An Experimentally Derived Stress Resultant Shell Model for Heart Valve Dynamic Simulations

In order to achieve a more realistic and accurate computational simulation of native and bioprosthetic heart valve dynamics, a finite shell element model was developed. Experimentally derived and uncoupled in-plane and bending behaviors were implemented into a fully nonlinear stress resultant shell element. Validation studies compared the planar biaxial extension and three-point bending simulations to the experimental data and demonstrated excellent fidelity. Dynamic simulations of a pericardial bioprosthetic heart valve with the developed shell element model showed significant differences in the deformation characteristics compared to the simulation with an assumed isotropic bending model. The new finite shell element model developed in the present study can also incorporate various types of constitutive models and is expected to help us to understand the complex dynamics of native and bioprosthetic heart valve function in physiological and pathological conditions.

[1]  F J Schoen,et al.  Prevention of calcification of glutaraldehyde-crosslinked porcine aortic cusps by ethanol preincubation: mechanistic studies of protein structure and water-biomaterial relationships. , 1998, Journal of biomedical materials research.

[2]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model. Part II: the linear theory; computational aspects , 1989 .

[3]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model. Part V: Nonlinear plasticity: formulation and integration algorithms , 1992 .

[4]  Michael S Sacks,et al.  Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar collagenous tissues. , 2003, Journal of biomechanical engineering.

[5]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model. Part III: computational aspects of the nonlinear theory , 1990 .

[6]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model. Part VII: Shell intersections with -DOF finite element formulations , 1993 .

[7]  Michael S Sacks,et al.  The effects of collagen fiber orientation on the flexural properties of pericardial heterograft biomaterials. , 2005, Biomaterials.

[8]  Michael S Sacks,et al.  On the biaxial mechanical properties of the layers of the aortic valve leaflet. , 2005, Journal of biomechanical engineering.

[9]  J. C. Simo,et al.  Formulation and computational aspects of a stress resultant geometrically exact shell model , 1990 .

[10]  Michael S. Sacks,et al.  Dynamic In Vitro Quantification of Bioprosthetic Heart Valve Leaflet Motion Using Structured Light Projection , 2001, Annals of Biomedical Engineering.

[11]  P M Pattany,et al.  Fatigue-induced changes in bioprosthetic heart valve three-dimensional geometry and the relation to tissue damage. , 1999, The Journal of heart valve disease.

[12]  Y. Fung,et al.  Biomechanics: Mechanical Properties of Living Tissues , 1981 .

[13]  Wei Sun,et al.  Multiaxial mechanical behavior of biological materials. , 2003, Annual review of biomedical engineering.

[14]  Y. C. Fung,et al.  What are the residual stresses doing in our blood vessels? , 2006, Annals of Biomedical Engineering.

[15]  John W. Hole,et al.  Hole's Human Anatomy and Physiology , 1997 .

[16]  R. Taylor,et al.  Theory and finite element formulation of rubberlike membrane shells using principal stretches , 1992 .

[17]  Peter Wriggers,et al.  Large strain analysis of soft biological membranes: Formulation and finite element analysis , 1996 .

[18]  M. Sacks,et al.  Biaxial mechanical response of bioprosthetic heart valve biomaterials to high in-plane shear. , 2003, Journal of biomechanical engineering.

[19]  J. Z. Zhu,et al.  The finite element method , 1977 .

[20]  M. Sacks,et al.  A method for planar biaxial mechanical testing that includes in-plane shear. , 1999, Journal of biomechanical engineering.

[21]  J. C. Simo,et al.  On stress resultant geometrically exact shell model. Part I: formulation and optimal parametrization , 1989 .

[22]  M. Sacks,et al.  Simulated bioprosthetic heart valve deformation under quasi-static loading. , 2005, Journal of biomechanical engineering.

[23]  Jia Lu,et al.  Dynamic simulation pericardial bioprosthetic heart valve function. , 2006, Journal of biomechanical engineering.

[24]  I. C. Howard,et al.  A two-dimensional finite element analysis of a bioprosthetic heart valve. , 1990, Journal of biomechanics.

[25]  Clifford Ambrose Truesdell,et al.  Exact theory of stress and strain in rods and shells , 1957 .

[26]  M. Thubrikar,et al.  Role of mechanical stress in calcification of aortic bioprosthetic valves. , 1983, The Journal of thoracic and cardiovascular surgery.

[27]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model , 1990 .

[28]  Komarakshi R Balakrishnan,et al.  Dynamic analysis of the aortic valve using a finite element model. , 2002, The Annals of thoracic surgery.

[29]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model. Part VI: Conserving algorithms for non‐linear dynamics , 1992 .

[30]  F J Schoen,et al.  Pathologic findings in explanted clinical bioprosthetic valves fabricated from photooxidized bovine pericardium. , 1998, The Journal of heart valve disease.

[31]  M. Sacks.  Biaxial Mechanical Evaluation of Planar Biological Materials , 2000 .

[32]  Michael S. Sacks,et al.  A novel bioreactor for the dynamic flexural stimulation of tissue engineered heart valve biomaterials. , 2003 .

[33]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[34]  F J Schoen,et al.  Pathology of Substitute Heart Valves: New Concepts and Developments , 1994, Journal of cardiac surgery.

[35]  M. Marchand,et al.  The last generation of pericardial valves in the aortic position: ten-year follow-up in 589 patients. , 1996, The Annals of thoracic surgery.

[36]  F J Schoen,et al.  Founder's Award, 25th Annual Meeting of the Society for Biomaterials, perspectives. Providence, RI, April 28-May 2, 1999. Tissue heart valves: current challenges and future research perspectives. , 1999, Journal of biomedical materials research.

[37]  M. Thubrikar.  The Aortic Valve , 1990 .

[38]  F J Schoen,et al.  Pathological considerations in replacement cardiac valves. , 1992, Cardiovascular pathology : the official journal of the Society for Cardiovascular Pathology.

[39]  L J Brossollet,et al.  A new approach to mechanical testing and modeling of biological tissues, with application to blood vessels. , 1996, Journal of biomechanical engineering.

[40]  S. Cowin,et al.  Biomechanics: Mechanical Properties of Living Tissues, 2nd ed. , 1994 .

[41]  S. BRODETSKY,et al.  Theory of Plates and Shells , 1941, Nature.

[42]  J. Weiss,et al.  Finite element implementation of incompressible, transversely isotropic hyperelasticity , 1996 .