An improved baseline model for a human arterial network to study the impact of aneurysms on pressure‐flow waveforms

In this study, an improved and robust one-dimensional human arterial network model is presented. The one-dimensional blood flow equations are solved using the Taylor-locally conservative Galerkin finite element method. The model improvements are carried out by adopting parts of the physical models from different authors to establish an accurate baseline model. The predicted pressure-flow waveforms at various monitoring positions are compared against in vivo measurements from published works. The results obtained show that wave shapes predicted are similar to that of the experimental data and exhibit a good overall agreement with measured waveforms. Finally, computational studies on the influence of an abdominal aortic aneurysm are presented. The presence of aneurysms results in a significant change in the waveforms throughout the network.

[1]  R. Löhner,et al.  Hemodynamic analysis of intracranial aneurysms with moving parent arteries: Basilar tip aneurysms , 2010, International journal for numerical methods in biomedical engineering.

[2]  D. Bessems,et al.  On the propagation of pressure and flow waves through the patient specific arterial system , 2003 .

[3]  K. Parker,et al.  Wave propagation in a model of the arterial circulation. , 2004, Journal of biomechanics.

[4]  Spencer J. Sherwin,et al.  Computational modelling of 1D blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system , 2003 .

[5]  H. Boom,et al.  The use of an analog computer in a circulation model. , 1963, Progress in cardiovascular diseases.

[6]  R. Budwig,et al.  Model studies of the flow in abdominal aortic aneurysms during resting and exercise conditions. , 1999, Journal of biomechanics.

[7]  Steven H Frankel,et al.  Numerical modeling of pulsatile turbulent flow in stenotic vessels. , 2003, Journal of biomechanical engineering.

[8]  R. Budwig,et al.  Steady flow in abdominal aortic aneurysm models. , 1993, Journal of biomechanical engineering.

[9]  Alfio Quarteroni,et al.  Mathematical Modelling and Numerical Simulation of the Cardiovascular System , 2004 .

[10]  D. Thijssen,et al.  Brachial artery blood flow responses to different modalities of lower limb exercise. , 2009, Medicine and science in sports and exercise.

[11]  J AlastrueyArimon.  Numerical modelling of pulse wave propagation in the cardiovascular system : development, validation and clinical applications. , 2006 .

[12]  A. Quarteroni,et al.  One-dimensional models for blood flow in arteries , 2003 .

[13]  W. P. Timlake,et al.  A theory of fluid flow in compliant tubes. , 1966, Biophysical journal.

[14]  van de Fn Frans Vosse,et al.  Computational modelling of endoleak after endovascular repair of abdominal aortic aneurysms , 2010 .

[15]  S. Sherwin,et al.  Analysing the pattern of pulse waves in arterial networks: a time-domain study , 2009 .

[16]  Xianghua Xie,et al.  Modelling pipeline for subject‐specific arterial blood flow—A review , 2011 .

[17]  Kenji Takizawa,et al.  Space–time fluid–structure interaction modeling of patient‐specific cerebral aneurysms , 2011 .

[18]  P N Tandon,et al.  A new model for blood flow through an artery with axisymmetric stenosis. , 1995, International journal of bio-medical computing.

[19]  V. Streeter,et al.  Pulsatile Pressure and Flow Through Distensible Vessels , 1963, Circulation research.

[20]  P. Nithiarasu,et al.  Patient‐specific blood flow simulation through an aneurysmal thoracic aorta with a folded proximal neck , 2011 .

[21]  P. Fischer,et al.  Direct numerical simulation of stenotic flows. Part 1. Steady flow , 2007, Journal of Fluid Mechanics.

[22]  S. Sherwin,et al.  One-dimensional modelling of a vascular network in space-time variables , 2003 .

[23]  N. Westerhof,et al.  Aortic Input Impedance in Normal Man: Relationship to Pressure Wave Forms , 1980, Circulation.

[24]  M. Deville,et al.  Pulsatile flow of non-Newtonian fluids through arterial stenoses. , 1996, Journal of biomechanics.

[25]  Y. Zhang,et al.  Estimating an equivalent wall‐thickness of a cerebral aneurysm through surface parameterization and a non‐linear spring system , 2011 .

[26]  Andrew J. Pullan,et al.  An Anatomically Based Model of Transient Coronary Blood Flow in the Heart , 2002, SIAM J. Appl. Math..

[27]  A Noordergraaf,et al.  Analog studies of the human systemic arterial tree. , 1969, Journal of biomechanics.

[28]  A. Quarteroni,et al.  Model reduction techniques for fast blood flow simulation in parametrized geometries , 2012, International journal for numerical methods in biomedical engineering.

[29]  P. Fischer,et al.  Direct numerical simulation of stenotic flows. Part 2. Pulsatile flow , 2007, Journal of Fluid Mechanics.

[30]  Alfio Quarteroni,et al.  Algorithms for the partitioned solution of weakly coupled fluid models for cardiovascular flows , 2011 .

[31]  Nan Xiao,et al.  Simulation of blood flow in deformable vessels using subject‐specific geometry and spatially varying wall properties , 2011, International journal for numerical methods in biomedical engineering.

[32]  Timothy J. Pedley,et al.  The fluid mechanics of large blood vessels , 1980 .

[33]  Nikos Stergiopulos,et al.  Pulse Wave Propagation in the Arterial Tree , 2011 .

[34]  Santabrata Chakravarty,et al.  Dynamic response of stenotic blood flow in vivo , 1992 .

[35]  S. Cavalcanti,et al.  Hemodynamics of an artery with mild stenosis. , 1995, Journal of biomechanics.

[36]  C. M. Rodkiewicz,et al.  On the abdominal aortic aneurysms: pulsatile state considerations. , 1997, Medical engineering & physics.

[37]  P. Nithiarasu,et al.  A 1D arterial blood flow model incorporating ventricular pressure, aortic valve and regional coronary flow using the locally conservative Galerkin (LCG) method , 2008 .

[38]  Mette S. Olufsen,et al.  Modeling the arterial system with reference to an anesthesia simulator , 1998 .

[39]  Lieve Lanoye,et al.  Effect of an Abdominal Aortic Aneurysm on Wave Reflection in the Aorta , 2008, IEEE Transactions on Biomedical Engineering.

[40]  E H WOOD,et al.  Comparison of Simultaneously Recorded Central and Peripheral Arterial Pressure Pulses During Rest, Exercise and Tilted Position in Man , 1955, Circulation research.

[41]  D. F. Young,et al.  Computer simulation of arterial flow with applications to arterial and aortic stenoses. , 1992, Journal of biomechanics.

[42]  Timothy J. Pedley,et al.  Numerical solutions for unsteady gravity-driven flows in collapsible tubes: evolution and roll-wave instability of a steady state , 1999, Journal of Fluid Mechanics.

[43]  N. Stergiopulos,et al.  Validation of a one-dimensional model of the systemic arterial tree. , 2009, American journal of physiology. Heart and circulatory physiology.

[44]  Tayfun E. Tezduyar,et al.  Space–time finite element computation of arterial fluid–structure interactions with patient‐specific data , 2010 .

[45]  A. P. Avó.  Multi-branched model of the human arterial system , 2006 .

[46]  E A Finol,et al.  Blood flow in abdominal aortic aneurysms: pulsatile flow hemodynamics. , 2001, Journal of biomechanical engineering.

[47]  Donald S Borrett,et al.  Evolutionary autonomous agents and the nature of apraxia , 2005, Biomedical engineering online.

[48]  Karim Azer,et al.  A One-dimensional Model of Blood Flow in Arteries with Friction and Convection Based on the Womersley Velocity Profile , 2007, Cardiovascular engineering.

[49]  M. Olufsen,et al.  Numerical Simulation and Experimental Validation of Blood Flow in Arteries with Structured-Tree Outflow Conditions , 2000, Annals of Biomedical Engineering.

[50]  R. Himeno,et al.  Biomechanical characterization of ventricular-arterial coupling during aging: a multi-scale model study. , 2009, Journal of biomechanics.

[51]  S. Sherwin,et al.  Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vitro measurements , 2011, Journal of biomechanics.

[52]  Ryutaro Himeno,et al.  Multi-scale modeling of the human cardiovascular system with applications to aortic valvular and arterial stenoses , 2009, Medical & Biological Engineering & Computing.

[53]  Toshio Kobayashi,et al.  Influence of wall thickness on fluid–structure interaction computations of cerebral aneurysms , 2010 .

[54]  L. Formaggia,et al.  Numerical modeling of 1D arterial networks coupled with a lumped parameters description of the heart , 2006, Computer methods in biomechanics and biomedical engineering.

[55]  F Mut,et al.  Clinical application of image‐based CFD for cerebral aneurysms , 2011, International journal for numerical methods in biomedical engineering.

[56]  P. Abbrecht,et al.  Digital computer simulation of human systemic arterial pulse wave transmission: a nonlinear model. , 1972, Journal of biomechanics.

[57]  K. Miller,et al.  A meshless Total Lagrangian explicit dynamics algorithm for surgical simulation , 2010 .

[58]  Aichi Chien,et al.  Computational hemodynamics framework for the analysis of cerebral aneurysms , 2011, International journal for numerical methods in biomedical engineering.

[59]  P. Hoskins,et al.  Numerical analysis of pulsatile blood flow and vessel wall mechanics in different degrees of stenoses. , 2007, Journal of biomechanics.

[60]  Alfio Quarteroni,et al.  A One Dimensional Model for Blood Flow: Application to Vascular Prosthesis , 2002 .

[61]  N. Stergiopulos,et al.  Assessment of distributed arterial network models , 1997, Medical and Biological Engineering and Computing.

[62]  Jonathan P. Mynard,et al.  One-dimensional Blood Flow Modelling with the Locally Conservative Galerkin ( LCG ) Method , 2007 .

[63]  Spencer J. Sherwin,et al.  COMPUTATIONAL MODELLING OF 1D BLOOD FLOW AND ITS APPLICATIONS. , 2002 .

[64]  Christian Reeps,et al.  Correlation of biomechanics to tissue reaction in aortic aneurysms assessed by finite elements and [18F]–fluorodeoxyglucose–PET/CT , 2012, International journal for numerical methods in biomedical engineering.

[65]  Alexander D. Shkolnik,et al.  Fluid-structure interaction in abdominal aortic aneurysms: effects of asymmetry and wall thickness , 2005, Biomedical engineering online.