Skip to main content
SpringerLink
Log in

Modeling active muscle contraction in mitral valve leaflets during systole: a first approach

  • Original Paper
  • Published:
Biomechanics and Modeling in Mechanobiology Aims and scope Submit manuscript

Abstract

The present study addresses the effect of muscle activation contributions to mitral valve leaflet response during systole. State-of-art passive hyperelastic material modeling is employed in combination with a simple active stress part. Fiber families are assumed in the leaflets: one defined by the collagen and one defined by muscle activation. The active part is either assumed to be orthogonal to the collagen fibers or both orthogonal to and parallel with the collagen fibers (i.e. an orthotropic muscle fiber model). Based on data published in the literature and information herein on morphology, the size of the leaflet parts that contain muscle fibers is estimated. These parts have both active and passive materials, the remaining parts consist of passive material only. Several solid finite element analyses with different maximum activation levels are run. The simulation results are compared to corresponding echocardiography at peak systole for a porcine model. The physiologically correct flat shape of the closed valve is approached as the activation levels increase. The non-physiological bulging of the leaflet into the left atrium when using passive material models is reduced significantly. These results contribute to improved understanding of the physiology of the native mitral valve, and add evidence to the hypothesis that the mitral valve leaflets not are just passive elements moving as a result of hemodynamic pressure gradients in the left part of the heart.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Boucek RJ, Bouckova B, Levy S (1978) Anatomical arrangement of muscle tissue in the anterior mitral leaflet in man. Cardiovasc Res 12: 675–680

    Article  Google Scholar 

  • Chen L, Yin FCP, May-Newman K (2004) The structure and mechanical properties of the mitral valve leaflet-strut chordae transition zone. J Biomech Engng 126: 244–251

    Article  Google Scholar 

  • Curtis BC, Priola DV (1992) Mechanical properties of the canine mitral valve: effects of autonomic stimulation. Am J Physiol 31: 56–62

    Google Scholar 

  • Dagum P, Timek TA, Green RG, Lai D, Daughters GT, Liang DH, Hayase M, Ingels NB, Miller DC (2000) Coordinate free analysis of mitral valve dynamics in normal and ischemic hearts. Circ 102: III-62–III-69

    Google Scholar 

  • DeBiasi S, Zucharello LV, Blum I (1984) Histochemical and ultrastructural study on the innervation of human and porcine atrio-ventricular valves. Anat Embryol 169: 159–165

    Article  Google Scholar 

  • Denoth J, Stussi E, Csucs G, Danuser G (2002) Single muscle fiber contraction is dictated by inter-sarcomere dynamics. J Theor Biol 216: 101–122

    Article  MathSciNet  Google Scholar 

  • Eckert CE, Zubiate B, Vergnat M, Gorman JH, Gorman RC, Sacks M (2009) In vivo dynamic deformation of the mitral valve annulus. Ann Biomed Engng 37: 1757–1771

    Article  Google Scholar 

  • Einstein DR, Kunzelman KS, Reinhall P, Nicosia M, Cochran RP (2004) Haemodynamic determinants of the mitral valve closure sound: a finite element study. Med Biol Engng Comput 42: 832–846

    Article  Google Scholar 

  • Einstein DR, Kunzelman KS, Reinhall P, Nicosia M, Cochran RP (2005) The relationship of normal and abnormal microstructural proliferation to the mitral valve closure sound. J Biomech Engng 127(1): 134–147

    Article  Google Scholar 

  • Flory PJ (1961) Thermodynamics relations for high elastic materials. Trans Faraday Soc 57: 829–838

    Article  MathSciNet  Google Scholar 

  • Filip DA, Radu A, Simionescu M (1986) Interstitial cells of the heart valves possess characteristics similar to smooth muscle cells. Circ Research 59: 310–320

    Google Scholar 

  • Fung YC (1993) Biomechanics—Mechanical properties of living issues, 2nd edn. Springer, New York

    Google Scholar 

  • Gordon AM, Huxley AF, Julian FJ (1966) The variation in isometric tension with sarcomere length in vertebrae muscle fibres. J Physiol 184: 170–192

    Google Scholar 

  • Givli S, Bhattacharya K (2009) A coarse-grained model of the myofibril: overall dynamics and the evolution of sarcomere non-uniformities. J Mech Phys Solids 57: 221–243

    Article  MATH  Google Scholar 

  • Gross L, Kugel MA (1931) Topographic anatomy and histology of the valves in the human heart. Am J Pathol 7: 445–473

    Google Scholar 

  • Göktepe S, Bothe W, Kvitting JPE, Swanson JC, Ingels NB, Miller DC, Kuhl E (2009) Anterior mitral leaflet curvature in the beating ovine heart: a case study using videofluoroscopic markers and subdivision surfaces. Biomech Model mechanobiol (in press)

  • Herrera AM, McParland BE, Blenkowska A, Tait R, Pare PD, Seow CY (2005) ‘Sarcomeres’ of smooth muscle: functional characteristics and ultrastructural evidence. J Cell Science 118: 2381–2392

    Article  Google Scholar 

  • Hill AV (1938) The heat of shortening and the dynamic constants of muscle. Proc R Soc 126: 136–195

    Article  Google Scholar 

  • Holzapfel GA (2000) Nonlinear Solid Mechanics. A Continuum Approach for Engineering. Wiley, Chichester

    MATH  Google Scholar 

  • Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elasticity 61: 1–48

    Article  MATH  MathSciNet  Google Scholar 

  • Humphrey JD (2002) Cardiovascular solid mechanics. Cells, tissues, and organs. Springer, New York, pp 139–140

    Google Scholar 

  • Hunter PJ, Nash MP, Sands GB (1997) Computational electromechanics of the heart. In: Panfilov AV, Holden AV (eds) Computational biology of the heart. Wiley, London, pp 345–407

    Google Scholar 

  • Itoh A, Krishnamurthy G, Swanson J, Ennis DB, Bothe W, Kuhl E, Karlsson M, Davis LR, Miller DC, Ingels NB (2009) Active stiffening of mitral valve leaflets in the beating heart. Am J Physiol Heart Circ Physiol 296: H1766–H1773

    Article  Google Scholar 

  • Kawano H, Kawai S, Shirai T, Okada R (1993) Morphological study on vagal innervation in human atriventricular valves using histochemical method. Jap Circ J 57: 753–759

    Google Scholar 

  • Krishnamurthy G, Itoh A, Bothe W, Swanson J, Kuhl E, Karlsson M, Miller DC, Ingels NB (2009) Stress-strain behavior of the mitral valve leaflets in the beating ovine heart. J Biomech 42: 1909–1916

    Article  Google Scholar 

  • Kunzelman KS, Cochran RP, Chuong C, Ring WS, Verrier ED, Eberhart RD (1993) Finite element analysis of the mitral valve. J Heart Valve Dis 2: 326–340

    Google Scholar 

  • Kunzelman KS, Cochran RP, Murphree SS, Ring WS, Verrier ED, Eberhart RC (1993) Differential collagen distribution in the mitral valve and its influence on biomechanical behavior. J Heart Valve Dis 2: 236–244

    Google Scholar 

  • Kunzelman KS, Cochran RP (1990) Mechanical properties of basal and marginal mitral valve chordae tendineae. ASAIO Trans 36: M405–408

    Google Scholar 

  • Liao J, Vesely I (2003) A structural basis for the size-related mechanical properties of mitral valve chordae tendineae. J Biomech 36(8): 1125–1133

    Article  Google Scholar 

  • Marron K, Yacoub MH, Polak JM, Sheppard MN, Whitehead BF, Leval MR, Anderson RH, Wharton J (1996) Innervation of human atrioventricular and arterial valves. Circ 94: 368–375

    Google Scholar 

  • Martins JAC, Pires EB, Salvado R, Dinis PB (1998) A numerical model of passive and active behavior of skeletal muscles. Comp Meth Appl Mech Engng 151: 419–433

    Article  MATH  Google Scholar 

  • May-Newman K, Yin FCP (1998) A constitutive law for mitral valve tissue. J Biomech Engng 120: 38–47

    Article  Google Scholar 

  • Montiel MM (1970) Muscular apparatus of the mitral valve in man and its involvement in left-sided cardiac hypertrophy. Amer J Cardiology 26: 341–344

    Article  Google Scholar 

  • Odegard GM, Donahue TLH, Morrow DA, Kaufman KR (2008) Constitutive modelling of skeletal muscle tissue with an explicit strain energy function. J Biomech Engng 130, paper 061017-1

    Google Scholar 

  • Prot V, Skallerud B, Holzapfel GA (2007) Transversely isotropic membrane shells with application to mitral valve mechanics. Constitutive modeling and finite element implementation. Int J Numer Meth Engng 71(8): 987–1008

    Article  MATH  MathSciNet  Google Scholar 

  • Prot V, Haaverstad R, Skallerud B (2009a) Finite element analysis of the mitral apparatus: annulus shape effect and chordal force distribution. J Biomech Mod Mechanobiol 8: 43–55

    Article  Google Scholar 

  • Prot V, Skallerud B, Sommer G, Holzapfel GA (2010) On modelling and analysis of healthy and pathological human mitral valves: two case studies. J Mech Beh Biomed Mater 3: 167–177

    Article  Google Scholar 

  • Prot V, Skallerud B (2009) Nonlinear solid finite element analysis of mitral valves with heterogeneous leaflet layers. Comp Mech 43: 353–368

    Article  MATH  Google Scholar 

  • Rachev A, Hayashi K (1999) Theoretical study of vascular smooth muscle contraction on strain and stress distribution in arteries. Annals Biomed Engng 27: 459–468

    Article  Google Scholar 

  • Ryan LP, Jackson BM, Eperjesi TJ, Plappert TJ, StJohn-Sutton M, Gorman RC, Gorman JH (2008) A methodology for assessing the human mitral leaflet curvature using real-time 3-dimensional echocardiography. J Thorac Cardiovasc Surg 136: 726–734

    Article  Google Scholar 

  • Sacks MS, He Z, Baijens L, Wanant S, Shah P, Sugimoto H, Yoganathan YP (2002) Surface strain in the anterior leaflet of the functioning mitral valve. Annals Biomech Engng 30: 1281–1290

    Article  Google Scholar 

  • Sacks MS, Enomoto Y, Graybill JR, Merryman WD, Zeeshan A, Yoganathan AP, Levy RJ, Gorman RC, Gorman JH (2006) In-vivo dynamic deformation of the mitral valve anterior leaflet. Ann Thoracic Surg 82: 1369–1378

    Article  Google Scholar 

  • Sanfilippo AJ, Harrigan P, Popovic AD, Weyman AE, Levine RA (1992) Papillary muscle traction in mitral valve prolapse: quantitation by two-dimensional echocardiography. J Am Coll Cardiol 19: 564–571

    Article  Google Scholar 

  • Sonnenblick EH, Napolitano LM, Daggett WM, Cooper T (1967) An intrinsic neuromuscular basis for mitral valve motion in the dog. Circ Res 21: 9–15

    Google Scholar 

  • Stålhand J, Klarbring A, Holzapfel GA (2007) Smooth muscle contraction: mechanochemical formulation for homogeneous finite strain. Progr Biophys Molecul Biol 96: 465–481

    Article  Google Scholar 

  • Timek TA, Lai DT, Dagum P, Tibayan F, Daughters GT, Liang D, Berry GJ, Miller DC, Ingels NB (2003) Ablation of mitral annular and leaflet muscle: effects on annular and leaflet dynamics. Am J Physiol Heart Circ Physiol 285: 1668–1674

    Google Scholar 

  • Tskhovrebova L, Trinick J, Sleep JA, Simmons RM (1997) Elasticity and unfolding of single molecules of the giant muscle protein titin. Nature 387: 308–312

    Article  Google Scholar 

  • Votta E, Caiani E, Veronesi F, Soncini M, Montevecchi FV, Redaelli A (2008) Mitral valve finite element modelling from ultrasound data: a pilot study for a new approach to understand mitral function and clinical scenarios. Phil Trans R Soc A 366: 3411–3434

    Article  Google Scholar 

  • Williams TH, Jew JY (2004) Is the mitral valve passive flap theory overstated? An active valve is hypothezised. Medical Hypotheses 62: 605–611

    Article  Google Scholar 

  • Wit AL, Fenoglio JJ, Hordof AJ, Reemtsma K (1979) Ultrastructure and transmembrane potentials of cardiac muscle in the human anterior mitral valve leaflet. Circ 59: 1284–1292

    Google Scholar 

  • Zulliger MA, Rachev A, Stergiopulos N (2004) A constitutive formulation of arterial mechanics including vascular smooth muscle tone. Am J Physiol Heart Circ 287: H1335–H1343

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Structural Engineering, Norwegian University of Science and Technology, Trondheim, Norway

    B. Skallerud

  2. Center for Biomedical Computing, Simula Research Laboratory, Fornebu, Norway

    V. Prot

  3. Department of Laboratory Medicine, Children’s and Women’s Health, Norwegian University of Science and Technology, Trondheim, Norway

    I. S. Nordrum

  4. Department of Pathology and Medical Genetics, St. Olavs Hospital, Trondheim, Norway

    I. S. Nordrum

Authors
  1. B. Skallerud
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Prot
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. S. Nordrum
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. Skallerud.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Skallerud, B., Prot, V. & Nordrum, I.S. Modeling active muscle contraction in mitral valve leaflets during systole: a first approach. Biomech Model Mechanobiol 10, 11–26 (2011). https://doi.org/10.1007/s10237-010-0215-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10237-010-0215-9

Keywords

Search

Navigation