Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2008, Article ID 579172, 30 pages
http://dx.doi.org/10.1155/2008/579172
Review Article

An Anisotropic Constitutive Equation for the Stress Tensor of Blood Based on Mixture Theory

1National Energy Technology Laboratory (NETL), U.S. Department of Energy, P.O. Box 10940, Pittsburgh, PA 15236, USA
2Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA

Received 20 June 2008; Accepted 18 July 2008

Academic Editor: K. R. Rajagopal

Copyright © 2008 Mehrdad Massoudi and James F. Antaki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [18 citations]

The following is the list of published articles that have cited the current article.

  • S J Hund, and J F Antaki, “An extended convection diffusion model for red blood cell-enhanced transport of thrombocytes and leukocytes,” Physics in Medicine and Biology, vol. 54, no. 20, pp. 6415–6435, 2009. View at Publisher · View at Google Scholar
  • R. You, J. Peddieson, J. Gadiyaram, and S. Munukutla, “Simulation of particle/fluid flows in vertical circular pipes,” International Journal of Non-Linear Mechanics, vol. 45, no. 5, pp. 490–506, 2010. View at Publisher · View at Google Scholar
  • Mehrdad Massoudi, Jeongho Kim, Samuel J. Hund, and James F. Antaki, “Application of the theory of interacting continua to blood flow,” ASME 2011 Summer Bioengineering Conference, SBC 2011, pp. 735–736, 2011. View at Publisher · View at Google Scholar
  • Chia-Yuan Chen, Michael J. Patrick, Paola Corti, William Kowalski, Beth L. Roman, and Kerem Pekkan, “Analysis of early embryonic great-vessel microcirculation in zebrafish using high-speed confocal μPIV,” Biorheology, vol. 48, no. 5-6, pp. 305–321, 2011. View at Publisher · View at Google Scholar
  • Mehrdad Massoudi, Jeongho Kim, and James F. Antaki, “Modeling and numerical simulation of blood flow using the theory of interacting continua,” International Journal of Non-Linear Mechanics, vol. 47, no. 5, pp. 506–520, 2012. View at Publisher · View at Google Scholar
  • Antonio Fasano, and Angiolo Farina, “Modeling high flux hollow fibers dialyzers,” Discrete and Continuous Dynamical Systems - Series B, vol. 17, no. 6, pp. 1903–1937, 2012. View at Publisher · View at Google Scholar
  • Jeongho Kim, Mehrdad Massoudi, James F. Antaki, and Alberto Gandini, “Removal of malaria-infected red blood cells using magnetic cell separators: A computational study,” Applied Mathematics and Computation, vol. 218, no. 12, pp. 6841–6850, 2012. View at Publisher · View at Google Scholar
  • Mehrdad Massoudi, Wei-Tao Wu, and Nadine Aubry, “Channel flow of a Mixture of granular materials and a fluid,” ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE), vol. 7, 2013. View at Publisher · View at Google Scholar
  • Wei-Tao Wu, Nadine Aubry, Jeongho Kim, and James F. Antaki, “A numerical study of blood flow using mixture theory,” International Journal of Engineering Science, vol. 76, pp. 56–72, 2014. View at Publisher · View at Google Scholar
  • Melek Usal, Cahit Kurbanoglu, and Lokman Yunlu, “A Mathematical Model for the Magnetoelastic Behavior of Anisotropic Magnetic Sensitive Materials Based on Continuum Theory,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 15, no. 6, pp. 387–396, 2014. View at Publisher · View at Google Scholar
  • Wei-Tao Wu, Nadine Aubry, and Mehrdad Massoudi, “On the coefficients of the interaction forces in a two-phase flow of a fluid infused with particles,” International Journal of Non-Linear Mechanics, vol. 59, pp. 76–82, 2014. View at Publisher · View at Google Scholar
  • Jeongho Kim, James F. Antaki, and Mehrdad Massoudi, “Computational study of blood flow in microchannels,” Journal of Computational and Applied Mathematics, 2015. View at Publisher · View at Google Scholar
  • Wei-Tao Wu, Fang Yang, James F. Antaki, Nadine Aubry, and Mehrdad Massoudi, “Study of blood flow in several benchmark micro-channels using a two-fluid approach,” International Journal of Engineering Science, vol. 95, pp. 49–59, 2015. View at Publisher · View at Google Scholar
  • Wei-Tao Wu, Nadine Aubry, James F. Antaki, and Mehrdad Massoudi, “Flow of blood in micro-channels: recent results based on mixture theory,” International Journal of Advances in Engineering Sciences and Applied Mathematics, 2016. View at Publisher · View at Google Scholar
  • Francesco Garzotto, Iacopo Borsi, Angiolo Farina, Claudio Ronco, Jeong Chul Kim, and Antonio Fasano, “Modeling blood filtration in hollow fibers dialyzers coupled with patient's body dynamics,” Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni, vol. 27, no. 4, pp. 369–412, 2016. View at Publisher · View at Google Scholar
  • Wei-Tao Wu, Nadine Aubry, James Antaki, Mark McKoy, and Mehrdad Massoudi, “Heat Transfer in a Drilling Fluid with Geothermal Applications,” Energies, vol. 10, no. 9, pp. 1349, 2017. View at Publisher · View at Google Scholar
  • Wei-Tao Wu, Nadine Aubry, Mehrdad Massoudi, and James F. Antaki, “Transport of platelets induced by red blood cells based on mixture theory,” International Journal of Engineering Science, vol. 118, pp. 16–27, 2017. View at Publisher · View at Google Scholar
  • Wei-Tao Wu, Yubai Li, Nadine Aubry, Mehrdad Massoudi, and James F. Antaki, “Numerical Simulation of Red Blood Cell-Induced Platelet Transport in Saccular Aneurysms,” Applied Sciences, vol. 7, no. 5, pp. 484, 2017. View at Publisher · View at Google Scholar