On Coupling a Lumped Parameter Heart Model and a Three-Dimensional Finite Element Aorta Model

Aortic flow and pressure result from the interactions between the heart and arterial system. In this work, we considered these interactions by utilizing a lumped parameter heart model as an inflow boundary condition for three-dimensional finite element simulations of aortic blood flow and vessel wall dynamics. The ventricular pressure–volume behavior of the lumped parameter heart model is approximated using a time varying elastance function scaled from a normalized elastance function. When the aortic valve is open, the coupled multidomain method is used to strongly couple the lumped parameter heart model and three-dimensional arterial models and compute ventricular volume, ventricular pressure, aortic flow, and aortic pressure. The shape of the velocity profiles of the inlet boundary and the outlet boundaries that experience retrograde flow are constrained to achieve a robust algorithm. When the aortic valve is closed, the inflow boundary condition is switched to a zero velocity Dirichlet condition. With this method, we obtain physiologically realistic aortic flow and pressure waveforms. We demonstrate this method in a patient-specific model of a normal human thoracic aorta under rest and exercise conditions and an aortic coarctation model under pre- and post-interventions.

[1]  K. Donald,et al.  CIRCULATORY STUDIES AT REST AND DURING EXERCISE IN COARCTATION OF THE AORTA BEFORE AND AFTER OPERATION , 1960, British heart journal.

[2]  H. Suga,et al.  Instantaneous Pressure‐Volume Relationships and Their Ratio in the Excised, Supported Canine Left Ventricle , 1974, Circulation research.

[3]  John W. Kirklin,et al.  Cardiac surgery: Morphology, diagnostic criteria, natural history, techniques, results, and indications , 1986 .

[4]  D. C. Miller,et al.  Cardiac Surgery—Morphology, Diagnostic Criteria, Natural History, Techniques, Results, and Indications , 1987 .

[5]  Michael M. Resch,et al.  Pulsatile non-Newtonian blood flow simulation through a bifurcation with an aneurysm. , 1989, Biorheology.

[6]  A Noordergraaf,et al.  Estimation of total systemic arterial compliance in humans. , 1990, Journal of applied physiology.

[7]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[8]  L. Franca,et al.  Stabilized finite element methods. II: The incompressible Navier-Stokes equations , 1992 .

[9]  T. Wonnacott,et al.  Relation between diameter and flow in major branches of the arch of the aorta. , 1992, Journal of biomechanics.

[10]  L. Franca,et al.  Stabilized Finite Element Methods , 1993 .

[11]  L. Quartapelle.  The incompressible Navier—Stokes equations , 1993 .

[12]  C. H. Chen,et al.  Single-beat estimation of end-systolic pressure-volume relation in humans. A new method with the potential for noninvasive application. , 1996, Circulation.

[13]  T. Nozawa,et al.  Energetically optimal left ventricular pressure for the failing human heart. , 1996, Circulation.

[14]  Rolf Rannacher,et al.  ARTIFICIAL BOUNDARIES AND FLUX AND PRESSURE CONDITIONS FOR THE INCOMPRESSIBLE NAVIER–STOKES EQUATIONS , 1996 .

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

[16]  P Segers,et al.  Use of pulse pressure method for estimating total arterial compliance in vivo. , 1999, American journal of physiology. Heart and circulatory physiology.

[17]  C. Taylor,et al.  Predictive medicine: computational techniques in therapeutic decision-making. , 1999, Computer aided surgery : official journal of the International Society for Computer Aided Surgery.

[18]  Kenneth E. Jansen,et al.  A stabilized finite element method for the incompressible Navier–Stokes equations using a hierarchical basis , 2001 .

[19]  A. Quarteroni,et al.  Coupling between lumped and distributed models for blood flow problems , 2001 .

[20]  A. Quarteroni,et al.  On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels , 2001 .

[21]  Patrick Segers,et al.  Relation of effective arterial elastance to arterial system properties. , 2002, American journal of physiology. Heart and circulatory physiology.

[22]  Peter J Hunter,et al.  Modeling total heart function. , 2003, Annual review of biomedical engineering.

[23]  P. Kolh,et al.  Systemic and pulmonary hemodynamics assessed with a lumped-parameter heart-arterial interaction model , 2003 .

[24]  David A Steinman,et al.  Finite-element modeling of the hemodynamics of stented aneurysms. , 2004, Journal of biomechanical engineering.

[25]  M. Seear,et al.  Descending aortic blood flow velocity as a noninvasive measure of cardiac output in children , 1994, Pediatric Cardiology.

[26]  Charles Taylor,et al.  EXPERIMENTAL AND COMPUTATIONAL METHODS IN CARDIOVASCULAR FLUID MECHANICS , 2004 .

[27]  Johnny T. Ottesen,et al.  Applied Mathematical Models in Human Physiology , 2004 .

[28]  I. Meredith,et al.  Waveform dispersion, not reflection, may be the major determinant of aortic pressure wave morphology. , 2005, American journal of physiology. Heart and circulatory physiology.

[29]  C. Putman,et al.  Characterization of cerebral aneurysms for assessing risk of rupture by using patient-specific computational hemodynamics models. , 2005, AJNR. American journal of neuroradiology.

[30]  C. Kleinstreuer,et al.  Blood flow and structure interactions in a stented abdominal aortic aneurysm model. , 2005, Medical engineering & physics.

[31]  Charles A. Taylor,et al.  Efficient anisotropic adaptive discretization of the cardiovascular system , 2006 .

[32]  Charles A. Taylor,et al.  A coupled momentum method for modeling blood flow in three-dimensional deformable arteries , 2006 .

[33]  Christopher P. Cheng,et al.  Abdominal aortic hemodynamics in young healthy adults at rest and during lower limb exercise: quantification using image-based computer modeling. , 2006, American journal of physiology. Heart and circulatory physiology.

[34]  D. Chapelle,et al.  MODELING AND ESTIMATION OF THE CARDIAC ELECTROMECHANICAL ACTIVITY , 2006 .

[35]  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.

[36]  Roy C. P. Kerckhoffs,et al.  Coupling of a 3D Finite Element Model of Cardiac Ventricular Mechanics to Lumped Systems Models of the Systemic and Pulmonic Circulation , 2006, Annals of Biomedical Engineering.

[37]  F. Migliavacca,et al.  Multiscale modelling in biofluidynamics: application to reconstructive paediatric cardiac surgery. , 2006, Journal of biomechanics.

[38]  Charles A. Taylor,et al.  Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries , 2006 .

[39]  A. Yoganathan,et al.  Introduction of a new optimized total cavopulmonary connection. , 2007, The Annals of thoracic surgery.

[40]  Wei Zhang,et al.  Application of Electrical Impedance Tomography for Continuous Monitoring of Retroperitoneal Bleeding After Blunt Trauma , 2009, Annals of Biomedical Engineering.

[41]  B. Lee,et al.  Michael-Type Addition Reactions in NIPAAm-Cysteamine Copolymers Follow Second Order Rate Laws with Steric Hindrance , 2009, Annals of Biomedical Engineering.

[42]  R. Wijesinghe,et al.  Detection of Peripheral Nerve and Skeletal Muscle Action Currents Using Magnetic Resonance Imaging , 2009, Annals of Biomedical Engineering.

[43]  Hamid Nayeb-Hashemi,et al.  The Combined Effect of Frontal Plane Tibiofemoral Knee Angle and Meniscectomy on the Cartilage Contact Stresses and Strains , 2009, Annals of Biomedical Engineering.

[44]  Charles A. Taylor,et al.  Augmented Lagrangian method for constraining the shape of velocity profiles at outlet boundaries for three-dimensional finite element simulations of blood flow , 2009 .

[45]  B. E. Lewandowski,et al.  In Vivo Demonstration of a Self-Sustaining, Implantable, Stimulated-Muscle-Powered Piezoelectric Generator Prototype , 2009, Annals of Biomedical Engineering.