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Keywords:

  • biomechanics;
  • lizard;
  • skull;
  • finite element analysis

Abstract

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. CONCLUSIONS
  7. Acknowledgements
  8. Literature Cited

Cranial sutures are sites of bone growth and development but micromovements at these sites may distribute the load across the skull more evenly. Computational studies have incorporated sutures into finite element (FE) models to assess various hypotheses related to their function. However, less attention has been paid to the sensitivity of the FE results to the shape, size, and stiffness of the modeled sutures. Here, we assessed the sensitivity of the strain predictions to the aforementioned parameters in several models of fronto-parietal (FP) suture in Lacerta bilineata. For the purpose of this study, simplifications were made in relation to modeling the bone properties and the skull loading. Results highlighted that modeling the FP as either an interdigitated suture or a simplified butt suture, did not reduce the strain distribution in the FP region. Sensitivity tests showed that similar patterns of strain distribution can be obtained regardless of the size of the suture, or assigned stiffness, yet the exact magnitudes of strains are highly sensitive to these parameters. This study raises the question whether the morphogenesis of epidermic scales in the FP region in the Lacertidae is related to high strain fields in this region, because of micromovement in the FP suture. Anat Rec, 2013. © 2012 Wiley Periodicals, Inc.

Sutures are sites of bone deposition and growth, which undergo many changes in terms of their stiffness and form over the growth and development of the skull (Herring,2008). However, the role and function of sutures in the adult skull has been the subject of debate among functional morphologists and palaeontologists. In fact, in a lot of taxa, many sutures do not fuse after the growth and developmental processes have effectively terminated, and the possible biomechanical roles of these elements during ontogeny and phylogeny are still not fully understood (Frazzetta, 1962; Herring, 1972; De Vree and Gans,1987; Jaslow,1990; Thomson,1995; Herrel et al.,2000; Mao,2002; Evans,2003; Rayfield, 2005b; Markey et al.,2006; Daza et al.,2008; Moreno et al.,2008; Hipsley et al.,2009; Jasinoski et al., 2009,2010; Moazen et al., 2009a,b; Wang et al.,2010, 2012; Reed et al.,2011; Jones et al., 2011). Micromovement at sutures may potentially lead to a uniform pattern of load distribution across the skull. This hypothesis has been tested using experimental strain recorded in vivo or in vitro models (Smith and Hylander,1985; Rafferty and Herring,1999; Kupczik et al., 2007).

Computational models are an additional means of testing hypotheses relating to skull mechanics, strain, and loading. The finite element (FE) method has recently gained popularity to analyze the role of sutures as modulators of the mechanical response of the skull to loading (Rayfield, 2005b; Jasinoski et al.,2009; Moazen et al., 2009b). Validity and sensitivity of these FE models is an important issue which needs to be addressed (Ross et al.,2005; Kupczik et al.,2007; Gröning et al.,2009; Bright and Rayfield,2011; Panagiotopoulou et al., 2011, 2012; Rayfield, 2011). While testing the validity of FE models is possible in the case of large living taxa, it is more challenging or impossible in the case of small animals or fossils. In these cases, sensitivity analysis can be considered as a way to understand how these models respond under a wide range of input parameters. These types of studies can be informative in terms of predicting the relative effect of certain parameters on the overall pattern of outputs. Several studies in the literature have assessed the sensitivity of FE models to bone material property assignment (Strait et al.,2005; Reed et al., 2011), and specified loading conditions (Ross et al.,2005; Grosse et al.,2007; Moazen et al., 2008a). However, in the case of incorporating the sutures in the FE models, few studies have assessed the sensitivity of the FE results to the sutures morphology and stiffness (Kupczik et al.,2007; Moazen et al., 2009b; Jasinoski et al.,2010; Wang et al.,2010; Reed et al.,2011; Bright, 2012).

Lacertidae is a large and diverse family of lizards, including about 280 species distributed throughout Eurasia and Africa (Arnold et al.,2007; Čerňanský,2010). In these lizards, the head is covered by plate like scales and supraciliary granules, which are composed of layers of keratin formed from cells produced by the living basal layer of the epidermis (the stratum germinativum). Epidermic scales can cover dermic bony plates called osteoderms. In turn, the layer of osteoderms covers the dorsal bones of the skull and is closely attached to them, especially in Lacertidae (Arnold et al.,2007; Ljubisavljević et al., 2011). Recent studies suggest that the fronto-parietal (FP) suture is an important morphogenetic element of cephalic scales and skull in lacertids (Barahona and Barbadillo,1998; Bruner and Costantini, 2007, 2009; Costantini et al.,2010). The tight developmental connection between scales and bones is also supported by their shape variation. The variation of the cephalic scales is largely characterized by a size-related pattern associated with negative allometry of the anterior region (frontal scales) and positive allometry of the posterior region (occipital, parietal, and interparietal scales; see Monteiro and Abe,1997; Bruner et al.,2005; Bruner and Costantini, 2007). This anteroposterior growth gradient matches the pattern of ossification of the underlying cranial bones (Barahona and Barbadillo, 1998).

The FP suture lies under the FP scales, thus between the anterior and posterior regions of the skull. It is widely considered to have a major evolutionary and ontogenetic role as a structural element during growth and development (Frazzetta,1962; Smith and Hylander,1985; Herrel et al.,2000; Metzger, 2002). Shape analyses revealed relevant patterns of morphological variation associated with this suture, related to allometric changes (Bruner and Costantini, 2009). The position of the suture within the spatial framework of cephalic scales is constant, independent of the species and of the allometric changes, suggesting a certain morphogenetic and phylogenetic stability (Costantini et al.,2010). The morphology of the suture (joint with Type-A interdigitations as described in Jones et al., 2011), is highly convoluted and interdigitated in the western green lizard Lacerta bilineata (Fig. 1) as well as in the other lacertid species investigated (Costantini et al.,2010). This suggests scarce or null kinetic movements at this junction.

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Figure 1. A: Model of head in dorsal view. B: Micro-CT section of the head showing the high level of interdigitation of the fronto-parietal suture (FPS) in Lacerta bilineata in transverse plane. C: Left lateral view of the head highlighting the applied force and constraint point in the FE models.

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The aim of this study was to analyze the sensitivity of strain predictions to the shape, size, and stiffness of the FP suture in L. bilineata using FE method. Several FE models were developed in which aforementioned parameters were varied. To assess the effect of these parameters on the strain predictions, the first and third principal strains and von Mises (VM) strain across the skull roof were recorded and compared between the models.

MATERIALS AND METHODS

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. CONCLUSIONS
  7. Acknowledgements
  8. Literature Cited

FE models of L. bilineata skull were developed where the FP suture was the only modeled suture. In the first step, level of interdigitation of the FP suture was decreased through virtual expansion of the suture (sensitivity to shape and size). However, this also increased the volume of the suture. Therefore, in the second step a series of imaginary models were developed in which the FP suture modeled as a butt suture to solely assess the effect of sutural size (sensitivity to size). In the third step, elastic modulus of the FP suture was varied in two of the interdigitated FP suture models (sensitivity to stiffness).

Model Construction

A dry head of a male adult L. bilineata (skull length ∼30.1 mm; skull width ∼15.7 mm) was scanned using high-resolution micro-Computed Tomography (micro-CT) at 45 kV X-ray tube voltage, 88 µA, 0.35° rotation step and 800 ns exposure time per individual shadow projection (lCT-80, Scanco Medical, Switzerland). The voxel size was 0.036 × 0.036 × 0.036 mm, with an average exposure time of 120 min per scan. ScanIP v2.1 (Simpleware, UK) image processing software was used to segment the skull and FP suture from the CT slice images (see Fig. 1). Subsequently, the original voxel size was re-sampled (i.e., skipping voxels to reduce the size of model) to 0.15 × 0.15 × 0.15 mm.

In this study the FP suture, together with the lateral sutures associated with the anteroposterior separation of the skull roof, were analyzed (Fig. 2). The sutures were segmented manually in Model 1a (M1a). Then, four additional models developed where the segmented suture was expanded by one voxel size (i.e. 0.15 mm) in x, y, and z direction individually, that is, M2, M3, and M4 respectively and in combination in all three directions in M5a. The aforementioned approach led to decrease in interdigitation level and increase in thickness of FP suture (sensitivity to shape and size). To solely assess the effect of thickness a series of imaginary butt (end-to-end) suture models were developed. The position of the butt suture was determined in the transverse plane. The most anterior and posterior points of the segmented FP suture in M1a were used to calculate the average point (in Y direction as shown in Fig. 2). This point was used to position the butt suture. The butt condition was modeled with 2, 3, 4, and 5 pixel in width in the models M6–M9, respectively (sensitivity to size; see Fig. 2 for a summary of the models). Using these models, the local strain fields were analyzed to ascertain the influence of the shape and size of the FP suture.

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Figure 2. Model of the head in dorsal view based on micro-CT after segmentation of the FP suture and other sutures associated with the anteroposterior separation of the skull roof. FP suture was modeled using different geometry (interdigitated and butt) and different thickness, to evaluate the influence of these choices in the FE models. Please note that M10 was not modeled and used for any FE analysis but highlights the relative position of the interdigitated and butt suture in M1a and M6.

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All the aforementioned models were transferred into meshed solid geometries (ScanFE v2.1-Simpleware, UK) that were composed of solid tetrahedral elements (four noded elements with linear displacement behavior). It should be noted that on average, there were about six elements across the thickness of the suture in M1a and number of elements across the suture was higher in the expanded suture models. Each model was consisted of over one million elements. All models were then imported into ABAQUS v6.9 (Simulia, Providence, RI) in preparation for FE analysis.

Material Properties

Bone was modeled as a homogeneous, isotropic material with an elastic modulus of 10, 000 MPa and a Poisson's ratio of 0.3 in all the models (Rayfield et al.,2001; Moazen et al., 2009a,b). Although bone is known to be anisotropic, previous studies (Strait et al., 2005) have shown that comparable patterns of strain are formed with an isotropic assumption. To assess the sensitivity of the local strain distribution to the shape and size of the FP suture, an elastic modulus of 10 MPa was assumed. This elastic modulus was subsequently varied based on published experimental data (McLaughlin et al.,2000; Radhakrishnan and Mao,2004; Kupczik et al., 2007) from 10 MPa in M1a and M5a to 1.2 MPa, 800 MPa, 8, 000 MPa, and 10, 000 MPa (fused) in M1b-e and M5b-e, respectively, to assess the sensitivity of the results to the stiffness of the FP suture. Note, M1e and M5e both represented a fused suture. A Poisson's ratio of 0.3 was used for all sutures. See Table 1 for a summary of the models.

Table 1. Models used in the analysis
 ModelSuture shapeAverage suture size in transverse plane (mm)Suture stiffness (MPa)
  1. Suture thickness (on average) is indicated in number of voxels multiplied by voxel size (each being 0.15 mm). The stiffness of the suture used in each model is also summarized.

Sensitivity to shape and sizeM1aInterdigitated0.610
M2Interdigitated0.7510
M3Interdigitated0.7510
M4Interdigitated0.7510
M5aInterdigitated0.910
M6Butt0.310
M7Butt0.4510
M8Butt0.610
M9Butt0.7510
Sensitivity to stiffnessM1bInterdigitated0.61.2
M1cInterdigitated0.6800
M1dInterdigitated0.68, 000
M1eInterdigitated0.610, 000
M5bInterdigitated0.91.2
M5cInterdigitated0.9800
M5dInterdigitated0.98, 000
M5eInterdigitated0.910, 000

Boundary Conditions

It is important to impose accurate boundary conditions in FE analysis to obtain results that correspond to the complex biological condition (Curtis et al.,2008; Moazen et al., 2008a). However, as far as the objective of this sensitivity study is concerned, a simplified boundary condition was imposed on the skull. The skull was loaded under a 10 N vertical load, which represented the bite force (similar to the experimental data of Herrel et al., 2001, 2004) via the most anterior teeth, while three nodes at the posterior part of the skull were fully constrained (occipital condyle; see Fig. 1c). This approach has been employed in previous studies (Tanne et al.,1988; Rayfield, 2005a) for comparative analysis. Moazen et al. (2008a) showed that this simplified approach underestimates the stress magnitude across the skull and generates a high stress concentration at the constrained point that is an artefact of the loading condition. However, simplified boundary conditions can provide a qualitative stress pattern across the frontal and nasal bone that is similar to a more physiologically accurate load, one that incorporates the effect of muscle forces.

Simulations and Measurements

A linear static FE analysis was carried out in all cases using ABAQUS v6.9. In all the models, first and third principal strains (where equation image), along with the VM strains were compared for eight selected regions across the skull roof. These regions (see Table 2 and Fig. 3; regions R1–R8) were selected to capture the quantitative effect of aforementioned modeling parameters on the surface strain distribution in the adjacent bones. An average of nine nodes within each location reported. To understand which strain values were most sensitive to each of the three studied parameters, the mean and standard deviation (SD) of the strain values (i.e., first, third, and VM strains) across each region and within each sensitivity test was identified. Then, relative deviations (RD) of strain values were calculated (RD = SD × 100/Mean; see Hamby, 1994). Note absolute values of the RD were reported for third principal strains. In addition, the first principal strain contour plots of the skull roof were compared across the models for qualitative comparison.

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Figure 3. Model M5a in dorsal view with the locations that strain data are taken from.

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Table 2. Location of strain predictions
Points strain predictedLocation
R1Anterior part of the left frontal
R2Anterior part of the right frontal
R3Posterior part of the right frontal
R4Posterior part of the left frontal
R5Anterolateral corner of the left parietal
R6Anterior part of the left parietal
R7Anterior part of the right parietal
R8Anterolateral corner of the right parietal

RESULTS

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. CONCLUSIONS
  7. Acknowledgements
  8. Literature Cited

Sensitivity to Shape and Size

A qualitative comparison of the first principal strain across the models (Fig. 4) highlights that modeling the FP suture as an interdigitated suture (M1a–M5) increased the strain in the FP region when compared with the model with a fused suture (M1e). The models with a butt FP suture, M6–M9, did not show marked differences in the pattern of strain distribution with the model with a fused suture. However, the first principal strain was lower in the model with fused suture in the parietal (around the parietal foramen). In addition, similar patterns of strain distribution were obtained regardless of the size of suture.

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Figure 4. First principal strain corresponding to the models with FP suture (on left) in comparison to the model with fused FP suture (on right).

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A quantitative comparison between different modeled sutural shapes and sizes for the FP suture is summarised in Table 3 and Fig. 5. These results show that:

  • 1
    An increased thickness of the FP suture generally led to an increased absolute strain magnitude for all three types of strain values reported (Fig. 5). For example, comparing M6–M9, the first principal strain increased by about 15, 25, and 10% in R2, R3, and R6, respectively; comparing M1a–M5a, the first principal strain increased by about 48, 42, and 46% in R2, R3, and R6 (see Table 3).
  • 2
    Strain values in the anterior regions of the skull roof were more sensitive to the changes in the size of the FP suture than the posterior regions (Fig. 5). For example, the RDs for the third principal strain in M1a–M5a, in the anterior regions of R1 and R2, were about 70 and 110%, respectively, whereas in the posterior regions of R5 and R6, the RDs were about 4 and 13%, respectively (Table 3).
  • 3
    Modeling the FP as an unfused suture, either as an interdigitated (M1a) or a butt (M6) suture, increased the VM strain in most of the selected regions when compared to the model with fused suture, that is, M1e (but see for example R2 in M1a, and R5 and R8 in M6). Full results of suture stiffness models (M1e and M5e) are presented in Table 4.
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Figure 5. Comparison of the first and third principal strains and VM strain between the models developed in this study across the FP suture. Note FP suture modeled with elastic modulus of 10 MPa in all models except M1e that modeled with elastic modulus of 10, 000 MPa.

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Table 3. Summary of the first and third principal strains and VM strain values between the models developed in this study across the selected regions in the frontal and parietal
 R1R2R3R4R5R6R7R8
  1. SD and RD highlight the SD and RD in each column (R1-R8) for the models with interdigitated (M1a-M5a) and butt (M6-M9) suture. Note absolute values of the RD were reported for the third principal strains.

First        
 M1a1.03E-041.50E-041.72E-041.59E-049.75E-043.91E-044.14E-045.19E-04
 M28.50E-051.19E-042.64E-042.50E-049.80E-044.56E-044.37E-045.39E-04
 M35.27E-053.30E-046.23E-043.02E-049.44E-044.85E-044.23E-045.14E-04
 M44.92E-052.07E-045.59E-042.88E-049.29E-044.69E-044.17E-045.33E-04
 M5a1.12E-042.22E-042.45E-045.79E-059.75E-045.73E-044.02E-044.53E-04
 Mean8.50E-052.07E-042.64E-042.50E-049.75E-044.69E-044.17E-045.19E-04
 SD2.87E-058.11E-052.03E-041.02E-042.25E-056.53E-051.26E-053.44E-05
 RD33.739.176.940.92.313.93.06.6
 M61.69E-041.04E-041.05E-041.30E-048.48E-043.44E-044.86E-044.68E-04
 M71.83E-041.05E-041.09E-041.37E-048.42E-043.55E-045.17E-044.68E-04
 M81.98E-041.15E-041.23E-041.54E-048.52E-043.70E-045.37E-044.67E-04
 M92.05E-041.20E-041.31E-041.61E-048.55E-043.77E-045.54E-044.71E-04
 Mean1.90E-041.10E-041.16E-041.45E-048.50E-043.63E-045.27E-044.68E-04
 SD1.62E-057.79E-061.21E-051.44E-055.93E-061.49E-052.91E-051.60E-06
 RD8.57.110.49.90.74.15.50.3
Third        
 M1a−1.29E-04−6.38E-05−7.46E-05−2.43E-04−8.99E-04−7.42E-04−4.20E-04−1.04E-03
 M2−1.26E-04−6.41E-05−1.17E-04−3.32E-04−9.69E-04−8.58E-04−2.72E-04−1.06E-03
 M3−1.07E-04−1.86E-04−3.47E-04−3.24E-04−9.74E-04−9.16E-04−2.60E-04−9.81E-04
 M4−1.12E-04−9.11E-05−2.46E-04−5.08E-04−9.56E-04−9.16E-04−2.43E-04−1.02E-03
 M5a−3.13E-04−2.95E-04−2.30E-04−1.39E-04−9.91E-04−1.07E-03−5.05E-04−8.77E-04
 Mean−1.26E-04−9.11E-05−2.30E-04−3.24E-04−9.69E-04−9.16E-04−2.72E-04−1.02E-03
 SD8.75E-051.00E-041.09E-041.36E-043.52E-051.17E-041.16E-047.04E-05
 RD69.6109.747.141.93.612.842.66.9
 M6−4.88E-04−1.85E-04−1.26E-04−1.45E-04−6.76E-04−5.46E-04−2.93E-04−8.84E-04
 M7−5.45E-04−2.18E-04−1.41E-04−1.43E-04−6.61E-04−5.69E-04−3.12E-04−8.79E-04
 M8−5.96E-04−2.56E-04−1.66E-04−1.43E-04−6.54E-04−5.86E-04−3.16E-04−8.79E-04
 M9−6.21E-04−2.77E-04−1.81E-04−1.46E-04−6.53E-04−6.00E-04−3.22E-04−8.82E-04
 Mean−5.71E-04−2.37E-04−1.53E-04−1.44E-04−6.58E-04−5.77E-04−3.14E-04−8.81E-04
 SD5.88E-054.05E-052.47E-051.60E-061.08E-052.35E-051.25E-052.55E-06
 RD10.317.116.11.11.64.14.00.3
VM        
 M1a2.03E-041.93E-042.25E-043.55E-041.62E-039.95E-047.23E-041.38E-03
 M21.87E-041.59E-043.53E-045.10E-041.69E-031.15E-036.31E-041.41E-03
 M31.40E-044.69E-048.79E-045.43E-041.66E-031.22E-036.09E-041.32E-03
 M41.46E-042.80E-047.53E-047.21E-041.63E-031.22E-035.89E-041.37E-03
 M5a4.00E-044.52E-044.12E-041.78E-041.70E-031.43E-037.89E-041.17E-03
 Mean1.87E-042.80E-044.12E-045.10E-041.66E-031.22E-036.31E-041.37E-03
 SD1.07E-041.44E-042.78E-042.05E-043.41E-051.57E-048.49E-059.66E-05
 RD57.051.467.440.22.012.913.57.0
 M66.40E-042.62E-042.01E-042.39E-041.33E-037.88E-046.97E-041.21E-03
 M77.11E-042.98E-042.19E-042.42E-041.31E-038.19E-047.42E-041.20E-03
 M87.78E-043.47E-042.53E-042.57E-041.31E-038.48E-047.66E-041.20E-03
 M98.10E-043.73E-042.74E-042.67E-041.32E-038.67E-047.87E-041.21E-03
 Mean7.45E-043.23E-042.36E-042.50E-041.31E-038.33E-047.54E-041.21E-03
 SD7.53E-054.98E-053.31E-051.31E-057.40E-063.43E-053.86E-053.14E-06
 RD10.115.414.05.20.64.15.10.3
Table 4. Summary of the first and third principal strains and VM strain values for M1a-e and M5a-e in the selected regions when varying the elastic module of this suture
 M1a-eM5a-e
R1R2R3R4R5R6R7R8R1R2R3R4R5R6R7R8
First                
 E = 1.21.08E-041.58E-041.98E-041.79E-049.75E-043.99E-044.02E-045.23E-041.84E-044.47E-045.06E-043.14E-051.03E-038.05E-046.71E-043.77E-04
 E = 101.03E-041.50E-041.72E-041.59E-049.75E-043.91E-044.14E-045.19E-041.12E-042.22E-042.45E-045.79E-059.75E-045.73E-044.02E-044.53E-04
 E = 8008.57E-051.42E-041.41E-041.27E-049.92E-043.03E-043.51E-044.93E-047.27E-059.87E-051.50E-041.88E-049.37E-043.32E-042.80E-044.82E-04
 E = 8, 0009.73E-051.87E-041.39E-041.07E-049.62E-043.19E-043.78E-044.88E-049.63E-051.85E-041.14E-047.51E-059.16E-043.40E-043.97E-044.67E-04
 E = 10, 0009.83E-051.81E-041.36E-041.02E-049.58E-043.26E-044.01E-044.87E-049.81E-051.90E-041.05E-046.02E-059.12E-043.58E-044.13E-044.67E-04
 Mean9.83E-051.58E-041.41E-041.27E-049.75E-043.26E-044.01E-044.93E-049.81E-051.90E-041.50E-046.02E-059.37E-043.58E-044.02E-044.67E-04
 SD8.32E-061.94E-052.68E-053.35E-051.34E-054.40E-052.49E-051.75E-054.23E-051.31E-041.67E-046.11E-055.09E-052.06E-041.44E-044.14E-05
 RD8.512.319.026.21.413.56.23.543.268.6111.4101.55.457.635.88.9
Third                
 E = 1.2−1.32E-04−6.6E-05−8.5E-05−2.70E-04−9.07E-04−7.55E-04−4.08E-04−1.04E-03−5.60E-04−6.15E-04−4.87E-04−8.21E-05−1.29E-03−1.72E-03−9.34E-04−7.05E-04
 E = 10−1.29E-04−6.38E-05−7.46E-05−2.43E-04−8.99E-04−7.42E-04−4.20E-04−1.04E-03−3.13E-04−2.95E-04−2.30E-04−1.39E-04−9.91E-04−1.07E-03−5.05E-04−8.77E-04
 E = 800−1.12E-04−6.63E-05−6.3E-05−1.50E-04−8.61E-04−5.52E-04−3.75E-04−1.02E-03−1.32E-04−6.13E-05−6.52E-05−1.65E-04−8.75E-04−6.07E-04−3.02E-04−9.53E-04
 E = 8, 000−1.07E-04−8.2E-05−6.2E-05−9.96E-05−8.16E-04−5.34E-04−3.43E-04−1.01E-03−1.06E-04−8.56E-05−5.56E-05−6.40E-05−7.97E-04−5.22E-04−2.94E-04−9.10E-04
 E = 10, 000−1.07E-04−8.49E-05−6.09E-05−9.37E-05−8.12E-04−5.35E-04−2.94E-04−1.01E-03−1.06E-04−8.64E-05−5.31E-05−5.61E-05−7.89E-04−5.21E-04−2.91E-04−9.05E-04
 Mean−1.12E-04−6.63E-05−6.31E-05−1.50E-04−8.61E-04−5.52E-04−3.75E-04−1.02E-03−1.32E-04−8.64E-05−6.52E-05−8.21E-05−8.75E-04−6.07E-04−3.02E-04−9.05E-04
 SD1.20E-051.00E-051.05E-058.13E-054.47E-051.14E-045.10E-051.28E-051.97E-042.36E-041.88E-044.80E-052.06E-045.19E-042.77E-049.62E-05
 RD10.715.116.654.15.220.713.61.2149.8272.9288.858.423.585.592.010.6
VM                
 E = 1.22.09E-042.02E-042.61E-043.97E-041.63E-031.01E-037.01E-041.39E-037.25E-049.33E-048.61E-041.05E-042.02E-032.27E-031.41E-039.40E-04
 E = 102.03E-041.93E-042.25E-043.55E-041.62E-039.95E-047.23E-041.38E-034.00E-044.52E-044.12E-041.78E-041.70E-031.43E-037.89E-041.17E-03
 E = 8001.73E-041.84E-041.87E-042.41E-041.61E-037.54E-046.29E-041.36E-031.86E-041.39E-041.97E-043.07E-041.57E-038.21E-045.03E-041.28E-03
 E = 8, 0001.78E-042.40E-041.82E-041.79E-041.54E-037.58E-046.26E-041.35E-031.76E-042.39E-041.49E-041.21E-041.49E-037.63E-046.08E-041.23E-03
 E = 10, 0001.78E-042.34E-041.78E-041.70E-041.54E-037.64E-046.11E-041.35E-031.77E-042.45E-041.38E-041.01E-041.48E-037.75E-046.22E-041.23E-03
 Mean1.78E-042.02E-041.87E-042.41E-041.61E-037.64E-046.29E-041.36E-031.86E-042.45E-041.97E-041.21E-041.57E-038.21E-046.22E-041.23E-03
 SD1.64E-052.51E-053.57E-051.03E-044.51E-051.34E-045.04E-051.78E-052.39E-043.18E-043.06E-048.65E-052.27E-046.52E-043.63E-041.35E-04
 RD9.212.419.142.82.817.68.01.3128.7129.8155.371.314.579.458.411.0

Sensitivity to Stiffness

The effect of varying the stiffness of the FP suture on the regional strain is shown in Table 4 and Fig. 6. These results show that decreasing the elastic modulus of the FP suture generally increased the magnitude of the third principal strain (but see for example R2 and R8 in M1a–e and M5a–e, respectively). Table 4 highlights the heightened sensitivity of the M5a–e (the expanded suture model), compared with the M1a–e (not expanded suture model) to changes in the stiffness. For example, considering R3 in M5a–e, the RDs for the first and third principal strains, as well as the VM strains, were about 111, 289, and 155%, respectively, while in M1a–e, these were about 19, 17, and 19%, respectively. Also, a comparison of the VM strain between M1e and M5e, for the model with fused suture, showed <5% difference for all the regions except R3, R4, and R8, where the values were about 29, 68, and 10%, respectively.

thumbnail image

Figure 6. Comparison of the first and third principal strains and VM strain between M1a–e and M5a–e across the FP suture varying the elastic module of this suture. Note elastic modulus is in MPa.

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DISCUSSION

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. CONCLUSIONS
  7. Acknowledgements
  8. Literature Cited

General Principles and Limitations

Computational modeling of biological structures generally requires simplifications and assumptions (Alexander, 2003). Understanding the effect of these simplifications on the outcome of the results is an important step that can be achieved using sensitivity analysis. Here, we aimed to address these simplifications in relation to the shape, size, and stiffness of the FP suture in a FE model of a lacertid skull. Considering the aim of this study, several key assumptions were undertaken. First, the bone was modeled as an isotropic structure, even though it is well known to be an anisotropic structure (Wang and Dechow, 2006). Therefore, this assumption could have had an effect on the magnitude of the strains predicted here; however, the pattern of the results obtained could be still valid (Strait et al., 2005). Second, a simplified loading condition was imposed upon the skull wherein a pure bending moment was generated via a bite force that was applied to the most anterior teeth, while concurrently, the skull was fully constrained at three nodes in the occipital condyle (as opposed to explicitly modeling the muscles and joint forces). These boundary conditions have a direct influence on the magnitudes of the strains reported here. Third, only one suture (FP) was incorporated, while in reality, the skull has multiple sutures. It is likely that the juxta-sutures would interact and distribute the strain across the skull more uniformly under different loading conditions. Therefore, the modeling of a single suture may have led to an unrealistic strain prediction. These aforementioned assumptions may have altered the strain values reported, nevertheless, remained consistent in each model to ensure the relative comparison between the cases remained valid. Furthermore, the present results are intended as a preliminary indication to a future study that will incorporate a more comprehensive biomechanical model.

Sensitivity Analysis

Sensitivity to shape and size of the suture in this study was carried out by virtual expansion of the interdigitated suture (M1a–M5). Sutural expansion not only reduced the level of interdigitation but also increased the volume of the suture. Therefore, to assess solely the effect of sutural size, butt suture models (M6–M9) were developed. Inevitably, the position of the butt suture models was not the same position as interdigitated suture models (see Fig. 2 for M10) therefore no comparison between the aforementioned models were made (i.e., M1a–M5 vs. M6–M9). Instead, the focus was on the level of differences in the results within each group of the models and in comparison to the fused suture model (M1e).

No major differences were observed in the strain pattern in the FP model with varying thicknesses in either of the interdigitated or butt suture models. In contrast, the magnitudes of the strains were highly sensitive to changes in these parameters. Quantitative comparisons across the models showed that the difference in strain is greater following an approximately two fold increase in the width of the suture (see Table 3 for M1a–5a), compared with changes by several orders of magnitude to the stiffness (see Table 4 for M1a–e). These results suggest that in modeling the interdigitated sutures, strain predictions in the neighboring bones are possibly more sensitive to the thickness than the stiffness of the suture. These findings are likely linked to increase of the wavelength of the suture as its volume increases and it becomes more similar to a butt joint. Therefore, movement across the suture is increased and strain within the bone is reduced (Jasinoski et al.,2010).

High RD were found when the suture stiffness of the model with expanded suture was varied (M5a–e), thus suggesting that in a model with expanded suture neighboring bones experience strain magnitudes that are highly sensitive to the stiffness of the suture. Heighten sensitivity of strain in adjacent bones to the stiffness of suture in the expanded suture models suggests that the segmentation process and the possible expansion of the suture, for example to obtain a better mesh quality for FE models can magnify the sensitivity of the results to the stiffness of the suture. While caution must be taken in interpretation of the results in such cases, it could be possible that a higher elastic property is required to be assigned to a model with an expanded suture to compensate for the effect of expansion. Overall, this point highlights (1) in modeling sutures it is important to capture correctly the thickness and geometry with high resolution CT scanning and careful segmentation and (2) the importance of incorporating more realistic elastic properties for the cranial joints, and thus, challenges further experimental data collection.

The higher sensitivity of the strain values (higher RD) in the anterior regions (R1-4), compared with the posterior regions (R5-8), could be an artefact of the boundary conditions by which the skull was loaded; the anterior part of the skull roof was unconstrained, while the posterior part was fully constrained. Therefore, varying the properties of the sutures had more of an impact on the anterior regions than the posterior regions (considering the movement across the FP suture). This observation highlights the importance of applying physiological loading conditions to the skull where muscle forces and joint forces would be expected (Duda et al.,1998; Curtis et al., 2008,2010; Moazen et al., 2008a,b).

The two models that replicated a fused FP suture, M1e and M5e, were segmented into different thicknesses and replicated as bone. Therefore, ideally both models should have generated similar results across the selected regions. While this was the case for majority of regions (difference of <5%), the difference between the strain values was higher than expected at R3 and R4 (29 and 68%). R3 and R4 are located on the anterior part of the skull and are relatively close to the FP suture. In including the suture in the FE model, and expanding it, it is likely that undesirable elements (with high aspect ratios) were formed at the interface between the bone and suture that resulted in discretization error (Schmidt et al., 2009). Similar effect was recently reported by Reed et al. (2011) in modeling the sutures in a mandible model where authors highlighted that this error can increase closer to the suture. Further studies are required to investigate discretization error when using FE models to investigate role of cranial sutures at the suture-bone interface.

Biomechanics of FP Region

Understanding form and function of the FP region has been of interest among functional morphologists (Frazzetta,1962; Smith and Hylander,1985; Herrel et al.,2000; Evans, 2008). It could potentially shed light on the evolution of cranial kinesis (Metzger, 2002) and the upper temporal fenestra (Carrol,1982; Evans,2003; Curtis et al., 2011). In Squamata (lizards, snakes, and amphisbaenians), there is a large diversity in the structure of this region. For example, in Iguanidae, Agamidae, Anguidae, Xenosauridae, and Varanidae, the upper temporal fenestra is usually open and the FP suture is relatively straight (Throckmorton,1976; Smith and Hylander,1985; Evans, 2008). Whereas in Cordyliformes, and Lacertidae the upper temporal fenestra is closed, or reduced, while the FP suture is highly interdigitated (Barahona and Barbadillo,1998; Evans,2008; Costantini et al.,2010). However, in Xantusiidae, the upper temporal fenestra is closed and the FP suture is relatively straight (Evans, 2008). The question that remains to be answered is whether the biomechanical factors play a role in such diversity. The FE method can be employed to investigate such hypotheses, yet, there are few studies that have implemented this technique in the study of the Squamata skulls (Moreno et al.,2008; Moazen et al., 2008a,b, 2009a,b).

Considering the assumptions that were made in this study, care should be taken in interpretation of results about the evolution of the cranial kinesis and upper temporal fenestra. Nevertheless, considering that the high level of strain present in the FP models with interdigitated suture, that is, M1a-5a could be reduced with the incorporation of the muscle forces, the cranial movement at the FP joint (see Frazzetta,1962; Metzger,2002; Payne et al., 2011) that occurs in geckoes (Herrel et al.,2000; Daza et al., 2008) and varanids (Smith and Hylander, 1985) is unlikely to be present in L. bilineata. In fact, this study suggests that such an active movement can impose an increase in the level of strain in the parietal area and therefore a scarce or null kinetic movement at this junction. Indeed, understanding the mechanism behind the ossification of the FP scales in the Lacertidae in this region becomes even more interesting. Small movements at this joint can generate a high level of compressive strain in the FP suture (Herring and Teng, 2000) that can potentially trigger the ossification of the scales in this region. Addressing these questions, in future studies might help to define the selective pressures linking variation in suture interdigitation to ecology and behavior of lacertid species.

CONCLUSIONS

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. CONCLUSIONS
  7. Acknowledgements
  8. Literature Cited

This study demonstrates the sensitivity of strain predictions in FE studies to the shape, size, and stiffness of cranial sutures. Similar patterns of strain distribution were obtained regardless of the size of the suture, yet the strain magnitudes were highly sensitive to this modeling parameter. In modeling the interdigitated sutures, the difference in strain predictions in the neighboring bones was greater following an approximately two fold increase in the width of the suture, compared with changes by several orders of magnitude to the stiffness (in the range of 1.2–10, 000 MPa). However, in a model with expanded interdigitated suture, strain magnitudes were highly sensitive to the stiffness of the suture. Future studies will be required to measure the stiffness of cranial joints in lizards and to assess the possible degree of movement at the FP suture in Lacertidae. A greater understanding of the sutures in the skull roof may elucidate the factors underlying the growth and development of the scales in this region.

Acknowledgements

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. CONCLUSIONS
  7. Acknowledgements
  8. Literature Cited

This work is partially supported by Ornis italica. The authors thank Philippe Young and Simpleware team for their cooperation with the use of their software for this study; Susan E Evans (Department of Anatomy and Developmental Biology, University College London) and Adam J Stops (Institute of Medical and Biological Engineering, University of Leeds) for discussion and comments on this study; and three anonymous reviewers for their insightful comments on the earlier version of this manuscript.

Literature Cited

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. CONCLUSIONS
  7. Acknowledgements
  8. Literature Cited