Stiffening of the Cardiac Wall by Coronary Blood Volume Increase: A Finite Element Simulation

  • Jacques M. Huyghe
  • Theo Arts
  • Dick H. van Campen
  • Roberts S. Reneman
Part of the NATO ASI Series book series (NSSA, volume 193)


A porous medium finite element model of the beating left ventricle is used to simulate the influence of the intracoronary blood volume on left ventricular mechanics. The spongy material is composed of incompressible solid (myocardial tissue) and incompressible fluid (coronary blood). The model is axisymmetric and allows for finite deformation, including torsion around the axis of symmetry. The total stress in the tissue is the sum of the intramyocardial pressure, effective passive stress due to myocardial deformation and the contractile fiber stress. The model is able to simulate a full cardiac cycle. Three-dimensional end-systolic deformation computed relative to the end-diastolic state is shown to be consistent with experimental data from the literature. The direction of maximal shortening varied less than 30° fiuni endocardium to epicardium while fiber direction varied by more than 100°. It is shown that the ventricular model exhibits diastolic stiffening following an increase of intracoronary blood volume. End-diastolic left ventricular pressure increases from 1.5 kPa to 2.0 kPa when raising intracoronary blood volume from 9 to 14 ml per 100 g myocardial tissue. The model simulation suggests that the mechanism underlying the increase in end-diastolic pressure at higher coronary blood volumes, is an increase in passive stiffness of the myocardial fibers. This increased stiffness is the combined result of an overall increase in strain in myocardial tissue and the non-linear stress-strain relationship of myocardial tissue.


Left ventricle porous medium mixture erectile properties diastole coronary perfusion. 


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  1. Huyghe, J.M., 1986, “Non-linear finite element models of the beating left ventricle and the intramyocardial coronary circulation”. Ph.D.-thesis. Eindhoven University of Technology, the Netherlands.Google Scholar
  2. Huyghe, J.M., Oomens, C.W., Van Campen, D.H. and Heethaar, R.M., 1989, Low Reynolds steady state flow through a branching network of rigid vessels: I. A mixture theory, Biorheology 26: 55.Google Scholar
  3. Huyghe, J.M., Oomens, C.W. and Van Campen, D.H., 1989, Low Reynolds number steady state flow through a branching network of rigid vessels: II A finite element mixture model, Biorheolocgv 26: 73.Google Scholar
  4. Morgenstern, C., Holtes, V., Arnold, G., Lochner, W., 1973, The influence of coronary pressure and coronary flow on intracoronary blood volume and geometry of the left ventricle, Pflueg. Arch., 340:101.Google Scholar
  5. Olsen, C.O., Attarian, D.E., Jones, R.N., Hill, R.C., Sink, J.D., Lee, K.L., Wechsler, A.S., 1981, The coronary pressure-flow determinants of left ventricular compliance in dogs, Circ. Res., 49:856.Google Scholar
  6. Prinzen, F.W., Arts, T., Van der Vusse,’G.J., and Reneman, R.S., 1984, Fiber shortening in the inner layers of the left ventricular wall as assessed from epicardial deformation during normoxia and ischemia, J. Biomech., 17: 801.Google Scholar
  7. Streeter, D.D. Jr. and Hanna, W.T., 1973, Engineering mechanics of successive states in canine left ventricular myocardium: II. Fiber angle and sarcomere length, Circ. Res., 33:657.Google Scholar
  8. Van Heuningen, R., Rijnsburger, W.H. and Ter Keurs, H.E. D.J.. 1982, Sarcomere length control in striated muscle, Am. J. Physiol., 242:H411.PubMedGoogle Scholar
  9. Vogel, W.M., Apstein, C.S., Briggs, L.L., Gaasch, L. and Ahn, J., 1982, Acute alterations in left ventricular diastolic chamber stiffness: role of the erectile effect of coronary arterial pressure and flow in normal and damaged hearts, Circ. Res., 51:465.PubMedCrossRefGoogle Scholar
  10. Waldman, L.K., Fung, Y.C. and Covell, J.W., 1985, Transmural myocardial deformation in the canine left ventricle; normal in vivo three-dimensional finite strains, Circ. Res., 57:152.CrossRefGoogle Scholar
  11. Waldman, L.K., Nosan, D., Villarreal, F. and Covell, J.W., 1988, Relation between transmural deformation and local myofiber direction in canine left ventricle, Circ. Res., 63:550.PubMedCrossRefGoogle Scholar
  12. Yin, C.P., Strumpf, R.K., Chew, P.H. and Zeger, S.L., 1987, Quantification of the mechanical properties of non-contracting canine myocardium under simultaneous biaxial loading, J. Biomech., 20:577.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Jacques M. Huyghe
    • 1
  • Theo Arts
    • 2
  • Dick H. van Campen
    • 4
  • Roberts S. Reneman
    • 3
  1. 1.Departments of Movement SciencesEindhoven University of TechnologyEindhoventhe Netherlands
  2. 2.Departments of BiophysicsEindhoven University of TechnologyEindhoventhe Netherlands
  3. 3.Departments of PhysiologyEindhoven University of TechnologyEindhoventhe Netherlands
  4. 4.Department of Mechanical EngineeringUniversity of LimburgMaastrichtthe Netherlands

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