Blood Flow Simulation and Applications
In the vascular system altered flow conditions, such as separation and flow-reversal zones play an important role in the development of arterial diseases. Nowadays computational biomechanics modeling is still in the research and development stage. This chapter presents a numerical computational methodology for blood flow simulation using the Finite Element method outlining field equations and approaches for numerical solutions. Due to the complexity of the vascular system simplifying assumptions for the mathematical modeling process are made. Two applications of the developed tool to describe arterial hemodynamics are presented, a flow simulation in the human carotid artery bifurcation and a search for an optimized geometry of an artificial bypass graft.
KeywordsPareto Front Pareto Optimal Solution Galerkin Formulation Carotid Artery Bifurcation Divider Wall
This work was partially done in the scope of project PTDC/SAU-BEB/102547/2008, “Blood flow simulation in arterial networks towards application at hospital”, financially supported by FCT – Fundação para a Ciência e a Tecnologia from Portugal.
- 1.Pedrizzetti G, Perktold K (2003) Cardiovascular fluid mechanics. Springer, New YorkGoogle Scholar
- 10.Himeno R (2003) Blood flow simulation toward actual application at hospital. In: The 5th Asian computational fluid dynamics, KoreaGoogle Scholar
- 18.Perktold K, Rappitsch G (1995) Mathematical modeling of local arterial flow and vessel mechanics. In: Crolet J, Ohayon R (eds) Computational methods for fluid structure interaction, vol 306, Pitman research notes in mathematics. Harlow, Longman, pp 230–245Google Scholar
- 21.Hughes TJR, Franca LP, Balestra M (1986) A new finite element method for computational fluid dynamics: V. Circumventing the Babuska-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal order interpolations. Comput Meth Appl Mech Eng 59:85–99MathSciNetMATHCrossRefGoogle Scholar
- 24.Schaffer JD (1985) Multi-objective optimization with vector evaluated genetic algorithms. In: Proceedings of the 1st international conference of genetic algorithms, pp 93–100Google Scholar
- 25.Marler RT, Arora JS (2009) The weighted sum method for multi-objective optimization: new insights. Struct Multidisc Optim. doi: 10.1007/s00158-009-0460-7