title: A cellular automata model of bone formation.
abstract: Bone remodeling is an elegantly orchestrated process by which osteocytes, osteoblasts and osteoclasts function as a syncytium to maintain or modify bone. On the microscopic level, bone consists of cells that create, destroy and monitor the bone matrix. These cells interact in a coordinated manner to maintain a tightly regulated homeostasis. It is this regulation that is responsible for the observed increase in bone gain in the dominant arm of a tennis player and the observed increase in bone loss associated with spaceflight and osteoporosis. The manner in which these cells interact to bring about a change in bone quality and quantity has yet to be fully elucidated. But efforts to understand the multicellular complexity can ultimately lead to eradication of metabolic bone diseases such as osteoporosis and improved implant longevity. Experimentally validated mathematical models that simulate functional activity and offer eventual predictive capabilities offer tremendous potential in understanding multicellular bone remodeling. Here we undertake the initial challenge to develop a mathematical model of bone formation validated with in vitro data obtained from osteoblastic bone cells induced to mineralize and quantified at 26 days of culture. A cellular automata model was constructed to simulate the in vitro characterization. Permutation tests were performed to compare the distribution of the mineralization in the cultures and the distribution of the mineralization in the mathematical models. The results of the permutation test show the distribution of mineralization from the characterization and mathematical model come from the same probability distribution, therefore validating the cellular automata model.
authors.affiliation: Department of Mathematics and Statistics, Youngstown State University, USA.
authors.forename: Gabrielle K
authors.initials: GK
authors.lastname: Van Scoy
authors.affiliation: Department of Biomedical Engineering, The University of Akron, USA.
authors.forename: Estee L
authors.initials: EL
authors.lastname: George
authors.affiliation: Department of Mathematics and Statistics, Youngstown State University, USA.
authors.forename: Flora
authors.initials: F
authors.lastname: Opoku Asantewaa
authors.affiliation: Department of Mathematics and Statistics, Youngstown State University, USA.
authors.forename: Lucy
authors.initials: L
authors.lastname: Kerns
authors.affiliation: Department of Biomedical Engineering, The University of Akron, USA.
authors.forename: Marnie M
authors.initials: MM
authors.lastname: Saunders
authors.affiliation: Department of Mathematics and Statistics, Youngstown State University, USA. Electronic address: aprietolangarica@ysu.edu.
authors.forename: Alicia
authors.initials: A
authors.lastname: Prieto-Langarica
mesh_terms: D000818:Animals; D016723:Bone Remodeling; D006801:Humans; D008962:Models, Theoretical; D010006:Osteoblasts / Q000502:physiology*; D010012:Osteogenesis / Q000502:physiology*
keywords: Agent-based model; Bone; Bone formation; Cellular automata; Mathematical models of bone formation; Osteoblast; Permutation tests