Fixed Points and Stability Analysis in the Motion of Human Heart Valve Leaflet

Emagbetere, Eyere; Salau, Tajudeen A.O.; Oluwole, Oluleke O.

doi:10.18052/www.scipress.com/IFSL.14.1

Paper Titles in Periodical

International Frontier Science Letters

IFSL Volume 14

IFSL > IFSL Volume 14 > Fixed Points and Stability Analysis in the Motion...

< Back to Volume

Fixed Points and Stability Analysis in the Motion of Human Heart Valve Leaflet

Full Text PDF

Abstract:

This work was set out to gain further insight into the kinetics of the human heart valve leaflet. The Korakianitis and Shi lumped parameter model was adopted for this study. The fixed points were determined, and then, their stability properties were assessed by evaluating eigenvalues of the Jacobian matrices. Normal physiological parameters for the valve model were simulated; based on which, a local bifurcation diagram was generated. Phase portraits were plotted from simulated responses, and were used to observe the qualitative properties of the valve leaflet motion. The evaluated fixed points were found to be dependent on pressure and flow effects, and independent on friction or damping effect. Observed switching of stability between the two fixed points indicated that the leaflet motion undergoes transcritical bifurcation. Of the two fixed points, one is always either a stable spiral or generative node while the other is a saddle. Numerical simulations were carried out to verify the analytical solutions.

Info:

Periodical:

International Frontier Science Letters (Volume 14)

Pages:

1-18

DOI:

https://doi.org/10.18052/www.scipress.com/IFSL.14.1

Citation:

E. Emagbetere et al., "Fixed Points and Stability Analysis in the Motion of Human Heart Valve Leaflet", International Frontier Science Letters, Vol. 14, pp. 1-18, 2019

Online since:

March 2019

Authors:

Eyere Emagbetere, Tajudeen A.O. Salau, Oluleke O. Oluwole

Keywords:

Heart Valve Model, Numerical Simulation, Phase Portraits, Transcritical Bifurcation

Export:

RIS, BibTeX, Text

Distribution:

Open Access

This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

[1] K. Huynh, Thrombosis leaflet motion after TAVI or SAVR, Nature Reviews Cardiology. 12 (2015).

DOI: https://doi.org/10.1038/nrcardio.2015.170

[2] R.R. Makkar et al., Possible subclinical leaflet thrombosis in bioprosthetic aortic valves, The New England Journal of medicine. 373(21) (2015) 2015-2024.

[3] J. C. Laschinger et al., Reduced leaflet motion in bioprosthetic aortic valves - the FDA perspective, The New England Journal of Medicine. 373(21) (2015) 1996-1998.

DOI: https://doi.org/10.1056/nejmp1512264

[4] D. Magnus et al., Hypo-attenuated leaflet thickening and reduced leaflet motion in sutureless bioprosthtic aortic valves, J. Am. Heart Assoc. 2017(6) (2017).

DOI: https://doi.org/10.1161/jaha.116.005251

[5] W.A. Seed, N.B. Wood, Development and evaluation of hot-film velocity probe for cardiovascular studies, Cardiovasc. Res. 4 (1970) 253-263.

[6] H.L. Falsetti et al., Sequential velocity development in the ascending and descending aorta of dog, Circulation Research 31(3) (1972) 328-338.

[7] M.J. Thubrikar, The aortic valve, CRC Press, Borca Raton, Florida, (1990).

[8] Z. He et al., In vitro dynamics strain behaviour of the mitral valve posterior leaflet, Transcactions of ASME. 127 (2005) 504-511.

[9] J.T. Fenner, W.M. Mackay, D. Wheatney, Laser profiling: a technique for the study of prosthetic leaflet heart valve motion, Physiol. Meas. 16 (1995).

DOI: https://doi.org/10.1088/0967-3334/16/3/005

[10] A.K. Iyengar et al., Dynamics In Vitro Quantification of Bioprosthetic Heart Valve Leaflet Motion Using Structured Light Projection, Annals of Biomedical Engineering. 29 (2001) 963-973.

DOI: https://doi.org/10.1114/1.1415523

[11] A.G.B. Donn et al., Laser profiling of bovine pericardial heart valves, Artif. Organs. 20 (1997) 436-439.

[12] G. Pache et al., Early hypo-attenuated leaflet thickening in balloon-expandable transcatheter aortic heart valves, European Heart Journal. 37 (2016) 2263-2271.

DOI: https://doi.org/10.1093/eurheartj/ehv526

[13] R. Yanagisawa et al., Incidence, predictors, and mid-term outcomes of possible leaflet thrombosis after TAVR, JACC: Cardiovasc. Imaging. 10(1) (2016) 1-11.

[14] E. J.Weinberg, D. Mofraad, M.R. Shahmizradi, On the multiscale modelling of heart valve biomechanics in health and disease, Biomech. Model Mechanobiol. 9 (2010) 373-387.

DOI: https://doi.org/10.1007/s10237-009-0181-2

[15] R. Zakerzadeh, M.-C. Hsu, M.S. Sacks, Computational methods for the aortic heart valve and its replacements, Expert Review of Medical Devices. 14(11) (2017) 849-866.

DOI: https://doi.org/10.1080/17434440.2017.1389274

[16] I. Borazjani, A review of fluid-structure interaction simulations of prosthetic heart valves, Journal of Long-Term Effects of Medical Implants. 25 (2015) 75-93.

DOI: https://doi.org/10.1615/jlongtermeffmedimplants.2015011791

[17] A. Joda et al., Multiphysics simulation of the effect of leaflet thickness inhomogeneity and material anisotropy on the stress–strain distribution on the aortic valve, Journal of Biomechnics. 49(12) (2016) 2502-2512.

DOI: https://doi.org/10.1016/j.jbiomech.2016.02.041

[18] H. Gao et al., A coupled mitral valve-left ventricle model with fluid-structure interaction. Journal of Medical Engineering & Physics. 47 (2017) 128-136.

[19] R. Mittal et al., Computational modeling of cardiac hemodynamics: current status and future outlook, Journal of Computational Physics. 305 (2016) 1065-1082.

[20] B. Su et al., Cardiac MRI based numerical modeling of left ventricular fluid dynamics with mitral valve incorporated, Journal of Biomechanics. 49(7) (2016) 1199-1205.

DOI: https://doi.org/10.1016/j.jbiomech.2016.03.008

[21] Z.C. Wang et al., Computational modeling for fluid–structure interaction of bioprosthetic heart valve with different suture density: comparison with dynamic structure simulation, International Journal of Pattern Recognition and Artificial Intelligence. 31(11) (2017).

DOI: https://doi.org/10.1142/s0218001417570075

[22] G. Luraghi et al., Evaluation of an aortic valve prosthesis: Fluid-structure interaction or structural simulation?, Journal of Biomechanics. 58 (2017) 45-51.

[23] W. Mao et al., Fully-coupled fluid-structure interaction simulation of the aortic and mitral valves in a realistic 3D left ventricle mode, PLOS ONE. 12(9) (2017).

DOI: https://doi.org/10.1371/journal.pone.0184729

[24] Y. Shi, P. Lawford, H. Rodney, Review of Zero-D and 2-D models of blood flow in the Cardiovascular system, PLOS ONE. (2011).

[25] J. Warner, D. Bohringer, M. Hexamer, Simulation and prediction of cardiotherapeutical phenomena from a pulsatile model coupled to the guyton circulatory model, IEEE Transactiosn on Biomedical Engineering. 49(5) (2002) 430-439.

DOI: https://doi.org/10.1109/10.995681

[26] Y. Shi, T.J.H. Yeo, Y. Zhao, Numerical simulation of a systemic flow test rig, ASAIO Journal. 50(1) (2004) 54-64.

DOI: https://doi.org/10.1097/01.mat.0000104820.40389.92

[27] A. Laadhari, A. Quarteroni, Numerical modeling of heart valves using resistive Eulerian surfaces, International Journal for Numerical Methods in Biomedical Engineering. 32(5) (2016) e02743.

DOI: https://doi.org/10.1002/cnm.2743

[28] T. Korakianitis, Y. Shi, Numerical simulation of cardiovascular dynamics with healthy and diseased heart valves, Journal of Biomechanics. 39 (2006) 1964-1982.

DOI: https://doi.org/10.1016/j.jbiomech.2005.06.016

[29] A.C. Guyton, J.E. Hall, Textbook of Medical Physiology, Elsevier Inc., Philadelphia, Pennsylvania, (2006).

[30] R.M. Berne, Cardiovascular Physiology, The C.V. Mosby Company, St. Louis, MO. (1981).

[31] E. Kreyszig, Advance Engineering Mathematcs, 9th edition, John Wiley & Sons, INC., Singapore, (2006).

[32] S.H. Strogatz, Non-linear Dynamics and Chaos with Applications to Physics, Biology, Chemistry, and Engineering. Reading, Massachusetts: Perseus Books Publishing, (1994).

[33] J.R. Taylor, Classical Mechanics, University Success Books, (2005).

[34] F.C. Moon, Chaotic Vibrations: An Introduction for Applied Scientist and Engineers. John Wiley and Sons Inc, New Jersey, (2004).

[35] M. Natick, Using MATLAB version 5.1, The Matworks, (1997).

[36] A. Ryuichi, N. Michihiro, V. Remi, Behind and Beyond the MATLAB ODE suite. CRM-2651, (2000).

[37] E. Emagbetere, O. Oluwole, T.A. O. Salau, Comparative study of Matlab ODE solvers for the Korakianitis and Shi model, Bulletin of Mathematical Sciences and Applications. 19 (2017) 31-44.

DOI: https://doi.org/10.18052/www.scipress.com/bmsa.19.31

[38] J.D. Bronzino, The Biomedical Engineering handbook, CRC Presss, Boca Raton, (1995).

[39] R.G. Leyh et al., Opening and closing characteristics of the aortic valve after different types of valve-preserving surgery, Circulation. 100(21) (1999) 2153-2160.

DOI: https://doi.org/10.1161/01.cir.100.21.2153

[40] M. Toma et al., Fluid-structure interaction analysis of ruptured mitral chordae tendinae, Annals of Biomedical Engineering. 45(3) (2017) 619-631.

Show More Hide

Cited By:

This article has no citations.