Tissue–fluid interface analysis using biphasic finite element method

References

• Alazmi , B and Vafai , K . 2001 . Analysis of fluid and heat transfer interfacial conditions between a porous medium and a fluid layer . Int J Heat Mass Transfer , 44 : 1735 – 1749 .
   Web of Science ®Google Scholar
• Almeida , ES and Spilker , RL . 1998 . Finite element formulations for hyperelastic transversely isotropic biphasic soft tissues . Comput Methods Appl Mech Engng , 151 ( 3/4 ) : 513 – 538 .
   Google Scholar
• Bathe , M and Kamm , RD . 1999 . A fluid–structure interaction finite element analysis of pulsatile blood flow through a compliant stenotic artery . J Biomech Eng , 21 : 361 – 369 .
   Google Scholar
• Chan , B , Donzelli , PS and Spilker , RL . 2000 . A mixed-penalty biphasic finite element formulation incorporating viscous fluids and material interfaces . Ann Biomed Eng , 28 ( 6 ) : 589 – 597 .
   PubMedGoogle Scholar
• Cieszko , M and Kubik , J . 1999 . Derivation of matching conditions at the contact surface between fluid-saturated porous solid and bulk fluid . Transport Porous Med , 34 : 319 – 336 .
   Web of Science ®Google Scholar
• Costa , VAF , Oliveira , LA , Baliga , BR and Sousa , ACM . 2004 . Simulation of coupled flows in adjacent porous and open domains using a control volume finite element method . Numer Heat Transfer A , 45 : 675 – 697 .
   Web of Science ®Google Scholar
• Damiano , ER , Duling , BR , Ley , K and Skalak , TC . 1996 . Axisymmetric pressure driven flow of rigid pellets through a cylindrical tube lined with a deformable porous wall layer . J Fluid Mech , 314 : 163 – 189 .
   Web of Science ®Google Scholar
• Gartling , DK , Hickox , CE and Givler , RC . 1996 . Simulation of coupled viscous and porous flow problems . Comp Fluid Dyn , 7 : 23 – 48 .
   Web of Science ®Google Scholar
• Hou , JS , Holmes , MH , Lai , WM and Mow , VC . 1989 . Boundary conditions at the cartilage–synovial fluid interface for joint lubrication and theoretical verifications . J Biomech Eng , 111 ( 1 ) : 78 – 87 .
   PubMed Web of Science ®Google Scholar
• Johnson , M and Tarbell , JM . 2001 . A biphasic, aniostropic model of the aortic wall . J Biomech Eng , 123 ( 1 ) : 52 – 57 .
   PubMedGoogle Scholar
• Massarotti , N , Nithiarasu , P and Zienkiewicz , OC . 2001 . Natural convection in porous medium–fluid interface problems . Int J Numer Methods Heat Fluid Flow , 11 ( 5 ) : 473 – 490 .
   Web of Science ®Google Scholar
• Pralhad , RN and Schultz , DH . 2004 . Modeling of arterial stenosis and its application to blood diseases . Math Biosci , 190 : 203 – 220 .
   PubMedGoogle Scholar
• Prosi , M , Zunino , P , Perktold , K and Quarteroni , A . 2005 . Mathematical and numerical models for transfer of low-density lipoproteins through the arterial walls: a new methodology for the model set up with applications to the study of disturbed lumenal flow . J Biomech , 38 ( 4 ) : 903 – 917 .
   PubMedGoogle Scholar
• Reddy , JN . 2004 . An introduction to nonlinear finite element analysis , Oxford : Oxford University Press .
   Google Scholar
• Reddy , JN . 2006 . An introduction to the finite element method , New York : McGraw-Hill .
   Google Scholar
• Reddy , JN . 2008 . An introduction to continuum mechanics with applications , Cambridge : Cambridge University Press .
   Google Scholar
• Roose , T , Netti , PA , Munn , LL , Boucher , Y and Jain , RK . 2003 . Solid stress generated by spheroid growth estimated using a linear poroelasticity model . Microvasc Res , 66 : 204 – 212 .
   PubMed Web of Science ®Google Scholar
• Spilker , RL and Maxian , TA . 1990 . A mixed-penalty finite element formulation of the linear biphasic theory for soft tissues . Int J Numer Methods Eng , 30 ( 5 ) : 1063 – 1082 .
   Google Scholar
• Spilker , RL and Suh , JK . 1990 . Formulation and evaluation of a finite element model for the biphasic model of hydrated soft tissues . Comput Struct , 35 ( 4 ) : 425 – 439 .
   Web of Science ®Google Scholar
• Spilker , RL , Suh , JK and Mow , VC . 1988 . Computational methods in bioengineering , New York : ASME .
   Google Scholar
• Stangeby , DK and Ethier , CR . 2002 . Computational analysis of coupled blood–wall arterial LDL transport . J Biomech Eng , 124 ( 1 ) : 1 – 8 .
   PubMedGoogle Scholar
• Tang , D , Yang , J , Yang , C and Ku , DN . 1999 . A nonlinear axisymmetric model with fluid–wall interactions for steady viscous flow in stenotic elastic tubes . J Biomech Eng , 121 : 494 – 501 .
   PubMedGoogle Scholar
• Tang , D , Yang , C , Kobayashi , S and Ku , DN . 2001 . Steady flow and wall compression in stenotic arteries: a three-dimensional thick-wall model with fluid–wall interactions . J Biomech Eng , 123 ( 6 ) : 548 – 557 .
   PubMed Web of Science ®Google Scholar
• Theodorou , G and Bellet , D . 1986 . Laminar flows of a non-Newtonian fluid in mild stenosis . Comput Method Appl Mech Eng , 54 ( 1 ) : 111 – 123 .
   Google Scholar
• Vankan , WJ , Huyghe , JM , Janssen , JD and Huson , A . 1996 . Poroelasticity of saturated solids with an application to blood perfusion . Int J Engng Sci , 34 ( 9 ) : 1019 – 1031 .
   Google Scholar
• Varghese , SS and Frankel , SH . 2003 . Numerical modeling of pulsatile turbulent flow in stenotic vessels . J Biomech Eng , 125 : 445 – 460 .
   PubMed Web of Science ®Google Scholar
• Vito , RP and Dixon , AS . 2003 . Blood vessel constitutive models . Annu Rev Biomed Eng , 5 : 413 – 439 .
   PubMed Web of Science ®Google Scholar
• Weinbaum , S , Tarbell , JM and Damiano , ER . 2007 . The structure and function of the endothelial glycocalyx layer . Annu Rev Biomed Eng , 9 : 121 – 167 .
   PubMed Web of Science ®Google Scholar