Hierarchical poroelasticity: movement of interstitial fluid between porosity levels in bones.

*(English)*Zbl 1185.74057Summary: The governing equations for the theory of poroelastic materials with hierarchical pore space architecture and compressible constituents undergoing small deformations are developed. These equations are applied to the problem of determining the exchange of pore fluid between the vascular porosity (PV) and the lacunar-canalicular porosity (PLC) in bone tissue due to cyclic mechanical loading and blood pressure oscillations. The result is basic to the understanding of interstitial flow in bone tissue that, in turn, is basic to understanding of nutrient transport from the vasculature to the bone cells buried in the bone tissue and to the process of mechanotransduction by these cells. A formula for the volume of fluid that moves between the PLC and PV in a cyclic loading is obtained as a function of the cyclic mechanical loading and blood pressure oscillations. Formulas for the oscillating fluid pore pressure in both the PLC and the PV are obtained as functions of the two driving forces, the cyclic mechanical straining and the blood pressure, both with specified amplitude and frequency. The results of this study also suggest a PV permeability greater than \(10^{ - 9} m^{2}\) and perhaps a little lower than \(10^{ - 8} m^{2}\). Previous estimates of this permeability have been as small as \(10^{ - 14} m^{2}\).

PDF
BibTeX
XML
Cite

\textit{S. C. Cowin} et al., Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 367, No. 1902, 3401--3444 (2009; Zbl 1185.74057)

Full Text:
DOI

##### References:

[1] | Beno, Journal of biomechanics 39 (13) pp 2378– (2006) |

[2] | Journal of Applied Physiology 12 pp 155– (1941) · JFM 67.0837.01 |

[3] | Journal of Applied Physiology 26 pp 182– (1955) · Zbl 0067.23603 |

[4] | J GEOPHYS RES 84 pp 7510– (1979) |

[5] | Journal of biomechanics 32 pp 218– (1999) |

[6] | TRANSP POROUS MEDIA 50 pp 35– (2003) |

[7] | J MECH PHYS SOLIDS 55 pp 161– (2007) · Zbl 1171.74017 |

[8] | Cowin, Journal of biomechanics 28 (11) pp 1281– (1995) |

[9] | J ZOOL LOND 206A pp 453– (1985) |

[10] | Scott, Journal of biomechanics 24 (2) pp 163– (1991) |

[11] | Edwards, Human pathology 39 (1) pp 49– (2008) |

[12] | Fornells, Annals of biomedical engineering 35 (10) pp 1687– (2007) |

[13] | PROC BIOENGINEERING CONF BED 50 pp 341– (2001) |

[14] | MECH MATER 40 pp 507– (2008) |

[15] | Goulet, Journal of biomechanics 41 (10) pp 2169– (2008) |

[16] | CAL TISSUE INT 36 pp 72S– (1984) |

[17] | Journal of biomechanics 11 pp 881– (1982) |

[18] | EUR J MECH A SOLIDS 15 pp 321– (1996) |

[19] | Li, Microvascular research 34 (3) pp 302– (1987) |

[20] | J GEOPHYS RES 76 pp 6414– (1971) |

[21] | J. MATER. RES. 23 pp 1307– (2008) |

[22] | MECH RES COMMUN 32 pp 645– (2005) · Zbl 1192.74258 |

[23] | Remond, Biomechanics and modeling in mechanobiology 7 (6) pp 487– (2008) |

[24] | REV GEOPHYS SPACE PHYS 14 pp 227– (1976) |

[25] | Smit, Journal of biomechanics 35 (6) pp 829– (2002) |

[26] | Steck, Journal of Theoretical Biology 220 (2) pp 249– (2003) |

[27] | Journal of biomedical engineering 125 pp 25– (2003) |

[28] | Vittas, Lymphology 22 (4) pp 173– (1989) |

[29] | Wang, Journal of biomechanics 32 (7) pp 663– (1999) |

[30] | Wehrli, Annals of biomedical engineering 33 (1) pp 79– (2005) |

[31] | Weinbaum, Journal of biomechanics 27 (3) pp 339– (1994) |

[32] | Zhang, Journal of biomechanical engineering 120 (6) pp 697– (1998) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.