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

Growth and patterning of craniofacial sutures are 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 (\emph{Polypterus bichir}) and a placoderm (\emph{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

Studi e documenti di Storia e Diritto, publication périodique de L'Accademia di conferenze storico-giuridiche

Vigneaux P. E. Studi e documenti di Storia e Diritto, publication périodique de L'Accademia di conferenze storico-giuridiche. In: Mélanges d'archéologie et d'histoire, tome 1, 1881. pp. 156-159

Studi e documenti di Storia e Diritto, publication périodique de L'Accademia di conferenze storico-giuridiche

Vigneaux P. E. Studi e documenti di Storia e Diritto, publication périodique de L'Accademia di conferenze storico-giuridiche. In: Mélanges d'archéologie et d'histoire, tome 1, 1881. pp. 156-159

Notice sur trois manuscrits inédits de la Vaticane

Vigneaux P. E. Notice sur trois manuscrits inédits de la Vaticane. In: Mélanges d'archéologie et d'histoire, tome 2, 1882. pp. 309-355

Parameter estimation in non-linear mixed effects models with SAEM algorithm: extension from ODE to PDE

Parameter estimation in non linear mixed effects models requires a large number of evaluations of the model to study. For ordinary differential equations, the overall computation time remains reasonable. However when the model itself is complex (for instance when it is a set of partial differential equations) it may be time consuming to evaluate it for a single set of parameters. The procedures of population parametrization (for instance using SAEM algorithms) are then very long and in some cases impossible to do within a reasonable time. We propose here a very simple methodology which may accelerate population parametrization of complex models, including partial differential equations models. We illustrate our method on the classical KPP equation