# Publications

### Submitted for publication (in alphabetical order by author)

- A. P. S. Bhalla, M. G. Knepley, M. F. Adams, R. D. Guy, and B. E. Griffith. Scalable smoothing strategies for a geometric multigrid method for the immersed boundary equations. Submitted (arXiv)
- L. Feng, N. Qi, H. Gao, W. Sun, M. Vazquez, B. E. Griffith, and X. Y. Luo. On the chordae structure and dynamic behaviour of the mitral valve. Submitted
- S. Jones, A. P. S. Bhalla, G. Katsikis, B. E. Griffith, and D. Klotsa. Transition in motility mechanism due to inertia in a model self-propelled two-sphere swimmer. Submitted

### Refereed journal articles

- S. G. Smith, B. E. Griffith, and D. A. Zaharoff. Analyzing the effects of instillation volume on intravesical delivery using biphasic solute transport in a deformable geometry.
*Math Med Biol*, accepted for publication - B. E. Griffith and X. Y. Luo. Hybrid finite difference/finite element version of the immersed boundary method.
*Int J Numer Meth Biomed Eng*, 33(11):e2888 (31 pages), 2017 (DOI, arXiv) - W. Kou, B. E. Griffith, J. E. Pandolfino, P. J. Kahrilas, and N. A. Patankar. A continuum mechanics-based musculo-mechanical model for esophageal transport.
*J Comput Phys*, 348:433–459, 2017 (DOI, arXiv) - Y. Bao, A. Donev, B. E. Griffith, D. M. McQueen, and C. S. Peskin. An immersed boundary method with divergence-free velocity interpolation.
*J Comput Phys*, 347:183–206, 2017 (DOI, arXiv) - H. Gao, L. Feng, N. Qi, C. Berry, B. E. Griffith, and X. Y. Luo. A coupled mitral valve-left ventricle model with fluid-structure interaction.
*Med Eng Phys*, 47:128–136, 2017 (DOI, arXiv) - A. Hasan, E. M. Kolahdouz, A. Enquobahrie, T. G. Caranasos, J. P. Vavalle, and B. E. Griffith. Image-based immersed boundary model of the aortic root.
*Med Eng Phys*, 47:72–84, 2017 (DOI, arXiv) - S. Rossi and B. E. Griffith. Incorporating inductances in tissue-scale models of cardiac electrophysiology.
*Chaos*, 27:093926 (18 pages), 2017 (DOI, arXiv) - A. P. Hoover, B. E. Griffith, and L. A. Miller. Quantifying performance in the medusan mechanospace with an actively swimming three-dimensional jellyfish model.
*J Fluid Mech*, 813:1112–1155, 2017 (DOI) - F. Balboa Usabiaga, B. Kallemov, B. Delmotte, A. P. S. Bhalla, B. E. Griffith, and A. Donev. Hydrodynamics of suspensions of passive and active rigid particles: A rigid multiblob approach.
*Comm Appl Math Comput Sci*, 11(2):217–296, 2016 (DOI, arXiv) - S. K. Jones, Y. J. Yun, T. L. Hedrick, B. E. Griffith, and L. A. Miller. Bristles reduce the force required to ‘fling’ wings apart in the smallest insects.
*J Exp Biol*, 219:3759–3772, 2016 (DOI) - E. D. Tytell, M. C. Leftwich, C.-Y. Hsu, B. E. Griffith, A. H. Cohen, A. J. Smits, C. Hamlet, and L. J. Fauci. The role of body stiffness in undulatory swimming: Insights from robotic and computational models.
*Phys Rev Fluids*, 1:073202 (17 pages), 2016 (DOI) - G. Sommer, S. Sherifova, P. J. Oberwalder, O. E. Dapunt, P. A. Ursomanno, A. DeAnda, B. E. Griffith, and G. A. Holzapfel. Mechanical strength of aneurysmatic and dissected human thoracic aortas at different shear loading modes.
*J Biomech*, 49(12):2374–2382, 2016 (DOI) - V. Flamini, A. DeAnda, and B. E. Griffith. Immersed boundary-finite element model of fluid-structure interaction in the aortic root.
*Theor Comput Fluid Dynam*, 30(1):139–164, 2016 (DOI, arXiv) - B. Kallemov, A. P. S. Bhalla, B. E. Griffith, and A. Donev. An immersed boundary method for rigid bodies.
*Comm Appl Math Comput Sci*, 11(1):79–141, 2016 (DOI, arXiv) - S. Land, V. Gurev, S. Arens, C. M. Augustin, L. Baron, R. Blake, C. Bradley, S. Castro, A. Crozier, M. Favino, T. E. Fastl, T. Fritz, H. Gao, A. Gizzi, B. E. Griffith, D. E. Hurtado, R. Krause, X. Y. Luo, M. P. Nash, S. Pezzuto, G. Plank, S. Rossi, D. Ruprecht, G. Seemann, N. P. Smith, J. Sundnes, J. J. Rice, N. Trayanova, D. Wang, Z. J. Wang, and S. A. Niederer. Verification of cardiac mechanics software: Benchmark problems and solutions for testing active and passive material behaviour.
*Proc R Soc A*, 471(2184):20150641 (20 pages), 2015 (DOI) - S. K. Jones, R. Laurenza, T. L. Hedrick, B. E. Griffith, and L. A. Miller. Lift vs. drag based mechanisms for vertical force production in the smallest flying insects.
*J Theor Biol*. 384:105–120, 2015 (DOI) - A. Kheradvar, E. M. Groves, A. Falahatpisheh, M. R. K. Mofrad, S. H. Alavi, R. Tranquillo, L. P. Dasi, C. A. Simmons, K. J. Grande-Allen, C. J. Goergen, F. Baaijens, S. H. Little, S. Canic, and B. Griffith. Emerging trends in heart valve engineering: Part IV. Computational modeling and experimental studies.
*Ann Biomed Eng*. 43(10):2314–2333, 2015 (DOI) - W. Kou, A. P. S. Bhalla, B. E. Griffith, J. E. Pandolfino, P. J. Kahrilas, and N. A. Patankar. A fully resolved active musculo-mechanical model for esophageal transport.
*J Comput Phys*, 298:446–465, 2015 (DOI, arXiv) - R. D. Guy, B. Phillip, and B. E. Griffith. Geometric multigrid for an implicit-time immersed boundary method.
*Adv Comput Math*, 41(3):636–662, 2015 (DOI, arXiv) - A. Kheradvar, E. M. Groves, C. A. Simmons, B. Griffith, S. H. Alavi, R. Tranquillo, L. P. Dasi, A. Falahatpisheh, K. J. Grande-Allen, C. J. Goergen, M. R. K. Mofrad, F. Baaijens, S. Canic, and S. H. Little. Emerging trends in heart valve engineering: Part III. Novel technologies for mitral valve repair and replacement.
*Ann Biomed Eng*, 43(4):858–870, 2015 (DOI) - A. Kheradvar, E. M. Groves, C. J. Goergen, S. H. Alavi, R. Tranquillo, C. A. Simmons, L. P. Dasi, K. J. Grande-Allen, M. R. K. Mofrad, A. Falahatpisheh, B. Griffith, F. Baaijens, S. H. Little, and S. Canic. Emerging trends in heart valve engineering: Part II. Novel and standard technologies for aortic valve replacement.
*Ann Biomed Eng*, 43(4):844–857, 2015 (DOI) - A. Kheradvar, E. M. Groves, L. P. Dasi, S. H. Alavi, R. Tranquillo, K. J. Grande-Allen, C. A. Simmons, B. Griffith, A. Falahatpisheh, C. J. Goergen, M. R. K. Mofrad, F. Baaijens, S. H. Little, and S. Canic. Emerging trends in heart valve engineering: Part I. Solutions for future.
*Ann Biomed Eng*, 43(4):833–843, 2015 (DOI) - S. Delong, Y. Sun, B. E. Griffith, E. Vanden-Eijnden, and A. Donev. Multiscale temporal integrators for fluctuating hydrodynamics.
*Phys Rev E*, 90(6):063312 (23 pages), 2014 (DOI, arXiv) - H. Gao, X. S. Ma, N. Qi, C. Berry, B. E. Griffith, and X. Y. Luo. A finite strain model of the human mitral valve with fluid structure interaction.
*Int J Numer Meth Biomed Eng,*30(12):1597–1613, 2014 (DOI) - H. Gao, H. M. Wang, C. Berry, X. Y. Luo, and B. E. Griffith. Quasi-static image-based immersed boundary-finite element model of left ventricle under diastolic loading.
*Int J Numer Meth Biomed Eng,*30(11):1199–1222, 2014 (DOI) - M. Cai, A. Nonaka, J. B. Bell, B. E. Griffith, and A. Donev. Efficient variable-coefficient finite-volume Stokes solvers.
*Comm Comput Phys,*16(5):1263–1297, 2014 (DOI, arXiv) - H. Gao, D. Carrick, C. Berry, B. E. Griffith, and X. Y. Luo. Dynamic finite-strain modelling of the human left ventricle in health and disease using an immersed boundary-finite element method.
*IMA J Appl Math,*79(5):978–1010, 2014 (DOI) - T. G. Fai, B. E. Griffith, Y. Mori, and C. S. Peskin. Immersed boundary method for variable viscosity and variable density problems using fast constant-coefficient linear solvers II: Theory.
*SIAM J Sci Comput*, 36(3):B589–B621, 2014 (DOI) - S. Delong, F. Balboa Usabiaga, R. Delgado-Buscalioni, B. E. Griffith, and A. Donev. Brownian dynamics without Green’s functions.
*J Chem Phys*, 140(13):134110 (23 pages), 2014 (DOI, arXiv) - F. Balboa Usabiaga, R. Delgado-Buscalioni, B. E. Griffith, and A. Donev. Inertial Coupling Method for particles in an incompressible fluctuating fluid.
*Comput Meth Appl Mech Eng*, 269:139–172, 2014 (DOI, arXiv) - H. M. Wang, X. Y. Luo, H. Gao, R. W. Ogden, B. E. Griffith, and C. Berry. A modified Holzapfel-Ogden law for a residually stressed finite strain model of the human left ventricle in diastole.
*Biomechan Model Mechanobiol*, 13(1):99–113, 2014 (DOI) - A. P. S. Bhalla, R. Bale, B. E. Griffith, and N. A. Patankar. Fully resolved immersed electrohydrodynamics for particle motion, electrolocation, and self-propulsion.
*J Comput Phys*, 256:88–108, 2014 (DOI) - A. P. S. Bhalla, B. E. Griffith, N. A. Patankar, and A. Donev. A minimally-resolved immersed boundary model for reaction-diffusion problems.
*J Chem Phys*, 139(21):214112 (15 pages), 2013 (DOI, arXiv) - B. E. Griffith and C. S. Peskin. Electrophysiology.
*Comm Pure Appl Math*, 66(12):1837–1913, 2013 (DOI) - T. G. Fai, B. E. Griffith, Y. Mori, and C. S. Peskin. Immersed boundary method for variable viscosity and variable density problems using fast constant-coefficient linear solvers I: Numerical method and results.
*SIAM J Sci Comput*, 35(5):B1132–B1161, 2013 (DOI) (Erratum: DOI) - 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) - 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(6):e100309 (16 pages), 2013 (DOI) - S. Delong, B. E. Griffith, E. Vanden-Eijnden, and A. Donev. Temporal integrators for fluctuating hydrodynamics.
*Phys Rev E*, 87(3):033302 (22 pages), 2013 (DOI, arXiv) - 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) - 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(1):83–103, 2013 (DOI) - 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 Simul*, 10(4):1369–1408, 2012 (DOI, arXiv) - B. E. Griffith and S. Lim. Simulating an elastic ring with bend and twist by an adaptive generalized immersed boundary method.
*Comm Comput Phys*, 12(2):433–461, 2012 (DOI) - B. E. Griffith. On the volume conservation of the immersed boundary method.
*Comm Comput Phys*, 12(2):401–432, 2012 (DOI) - 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.
*Biomech Model Mechanobiology*, 11(6):815–827, 2012 (DOI) - B. E. Griffith. Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions.
*Int J Numer Meth Biomed Eng*, 28(3):317–345, 2012 (DOI, arXiv) (Erratum: DOI. 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 arXiv reprint) - P. E. Hand and B. E. Griffith. Empirical study of an adaptive multiscale model for simulating cardiac conduction.
*Bull Math Biol*, 73(12):3071–3089, 2011 (DOI) - P. E. Hand and B. E. Griffith. Adaptive multiscale model for simulating cardiac conduction.
*Proc Natl Acad Sci U S A*, 107(33):14603–14608, 2010 (DOI) - 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(13):5208–5227, 2010 (DOI) - 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(20):7565–7595, 2009 (DOI) - P. E. Hand, B. E. Griffith, and C. S. Peskin. Deriving macroscopic myocardial conductivities by homogenization of microscopic models.
*Bull Math Biol*, 71(7):1707–1726, 2009 (DOI) - B. E. Griffith, X. Y. 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(1):137–177, 2009 (DOI) - 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(1):10–49, 2007 (DOI) - 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(1):75–105, 2005 (DOI) - S. J. Cox and B. E. Griffith. Recovering quasi-active properties of dendritic neurons from dual potential recordings.
*J Comput Neurosci*, 11(2):95–110, 2001 (DOI) - L. J. Gray and B. E. Griffith. A faster Galerkin boundary integral algorithm.
*Comm Numer Meth Eng*, 14(12):1109–1117, 1998 (DOI)

### Refereed book chapters

- D. M. McQueen, T. O’Donnell, B. E. Griffith, and C. S. Peskin. Constructing a Patient-Specific Model Heart from CT Data. In N. Paragios, N. Ayache, and J. Duncan, editors, Handbook of Biomedical Imaging, pages 183–197. Springer-Verlag, New York, NY, USA, 2015 (DOI)
- T. Skorczewski, B. E. Griffith, and A. L. Fogelson. Multi-bond models for platelet adhesion and cohesion. In S. D. Olson and A. T. Layton, editors, Biological Fluid Dynamics: Modeling, Computation, and Applications, Contemporary Mathematics, pages 149–172. American Mathematical Society, Providence, RI, USA, 2014 (DOI)
- 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, pages 105–130. John Wiley and Sons, Hoboken, NJ, USA, 2009 (DOI)

### Refereed conference proceedings and abstracts

- H. Gao, N. Qi, X. S. Ma, B. E. Griffith, C. Berry, and X. Y. Luo. Fluid-structure interaction model of human mitral valve within left ventricle. In H. van Assen, P. Bovendeerd, and T. Delhaas, editors,
*Functional Imaging and Modeling of the Heart: 8th International Conference, FIMH 2015, Maastricht, The Netherlands, June 25–27, 2015*, volume 9126 of*Lecture Notes in Computer Science*, pages 330–337, 2015 (DOI) - A. Ward, S. Maddalo, S. Lavallee, V. Flamini, A. DeAnda, and B. Griffith. Influence of anti-hypertensive medications on aortic peak stress.
*Circulation*, 130:A17405, 2014 - B. E. Griffith, V. Flamini, A. DeAnda, and L. Scotten. Simulating the dynamics of an aortic valve prosthesis in a pulse duplicator: Numerical methods and initial experience.
*J Med Dev*, 7(4):040912 (2 pages), 2013 (DOI) - S. L. Maddalo, A. Ward, V. Flamini, B. Griffith, P. Ursomanno, and A. DeAnda. Antihypertensive strategies in the management of aortic disease.
*J Am Coll Surg*, 217(3):S39, 2013 (DOI) - H. Gao, B. E. Griffith, D. Carrick, C. McComb, C. Berry, and X. Y. Luo. Initial experience with a dynamic imaging-derived immersed boundary model of human left ventricle. In S. Ourselin, D. Rueckert, and N. Smith, editors,
*Functional Imaging and Modeling of the Heart: 7th International Conference, FIMH 2013, London, UK, June 20–22, 2013*, volume 7945 of Lecture Notes in Computer Science, pages 11–18, 2013 (DOI)

### Other conference publications

- V. Flamini, A. DeAnda, and B. E. Griffith. Simulating the effects of intersubject variability in aortic root compliance by the immersed boundary method. In P. Nithiarasu, R. Lohner, and K. M. Liew, editors,
*Proceedings of the Third International Conference on Computational & Mathematical Biomedical Engineering*, 2013 - X. S. Ma, H. Gao, N. Qi, C. Berry, B. E. Griffith, and X. Y. Luo. Image-based immersed boundary/finite element model of the human mitral valve. In P. Nithiarasu, R. Lohner, and K. M. Liew, editors,
*Proceedings of the Third International Conference on Computational & Mathematical Biomedical Engineering*, 2013

### Other non-refereed works

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

### PhD Thesis

- B. E. Griffith.
*Simulating the blood-muscle-valve mechanics of the heart by an adaptive and parallel version of the immersed boundary method*. PhD thesis, Courant Institute of Mathematical Sciences, New York University, 2005