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.

[1]  Peter Boesiger,et al.  Blood flow in the human ascending aorta: a combined MRI and CFD study , 2003 .

[2]  I. Babuska.  The finite element method with Lagrangian multipliers , 1973 .

[3]  Catarina F. Castro,et al.  Eliminating Forging Defects Using Genetic Algorithms , 2005 .

[4]  John W. Fowler,et al.  A multi-population genetic algorithm to solve multi-objective scheduling problems for parallel machines , 2003, Comput. Oper. Res..

[5]  A. Chorin.  Numerical Solution of the Navier-Stokes Equations* , 1989 .

[6]  Thomas J. R. Hughes,et al.  Finite element modeling of blood flow in arteries , 1998 .

[7]  D. Ku,et al.  Pulsatile Flow and Atherosclerosis in the Human Carotid Bifurcation: Positive Correlation between Plaque Location and Low and Oscillating Shear Stress , 1985, Arteriosclerosis.

[8]  Michael M. Resch,et al.  Pulsatile non-Newtonian flow characteristics in a three-dimensional human carotid bifurcation model. , 1991, Journal of biomechanical engineering.

[9]  Gianni Pedrizzetti,et al.  Cardiovascular fluid mechanics , 2003 .

[10]  I. Babuska,et al.  Analysis of mixed methods using mesh dependent norms , 1980 .

[11]  R. Courant.  Variational methods for the solution of problems of equilibrium and vibrations , 1943 .

[12]  N M Maurits,et al.  The influence of vessel wall elasticity and peripheral resistance on the carotid artery flow wave form: a CFD model compared to in vivo ultrasound measurements. , 2007, Journal of biomechanics.

[13]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[14]  A. Chorin.  Numerical solution of the Navier-Stokes equations , 1968 .

[15]  Alfio Quarteroni,et al.  Computational vascular fluid dynamics: problems, models and methods , 2000 .

[16]  H. M. Bücker,et al.  Sensitivity of shear rate in artificial grafts using automatic differentiation , 2009 .

[17]  Luísa Costa Sousa,et al.  Optimisation of shape and process parameters in metal forging using genetic algorithms , 2004 .

[18]  F. Brezzi.  On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers , 1974 .

[19]  H. M. Bücker,et al.  Sensitivity of optimal shapes of artificial grafts with respect to flow parameters , 2010 .

[20]  V. J. Modi,et al.  Fluid mechanics of stenosed arteries , 1995 .

[21]  Matthieu De Beule,et al.  Patient-specific computational fluid dynamics: structured mesh generation from coronary angiography , 2010, Medical & Biological Engineering & Computing.

[22]  R. Marler,et al.  The weighted sum method for multi-objective optimization: new insights , 2010 .

[23]  T. Hughes,et al.  The Galerkin/least-squares method for advective-diffusive equations , 1988 .

[24]  Bernhard Preim,et al.  Implicit vessel surface reconstruction for visualization and CFD simulation , 2008, International Journal of Computer Assisted Radiology and Surgery.

[25]  W. Shyy,et al.  Fluid flow structure in arterial bypass anastomosis. , 2005, Journal of biomechanical engineering.

[26]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuscka-Brezzi condition: A stable Petrov-Galerkin formulation of , 1986 .

[27]  M. Kaazempur-Mofrad,et al.  Characterization of the Atherosclerotic Carotid Bifurcation Using MRI, Finite Element Modeling, and Histology , 2004, Annals of Biomedical Engineering.

[28]  Carlos Alberto Conceição António,et al.  Optimisation of forging process parameters using genetic algorithms , 2004 .

[29]  M. Heinkenschloss,et al.  Shape optimization in steady blood flow: A numerical study of non-Newtonian effects , 2005, Computer methods in biomechanics and biomedical engineering.

[30]  R. Himeno,et al.  Blood Flow Simulation toward Actual Application at Hospital , 2003 .

[31]  I. Kim,et al.  Adaptive weighted sum method for multiobjective optimization: a new method for Pareto front generation , 2006 .