Fixed Points and Stability Analysis in the Motion of Human Heart Valve Leaflet
| Autor: | T. A. O. Salau, Eyere Emagbetere, Oluleke Oluwole |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Computer simulation
Phase portrait 0206 medical engineering Mathematical analysis Human heart Motion (geometry) 02 engineering and technology General Medicine 030204 cardiovascular system & hematology Fixed point 020601 biomedical engineering Stability (probability) 03 medical and health sciences 0302 clinical medicine Transcritical bifurcation Valve leaflet Mathematics |
| Zdroj: | International Frontier Science Letters. 14:1-18 |
| ISSN: | 2349-4484 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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