Boyce Griffith Boyce E. Griffith
Assistant Professor of Medicine and Mathematics
New York University

Faculty, Leon H. Charney Division of Cardiology, Department of Medicine, New York University School of Medicine
Associated Faculty, Department of Mathematics, Courant Institute of Mathematical Sciences, New York University
Affiliated Faculty, Sackler Institute of Graduate Biomedical Sciences, New York University School of Medicine
Affiliated Faculty, Center for Health Informatics and Bioinformatics, New York University School of Medicine

email: boyce.griffith@nyumc.org or griffith@cims.nyu.edu
phone: 212.263.4131 (office), 212.263.4129 (fax)
web: http://www.cims.nyu.edu/~griffith

Software

IBAMR: IBAMR is a distributed-memory parallel implementation of the immersed boundary (IB) method with support for Cartesian grid adaptive mesh refinement (AMR). Support for distributed-memory parallelism is via MPI, the Message Passing Interface. Support for spatial adaptivity is via SAMRAI, the Structured Adaptive Mesh Refinement Application Infrastructure, which is developed at the Center for Applied Scientific Computing at Lawrence Livermore National Laboratory.

This implementation of the IB method also makes extensive use of functionality provided by several high-quality third-party software libraries, including:

IBAMR outputs visualization files that can be read by the VisIt Visualization Tool. Work is also underway to implement support for finite element mechanics models in IBAMR via the libMesh finite element library.

IBAMR source code is hosted by Google Code at http://ibamr.googlecode.com.

Multi-beat simulations of the fluid dynamics of the aortic heart valve with physiological driving and loading conditions using the immersed boundary method.

valve testervalve mounted in valve tester

A model aortic valve is mounted in a semi-rigid aortic root model with anatomically realistic aortic sinuses. This "valve tester" is immersed in a fluid box. Pressure boundary conditions are imposed at the inlet (bottom) of the vessel using a prescribed left ventricular pressure waveform, and at the outlet (top) of the vessel using a Windkessel model. (See schematic diagram below.)

schematic diagram of the valve tester

Schematic diagram showing how boundary conditions are imposed on the model vessel. At the upstream boundary, a time-dependent left-ventricular pressure waveform is prescribed. At the downstream boundary, the three-dimensional fluid-structure interaction model is coupled to a three-element Windkessel model fit to human data. Notice that the flow rate is not prescribed in this model, but rather emerges during the computation.

side view of the model aortic valve and vessel top and side views of the model aortic valve

The opening and closing dynamics of the model aortic valve. The lower inset shows the prescribed driving pressure (blue curve) and computed loading pressure (green curve). The upper inset shows the computed flow rate through the model valve (blue curve). Net flow through the model valve is approximately 65 ml per cardiac cycle, which is within the physiological range. Notice that the flow rate is not specified in the model; rather, it emerges during the course of the fluid-structure interaction simulation. (Click on the above images to view linked QuickTime movies.)

side view of the model aortic valve and the axial (streamwise) fluid velocity

The opening and closing dynamics of the model aortic valve along with the axial (streamwise) fluid velocity. The fluid velocity is shown on a plane that bisects the model vessel and one of the model valve leaflets. Forward flow is indicated in red, reverse flow is indicated in blue. Notice that, except for the first beat, the model valve permits essentially no regurgitation during closure. (Click on the above image to view linked QuickTime movie.)

For further details, see: B.E. Griffith. Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions. Int J Numer Meth Biomed Eng, 28:317-345, 2012. (DOI, PDF)

Simulations of a prosthetic mitral heart valve using the immersed boundary method.

prosthetic mitral valveimmersed boundary model of prosthetic mitral valve

A chorded prosthetic mitral valve (left panel) and the corresponding immersed boundary model (right panel).

the mitral valve tester

The model mitral valve is mounted in a rigid tube that is immersed in a fluid box. Time-dependent velocity boundary conditions are prescribed at the upstream boundary (located at the left of the figure) and zero-pressure boundary conditions are prescribed at the downstream boundary (located at the right of the figure).

side view of mitral valve top view of mitral valve

The opening and closing dynamics of the model prosthetic mitral valve viewed from the side (left panel) and top (right panel). (Click on the above images to view linked QuickTime movies.)

mitral valve streamlines mitral valve streamlines mitral valve streamlines

Streamlines during the opening phase of the model mitral valve.

For further details, see: B.E. Griffith, X. Luo, D.M. McQueen, and C.S. Peskin. Simulating the fluid dynamics of natural and prosthetic heart valves using the immersed boundary method. Int J Appl Mech, 1:137-177, 2009. (DOI, PDF)

Simulations of the electrical function of the heart by an immersed boundary approach to the bidomain equations.

transmembrane potential difference transmembrane potential difference and extracellular potential transmembrane potential difference on a two-dimensional slice transmembrane potential difference and extracellular potential on a two-dimensional slice

Click on the above images to view the corresponding animated GIFs.

Simulations of cardiac fluid mechanics by an adaptive version of the immersed boundary method.

fiber structure of the heartblood flow within the heartblood flow through heart valvespressure within the heart

Click on the above images to view the corresponding animated GIFs. Additional animations are available here, and an overview of the three-dimensional fiber structure of the heart and great vessels used in this work is available here.

Publications, talks, and other conference contributions
Curriculum Vitae (PDF)
Research Interests
Mathematical and computational methods in medicine and biology; computer simulation in physiology, especially cardiovascular mechanics and fluid-structure interaction, cardiac electrophysiology, and cardiac electro-mechanical coupling; adaptive numerical methods; high-performance computing

Publications

  1. H.M. Wang, X.Y. Luo, H. Gao, R.W. Ogden, B.E. Griffith, C. Berry, and T.J. Wang. A modified Holzapfel-Ogden law for a residually stressed finite strain model of the human left ventricle in diastole. Biomech Model Mechanobiol, to appear.
  2. A.P.S. Bhalla, R. Bale, B.E. Griffith, and N.A. Patankar. A unified mathematical framework and an adaptive numerical method for fluid-structure interaction with rigid, deforming, and elastic bodies. J Comput Phys, 250:446-476, 2013. (DOI)
  3. A.P.S. Bhalla, B.E. Griffith, and N.A. Patankar. A forced damped oscillation framework for undulatory swimming provides new insights into how propulsion arises in active and passive swimming. PLoS Comput Biol, 9:e100309 (16 pages), 2013. (DOI)
  4. S. Delong, B.E. Griffith, E. Vanden-Eijnden, and A. Donev. Temporal integrators for fluctuating hydrodynamics. Phys Rev E, 87:033302 (22 pages), 2013. (DOI, PDF)
  5. X.S. Ma, H. Gao, B.E. Griffith, C. Berry, and X.Y. Luo. Image-based fluid-structure interaction model of the human mitral valve. Comput Fluid, 71:417-425, 2013. (DOI, PDF)
  6. H.M. Wang, H. Gao, X.Y. Luo, C. Berry, B.E. Griffith, R.W. Ogden, and T.J. Wang. Structure-based finite strain modelling of the human left ventricle in diastole. Int J Numer Meth Biomed Eng, 29:83-103, 2013. (DOI, PDF)
  7. F. Balboa Usabiaga, J.B. Bell, R. Delgado-Buscalioni, A. Donev, T. Fai, B.E. Griffith, and C.S. Peskin. Staggered schemes for fluctuating hydrodynamics. Multiscale Model Sim, 10:1369-1408, 2012. (DOI, PDF)
  8. B.E. Griffith and S. Lim. Simulating an elastic ring with bend and twist by an adaptive generalized immersed boundary method. Commun Comput Phys, 12:433-461, 2012. (DOI, PDF)
  9. B.E. Griffith. On the volume conservation of the immersed boundary method. Commun Comput Phys, 12:401-432, 2012. (DOI, PDF)
  10. X.Y. Luo, B.E. Griffith, X.S. Ma, M. Yin, T.J. Wang, C.L. Liang, P.N. Watton, and G.M. Bernacca. Effect of bending rigidity in a dynamic model of a polyurethane prosthetic mitral valve. Biomechan Model Mechanobiol, 11:815-827, 2012. (DOI, PDF)
  11. B.E. Griffith. Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions. Int J Numer Meth Biomed Eng, 28:317-345, 2012. (DOI, PDF; the published version of this paper includes significant typographical errors that were introduced by the publisher following the proofing process; these errors do not appear in the linked PDF document)
    Erratum: B.E. Griffith. Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions. Int J Numer Meth Biomed Eng, 29:698-700, 2013. (DOI)
  12. P.E. Hand and B.E. Griffith. Empirical study of an adaptive multiscale model for simulating cardiac conduction. Bull Math Biol, 73:3071-3089, 2011. (DOI, PDF)
  13. P.E. Hand and B.E. Griffith. Adaptive multiscale model for simulating cardiac conduction. Proc Natl Acad Sci U S A, 107:14603-14608, 2010. (DOI, PDF; Supporting Information: HTTP, PDF)
  14. P. Lee, B.E. Griffith, and C.S. Peskin. The immersed boundary method for advection-electrodiffusion with implicit timestepping and local mesh refinement. J Comput Phys, 229:5208-5227, 2010. (DOI, PDF)
  15. B.E. Griffith. An accurate and efficient method for the incompressible Navier-Stokes equations using the projection method as a preconditioner. J Comput Phys, 228:7565-7595, 2009. (DOI, PDF)
  16. P.E. Hand, B.E. Griffith, and C.S. Peskin. Deriving macroscopic myocardial conductivities by homogenization of microscopic models. Bull Math Biol, 71:1707-1726, 2009. (DOI, PDF)
  17. B.E. Griffith, X. Luo, D.M. McQueen, and C.S. Peskin. Simulating the fluid dynamics of natural and prosthetic heart valves using the immersed boundary method. Int J Appl Mech, 1:137-177, 2009. (DOI, PDF)
  18. B.E. Griffith, R.D. Hornung, D.M. McQueen, and C.S. Peskin. An adaptive, formally second order accurate version of the immersed boundary method. J Comput Phys, 223:10-49, 2007. (DOI, PDF)
  19. B.E. Griffith and C.S. Peskin. On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems. J Comput Phys, 208:75-105, 2005. (DOI, PDF)
  20. S.J. Cox and B.E. Griffith. Recovering quasi-active properties of dendritic neurons from dual potential recordings. J Comput Neurosci, 11:95-110, 2001. (DOI, PDF)
  21. L.J. Gray and B.E. Griffith. A faster Galerkin boundary integral algorithm. Comm Numer Meth Eng, 14:1109-1117, 1998. (DOI, PDF)

Submitted for publication (in alphabetical order by first author)

  1. F. Balboa Usabiaga, R. Delgado-Buscalioni, B.E. Griffith, and A. Donev. Inertial Coupling Method for particles in an incompressible fluctuating fluid. (PDF)
  2. A.P.S. Bhalla, R. Bale, B.E. Griffith, and N.A. Patankar. Fully resolved immersed electrohydrodynamics for particle motion, electrolocation, and self- propulsion. (PDF)
  3. A.P.S. Bhalla, B.E. Griffith, N.A. Patankar, and A. Donev. An immersed boundary method for reaction-diffusion problems.
  4. D. Devendran and B.E. Griffith. Comparison of two approaches to using finite element methods for structural mechanics with the immersed boundary method.
  5. T.G. Fai, B.E. Griffith, Y. Mori, and C.S. Peskin. Immersed boundary method for variable viscosity and variable density problems using fast linear solvers. I: Numerical method and results.
  6. T.G. Fai, B.E. Griffith, Y. Mori, and C.S. Peskin. Immersed boundary method for variable viscosity and variable density problems using fast linear solvers. II: Theory.
  7. H. Gao, B.E. Griffith, D. Carrick, C. Berry, and X.Y. Luo. Imaging-derived immersed boundary model of the left ventricle from diastole to systole.
  8. B.E. Griffith and X. Luo. Hybrid finite difference/finite element version of the immersed boundary method. (PDF)
  9. B.E. Griffith and C.S. Peskin. Electrophysiology.
  10. R.D. Guy, B. Phillip, and B.E. Griffith. Geometric multigrid for an implicit-time immersed boundary method.
  11. T. Skorczewski, B.E. Griffith, and A.L. Fogelson. Multi-bond models for platelet adhesion and cohesion.

Book chapters

  1. D.M. McQueen, T. O'Donnell, B.E. Griffith, and C.S. Peskin. Constructing a Patient-Specific Model Heart from CT Data. In J. Duncan and N. Ayache, editors, Handbook of Biomedical Imaging. Springer-Verlag, to appear.
  2. B.E. Griffith, R.D. Hornung, D.M. McQueen, and C.S. Peskin. Parallel and Adaptive Simulation of Cardiac Fluid Dynamics. In M. Parashar and X. Li, editors, Advanced Computational Infrastructures for Parallel and Distributed Adaptive Applications. John Wiley and Sons, 2009. (PDF)

Conference proceedings

  1. B.E. Griffith, D.M. McQueen, and C.S. Peskin. Simulating cardiovascular fluid dynamics by the immersed boundary method. 47th AIAA Aerospace Sciences Meeting, 5-8 Jan 2009, Orlando, Florida, Paper Number AIAA-2009-158, 2009. (PDF)

Technical reports

  1. S.J. Cox and B.E. Griffith. A fast, fully implicit backward Euler solver for dendritic neurons. Rice University Department of Computational and Applied Mathematics, Technical Report TR00-32, 2000.

Theses

  1. B.E. Griffith. Simulating the blood-muscle-valve mechanics of the heart by an adaptive and parallel version of the immersed boundary method. Ph.D. Thesis. Courant Institute of Mathematical Sciences, New York University, 2005. (PS, PDF)

Revised 2013.06.17 by griffith@cims.nyu.edu.