Recent advances in computational methodology for simulation of mechanical circulatory assist devices

Ventricular assist devices (VADs) provide mechanical circulatory support to offload the work of one or both ventricles during heart failure. They are used in the clinical setting as destination therapy, as bridge to transplant, or more recently as bridge to recovery to allow for myocardial remodeling. Recent developments in computational simulation allow for detailed assessment of VAD hemodynamics for device design and optimization for both children and adults. Here, we provide a focused review of the recent literature on finite element methods and optimization for VAD simulations. As VAD designs typically fall into two categories, pulsatile and continuous flow devices, we separately address computational challenges of both types of designs, and the interaction with the circulatory system with three representative case studies. In particular, we focus on recent advancements in finite element methodology that have increased the fidelity of VAD simulations. We outline key challenges, which extend to the incorporation of biological response such as thrombosis and hemolysis, as well as shape optimization methods and challenges in computational methodology. WIREs Syst Biol Med 2014, 6:169–188. doi: 10.1002/wsbm.1260

[1]  Kyung Hyun Ahn,et al.  Shear induced damage of red blood cells monitored by the decrease of their deformability , 2004 .

[2]  William R Wagner,et al.  Elimination of adverse leakage flow in a miniature pediatric centrifugal blood pump by computational fluid dynamics-based design optimization. , 2005, ASAIO journal.

[3]  Danny Bluestein,et al.  A novel mathematical model of activation and sensitization of platelets subjected to dynamic stress histories , 2013, Biomechanics and Modeling in Mechanobiology.

[4]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[5]  James F. Antaki,et al.  Computational Fluid Dynamics-Based Design Optimization for an Implantable Miniature Maglev Pediatric Ventricular Assist Device , 2012 .

[6]  James F. Antaki,et al.  A computational and experimental comparison of two outlet stators for the Nimbus LVAD , 1999 .

[7]  A. Quarteroni,et al.  OPTIMAL CONTROL AND SHAPE OPTIMIZATION OF AORTO-CORONARIC BYPASS ANASTOMOSES , 2003 .

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

[9]  Sarah Furness,et al.  The Berlin Heart EXCOR Pediatrics-The SickKids Experience 2004-2008. , 2010, Artificial organs.

[10]  Steven Deutsch,et al.  The influence of operational protocol on the fluid dynamics in the 12 cc Penn state pulsatile pediatric ventricular assist device: the effect of end-diastolic delay. , 2010, Artificial organs.

[11]  Thomas J. R. Hughes,et al.  Isogeometric shell analysis: The Reissner-Mindlin shell , 2010 .

[12]  Marek Behr,et al.  The Shear-Slip Mesh Update Method , 1999 .

[13]  Shmuel Einav,et al.  The Syncardia(™) total artificial heart: in vivo, in vitro, and computational modeling studies. , 2013, Journal of biomechanics.

[14]  A. J. Booker,et al.  A rigorous framework for optimization of expensive functions by surrogates , 1998 .

[15]  C. Canter,et al.  Biventricular Assist Devices as a Bridge to Heart Transplantation in Small Children , 2008, Circulation.

[16]  H. Reul,et al.  Estimation of Shear Stress-related Blood Damage in Heart Valve Prostheses - in Vitro Comparison of 25 Aortic Valves , 1990, The International journal of artificial organs.

[17]  M C Oz,et al.  Long-term use of a left ventricular assist device for end-stage heart failure. , 2001, The New England journal of medicine.

[18]  Thomas J. R. Hughes,et al.  Multiscale and Stabilized Methods , 2007 .

[19]  Yuri Bazilevs,et al.  Fluid–structure interaction simulation of pulsatile ventricular assist devices , 2013, Computational Mechanics.

[20]  C. Warnes,et al.  The adult with congenital heart disease: born to be bad? , 2005, Journal of the American College of Cardiology.

[21]  Christopher M Haggerty,et al.  Laser flow measurements in an idealized total cavopulmonary connection with mechanical circulatory assistance. , 2011, Artificial organs.

[22]  Aaron L Fogelson,et al.  Platelet-wall interactions in continuum models of platelet thrombosis: formulation and numerical solution. , 2004, Mathematical medicine and biology : a journal of the IMA.

[23]  Rebecca Peterson,et al.  Animal model development for the Penn State pediatric ventricular assist device. , 2009, Artificial organs.

[24]  Yuri Bazilevs,et al.  Space–Time and ALE-VMS Techniques for Patient-Specific Cardiovascular Fluid–Structure Interaction Modeling , 2012 .

[25]  Marek Behr,et al.  Transient stress‐based and strain‐based hemolysis estimation in a simplified blood pump , 2013, International journal for numerical methods in biomedical engineering.

[26]  S. Mittal,et al.  Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements , 1992 .

[27]  D. Mozaffarian,et al.  Executive summary: heart disease and stroke statistics--2010 update: a report from the American Heart Association. , 2010, Circulation.

[28]  D B Olsen,et al.  Blood flow in a continuous flow ventricular assist device. , 1999, Artificial organs.

[29]  Tayfun E. Tezduyar,et al.  Shear-Slip Mesh Update in 3D Computation of Complex Flow Problems with Rotating Mechanical Components , 2001 .

[30]  Charles Audet,et al.  Convergence Results for Pattern Search Algorithms are Tight , 2002 .

[31]  Hélène A. Simon,et al.  A Numerical Investigation of Blood Damage in the Hinge Area of Aortic Bileaflet Mechanical Heart Valves During the Leakage Phase , 2012, Annals of Biomedical Engineering.

[32]  Yuri Bazilevs,et al.  ALE-VMS AND ST-VMS METHODS FOR COMPUTER MODELING OF WIND-TURBINE ROTOR AERODYNAMICS AND FLUID–STRUCTURE INTERACTION , 2012 .

[33]  Akif Ündar,et al.  Mechanical Circulatory Support for End-Stage Heart Failure in Repaired and Palliated Congenital Heart Disease , 2011, Current cardiology reviews.

[34]  John E. Dennis,et al.  A framework for managing models in nonlinear optimization of computationally expensive functions , 1999 .

[35]  Christine E. Peyton,et al.  Predicting recovery: successful explant of a ventricular assist device in a child with dilated cardiomyopathy. , 2010, The Journal of heart and lung transplantation : the official publication of the International Society for Heart Transplantation.

[36]  Steven Deutsch,et al.  Assessment of CFD Performance in Simulations of an Idealized Medical Device: Results of FDA’s First Computational Interlaboratory Study , 2012 .

[37]  Alison L. Marsden,et al.  Constrained optimization of an idealized Y-shaped baffle for the Fontan surgery at rest and exercise , 2010 .

[38]  James F. Antaki,et al.  Computational Simulation of Platelet Deposition and Activation: I. Model Development and Properties , 1999, Annals of Biomedical Engineering.

[39]  J F Antaki,et al.  A mathematical model for shear-induced hemolysis. , 1995, Artificial organs.

[40]  A. Marsden,et al.  A comparison of outlet boundary treatments for prevention of backflow divergence with relevance to blood flow simulations , 2011 .

[41]  Steven Deutsch,et al.  EXPERIMENTAL FLUID MECHANICS OF PULSATILE ARTIFICIAL BLOOD PUMPS , 2006 .

[42]  D. Goldstein,et al.  Left ventricular assist devices and bleeding: adding insult to injury. , 2003, The Annals of thoracic surgery.

[43]  Marcel C M Rutten,et al.  A mathematical model to evaluate control strategies for mechanical circulatory support. , 2009, Artificial organs.

[44]  Yuri Bazilevs,et al.  Fluid–structure interaction modeling of wind turbines: simulating the full machine , 2012, Computational Mechanics.

[45]  S. Deutsch,et al.  Integrating particle image velocimetry and laser Doppler velocimetry measurements of the regurgitant flow field past mechanical heart valves. , 2001, Artificial organs.

[46]  Yuri Bazilevs,et al.  Computational Fluid-Structure Interaction: Methods and Applications , 2013 .

[47]  William A Smith,et al.  Evaluation of Computational Models for Hemolysis Estimation , 2005, ASAIO journal.

[48]  Tayfun E. Tezduyar,et al.  Flow simulation and high performance computing , 1996 .

[49]  Jiafeng Zhang,et al.  Comparison and experimental validation of fluid dynamic numerical models for a clinical ventricular assist device. , 2013, Artificial organs.

[50]  Parviz Moin,et al.  Suppression of vortex-shedding noise via derivative-free shape optimization , 2004 .

[51]  Thomas J. R. Hughes,et al.  NURBS-based isogeometric analysis for the computation of flows about rotating components , 2008 .

[52]  J F Antaki,et al.  Computational fluid dynamics as a development tool for rotary blood pumps. , 2001, Artificial organs.

[53]  Steven Deutsch,et al.  Multilaboratory particle image velocimetry analysis of the FDA benchmark nozzle model to support validation of computational fluid dynamics simulations. , 2011, Journal of biomechanical engineering.

[54]  Gianluigi Rozza,et al.  Shape Design in Aorto-Coronaric Bypass Anastomoses Using Perturbation Theory , 2006, SIAM J. Numer. Anal..

[55]  Alison L. Marsden,et al.  Patient-Specific Multiscale Modeling of Blood Flow for Coronary Artery Bypass Graft Surgery , 2012, Annals of Biomedical Engineering.

[56]  T David,et al.  Platelet deposition in stagnation point flow: an analytical and computational simulation. , 2001, Medical engineering & physics.

[57]  W. Morrow,et al.  Preliminary Single Center North American Experience With The Berlin Heart Pediatric EXCOR Device , 2008, ASAIO journal.

[58]  Mehdi Behbahani,et al.  A review of computational fluid dynamics analysis of blood pumps , 2009, European Journal of Applied Mathematics.

[59]  Roland Wüchner,et al.  Isogeometric shell analysis with Kirchhoff–Love elements , 2009 .

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

[61]  R. Cheng,et al.  Three-Dimensional Fluid-Structure Interaction Simulation of Bileaflet Mechanical Heart Valve Flow Dynamics , 2004, Annals of Biomedical Engineering.

[62]  Gianluigi Rozza,et al.  A Mathematical Approach in the Design of Arterial Bypass Using Unsteady Stokes Equations , 2006, J. Sci. Comput..

[63]  G D Stubley,et al.  Theoretical and experimental analysis of cellular adhesion to polymer surfaces. , 1987, Journal of biomedical materials research.

[64]  Fotis Sotiropoulos Computational Fluid Dynamics for Medical Device Design and Evaluation: Are We There Yet? , 2012 .

[65]  K Affeld,et al.  Mathematical Model of Platelet Deposition under Flow Conditions , 2004, The International journal of artificial organs.

[66]  Klaus Affeld,et al.  Numerical estimation of blood damage in artificial organs. , 2004, Artificial organs.

[67]  Søren Nymand Lophaven,et al.  DACE - A Matlab Kriging Toolbox, Version 2.0 , 2002 .

[68]  Marek Behr,et al.  Hemolysis estimation in a centrifugal blood pump using a tensor-based measure. , 2006, Artificial organs.

[69]  Eugene H Blackstone,et al.  Prospective trial of a pediatric ventricular assist device. , 2012, The New England journal of medicine.

[70]  Edward N. Tinoco,et al.  Thirty Years of Development and Application of CFD at Boeing Commercial Airplanes, Seattle , 2003 .

[71]  C Bludszuweit,et al.  Three-dimensional numerical prediction of stress loading of blood particles in a centrifugal pump. , 1995, Artificial organs.

[72]  M. Ertan Taskin,et al.  Study of flow-induced hemolysis using novel Couette-type blood-shearing devices. , 2011, Artificial organs.

[73]  J. Dennis,et al.  Trailing-edge noise reduction using derivative-free optimization and large-eddy simulation , 2007, Journal of Fluid Mechanics.

[74]  Giancarlo Pennati,et al.  Use of mathematic modeling to compare and predict hemodynamic effects of the modified Blalock-Taussig and right ventricle-pulmonary artery shunts for hypoplastic left heart syndrome. , 2008, The Journal of thoracic and cardiovascular surgery.

[75]  Timothy M. Mauery,et al.  COMPARISON OF RESPONSE SURFACE AND KRIGING MODELS FOR MULTIDISCIPLINARY DESIGN OPTIMIZATION , 1998 .

[76]  G. Arwatz,et al.  A viscoelastic model of shear-induced hemolysis in laminar flow. , 2013, Biorheology.

[77]  Charles Audet,et al.  A Pattern Search Filter Method for Nonlinear Programming without Derivatives , 2001, SIAM J. Optim..

[78]  J. Oden,et al.  Finite Element Methods for Flow Problems , 2003 .

[79]  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.

[80]  Pier Luca Maffettone,et al.  Equation of change for ellipsoidal drops in viscous flow , 1998 .

[81]  Clement Kleinstreuer,et al.  Particle-hemodynamics modeling of the distal end-to-side femoral bypass: effects of graft caliber and graft-end cut. , 2003, Medical engineering & physics.

[82]  Charles Audet,et al.  Mesh Adaptive Direct Search Algorithms for Constrained Optimization , 2006, SIAM J. Optim..

[83]  Leif Kobbelt,et al.  An intuitive framework for real-time freeform modeling , 2004, SIGGRAPH 2004.

[84]  Katharine H Fraser,et al.  Evaluation of Eulerian and Lagrangian Models for Hemolysis Estimation , 2012, ASAIO journal.

[85]  Brandon W. Coats,et al.  Cavopulmonary assist for the univentricular Fontan circulation: von Kármán viscous impeller pump. , 2010, The Journal of thoracic and cardiovascular surgery.

[86]  Umberto Morbiducci,et al.  The power-law mathematical model for blood damage prediction: analytical developments and physical inconsistencies. , 2004, Artificial organs.

[87]  Jun Chen,et al.  Performance evaluation of a pediatric viscous impeller pump for Fontan cavopulmonary assist. , 2013, The Journal of thoracic and cardiovascular surgery.

[88]  Shmuel Einav,et al.  Device Thrombogenicity Emulation: A Novel Method for Optimizing Mechanical Circulatory Support Device Thromboresistance , 2012, PloS one.

[89]  Marek Behr,et al.  A tensor-based measure for estimating blood damage. , 2004, Artificial organs.

[90]  Christian H. Bischof,et al.  Interactive Blood Damage Analysis for Ventricular Assist Devices , 2008, IEEE Transactions on Visualization and Computer Graphics.

[91]  G Rosenberg,et al.  Finite element analysis of stresses developed in the blood sac of a left ventricular assist device. , 2009, Medical engineering & physics.

[92]  Nader Moazami,et al.  Extended mechanical circulatory support with a continuous-flow rotary left ventricular assist device. , 2009, Journal of the American College of Cardiology.

[93]  A. Marsden,et al.  The impact of uncertainty on shape optimization of idealized bypass graft models in unsteady flow , 2010 .

[94]  Charles Audet Convergence Results for Generalized Pattern Search Algorithms are Tight , 2004 .

[95]  Yuri Bazilevs,et al.  Finite element simulation of wind turbine aerodynamics: validation study using NREL Phase VI experiment , 2014 .

[96]  Gianluigi Rozza,et al.  On optimization, control and shape design of an arterial bypass , 2005 .

[97]  Thomas J. R. Hughes,et al.  Isogeometric Analysis: Toward Integration of CAD and FEA , 2009 .

[98]  T. Timek,et al.  Pneumatic paracorporeal ventricular assist device in infants and children: initial Stanford experience. , 2007, The Journal of heart and lung transplantation : the official publication of the International Society for Heart Transplantation.

[99]  K. Rajagopal,et al.  A Model for the Formation and Lysis of Blood Clots , 2006, Pathophysiology of Haemostasis and Thrombosis.

[100]  J F Antaki,et al.  Computational flow optimization of rotary blood pump components. , 1995, Artificial organs.

[101]  Krishnan Mahesh,et al.  Predicting Unsteady Loads in Marine Propulsor Crashback Using Large Eddy Simulation , 2012 .

[102]  Thomas J. R. Hughes,et al.  A large deformation, rotation-free, isogeometric shell , 2011 .

[103]  Bartley P Griffith,et al.  Computational and experimental evaluation of the fluid dynamics and hemocompatibility of the CentriMag blood pump. , 2006, Artificial organs.

[104]  Steven Deutsch,et al.  A fluid dynamics study in a 50 cc pulsatile ventricular assist device: influence of heart rate variability. , 2011, Journal of biomechanical engineering.

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

[106]  James F. Antaki,et al.  Simulation of platelet deposition in disturbed flow , 2002, Proceedings of the Second Joint 24th Annual Conference and the Annual Fall Meeting of the Biomedical Engineering Society] [Engineering in Medicine and Biology.

[107]  Alison L. Marsden,et al.  A modular numerical method for implicit 0D/3D coupling in cardiovascular finite element simulations , 2013, J. Comput. Phys..

[108]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.

[109]  Boyce E. Griffith,et al.  Simulating the fluid dynamics of natural and prosthetic heart valves using the immersed boundary method , 2009 .

[110]  Franck Nicoud,et al.  Level set methods to build moving meshes for patient specific blood flow simulations , 2005 .

[111]  L. Formaggia,et al.  Computational models to predict stenosis growth in carotid arteries: which is the role of boundary conditions? , 2009, Computer methods in biomechanics and biomedical engineering.

[112]  Forrester T. Johnson,et al.  THIRTY YEARS OF DEVELOPMENT AND APPLICATION OF CFD AT BOEING COMMERCIAL AIRPLANES, SEATTLE , 2005 .

[113]  Jerrold E. Marsden,et al.  Study of blood flow impact on growth of thrombi using a multiscale model , 2009 .

[114]  A. Huerta,et al.  Finite Element Methods for Flow Problems , 2003 .

[115]  Zhiliang Xu,et al.  Multiscale models of thrombogenesis , 2012, Wiley interdisciplinary reviews. Systems biology and medicine.

[116]  A. Lorts,et al.  Pediatric Mechanical Circulatory Support , 2013, The Korean journal of thoracic and cardiovascular surgery.

[117]  Danny Bluestein,et al.  High-Shear Stress Sensitizes Platelets to Subsequent Low-Shear Conditions , 2010, Annals of Biomedical Engineering.

[118]  Shawn C Shadden,et al.  Optimization of a Y-graft design for improved hepatic flow distribution in the fontan circulation. , 2013, Journal of biomechanical engineering.

[119]  Steven Deutsch,et al.  Flow Visualization of a Pediatric Ventricular Assist Device During Stroke Volume Reductions Related to Weaning , 2011, Annals of Biomedical Engineering.

[120]  Meng Wang,et al.  Optimal Aeroacoustic Shape Design Using the Surrogate Management Framework , 2003 .

[121]  Steven Deutsch,et al.  Flow Visualization of Three-Dimensionality Inside the 12 cc Penn State Pulsatile Pediatric Ventricular Assist Device , 2010, Annals of Biomedical Engineering.

[122]  A. Redaelli,et al.  Platelet damage accumulation: In vitro and mathematical models , 2007, 2007 IEEE 33rd Annual Northeast Bioengineering Conference.

[123]  Zhiliang Xu,et al.  A multiscale model of venous thrombus formation with surface-mediated control of blood coagulation cascade. , 2010, Biophysical journal.

[124]  Thomas J. R. Hughes,et al.  Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device , 2009 .

[125]  André Garon,et al.  Fast three-dimensional numerical hemolysis approximation. , 2004, Artificial organs.

[126]  André Garon,et al.  Asymptotically consistent numerical approximation of hemolysis. , 2006, Journal of biomechanical engineering.

[127]  Charles Audet,et al.  A method for stochastic constrained optimization using derivative-free surrogate pattern search and collocation , 2010, J. Comput. Phys..

[128]  Duo Xu,et al.  Experimental characterization of powered Fontan hemodynamics in an idealized total cavopulmonary connection model , 2013 .

[129]  Michael Schäfer,et al.  A numerical approach for shape optimization of fluid flow domains , 2005 .

[130]  Alison L. Marsden,et al.  A computational framework for derivative-free optimization of cardiovascular geometries , 2008 .

[131]  K. B. Chandran,et al.  Towards Non-thrombogenic Performance of Blood Recirculating Devices , 2010, Annals of Biomedical Engineering.

[132]  D. Levy,et al.  Survival After the Onset of Congestive Heart Failure in Framingham Heart Study Subjects , 1993, Circulation.

[133]  D. Mozaffarian,et al.  Heart disease and stroke statistics--2010 update: a report from the American Heart Association. , 2010, Circulation.

[134]  Robert L Kormos,et al.  The Fourth INTERMACS Annual Report: 4,000 implants and counting. , 2012, The Journal of heart and lung transplantation : the official publication of the International Society for Heart Transplantation.

[135]  Xinwei Song,et al.  Computational fluid dynamics prediction of blood damage in a centrifugal pump. , 2003, Artificial organs.

[136]  L. Miller,et al.  Left ventricular assist devices are underutilized. , 2011, Circulation.

[137]  Andres Ceballos,et al.  Computational fluid dynamics analysis of surgical adjustment of left ventricular assist device implantation to minimise stroke risk , 2013, Computer methods in biomechanics and biomedical engineering.

[138]  J F Antaki,et al.  Fluid dynamic characterization of operating conditions for continuous flow blood pumps. , 1999, ASAIO journal.

[139]  N. Filipovic,et al.  Modelling thrombosis using dissipative particle dynamics method , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[140]  Harvey S Borovetz,et al.  The national heart, lung, and blood institute pediatric circulatory support program: a summary of the 5-year experience. , 2011, Circulation.

[141]  T. Hughes,et al.  Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows , 2007 .

[142]  Yuri Bazilevs,et al.  The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches , 2010 .

[143]  K Affeld,et al.  Fluid mechanics of the stagnation point flow chamber and its platelet deposition. , 1995, Artificial organs.

[144]  James F. Antaki,et al.  Computational Simulation of Platelet Deposition and Activation: II. Results for Poiseuille Flow over Collagen , 1999, Annals of Biomedical Engineering.

[145]  L. J. Wurzinger,et al.  Mechanical bloodtrauma. An overview , 1986 .

[146]  Katharine H Fraser,et al.  The use of computational fluid dynamics in the development of ventricular assist devices. , 2011, Medical engineering & physics.