|Caecilian jaw closing mechanics - integrating two muscle systems
Thomas Kleinteich (corresponding author)
Universität Hamburg, Biozentrum Grindel und Zoologisches Museum
20146 Hamburg, Germany
Phone: ++49 40 42838 2283
Fax: ++49 40 42838 3937
Universität Hamburg, Biozentrum Grindel und Zoologisches Museum
20146 Hamburg, Germany
Adam P. Summers
University of California Irvine
Irvine, CA 92697
Words (including list of references): 7567
7 figures - 5 color
Published in: Journal of the Royal Society Interface 5 (2008) 29, 1491-1504
Available online: http://rsif.royalsocietypublishing.org/content/5/29/1491.abstract
Abstract - Caecilians (Lissamphibia: Gymnophiona) are unique among vertebrates in having two sets of jaw closing muscles, one on either side of the jaw joint. Using data from high resolution x-ray radiation computed tomography scans, we modeled the effect of these two muscle groups (mm. levatores mandibulae and m. interhyoideus posterior) on bite force over a range of gape angles, employing a simplified lever arm mechanism that takes into account muscle cross sectional area and fiber angle. Measurements of lever arm lengths, muscle fiber orientations, and physiological cross sectional area of cranial muscles were available from three caecilian species; Ichthyophis cf. kohtaoensis, Siphonops annulatus, Typhlonectes natans. The maximal gape of caecilians is restricted by a critical gape angle above which the mm. levatores mandibulae will open the jaw and destabilize the mandibular joint. The presence of destabilizing forces in the caecilian jaw mechanism may be compensated for by a mandibular joint in that the fossa is wrapped around the condyle to resist dislocation. The caecilian skull is streptostylic; the quadrate-squamosal complex moves with respect to the rest of the skull. This increases the leverage of the jaw closing muscles. We also demonstrate that the unusual jaw joint requires streptostyly because there is a dorsolateral movement of the quadrate-squamosal complex when the jaw closes. The combination of the two jaw closing systems results in high bite forces over a wide range of gape angles, an important advantage for generalist feeders like caecilians. The relative sizes and leverage mechanics of the two closing systems allow one to exert more force when the other has a poor mechanical advantage. This effect is seen in all three species we examined. In the aquatic T. natans, with its less well-roofed skull, there is a larger contribution of the mm. levatores mandibulae to total bite force than in the terrestrial I. cf. kohtaoensis and S. annulatus.
Keywords: Gymnophiona, amphibian cranial morphology, bite force modeling, high resolution µct, automated measurement of muscle fiber angles
Caecilians (Gymnophiona) are fossorial, limbless amphibians, comprising 171 species with circumtropical distribution (Frost, 2007). Their burrowing lifestyle places special demands on their cranial anatomy, and the caecilian skull is compact and wedge-shaped, with many bones fused into compound elements (for a review see Wake, 2003). Caecilians are also unique among vertebrates in possessing two sets of jaw closing mechanisms that act on either side of the jaw joint. In addition to the usual complement of jaw adductors anterior to the jaw joint (mm. levatores mandibulae), a hyobranchial muscle posterior to the joint (m. interhyoideus posterior) acts as an accessory jaw closing muscle.
The jaw closing function of the m. interhyoideus posterior was proposed by Bemis et al. (1983) and Nussbaum (1983), who realized that its insertions on the ventral side of the retroarticular process of the lower jaw allowed it to adduct the mandible (Figure 1). Using electromyography, Bemis et al. (1983) showed that the m. interhyoideus posterior acts synergistically with the primary jaw closing muscles. The jaw closing function of the m. interhyoideus posterior has been proposed as an adaptation to a fossorial lifestyle (Nussbaum, 1983). The reasoning is, that in compact caecilian skulls, space for the mm. levatores mandibulae is restricted by the squamosal; a bone that covers large parts of the lateral face of the skull. The restriction on the size of the mm. levatores mandibulae demands the use of the m. interhyoideus posterior as an accessory jaw closing muscle to generate appropriate bite forces.
Although the cranium in caecilians is compact and solid, the morphology of the quadrate and the squamosal (quadrate-squamosal-complex) led to the hypothesis that caecilian skulls are kinetic (streptostylic) (Luther, 1914; Marcus et al., 1933; de Villiers, 1936; Iordanski, 1990, 2000; Wilkinson and Nussbaum, 1997). Indeed, manipulating the skull of a freshly killed Dermophis mexicanus specimen showed that the quadrate and the squamosal could rotate slightly (Wake and Hanken, 1982). A model of bite force generated by the m. interhyoideus posterior demonstrated the unusual, and counterintuitive result that force steadily decreases during jaw closure. However, two factors can ameliorate this loss in force: a retroarticular process that curves upward, giving a better mechanical advantage (O'Reilly, 2000) and the streptostylic joints in the skull which act as a second leverage system (Summers and Wake, 2005).
Previous mathematical descriptions of the function of the m. interhyoideus posterior were based on the assumption that muscle fiber orientation in the m. interhyoideus posterior is aligned exactly along the long axis of the animal and the force acts in caudal direction (Summers and Wake 2005). However, studies of the cranial musculature in caecilians (Wiedersheim, 1879; Luther, 1914; Lawson, 1965; Bemis et al., 1983; Nussbaum, 1983; Iordanski, 1996; Wilkinson and Nussbaum, 1997; Kleinteich and Haas, 2007) show that the fiber orientation of the m. interhyoideus posterior in most caecilian species is oblique rather than purely anteroposterior; the muscle fibers run in the caudal and ventral directions. A second simplification in the previous model was to ignore the jaw closing function of the mm. levatores mandibulae. These are the only jaw closing muscles in most other vertebrates and are quite substantial in size, so it is important that any model of caecilian jaw function includes the contribution of these muscles.
The goals of this study are five-fold: 1) we propose a new model of jaw function that includes the contribution of fiber angles that are not aligned with the long axis of the body; 2) we extend the model to include the ancestral jaw closing muscles, the mm. levatores mandibulae; 3) we estimate the effective mechanical advantages of these two jaw closing systems over different gape angles to test the hypothesis that the two systems contribute best to different parts of jaw closure; 4) with values derived from high resolution, synchrotron based x-ray radiation computed tomography (ct) scan data we calculate a theoretical bite force across a range of gapes and the contributions of the two closing systems to the maximal bite force; and 5) we use physical and computer models to describe the complex movements at the jaw joint during the doubly actuated closure of the gape.
2. MATERIALS AND METHODS
We studied the jaw lever mechanics of three specimens from different caecilian species (Table 1; Figure 2): I. kohtaoensis Taylor, 1960, Typhlonectes natans (Fischer in Peters, 1880), and Siphonops annulatus (Mikan, 1820). All specimens are stored in the herpetological collection of the zoological museum Hamburg (ZMH). Our sampling comprises basal (I. cf. kohtaoensis) and derived clades within the Gymnophiona (Figure 2) and two different skull architectures: I. cf. kohtaoensis and S. annulatus have stegokrotaphic skulls (closed temporal region; Figure 2); T. natans has a zygokrotaphic skull (temporal region with wide gap between squamosal and parietal; Figure 2). Due to unsolved problems in the taxonomy of and within the genus Ichthyophis (see Gower et al. 2002) we use I. cf. kohtaoensis herein for specimen ZMH A08981. The current taxonomic status of Ichthyophis kohtaoensis is highly debated and under revision. Further, the genus Ichthyophis has been shown to be paraphyletic (Gower et al., 2002, Frost et al., 2006, Roelants et al., 2007; Figure 1).
Specimens were decapitated between the 5th and 6th annulus (i.e. in the anterior trunk region). All specimens had been stored in 70% EtOH. We stepwise (50% EtOH; 30% EtOH) transfered the separated heads to distilled water; every step was maintained for 24 hours. We freeze dried the specimens following the procedure by Meryman (1960, 1961). The separated heads were frozen at -80°C for 4 hours. After freezing, we dried the samples under low pressure for 4 days. Upon visual inspection the heads were unchanged after freeze drying, however there were minor changes in the size of the samples (Table 1).
High resolution synchrotron based x-ray ct imaging was performed at Beamline W2 (maintained by the GKSS research center Geesthacht) of the DORIS III accelerator ring at the German Electron Synchrotron (DESY) in Hamburg, Germany. The specimens were scanned with a 30 keV x-ray beam. X-ray images were captured over a rotation of 180° in 0.25° steps for the I. cf. kohtaoensis and T. natans specimens; the S. annulatus specimen was rotated 360°. The resulting x-ray dataset was converted to a VGStudio Max® (Volume Graphics GmbH, Heidelberg, Germany) volume rendering dataset. The datasets have a resolution of 6.83 µm (I. cf. kohtaoensis and T. natans) respectively 9.2 µm (S. annulatus) in x, y, and z orientation. Neighboring voxels of the volume dataset have been merged to reduce the size of the dataset (binding). Different graduations of these resampled datasets (twofold, threefold, and fourfold binding) were available for analysis. We used the software packages VGStudio Max® 1.2 and Amira® 4.1 (Mercury Computer Systems) for processing, analyzing, and segmentation of the resulting volumetric 3D datasets. Surface rendering and animation was performed with Alias Wavefront Maya® 6.0.
The model used to calculate force transmission of the m. interhyoideus posterior is based on the model presented by Summers and Wake (2005). To account for fiber orientations of the m. interhoideus posterior, we added fiber angle ε to the model (Figure 1). We calculated the effective mechanical advantage EMAIHP (bite force per unit muscle force; based on Biewener, 1989) for the m. interhyoideus posterior by (Figure 1):
(1) EMAIHP = Fbite / FIHP = sin(α + γ + ε) * (lRP / lLJ) + sin(δ - ε) * cos(α + δ)
With Fbite = output bite force, FIHP = force generated by the m. interhyoideus posterior, lRP = length of the retroarticular process of the lower jaw, lLJ = distance from the rostral tip of the lower jaw to the jaw articulation, α = gape angle, γ = retroarticular angle with respect to the anteroposterior axis, δ = quadrate-squamosal angle with respect to the anteroposterior axis, and ε = muscle fiber orientation of the m. interhyoideus posterior with respect to the anteroposterior axis. In this equation and the next, the first term represents the force generated through the conventional simple lever system of the jaws and the second term accounts for the streptostylic suspension of the jaws.
We developed a second lever arm model for the mm. levatores mandibulae group (Figure 1). This group comprises three muscles in adult caecilians; m. levator mandibulae articularis, m. levator mandibulae internus, m. levator mandibulae longus (Wiedersheim, 1879; Luther, 1914; Edgeworth, 1935; Lawson, 1965; Bemis et al., 1983; Iordanski, 1996; Wilkinson and Nussbaum, 1997; a table of synonyms was presented by Kleinteich and Haas, 2007). The effective mechanical advantage for single muscles in this group EMALEV is calculated by:
(2) EMALEV = Fbite / FLEV = sin(β - α) * (lLEV / lLJ) + sin(β + δ) * cos(α + δ)
With Fbite = output bite force, FLEV = force generated by muscles of the mm. levatores mandibulae group, lLEV = distance from the insertion of the muscles to the jaw articulation, lLJ = distance from the rostral tip of the lower jaw to the jaw articulation, α = gape angle, β = muscle fiber orientation of the muscles with respect to the anteroposterior axis, and δ = quadrate-squamosal angle with respect to the anteroposterior axis.
Besides the mm. levatores mandibulae group the nervus trigeminus innervated jaw musculature of caecilians comprises three additional muscles that are not considered in this paper, i.e. the m. intermandibularis, the m. levator quadrati, and the m. pterygoideus (Iordanski, 1996; Haas, 2001; Kleinteich and Haas, 2007). The m. interhyoideus lowers the buccal floor. The function of the m. levator quadrati and m. pterygoideus is poorly known, however both insert on the quadrate and thus are likely to be involved in movements of the quadrate (streptostyly) rather than jaw closure.
Measurements of anatomical characters are based on lateral views of rendered ct datasets. We used the freely available image analysis software ImageJ 1.36b (NIH; http://rsb.info.nih.gov/ij/download.html) for all measurements. We did all measurements for both sides of the body of the animals; the average value of both measurements was used for further calculations.
For measurements of muscle fiber orientations (β and ε) we generated 8 bit gray-scale image stacks of sagittal sections parallel to the muscle in the ct datasets. These image stacks were generated with the oblique slice function of Amira®. For every investigated muscle we adjusted the plane of section so that sections were parallel to the muscle fibers in lateral view. We converted the gray-scale image stacks into binary data with the adjust > threshold function of ImageJ. The resulting dataset (Figure 3C) contained only musculature (black) and background (white). Muscle fiber orientations were measured automatically with ImageJ, and to reduce noise we excluded particles less than 25 pixels in area and with a circularity greater than 0.3 (Figure 3D) from the analysis. Measured muscle fiber angles are distributed (Figure 3E) around a mean value. Standard deviations of muscle fiber orientations are given in Table 2. The standard deviation of muscle fiber angles can be interpreted as an estimate for the diversity of fiber orientations within a muscle. We calculated effective mechanical advantages for the mean and the minimal and maximal values that were derived from the standard deviation of muscle fiber orientations. However, muscles are treated as idealized parallel fibered structures herein and the mean fiber orientation was used for interpretation of the jaw closing mechanism.
Theoretical forces that can be generated by a single muscle were calculated by:
(3) Fmuscle = (V / l) * pMIS
Where Fmuscle=force generated by a muscle, V = the volume of the muscle, l = length of the muscle in the direction of the fiber orientation, and pMIS = the maximal isometric stress (pMIS = 250 kPa; Herzog, 1995). The ratio of muscle volume to muscle length is a measure for physiological cross-sectional area (PCSA).
Total bite force for the entire jaw closing system (i.e. both jaw closing systems and both sides of the skull) is calculated as the doubled sum of bite forces from single muscles, assuming bilateral symmetry.
We measured volumes and lengths of the muscles by separating single muscles out of the ct datasets (segmentation). Surfaces were generated out of the segmented datasets and measured with the lineprobe and areavolume tools in Amira®. Volume and length measurements are averages of values from both sides of the body. To interactively explore possible movements of the cranial bones we produced physical models of the caecilian skulls including the lower jaws on a ZPrinter® 310 rapid prototyping machine (ZCorp, Burlington, MA). The models were based on the ct datasets. We segmented the quadrate-squamosal complex, the pterygoid, and the stapes on the right hand side of the skull with Amira® 4.1 in order to produce separated models for those parts. The resulting physical models are scaled up in size (I. kohtaoensis and T. natans scale factor: 14.5; S. annulatus scale factor: 10.7) compared to the skulls in the specimens. The physical models were manipulated by hand to estimate the degrees of lower jaw and quadrate-squamosal movements. We then used Maya® 6.0 to animate the VRML dataset of the I. kohtaoensis specimen. The computer animation is based on the results of the interaction with the physical model for this species. Movie files of the animation are available as supplementary information.
All measurements used for calculations of effective mechanical advantages and bite forces over gape angles are listed in table 2. The ratios of the lengths of the in-lever to the out-lever for the mm. levatores mandibulae range from 0.055 (m. levator mandibulae articularis in S. annulatus) to 0.264 (m. levator mandibulae longus in T. natans). The lever arm ratios are higher for the m. interhyoideus posterior in all three investigated species; 0.404 in I. kohtaoensis, 0.58 in S. annulatus, and 0.538 in T. natans.
Average muscle fiber angle orientations of the levator mandibulae complex relative to the anteroposterior axis range from 79.2° (m. levator mandibulae longus in T. natans) to 125.5° (m. levator mandibulae internus in T. natans). The fibers of the m. interhyoideus posterior are oriented on average 41.2° in I. kohtaoensis, 36.2° in S. annulatus, and 57.3° in T. natans.
The m. levator mandibulae articularis has the smallest ratio of muscle volume to muscle length (physiological cross-sectional area - PCSA) in all investigated specimens. PCSA values of the m. levator mandibulae articularis are between 0.212 mm² (T. natans) and 0.409 mm² (I. kohtaoensis). The PCSA range from 0.295 mm² (T. natans) to 1.628 mm² (S. annulatus) for the m. levator mandibulae internus; from 0.491 mm² (I. cf. kohtaoensis) to 1.011 mm² (S. annulatus) for the m. levator mandibulae longus. In the three investigated caecilian species the m. interhyoideus posterior has the largest PCSA value of all muscles; 4.363 mm² in I. cf. kohtaoensis, 4.195 mm² in S. annulatus, and 2.128 mm² in T. natans.
Calculated maximal bite forces range from 0.053 N (m. levator mandibulae articularis in T. natans) to 0.407 N (m. levator mandibulae internus in S. annulatus) for the levator mandibulae group; from 0.53 N (T. natans) to 1.09 N (I. kohtaoensis) for the m. interhyoideus posterior.
The retroarticular process of the lower jaw is angled 32.7° dorsally in I. kohtaoensis, 16.8° in S. annulatus, and 22.3° in T. natans with respect to the anteroposterior axis. The quadrate-squamosal complex is oriented at 26° to the anteroposterior axis in I. cf. kohtaoensis, 27.5° in S. annulatus, and 26.2° in T. natans.
3.1 Effective mechanical advantage and gape angle
The effective mechanical advantages (EMA) of all mm. levatores mandibulae is maximal at a closed lower jaw in all investigated species (Figure 4; Table 3). With increasing gape angle, the EMA of the mm. levatores mandibulae decreases. The muscles of the levator mandibulae group in the investigated species have critical values for gape angles above those the effective mechanical advantages become negative (Figure 4). Critical gape angles range from 64.4° (m. levator mandibulae articularis in S. annulatus) to 84.8° (m. levator mandibulae internus in T. natans) (Table 3).
The effective mechanical advantage of the m. interhyoideus posterior in the three investigated species increases with increasing gape angle, reaches a maximum value at gape angles of 55.2° (I. kohtaoensis), 51.8° (S. annulatus), and 78.3° (T. natans), and decreases with increasing gape angles above the optimal gape (Figure 4; Table 3). None of the investigated species shows a critical gape angle for the m. interhyoideus posterior.
Maximal effective mechanical advantages of the mm. levatores mandibulae range from 0.64 (m. levator mandibulae internus in T. natans) to 1.12 (m. levator mandibulae longus in T. natans). The maximal EMA values of the m. interhyoideus posterior are lower than for the levator mandibulae group; they range in between 0.28 (I. kohtaoensis) and 0.53 (S. annulatus) (Table 3).
3.2 Bite force and gape angle
In the three investigated species the mm. levatores mandibulae contribute best to total bite force (i.e. the sum of bite forces from all jaw closing muscles) at a closed lower jaw. The mm. levatores mandibulae generated forces decrease with increasing gape angle; i.e. when the jaw opens. The force output of the m. interhyoideus posterior increases with wider gape angles (Figure 5) until it reaches a maximum value. Total bite force is almost constant at small gape angles (0° - 30°) and decreases with higher gape angles (Figure 5).
In I. kohtaoensis the calculated forces for the mm. levatores mandibulae for one side of the body with a closed lower jaw are 0.094 N (m. levator mandibulae articularis), 0.111 N (m. levator mandibulae internus), and 0.124 N (m. levator mandibulae lonugs) (Table 4). The m. interhyoideus posterior contributes 0.174 N to the bite force when the jaws are closed, the calculated maximum value is 0.305 N at a gape angle of 55° (Figure 5; Table 4). The bilateral sum of all muscles shows a maximum total bite force of 1.045 N at a gape angle of 16° (Table 4).
In S. annulatus the m. levator mandibulae articularis contributes 0.041 N, the m. levator mandibulae internus 0.355 N, the m. levator mandibulae longus 0.235 N, and the m. interhyoideus posterior 0.347 N to the estimated bite force when the jaws are closed (Table 4). The m. interhyoideus posterior reaches a maximal force value of 0.557 N at a gape angle of 55°. The calculated total bite force for both sides of the body is maximal at a gape angle of 13° when the animal can exert 2.0 N.
In T. natans we calculated for the mm. levatores mandibulae bite forces at a closed lower jaw of 0.059 N (m. levator mandibulae articularis), 0.048 N (m. levator mandibulae internus), and 0.255 N (m. levator mandibulae longus). The m. interhyoideus posterior contributes 0.037 N to the estimated total bite force at zero gape (Table 4). Maximum bite force of 0.173 N is generated by the m. interhyoideus posterior at a gape angle of 78°. Total bite force for all muscles on both sides of the head was calculated with a maximum value of 0.796 N at a gape angle of 6° (Table 4).
3.3 Impact of different fiber orientations
The standard deviation for values of muscle fibers angles range from 24.7° (m. levator mandibulae articularis in Ichthyophis cf. kohtaoensis) to 35.4° (m. levator mandibulae longus in Typhlonectes natans) (Table 2). Effective mechanical advantages (EMA) and thus bite forces increase with smaller values for muscle fiber angles in all investigated species and muscles, larger fiber angles decrease EMA and bite force (Table 3 and 4).
The gape angle at which the muscles have their best EMA increases with increasing fiber angle (Table 3) for the m. levator mandibulae internus and the m. interhyoideus posterior and thus variation in fiber orientation has an effect on total bite force over gape angle (Table 4).
Critical gape angles increase with increasing fiber angle for all muscles. For the m. levator mandibulae internus the increase in critical gape angle results in a critical gape that is beyond the maximal gape angle considered herein (90°) (Table 3).
3.4 Rapid prototyping and animation
The scaled up, rapid prototyped models of the lower jaw clearly show a partially captured mandibular joint (Figure 6 A, D, G) in that the fossa of the jaw joint in the pseudoangular is a deep mediocaudally oriented ridge (Figure 6 C, F, I) that wraps around the condyle of the quadrate. Interactive manipulation of the rapid prototyped models and the resulting three dimensional computer animation (see supplementary information) show substantial dorsolateral movement of the quadrate-squamosal complex as the lower jaw closes. This movement is driven by the mediocaudally oriented fossa of the lower jaw, that necessitates some degree of lateral movement of the lower jaw as the jaw opens (Figure 7; supplementary information).
Our analysis of the caecilian jaw function has brought to light several interesting features of these unusual amphibians. When the gape angle exceeds some critical angle the force generated by one set of jaw muscles transitions from closing the jaws to opening them (Figure 4). The previous model of jaw function did not predict this because it did not account for the fiber orientation of the muscles, realistic orientations of the quadrate-squamosal complex, or the levator muscle complex (Summers and Wake 2005). The critical gape angle has two important consequences: first, as gape increases the contribution of the levator complex will decrease (Figures 4 and 5); secondly, the forces oriented at oblique angles relative to the long axis of the jaw are one set that will tend to destabilize the jaw joint. Our model suggests that at gape angles higher than approximately 70° the mm. levatores mandibulae will open the lower jaw and thus counteract to the m. interhyoideus posterior. Although the m. interhyoideus posterior has its peak mechanical advantage at rather high gape angles (Table 3, Figure 4) and thus has the potential to compensate for the mm. levatores mandibulae, this theoretical scenario seems to be of little biological relevance. Gape angle data is available from Ichthyophis kohtaoensis, T. natans and Hypogeophis rostratus, which show peak gape angles of no more than 60° (O’Reilly, 2000). This coincides with our model predictions that critical gape angles for single muscles of the mm. levatores mandibulae are at around 65° for the three investigated species (Table 3, Figure 4).
The synchrotron x-ray radiation based ct image data made it possible to measure fiber angles for a large number of fibers relative to methods that rely on a dissecting scope and goniometer (thousands versus dozens) in a reasonable investment of time. However the technique may also introduce errors. These fall into two categories, those that affect the measurement of cross-sectional area and those that affect the angles measured. Two sources of error are apparent, the first is that the specimen must be freeze dried in order to visualize the soft tissues clearly, and secondly the method we developed is two dimensional, whereas the muscles are three dimensional structures. We do not suppose that the estimation of volume from the freeze-dried specimens is very different than would be obtained from fresh material. Shrinkage that occurs during the fixation of specimens in formalin and storage in ethanol usually decreases the volume by ~20-25% (Böck, 1989). However, most of this shrinkage (~20%; Böck, 1989) is caused by dehydration, which was at least partially compensated by rehydration of the specimens prior to freeze drying. Freeze drying itself is known to reduce volume by about ~15% (Boyde, 1978). Thus, we estimate the volume shrinkage due to fixation and drying to not more than ~25%. Bite force would then be underestimated by about 17%. We virtually sectioned the 3-dimensional muscle volume in a plane that was as nearly parallel to the fiber direction as we could estimate from a lateral projection. The distribution of fibers angles (Figure 3E) suggests that we have successfully estimated the orientations from muscle fibers and the mean fiber angle. Furthermore, figure 3C shows all potential fibers and when compared to figure 3D, which shows only the measured fibers, it is clear that we have managed to section in a plane parallel to the majority of the fibers. The most extreme fiber angles that were derived from standard deviation values within the sample can result in a different behavior of the model (Tables 3 and 4). In vivo it seems also possible that muscle fibers change their orientation during shortening, an effect that is not considered herein. However, based on the distribution of fiber angles (Figure 3E) we suggest that the average value of fiber angle is a decent estimation to interpret muscle function. Most fibers have an average fiber orientation and higher and lower values for muscle fiber angles seem likely to outweigh each other in the animal. Literature estimates of fiber directions are also made from two-dimensional projections of the muscles and because of the laborious nature of making angular measurements by hand are always on a very small subset of muscle fibers. We suggest that the synchrotron method yields results that are more representative of the actual muscle architecture and it has the advantage of being able to be extended into true three-dimensionality.
The unusual, partially captive rotating joint of the lower jaw of caecilians (Figure 6) could be explained by two factors. Consider the force generated by the jaw muscles. There is a component of this force perpendicular to the jaw or retroarticular process that closes the gape. Another component - parallel to the jaw - tends to dislocate the jaw joint. The existence of a critical angle implies that as the gape increases the component perpendicular to the jaws decreases, therefore the parallel component of the muscle force will increase. So, with increasing gape there is a greater force tending to dislocate the jaws. The m. interhyoideus posterior itself, because it acts on the opposite side of the jaw than the levator mandibulae complex, will exert tension to the mandibular joint. This force tends to loose the connection between lower jaw and jaw joint. The way in which the mandibular fossa of the lower jaw is wrapped around the condyle of the articular bone stabilizes the joint against these forces. An analogue for this joint is seen in mammal carnivores (particularly the Mustelids), in which the condylar process of the mandible is captured by the squamosal bone (Scapino, 1976, 1981; Radinsky, 1982; Riley, 1985). Besides the skeletal features, the m. pterygoideus (innervated by cranial nerve V) seems likely to stabilize the mandibular joint as well.
Every jaw closing muscle has its own critical angle, and the two sets of jaw closers have quite different average critical angles — this means that for any biologically relevant gape there is some muscle in one of the two systems that can exert a closing force. An implication of the different critical angles is that the contribution of single muscles to closing force will vary with gape angle. For example, in I. kohtaoensis at a gape of 10 the mm. levatores mandibulae contribute ~60% of the total closing force, whereas when the mouth is open to 50 they contribute only 35%. The net effect of this variation is that as the force from the mm. levatores mandibulae is decreasing the force of the second jaw closing system, the m. interhyoideus posterior, is increasing and the total force exerted at the tips of the jaws is similar over a wide range of gape. If we consider the jaw closing force of all three caecilians between 0 and 35 gape angles the closing force varies less than 10% from its peak value (figure 5), and over the most extreme gape angles (~60) seen in the literature the force drops just 29% (I. cf. kohtaoensis), 33% (S. annulatus), or 43% (T. natans) from the peak. Maintaining high closing forces over a wide range of gapes seems important for dietary generalists, such as these three species (Moodie, 1978; Gudynas et al., 1988; Verdade, 2000; Presswell et al., 2002; Kupfer and Maraun, 2003; Gaborieau and Measey, 2004; Measey et al., 2004; Kupfer et al., 2005).
These theoretical models of bite force have proven quite robust relative to measured bite force in a wide variety of organisms (Herrel et al., 1998, 2002; Greaves, 2000; Herrel and Aerts, 2003; Westneat, 2003; Huber and Motta, 2004; Huber et al., 2005) and there is some evidence to suggest our model is also close to measured caecilian bite force. Models of bite force based on geometry and the physiological cross sectional area (PCSA) of muscle often underestimate the actual forces measured during biting in vivo (Herrel et al., 1998, 2008; Meyers et al., 2002; but see Huber et al., 2005). This may be because the models typically do not take into account all of the potential jaw closers, or more probably the models ignore the effects of non-closing muscles on bite force. When bite forces are measured with a force transducer the animal has some contact with either the substrate or the experimenter and has the opportunity to exploit the effects of trunk musculature to aid in jaw closure. The two experimentally determined bite forces for caecilians are 0.62N and 1.09N for Boulengerula taitanus and Schistometopum thomense (Measey and Herrel, 2006) - comparable values to our calculated peak forces (0.8N - 2.0N). However, our values are proportionally lower in light of the size of our three individuals relative to the substantially smaller animals in the experimental study. Bite forces from similar sized animals are quite a bit higher (~3N-6N) (Anthony Herrel pers. comm.) The differences between our theoretical values and the measured forces might be explained as an effect of the animals recruiting body musculature, in this case vertebral muscles, to augment the levator and IHP systems. This is supported by the activation of trunk musculature during the static pressure phase of the caecilian bite cycle as shown electromyographically by Bemis et al. (1983). Further, caecilians will spin about their long axis, using this rotational movement to shear prey against the sides of their burrow, or to determine its size (Measey and Herrel, 2006).
Streptostyly, the mobile joint between the quadrate-squamosal and the neurocranium seems at odds with the otherwise tightly fused caecilian skull - we propose two advantages to this architecture: first, streptostyly compensates for lateral movements of the lower jaw; secondly, the rotational movement of the quadrate-squamosal contributes additionally to bite force by shortening the distance between lower and upper jaw.
When we produced the oversized prototypes of skulls and jaws from the ct scan data it became clear that the joint between the lower jaw and the quadrate-squamosal has a very limited range of motion. Rather than the loose saddle joint we had expected, the quadrate-squamosal is firmly captured in a groove of the pseudoangular, and is a rotational joint with very little mobility off the rotational axis (Figure 6). Because the axis of the mandibular joint is not perpendicular to the long axis of the lower jaw, to open the mouth the lower jaw will rotate downwards and laterally. The lateral movement of the lower jaw must be compensated for by a lateral rotation of the quadrate-squamosal (Figure 7, supplementary information). The two bones of the lower jaw, i.e. pseudodentary and pseudoangluar, share a rather loose suture and there seems to be potential for intramandibular mobility. If true, movements within the lower jaw could be related to the lateral component during jaw closure. As an aside, the deep groove in the pseudoangular (Figure 6) was previously mentioned by Wiedersheim (1879), who interprets this structure as comparable to the jaw joint in teleosts or lungfishes; and Marcus et al. (1933), who believed that the deep groove tightens the mandibular joint during the action of the m. pterygoideus. We suggest that this tight joint is an adaptation to the two forces that tend to dislocate the jaw during feeding.
Another advantage of streptostyly is highlighted by the high effective mechanical advantage of the levators. The second mobile joint of the jaws forms an unusual lever system that converts some of the force that tends to dislocate the lower jaw into a closing force. This streptostyly based closing force is due to the upward rotation of the quadrate-squamosal (and thus the mandibular joint itself) which moves the lower jaw towards the upper jaw. The streptostyly component of bite force is added to the force that that results from the regular closing movement of the lower jaw. This mechanism amplifies the mechanical advantage of the levators in particular, though it also helps the IHP system (Summers and Wake, 2005). In both I. kohtaoensis and T. natans one of the levators, the m. levator mandibulae longus, has an effective mechanical advantage greater than 1. This means that despite inserting rather close to the jaw joint it exerts as much, or even a little more, force at the tips of the jaws than it develops at its insertion. Indeed, it had been proposed that the muscles of the levator mandibulae group are so close to the joint that they might be adapted for high-speed closure of the jaws (Summers and Wake, 2005), we find instead that, like the m. interhyoideus posterior they are well suited to exerting large forces on prey.
An interesting connection to skull architecture comes from understanding the mm. levatores mandibulae as important contributors to bite force. Many caecilian skulls, including two of the species we looked at here, are stegokrotaphic, that is, the temporal region of the skull is roofed with bone. In contrast, T. natans is zygokrotaphic - there is a significant opening between the squamosal and the parietal bones, which leaves substantially more room for jaw levator muscles. This architectural difference is reflected in the relative contributions to force of the two jaw adductor systems to closing force. In the two stegokrotaphic species the levators contribute ~65% - 42% of the total force at gapes from 0 - 35, but in the zygokrotaphic species these same muscles contribute ~91% - 64% at the same gape angles. We attribute this difference to the zygokrotaphic species being able to pack more muscle, with better lever arms, into the skull than can the two species with the roofed temporal region. It is tempting to extrapolate further from this small data set, perhaps into the realm of ecology, where T. natans is an aquatic animal while both I. kohtaoensis and S. annulatus are terrestrial and fossorial. However, with the confounding effects of phylogeny and ecology and the very limited sample size used for our study, there is nothing that can be said at the moment. If a large contribution from the mm. levatores mandibulae is characteristic of aquatic feeding we might expect to see similar force contribution patterns in those species of caecilians with aquatic larvae (i.e. Rhinatrematidae, Ichthyophiids, Uraeotyphlidae, and some Caeciliidae). There is also an opportunity to further our understanding by examining an independent radiation of zygokrotaphic but terrestrial caecilians; i.e. the Scolecomorphidae.
We thank Anthony Herrel (Harvard) for helpful comments and for sharing information on caecilian in vivo bite forces. We also are grateful to Marvalee Wake (Berkeley), Mark Wilkinson, and David Gower (both London) for fruitful discussions on caecilian cranial anatomy. The members of the UC Irvine Biomechanics lab have been helpful by providing comments to improve earlier drafts of the manuscript. Georg Petschenka (Hamburg) gave a helpful introduction to freeze drying. The ct imaging was performed at the DORIS III accelerator ring of the DESY Hamburg with the tremendous support of Felix Beckmann and Julia Herzen from the GKSS research center Geesthacht (project number I-20060152). TK is supported by the Studienstiftung des deutschen Volkes. TK and AH are funded by the German Research Foundation (DFG) grant HA2323/10-1; APS is supported by the National Science Foundation (NSF) grant IBN-0317155.
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able 1. Specimens used in this study
Table 2. Measurements of functional important anatomical characters and calculation of maximal force of single muscles for the three investigated species
Table 3. Calculations of effective mechanical advantages (EMA) and functionally important gape angles (α) for single muscles. Results shown for calculations with mean muscle fiber angles (βmean/εmean), minimal fiber angles (βmin/εmin), and maximal fiber angles (βmax/εmax)
Table 4. Calculated maximum bite force values and bite forces at a closed lower jaw for cranial muscles in the three investigated species. Results shown for calculations with mean muscle fiber angles (βmean), minimal fiber angles (βmin), and maximal fiber angles (βmax)
Figure 1. Representation of the lever arm model used to predict bite forces in the caecilian jaw closing mechanism drawn over a reconstruction of the skull in lateral view of Icthyophis cf. kohtaoensis. Bite forces were calculated for a range of gape angles () from 0 - 90. Two jaw closing mechanisms, one actuated by the mm. levatores mandibulae and the other actuated by the m. interhyoideus posterior are shown. The bite force at the tip of the lower jaw Fbite is a function of the forces generated by the two closing systems. The mm. levatores mandibulae closure system is described by the force generated by the muscles (Flev), acting on an input lever arm lLEV, with a muscle fiber orientation of . The m. interhyoideus posterior closure system acts on a lever arm lRP, with a force of FIHP and a fiber orientation of . Two aspects of skull anatomy are captured with angular measurements: the angle of the quadrate-squamosal complex () and the angle of the retroarticular process of the lower jaw with a line drawn from the lower jaw joint to the tip of the lower jaw ().
Figure 2. Phylogeny of the Gymnophiona (Roelants et al. 2007) showing the genera of the species for which we modeled jaw closing forces in bold face. Ichthyophis is a paraphyletic genus that appears in two places on the cladogram and we do not know to which clade Ichthyophis cf. kohtaoensis belongs. The skulls are 3-dimensional reconstructions from ct image data from I. kohtaoensis, Typhlonectes natans, and Siphonops annulatus shown in dorsal view to emphasize the differences in the temporal region.
Figure 3. A method for measuring muscle fiber angle from high resolution, synchrotron based x-ray ct scan data. A) A volume rendering of the ct image data for Ichthyophis cf. kohtaoensis shown in lateral view with the skin removed to reveal the underlying skeleton and muscles. The squamosal bone has also been removed to show the levator mandibulae muscle complex. B) A contrast enhanced, gray scale image of a parasagittal section of the m. interhyoideus posterior from the ct image data. C) The section in B thresholded to emphasize the muscle fibers. D) The section shown in C with all connected areas smaller than 25 pixels in area removed, and all areas with a circularity of more than 0.3 removed. The remaining areas are muscle fibers with measurable angles. E) histogram showing the distribution of angular measurements for the 6797 fibers measured from the image stack for the m. interhyoideus posterior from the left side of I. kohtaoensis that included image B).
Figure 4. The effective mechanical advantage (EMA) of each of the jaw closing muscles for three species of caecilian, Ichthyophis cf. kohtaoensis, Siphonops annulatus, and Typhlonectes natans. This is the amount of amplification of the actual muscle force that will appear at the tip of the lower jaw. At an EMA greater than 0 the muscle tends to close the jaw and at and EMA less than 0 it tends to pull the jaw open. This critical gape angle, where EMA = 0 varies by species and is not seen for the interhyoideus posterior (IHP). This illustrates that some architectures are force amplifiers. At small gape angles the m. levator mandibulae longus can have an EMA greater than 1, this means that the force at the tip of the jaws exceeds the force generated by the jaw muscle. The maximum EMA of the three adductor muscle is when the jaws are closed, whereas for the IHP there is a peak EMA between 50 and 80 gape angle.
Figure 5. Modeled bite forces at varying gape angles for three species of caecilian: Ichthyophis cf. kohtaoensis, Siphonops annulatus, and Typhlonectes natans. The left panels show absolute force generated by the four jaw closing muscles and the sum of the forces of the three mm. levatores mandibulae as well as the total bite force as sum of all four muscles for both sides of the skull. The right panels show the relative contributions of single muscles (for both skull sides) to the total bite force.
Figure 6. Anatomy of the mandibular joint in three species of caecilan: Ichthyophis cf. kohtaoensis (A-C), Siphonops annulatus (D-F), and Typhlonectes natans (G-I) reconstructed from ct image data. Surface renderings of the skull and lower jaw in lateral view (A,D,G) showing the articulation between the pseudoangular and the quadrate (arrow). The disarticulated lower jaw showing the deep groove of the mandibular fossa (B, E, H). Dorsal views of the lower jaws (C,F, I) showing the fossa on the left side (arrow) and tracing its oblique orientation on the right side (solid line).
Figure 7. Movements of the quadrate-squamosal complex in Ichthyophis cf. kohtaoensis reconstructed from ct image data and based on interactive manipulation of rapid prototyped skulls. Surface renderings of the skull and lower jaw. Left column - lateral view; right column - dorsal view. The anatomy of the mandibular joint causes a mediolateral movement of the lower jaw, during opening and closing movements. The mediolateral movement is compensated by movements of the quadrate-squamosal complex.