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Aortic Valve Modelling Sourav Patnaik Agricultural and Biological Engineering Department Mississippi State University Image Source : http://www.adina.com/newsg0P.shtml
Common causes of aortic stenosisinclude rheumatic fever, degenerative calcification, and congenital diseases such as bicuspid aortic valve.
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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
Aortic Valves are either Mechanical/Bioprosthetic in origin or Tissue Engineered.
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No of Valve replacements in USA annually ~ 50000 (1999)1
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Nov 2, 2009 : Worldâ€™s first human robotic endoscopic aortic valve replacement performed at Banner Baywood Health Hospital in Phoenix, Arizona 2
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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., Oâ€™Connor, G. T., Baldwin, J. C., (2001). Aortic valve replacement: current clinical practice and opportunities for quality improvement. CurrOpinCardiol. 16 : 152â€“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
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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
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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) : 1799â€“1819
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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.
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Generally done with help of imaging tools such as CT, MRI, Ultrasound etc.
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Constitutive Model for the solid mechanics. Types :
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Phenomological Models â€“ Not much of geometry is concerned. Resulting
stress-strain response is then fit to experimental stress-strain data.
Transversely Isotropic Models â€“ assumption of transverse isotropy properties.
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Planar Fiber Models - overall tissue behavior to the behavior of a single fiber or bundle of fibers.
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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.
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A software is used to perform the required calculation and generate output.
Fungâ€™s Model
Fung proposed an exponential stress-strain law which described the highly non-linear elastic properties of these tissues under uniaxial conditions.
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He proposed a quasi-linear viscoelastic law which combined creep, relaxation and hysteresis (viscoelastic features).
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Fung modified Hillâ€™s famous equation for skeletal muscle for the basic mathematical model of the heart muscle.
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According to Fungâ€™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. â€śBertâ€ť Fung: The Father of Modern Biomechanics. MCB, vol.1, no.1, pp.5-22.
Euler's Method is used for the fluid domain but it is very complex when we
consider fluid â€“ 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 thebloodâ€“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.
method is a combination of the two methods for solving the short comings of either methods alone2 â€śComputational grid is neither moved with the boundary (Lagrangian) or held fixed (Eulerian)â€ť . 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 fluidâ€“structure interaction approach.Journal of Biomechanics 41 : 2539â€“2550. 2 De Hart, J., Peters, G.W.M., Schreurs, P.J.G., Baaijens, F. P. T., (2003) . A three-dimensional computational analysis of fluidâ€“structure interaction in the aortic valve. Journal of Biomechanics 36 :103â€“112.
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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 fluidâ€“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 (41â€“43) : 5685â€“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 : 3514â€“3523.
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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 259â€“266 .
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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.
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Similar work This study concluded that the valve leaflet exhibits nonâ€“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. Nonâ€“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.
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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 fluidâ€“structure interaction in the aortic valve. Journal of Biomechanics 39 158â€“169.
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