Vibration exercise for treatment of osteoporosis: A theoretical model

Majid Aleyaasin, John J Harrigan

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Orthopaedic rehabilitation of osteoporosis by muscle vibration exercise is investigated theoretically using Wolff's theory of strain-induced bone ‘remodelling’. The remodelling equation for finite amplitude vibration to be transmitted to the bone via muscle corresponds to a slowly time-varying non-linear dynamic system. This slowly time-varying system is governed by a Riccatti equation with rapidly varying coefficients that oscillate with the frequency of the applied vibration. An averaging technique is used to determine the effective force transmitted to the bone. This force is expressed in terms of the stiffness and damping parameters of the connected muscle. The analytical result predicts that, in order to obtain bone reinforcement, the frequency and amplitude of vibration should not exceed specified levels. Furthermore, low-frequency vibration does not stimulate the bone sufficiently to cause significant remodelling. The theoretical model herein confirms the clinical recommendations regarding vibration exercise and its effects on rehabilitation. In a numerical example, the model predicts that a femur with reduced bone mass as a result of bed rest will be healed completely by vibration consisting of an acceleration of 2g applied at a frequency of 30¿Hz over a period of 250 days.
Original languageEnglish
Pages (from-to)1161-1166
Number of pages6
JournalProceedings of the Institution of Mechanical Engineers. Part H, Journal of Engineering in Medicine
Volume222
Issue number7
DOIs
Publication statusPublished - 1 Oct 2008

Fingerprint

Bone
Muscle
Patient rehabilitation
Time varying systems
Orthopedics
Reinforcement
Dynamical systems
Damping
Stiffness

Keywords

  • bone remodelling
  • theoretical biomechanics
  • muscle vibration
  • osteoporosis

Cite this

@article{f22da75f19bb49018d4a795a23ec56ea,
title = "Vibration exercise for treatment of osteoporosis: A theoretical model",
abstract = "Orthopaedic rehabilitation of osteoporosis by muscle vibration exercise is investigated theoretically using Wolff's theory of strain-induced bone ‘remodelling’. The remodelling equation for finite amplitude vibration to be transmitted to the bone via muscle corresponds to a slowly time-varying non-linear dynamic system. This slowly time-varying system is governed by a Riccatti equation with rapidly varying coefficients that oscillate with the frequency of the applied vibration. An averaging technique is used to determine the effective force transmitted to the bone. This force is expressed in terms of the stiffness and damping parameters of the connected muscle. The analytical result predicts that, in order to obtain bone reinforcement, the frequency and amplitude of vibration should not exceed specified levels. Furthermore, low-frequency vibration does not stimulate the bone sufficiently to cause significant remodelling. The theoretical model herein confirms the clinical recommendations regarding vibration exercise and its effects on rehabilitation. In a numerical example, the model predicts that a femur with reduced bone mass as a result of bed rest will be healed completely by vibration consisting of an acceleration of 2g applied at a frequency of 30¿Hz over a period of 250 days.",
keywords = "bone remodelling, theoretical biomechanics, muscle vibration, osteoporosis",
author = "Majid Aleyaasin and Harrigan, {John J}",
year = "2008",
month = "10",
day = "1",
doi = "10.1243/09544119JEIM439",
language = "English",
volume = "222",
pages = "1161--1166",
journal = "Proceedings of the Institution of Mechanical Engineers. Part H, Journal of Engineering in Medicine",
issn = "0954-4119",
publisher = "SAGE Publications Ltd",
number = "7",

}

TY - JOUR

T1 - Vibration exercise for treatment of osteoporosis

T2 - A theoretical model

AU - Aleyaasin, Majid

AU - Harrigan, John J

PY - 2008/10/1

Y1 - 2008/10/1

N2 - Orthopaedic rehabilitation of osteoporosis by muscle vibration exercise is investigated theoretically using Wolff's theory of strain-induced bone ‘remodelling’. The remodelling equation for finite amplitude vibration to be transmitted to the bone via muscle corresponds to a slowly time-varying non-linear dynamic system. This slowly time-varying system is governed by a Riccatti equation with rapidly varying coefficients that oscillate with the frequency of the applied vibration. An averaging technique is used to determine the effective force transmitted to the bone. This force is expressed in terms of the stiffness and damping parameters of the connected muscle. The analytical result predicts that, in order to obtain bone reinforcement, the frequency and amplitude of vibration should not exceed specified levels. Furthermore, low-frequency vibration does not stimulate the bone sufficiently to cause significant remodelling. The theoretical model herein confirms the clinical recommendations regarding vibration exercise and its effects on rehabilitation. In a numerical example, the model predicts that a femur with reduced bone mass as a result of bed rest will be healed completely by vibration consisting of an acceleration of 2g applied at a frequency of 30¿Hz over a period of 250 days.

AB - Orthopaedic rehabilitation of osteoporosis by muscle vibration exercise is investigated theoretically using Wolff's theory of strain-induced bone ‘remodelling’. The remodelling equation for finite amplitude vibration to be transmitted to the bone via muscle corresponds to a slowly time-varying non-linear dynamic system. This slowly time-varying system is governed by a Riccatti equation with rapidly varying coefficients that oscillate with the frequency of the applied vibration. An averaging technique is used to determine the effective force transmitted to the bone. This force is expressed in terms of the stiffness and damping parameters of the connected muscle. The analytical result predicts that, in order to obtain bone reinforcement, the frequency and amplitude of vibration should not exceed specified levels. Furthermore, low-frequency vibration does not stimulate the bone sufficiently to cause significant remodelling. The theoretical model herein confirms the clinical recommendations regarding vibration exercise and its effects on rehabilitation. In a numerical example, the model predicts that a femur with reduced bone mass as a result of bed rest will be healed completely by vibration consisting of an acceleration of 2g applied at a frequency of 30¿Hz over a period of 250 days.

KW - bone remodelling

KW - theoretical biomechanics

KW - muscle vibration

KW - osteoporosis

U2 - 10.1243/09544119JEIM439

DO - 10.1243/09544119JEIM439

M3 - Article

VL - 222

SP - 1161

EP - 1166

JO - Proceedings of the Institution of Mechanical Engineers. Part H, Journal of Engineering in Medicine

JF - Proceedings of the Institution of Mechanical Engineers. Part H, Journal of Engineering in Medicine

SN - 0954-4119

IS - 7

ER -