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Continuum Mechanics and Thermodynamics

, Volume 30, Issue 5, pp 995–1009 | Cite as

New description of gradual substitution of graft by bone tissue including biomechanical and structural effects, nutrients supply and consumption

  • Yanfei Lu
  • Tomasz Lekszycki
Open Access
Original Article
  • 91 Downloads

Abstract

A new description of graft substitution by bone tissue is proposed in this work. The studied domain is considered as a continuum model consisting of a mixture of the bone tissue and the graft material. Densities of both components evolve in time as a result of cellular activity and biodegradation. The proposed model focuses on the interaction between the bone cell activity, mechanical stimuli, nutrients supply and scaffold microstructure. Different combinations of degradation rate and stiffness of the graft material were examined by numerical simulation. It follows from the calculations that the degradation rate of the scaffold should be tuned to the synthesis/resorption rate of the tissue, which are dependent among the others on scaffold porosity changes. Simulation results imply potential criteria to choose proper bone substitute material in consideration of degradation rate, initial porosity and mechanical characteristics.

Keywords

Bone regeneration Bioresorbable and biodegradable material Microstructure Nutrients supply Numerical simulation 

List of symbols

\(\varvec{\varepsilon }\)

Strain

\(\varvec{\sigma }\)

Stress

\(W_\mathrm{s}\)

Strain energy

\(\varphi \)

Porosity

E

Young’s modulus

\(d_\mathrm{a}\), \(d_\mathrm{s}\)

Normalized sensor/actor cell densities

S

Mechanical stimulus

\(S_0\)

Reference stimulus

R

Nutrients consumption rate

\(z_\mathrm{s}\), \(z_\mathrm{a}\)

Sensor/actor cell activities

L

Coefficient defining the range of stimulus without cell activity

\(A_\mathrm{m0}\)

Degradation rate of bone substitute material

\(s_\mathrm{b}\), \(r_\mathrm{b}\), \(r_\mathrm{m}\)

Synthesis / resorption coefficients

Notes

Acknowledgements

This research was supported by Warsaw University of Technology Dean’s grant for young researchers No. 504/03098/1101 and Polish National Science Centre (NCN) grant Preludium No. 2017/25/N/ST7/02334.

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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Faculty of Engineering ProductionWarsaw University of TechnologyWarsawPoland
  2. 2.Department of Experimental Physiology and PathophysiologyMedical University of WarsawWarsawPoland

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