponds to events 4 and 5 of the in vitro data, i.e. radular
closure and odontophore elongation.
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Fig. 12. Kinematics of the I2 muscle predicted by the model and compared with I2
lengths measured in the same magnetic resonance images (MRIs). Data in
A—D are plotted as length (mm) as a function of time (ms). Data from the
model are plotted using a black line; data measured from MRIs are plotted
using a grey line. Frame numbers for sequences and for the onset of t4,
t1 and t2 periods are given in Neustadter et al.
(2002) and in the legend to
Fig. 7. (A) I2 kinematics in
the first swallow. (B) I2 kinematics in the second swallow. (C) I2 kinematics
in the third swallow. (D) I2 kinematics in the fourth swallow. (E) Normalized,
averaged and smoothed I2 kinematics during a swallowing cycle. Values are
means ±1 S.D. (N=4).
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Fig. 10. Validation of the model using coronal sections. In each row, the sequence
of images is the interleaved coronal MRI, the coronal slice through the
three-dimensional model and the symmetric difference between them. In the
images showing the symmetric differences, white indicates areas that are in
both coronal images, whereas grey indicates areas that differ. (A) Transition;
sequence 7732-S3, frame 18. (B) Peak protraction; sequence 7732-S3, frame 24.
(C) Peak retraction; sequence 7732-S3, frame 36.
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Fig. 11. Three-dimensional reconstruction of the buccal mass during a swallowing
cycle. The I1/I3 muscles are shown as a continuous blue mesh, the odontophore
is shown as a continuous yellow mesh and the radular stalk is shown as a red
solid. Views are shown in orthographic projection. (A) Side views of
transition, protraction and retraction. Compare the mid-sagittal slices shown
in Fig. 9. (B) Top view of
transition, protraction and retraction. Compare the coronal slices shown in
Fig. 10. To generate these
views, the lateral groove (posteriormost edge of the I1/I3/jaw muscle complex)
has been rotated so that it is vertical. (C) Front view of transition,
protraction and retraction. The left, middle and right columns are based on
frames 17, 24 and 35, respectively, of sequence 7732-S3. Compare
fig. 9 of Drushel et al.
(2002), which shows a
three-dimensional reconstruction of a previous odontophore-centric model of
the buccal mass for sequence 7732-S3, frames 15 (left), 26 (middle) and 35
(right).
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Fig. 13. Kinematics of the antero-posterior lengths of the I3 muscle compared with
measurements in the same magnetic resonance images (MRIs). Data in A—D
are plotted as length (mm) as a function of time (ms). Data from the model are
plotted using a black line; data measured from the MRIs are plotted using a
grey line. On the left side are plots of the antero-posterior I3 length on the
dorsal side of the model. On the right side are plots of the antero-posterior
I3 length on the ventral side of the model. The match to the lengths on the
ventral surface is good but, in three out of the four swallows, the match to
the antero-posterior length of I3 on the dorsal surface is poor, especially
during late protraction and most of retraction. (A) I3 antero-posterior
kinematics in the first swallow. (B) I3 antero-posterior kinematics in the
second swallow. (C) I3 antero-posterior kinematics in the third swallow. (D)
I3 antero-posterior kinematics in the fourth swallow. (E) Normalized, averaged
and smoothed I3 antero-posterior kinematics during a swallowing cycle. Values
are means ±1 S.D. (N=4). At the protraction/retraction
transition and early in retraction (t4/t1 transition and early
t1), the model underestimates the length of the ventral surface
because of its inability to represent stretch of the ventral I3 muscle around
the prow.
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Fig. 14. Kinematics of the dorso-ventral lengths of the I3 muscle compared with
measurements in the same magnetic resonance images (MRIs). Data in A—D
are plotted as length (mm) as a function of time (ms). Data from the model are
plotted using a black line; data measured from the MRIs are plotted using a
grey line. On the left side are plots of the dorso-ventral I3 length at the
lateral groove. On the right side are plots of the dorso-ventral I3 length at
the jaws. The match between the model and measured data is excellent for all
four swallows throughout the swallowing cycle. (A) I3 dorso-ventral kinematics
in the first swallow. (B) I3 dorso-ventral kinematics in the second swallow.
(C) I3 dorso-ventral kinematics in the third swallow. (D) I3 dorso-ventral
kinematics in the fourth swallow. (E) Normalized, averaged and smoothed I3
dorso-ventral kinematics during a swallowing cycle. Values are means ±1
S.D. (N=4). Note the overall match in the right-hand and left-hand
plots between the average model data and the average MRI data. The model
overestimates the dorso-ventral length of I3 at the lateral groove during
protraction (t4 period, left).
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Fig. 15. Kinematics of the medio-lateral widths of the I3 muscle compared with
measurements in a transilluminated juvenile Aplysia californica.
(A—D) Widths of the continuous mesh representing the I3 muscle at six
evenly spaced locations along its antero-posterior length for the first to the
fourth swallows; (E—G) widths of the I3 muscle measured at six evenly
spaced locations along its antero-posterior length from dorsal views of
transilluminated juveniles in three successive swallows, as described in the
legend to fig. 6A in Drushel et
al. (2002). Data in E—G
are smoothed using a moving average over three successive data points and are
plotted as length (mm) as a function of time (ms). The top trace in each set
of six traces is the medio-lateral width of I3 at the lateral groove, whereas
the bottom trace in each set corresponds to the medio-lateral width of I3 at
the jaws. Variability from swallow to swallow is evident both in the traces
generated by the model and in the measurements from the transilluminated
juvenile animal.
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Fig. 17. Kinematics of the medio-lateral half-width of the odontophore estimated
from the model. Data are plotted as width (mm) as a function of time (ms).
Half the width of the odontophore is plotted, since this provides an estimate
of the width of one of the paired I4 muscles, which constitute most of the
width of the odontophore. (A) Medio-lateral half-width in the first swallow.
(B) Medio-lateral half-width in the second swallow. (C) Medio-lateral
half-width in the third swallow. (D) Medio-lateral half-width in the fourth
swallow. (E) Normalized, averaged and smoothed medio-lateral odontophore
half-width during a swallowing cycle. Values are means ±1 S.D.
(N=4).
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Fig. 16. Kinematics of the I7 muscle estimated from the model. Data are plotted as
length (mm) as a function of time (ms). (A) I7 length in the first swallow.
(B) I7 length in the second swallow. (C) I7 length in the third swallow. (D)
I7 length in the fourth swallow. (E) Normalized, averaged and smoothed I7
length during a swallowing cycle. Values are means ±1 S.D.
(N=4).
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Fig. 20. Schematic representation of neural and muscular activations during a single
swallowing cycle. Images of extracellular recordings from nerve and muscle in
intact, behaving animals were scanned from several different sources.
Simultaneous recording from buccal nerve 2 (BN2) and the radular nerve (RN)
were taken from Morton and Chiel
(1993a). Simultaneous
recordings from BN1, BN2 and BN3 were taken from unpublished observations of
D. W. Morton and H. J. Chiel. Simultaneous recordings from muscle I2 and from
BN2 were taken from Hurwitz et al.
(1996). Extracellular
recordings from muscle I5 (ARC) were taken from Cropper et al.
(1990b) and were aligned with
simultaneous recordings taken from I5, BN2 and RN during in vitro
ingestive patterns (D. W. Morton and H. J. Chiel, unpublished data).
Recordings from I10 (representative of activity in I7, I8, I9 and I10; thus,
the schematic is labeled I7 in the figure) were taken from Evans et al.
(1996). The lengths of the
scanned recordings were scaled relative to one another using the duration of
the inward movement of seaweed, the duration of the burst on BN2 or the total
duration of the cycle (onset of I2 activity to end of BN2 burst), depending on
which features were common between the data sets. The data sets were then
aligned by the onset of the inward movement of seaweed. Boxes were then drawn
around the resulting extracellular recordings, providing a schematic
representation of the relative sizes of the extracellular units and their
timing relative to one another.
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© The Company of Biologists Ltd 2002
