TY - JOUR
T1 - A computational analysis of bone formation in the cranial vault in the mouse
AU - Lee, Chanyoung
AU - Richtsmeier, Joan T.
AU - Kraft, Reuben H.
N1 - Publisher Copyright:
© 2015 Lee, Richtsmeier and Kraft.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84995441412&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84995441412&partnerID=8YFLogxK
U2 - 10.3389/fbioe.2015.00024
DO - 10.3389/fbioe.2015.00024
M3 - Article
AN - SCOPUS:84995441412
SN - 2296-4185
VL - 3
JO - Frontiers in Bioengineering and Biotechnology
JF - Frontiers in Bioengineering and Biotechnology
IS - MAR
M1 - 00024
ER -