Modeling Left Ventricular Blood Flow Using Smoothed Particle Hydrodynamics

This study aims to investigate the capability of smoothed particle hydrodynamics (SPH), a fully Lagrangian mesh-free method, to simulate the bulk blood flow dynamics in two realistic left ventricular (LV) models. Three dimensional geometries and motion of the LV, proximal left atrium and aortic root are extracted from cardiac magnetic resonance imaging and multi-slice computed tomography imaging data. SPH simulation results are analyzed and compared with those obtained using a traditional finite volume-based numerical method, and to in vivo phase contrast magnetic resonance imaging and echocardiography data, in terms of the large-scale blood flow phenomena usually clinically measured. A quantitative comparison of the velocity fields and global flow parameters between the in silico models and the in vivo data shows a reasonable agreement, given the inherent uncertainties and limitations in the modeling and imaging techniques. The results indicate the capability of SPH as a promising tool for predicting clinically relevant large-scale LV flow information.

[1]  Salvatore Marrone,et al.  An accurate SPH modeling of viscous flows around bodies at low and moderate Reynolds numbers , 2013, J. Comput. Phys..

[2]  David N Firmin,et al.  Flow measurement by magnetic resonance: a unique asset worth optimising. , 2007, Journal of cardiovascular magnetic resonance : official journal of the Society for Cardiovascular Magnetic Resonance.

[3]  A. Colagrossi,et al.  Numerical simulation of interfacial flows by smoothed particle hydrodynamics , 2003 .

[4]  Siamak N. Doost,et al.  The numerical analysis of non-Newtonian blood flow in human patient-specific left ventricle , 2016, Comput. Methods Programs Biomed..

[5]  Sophie Papst,et al.  Computational Methods For Fluid Dynamics , 2016 .

[6]  G. Pedrizzetti,et al.  Combined experimental and numerical analysis of the flow structure into the left ventricle. , 2007, Journal of biomechanics.

[7]  J. Morris,et al.  Modeling Low Reynolds Number Incompressible Flows Using SPH , 1997 .

[8]  T. Schaeffter,et al.  Four‐dimensional (4D) flow of the whole heart and great vessels using real‐time respiratory self‐gating , 2009, Magnetic resonance in medicine.

[9]  Jung Hee Seo,et al.  Computational modeling and analysis of intracardiac flows in simple models of the left ventricle , 2012 .

[10]  D. Comaniciu,et al.  Patient-specific modelling of whole heart anatomy, dynamics and haemodynamics from four-dimensional cardiac CT images , 2011, Interface Focus.

[11]  Nikolaus A. Adams,et al.  A multi-phase SPH method for macroscopic and mesoscopic flows , 2006, J. Comput. Phys..

[12]  V L Morgan,et al.  Normal human right and left ventricular mass, systolic function, and gender differences by cine magnetic resonance imaging. , 1999, Journal of cardiovascular magnetic resonance : official journal of the Society for Cardiovascular Magnetic Resonance.

[13]  Guirong Liu.  Mesh Free Methods: Moving Beyond the Finite Element Method , 2002 .

[14]  Fotis Sotiropoulos,et al.  On the three-dimensional vortical structure of early diastolic flow in a patient-specific left ventricle. , 2012, European journal of mechanics. B, Fluids.

[15]  Guang-Zhong Yang,et al.  Progress Towards Patient-Specific Computational Flow Modeling of the Left Heart via Combination of Magnetic Resonance Imaging with Computational Fluid Dynamics , 2004, Annals of Biomedical Engineering.

[16]  Wei Sun,et al.  Simulations of transcatheter aortic valve implantation: implications for aortic root rupture , 2015, Biomechanics and modeling in mechanobiology.

[17]  Franck Nicoud,et al.  Image-based large-eddy simulation in a realistic left heart , 2014 .

[18]  L. Zhong,et al.  Three‐dimensional CFD/MRI modeling reveals that ventricular surgical restoration improves ventricular function by modifying intraventricular blood flow , 2014, International journal for numerical methods in biomedical engineering.

[19]  Ottavio Alfieri,et al.  The vortex—an early predictor of cardiovascular outcome? , 2014, Nature Reviews Cardiology.

[20]  Fotis Sotiropoulos,et al.  Fluid-structure interaction of an aortic heart valve prosthesis driven by an animated anatomic left ventricle , 2013, J. Comput. Phys..

[21]  Wing Kam Liu,et al.  Lagrangian-Eulerian finite element formulation for incompressible viscous flows☆ , 1981 .

[22]  Matteo Antuono,et al.  Theoretical Analysis of the No-Slip Boundary Condition Enforcement in SPH Methods , 2011 .

[23]  T. Z. Teisseyre,et al.  Comparison of particle image velocimetry and phase contrast MRI in a patient-specific extracardiac total cavopulmonary connection. , 2008, Journal of biomechanical engineering.

[24]  Raad H. Mohiaddin,et al.  Magnetic resonance velocity mapping of normal human transmitral velocity profiles , 2005, Heart and Vessels.

[25]  S. Adami.  Modeling and Simulation of Multiphase Phenomena with Smoothed Particle Hydrodynamics , 2014 .

[26]  J. Hennig,et al.  Time‐resolved 3D MR velocity mapping at 3T: Improved navigator‐gated assessment of vascular anatomy and blood flow , 2007, Journal of magnetic resonance imaging : JMRI.

[27]  Jung Hee Seo,et al.  Effect of diastolic flow patterns on the function of the left ventricle , 2013 .

[28]  P. Cleary,et al.  AN INVESTIGATION OF PULSATILE BLOOD FLOW IN A BIFURCATION ARTERY USING A GRID-FREE METHOD , 2006 .

[29]  Guirong Liu.  Meshfree Methods: Moving Beyond the Finite Element Method, Second Edition , 2009 .

[30]  Matthias Müller,et al.  Interactive blood simulation for virtual surgery based on smoothed particle hydrodynamics. , 2004, Technology and health care : official journal of the European Society for Engineering and Medicine.

[31]  K. Young,et al.  AMERICAN SOCIETY OF MECHANICAL ENGINEERS. , 1880, Science.

[32]  H. Howie Huang,et al.  Computational modeling of cardiac hemodynamics: Current status and future outlook , 2016, J. Comput. Phys..

[33]  Wei Sun,et al.  Dimensional Analysis of Aortic Root Geometry During Diastole Using 3D Models Reconstructed from Clinical 64-Slice Computed Tomography Images , 2011 .

[34]  I. Demirdzic,et al.  Space conservation law in finite volume calculations of fluid flow , 1988 .

[35]  Catherine M. Otto,et al.  Textbook of Clinical Echocardiography , 2004 .

[36]  Scott Kulp,et al.  Practical patient-specific cardiac blood flow simulations using SPH , 2013, 2013 IEEE 10th International Symposium on Biomedical Imaging.

[37]  J. Monaghan,et al.  A turbulence model for Smoothed Particle Hydrodynamics , 2009, 0911.2523.

[38]  B. Rogers,et al.  Smoothed particle hydrodynamics method applied to pulsatile flow inside a rigid two‐dimensional model of left heart cavity , 2012, International journal for numerical methods in biomedical engineering.

[39]  Ibrahim Hassan,et al.  Modeling unsteady flow characteristics using smoothed particle hydrodynamics , 2013 .

[40]  A. D. Gosman,et al.  Computational Flow Modeling of the Left Ventricle Based on In Vivo MRI Data: Initial Experience , 2001, Annals of Biomedical Engineering.

[41]  Gil Marom,et al.  Numerical Methods for Fluid–Structure Interaction Models of Aortic Valves , 2014, Archives of Computational Methods in Engineering.

[42]  B. Carroll,et al.  Flow quantification using fast cine phase-contrast MR imaging, conventional cine phase-contrast MR imaging, and Doppler sonography: in vitro and in vivo validation. , 1997, AJR. American journal of roentgenology.

[43]  Nasser Fatouraee,et al.  The impact of valve simplifications on left ventricular hemodynamics in a three dimensional simulation based on in vivo MRI data. , 2016, Journal of biomechanics.

[44]  Bradley D. Allen,et al.  4D flow imaging with MRI. , 2014, Cardiovascular diagnosis and therapy.

[45]  Guirong Liu,et al.  Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments , 2010 .

[46]  Alejandro F. Frangi,et al.  Numerical simulation of blood flow in the left ventricle and aortic sinus using magnetic resonance imaging and computational fluid dynamics , 2014, Computer methods in biomechanics and biomedical engineering.

[47]  Charles H. Bloodworth,et al.  Fluid–structure interaction and structural analyses using a comprehensive mitral valve model with 3D chordal structure , 2017, International journal for numerical methods in biomedical engineering.

[48]  C. Peskin.  Flow patterns around heart valves: A numerical method , 1972 .

[49]  Jung Hee Seo,et al.  Multiphysics computational models for cardiac flow and virtual cardiography , 2013, International journal for numerical methods in biomedical engineering.

[50]  Jung Hee Seo,et al.  Effect of trabeculae and papillary muscles on the hemodynamics of the left ventricle , 2016 .

[51]  Richard Frayne,et al.  Accuracy of MR phase contrast velocity measurements for unsteady flow , 1995, Journal of magnetic resonance imaging : JMRI.

[52]  J. Christiansen,et al.  Assessment of valvular heart disease by cardiovascular magnetic resonance imaging: a review. , 2011, Heart, lung & circulation.

[53]  Wei Sun,et al.  Fluid–Structure Interaction Study of Transcatheter Aortic Valve Dynamics Using Smoothed Particle Hydrodynamics , 2016, Cardiovascular engineering and technology.

[54]  Damien Violeau,et al.  Numerical modelling of complex turbulent free‐surface flows with the SPH method: an overview , 2007 .

[55]  Patrick J. Fox,et al.  A pore‐scale numerical model for flow through porous media , 1999 .

[56]  J. Monaghan.  Smoothed particle hydrodynamics , 2005 .

[57]  Tino Ebbers,et al.  Patient-Specific Simulation of Cardiac Blood Flow From High-Resolution Computed Tomography. , 2016, Journal of biomechanical engineering.

[58]  A P Yoganathan,et al.  Left ventricular blood flow patterns in normal subjects: a quantitative analysis by three-dimensional magnetic resonance velocity mapping. , 1995, Journal of the American College of Cardiology.

[59]  Yuefan Deng,et al.  Particle-Based Methods for Multiscale Modeling of Blood Flow in the Circulation and in Devices: Challenges and Future Directions , 2010, Annals of Biomedical Engineering.