Growth of the flat bones of the membranous neurocranium: a computational model

Paediatric skull growth models: A systematic review of applications to normal skulls and craniosynostoses

INTRODUCTION

Craniosynostoses affect 1/2000 births and their incidence is currently increasing. Without surgery, craniosynostosis can lead to neurological issues due to restrained brain growth and social stigma due to abnormal head shapes. Understanding growth patterns is essential to develop surgical planning approaches and predict short- and long-term post-operative results. Here we provide a systematic review of normal and pathological cranial vault growth models.

MATERIAL AND METHODS

The systematic review of the literature identified descriptive and comprehensive skull growth models with the following criteria: full text articles dedicated to the skull vault of children under 2 years of age, without focus on molecular and cellular mechanisms. Models were analysed based on initial geometry, numerical method, age determination method and validation process.

RESULTS

A total of 14 articles including 17 models was reviewed. Four descriptive models were assessed, including 3 models using statistical analyses and 1 based on deformational methods. Thirteen comprehensive models were assessed including 7 finite element models and 6 diffusion models. Results from the current literature showed that successful models combined analyses of cranial vault shape and suture bone formation.

DISCUSSION

Growth modelling is central when assessing craniofacial architecture in young patients and will be a key factor in the development of future customized treatment strategies. Recurrent technical difficulties were encountered by most authors when generalizing a specific craniosynostosis model to all types of craniosynostoses, when assessing the role of the brain and when attempting to relate the age with different stages of growth.

A review of regulated self-organizing approaches for tissue regeneration

Tissue and organ regeneration is the dynamic process by which a population of cells rearranges into a specific form with specific functions. Traditional tissue regeneration utilizes tissue grafting, cell implantation, and structured scaffolds to achieve clinical efficacy. However, tissue grafting methods face a shortage of donor tissue, while cell implantation may involve leakage of the implanted cells without a supportive 3D matrix. Cell migration, proliferation, and differentiation in structured scaffolds may disorganize and frustrate the artificially pre-designed structures, and sometimes involve immunogenic reactions. To overcome this limitation, the self-organizing properties and innate regenerative capability of tissue/organism formation in the absence of guidance by structured scaffolds has been investigated. This review emphasizes the growing subfield of the regulated self-organizing approach for neotissue formation and describes advances in the subfield using diverse, cutting-edge, inter-disciplinarity technologies. We cohesively summarize the directed self-organization of cells in the micro-engineered cell-ECM system and 3D/4D cell printing. Mathematical modeling of cellular self-organization is also discussed for providing rational guidance to intractable problems in tissue regeneration. It is envisioned that future self-organization approaches integrating biomathematics, micro-nano engineering, and gene circuits developed from synthetic biology will continue to work in concert with self-organizing morphogenesis to enhance rational control during self-organizing in tissue and organ regeneration.

Fgfr3 Is a Positive Regulator of Osteoblast Expansion and Differentiation During Zebrafish Skull Vault Development

Gain or loss-of-function mutations in fibroblast growth factor receptor 3 (FGFR3) result in cranial vault defects highlighting the protein's role in membranous ossification. Zebrafish express high levels of fgfr3 during skull development; in order to study FGFR3's role in cranial vault development, we generated the first fgfr3 loss-of-function zebrafish (fgfr3^lof/lof ). The mutant fish exhibited major changes in the craniofacial skeleton, with a lack of sutures, abnormal frontal and parietal bones, and the presence of ectopic bones. Integrated analyses (in vivo imaging and single-cell RNA sequencing of the osteoblast lineage) of zebrafish fgfr3^lof/lof revealed a delay in osteoblast expansion and differentiation, together with changes in the extracellular matrix. These findings demonstrate that fgfr3 is a positive regulator of osteogenesis. We conclude that changes in the extracellular matrix within growing bone might impair cell-cell communication, mineralization, and new osteoblast recruitment. © 2020 American Society for Bone and Mineral Research.

A coupled reaction-diffusion-strain model predicts cranial vault formation in development and disease

How cells utilize instructions provided by genes and integrate mechanical forces generated by tissue growth to produce morphology is a fundamental question of biology. Dermal bones of the vertebrate cranial vault are formed through the direct differentiation of mesenchymal cells on the neural surface into osteoblasts through intramembranous ossification. Here we join a self-organizing Turing mechanism, computational biomechanics, and experimental data to produce a 3D representative model of the growing cerebral surface, cranial vault bones, and sutures. We show how changes in single parameters regulating signaling during osteoblast differentiation and bone formation may explain cranial vault shape variation in craniofacial disorders. A key result is that toggling a parameter in our model results in closure of a cranial vault suture, an event that occurred during evolution of the cranial vault and that occurs in craniofacial disorders. Our approach provides an initial and important step toward integrating biomechanics into the genotype phenotype map to explain the production of variation in head morphology by developmental mechanisms.

Midface and upper airway dysgenesis in FGFR2-related craniosynostosis involves multiple tissue-specific and cell cycle effects

Midface dysgenesis is a feature of more than 200 genetic conditions in which upper airway anomalies frequently cause respiratory distress, but its etiology is poorly understood. Mouse models of Apert and Crouzon craniosynostosis syndromes exhibit midface dysgenesis similar to the human conditions. They carry activating mutations of Fgfr2, which is expressed in multiple craniofacial tissues during development. Magnetic resonance microscopy of three mouse models of Apert and Crouzon syndromes revealed decreased nasal passage volume in all models at birth. Histological analysis suggested overgrowth of the nasal cartilage in the two Apert syndrome mouse models. We used tissue-specific gene expression and transcriptome analysis to further dissect the structural, cellular and molecular alterations underlying midface and upper airway dysgenesis in Apert Fgfr2^+/S252W mutants. Cartilage thickened progressively during embryogenesis because of increased chondrocyte proliferation in the presence of Fgf2 Oral epithelium expression of mutant Fgfr2, which resulted in a distinctive nasal septal fusion defect, and premature facial suture fusion contributed to the overall dysmorphology. Midface dysgenesis in Fgfr2-related craniosynostosis is a complex phenotype arising from the combined effects of aberrant signaling in multiple craniofacial tissues.

Integration of Brain and Skull in Prenatal Mouse Models of Apert and Crouzon Syndromes

The brain and skull represent a complex arrangement of integrated anatomical structures composed of various cell and tissue types that maintain structural and functional association throughout development. Morphological integration, a concept developed in vertebrate morphology and evolutionary biology, describes the coordinated variation of functionally and developmentally related traits of organisms. Syndromic craniosynostosis is characterized by distinctive changes in skull morphology and perceptible, though less well studied, changes in brain structure and morphology. Using mouse models for craniosynostosis conditions, our group has precisely defined how unique craniosynostosis causing mutations in fibroblast growth factor receptors affect brain and skull morphology and dysgenesis involving coordinated tissue-specific effects of these mutations. Here we examine integration of brain and skull in two mouse models for craniosynostosis: one carrying the FGFR2c C342Y mutation associated with Pfeiffer and Crouzon syndromes and a mouse model carrying the FGFR2 S252W mutation, one of two mutations responsible for two-thirds of Apert syndrome cases. Using linear distances estimated from three-dimensional coordinates of landmarks acquired from dual modality imaging of skull (high resolution micro-computed tomography and magnetic resonance microscopy) of mice at embryonic day 17.5, we confirm variation in brain and skull morphology in Fgfr2c^C342Y/+ mice, Fgfr2^+/S252W mice, and their unaffected littermates. Mutation-specific variation in neural and cranial tissue notwithstanding, patterns of integration of brain and skull differed only subtly between mice carrying either the FGFR2c C342Y or the FGFR2 S252W mutation and their unaffected littermates. However, statistically significant and substantial differences in morphological integration of brain and skull were revealed between the two mutant mouse models, each maintained on a different strain. Relative to the effects of disease-associated mutations, our results reveal a stronger influence of the background genome on patterns of brain-skull integration and suggest robust genetic, developmental, and evolutionary relationships between neural and skeletal tissues of the head.

A COMPUTATIONAL ANALYSIS OF BONE FORMATION IN THE CRANIAL VAULT USING A COUPLED REACTION-DIFFUSION-STRAIN MODEL

Bones of the murine cranial vault are formed by differentiation of mesenchymal cells into osteoblasts, a process that is primarily understood to be controlled by a cascade of reactions between extracellular molecules and cells. We assume that the process can be modeled using Turing's reaction-diffusion equations, a mathematical model describing the pattern formation controlled by two interacting molecules (activator and inhibitor). In addition to the processes modeled by reaction-diffusion equations, we hypothesize that mechanical stimuli of the cells due to growth of the underlying brain contribute significantly to the process of cell differentiation in cranial vault development. Structural analysis of the surface of the brain was conducted to explore the effects of the mechanical strain on bone formation. We propose a mechanobiological model for the formation of cranial vault bones by coupling the reaction-diffusion model with structural mechanics. The mathematical formulation was solved using the finite volume method. The computational domain and model parameters are determined using a large collection of experimental data that provide precise three dimensional (3D) measures of murine cranial geometry and cranial vault bone formation for specific embryonic time points. The results of this study suggest that mechanical strain contributes information to specific aspects of bone formation. Our mechanobiological model predicts some key features of cranial vault bone formation that were verified by experimental observations including the relative location of ossification centers of individual vault bones, the pattern of cranial vault bone growth over time, and the position of cranial vault sutures.

Directing three-dimensional multicellular morphogenesis by self-organization of vascular mesenchymal cells in hyaluronic acid hydrogels

BACKGROUND

Physical scaffolds are useful for supporting cells to form three-dimensional (3D) tissue. However, it is non-trivial to develop a scheme that can robustly guide cells to self-organize into a tissue with the desired 3D spatial structures. To achieve this goal, the rational regulation of cellular self-organization in 3D extracellular matrix (ECM) such as hydrogel is needed.

RESULTS

In this study, we integrated the Turing reaction-diffusion mechanism with the self-organization process of cells and produced multicellular 3D structures with the desired configurations in a rational manner. By optimizing the components of the hydrogel and applying exogenous morphogens, a variety of multicellular 3D architectures composed of multipotent vascular mesenchymal cells (VMCs) were formed inside hyaluronic acid (HA) hydrogels. These 3D architectures could mimic the features of trabecular bones and multicellular nodules. Based on the Turing reaction-diffusion instability of morphogens and cells, a theoretical model was proposed to predict the variations observed in 3D multicellular structures in response to exogenous factors. It enabled the feasibility to obtain diverse types of 3D multicellular structures by addition of Noggin and/or BMP2.

CONCLUSIONS

The morphological consistency between the simulation prediction and experimental results probably revealed a Turing-type mechanism underlying the 3D self-organization of VMCs in HA hydrogels. Our study has provided new ways to create a variety of self-organized 3D multicellular architectures for regenerating biomaterial and tissues in a Turing mechanism-based approach.

Osterix/Sp7 limits cranial bone initiation sites and is required for formation of sutures

During growth, individual skull bones overlap at sutures, where osteoblast differentiation and bone deposition occur. Mutations causing skull malformations have revealed some required genes, but many aspects of suture regulation remain poorly understood. We describe a zebrafish mutation in osterix/sp7, which causes a generalized delay in osteoblast maturation. While most of the skeleton is patterned normally, mutants have specific defects in the anterior skull and upper jaw, and the top of the skull comprises a random mosaic of bones derived from individual initiation sites. Osteoblasts at the edges of the bones are highly proliferative and fail to differentiate, consistent with global changes in gene expression. We propose that signals from the bone itself are required for orderly recruitment of precursor cells and growth along the edges. The delay in bone maturation caused by loss of Sp7 leads to unregulated bone formation, revealing a new mechanism for patterning the skull and sutures.

A MULTISCALE COMPUTATIONAL MODEL FOR THE GROWTH OF THE CRANIAL VAULT IN CRANIOSYNOSTOSIS

Craniosynostosis is a condition defined by premature closure of cranial vault sutures, which is associated with abnormalities of the brain and skull. Many causal relationships between discovered mutations and premature suture closure have been proposed but an understanding of the precise mechanisms remains elusive. This article describes a computational framework of biological processes underlying cranial growth that will enable a hypothesis driven investigation of craniosynostosis phenotypes using reaction-diffusion-advection methods and the finite element method. Primary centers of ossification in cranial vault are found using activator-substrate model that represents the behavior of key molecules for bone formation. Biomechanical effects due to the interaction between growing bone and soft tissue is investigated to elucidate the mechanism of growth of cranial vault.

A computational analysis of bone formation in the cranial vault in the mouse

Bones of the cranial vault are formed by the differentiation of mesenchymal cells into osteoblasts on a surface that surrounds the brain, eventually forming mineralized bone. Signaling pathways causative for cell differentiation include the actions of extracellular proteins driven by information from genes. We assume that the interaction of cells and extracellular molecules, which are associated with cell differentiation, can be modeled using Turing's reaction-diffusion model, a mathematical model for pattern formation controlled by two interacting molecules (activator and inhibitor). In this study, we hypothesize that regions of high concentration of an activator develop into primary centers of ossification, the earliest sites of cranial vault bone. In addition to the Turing model, we use another diffusion equation to model a morphogen (potentially the same as the morphogen associated with formation of ossification centers) associated with bone growth. These mathematical models were solved using the finite volume method. The computational domain and model parameters are determined using a large collection of experimental data showing skull bone formation in mouse at different embryonic days in mice carrying disease causing mutations and their unaffected littermates. The results show that the relative locations of the five ossification centers that form in our model occur at the same position as those identified in experimental data. As bone grows from these ossification centers, sutures form between the bones.

Optimal bone density distributions: numerical analysis of the osteocyte spatial influence in bone remodeling

In this paper a control and optimization procedure for bone remodeling simulations was adopted to study the effect of the osteocyte influence range on the predicted density distribution. In order to reach this goal, the osteocyte network regulating bone remodeling process in a 2-D bone sample was numerically simulated. The assumed proportional-integral-derivative (PID) bone remodeling rule was related to the error signal between the strain energy density and a selected target. Furthermore the control parameters and the target were optimally determined minimizing a suitable cost index: the goal was to minimize the final mass and the energy thus maximizing the stiffness. The continuum model results show that the developed and adapted trabecular structure was consistent with the applied loads and only depended on the external forces, the value of the cost index, the maximum attainable elastic modulus value (hence, the maximum density value) and the value of the energy target. The remodeling phenomenon determined the number and thickness of the trabeculae which are formed from a uniform distribution of mass density in the considered domain; this number and these thicknesses are controlled by the values assigned to the parameters of the model. In particular, the osteocyte decay distance (D) of the influence range affected the trabecular patterns formation, showing an important effect in the adaptive capacity of the optimization numerical model.