Skull bones and sutures full#

The overall structure of this study is schematically presented in Fig 2. Finally, we demonstrated experimentally that the noise of the osteogenic signal existed in the developing skull, and the scaling of the anterior part of the sagittal suture was consistent with the model predictions. Subsequently, utilizing previous studies of dynamic scaling, we introduced time–space-dependent noise to the model and showed that this system could exhibit scaling.

Next, we reduced the model to the dynamics of the centerline h( x, t). To understand this pattern formation, we started from our previous model and chose parameter sets which do not show interface instability. We focus on the anterior part of the sagittal suture, which exhibits less prominent interdigitation and more random characteristics than other sutures ( Fig 1). In the present study, therefore, we propose a new mechanism for suture fractal pattern formation that incorporates a noise term. For example, in our previous study, we introduced time-dependent diffusion terms to reproduce the fractal structure however, in a subsequent study that used computed tomography, we were unable to detect the addition of small structures to the large structures during development, which is expected in a model with time-dependent diffusion terms.

However, these models produced results inconsistent with the experimental observations. applied the Eden model to the formation of the curvature of skull sutures, (ii) Zollikofer and Weissmann applied the diffusion-limited aggregation method to the formation of skull suture interdigitation, and (iii) we suggested that the formation of skull suture curvature based on the time-dependent diffusion term was equivalent to the Koch curvature generation. These measurements have mainly been used for classification or diagnostic purposes however, studies are yet to reveal the mechanism of fractal pattern formation.Īlthough various models have been proposed for the formation of fractal structures, e.g., the Eden collision model, the Koch curve and diffusion-limited aggregation, their application to suture pattern formation has been unsuccessful. Until recently, researchers generally measured the fractal dimension by the box-counting method. The interdigitation of sutures results in a fractal structure, which was initially reported in the mid-1980s. The suture tissue is known to mechanically connect the skull bones, and the interdigitation is assumed to reinforce the mechanical strength of the connection. Consequently, suture tissue can be used to estimate the age of a person in forensic science techniques. After adolescence, the skull bones gradually fuse and the suture tissues disappear. At birth, the suture tissue is thick and straight however, as the skull develops, the sutures gradually becomes thinner and begins to form winding and interdigitated patterns. During development, the suture tissue acts as the growth center of the skull the premature disappearance of the suture tissue causes the skull deformation known as craniosynostosis. They perform multiple functions, and they have been extensively studied as a model system of skeletal development. Sutures are the thin, soft tissues between skull bones. Furthermore, we observed experimentally that stochastic fluctuation of the osteogenic signal exists in the developing skull, and found that actual suture patterns followed a scaling law similar to that of the theoretical prediction.

Skull bones and sutures full#

We showed theoretically that the final pattern from the model follows a scaling law due to the scaling of the dispersion relation in the full model, which we confirmed numerically.

We reduced our previous model to represent the linear dynamics of the centerline of the suture tissue and included a time–space-dependent noise term. In the present study, we focused on the anterior part of the sagittal suture and formulated a new mathematical model with time–space-dependent noise that was able to generate the fractal structure. However, the generated pattern had a specific characteristic length, and the model was unable to produce a fractal structure with the model. In a previous study, we reproduced the formation of the interdigitation pattern in a mathematical model combining an interface equation and a convolution kernel. Although various molecules involved in suture development have been identified, the mechanism underlying the pattern formation remains unknown. Moreover, the final winding pattern had been shown to have fractal characteristics. In a newborn skull, the sutures are straight however, as the skull develops, the sutures wind dynamically to form an interdigitation pattern. Sutures, the thin, soft tissue between skull bones, serve as the major craniofacial growth centers during postnatal development.