### Abstract

This paper is concerned with the formulation of a mathematical model to describe mechanical bone remodeling process. Firstly, mechanical stimulus is defined as a function of the rate-ofdeformation power per unit mass. Physiological signal transmission processes of remodeling from the mechanical stimulus to change of bone density are described by n + 1 sequential evolution equations with n + l macroscopic internal state variables. The evolution equations are established on the basis of the experimental results in a literature. The value of the internal variable in the last step specifies the balance level of bone density, which is the target of the current bone density. The comparison of the predicted results with the corresponding experimental ones shows that this model can quantitatively describe a time-dependent process of bone remodeling.

Original language | English |
---|---|

Pages (from-to) | 191-197 |

Number of pages | 7 |

Journal | Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A |

Volume | 66 |

Issue number | 641 |

Publication status | Published - 2000 |

Externally published | Yes |

### Fingerprint

### Keywords

- Biomechanics
- Bone
- Mathematical model
- Remodeling

### ASJC Scopus subject areas

- Mechanical Engineering
- Mechanics of Materials
- Materials Science(all)

### Cite this

*Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A*,

*66*(641), 191-197.

**Formulation of a mathematical model for mechanical bone remodeling process.** / Tanaka, Eiichi; Yamamoto, Sota; Aoki, Yoichi; Okada, Takahiro; Yamada, Hiroshi.

Research output: Contribution to journal › Article

*Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A*, vol. 66, no. 641, pp. 191-197.

}

TY - JOUR

T1 - Formulation of a mathematical model for mechanical bone remodeling process

AU - Tanaka, Eiichi

AU - Yamamoto, Sota

AU - Aoki, Yoichi

AU - Okada, Takahiro

AU - Yamada, Hiroshi

PY - 2000

Y1 - 2000

N2 - This paper is concerned with the formulation of a mathematical model to describe mechanical bone remodeling process. Firstly, mechanical stimulus is defined as a function of the rate-ofdeformation power per unit mass. Physiological signal transmission processes of remodeling from the mechanical stimulus to change of bone density are described by n + 1 sequential evolution equations with n + l macroscopic internal state variables. The evolution equations are established on the basis of the experimental results in a literature. The value of the internal variable in the last step specifies the balance level of bone density, which is the target of the current bone density. The comparison of the predicted results with the corresponding experimental ones shows that this model can quantitatively describe a time-dependent process of bone remodeling.

AB - This paper is concerned with the formulation of a mathematical model to describe mechanical bone remodeling process. Firstly, mechanical stimulus is defined as a function of the rate-ofdeformation power per unit mass. Physiological signal transmission processes of remodeling from the mechanical stimulus to change of bone density are described by n + 1 sequential evolution equations with n + l macroscopic internal state variables. The evolution equations are established on the basis of the experimental results in a literature. The value of the internal variable in the last step specifies the balance level of bone density, which is the target of the current bone density. The comparison of the predicted results with the corresponding experimental ones shows that this model can quantitatively describe a time-dependent process of bone remodeling.

KW - Biomechanics

KW - Bone

KW - Mathematical model

KW - Remodeling

UR - http://www.scopus.com/inward/record.url?scp=77949670956&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949670956&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:77949670956

VL - 66

SP - 191

EP - 197

JO - Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A

JF - Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A

SN - 0387-5008

IS - 641

ER -