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Aortic Valve Modelling

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Computational Simulation basics

Computational Simulation basics

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  • 1. Aortic Valve Modelling
    Sourav Patnaik
    Agricultural and Biological Engineering Department
    Mississippi State University
    Image Source : http://www.adina.com/newsg0P.shtml
  • 2. Aortic Valve: Introduction
    • Aortic valve acts a “outflow valve”.
    • 3. It consist of three leaflets which regulate the blood flow to the body.
    • 4. Located between left ventricle and the aorta.
    • 5. Left ventricle pumps blood to the rest of the body, thus harder job than the right side. So more pressure is experienced by the aortic valve.
    Image Source –
    http://ect.downstate.edu/courseware/haonline/figs/l20/200702.htm
  • 6. Aortic Valve : Working
    Step 1:
    • Dark bluish blood (low in oxygen) flows back to the heart after circulating through the body.
    • 7. Blood enters the right atrium.
    • 8. This chamber empties blood through the tricuspid valve (Figure B) into the right ventricle.
    Step 2:
    • The right ventricle pumps the blood under low pressure through the pulmonary valve into the pulmonary artery.
    • 9. Blood goes to the lungs where it gets fresh oxygen (Figure C).
    Source : http://www.americanheart.org/presenter.jhtml?identifier=11064
  • 10. Aortic Valve : Working (cont’d)
    Step 3:
    • Oxygenated blood returns to the left heart through the pulmonary veins to the left atrium.
    • 11. Blood then passes through the mitral valve (Figure D) and enters the left ventricle.
    Step 4:
    • The left ventricle pumps the oxygenated blood out through the aortic valve into the aorta (Figure E).
    • 12. The aorta takes blood to the body’s general circulation.
    Source : http://www.americanheart.org/presenter.jhtml?identifier=11064
  • 13. Diastole/Systole
  • 14. Aortic Valve Diseases
    • Common causes of aortic stenosisinclude rheumatic fever, degenerative calcification, and congenital diseases such as bicuspid aortic valve.
    • 15. Common causes of aortic regurgitation include dilation of the aorta, previous rheumatic fever, infection, i.e. infective endocarditis, myxomatous degeneration of the aortic valve, and Marfan's syndrome.
    Tricuspid aortic valve Bicuspid aortic valve 1
    Damage/infection of the aortic valve 2
    Image Source:
    1 http://www.surgery.ucla.edu/cardiac/images/valves_lg.jpg
    2 http://www.aurorahealthcare.org/healthgate/images/diseased_aortic_valve.jpg
  • 16. Aortic Valve Replacement
    • Aortic Valves are either Mechanical/Bioprosthetic in origin or Tissue Engineered.
    • 17. No of Valve replacements in USA annually ~ 50000 (1999)1
    • 18. Nov 2, 2009 : World’s first human robotic endoscopic aortic valve replacement performed at Banner Baywood Health Hospital in Phoenix, Arizona 2
    • 19. Nov 11, 2009 : Half of eligible patients in USA are not getting aortic valve replacement surgery 3
    Image Source
    http://www.clarian.org/ADAM/doc/HealthIllustratedEncyclopedia/3/100161.htm
    1 Birkmeyer, N. J. O., O’Connor, G. T., Baldwin, J. C., (2001). Aortic valve replacement: current clinical practice and
    opportunities for quality improvement. CurrOpinCardiol. 16 : 152–157.
    2 http://www.reuters.com/article/pressRelease/idUS96716+02-Nov-2009+PRN20091102?sp=true
    3 http://www2.med.umich.edu/prmc/media/newsroom/details.cfm?ID=1371
  • 20. Tissue Engineered Heart Valves*
    • PGA scaffold seeded with vascular wall cells
    • 21. 21 days in reactor (in vitro); 6- 20 weeks ~ implanted in
    sheep (in vivo).
    *Hoerstrup SP, Sodian R, Daebritz S, Wang J, Bacha E A, Martin D P, Moran A M, Guleserian K J, Sperling J S, Hatsuoka S, Kaushal S, Vacanti J P, Schoen F J, Mayer J E (2000) Functional living trileaflet heart valves grown in vitro. Circulation 102(III): 44-49
  • 22. Comparison of Replacement Heart Valves
    Source:
    Mendelson, K., Schoen, F. J., (2006). Heart Valve Tissue Engineering: Concepts, Approaches, Progress, and Challenges. Annals of Biomedical Engineering, 34( 12) : 1799–1819
  • 23. Need of Modelling/Simulation*
    • Understand the mechanics of the material (in this case ~ tissue).
    • 24. Make necessary changes to the process, design or protocol etc. for efficiency.
    • 25. Provides practical feedback when designing real world systems.
    • 26. Reduces cost, time and effort.
    • 27. Aim for the future
    • 28. To build patient specific FE models
    • 29. Use as a tool for preoperative planning
    • 30. Effective means for teaching or demonstrating concepts to students
    Overall Objective : To develop a model to study the working of aortic valve so that we can compare mechanical properties of Tissue Engineered Valve and native valve.
    *Huet B, Martin J. (1980). Modelling and simulation of information systems on computer: methodological advantages. Med Inform. 5(3):193-203.
  • 31. Soft Tissue Modelling
    • Description of the physical geometry
    • 32. Generally done with help of imaging tools such as CT, MRI, Ultrasound etc.
    • 33. Constitutive Model for the solid mechanics. Types :
    • 34. Phenomological Models – Not much of geometry is concerned. Resulting
    stress-strain response is then fit to experimental stress-strain data.
    • Transversely Isotropic Models – assumption of transverse isotropy properties.
    • 35. Planar Fiber Models - overall tissue behavior to the behavior of a single fiber or bundle of fibers.
    • 36. Unit-Cell Models - derived completely from the observed fibrous structure.
    Soft tissues are generally modeled as nearly viscoelastic characteristics (creep, stress relaxation, and hysteresis), incompressible, nonlinear and anisotropic.
    Weinberg , E (2005). Dynamic Simulation of Heart Mitral Valve with Transversely Isotropic Material Model. (Thesis) Masters of Science, Mechanical Engineering, Massachusetts Institute of Technology, 2005.
  • 37. Soft Tissue Modelling
    • Description of fluid behavior : Navier–Stokes equations
    • 38. In simulation, Blood is assumed to be incompressible, homogenous, Newtonian, continuous with suitable boundary conditions.
    • 39. In case of some diseases blood flow can be turbulent.
    • 40. Output :
    • 41. A software is used to perform the required calculation and generate output.
  • Fung’s Model
    • Fung proposed an exponential stress-strain law which described the highly non-linear elastic properties of these tissues under uniaxial conditions.
    • 42. He proposed a quasi-linear viscoelastic law which combined creep, relaxation and hysteresis (viscoelastic features).
    • 43. Fung modified Hill’s famous equation for skeletal muscle for the basic mathematical model of the heart muscle.
    • 44. According to Fung’s model, soft tissues may be characterized as quasi-incompressible, non-homogeneous, non-isotropic, non-linear viscoelastic materials likely to undergo large deformations.
    Kassab, G. S., (2004). Y.C. “Bert” Fung: The Father of Modern Biomechanics. MCB, vol.1, no.1, pp.5-22.
  • 45. FSI Method
    • Fluid–structure interaction (FSI) methodis a major tool to optimize the
    Mechanical Heart Valve design1, blood – valve interaction2
    • Euler's Method is used for the fluid domain but it is very complex when we
    consider fluid – solid interaction problem.
    Defn: It is a first-order numerical procedure for solving ordinary
    differential equations (ODEs) with a given initial value.
    • Lagrange multiplier based fictitious domain method has been used to
    study theblood–valve interaction 1,2 . But a pure Lagrange frame is
    incapable for physiological fluids like blood.
    Defn : It is a differential equation whose solutions are the functions for
    which a given functional is stationary.
    • Mixed Lagrangian-Eulerianor Arbitrary LagrangianEulerian (ALE)
    method is a combination of the two methods for solving the short
    comings of either methods alone2
    “Computational grid is neither moved with the boundary (Lagrangian)
    or held fixed (Eulerian)” .
    1 M. Nobili, Morbiduccib, U., Ponzinic, R., Gaudiod, C. D., Balduccid, A., Grigionid, M., Montevecchib, F. M., Redaelli ,
    A., (2008). Numerical simulation of the dynamics of a bileaflet prosthetic heart valve using a fluid–structure interaction approach.Journal of Biomechanics 41 : 2539–2550.
    2 De Hart, J., Peters, G.W.M., Schreurs, P.J.G., Baaijens, F. P. T., (2003) . A three-dimensional computational analysis of
    fluid–structure interaction in the aortic valve. Journal of Biomechanics 36 :103–112.
  • 46. Alternative ALE method
    An alternative to the ALE approach is the Coupled Momentum Method
    (CMM) of Figueroa et al. 2006.
    In this model the wall motion was minimum and it was simplified based on
    elastodynamic equations
    CMM is highly efficient for large scale fluid–structure interaction
    and wave propagation problems wherein underlying assumptions
    of small deformation and thin walls are valid
    Figueroa, C.A. , Vignon-Clementel, I.E. , Jansen, K.C., Hughes, T.J.R., Taylor, C.A. (2006). A coupled momentum method for modeling blood flow in three-dimensional deformable arteries, Comput. Methods Appl. Mech. Engrg. 195 (41–43) : 5685–5706.
    Taylor, C.A. Humphrey, J.D. (2009). Open problems in computational vascular biomechanics: Hemodynamics and arterial wall mechanics. Comput. Methods Appl. Mech. Engrg. 198 : 3514–3523.
  • 47. Similar Work
    From computer generated analysis, researchers were able to conclude that leaflets of the valve open by a combination of root expansion in a radial direction and leaflet movement in the direction of blood flow*.
    They compared natural valve with a valve with stiffened root.
    * Howard, I. C., Patterson E. A., Yoxall, A., (2003). On the opening mechanism of the aortic valve: some observations from simulations. Journal of Medical Engineering & Technology, Volume 27, Number 6, (November/December 2003), pages 259–266 .
  • 48. Similar Work
    Stress on the valve is studied using the fluid-structure interaction process and it is
    modelled using the ALE method.
    The only change in this work is the different layers of the valve come into account.
    Konderla, P., Patralski, K., (2006). THE STRESS ANALYSIS OF THE AORTIC VALVE LEAFLET MODEL DURING THE FLOW IN THE CARDIAC CYCLE. Journal of Biomechanics 41(S1) 16th ESB Congress, Posters.
  • 49. Similar work
    This study concluded that the valve leaflet exhibits non–linearity and anisotropy, even though the model was simplified for computational purposes.
    Linear elastic modelsfor the aortic valve leaflets with parameters used in previous studies were then compared with hyperelasticmaterials.
    Non–linear matrix was used with exponential stress-strain characteristics reinforced by only one fibre layer.
    The hyper- elastic model in this case showed better curve fit with the uniaxial loading data.
    Kocha, T. M., Reddy, B. D., Zilla, v, Franz, T., (2007). Comparison of Linear and Non-linear Constitutive Models for Aortic Valve Leaflets in a Finite Element Analysis of the Aortic Valve.Unpublished presentation.
  • 50. Similar work
    A three-dimensional model of the left ventricle was done : the ventricular model and aortic valve model.
    The resultant force generated ventricular model was used as input in the aortic valve model.
    Both models were based on fluid- structure interaction.
    The advantages of this model was the 3D geometry was better and hence similar to the physiological condition.
    Carmody, C.J., Burriesci, G., Howard, I.C., Patterson, E.A., (2006). An approach to the simulation of fluid–structure interaction in the aortic valve. Journal of Biomechanics 39 158–169.
  • 51. Thank you