Bone remodeling: an improved spatiotemporal mathematical model

• Published in: Archive of applied mechanics (1991) Vol. 90; no. 3; pp. 635 - 649
• Main Authors: Peyroteo, M. M. A., Belinha, J., Dinis, L. M. J. S., Jorge, R. M. Natal
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-03-2020; Springer Nature B.V
• Subjects: Biomedical materials; Bulk density; Classical Mechanics; Computer simulation; Engineering; Finite element method; Mathematical analysis; Mathematical models; Numerical methods; Original; Osteoblasts; Osteoporosis; Spatial distribution; Theoretical and Applied Mechanics; Two dimensional models; Vertebrates; Osteoblast; Osteoclast; Bone mass; Biomathematics; Bone remodeling; Numerical discretization
• ISSN: 0939-1533; 1432-0681
• DOI: 10.1007/s00419-019-01631-z

Bone remodeling is a key process in vertebrate organisms, since it is responsible for maintaining skeleton’s integrity. However, in some pathological conditions, such as osteoporosis or Paget’s disease, bone’s function becomes compromised. To gain a better understanding about these conditions, bone remodeling has become a determinant subject of research. Remodeling implies resorption of bone by osteoclasts followed by formation of new tissue by osteoblasts. The interaction between these two bone cells is reproduced in this work by extending the bone remodeling model of Ayati et al. (Biol Direct 5:28, 2010.
https://doi.org/10.1186/1745-6150-5-28
). Also, for the first time, a discrete numerical method—finite element method (FEM)—is applied to solve the remodeling equations and analyze the results. A single cycle of remodeling is simulated using a two-dimensional bone patch. Results show that the developed mathematical model is able to correlate bone cell dynamics with different phases of the remodeling process, allowing to obtain the transient spatial distribution of bone’s apparent density along time. Thus, the presented model reveals itself as a successful approach, producing an accurate temporal-spatial evolution of bone cells during an event of bone remodeling.