A Sensitivity Analysis to the Role of the Fronto-Parietal Suture in Lacerta bilineata: A Preliminary Finite Element Study MEHRAN MOAZEN, 1 * DAVID COSTANTINI, 2 AND EMILIANO BRUNER 3 1 Institute of Medical and Biological Engineering, School of Mechanical Engineering, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, UK 2 Institute for Biodiversity, Animal Health and Comparative Medicine, College of Medical, Veterinary and Life Sciences, University of Glasgow, Graham Kerr Building, Glasgow G12 8QQ, UK 3 Grupo de Paleobiologı ´a, Centro Nacional de Investigacion sobre la Evolucion Humana, Paseo de Atapuerca s/n, 09002, Burgos, Spain ABSTRACT Cranial sutures are sites of bone growth and development but micro- movements 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, 296:198–209, 2013. V C 2012 Wiley Periodicals, Inc. Key words: biomechanics; lizard; skull; finite element analysis 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 (Her- ring, 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 termi- nated, 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; Her- rel 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 *Correspondence to: Mehran Moazen, PhD, Institute of Medical and Biological Engineering, School of Mechanical Engineering, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, UK. Fax: þ44 (0) 113 24 24611. E-mail: Mehran_Moazen@ yahoo.com Received 13 June 2012; Accepted 22 October 2012. DOI 10.1002/ar.22629 Published online 28 November 2012 in Wiley Online Library (wileyonlinelibrary.com). THE ANATOMICAL RECORD 296:198–209 (2013) V V C 2012 WILEY PERIODICALS, INC.
Transcript
A Sensitivity Analysis to the Role of theFronto-Parietal Suture in Lacerta
bilineata: A Preliminary Finite ElementStudy
MEHRAN MOAZEN,1* DAVID COSTANTINI,2 AND EMILIANO BRUNER3
1Institute of Medical and Biological Engineering, School of Mechanical Engineering,University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, UK
2Institute for Biodiversity, Animal Health and Comparative Medicine, College of Medical,Veterinary and Life Sciences, University of Glasgow, Graham Kerr Building,
Glasgow G12 8QQ, UK3Grupo de Paleobiologıa, Centro Nacional de Investigaci�on sobre la Evoluci�on Humana,
Paseo de Atapuerca s/n, 09002, Burgos, Spain
ABSTRACTCranial sutures are sites of bone growth and development but micro-
movements at these sites may distribute the load across the skull moreevenly. 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 sensitivityof the strain predictions to the aforementioned parameters in several modelsof fronto-parietal (FP) suture in Lacerta bilineata. For the purpose of thisstudy, simplifications were made in relation to modeling the bone propertiesand the skull loading. Results highlighted that modeling the FP as either aninterdigitated suture or a simplified butt suture, did not reduce the straindistribution in the FP region. Sensitivity tests showed that similar patternsof strain distribution can be obtained regardless of the size of the suture, orassigned stiffness, yet the exact magnitudes of strains are highly sensitive tothese parameters. This study raises the question whether the morphogenesisof epidermic scales in the FP region in the Lacertidae is related to highstrain fields in this region, because of micromovement in the FP suture.Anat Rec, 296:198–209, 2013. VC 2012 Wiley Periodicals, Inc.
Key words: biomechanics; lizard; skull; finite element analysis
Sutures are sites of bone deposition and growth, whichundergo many changes in terms of their stiffness andform over the growth and development of the skull (Her-ring, 2008). However, the role and function of sutures inthe adult skull has been the subject of debate amongfunctional morphologists and palaeontologists. In fact, ina lot of taxa, many sutures do not fuse after the growthand developmental processes have effectively termi-nated, and the possible biomechanical roles of theseelements during ontogeny and phylogeny are still notfully understood (Frazzetta, 1962; Herring, 1972; DeVree and Gans, 1987; Jaslow, 1990; Thomson, 1995; Her-rel 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; Reedet al., 2011; Jones et al., 2011). Micromovement atsutures may potentially lead to a uniform pattern ofload distribution across the skull. This hypothesis hasbeen tested using experimental strain recorded in vivo
*Correspondence to: Mehran Moazen, PhD, Institute ofMedical and Biological Engineering, School of MechanicalEngineering, University of Leeds, Woodhouse Lane, Leeds, LS29JT, UK. Fax: þ44 (0) 113 24 24611. E-mail: [email protected]
Received 13 June 2012; Accepted 22 October 2012.
DOI 10.1002/ar.22629Published online 28 November 2012 in Wiley Online Library(wileyonlinelibrary.com).
THE ANATOMICAL RECORD 296:198–209 (2013)
VVC 2012 WILEY PERIODICALS, INC.
or in vitro models (Smith and Hylander, 1985; Raffertyand Herring, 1999; Kupczik et al., 2007).
Computational models are an additional means oftesting hypotheses relating to skull mechanics, strain,and loading. The finite element (FE) method hasrecently gained popularity to analyze the role of suturesas modulators of the mechanical response of the skull toloading (Rayfield, 2005b; Jasinoski et al., 2009; Moazenet al., 2009b). Validity and sensitivity of these FE modelsis an important issue which needs to be addressed (Rosset al., 2005; Kupczik et al., 2007; Gr€oning et al., 2009;Bright and Rayfield, 2011; Panagiotopoulou et al., 2011,2012; Rayfield, 2011). While testing the validity of FEmodels is possible in the case of large living taxa, it ismore challenging or impossible in the case of small ani-mals or fossils. In these cases, sensitivity analysis canbe considered as a way to understand how these modelsrespond under a wide range of input parameters. Thesetypes of studies can be informative in terms of predicting
the relative effect of certain parameters on the overallpattern of outputs. Several studies in the literature haveassessed the sensitivity of FE models to bone materialproperty 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, inthe case of incorporating the sutures in the FE models,few studies have assessed the sensitivity of the FEresults to the sutures morphology and stiffness (Kupcziket 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 Eur-asia and Africa (Arnold et al., 2007; Cernansky, 2010).In these lizards, the head is covered by plate like scalesand supraciliary granules, which are composed of layersof keratin formed from cells produced by the living basallayer of the epidermis (the stratum germinativum). Epi-dermic scales can cover dermic bony plates called
Fig. 1. A: Model of head in dorsal view. B: Micro-CT section of the head showing the high level ofinterdigitation of the fronto-parietal suture (FPS) in Lacerta bilineata in transverse plane. C: Left lateralview of the head highlighting the applied force and constraint point in the FE models.
SENSITIVITY ANALYSIS IN A LIZARD SUTURE 199
osteoderms. In turn, the layer of osteoderms covers thedorsal bones of the skull and is closely attached to them,especially in Lacertidae (Arnold et al., 2007; Ljubisavl-jevic et al., 2011). Recent studies suggest that the fronto-parietal (FP) suture is an important morphogenetic ele-ment of cephalic scales and skull in lacertids (Barahonaand Barbadillo, 1998; Bruner and Costantini, 2007, 2009;Costantini et al., 2010). The tight developmental connec-tion between scales and bones is also supported by theirshape variation. The variation of the cephalic scales islargely characterized by a size-related pattern associatedwith negative allometry of the anterior region (frontalscales) and positive allometry of the posterior region(occipital, parietal, and interparietal scales; see Monteiroand Abe, 1997; Bruner et al., 2005; Bruner and Costan-tini, 2007). This anteroposterior growth gradientmatches the pattern of ossification of the underlying cra-nial bones (Barahona and Barbadillo, 1998).
The FP suture lies under the FP scales, thus betweenthe anterior and posterior regions of the skull. It iswidely considered to have a major evolutionary andontogenetic role as a structural element during growthand development (Frazzetta, 1962; Smith and Hylander,1985; Herrel et al., 2000; Metzger, 2002). Shape analysesrevealed relevant patterns of morphological variationassociated with this suture, related to allometric changes(Bruner and Costantini, 2009). The position of thesuture within the spatial framework of cephalic scales isconstant, independent of the species and of the allomet-ric changes, suggesting a certain morphogenetic andphylogenetic stability (Costantini et al., 2010). The mor-phology of the suture (joint with Type-A interdigitationsas described in Jones et al., 2011), is highly convolutedand interdigitated in the western green lizard Lacertabilineata (Fig. 1) as well as in the other lacertid speciesinvestigated (Costantini et al., 2010). This suggestsscarce or null kinetic movements at this junction.
The aim of this study was to analyze the sensitivity ofstrain predictions to the shape, size, and stiffness of theFP suture in L. bilineata using FE method. Several FEmodels were developed in which aforementioned parame-ters were varied. To assess the effect of these parameterson the strain predictions, the first and third principalstrains and von Mises (VM) strain across the skull roofwere recorded and compared between the models.
MATERIALS AND METHODS
FE models of L. bilineata skull were developed wherethe FP suture was the only modeled suture. In the firststep, level of interdigitation of the FP suture wasdecreased through virtual expansion of the suture (sensi-tivity to shape and size). However, this also increased thevolume of the suture. Therefore, in the second step a se-ries of imaginary models were developed in which the FPsuture modeled as a butt suture to solely assess the effectof sutural size (sensitivity to size). In the third step, elas-tic modulus of the FP suture was varied in two of theinterdigitated 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 usinghigh-resolution micro-Computed Tomography (micro-CT)
at 45 kV X-ray tube voltage, 88 mA, 0.35� rotation stepand 800 ns exposure time per individual shadow projec-tion (lCT-80, Scanco Medical, Switzerland). The voxelsize was 0.036 � 0.036 � 0.036 mm, with an average ex-posure time of 120 min per scan. ScanIP v2.1(Simpleware, UK) image processing software was usedto segment the skull and FP suture from the CT sliceimages (see Fig. 1). Subsequently, the original voxel sizewas re-sampled (i.e., skipping voxels to reduce the sizeof model) to 0.15 � 0.15 � 0.15 mm.
In this study the FP suture, together with the lateralsutures associated with the anteroposterior separation ofthe skull roof, were analyzed (Fig. 2). The sutures weresegmented manually in Model 1a (M1a). Then, four addi-tional models developed where the segmented suturewas expanded by one voxel size (i.e. 0.15 mm) in x, y,and z direction individually, that is, M2, M3, and M4respectively and in combination in all three directions inM5a. The aforementioned approach led to decrease ininterdigitation level and increase in thickness of FPsuture (sensitivity to shape and size). To solely assessthe effect of thickness a series of imaginary butt (end-to-end) suture models were developed. The position of thebutt suture was determined in the transverse plane. Themost anterior and posterior points of the segmented FPsuture in M1a were used to calculate the average point(in Y direction as shown in Fig. 2). This point was usedto position the butt suture. The butt condition was mod-eled with 2, 3, 4, and 5 pixel in width in the models M6–M9, respectively (sensitivity to size; see Fig. 2 for a sum-mary of the models). Using these models, the local strainfields were analyzed to ascertain the influence of theshape and size of the FP suture.
All the aforementioned models were transferred intomeshed solid geometries (ScanFE v2.1-Simpleware, UK)that were composed of solid tetrahedral elements (fournoded elements with linear displacement behavior). Itshould be noted that on average, there were about sixelements across the thickness of the suture in M1a andnumber of elements across the suture was higher in theexpanded suture models. Each model was consisted ofover one million elements. All models were thenimported into ABAQUS v6.9 (Simulia, Providence, RI) inpreparation for FE analysis.
Material Properties
Bone was modeled as a homogeneous, isotropic materialwith an elastic modulus of 10, 000 MPa and a Poisson’s ra-tio of 0.3 in all the models (Rayfield et al., 2001; Moazenet al., 2009a,b). Although bone is known to be anisotropic,previous studies (Strait et al., 2005) have shown that com-parable patterns of strain are formed with an isotropicassumption. To assess the sensitivity of the local straindistribution to the shape and size of the FP suture, anelastic modulus of 10 MPa was assumed. This elastic mod-ulus was subsequently varied based on publishedexperimental data (McLaughlin et al., 2000; Radhak-rishnan and Mao, 2004; Kupczik et al., 2007) from 10 MPain M1a and M5a to 1.2 MPa, 800 MPa, 8, 000 MPa, and 10,000 MPa (fused) in M1b-e and M5b-e, respectively, toassess the sensitivity of the results to the stiffness of theFP suture. Note, M1e and M5e both represented a fusedsuture. A Poisson’s ratio of 0.3 was used for all sutures.See Table 1 for a summary of the models.
Suture thickness (on average) is indicated in number of voxels multiplied by voxel size (each being 0.15 mm). The stiffnessof the suture used in each model is also summarized.
Fig. 2. Model of the head in dorsal view based on micro-CT aftersegmentation of the FP suture and other sutures associated with theanteroposterior separation of the skull roof. FP suture was modeledusing different geometry (interdigitated and butt) and different thick-
ness, to evaluate the influence of these choices in the FE models.Please note that M10 was not modeled and used for any FE analysisbut highlights the relative position of the interdigitated and butt suturein M1a and M6.
SENSITIVITY ANALYSIS IN A LIZARD SUTURE 201
Boundary Conditions
It is important to impose accurate boundary conditionsin FE analysis to obtain results that correspond to thecomplex biological condition (Curtis et al., 2008; Moazenet al., 2008a). However, as far as the objective of this sen-sitivity study is concerned, a simplified boundarycondition was imposed on the skull. The skull was loadedunder a 10 N vertical load, which represented the biteforce (similar to the experimental data of Herrel et al.,2001, 2004) via the most anterior teeth, while three nodesat the posterior part of the skull were fully constrained(occipital condyle; see Fig. 1c). This approach has beenemployed in previous studies (Tanne et al., 1988; Ray-field, 2005a) for comparative analysis. Moazen et al.(2008a) showed that this simplified approach underesti-mates the stress magnitude across the skull andgenerates a high stress concentration at the constrainedpoint that is an artefact of the loading condition. How-ever, simplified boundary conditions can provide aqualitative stress pattern across the frontal and nasalbone that is similar to a more physiologically accurateload, one that incorporates the effect of muscle forces.
Simulations and Measurements
A linear static FE analysis was carried out in all casesusing ABAQUS v6.9. In all the models, first and thirdprincipal strains (wheree1 > e2 > e3), along with the VMstrains were compared for eight selected regions acrossthe skull roof. These regions (see Table 2 and Fig. 3;regions R1–R8) were selected to capture the quantitativeeffect of aforementioned modeling parameters on thesurface strain distribution in the adjacent bones. An av-erage of nine nodes within each location reported. Tounderstand which strain values were most sensitive toeach of the three studied parameters, the mean andstandard deviation (SD) of the strain values (i.e., first,third, and VM strains) across each region and withineach sensitivity test was identified. Then, relative devia-tions (RD) of strain values were calculated (RD ¼ SD �100/Mean; see Hamby, 1994). Note absolute values of theRD were reported for third principal strains. In addition,the first principal strain contour plots of the skull roofwere compared across the models for qualitativecomparison.
RESULTS
Sensitivity to Shape and Size
A qualitative comparison of the first principal strainacross the models (Fig. 4) highlights that modeling theFP suture as an interdigitated suture (M1a–M5)increased the strain in the FP region when comparedwith the model with a fused suture (M1e). The modelswith a butt FP suture, M6–M9, did not show marked dif-ferences in the pattern of strain distribution with themodel with a fused suture. However, the first principalstrain was lower in the model with fused suture in theparietal (around the parietal foramen). In addition, simi-lar patterns of strain distribution were obtainedregardless of the size of suture.
A quantitative comparison between different modeledsutural shapes and sizes for the FP suture is summar-ised in Table 3 and Fig. 5. These results show that:
1. An increased thickness of the FP suture generally ledto an increased absolute strain magnitude for allthree types of strain values reported (Fig. 5). Forexample, comparing M6–M9, the first principal strainincreased by about 15, 25, and 10% in R2, R3, and
TABLE 2. Location of strain predictions
Points strainpredicted Location
R1 Anterior part of the left frontalR2 Anterior part of the right frontalR3 Posterior part of the right frontalR4 Posterior part of the left frontalR5 Anterolateral corner of the
left parietalR6 Anterior part of the left parietalR7 Anterior part of the right parietalR8 Anterolateral corner of the
right parietal
Fig. 3. Model M5a in dorsal view with the locations that strain dataare taken from.
202 MOAZEN ET AL.
R6, respectively; comparing M1a–M5a, the first prin-cipal 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 roofwere more sensitive to the changes in the size of theFP suture than the posterior regions (Fig. 5). Forexample, the RDs for the third principal strain inM1a–M5a, in the anterior regions of R1 and R2, wereabout 70 and 110%, respectively, whereas in the pos-terior regions of R5 and R6, the RDs were about 4and 13%, respectively (Table 3).
3. Modeling the FP as an unfused suture, either as aninterdigitated (M1a) or a butt (M6) suture, increasedthe VM strain in most of the selected regions whencompared to the model with fused suture, that is,M1e (but see for example R2 in M1a, and R5 and R8in M6). Full results of suture stiffness models (M1eand M5e) are presented in Table 4.
Sensitivity to Stiffness
The effect of varying the stiffness of the FP suture onthe regional strain is shown in Table 4 and Fig. 6. Theseresults show that decreasing the elastic modulus of theFP suture generally increased the magnitude of thethird principal strain (but see for example R2 and R8 inM1a–e and M5a–e, respectively). Table 4 highlights the
heightened sensitivity of the M5a–e (the expandedsuture model), compared with the M1a–e (not expandedsuture model) to changes in the stiffness. For example,considering R3 in M5a–e, the RDs for the first and thirdprincipal strains, as well as the VM strains, were about111, 289, and 155%, respectively, while in M1a–e, thesewere about 19, 17, and 19%, respectively. Also, a com-parison of the VM strain between M1e and M5e, for themodel with fused suture, showed <5% difference for allthe regions except R3, R4, and R8, where the valueswere about 29, 68, and 10%, respectively.
DISCUSSION
General Principles and Limitations
Computational modeling of biological structures gener-ally requires simplifications and assumptions (Alexander,2003). Understanding the effect of these simplifications onthe outcome of the results is an important step that canbe achieved using sensitivity analysis. Here, we aimed toaddress these simplifications in relation to the shape, size,and stiffness of the FP suture in a FE model of a lacertidskull. Considering the aim of this study, several keyassumptions were undertaken. First, the bone was mod-eled as an isotropic structure, even though it is wellknown to be an anisotropic structure (Wang and Dechow,2006). Therefore, this assumption could have had an effect
Fig. 4. First principal strain corresponding to the models with FP suture (on left) in comparison to themodel with fused FP suture (on right).
SENSITIVITY ANALYSIS IN A LIZARD SUTURE 203
on the magnitude of the strains predicted here; however,the pattern of the results obtained could be still valid (Straitet al., 2005). Second, a simplified loading condition wasimposed upon the skull wherein a pure bending momentwas generated via a bite force that was applied to the mostanterior teeth, while concurrently, the skull was fully con-strained at three nodes in the occipital condyle (as opposedto explicitly modeling the muscles and joint forces). Theseboundary conditions have a direct influence on the magni-tudes of the strains reported here. Third, only one suture(FP) was incorporated, while in reality, the skull has multi-ple sutures. It is likely that the juxta-sutures would interactand distribute the strain across the skull more uniformlyunder different loading conditions. Therefore, the modeling
of a single suture may have led to an unrealistic strain pre-diction. These aforementioned assumptions may havealtered the strain values reported, nevertheless, remainedconsistent in each model to ensure the relative comparisonbetween the cases remained valid. Furthermore, the pres-ent results are intended as a preliminary indication to afuture study that will incorporate a more comprehensivebiomechanical model.
Sensitivity Analysis
Sensitivity to shape and size of the suture in thisstudy was carried out by virtual expansion of the inter-digitated suture (M1a–M5). Sutural expansion not only
TABLE 3. Summary of the first and third principal strains and VM strain values between the models devel-oped in this study across the selected regions in the frontal and parietal
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.
204 MOAZEN ET AL.
reduced the level of interdigitation but also increased thevolume of the suture. Therefore, to assess solely the effectof sutural size, butt suture models (M6–M9) were devel-oped. Inevitably, the position of the butt suture modelswas not the same position as interdigitated suture models(see Fig. 2 for M10) therefore no comparison between theaforementioned models were made (i.e., M1a–M5 vs. M6–M9). Instead, the focus was on the level of differences inthe results within each group of the models and in compar-ison to the fused suture model (M1e).
No major differences were observed in the strain pat-tern in the FP model with varying thicknesses in eitherof the interdigitated or butt suture models. In contrast,the magnitudes of the strains were highly sensitive tochanges in these parameters. Quantitative comparisonsacross the models showed that the difference in strain isgreater following an approximately two fold increase inthe width of the suture (see Table 3 for M1a–5a), com-pared with changes by several orders of magnitude tothe stiffness (see Table 4 for M1a–e). These results sug-gest that in modeling the interdigitated sutures, strainpredictions in the neighboring bones are possibly more
sensitive to the thickness than the stiffness of thesuture. These findings are likely linked to increase ofthe wavelength of the suture as its volume increasesand it becomes more similar to a butt joint. Therefore,movement across the suture is increased and strainwithin the bone is reduced (Jasinoski et al., 2010).
High RD were found when the suture stiffness of themodel with expanded suture was varied (M5a–e), thussuggesting that in a model with expanded suture neigh-boring bones experience strain magnitudes that arehighly sensitive to the stiffness of the suture. Heightensensitivity of strain in adjacent bones to the stiffness ofsuture in the expanded suture models suggests that thesegmentation process and the possible expansion of thesuture, for example to obtain a better mesh quality forFE models can magnify the sensitivity of the results tothe stiffness of the suture. While caution must be takenin interpretation of the results in such cases, it could bepossible that a higher elastic property is required to beassigned to a model with an expanded suture to compen-sate for the effect of expansion. Overall, this pointhighlights (1) in modeling sutures it is important to cap-ture correctly the thickness and geometry with highresolution CT scanning and careful segmentation and (2)the importance of incorporating more realistic elasticproperties for the cranial joints, and thus, challengesfurther experimental data collection.
The higher sensitivity of the strain values (higher RD)in the anterior regions (R1-4), compared with the poste-rior regions (R5-8), could be an artefact of the boundaryconditions by which the skull was loaded; the anteriorpart of the skull roof was unconstrained, while the pos-terior part was fully constrained. Therefore, varying theproperties of the sutures had more of an impact on theanterior regions than the posterior regions (consideringthe movement across the FP suture). This observationhighlights the importance of applying physiological load-ing conditions to the skull where muscle forces and jointforces would be expected (Duda et al., 1998; Curtiset al., 2008, 2010; Moazen et al., 2008a,b).
The two models that replicated a fused FP suture,M1e and M5e, were segmented into different thicknessesand replicated as bone. Therefore, ideally both modelsshould have generated similar results across the selectedregions. While this was the case for majority of regions(difference of <5%), the difference between the strainvalues was higher than expected at R3 and R4 (29 and68%). R3 and R4 are located on the anterior part of theskull and are relatively close to the FP suture. In includ-ing the suture in the FE model, and expanding it, it islikely that undesirable elements (with high aspectratios) were formed at the interface between the boneand suture that resulted in discretization error (Schmidtet al., 2009). Similar effect was recently reported byReed et al. (2011) in modeling the sutures in a mandiblemodel where authors highlighted that this error canincrease closer to the suture. Further studies arerequired to investigate discretization error when usingFE models to investigate role of cranial sutures at thesuture-bone interface.
Biomechanics of FP Region
Understanding form and function of the FP regionhas been of interest among functional morphologists
Fig. 5. Comparison of the first and third principal strains and VMstrain between the models developed in this study across the FPsuture. Note FP suture modeled with elastic modulus of 10 MPa in allmodels except M1e that modeled with elastic modulus of 10, 000MPa.
SENSITIVITY ANALYSIS IN A LIZARD SUTURE 205
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(Frazzetta, 1962; Smith and Hylander, 1985; Herrelet al., 2000; Evans, 2008). It could potentially shed lighton the evolution of cranial kinesis (Metzger, 2002) andthe upper temporal fenestra (Carrol, 1982; Evans, 2003;Curtis et al., 2011). In Squamata (lizards, snakes, andamphisbaenians), there is a large diversity in the struc-ture of this region. For example, in Iguanidae,Agamidae, Anguidae, Xenosauridae, and Varanidae, theupper temporal fenestra is usually open and the FPsuture is relatively straight (Throckmorton, 1976; Smithand Hylander, 1985; Evans, 2008). Whereas in Cordyli-formes, and Lacertidae the upper temporal fenestra isclosed, or reduced, while the FP suture is highly interdi-gitated (Barahona and Barbadillo, 1998; Evans, 2008;Costantini et al., 2010). However, in Xantusiidae, theupper temporal fenestra is closed and the FP suture isrelatively straight (Evans, 2008). The question thatremains to be answered is whether the biomechanicalfactors play a role in such diversity. The FE method canbe employed to investigate such hypotheses, yet, there
are few studies that have implemented this technique inthe study of the Squamata skulls (Moreno et al., 2008;Moazen et al., 2008a,b, 2009a,b).
Considering the assumptions that were made in thisstudy, care should be taken in interpretation of resultsabout the evolution of the cranial kinesis and upper tem-poral fenestra. Nevertheless, considering that the highlevel of strain present in the FP models with interdigi-tated suture, that is, M1a-5a could be reduced with theincorporation of the muscle forces, the cranial movementat 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 andHylander, 1985) is unlikely to be present in L. bilineata.In fact, this study suggests that such an active move-ment can impose an increase in the level of strain in theparietal area and therefore a scarce or null kinetic move-ment at this junction. Indeed, understanding themechanism behind the ossification of the FP scales inthe Lacertidae in this region becomes even more inter-esting. Small movements at this joint can generate ahigh level of compressive strain in the FP suture (Her-ring and Teng, 2000) that can potentially trigger theossification of the scales in this region. Addressing thesequestions, in future studies might help to define theselective pressures linking variation in suture interdigi-tation to ecology and behavior of lacertid species.
CONCLUSIONS
This study demonstrates the sensitivity of strain predic-tions in FE studies to the shape, size, and stiffness ofcranial sutures. Similar patterns of strain distributionwere obtained regardless of the size of the suture, yet thestrain magnitudes were highly sensitive to this modelingparameter. In modeling the interdigitated sutures, the dif-ference in strain predictions in the neighboring bones wasgreater following an approximately two fold increase inthe width of the suture, compared with changes by severalorders of magnitude to the stiffness (in the range of 1.2–10, 000 MPa). However, in a model with expanded interdi-gitated suture, strain magnitudes were highly sensitive tothe stiffness of the suture. Future studies will be requiredto measure the stiffness of cranial joints in lizards and toassess the possible degree of movement at the FP suturein Lacertidae. A greater understanding of the sutures inthe skull roof may elucidate the factors underlying thegrowth and development of the scales in this region.
ACKNOWLEDGEMENT
This work is partially supported by Ornis italica. Theauthors thank Philippe Young and Simpleware team fortheir cooperation with the use of their software for thisstudy; Susan E Evans (Department of Anatomy and Devel-opmental Biology, University College London) and Adam JStops (Institute of Medical and Biological Engineering,University of Leeds) for discussion and comments on thisstudy; and three anonymous reviewers for their insightfulcomments on the earlier version of this manuscript.
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Fig. 6. Comparison of the first and third principal strains and VMstrain between M1a–e and M5a–e across the FP suture varying theelastic module of this suture. Note elastic modulus is in MPa.
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