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A poroelastic model valid in large strains with applications to perfusion in cardiac modeling - Computational Mechanics

  • ️Vignon-Clementel, I. E.
  • ️Thu Dec 10 2009

  • Spaan J, Kolyva C, van den Wijngaard J, ter Wee R, van Horssen P, Piek J, Siebes M (2008) Coronary structure and perfusion in health and disease. Phil Trans R Soc A 366(1878): 3137–3153

    Article  Google Scholar 

  • Horssen P, Wijngaard JPHM, Siebes M, Spaan JAE (2009) Improved regional myocardial perfusion measurement by means of an imaging cryomicrotome. In: 4th European conference of the international federation for medical and biological engineering. Springer, New York, pp 771–774

  • Westerhof N, Boer C, Lamberts RR, Sipkema P (2006) Cross-talk between cardiac muscle and coronary vasculature. Physiol Rev 86(4): 1263–1308

    Article  Google Scholar 

  • Smith N, Kassab G (2001) Analysis of coronary blood flow interaction with myocardial mechanics based on anatomical models. Phil Trans R Soc Lond A 359: 1251–1262

    Article  Google Scholar 

  • Smith N (2004) A computational study of the interaction between coronary blood flow and myocardial mechanics. Physiol Meas 25(4): 863–877

    Article  Google Scholar 

  • Terzaghi K (1943) Theoretical soil mechanics. Wiley, New York

    Book  Google Scholar 

  • Biot MA (1956) Theory of propagation of elastic waves in a fluid-saturated porous solid. II Higher frequency range. J Acoust Soc Am 28: 179–191

    Article  MathSciNet  Google Scholar 

  • Biot MA (1972) Theory of finite deformations of porous solids. Indiana Univ Math J 21: 597–620

    Article  MathSciNet  Google Scholar 

  • May-Newman K, McCulloch AD (1998) Homogenization modeling for the mechanics of perfused myocardium. Prog Biophys Mol Biol 69: 463–481

    Article  Google Scholar 

  • Almeida E, Spilker R (1998) Finite element formulations for hyperelastic transversely isotropic biphasic soft tissues. Comput Methods Appl Mech Eng 151(3–4): 513–538

    Article  MATH  Google Scholar 

  • Yang Z, Smolinski P (2006) Dynamic finite element modeling of poroviscoelastic soft tissue. Comput Methods Biomech Biomed Eng 9(1): 7–16

    Article  Google Scholar 

  • Borja R (2006) On the mechanical energy and effective stress in saturated and unsaturated porous continua. Int J Solids Struct 43(6): 1764–1786

    Article  MATH  Google Scholar 

  • Badia S, Quaini A, Quarteroni A (2009) Coupling Biot and Navier–Stokes equations for modelling fluid–poroelastic media interaction. J Comput Phys (to appear)

  • Koshiba N, Ando J, Chen X, Hisada T (2007) Multiphysics simulation of blood flow and LDL transport in a porohyperelastic arterial wall model. J Biomech Eng 129: 374

    Article  Google Scholar 

  • Calo V, Brasher N, Bazilevs Y, Hughes T (2008) Multiphysics model for blood flow and drug transport with application to patient-specific coronary artery flow. Comput Mech 43(1): 161–177

    Article  MATH  Google Scholar 

  • Feenstra P, Taylor C (2009) Drug transport in artery walls: a sequential porohyperelastic-transport approach. Comput Methods Biomech Biomed Eng 12(3): 263–276

    Article  Google Scholar 

  • Huyghe JM, van Campen DH (1991) Finite deformation theory of hierarchically arranged porous solids: I. Balance of mass and momentum. Int J Eng Sci 33(13): 1861–1871

    Article  Google Scholar 

  • Huyghe JM, van Campen DH (1991) Finite deformation theory of hierarchically arranged porous solids: II. Constitutive behaviour. Int J Eng Sci 33(13): 1861–1871

    Article  Google Scholar 

  • Cimrman R, Rohan E (2003) Modelling heart tissue using a composite muscle model with blood perfusion. In: Bathe KJ (ed) Computational fluid and solid mechanics, 2nd MIT conference, pp 1642–1646

  • Vankan W, Huyghe J, Janssen J, Huson A (1997) A finite element mixture model for hierarchical porous media. Int J Numer Methods Eng 40: 193–210

    Article  Google Scholar 

  • Coussy O (1995) Mechanics of porous continua. Wiley, New York

    MATH  Google Scholar 

  • de Buhan P, Chateau X, Dormieux L (1998) The constitutive equations of finite-strain poroelasticity in the light of a micro-macro approach. Eur J Mech A/Solids 17(6): 909–922

    Article  MATH  MathSciNet  Google Scholar 

  • Ciarlet PG, Geymonat G (1982) Sur les lois de comportement en élasticité non linéaire. CRAS Série II 295: 423–426

    MATH  MathSciNet  Google Scholar 

  • Sainte-Marie J, Chapelle D, Cimrman R, Sorine M (2006) Modeling and estimation of the cardiac electromechanical activity. Comput Struct 84: 1743–1759

    Article  MathSciNet  Google Scholar 

  • Brezzi F, Fortin M (1991) Mixed and hybrid finite element method. Springer, New York

    Google Scholar 

  • Irons B, Tuck R (1969) A version of the Aitken accelerator for computer implementation. Int J Numer Methods Eng 1: 275–277

    Article  MATH  Google Scholar 

  • Bestel J, Clément F, Sorine M (2001) A biomechanical model of muscle contraction. In: Niessen WJ, Viergever MA (eds) Lectures Notes in Computer Science, vol 2208. Springer-Verlag, New York, pp 1159–1161

    Google Scholar 

  • Krejčí P, Sainte-Marie J, Sorine M, Urquiza J (2005) Solutions to muscle fiber equations and their long time behaviour. Nonlinear Anal: Real World Anal 7(4): 535–558

    Article  Google Scholar 

  • Chapelle D, Le Tallec P, Moireau P (2009) Mechanical modeling of the heart contraction. (in preparation)

  • Chapelle D, Fernánde M, Gerbeau J-F, Moireau P, Sainte- Marie J, Zemzemi N (2009) Numerical simulation of the electromechanical activity of the heart. In: FIMH, vol 5528 of Lecture Notes in Computer Science, pp 357–365

  • Boulakia M, Cazeau S, Fernández MA, Gerbeau J-F, Zemzemi N (2009) Mathematical modeling of electrocardiograms: a numerical study. Research Report RR-6977, INRIA. URL http://hal.inria.fr/inria-00400490/en/

  • Zinemanas D, Beyar R, Sideman S (1995) An integrated model of LV muscle mechanics, coronary flow, and fluid and mass transport. Am J Physiol Heart Circ Physiol 268(2): H633–H645

    Google Scholar 

  • Kassab GS, Le KN, Fung Y-CB (1999) A hemodynamic analysis of coronary capillary blood flow based on anatomic and distensibility data. Am J Physiol Heart Circ Physiol 277(6): H2158–H2166

    Google Scholar 

  • Fronek K, Zweifach B (1975) Microvascular pressure distribution in skeletal muscle and the effect of vasodilation. Am J Physiol 228(3): 791–796

    Google Scholar 

  • Berne R, Levy M (2001) Cardiovascular physiology. St Louis, Mosby

  • Gonzalez F, Bassingthwaighte JB (1990) Heterogeneities in regional volumes of distribution and flows in rabbit heart. Am J Physiol Heart Circ Physiol 258(4): H1012–H1024

    Google Scholar 

  • May-Newman K, Chen C, Oka R, Haslim R, DeMaria A (2001) Evaluation of myocardial perfusion using three-dimensional myocardial contrast echocardiography. In: Nuclear science symposium conference record, vol 3. IEEE, pp 1691–1694

  • Ghista D, Ng E (2007) Cardiac perfusion and pumping engineering. World Scientific, Singapore

    Google Scholar 

  • Huyghe JM, Arts T, van Campen DH, Reneman RS (1992) Porous medium finite element model of the beating left ventricle. Am J Physiol Heart Circ Physiol 262(4): H1256–H1267

    Google Scholar 

  • Ashikaga H, Coppola BA, Yamazaki K, Villarreal FJ, Omens JH, Covell JW (2008) Changes in regional myocardial volume during the cardiac cycle: implications for transmural blood flow and cardiac structure. Am J Physiol Heart Circ Physiol 295(2): H610–H618

    Article  Google Scholar 

  • Goto M, Flynn AE, Doucette JW, Jansen CM, Stork MM, Coggins DL, Muehrcke DD, Husseini WK, Hoffman JI (1991) Cardiac contraction affects deep myocardial vessels predominantly. Am J Physiol Heart Circ Physiol 261(5): H1417–H1429

    Google Scholar 

  • Gregg D, Green H (1940) Registration and interpretation of normal phasic inflow into a left coronary artery by an improved differential manometric method. Am J Physiol 130: 114–125

    Google Scholar 

  • Nichols W, O’Rourke M (2005) McDonald’s blood flow in arteries. Hodder Arnold