Individual-based modelling of population growth and diffusion in discrete time.

Individual-based models (IBMs) of human populations capture spatio-temporal dynamics using rules that govern the birth, behavior, and death of individuals. We explore a stochastic IBM of logistic growth-diffusion with constant time steps and independent, simultaneous actions of birth, death, and movement that approaches the Fisher-Kolmogorov model in the continuum limit. This model is well-suited to parallelization on high-performance computers.

A bidirectional interface growth model for cranial interosseous suture morphogenesis.

Interosseous sutures exhibit highly variable patterns of interdigitation and corrugation. Recent research has identified fundamental molecular mechanisms of suture formation, and computer models have been used to simulate suture morphogenesis. However, the role of bone strain in the development of complex sutures is largely unknown, and measuring suture morphologies beyond the evaluation of fractal dimensions remains a challenge.

A morphogenetic model of cranial pneumatization based on the invasive tissue hypothesis.

The interpretation of patterns of cranial pneumatization in terms of evolution, development, and function is controversial, because these structures exhibit extreme diversity and variability among and within taxa. However, there is general consensus that air-filled spaces are formed by invasion of mucous epithelial tissue from the nasopharyngeal cavity into the surrounding cranial bones. This investigation presents a morphogenetic model of pneumatization, which combines empirical data about epithelial growth with physical concepts of surface growth.