Analysis of Blood Flow Bifurcation Phenomena in Mitral Valve: A Numerical Approach to Predict Cardiac Arrest

Document Type : Regular Article

Authors

1 Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology Chennai, Tamilnadu-600127, India

2 Department of Mathematics, National Institute of Technology Silchar, Silchar-788010, Assam, India

3 Department of Mathematics, Alipurduar University, Alipurduar, West Bengal-736121, India

Abstract

Employing FVM, we have investigated numerically the rheological behavior of bifurcation phenomena of blood flow at various Reynolds numbers (Re) and at various values of contraction ratio (h), defined as the ratio of the inlet to narrow sections width of a two-dimensional planner contraction-expansion channel. Blood flow bifurcation through a planar contraction-expansion channel is analogous to the case of regurgitation (i.e., abnormal leakage of blood) in the mitral valve. In this work, we have studied the blood flow bifurcation characteristics including the normalized axial velocity profile, velocity gradient, dimensionless pressure, dimensionless longitudinal pressure gradient, pressure and skin friction coefficients on both the channel walls and analyzed the pressure drop, excess pressure drop for different values of Re. Secondly, blockage in the mitral valve is studied for different values of h. Pressure drops for various values of h are also studied to measure blood pressure. Correlation analyses are presented for normalized vortex length in terms of critical values of Re and h. It is revealed that if Re goes on increasing to 14.4 or more, flow breaks the symmetry at h = 15, and for each , recirculation length increases linearly with the increase in Re but decreases valve flaps that reduce blood flow to the heart muscles.

Keywords

References

Abbot, D. E. and J. S. Kline (1962). Experimental investigation of subsonic turbulent flow over single and double backward facing steps. Journal of Basic Engineering 84, 317- 325.##
Alves, M. A., J. P. Oliveira and T. F. Pinho (2004). On the effect of contraction ratio in visco elastic flow. Journal of Non-Newtonian Fluid Mechanics 122, 117-130.##
Ashkezari, K. H. A., M. Dizani and A. Shamloo (2022). Integrating hydrodynamic and acoustic cell separation in a hybrid microfluidic device: a numerical analysis. Acta Mechanica 233(5), 1881-1894.##
Astarita, G. and G. Greco (1968). Excess presssure drop in laminar flow through sudden contraction. Industrial & Engineering Chemistry Fundamentals 7(1), 27-31.##
Bakirtas, I. and H. Demiray (2005). Weakly non-linear waves in a tapered elastic tube filled with an inviscid fluid. International Journal of Non-Linear Mechanics 40, 785-793.##
Balloch, A., P. Townsend and M. F. Ebster (1995). On two and three-dimensional expansion flows. Computers & Fluids 24, 863-897.##
Battaglia, F., J. S. Tavener, K. A. Kulkarni and L. C. A. Merkle (1997). Bifurcation of low reynolds number flows in symmetric channels. American Institute of Aeronautics and Astronautics 35, 99-105.##
Boodaghi, M. and A. Shamloo (2020). A comparison of different geometrical elements to model fluid wicking in paper based microfluidic devices. AIChE Journal 66(1), e16756.##
Boughamoura, A., H. Abbassi and B. Nasrallah (2003). Piston-driven laminar flow and heat transfer in a plane channel with a sudden expansion. Computational Mechanics 30, 410-420.##
Cantwell, C. D., D. Barkley and M. H. Blackburn (2010). Transient growth analysis of flow through a sudden expansion in a circular pipe. Physics of Fluids 22(3), 1-15.##
Castillo, T. L., O. G. Castrejn, J. F. J. Alvarado and O. Manero (2014). Prediction of excess pressure drop in contraction-expansion flow by molecular dynamics: Axi-symmetric and planar contaurations. Journal of Non-Newtonian Fluid Mechanics 210, 1-11.##
Chen, J. H., G. W. Pritchard and J. S. W. Tavener (1995). Bifurcation for flow past a cylinder between parallel planes. Journal of Fluid Mechanics 284, 23-41.##
Cherdron, W., F. Durst and J. H. Whitelaw (1978). Asymmetric flows and instabilities in symmetric ducts with sudden expansions. Journal of Fluid Mechanics 84, 13-31.##
Davies, J., Z. Whinnett, D. Francis, K. Willson, R. Foale, I. Malik, A. Huges, K. Parker and J. Mayet (2006). Use of simultaneous pressure and velocity measurments to estimate arterial wave speed at a single site in humans. American Journal of Physiology-Heart and Circulatory physiology 290 (2), 15-35.##
Dhinakaran, S., N. S. M. Oliveria, T. F. Pinho and A. M. Alves (2013). Steady flow of power-law fluids in a 1:3 planar sudden expansion. Journal of Non-Newtonian Fluid Mechanics 198, 48-58.##
Drikakis, D. (1997). Bifurcation phenomena in incompressible sudden expansion flows. Physics of Fluids 9, 76-86.##
Durst, F., F. C. J. Pereira and C. Tropea (1993). The plane symmetric sudden- expansion flow at low Reynolds numbers. Journal of Fluid Mechanics 248, 567- 581.##
Fearn, R. M., T. Mullin and A. K. Cliffe (1990). Nonlinear flow phenomena in a symmetric sudden expansion. Journal of Fluid Mechanics 211, 595-608.##
Formaggia, L., A. Quarteroni and A. Veneziani (2009). Cardiovascular and Mathematics. Modeling and Numerical Simulation 1, 15-27.##
Ghosh, S., V. V. R. Kaushik, G. Das and K. P. Das (2012). CFD simulation of core annular flow through sudden contraction and expansion. Journal of Petroleum Science and Engineering 86-87, 153-164.##
Hajji, H., L. Kolsi, K. Ghachem, C. Maatki, A. K. Hussein and M. N. Borjini (2021). Numerical study of heat transfer and flow structure over a microscale backstep. Alexandria Engineering Journal 60, 2759-2768.##
Kadja, M., D. Touzopoulos and G. Bergeles (2002). Numerical investigation of bifurcation phenomena occurring in flows through planar sudden expansions. Acta Mechanica 153, 47-61.##
Kang, K., W. K. Koelling and J. L. Lee (2006). Microdevice end pressure evaluations with Bagley correction. Microfluid Nanofluid 2, 223-235.##
Korakianitis, T. and Y. Shi (2006). Numerical simulation of cardiovascular dynamics with healthy and diseased heart valves. Journal of Biomechanics 39, 1964-1982.##
Leonard, P. B. (1979). A stable and accurate convective modeling procedure based on quadratic upstream interpolation. Computer Methods in Applied Mechanics and Engineering 19, 59-98.##
Mishra, S. and K. Jayaraman (2002). Asymmetric flows in planar symmetric channels with large expansion ratio. International Journal for Numerical Methods in Fluids 38(10), 945-962.##
Moallemi, N, J. R. Brinkerhoff (2006). Numerical analysis of laminar and transitional flow in a planarsudden expansion. Computers and Fluids 140, 209-221.##
Oliveira, M. S. N., L. E. Rodd, H. G. McKinley and L. Rodd (2008). Simulations of extensional flow in microrheometric devices. Microfluidics and Nanofluidics 5, 809-826.##
Pal, R. and C. Hwang (1997). Flow of 2-phase Oil/Water through sudden expansion and contraction. Chemical Engineering Journal 68, 157-163.##
Patlazhan, S. A., I. V. Kravchenko, R. Muller, Y. Hoarau, Y. Remond and A. Berlin (2017). Bifurcation of a Newtonian-fluid flow in a planar channel with sudden contraction and expansion. Dokaldy Physics 62, 145-148.##
Saha, S. (2021a). Numerical simulation of turbulent flow through a sudden expansion channel: comparison between three model. Lecture Notes in Mechanical Engineering 49-56.##
Saha, S. (2021b). A Survey on flow phenomena and heat transfer through expansion geometry. Lecture Notes in Mechanical Engineering 257-266.##
Saha, S. and A. N. Das (2021). flow bifurcation phenomena of shear-thinning and newtonian fluids in a rectangular channel in presence of intermediate steps: using carreau-yasuda model. Journal of Applied Fluid Mechanics 14(4), 1283-1293.##
Saha, S. and A. N. Das (2022). Hydro-thermal analysis of water-Al2O3 nanofluid flow through a sudden expansion channel with intermediate step. Kuwait Journal of Science 49(4).##
Saha, S., P. Biswas and S. Nath (2020). Bifurcation phenomena for incompressible laminar flow in expansion channel to study Coanda effect. Journal of Interdisciplinary Mathematics 23(2), 493-502.##
Saha, S., P. Biswas, K. Jha, A. N. Das and R. Choudhary (2021). Newtonian hydro-thermal phenomena through a sudden expansion channel with or without baffles. Kuwait Journal of Science.##
Saha, S., S. Raut and A. N. Das (2022). Thermal enhancement and entropy generation of laminar water-Al2O3 nano-fluid flow through a sudden expansion channel with bell-shaped surface. International Journal of Fluid Mechanics Research 48(3), 65-78.##
Sanmigue, R. E., C. Pino and C. M. Gutie. (2010). Global mode analysis of a pipe flow through a 1:2 axisymmetric sudden expansion. Physics of Fluids 22, 1-4.##
Shamloo, A. and F. Y. Parast (2019). Simulation of blood particle separation in a trapezoidal microfluidic device by acoustic force. IEEE Transactions on Electron Devices 66(3), 1495-1503.##
Shamloo, A., P. Vatankhah and M. A. Bijarchi (2016). Numerical optimization and inverse study of a microfluidic device for blood plasma separation. European Journal of Mechanics-B/Fluids 57, 31-39.##
Shapira, M., D. Degani and D. Weihs (1990). Stability and existence of multiple solutions for viscous flow in suddenly enlarged channels. Computers & Fluids 18, 239-258.##
Sobey, I. J. and G. P. Drazin (1986). Bifurcations of two-dimensional channel flows. Journal of Fluid Mechanics 171, 263-287.##
Ternik, P. (2010). New contributions on laminar flow of inelastic non-Newtonian fluid in the two-dimensional symmetric expansion: Creeping and slowly moving flow conditions. Journal of Non-Newtonian Fluid Mechanics 165, 1400-1411.##
Ternik, P., J. Marn and Z. Zunic (2006). Non-Newtonian fluid flow through a planar symmetric expansion: Shear-thickening fluids. Journal of Non-Newtonian Fluid Mechanics 13, 136-148.##
Touzopoulos, D. and G. Bergeles (1998). Numerical investigations of the laminar steady incompressible sudden-expansion flow. Proceedings European Congress on Computational Methods in Applied Sciences and Engineering 98, 906-912.##
Tsai, C. H., T. H. Chen, N. Y. Wang, C. H. Lin and M. L. Fu (2007). Capabilities and limitations of 2-dimensional and 3-dimensional numerical methods in modeling the fluid flow in sudden expansion microchannels. Microfluid. Nanofluid 3(1), 13-18.##
Van Doormaal, J. P. and G. D. Raithby (1984). Enhancements of the SIMPLE method for predicting incompressible fluid flows. Numerical Heat Transfer 7, 147-163.##
Verlinden, J. E., M. Madadelahi, E. Sarajlic, A. Shamloo, A. H. Engel, U. Staufer and M. K. Ghatkesar (2020). Volume and concentration dosing in picolitres using a two-channel microfluidic AFM cantilever. Nanoscale 12(18), 10292-10305.##
Wang, J. J. and H. K. Parker (2004). Wave propagation in a model of the arterial circulation. Journal of Biomechanical Engineering 37, 457-470.##
Zhao, W., K. T. Peter, R. Horswell, Y. Wang, W. Li, B. Heymsfield, W. Cefalu, H. Donna and H. Gang (2013). Aggressive Blood Pressure Control Increases Coronary Heart Disease Risk Among Diabetic Patients. Diabetes Care 36(10), 3287-3296.##

Files

Cited by

History

  • Received: 06 June 2022
  • Revised: 08 October 2022
  • Accepted: 22 October 2022
  • Available online: 01 March 2023

Share

How to cite

Statistics