Mechanics of cranial sutures using the finite element method

To investigate how cranial suture morphology and the arrangement of sutural collagen fibres respond to compressive and tensile loads, an idealised bone–suture–bone complex was analysed using a two-dimensional finite element model. Three suture morphologies were simulated with an increasing interdigitation index (I.I.): butt-ended, moderate interdigitated, and complex interdigitated. The collagen matrix within all sutures was modelled as an isotropic material, and as an orthotropic material in the interdigitated sutures with fibre alignment as reported in studies of miniature pigs. Static uniform compressive or tensile loading was applied to the complex. In interdigitated sutures with isotropic material properties, the orientation of the maximum (tensile) principal stresses within the suture matched the collagen fibre orientation observed in compressed and tensed sutures of miniature pigs. This suggests that randomly arranged sutural collagen fibres could optimise to an orientation most appropriate to withstand the predominant type of loading. A compression-resistant fibre arrangement imparted the highest suture strain energy relative to the isotropic and tension-resistant arrangements, indicating that this configuration maximises energy storage. A comparison across the different suture morphologies indicated that bone strain energy generally decreased with a decrease in I.I., irrespective of the sutural fibre arrangement. However, high bone stress at the interdigitation apices shifted to the limbs of the suture with an increase in I.I. These combined findings highlight the importance of suture morphology and anisotropy as properties having a significant influence on sutural mechanics.     

Calvarial suture interdigitation in hadrosaurids (Ornithischia: Ornithopoda): Perspectives through ontogeny and evolution

Lambeosaurine hadrosaurids exhibited extreme modifications to the skull, where the premaxillae, nasals, and prefrontals were modified to form their iconic supracranial crests. This morphology contrasts with their sister group, Hadrosaurinae, which possessed the plesiomorphic arrangement of bones. Although studies have discussed differences between lambeosaurine and hadrosaurine skull morphology and ontogeny, there is little information detailing suture modifications through ontogeny and evolution. Suture morphology is of particular interest due to its correlation with the mechanical loading of the skull in extant vertebrates. We quantify and contrast the morphology of calvarial sutures in iguanodontians and ontogenetic series of Corythosaurus and Gryposaurus to test whether the evolution of lambeosaurine crests impacted the mechanical loading of the skull. We found that suture interdigitation (SI) increases through ontogeny in hadrosaurids, although this increase is more extreme in Corythosaurus than Gryposaurus, and overall suture complexity (i.e., overall shape) remained constant. Lambeosaurines also have higher SI than other iguanodontians, even in crestless juveniles, suggesting that increased sinuosity is unrelated to the structural support of the crest. Hadrosaurines and basal iguanodontians did not differ. Similarly, lambeosaurines have more complexly shaped sutures than hadrosaurines and basal iguanodontians, while the latter two groups do not differ. Taken together, these results suggest that lambeosaurine calvarial sutures are more interdigitated than other iguanodontians, and although suture sinuosity increased through ontogeny, the suture shape remained constant. These ontogenetic and evolutionary patterns suggest that increased suture complexity in lambeosaurines coincided with crest evolution, and corresponding modifications to their facial skeleton altered the distribution of stress while feeding.     

Functional implications of dicynodont cranial suture morphology

Cranial suture morphology of Lystrosaurus and the generalized dicynodont Oudenodon was investigated to determine the strain environment during mastication, which in turn may indicate a difference in cranial function between the two taxa. Finite element (FE) analysis indicated that less strain accumulated in the cranium of Lystrosaurus during orthal bite simulations than in Oudenodon. Despite the overall difference in strain magnitude, moderate to high FE‐predicted strain accumulated in similar areas of the cranium of both taxa. The suture morphology in these cranial regions of Lystrosaurus and Oudenodon was investigated further by examination of histological sections and supplemented by observations of serial sections and computed tomography (CT) scans. The predominant type of strain from selected blocks of finite elements that contain sutures was determined, enabling comparison of suture morphology to strain type. Drawing from strain‐suture correlations established in extant taxa, the observed patterns of sutural morphology for both dicynodonts were used to deduce cranial function. The moderate to high compressive and tensile strain experienced by the infraorbital bar, zygomatic arch, and postorbital bar of Oudenodon and Lystrosaurus may have been decreased by small adjustive movements at the scarf sutures in those regions. Disparities in cranial suture morphology between the two taxa may reflect differences in cranial function. For instance, the tongue and groove morphology of the postorbital‐parietal suture in Oudenodon could have withstood the higher FE‐predicted tensile strain in the posterior skull roof. The scarf premaxilla‐nasal suture of Lystrosaurus provided an additional region of sutural mobility in the anterior surface of the snout, suggesting that Lystrosaurus may have employed a different biting regime than Oudenodon. The morphology of several sutures sampled in this study correlated with the FE‐predicted strain, although other cranial functional hypotheses remain to be tested. J. Morphol., 2010. © 2010 Wiley‐Liss, Inc.     

Cranial suture complexity in white-tailed deer (Odocoileus virginianus)

Neurocranial expansion and mastication are commonly implicated as the two major biomechanical factors affecting suture morphology. In deer the antlers provide an additional source of biomechanical stress acting on the skull. Equivalent stresses are not found in females, who lack antlers. We analyzed the complexity and interdigitation of the interfrontal and coronal sutures that surround the antler-bearing frontal bones of (n = 67) white-tailed deer (Odocoileus virginianus) to 1) evaluate changes in suture morphology throughout ontogeny, and 2) test the hypothesis that male deer have more complex sutures than females. Two methods were used to quantify suture morphology: fractal analysis and length-ratios (actual suture length divided by direct straightline length). Both techniques produced similar results, although the two methods cannot be considered equivalent. Suture complexity increases markedly throughout ontogeny, but appears to level off after animals have reached adulthood. Cranial size in males, but not females, continues to increase in adults. No significant increase in suture complexity with age in the adult cohort was detected. While deer are highly dimorphic in size and the presence of antlers, no significant differences existed between males and females for any measure of suture complexity. No consistent patterns emerged between suture complexity and skull size or antler characteristics. The presence of antlers appears to have a minimal effect on suture complexity in white-tailed deer. Factors that may contribute to the lack of dimorphism in suture complexity are discussed.     

Mechanical properties of cranial sutures

Many bones in mammalian skulls are linked together by cranial sutures, connective tissue joints that are morphologically variable and show different levels of interdigitation among and within species. The goal of this investigation was to determine whether sections of skull with cranial sutures have different mechanical properties than adjacent sections without sutures, and if these properties are enhanced with increased interdigitation. To test these hypotheses, bending strength and impact energy absorption were measured for samples of goat (Capra hircus) cranial bone without sutures and with sutures of different degrees of interdigitation. Bending strength was measured under both dynamic (9.7 mm displacement s-1) and relatively static (0.8 mm s-1) conditions, and at either speed, increased sutural interdigitation provided increased strength during three-point bending. However, except for very highly interdigitated sutures loaded slowly, sutures were not as strong in bending as bone. In contrast, sutures absorbed from 16% to 100% more energy per unit volume during impact loading than did bone. This five-fold increase in energy absorption by the sutures was significantly correlated with increased sutural interdigitation.     

Noninvasive prediction of vertebral body compressive strength using nonlinear finite element method and an image based technique

Noninvasive prediction of vertebral body strength under compressive loading condition is a valuable tool for the assessment of clinical fractures. This paper presents an effective specimen-specific approach for noninvasive prediction of human vertebral strength using a nonlinear finite element (FE) model and an image based parameter based on the quantitative computed tomography (QCT). Nine thoracolumbar vertebrae excised from three cadavers with an average age of 42 years old were used as the samples. The samples were scanned using the QCT. Then, a segmentation technique was performed on each QCT sectional image. The segmented images were then converted into three-dimensional FE models for linear and nonlinear analyses. A new material model was implemented in our nonlinear model being more compatible with real mechanical behavior of trabecular bone. A new image based MOS (Mechanic of Solids) parameter named minimum sectional strength ((σ_uA)_min) was used for the ultimate compressive strength prediction. Subsequently, the samples were destructively tested under uniaxial compression and their experimental ultimate compressive strengths were obtained. Results indicated that our new implemented FE model can predict ultimate compressive strength of human vertebra with a correlation coefficient (R² = 0.94) better than usual linear and nonlinear FE models (R² = 0.83 and 0.85 respectively). The image based parameter introduced in this study ((σ_uA)_min) was also correlated well with the experimental results (R² = 0.86). Although nonlinear FE method with new implemented material model predicts compressive strength better than the (σ_uA)_min, this parameter is clinically more feasible due to its simplicity and lower computational costs. This can make future applications of the (σ_uA)_min more justified for human vertebral body compressive strength prediction.     

Experimental and finite element analysis of the mouse caudal vertebrae loading model: prediction of cortical and trabecular bone adaptation

In this study, we attempt to predict cortical and trabecular bone adaptation in the mouse caudal vertebrae loading model using knowledge of bone’s local mechanical environment at the onset of loading. In a previous study, we demonstrated appreciable 25.9 and 11% increases in both trabecular and cortical bone volume density, respectively, when subjecting the fifth caudal vertebrae (C5) of C57BL/6 (B6) mice to an acute loading regime (amplitude of 8N, 3000 cycles, 10 Hz, 3 times a week for 4 weeks). We have also established a validated finite element (FE) model of the C5 vertebra using micro-computed tomography (micro-CT), which characterizes, in 3D, the micro-mechanical strains present in both cortical and trabecular compartments due to the applied loads. To investigate the relationship between load-induced bone adaptation and mechanical strains in-vivo and in-silico data sets were compared. Using data from the previous cross-sectional study, we divided cortical and trabecular compartments into 15 subregions and determined, for each region, a bone formation parameter ΔBV/BS (a cross-sectional measure of the bone volume added to cortical and trabecular surfaces following the described loading regime). Linear regression was then used to correlate mean regional values of ΔBV/BS with mean values of mechanical strains derived from the FE models which were similarly regionalized. The mechanical parameters investigated were strain energy density (SED), the orthogonal strains (e _x , e _y , e _z ) and the three shear strains (e _xy , e _yz , e _zx ). For cortical regions, regression analysis showed SED to correlate extremely well with ΔBV/BS (R ² =?0.82) and e _z (R ²?=?0.89). Furthermore, SED was found to predict expansion of the cortical shell correlating significantly with the regional percentage increases in cortical tissue volume (R ² = 0.92), cortical marrow volume (R ² =?0.91) and cortical thickness (R ² = 0.56). For trabecular regions, FE parameters were found not to correlate with load-induced trabecular bone morphology. These results indicate that load-induced cortical morphology can be predicted from population data, whereas the prediction of trabecular morphology requires subject-specific micro- architecture.     

Linking form and function of the fibrous joints in the skull: a new quantification scheme for cranial sutures using the extant fish Polypterus endlicherii

The aim of this study is to connect specific sutural morphologies with the specific types of deformation they experience. To meet this goal, we quantified the morphologies of the interfrontal (IF), interparietal (IP), and frontoparietal (FP) sutures in the extant fish Polypterus endlicherii, and used our published measurements of in vivo deformation of these sutures during feeding to infer how suture morphology and function are connected. Specifically, we found that three relatively simple measures of cross-sectional suture complexity (i.e., the ratio of total sutural length to its shortest end-to-end length; amount of sutural overlap; and size of the largest interdigitation) can be used to distinguish between the IF, FP, and IP sutures, which exhibit very different cross-sectional shapes and responses to loading. Interestingly, these differences in cross-sectional morphology are not reflected by the linear traces of these sutures on the surface of the skull, implying that cross-sectional shape of a suture must be known to infer the loading conditions it experiences. Plotting the three cross-sectional metrics against one another to yield a sutural morphospace shows that the IF, IP, and FP sutures define regions that are largely distinct from one another. Our previous measurements of strain across these sutures suggested that the FP region would lie between the IF and IP regions; instead, the FP region is largely set apart from the other two fields. Based on this discovery, and on the locations of cranial muscles, we propose a new model of deformation in the skull of P. endlicherii during feeding, in which rotation parallel to the skull roof is combined with bending, subjecting the FP suture to complex shearing. Finally, although the sutures of P. endlicherii appear to be significantly less complex than those of mammals, these fish sutures show a similar range of morphologies and perform similar functions as do mammalian sutures.     

Cranial suture complexity in caviomorph rodents (Rodentia; Ctenohystrica)

Due to their flexibility, sutures are regions that experience greater strains than the surrounding rigid cranial bones. Cranial sutures differ in their degree of interdigitation or complexity. There is evidence indicating that a more convoluted suture better enables the absorption of high stresses coming from dynamic masticatory forces, and other functions. The Order Rodentia is an interesting clade to study this because of its taxa with diverse chewing modes. Due to repeated loading resulting from gnawing and grinding, energy absorption by the sutures might be a crucial factor in these mammals. Species within the infraorder Caviomorpha were chosen as a case study because of their ecomorphological and dietary diversity. This study compared five sutures from the rostrum and cranial vault across seven caviomorph families, and assessed their complexity by means of the relative length and fractal dimension. Across these rodents, cranial sutures are morphologically quite diverse. We found that the sutures connecting the rostrum with the vault were relatively more interdigitated than those in the cranial vault itself, especially premaxillofrontal sutures. Suture interdigitation was higher in species that display chisel‐tooth digging and burrowing behaviors, especially in the families Ctenomyidae and Octodontidae, than those in families Dasyproctidae and Cuniculidae, which have more gracile masticatory systems. The reconstruction of the ancestral character state, on family and species phylogeny, points toward low suture interdigitation (i.e., low length ratio) as a likely ancestral state for interfrontal, premaxillofrontal and maxillofrontal sutures. Interspecific differences in suture morphology shown here might represent adaptations to different mechanical demands (i.e., soft vs. tough foods) or behaviors (e.g., chisel‐tooth digging), which evolved in close association with the diverse environments occupied by caviomorph rodents.     

Craniofacial sutures: morphology, growth, and in vivo masticatory strains.

The growth and morphology of craniofacial sutures are thought to reflect their functional environment. However, little is known about in vivo sutural mechanics. The present study investigates the strains experienced by the internasal, nasofrontal, and anterior interfrontal sutures during masticatory activity in 4-6-month-old miniature swine (Sus scrofa). Measurements of the bony/fibrous arrangements and growth rates of these sutures were then examined in the context of their mechanical environment. Large tensile strains were measured in the interfrontal suture (1,036 microepsilon +/- 400 SD), whereas the posterior internasal suture was under moderate compression (-440 microepsilon +/- 238) and the nasofrontal suture experienced large compression (-1,583 microepsilon +/- 506). Sutural interdigitation was associated with compressive strain. The collagen fibers of the internasal and interfrontal sutures were clearly arranged to resist compression and tension, respectively, whereas those of the nasofrontal suture could not be readily characterized as either compression or tension resisting. The average linear rate of growth over a 1-week period at the nasofrontal suture (133.8 micrometer, +/- 50.9 S.D) was significantly greater than that of both the internasal and interfrontal sutures (39.2 micrometer +/- 11.4 and 65. 5 micrometer +/- 14.0, respectively). Histological observations suggest that the nasofrontal suture contains chondroid tissue, which may explain the unexpected combination of high compressive loading and rapid growth in this suture.     

A mathematical model for mechanotransduction at the early steps of suture formation

Growth and patterning of craniofacial sutures is subjected to the effects of mechanical stress. Mechanotransduction processes occurring at the margins of the sutures are not precisely understood. Here, we propose a simple theoretical model based on the orientation of collagen fibres within the suture in response to local stress. We demonstrate that fibre alignment generates an instability leading to the emergence of interdigitations. We confirm the appearance of this instability both analytically and numerically. To support our model, we use histology and synchrotron X-ray microtomography and reveal the fine structure of fibres within the sutural mesenchyme and their insertion into the bone. Furthermore, using a mouse model with impaired mechanotransduction, we show that the architecture of sutures is disturbed when forces are not interpreted properly. Finally, by studying the structure of sutures in the mouse, the rat, an actinopterygian (Polypterus bichir) and a placoderm (Compagopiscis croucheri), we show that bone deposition patterns during dermal bone growth are conserved within jawed vertebrates. In total, these results support the role of mechanical constraints in the growth and patterning of craniofacial sutures, a process that was probably effective at the emergence of gnathostomes, and provide new directions for the understanding of normal and pathological suture fusion.     

Mechanical Properties of Calvarial Bones in a Mouse Model for Craniosynostosis

The mammalian cranial vault largely consists of five flat bones that are joined together along their edges by soft fibrous tissues called sutures. Premature closure of the cranial sutures, craniosynostosis, can lead to serious clinical pathology unless there is surgical intervention. Research into the genetic basis of the disease has led to the development of various animal models that display this condition, e.g. mutant type Fgfr2^C342Y/+ mice which display early fusion of the coronal suture (joining the parietal and frontal bones). However, whether the biomechanical properties of the mutant and wild type bones are affected has not been investigated before. Therefore, nanoindentation was used to compare the elastic modulus of cranial bone and sutures in wild type (WT) and Fgfr2^C342Y/+mutant type (MT) mice during their postnatal development. Further, the variations in properties with indentation position and plane were assessed. No difference was observed in the elastic modulus of parietal bone between the WT and MT mice at postnatal (P) day 10 and 20. However, the modulus of frontal bone in the MT group was lower than the WT group at both P10 (1.39±0.30 vs. 5.32±0.68 GPa; p<0.05) and P20 (5.57±0.33 vs. 7.14±0.79 GPa; p<0.05). A wide range of values was measured along the coronal sutures for both the WT and MT samples, with no significant difference between the two groups. Findings of this study suggest that the inherent mechanical properties of the frontal bone in the mutant mice were different to the wild type mice from the same genetic background. These differences may reflect variations in the degree of biomechanical adaptation during skull growth, which could have implications for the surgical management of craniosynostosis patients.     

Functional implications of squamosal suture size in paranthropus boisei

It has been hypothesized that the extensively overlapping temporal and parietal bones of the squamosal sutures in Paranthropus boisei are adaptations for withstanding loads associated with feeding. Finite element analysis (FEA) was used to investigate the biomechanical effects of suture size (i.e., the area of overlap between the temporal and parietal bones) on stress, strain energy, and strain ratio in the squamosal sutures of Pan troglodytes and P. boisei (specimen OH 5) during biting. Finite element models (FEMs) of OH 5 and a P. troglodytes cranium were constructed from CT scans. These models contain sutures that approximate the actual suture sizes preserved in both crania. The FEM of Pan was then modified to create two additional FEMs with squamosal sutures that are 50% smaller and 25% larger than those in the original model. Comparisons among the models test the effect of suture size on the structural integrity of the squamosal suture as the temporal squama and parietal bone move relative to each other during simulated premolar biting. Results indicate that with increasing suture size there is a decreased risk of suture failure, and that maximum stress values in the OH 5 suture were favorable compared to values in the Pan model with the normal suture size. Strain ratios suggest that shear is an important strain regime in the squamosal suture. This study is consistent with the hypothesis that larger sutures help reduce the likelihood of suture failure under high biting loads. Am J Phys Anthropol 153:260–268, 2014. © 2013 Wiley Periodicals, Inc.     

The importance of craniofacial sutures in biomechanical finite element models of the domestic pig

Craniofacial sutures are a ubiquitous feature of the vertebrate skull. Previous experimental work has shown that bone strain magnitudes and orientations often vary when moving from one bone to another, across a craniofacial suture. This has led to the hypothesis that craniofacial sutures act to modify the strain environment of the skull, possibly as a mode of dissipating high stresses generated during feeding or impact. This study tests the hypothesis that the introduction of craniofacial sutures into finite element (FE) models of a modern domestic pig skull would improve model accuracy compared to a model without sutures. This allowed the mechanical effects of sutures to be assessed in isolation from other confounding variables. These models were also validated against strain gauge data collected from the same specimen ex vivo. The experimental strain data showed notable strain differences between adjacent bones, but this effect was generally not observed in either model. It was found that the inclusion of sutures in finite element models affected strain magnitudes, ratios, orientations and contour patterns, yet contrary to expectations, this did not improve the fit of the model to the experimental data, but resulted in a model that was less accurate. It is demonstrated that the presence or absence of sutures alone is not responsible for the inaccuracies in model strain, and is suggested that variations in local bone material properties, which were not accounted for by the FE models, could instead be responsible for the pattern of results.     

Craniosynostosis and altered patterns of fetal TGF-beta expression induced by intrauterine constraint

Recent work has demonstrated that fusion of the calvarial sutures is mediated by locally elaborated soluble growth factors, including the transforming growth factor-betas (TGF-betas), leading some to speculate that external biomechanical forces play little role in suture development. Clinical evidence has long suggested, however, that fetal head constraint may play a critical role in the pathogenesis of many cases of nonsyndromic craniosynostosis. The purpose of these experiments was to test the hypothesis that intrauterine constraint leads to an alteration in normal patterns of TGF-beta expression and that these alterations are associated with craniosynostosis. Fetal constraint was induced by allowing C57Bl/6 murine fetuses to grow for 2.5 days beyond the normal 20-day gestation by performing uterine cerclage on the eighteenth day. Cranial suture morphology was examined in hematoxylin and eosin-stained sections and in cleared whole-mount specimens, double stained with alizarin red S and Alcian blue. Expression patterns of TGF-beta1 and TGF-beta3 were examined by immunohistochemical techniques. Gross and microscopic examination of the cranial sutures of 17 constrained fetuses revealed changes that ranged from narrowing to complete osseous obliteration of the coronal and squamosal sutures. All sutures of 14 nonconstrained control pups remained patent. Fetal head constraint was associated with increased TGF-beta1 immunoreactivity within the new bone and the underlying dura when compared with nonconstrained age-matched controls. TGF-beta3 immunoreactivity was associated with the dura underlying patent, nonconstrained sutures, whereas constraint-induced synostosis was characterized by down-regulation of dural TGF-beta3 expression. These experiments confirm the ability of intrauterine constraint to induce premature fusion of the cranial sutures and provide evidence that intrauterine head constraint induces the expression of osteogenic growth factors in fetal calvarial bone and the underlying dura.     

Strain accommodation in the zygomatic arch of the pig: A validation study using digital speckle pattern interferometry and finite element analysis

It has been repeatedly suggested that mammalian cranial sutures act not only to allow growth but also to reduce the levels of strain experienced by the skull during feeding. However, because of the added complexity they introduce, sutures are rarely included in finite element (FE) models, despite their potential to influence strain results. Because sutures present different morphologies and with differing degrees of internal fusion, many different methods of modeling may be necessary to accurately measure strain environments. Alternatively, these variables may exert very little influence on the scale of a whole‐skull model. To validate suture modeling methods, four alternative ways of including a suture in 3D FE models of the pig zygomatic arch were considered and compared with ex vivo experimental data from digital speckle pattern interferometry (DSPI). The use of DSPI rather than traditional strain gauge techniques allows strain gradients around the suture as well as the motions of the two bones to be observed. Results show that the introduction of 3D elements assigned more compliant material properties than the surrounding bone, is the most effective way of modeling both morphologies of suture, both in tension and compression. However, models containing no suture are almost indistinguishable from these compliant suture models, beyond the high strain gradient immediately adjacent to the suture. Conversely, modeling the suture as an open break in the mesh, or with spring elements assigned suture properties, fails to reproduce the experiment. Thus, although a solid but flexible model of sutures is preferred, the similarity between these models and those without sutures tentatively suggests that such extra detail may be unnecessary in pigs if the behavior of the whole skull is of interest. J. Morphol., 2011. © 2011 Wiley‐Liss, Inc.     

A genomic survey of the fish parasite Spironucleus salmonicida indicates genomic plastiCity among diplomonads and significant lateral gene transfer in eukaryote genome evolution

Background

Craniosynostosis, the premature fusion of calvarial sutures, is a common craniofacial abnormality. Causative mutations in more than 10 genes have been identified, involving fibroblast growth factor, transforming growth factor beta, and Eph/ephrin signalling pathways. Mutations affect each human calvarial suture (coronal, sagittal, metopic, and lambdoid) differently, suggesting different gene expression patterns exist in each human suture. To better understand the molecular control of human suture morphogenesis we used microarray analysis to identify genes differentially expressed during suture fusion in children with craniosynostosis. Expression differences were also analysed between each unfused suture type, between sutures from syndromic and non-syndromic craniosynostosis patients, and between unfused sutures from individuals with and without craniosynostosis.

Results

We identified genes with increased expression in unfused sutures compared to fusing/fused sutures that may be pivotal to the maintenance of suture patency or in controlling early osteoblast differentiation (i.e. RBP4, GPC3, C1QTNF3, IL11RA, PTN, POSTN). In addition, we have identified genes with increased expression in fusing/fused suture tissue that we suggest could have a role in premature suture fusion (i.e. WIF1, ANXA3, CYFIP2). Proteins of two of these genes, glypican 3 and retinol binding protein 4, were investigated by immunohistochemistry and localised to the suture mesenchyme and osteogenic fronts of developing human calvaria, respectively, suggesting novel roles for these proteins in the maintenance of suture patency or in controlling early osteoblast differentiation. We show that there is limited difference in whole genome expression between sutures isolated from patients with syndromic and non-syndromic craniosynostosis and confirmed this by quantitative RT-PCR. Furthermore, distinct expression profiles for each unfused suture type were noted, with the metopic suture being most disparate. Finally, although calvarial bones are generally thought to grow without a cartilage precursor, we show histologically and by identification of cartilage-specific gene expression that cartilage may be involved in the morphogenesis of lambdoid and posterior sagittal sutures.

Conclusion

This study has provided further insight into the complex signalling network which controls human calvarial suture morphogenesis and craniosynostosis. Identified genes are candidates for targeted therapeutic development and to screen for craniosynostosis-causing mutations.     

The effects of morphological irregularity on the mechanical behavior of interdigitated biological sutures under tension

Irregular interdigitated morphology is prevalent in biological sutures in nature. Suture complexity index has long been recognized as the most important morphological parameter to govern the mechanical properties of biological sutures. However, the suture complexity index alone does not reflect all aspects of suture morphology. The goal of this investigation was to determine that besides suture complexity index, whether the degree of morphological irregularity of biological sutures has influences on the mechanical properties, and if there is any, how to quantify these influences. To explore these issues, theoretical and finite element (FE) suture models with the same suture complexity index but different levels of morphological irregularity were developed. The quasi-static stiffness, strength for damage initiation and post-failure process of irregular sutures were studied. It was shown that for the same suture complexity index, when the level of morphological irregularity increases, the overall strain to failure will increase while tensile stiffness is retained; also, the total energy to fracture increases with a sacrifice in strength to damage initiation. These results reveal that morphological irregularity is another important independent parameter to govern and balance the mechanical properties of biological sutures. Therefore, from the mechanics point of view, the prevalence of irregular suture morphology in nature is a merit, not a defect.     

The mathematical model of concentration polarization coefficient in membrane transport and volume flows

In this paper, the authors investigate the membrane transport of aqueous non-electrolyte solutions in a single-membrane system with the membrane mounted horizontally. The purpose of the research is to analyze the influence of volume flows on the process of forming concentration boundary layers (CBLs). A mathematical model is provided to calculate dependences of a concentration polarization coefficient (ζ _s ) on a volume flux (J _vm ), an osmotic force (Δπ) and a hydrostatic force (ΔP) of different values. Property ζ _s ?=?f(J _vm ) for J _vm ?>?0 and for J _vm ?≈?0 and property ζ _s ?=?f(ΔC ₁) are calculated. Moreover, results of a simultaneous influence of ΔP and Δπ on a value of coefficient ζ _s when J _vm ?=?0 and J _vm ?≠?0 are investigated and a graphical representation of the dependences obtained in the research is provided. Also, mathematical relationships between the coefficient ζ _s and a concentration Rayleigh number (R _C ) were studied providing a relevant graphical representation. In an experimental test, aqueous solutions of glucose and ethanol were used.