Table 1.
Summary of individuals modeled in the study.
Fig 1.
Visualization of each of the models, to scale, with gray color indicating cranial bone and orange indicating cranial suture.
The views presented are, from left to right, front view, vertex view, back view, and right lateral view.
Fig 2.
Muscle attachments and force vectors for mandible and cranium.
Key: Light pink = posterior temporalis (PT); Dark pink = anterior temporalis (AT); Light blue = deep masseter (DM); Dark blue = superficial masseter (SM); Green = medial pterygoid (MP); Indigo and violet = lateral pterygoid (LP); Yellow = palate (P). Yellow arrows denote the direction of muscle vectors, from the centroid of the muscle origin on the cranium to the centroid of the muscle insertion on the mandible. Note, the LP was not included in modeling as it is not significantly involved in jaw closing but is included for ease of anatomical reference.
Fig 3.
Strain regimes created by bilateral activation of each of the major masticatory muscle groups during right sided chew in model A1, with a fully patent metopic suture.
Axial strains denoted by εxx (superior-inferior), εyy (anterior-posterior), and εzz (medial-lateral). Shear strains denoted by εxy (sagittal shear), εxz (coronal shear), and εyz (transverse shear). For axial strains, warm colors indicate tension and cool colors indicate compression. For shear strains, warm colors denote positive shear and cool colors denote negative shear. The medial pterygoids placed the metopic suture under medial-lateral compression, the coronal sutures under anterior-posterior compression, and the squamous sutures under superior inferior compression. The temporalis placed those sutures under tension, compression, and compression respectively. The temporalis also placed large amounts of shear strain on all the cranial vault sutures. The masseters placed the metopic suture under medial-lateral tension and the nasofrontal suture under negative transverse shear.
Fig 4.
Direction of axial strain across cranial vault sutures during bilateral activation of individual muscle groups (medial pterygoid, masseter, temporalis) with a right-sided chew, applied negative palatal pressure with a midline latch point, physiologic chewing, and physiologic suckling.
Cranial vault sutures are labeled in top right panel, alongside the legend for tensile (red arrows) and compressive (blue arrows) strain. Note, arrows only denote direction of axial strain across the suture (i.e., compression or tension), not the magnitude. No arrows are included for axial strain across the metopic suture, anterior fontanelle, and sagittal suture in the negative palatal pressure model due to the low magnitude of strain across these sutures (<1 με).
Table 2.
Average strain at the sutures from the bilateral activation of the respective muscle groups and the application of negative palatal pressure.
Fig 5.
Axial stress and strain in the superior-inferior (σxx and εxx) and medial-lateral (σzz and εzz) directions in each of the models during right-sided chew.
Left and right panels respectively shown stress and strain. In all models, superior-inferior stress and strain were the highest along the lateral maxillary vertical buttress, from the zygoma along the lateral orbital wall. The high levels of superior-inferior axial stress along the lateral orbital wall corresponded to tensile (positive, red) superior-inferior strain in the region, with corresponding compressive (negative, blue) superior-inferior strain along the medial orbital wall. Medial-lateral stress and strain were the highest along the transverse maxillary buttress, specifically the lower transverse buttress along the alveolar process and the upper transverse buttress along the inferior orbital rim. Stress and strain following the maxillary buttresses provides supporting evidence that the models are correctly modeling the physiologic mechanical landscape.
Fig 6.
Strains perpendicular to suture for each model during chewing (Left) and suckling (Right), box-plots color coded by stage of metopic suture closure. Green plots are models with fully patent metopic suture, yellow plots are models with partially closed metopic sutures, blue plots are models with physiologically fully closed metopic sutures, and red plots are models with metopic craniosynostosis. Positive and negative strain respectively show tension and compression. For sagittal and metopic sutures, axial strain perpendicular to the suture is medial-lateral strain; coronal suture = antero-posterior strain; lambdoid suture = max of superior-inferior and medial-lateral strains; squamous = superior-inferior strain. Models with fully patent metopic sutures had highest magnitudes of cross-sutural strain across the metopic and squamous sutures. In models with increasing degrees of metopic suture closure, the magnitude of cross-sutural strain across the metopic suture decreased, but no such trend was observed across the remaining sutures. Cross-sutural strain during suckling tended to be of higher magnitudes than during chewing.
Fig 7.
Average shear strains experienced by each suture in each model during suckling (top panel) and chewing (bottom panel). Grey bar (εyz) indicates average magnitude of transverse shear, orange bar (εxz) indicates average magnitude of coronal shear, and blue bar (εxy) indicates average magnitude of sagittal shear. The number atop each bar represents the sum of each of the average magnitudes. The largest shear strains were experienced by the squamous and coronal sutures. In models with a fully patent metopic suture (A1, A2), and in models with a partially closed metopic suture (B1, B2), the total shear strain experienced by the coronal and squamous sutures tended to be higher than the total shear strain experienced by the metopic suture.
Fig 8.
Average magnitude of medial-lateral strain (εzz) along mid-sagittal plane during right-sided chew and suckling for models in the respectively labeled stages of metopic suture closure.
Theta calculated as , with Ux and Uy representing the x and y-coordinates of the node respectively; moving left to right along the x-axis of each graph is the path from the nasion along the metopic suture, past the anterior fontanelle, and along the sagittal suture towards the posterior fontanelle. Color coding represents which portion of the mid-line of the cranial vault is being represented. In both fully patent metopic models (A1, A2), there were local minima of compressive/tensile medial-lateral strain at the anterior fontanelle and nasion. In A1, the fully patent metopic suture model in which the metopic suture had not yet begun narrowing, a maximum strain value was observed at the inferior aspect of the metopic suture. In the partially closed models (B1, B2), local minima were observed at the anterior fontanelles.
Fig 9.
Cumulative shear strain (, where
denotes the magnitude of the average of the respective nodal strain) along mid-sagittal plane during right-sided chew and suckling for models in the respectively labeled stages of metopic suture closure.
Theta calculated as , with Ux and Uy representing the x and y-coordinates of the node respectively; moving left to right along the x-axis of each graph is the path from the nasion along the metopic suture, past the anterior fontanelle, and along the sagittal suture towards the posterior fontanelle. Color coding represents which portion of the mid-line of the cranial vault is being represented. In fully patent models (A1, A2) cumulative shear strain was higher during chewing than suckling at the metopic suture, and in A1, a local maximum was observed at the nasion. In partially and fully closed models (B1, B2, C1, C2, X1, X2), local maxima were observed at the anterior fontanelle.
Fig 10.
Maximum principal strain in the upper face during right-sided chew (top 2 rows) and suckling (bottom 2 rows). Warmer colors indicate increased magnitude of strain. The frontal prominence, supraorbital region, and lateral orbital wall in the severe metopic craniosynostosis model (X1) experienced lower strains than the models with physiologically closed metopic sutures (C1, C2). In the non-metopic craniosynostosis models (A1, A2, B1, B2, C1, C2), partial and full closure of the metopic suture correlated with increased strains in the aforementioned regions. The less severe metopic craniosynostosis model (X2) had strain regimes that mirrored that of the physiologically closed suture models.
Fig 11.
Stress (von Mises) in the upper face during right-sided chew (top 2 rows) and suckling (bottom 2 rows). Warm colors indicate increased magnitude of stress, while cool colors indicate low magnitudes of stress. The frontal prominence, supraorbital region, and lateral orbital wall in the severe metopic craniosynostosis model (X1) experienced lower von Mises stress than the models with physiologically closed metopic sutures (C1, C2). The less severe metopic craniosynostosis model (X2) had stress regimes that mirrored that of the physiologically closed suture models.