A Multiscale Triphasic Biomechanical Model for Tumors’ Classification

  • K. Barber
  • C. S. Drapaca
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)

Abstract

The aim of this paper is to formulate a novel mathematical model that will be able to differentiate not only between normal and abnormal tissues, but, more importantly, between benign and malignant tumors. We present some very promising preliminary results of a multiscale triphasic model for biological tissues that couple the electro-chemical processes that take place in tissue’s microstructure and tissue’s biomechanics. The multiscaling is based on a recently developed homogenization technique for materials with evolving microstructure.

Keywords

Permeability Hydrated Convection Nite Incompressibility 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    F. A. Duck, Physical Properties of Tissues- A Comprehensive Reference Book, 6th edition, Sheffield, UK: Academic, 1990.Google Scholar
  2. 2.
    Y.C. Fung, Biomechanics - Mechanical Properties of Living Tissues, 2nd edition, Springer, New York, 1993.Google Scholar
  3. 3.
    W.Y. Gu, W.M. Lai and V.C. Mow, A mixture theory for charged-hydrated soft tissues containing multi-electrolytes: passive transport and swelling behaviors, J. Biomech. Engrg. 120, 169–180, 1998.CrossRefGoogle Scholar
  4. 4.
    R. Muthupillai, D.J. Lomas, P.J. Rossman, J.F. Greenleaf, A. Manduca and R.L. Ehman, Magnetic resonance elastography by direct visualization of propagating acoustic strain waves, Science 269, 1854–1857, 1995.CrossRefGoogle Scholar
  5. 5.
    R. Muthupillai, P.J Rossman, D.J. Lomas, J.F. Greenleaf, S.J. Riederer and R.L. Ehman, Magnetic resonance imaging of transverse acoustic strain waves, Magn. Reson. Med. 36, 266–274, 1996.Google Scholar
  6. 6.
    D.N. Sun, W.Y. Gu, X.E. Guo, W.M. Lai and V.C. Mow, A mixed _nite element formulation of triphasic mechanoelectrochemical theory for charged, hydrated biological soft tissues, Int. J. Numer. Meth. Engng. 45, 1375–1402, 1999.MATHCrossRefGoogle Scholar
  7. 7.
    M.A. Peter, Homogenization in domains with evolving microstructure, C.R. Mechanique 335, 357–362, 2007.Google Scholar
  8. 8.
    M.A. Peter, Homogenization of a chemical degradation mechanism inducing an evolving microstructure, C.R. Mecanique, 335, 679–684, 2007.Google Scholar
  9. 9.
    M.A. Peter, M. Bohm, Multiscale modeling of chemical degradation mechanisms in porous media with evolving microstructure, Multiscale Model.Simul. 7(4), 1643–1668, 2009.MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    B. Alberts, A. Johnston, J. Lewis, M. Raff, K. Roberts, P. Walter, Molecular Biology of the Cell, 5th Ed, 2007.Google Scholar
  11. 11.
    C.S. Drapaca, A.J. Palocaren, Biomechanical modeling of tumor classification and growth, Rev.Roum.Sci.Tech.- Mec.Appl., 55(2), 115–124, 2010.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • K. Barber
    • 1
  • C. S. Drapaca
    • 1
  1. 1.Department of Engineering Science and MechanicsThe Pennsylvania State UniversityUniversity ParkUSA

Personalised recommendations