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Radula-centric and odontophore-centric kinematic models of swallowing in Aplysia californica
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.
Author for correspondence at address 1 (e-mail:
hjc{at}po.cwru.edu
)
Accepted 10 April 2002
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Summary |
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 TOP Summary IntroductionMaterials and methodsResultsDiscussionReferences |
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Key words: kinematic model, buccal mass, Aplysia californica, swallowing, magnetic resonance imaging
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Introduction |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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). Unlike
human-engineered devices, which are designed to be functionally decomposable
(for ease of both maintenance and integration with existing devices), animals
have complex, multi-functional components. The same anatomical parts of an
animal may be used in completely different ways, depending upon circumstances.
Experimental observations of neural function may not be interpretable unless
considered in conjunction with the properties of the body being controlled,
and the converse is equally true.
Feeding behavior, which includes both appetitive and consummatory
components under the control of motivational variables, requires a continuous
interaction between the nervous system and the periphery during its execution
and is therefore well-suited for the study of the interplay between neural
control and the periphery. The feeding cycle of the marine mollusc Aplysia
californica is one of several tractable model systems. The buccal mass of
A. californica has a basic repertoire of movements that can be
combined in several ways to create distinct behaviors at the organismal level,
depending upon sensory feedback. The tongue-like radula/odontophore is capable
of anterior and posterior movement (protraction and retraction) as well as
opening and closure of the radular halves. These movements are caused by
contractions of various muscles within the buccal mass. The relative timing
between the protraction/retraction and opening/closure behaviors determines
whether attempts are made to grasp prospective food (biting), which is either
swallowed if edible or rejected if inedible or noxious
(Church and Lloyd, 1994;
Morton and Chiel, 1993a).
The buccal mass of A. californica undergoes characteristic shape
changes during the feeding cycle. In two-axis studies of transilluminated
juveniles in vivo, Drushel et al.
(1997) found that the buccal
mass could assume three distinct classes of shape (in lateral view), which
correlated with three distinct phases of the feeding cycle: round (peak
protraction), ovoid (neutral `rest' and transition) and 
-shaped (peak
retraction). The shapes, which are outlines of the entire buccal mass, allow
some inferences about the arrangement and function of internal structures. For
example, the vertical part of the peak-retraction shape contains the
protruding radular stalk cartilage (which must also be positioned vertically),
whereas the horizontal part is the closed I1/I3 muscle and jaw cartilage
complex. Viewed dorsally, the buccal mass at peak retraction is elongated
antero-posteriorly and narrow medio-laterally. In contrast, the round
peak-protraction shape represents the radula/odontophore protruding into the
I1/I3 halves, and the radular stalk, deep inside the buccal mass, does not
extend beyond the smooth outline formed by the I1/I3, I4 and I2 muscles.
Viewed dorsally, the buccal mass at peak protraction is foreshortened
antero-posteriorly and much wider medio-laterally. These kinematics suggest
that medio-lateral contraction of the I1/I3 muscle could squeeze the
radula/odontophore posteriorly, causing retraction and possibly assisting with
radular closure.
Kinematic modeling may be used to test more elaborate hypotheses about
muscle functions in the A. californica buccal mass, especially for
internal muscles that cannot be observed in transilluminated animals or in
in vitro preparations without dissection (which disrupts potentially
critical interconnections between muscles). In a kinematic model, anatomical
structures are represented as separate objects that are connected, move and
change shape/dimensions according to anatomical rules; no forces (kinetics)
are involved. Qualitatively good results could be achieved by representing the
radula/odontophore as a fixed-diameter sphere that could be rotated and
translated anteriorly and posteriorly through a stack of six tori
(representing the I1/I3 muscle), the sphere being attached ventrally to the
first torus in the stack, and the tori each remaining isovolumetric during
deformation (Drushel et al.,
1998). These approximations allowed the model to be completely
analytical and to run rapidly on contemporary computers. The overall buccal
mass shapes generated by a spherical radula/odontophore, however, proved
quantitatively inaccurate (especially for peak retraction) compared with data
from transilluminated juveniles (Drushel et
al., 1997), so a revised, non-analytical model was developed that
used in-vitro-derived volumetric databases to represent the
radula/odontophore at different points in the feeding cycle
(Drushel et al., 1998). No
single fixed radula/odontophore shape was suitable through an entire feeding
cycle (approximately 110 ° of rotation), but fixed shapes worked in that
part of the feeding cycle from which they had been derived (e.g. the
peakretraction shape was good in the retraction part of the cycle, but failed
in the protraction part). Even though the second model was successful only in
portions of the feeding cycle and took much longer to run, it allowed
predictions of the lengths of the I1/I3 and I2 muscles and suggested periods
of activation for the muscles that were consistent with existing neural and
electromyographic recordings.
These results suggest that an accurate, three-dimensional kinematic model
of the radula/odontophore, capable of smooth transformations between the
round, ovoid and shapes, might be developed that could then be
inserted into the existing kinematic model of the buccal mass. Detailed
three-dimensional kinematic analyses of the radula/odontophore in
vivo and in vitro are necessary to provide the necessary input
parameters and constraints for such a model (Neustadter et al.,
2002a,b).
Since the radula/odontophore shape is critical for the overall shape of the
buccal mass model, the same qualitative and quantitative constraints used
previously will serve to validate the new model — if the modeled
radula/odontophore yields an inaccurate buccal mass shape (in all three
dimensions), there is likely to be some flaw in the modeled
radula/odontophore. In addition, the new radula/odontophore model can have its
own anatomically derived internal structure, which allows predictions to be
made about the shape and position of the component parts and leads to new
hypotheses about their functions during the feeding cycle.
Kinematic modeling is an iterative process, and failure is as informative
as success. The present paper describes a sequence of kinematic models, each
of which represents some improvement upon its predecessor, each developed in
response to specific predictions that were tested experimentally or against
higher-resolution data. The first model of the radula/odontophore is
radula-centric (where the radula and other internal components directly
specify the overall shape) and the second is odontophore-centric (where the
radula/odontophore is modeled as a closed surface `skin' and internal
components are constrained to be inside). Both models make use of magnetic
resonance (MR) imaging data from isolated buccal masses (high spatial
resolution) and feeding animals (real-time, high temporal resolution;
Neustadter et al., 2002a). Our
ultimate goal is a complete description of the interplay between neural
control and peripheral biomechanics in the feeding behavior of A.
californica.
The kinematic models and analyses presented here rely heavily upon prior
published work from our laboratory (Drushel et al.,
1997,
1998). Since both magnetic
resonance imaging (MRI) data and kinematic modeling methods are novel to the
field of molluscan feeding, we have chosen to present many details to give the
reader ample means to evaluate our results critically. We recognize that a
long paper is the result.
As adjuncts to the text, we provide digital movies of swallowing in A.
californica (in QuickTime format), three of the radula-centric model and
three of the odontophore-centric model: the movie entitled `116-133.mov' shows
the midsagittal MRI sequence 5385-S1/116-133. The movies entitled `RC-AP.mov',
`RC-DV.mov' and `RC-LM.mov' show three-dimensional renderings of the
radula-centric model from antero-posterior, dorso-ventral and latero-medial
viewpoints, respectively, which are composites based upon MR sequences such as
those shown in `116-133.mov'. These three movies are rendered in a perspective
view. The movies entitled `OC-DV.mov', `OC-LM.mov' and `OC-OB.mov' show
three-dimensional renderings of the odontophore-centric model from
dorso-ventral, latero-medial and oblique viewpoints, respectively, to match
the MR images in `116-133.mov'. These three movies are rendered in
orthographic projection. Further technical details are given in the first
frame of each movie. Movies of the radula-centric and odontophore-centric
models are not the final kinematic models discussed in the text, but are
qualitatively similar. They were created for preliminary presentations of this
work that have appeared in abstract form
(Chiel et al., 1999;
Sutton et al., 2000).
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Materials and methods |
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Animals and anatomical methods
Adult Aplysia californica Cooper were obtained from Marinus (Long
Beach, California, USA) and maintained in tanks of aerated artificial sea
water at 16 °C. Animals used for anatomical studies were anesthetized by
injection of isotonic aqueous MgCl2 (333 mmol l-1) into
the hemocoel. Buccal masses were dissected out and either studied immediately
or fixed overnight in 10% (v/v) formalin in Aplysia saline, pH
7.5.
Feeding cycle landmark timing nomenclature
Feeding cycle landmark timing intervals are used as defined for
transilluminated juvenile A. californica in
(Drushel et al., 1997):
t1 (peak protraction to peak retraction), t2 (peak
retraction to loss of shape), t3 (loss of shape to
start of anterior buccal mass movement) and t4 (start of anterior
buccal mass movement to peak protraction). In the present work, however, we
have chosen to begin the feeding cycle with t4 rather than
t1. Mid-sagittal MR images allow the precise onset of protraction to
be observed because the radula/odontophore is directly visible (unlike in
transilluminated juveniles, in which peak protraction and retraction were the
most unambiguous landmarks), and studies have shown that all feeding responses
in A. californica are initiated with protraction
(Hurwitz et al., 1996). In
addition, beginning at t4 allows the most variable interval,
t3 (which probably corresponds to the inter-swallow interval), to be
placed at the end of the feeding cycle (see Table 1 of
Drushel et al., 1997). For
consistency with published work, we retain the t1-t4 nomenclature
without renumbering.
MRI data acquisition and analysis
A novel real-time MRI interface, imaging tank and coil and continuous
feeding apparatus were developed to visualize swallowing behavior in adult
A. californica (Neustadter et
al., 2002a). Briefly, an Elscint 2T Prestige whole-body MRI system
was used to acquire high-temporal-resolution MR images (250 ms or 310 ms per
frame) with an acquisition matrix of 64x128 voxels (each voxel 1.0
mmx1.0 mmx3.0 mm). The primary aim was to study the mid-sagittal
plane, since many movements and rotations of the buccal mass and
radula/odontophore (e.g. protraction and retraction) are confined to this
plane. To allow animals to feed continuously with a minimum of body movement,
two different types of feeding stimulus were used: (i) polyethylene tubes,
1.27 mm outside diameter, 0.86 mm inside diameter, after stimulation of the
lips with aqueous seaweed extract; and (ii) seaweed-flavored spaghetti noodles
wound on a spool in the imaging tank. Orthogonal images in the axial and
coronal planes were used to verify that the animals were correctly oriented
for mid-sagittal imaging (i.e. were not twisted or skewed out of the imaging
plane).
One anesthetized buccal mass was imaged at high spatial resolution (each voxel 0.3 mmx0.3 mmx1.0 mm, total acquisition time 96 s per slice) for anatomical studies. These images were used to establish a consistent set of dimensions (and volumes) for structures to be modeled.
Grayscale TIFF images of MRI frames were assembled into digital movies in QuickTime format (Apple Computer). Measurements and other observations were made directly from the movie frames. The ability to switch rapidly back and forth between adjacent frames is crucial for detecting subtle movements of internal structures. Canvas 3.5.3 (Deneba Software) was used to determine the coordinates of extrema and control points in MR images used for the odontophorecentric model.
Buccal mass kinematic model
A slightly revised version of the second (non-analytical) kinematic model
described in Drushel et al.
(1998) was used. Briefly, the
model consists of a three-dimensional representation of the
radula/odontophore, which is rotated anteriorly and posteriorly through a
stack of roughly concentric rings that represent the I1/I3 muscle complex.
Each ring changes its dimensions isovolumetrically to conform to the shape of
the underlying radula/odontophore shape, with the added constraint that ring
closure occurs medio-laterally (to model the effect of the jaw cartilages).
The radula/odontophore is joined to the ventral first I1/I3 muscle ring at a
`hinge'; it is about this point that radula/odontophore rotation takes place.
The I2 muscle is represented as a thin band wrapping around the posterior end
of the radula/odontophore and connecting the dorsal and ventral portions of
the first I1/I3 muscle ring.
Radula/odontophore shapes generated by the radula/odontophore models (see below) were converted to the volumetric database format required by the buccal mass model. The buccal mass model was modified to run a sequence of multiple volumetric databases at one rotation step each (the 1998 version of the model rotated a single volumetric database through multiple steps). The ability to specify individual I1/I3 ring parameters was also added (the published model made each ring a fixed-scaled reduction of the previous ring). The core functionality of the model, however, is unchanged from the 1998 version. The model computes the length of the I2 muscle and the dimensions of the individual I1/I3 rings.
The model was implemented in Microsoft QuickBASIC 4.5 for MS-DOS with SVGA graphics and extended memory libraries (Zephyr Software) When run on a Pentium III/450 MHz computer in a full-screen MS-DOS session (under Microsoft Windows 98), each rotational step of the model took approximately 3 min. The source code is available from the authors upon request.
POV-Ray 3.1 for Windows (The Persistence of Vision Development Team) was used to create ray-traced three-dimensional images of model outputs. Several utility programs were written in QuickBASIC to convert model outputs into POV-Ray-compatible format.
Radula/odontophore modeling strategies
We considered two approaches for designing a kinematic model of the
radula/odontophore: inside-out versus outside-in. An inside-out model
specifies the desired internal components, defines rules for their
attachments, movements and dimensional changes and then stretches a `skin'
over them to create a closed three-dimensional volume. An outside-in model
uses rules derived from available biological data to specify a closed
three-dimensional volume in its entirety; desired internal components are then
constrained to fit inside this volume. In both cases, the final object is
converted into the volumetric database format required by the buccal mass
kinematic model, at the appropriate scale.
Radula-centric model
As a first step towards a detailed kinematic model of the
radula/odontophore, we hypothesized that radular movements were the chief
determinant of overall radula/odontophore shape. An inside-out model was
designed around two radular halves that would be capable of opening and
closure; hereafter, this is termed the radula-centric model
(Fig. 1). The model consists of
two radular halves, a radular stalk and two I7 muscles. Analytical functions
are used to model all objects for fast computation.
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The curved dorsal surface of each radular half is modeled using quadrants
of ellipses and segments of parabolas, and a small portion of the flat inner
cleft surface was included (Fig.
1A-C). The radular halves are attached anteriorly and can open and
close by a combination of yaw (opening in the horizontal plane,
y) and roll (rotating inwards or outwards upon their long
axis, r). The radular halves can also pitch up and down
(p) in the mid-sagittal plane; the pivot point is above the
top of the radular stalk. (Empty space was left to allow for unmodeled soft
tissues.) These motions were decided upon after extensive manipulation of
dissected radula/odontophores from anesthetized buccal masses. The radular
halves are treated as rigid bodies and do not change any of their dimensions
as they move.
The radular stalk itself is a cylinder that is flat dorsally and has a rounded ventral dome (Fig. 1A). It is represented as a rigid body of fixed dimensions.
The I7 muscles are two cylinders, each parasagittal, whose long axes extend antero-dorsally from a point on the anteroventral radular stalk to a fixed point in space that represents the I7 muscles' attachment to the radular surface. This is the skirtlike portion of the radular surface that extends ventrally from the point at which the radular cleft begins. The position of the point is computed as a fixed arc length of an ellipse connecting the anterior tip of the radula and the ventral dome of the radular stalk. As the radular halves pitch, yaw or roll, the I7 endpoints change (Fig. 1C, arrowhead). The actual I7 cylinders stop slightly short of the endpoints in an attempt to avoid overlapping of the muscle objects with their attachments at shallow angles of attachment. The radius of the I7 cylinders is adjusted such that the volume of each cylinder remains constant. The antero-ventral attachment of the I7 muscles is used as the hinge point for the buccal mass model; this is where the radula/odontophore is attached to the ventral part of the first I1/I3 ring.
The dimensions of all objects were chosen to match a scale clay model of the radula/odontophore, which had been constructed for reference on the basis of several dissections of unfixed buccal masses. This model was presumed to represent a `rest' state. The overall validity of the clay model was confirmed by subsequent high-spatial-resolution MR imaging of anesthetized buccal masses in vitro. Values and timing for the radular stalk and pitch angles (Fig. 1E,F) were determined from a study of real-time MR image sequences taken from swallowing animals. Values and timing for the radular yaw and roll angles (Fig. 1G) were estimated from color VHS videotaped sequences of biting in adult animals (30 frames s-1) and from coronal and axial MR images.
The model was implemented in QuickBASIC and run in the computer environment described above. An interactive program was used to set the pitch, yaw and roll angles of the radular halves, one frame at a time. The objects could be rotated freely about any axis in real time for inspection. When each frame was complete, it was exported as a volumetric database by slicing through it in the axial plane (perpendicular to the antero-posterior axis). An elliptical skin was stretched over the objects in each slice (in two ventral quadrants), to fill in the empty spaces (presumably the I4, I5 and I6 muscles) and create a solid object, as each slice was exported (Fig. 1D). The length and radius of the I7 muscle were computed by the model. Not counting time to enter the parameters, the generation of each frame's volumetric database took approximately 5 min.
Odontophore-centric model
Even if radular movements are the primary determinant of overall
radula/odontophore shape, it is possible that specific shapes may arise from
interactions between multiple internal structures, including some not
represented in the radula-centric model. To test this hypothesis, an
outside-in model was designed to specify an entire radula/odontophore object
whose volume would be kept constant during dimensional changes; hereafter,
this is termed the odontophore-centric model
(Fig. 2). A radular stalk and
two I7 muscles are positioned inside this volume at defined connection points.
For fast computation, analytical functions are used to model the
radula/odontophore and the I7 muscles. The radular stalk has a realistic but
fixed shape derived from high-spatial-resolution MR images of an anesthetized
buccal mass.
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The radula/odontophore is constructed in octants, each bounded in three
planes by superellipse curves. The superellipse function, given parametrically
as:
 | (1) |
 | (2) |
2
and
0n
, can generate curves of varying convexity or
concavity, roundness or flatness depending upon the value of the n
parameter (Fig. 2A). Parameters
a and b are equivalent to the major and minor axes,
respectively, of a standard ellipse. A mid-sagittal MR image is used to
constrain four superellipse curves to best represent the outline of the
radula/odontophore in that image (Fig.
2B). The coordinates of the anterior, posterior, dorsal and
ventral extrema are selected manually; these determine the superellipse
quadrant boundaries. The ventral extremum was defined to be the same as the
ventral vertex of the radular stalk; this provided a place of attachment for
the stalk. Four additional surface points per quadrant are chosen manually to
control the curvature. The `best' value of the n parameter is then
determined for each quadrant using an algorithm that minimizes the sum of
distances of closest approach of the superellipse curve to the control
points.
Because the radula/odontophore consists of symmetrical right and left
halves, only four more out-of-plane superellipse curves are needed to create a
complete three-dimensional shape, as well as the maximum medio-lateral width
for the radula/odontophore (Fig.
2D,E). The default value n=1.0 (ellipse) is used for the
four out-of-plane curves because there are no real-time MRI data available in
the third dimension to suggest any different value. (Note that
high-spatial-resolution MRI data are available for anesthetized buccal masses,
but qualitative examination of their odontophores indicated that their shapes
could be characterized by values of n that did not differ
significantly from 1.0.) All radula/odontophores are assumed to be globally
convex shapes (0n2) to simplify volume computations (see
below).
We hypothesize that, because it is constructed mainly of water-containing
muscle and cartilage, the radula/odontophore is a muscular hydrostat
(Kier and Smith, 1985); hence,
the radula/odontophore model must be isovolumetric with dimensional changes
over time. For any MRI-constrained model frame, the medio-lateral width is the
free parameter that is varied until the volume is equal to some predetermined
constant. This standard volume is determined from the high-spatial-resolution
MR images of anesthetized buccal masses and scaled between different animals
using the height of the radular stalk. Total volume is computed by decomposing
the model (which is created as a mesh of surface triangles) into tetrahedra,
using the centroid of the model as one vertex and the vertices of each surface
triangle to define each tetrahedron, and summing the volumes of each
tetrahedron (calculated by analytical formula;
Bronshtein and Semendyayev,
1985). This method is valid only if the radula/odontophore model
is globally convex; this is guaranteed by appropriate choice of the n
superellipse parameter.
Note that radular opening and closure are not explicitly represented by this model because there are no anatomical structures present to simulate it. This does not present a difficulty to the buccal mass model (which is affected only by the maximum width), but if the actual cleft created during radular opening in vivo is large, then the odontophore-centric radula/odontophore model may not become physiologically wide enough (for example, during the protraction phase of swallowing) because the radula/odontophore is modeled as a globally convex solid and where the cleft ought to be will be `filled in' by the volume calculator.
The radular stalk model is a mesh of surface triangles created from the smoothed, stacked outlines of the radular stalk as seen in adjacent horizontal sections of high-spatial-resolution MR images of an anesthetized buccal mass. The height of the radular stalk is used as a scale bar between different animals. The radular stalk is positioned inside the radula/odontophore such that the ventral vertex of the stalk (i.e. the dome) is connected to the ventral vertex of the radula/odontophore (Fig. 2C). It does not change size or shape during the model feeding cycle.
The I7 muscles are two parasagittal cylinders (as in the radula-centric model) with conical end-caps, the tips being the attachment points. This was an attempt to model the elastic tissue at the attachment points and to avoid problems observed in the radula-centric formulation (see Results). The I7 muscles extend antero-dorsally from an anatomically defined point on the antero-ventral radular stalk to a defined endpoint on the dorsal radula/odontophore surface. This endpoint is selected from each mid-sagittal MRI frame by drawing a line from the ventral I7 attachment point along the trajectory of the muscle, through its actual insertion on the inner (posterior) surface of the I6 muscle and outwards to the radula/odontophore surface (Fig. 2B). Since this model is outside-in, the model does not represent the thickness of the I6 muscle, so it uses the corresponding radula/odontophore surface point (which is usually close to the anterior tip of the radula) as an approximation. A fixed-arc-length approximation similar to that used in the radula-centric model was tested but was too inaccurate in both length and trajectory (data not shown). As the endpoints of I7 change, the radius is changed to maintain a constant volume (cylinder + both end caps).
The dimensions of all objects were chosen with reference to the static and real-time MR images, then scaled through the radular stalk height to facilitate comparison with the radulacentric model output.
The model was implemented in QuickBASIC and run in the computer environment described above. The interactive features of the radula-centric model program were retained, but an unattended batch-processing mode was added. The length and radius of the I7 muscle and the maximum medio-lateral width of the radula/odontophore were computed by the model. The generation time for each frame's volumetric database was approximately 10 min.
Validation of model output
Shape space analysis
By approximating the mid-sagittal outline of the buccal mass as four
ellipse quadrants and defining the shape parameters ellipticity (how
elliptical or circular a shape is) and eccentricity (how skewed or symmetrical
a shape is), it was possible to quantify the shape changes observed in the
buccal mass during the feeding cycle in transilluminated juveniles
(Drushel et al., 1997). Plots
of eccentricity versus ellipticity form a two-dimensional shape space
through which the buccal mass travels during the feeding cycle
(Fig. 3). This analysis was
subsequently used to evaluate the performance of two kinematic models of
swallowing (Drushel et al.,
1998). In the present study, shape space analysis was performed
upon mid-sagittal MR images and upon model output frames, with the presumption
that successful models would accurately reproduce the shape space plots of the
MRI swallowing sequences upon which they were based. Manual tracings were made
of the outlines of the buccal mass (MRI or modeled), converted to grayscale
TIFF images of solid black shapes and median-filtered with a radius of 15
pixels using Adobe Photoshop (versions 4.0-5.5, Adobe Systems), and the
ellipticity and eccentricity parameters were then determined by a computer
analysis program.
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Measurements from dorso-ventral views of transilluminated
juveniles
Dorso-ventral views of swallowing in transilluminated juveniles, originally
obtained to ensure that medio-lateral views were parallax-free
(Drushel et al., 1997),
contained important information about the change in medio-lateral width of the
buccal mass during the feeding cycle, including changes in the width of the
I1/I3 muscle complex. The length and width changes of I1/I3 were measured in
three consecutive transilluminated swallowing sequences
(Fig. 4). Because of
uncertainty in determining the lateral borders of I1/I3, three of us (G.P.S.,
E.V.M. and B.W.A.) independently performed the width measurements, and all
three data sets were averaged. For purposes of comparison with buccal mass
models, in which the I1/I3 muscle complex is represented as discrete rings,
the I1/I3 region in vivo was divided into six segments of equal
antero-posterior thickness, and the medio-lateral width of each of these
`rings' was measured. This method provided more spatial detail about the
in vivo shape changes and did not assume, for example, that there is
a linear change in width from anterior to posterior. The medio-lateral changes
in modeled I1/I3 rings were compared with these in vivo data.
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Results |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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Comparison of transilluminated and MR images
The in vivo kinematics of the buccal mass during swallowing in
A. californica was first described in juveniles using the
non-invasive technique of transillumination
(Drushel et al., 1997). The
outline of the transilluminated buccal mass constrains the position of
internal structures, but the exact positions and shapes of the internal
structures can be deduced only at some points in the feeding cycle (e.g. the
radular stalk at peak retraction). High-temporal-resolution mid-sagittal MRI
of swallowing in adults is non-invasive and can show not only the buccal mass
outline but also the exact positions and shapes of structures inside the
buccal mass. This yields more accurate parameters for kinematic models of the
radula/odontophore and enables comparison of buccal mass kinematics in adults
and juveniles in vivo.
Buccal mass shapes
The outer shapes of the buccal mass are very similar between mid-sagittal
MR images of adults and latero-medial transilluminated juveniles
(Fig. 5). The distinctive ovoid
(shape 2, transition/rest), round (shape 1, peak protraction) and
(shape 3, peak retraction) shapes, first described in transilluminated
juveniles (Drushel et al.,
1997), are also observed in the MR images. Outlines must be drawn
with caution, however, because some internal structures that are opaque to
transillumination (thus casting a dark shadow) are not distinct from the
`background' gray color in the MR images
(Fig. 5D, dotted lines around
elastic mouth tissue) or may appear white (indicating a high water content,
e.g. the cartilaginous radular stalk). Shape space plots of buccal mass
outlines from MR images may be different from those determined previously from
transilluminated images simply as a result of the omission or inclusion of
such differentially visible structures. In general, shape space analysis shows
peak protraction (Fig. 3C,
frame 3) to have greater ellipticity than transition/rest (frames 1 and 11)
and peak retraction (frame 8) to have greater eccentricity than
transition/rest or peak protraction, similar to transilluminated juveniles
(compare Fig. 3C, which shows
shape space analyses of transilluminated data, and Figs
8A,
10B,
12B, which show shape space
analyses of MR data; see Fig.
3C for mathematical definitions of ellipticity and eccentricity
parameters). As in the shape space plots of individual swallows from
transilluminated juveniles (but not in the mean normalized swallow plot shown
in Fig. 3C; see
Fig. 7 of
Drushel et al., 1997), MRI
shape space plots show some hysteresis: the path taken through shape space
from peak protraction back to rest is not the same as the path from rest to
peak protraction (see especially Fig.
10B).
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Internal structures
Mid-sagittal, high-temporal-resolution MR images of the buccal mass of
adult A. californica during swallowing reveal significantly more
internal anatomical details than corresponding latero-medial views of
transilluminated juveniles (Fig.
5; Neustadter et al., 2002). The position, orientation and shape
of the radula/odontophore within the buccal mass are clearly visible, as are
the dorsal and ventral endpoints of the I1/I3 muscle (which establish the line
of the lateral groove). The internal structure of the radula/odontophore can
also be seen: the radular stalk, radular surface and 16 muscles are clearly
differentiated. The mid-sagittal outline of the radula/odontophore itself
changes shape during the feeding cycle. Qualitatively, during the progress
from rest to peak protraction to peak retraction, the radula/odontophore
outline changes from oval to round to rectangular. Such changes could only be
inferred from the transilluminated buccal mass outlines.
I1/I3 muscle kinematics in transilluminated juveniles
The I1/I3 muscle complex changes shape as the radula/odontophore moves
through it. These shape changes may be both passive (due to forces exerted by
the radula/odontophore) and active (due to I1/I3 muscle contraction). A
kinematic model cannot make any assumptions about the passive or active nature
of the shape changes because no forces are represented. The buccal mass model
used here assumes that the I1/I3 muscle is at rest unless it is being
stretched by the presence of the radula/odontophore within its lumen. Thus,
characterization of the actual I1/I3 muscle dimensions during swallowing
in vivo provides important data with which to validate the
performance of kinematic models of the radula/odontophore and the buccal
mass.
The antero-posterior length of the dorsal I1/I3 muscle complex changes
during the feeding cycle, as estimated from three consecutive swallows in a
transilluminated juvenile (Fig.
6A). The minimum length occurs at peak protraction (t4/t1
boundary), increasing to a maximum length at peak retraction (t1/t2
boundary), after which there is no apparent change in length until the start
of protraction (t3/t4 boundary). The maximum length is approximately
21% greater than the minimum length, which agrees well with the 17% length
change observed in a dopamine-treated buccal mass in vitro
(Drushel et al., 1998).
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The medio-lateral width of the I1/I3 muscle complex also changes during the
feeding cycle, and different regions change width at different rates,
depending upon position along the antero-posterior axis
(Fig. 6B). In the resting
buccal mass, the I1/I3 complex is widest at the lateral groove and narrows to
a minimum at the anterior end of the buccal mass. At all of six equally spaced
reference `rings' along the antero-posterior axis, I1/I3 reaches a maximum
width at peak protraction (t4/t1 boundary), and a minimum
approximately 0.1 s (normalized) after peak retraction (t1/t2
boundary), after which the widths increase to an intermediate level (during
t3). The width change during protraction (t4) is greatest in
the most anterior regions, with the sharpest increase approximately 0.2 s
(normalized) before peak protraction. For example, the width of ring 6
(anteriormost) increases by 0.6 mm (50%) during t4, whereas the width
of ring 1 (posteriormost) increases by only 0.3 mm (10%). This 2:1 expansion
ratio is also observed in high-temporal-resolution coronal sections of
MR-imaged swallowing in vivo (see
Fig. 9 of
Neustadter et al., 2002a).
During retraction (t1), the width of the more anterior regions
decreases more quickly than that of the more posterior regions. This is
consistent with the width changes expected by movement of the (relatively)
spherical radula/odontophore through the I1/I3 complex during protraction and
retraction.
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Radular pitch angle in MR-imaged adults
In nine normalized swallows in an MR-imaged adult, the pitch angle of the
radula (Fig. 1F) is constant
(0° is horizontal) during protraction (t4), decreases to a
minimum of approximately -70° (pitched up, towards the dorsal surface)
during retraction (t1) and then returns to the initial value during
transition (t3). This change in pitch angle is consistent with the
change in radula/odontophore shape from round at peak protraction to
rectangular at peak retraction and then back to oval during transition/rest
(Fig. 5D-F).
The concept of `radular pitch' as a rigid body rotation is specific to the radula-centric kinematic model. However, the anatomical landmarks used to measure the pitch angle (i.e. a line from the postero-dorsal radular stalk to the anteriormost tip of the radular surface) are visible in all mid-sagittal MR images. Thus, the kinematics of the pitch angle should be reproduced by any model containing a representation of those landmarks irrespective of whether the pitch angle is a formal input. A smoothed version of Fig. 1F was used as an input for the radula-centric kinematic model.
Radula stalk rotation in MR-imaged adults
The rotation of the radular stalk (after removal of buccal mass rotation,
buccal mass angle 0°) was measured in several different swallow sequences
from mid-sagittal MR images of three different adults. In four normalized
polyethylene tube swallows, the angle of the radular stalk
(Fig. 1E) increases from 0°
at rest to a maximum of approximately +90° midway through retraction
(t1), falling to a plateau of 0° by the start of transition
(t2/t3 boundary). In another polyethylene tube swallow (MRI sequence
7732-S3/15-38, see Fig. 10A),
beginning from a rest position of -20° from vertical, the stalk rotates
anteriorly to +80° at peak protraction. In a seaweed noodle swallow (MRI
sequence 7725-S2/44-66, see Fig.
12A), beginning from a rest position of -10° (tilted
posteriorly from vertical), the stalk rotates anteriorly during protraction
(t4) and continues to reach a maximum of +90° during
mid-retraction (t1) before rotating posteriorly to the rest value at
the start of transition (t2/t3 boundary). The magnitudes of these
rotations are similar.
The shape of the stalk angle curves suggests that rotation and translation of the radula/odontophore are independent movements (Neustadter et al., 2002). In Fig. 1E (see also Fig. 12A), at the peak of protraction as determined by the movement of the entire buccal mass (t4/t1 boundary), the radular stalk has completed only two-thirds of its final anterior rotation; this rotation is not completed until the buccal mass (and indeed the radula/odontophore) is already translating posteriorly during retraction. Stalk rotation continues for another 15° in the anterior direction even as the buccal mass is retracting posteriorly. In Fig. 10A, however, the peak anterior rotation corresponds to the peak of protraction (as determined by buccal mass movements, not internal movements of the radula/odontophore).
Radula-centric kinematic model
The radula-centric kinematic model of the radula/odontophore generates a
range of continuous shapes by the roll, pitch and yaw of rigid-body radular
halves according to parameters extracted from high-temporal-resolution
mid-sagittal MR images of swallowing adults. The sequence of
radula/odontophore shapes, when inserted into the buccal mass model, generates
a continuous range of buccal mass shapes. Previous kinematic models of the
buccal mass used fixed radula/odontophore shapes throughout the feeding cycle
(Drushel et al., 1998). Model
performance is evaluated by comparison with all available kinematic data.
Three-dimensional views
The radula-centric kinematic model yields realistic three-dimensional
radula/odontophore shapes (Fig.
7) whose two-dimensional projections in lateral view resemble
those of both transilluminated juveniles and MR-imaged adults
(Fig. 5). Allowing for
unmodeled dorsal buccal cavity tissue, the model accurately reproduces the
ovoid, round and shapes of rest/transition, peak protraction and peak
retraction, respectively (Fig.
7A-C). The buccal mass shortens antero-posteriorly from rest to
peak protraction and lengthens to a maximum at peak retraction.
As the radula/odontophore is protracted into the I1/I3 muscle complex, the rings expand and conform to the shape of the odontophore. Viewed dorsally, the I1/I3 complex changes from trapezoidal (rest, Fig. 7D) to rectangular (peak protraction, Fig. 7E). As the radula/odontophore retracts, the I1/I3 complex becomes trapezoidal again (peak retraction, Fig. 7F) and is narrower medio-laterally than at rest. This is due to shape changes of the radula/odontophore: at rest (and for the first half of protraction), the radular halves are open (roll and yaw, Fig. 1G), and the location of the lateral groove and hinge is such that the posterior I1/I3 rings must stretch over the wide radula/odontophore. At peak retraction, the I1/I3 rings are completely closed upon themselves in the mid-sagittal plane (Fig. 7I). In addition, because the radular halves are rigid bodies whose basic shape was defined from a fully closed radula/odontophore, their opening creates a blunt shape to which the I1/I3 cannot conform without gaps (Fig. 7G). Even when closed, the radula/odontophore is too wide for the I1/I3 muscle model at peak protraction when the large dorsal surface of the radula/odontophore is rotated approximately 90° anteriorly into the jaws; additional gaps then appear between the I1/I3 rings (Fig. 7H).
While the endpoints of the I7 muscles are anatomically consistent with the placement of the radular halves and radular stalk (based upon MR images), the cylindrical representation in inaccurate because of the unmodeled volume at the endpoints. Maintaining an isovolumetric constraint only for the central portion of the I7 muscles makes them too thick at peak protraction (Fig. 7B). Finally, as a result of over-simplification of its shape, the radular stalk cylinder overlaps with the I7 muscles during model frames around peak retraction (Fig. 7C). (For simplicity, the radula-centric model does not attempt to make the I7 muscles conform to any underlying structures.)
Quantitative results
The shape space plot of the radula-centric model
(Fig. 8B) is a continuous
closed path that occupies the same region of shape space as the plots of
swallows in transilluminated juveniles
(Fig. 3C). It also has rough
similarities to that of MRI sequence 5385-S1/116-133, the swallowing sequence
upon which its I1/I3 placement parameters were based
(Fig. 8A). The radula-centric
model has a clear hysteresis loop from peak protraction to peak retraction
(frames 29-37), similar to the individual swallows in transilluminated
juveniles (Drushel et al.,
1997); however, the MRI shape space plot has no clear hysteresis.
The large positive ellipticity value (i.e. the shape is taller dorso-ventrally
than long antero-posteriorly) and small positive eccentricity (i.e. the shape
is skewed more posteriorly than anteriorly) for peak retraction in the MRI
data (frame 128, Fig. 8A) are
due to the presence of elastic jaw tissue, clearly different from the I1/I3
muscle, which was not included in the traced outline. Ring 5 of the modeled
I1/I3 muscle complex accounts for this non-I1/I3 tissue, shifting the entire
shape space plot to the left.
The lengths of the modeled I2, I7 and I1/I3 muscles show changes during the feeding cycle consistent with the movements of the radula/odontophore and buccal mass. The I2 muscle (Fig. 8C) shortens to 60% of rest length during protraction (t4) and lengthens to 158% of rest length during retraction (t1); the overall length change is approximately 270% of the minimum. The length of the I7 muscle (Fig. 8C) mostly follows the change in radular pitch angle (Fig. 1G): constant with a small decrease to 80% of rest length before the peak of protraction (t4/t1 boundary), then increasing to 320% of rest length until half-way through retraction (t1), and finally a return to the rest length during t2 and t3 (peak retraction through transition); the overall length change is approximately 400% of the minimum. The antero-posterior length of the I1/I3 muscle complex (Fig. 8D) decreases to 90% of rest length approximately two-thirds of the way through protraction (t4), then increases to 110% of rest length during retraction (t1); the overall length change is approximately 125% of the minimum.
The individual I1/I3 rings (Fig. 8E) change their mediolateral width to conform to the radula/odontophore shape as it is moved through them. The posterior rings (1 and 2) are wide at rest since they are close to the lateral groove and overlap the radula/odontophore, whereas the anterior rings (3-5) are closed and narrow. The anterior rings expand very sharply (frames 6-14) as the open, blunt-faced radula/odontophore protracts through them; the posterior rings actually shrink slightly as narrower stalk regions of the radula/odontophore are rotated anteriorly. A similar sharp decline in width is seen in all rings during mid-retraction (t1), at which point (frames 41-52) the radula/odontophore is completely posterior to all the rings and is undergoing internal movements that do not impinge upon the rings. During the transition period (t3), the radula/odontophore moves anteriorly to its rest position and the I1/I3 rings open to accommodate it. Ring 4 experiences the largest changes in medio-lateral width, approximately 285% of its minimum.
The radula-centric model of the radula/odontophore duplicates the overall shape changes of the buccal mass and relates radular opening and closure to radula/odontophore rotation within the buccal mass. The fact that rigid bodies are used to represent the radular halves, however, leads to sudden, non-physiological width changes in the modeled I1/I3 muscle complex. Radular opening and closure are likely to be more complicated than a set of rigid-body rotations. Unmodeled structures are likely to contribute significantly to the overall radula/odontophore shape. We thus turned to an odontophore-centric model in an attempt to construct radula/odontophores whose shapes were more explicitly constrained by the non-analytical shapes seen in high-temporal-resolution mid-sagittal MR images. Swallows of both polyethylene tubes and seaweed noodles were modeled because both methods of feeding seemed successful in limiting out-of-plane animal movements (necessary to obtain precise mid-sagittal images) while eliciting vigorous feeding responses.
Odontophore-centric kinematic model, MRI sequence 7732-S3/15-38
(polyethylene tube swallow)
Three-dimensional views
The odontophore-centric kinematic model was used to generate a
three-dimensional representation of a parallax-free MR-imaged swallowing
sequence, 7732-S3/15-38 (Fig.
9). This corresponds to swallow 3 of Neustadter et al. (2002). The
animal in this sequence was swallowing a polyethylene tube after arousal with
aqueous seaweed extract. Unlike the radula-centric model, no averaged or
composite data from multiple swallows were used, only measurements taken from
this particular sequence. Only four I1/I3 rings were needed to represent the
I1/I3 muscle complex (compared with five used for the radula-centric model).
The model radula/odontophore outlines are very similar to those observed in
the corresponding MR images (compare Fig.
9A-C and Fig.
9G-I). Unlike the radula-centric model, the rest and
peak-protraction radula/odontophore models are not excessively wide
medio-laterally (compare Fig.
7D,E and Fig.
9J,K). Furthermore, the mediolateral width of the overall buccal
mass is correctly widest at peak protraction
(Fig. 9K) in accord with
dorso-ventral video recordings from transilluminated juveniles
(Drushel et al., 1997). The
radula/odontophore is narrowest at peak retraction
(Fig. 9L). The shape
(Fig. 9I) is not as pronounced
as in the radula-centric model (Fig.
7C) because the 7732-S3/15-38 sequence has a weak retraction
(Fig. 9C; compare
Fig. 5F and
Fig. 11C) and the model run
attempts to reproduce the MR images as exactly as possible. Nonetheless, the
isovolumetric constraint upon shape changes causes the elongated
radula/odontophore of peak retraction to have a narrow medio-lateral width
(volume is redistributed dorsally and ventrally).
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The I1/I3 muscle complex is adequately represented during the first part of protraction (t4), the last part of retraction (t1) and the remainder of the feeding cycle through transition (t2 and t3). Around peak protraction, however, the model begins to turn itself inside out: the dorsal I1/I3 muscle rings are too far posterior, even though the ventral I1/I3 rings are correctly attached (Fig. 9H,K). This results in the radula/odontophore protruding through the anteriormost ring, as if it were a model of a full bite rather than a swallow. In the actual MR image, the radula/odontophore is clearly posterior to the opening of the jaws (Fig. 9B). The region corresponding to the modeled first I1/I3 ring seems to be stretched posteriorly at peak protraction (Fig. 9B, dotted line), leaving the region corresponding to the second ring in nearly the same position (relative to the opening of the jaws) that it occupied at rest (Fig. 9A). At peak retraction (Fig. 9C), the ventral I1/I3 region no longer appears to be stretched, and the actual I1/I3 muscles again correspond closely to the modeled rings. At no point, however, do any of the I1/I3 rings pull apart from each other as in the radula-centric model; the odontophore-centric radula/odontophore (by construction) lacks blunt, sharply flattened surfaces that would cause the rings suddenly to increase in medio-lateral width.
The I7 muscle changes length as its endpoints change on the surface of the radula/odontophore. Because the volume of the attachment points is explicitly represented (by cones), together with that of the cylindrical belly, the I7 muscle diameter changes are much less pronounced than in the radula-centric model representation (Fig. 9G-L). In addition, since the anterior endpoints are not attached to rolling or yawing radular halves (compare Fig. 1C), the I7 muscles always run parallel to the mid-sagittal plane. The anatomically correct radular stalk (reconstructed from high-spatial-resolution MR images of an anesthetized buccal mass) is narrower in diameter dorsally than ventrally, so that the modeled I7 muscle is able to (effectively) pitch posteriorly without colliding with the modeled stalk (compare Fig. 7C and Fig. 9I).
Quantitative results
The shape space plots of both the original MR-imaged swallow
(Fig. 10B) and the
odontophore-centric model (Fig.
10C) occupy a larger region of shape space than those of
transilluminated juveniles (Fig.
3C). In both plots, the points around peak protraction have large
positive ellipticity. In the case of the MR images, this is due to omission of
anterior elastic tissue from the buccal mass outline. The odontophorecentric
model plot, however, has even higher ellipticity because the I1/I3 muscle
rings are too far posterior (Fig.
9H) as a result of stretching of the ventral I1/I3 muscle area
seen in the MR images (Fig. 9B,
dotted line). The foreshortened I1/I3 ring stack also affects the eccentricity
parameter, causing the model buccal masses to be skewed anteriorly (negative
eccentricity, frames 19-22). Rest (frames 15 and 38) and peak retraction
(frame 35), however, are comparable between MR images and model
(Fig. 10B,C).
Odontophore-centric model representations of the I2, I7 and I1/I3 muscles
show length changes that are qualitatively similar to those in the
radula-centric model, but quantitatively less extreme. The I2 muscle
(Fig. 10D) decreases to 50% of
rest length during protraction (t4), then increases to 110% of rest
length by the peak of retraction (t1/t2 boundary), after which it
returns to the rest value; the overall length change is approximately 210% of
the minumum. After an initial increase of 50% from rest length, the I7 muscle
(Fig. 10D) remains at constant
length throughout protraction (t4). During retraction (t1),
I7 increases to 250% of rest length, reaching a maximum at peak retraction
(t1/t2 boundary), then returning to the rest value. The
antero-posterior length of the I1/I3 muscle complex
(Fig. 10E) decreases to 85% of
rest length during protraction (t4), then increases to 110% of rest
length during retraction (t1) and through the loss of the
shape (t2), and finally decreases to the rest length; the overall
length change is approximately 130% of the minimum. The I1/I3 muscle rings
change width more gradually than in the radula-centric model, but there are
still some rapid transitions (Fig.
10F; compare Fig.
8E). The posteriormost rings (1 and 2) open abruptly as the
radula/odontophore begins the anterior rotation of protraction (at rest, the
radula/odontophore is posterior to all four rings, so all are completely
closed), but the anterior rings (3 and 4) open more gradually. The rings close
rapidly in an antero-posterior wave during the second half of retraction
(t1). Ring 3 experiences the greatest length change, an approximately
210% increase from the minimum (rest) value.
Odontophore-centric kinematic model, MRI sequence 7725-S2/44-66
(seaweed noodle swallow)
Three-dimensional views
The odontophore-centric kinematic model was used to generate a
three-dimensional representation of a second parallax-free MR-imaged
swallowing sequence, 7725-S2/44-66 (
