Academic Research
Before I became an entrepreneur in 2012, I spent a wonderful decade living the life of a curious academic. During that time, I delved deep into continuum field theory and numerical algorithms. My focus was on applications in biophysics. If you’re interested, I’ve provided some links on this page that showcase my work, including some of my scientific writing and talks. Feel free to take a look!
Primary investigations
Cardiac mechanics
Modelling the active mechanical response of ventricular myocardium.
Chondrocyte physiology
Better understanding the cell type responsible for the synthesis of cartilage.
Multiphase flow in porous media
A robust, errorcontrolled implementation that’s human readable.
Automated mechanics
Automated finite element methods reduce tedium and errors.
Robust methods for flows
Accurate and efficient modelling of aneurysm growth.
Phase transfer in batteries
Modelling mechanical phenomena associated with ion transport.
Energetics of tumours
Modelling the biochemomechanics of tumour growth.
Tissue growth and development
A continuum theory of multiphase mixtures for modelling biological growth.
Curiosities along the way
NavierStokes formulation
Theoretically equivalent formulations aren’t always equal in practice.
Numerical relativity
Differential geometry and numerical methods for 4D spacetime.
Shape reconstruction
Level sets in shape reconstruction from unorganised data sets.
Journal articles

“The roles of K+ currents in human articular chondrocyte electrophysiology: A computational perspective”
H. Narayanan, M. M. Maleckar, R. B. Clark, J. R. Wilson, W. R. Giles
Under preparation 
“An adaptive finite element method for fluidstructure interaction”
[preprint]
K. Selim, A. Logg, H. Narayanan, M. G. Larson
Submitted 
“In silico estimates of the free energy changes in growing, avascular, tumor spheroids”
[postprint]
[preprint]
H. Narayanan, S. N. Verner, K. L. Mills, R. Kemkemer, K. Garikipati
Journal of Physics: Condensed Matter
Vol. 22(19), 2010 
“The micromechanics of fluidsolid interactions during growth in porous soft biological tissue”
[postprint]
[preprint]
H. Narayanan, E. M. Arruda, K. Grosh, K. Garikipati
Biomechanics and Modeling in Mechanobiology
Vol. 8(3), pp. 167–181, 2009 
“The continuum elastic and atomistic viewpoints on the formation volume and strain energy of a point defect”
[postprint]
[preprint]
K. Garikipati, M. Falk, M. Bouville, B. Puchala, H. Narayanan
Journal of the Mechanics and Physics of Solids
Vol. 54(9), pp. 1929–1951, 2006 
“Biological remodelling: Stationary energy, configurational change, internal variables and dissipation”
[postprint]
[preprint]
K. Garikipati, J. Olberding, H. Narayanan, E. M. Arruda, K. Grosh, S. Calve
Journal of the Mechanics and Physics of Solids
Vol. 54(7), pp. 1493–1515, 2006 
“A continuum treatment of growth in biological tissue: The coupling of mass transport and mechanics”
[postprint]
[preprint]
K. Garikipati, E. M. Arruda, K. Grosh, H. Narayanan, S. Calve
Journal of the Mechanics and Physics of Solids
Vol. 52(7), pp. 1595–1625, 2004
Chapters in books

“A computational framework for nonlinear elasticity”
[postprint]
[preprint]
H. Narayanan
Automated Solution of Differential Equations by the Finite Element Method, A. Logg, KA. Mardal, G. N. Wells (Eds.)
Chap. 27, pp. 527–544, 2012 
“A comparison of some finite element schemes for the incompressible NavierStokes equations”
[postprint]
[preprint]
K. ValenSendstad, A. Logg, KA. Mardal, H. Narayanan, M. Mortensen
Automated Solution of Differential Equations by the Finite Element Method, A. Logg, KA. Mardal, G. N. Wells (Eds.)
Chap. 21, pp. 395–417, 2012 
“Characterization and modeling of growth and remodeling in tendon and soft tissue constructs”
[postprint]
[preprint]
E. M. Arruda, S. Calve, K. Garikipati, K. Grosh, H. Narayanan
Mechanics of Biological Tissue, G. A. Holzapfel, R. W. Ogden (Eds.)
Chap. 5, pp. 63–75, 2006 
“Material forces in the context of biotissue remodelling”
[postprint]
[preprint]
K. Garikipati, H. Narayanan, E. M. Arruda, K. Grosh, S. Calve
Mechanics of Material Forces, P. Steinmann, G. A. Maugin (Eds.)
Chap. 8, pp. 77–84, 2005
Conference proceedings

“Experimental and computational investigation of viscoelasticity of native and engineered ligament and tendon”
[postprint]
[preprint]
J. Ma, H. Narayanan, K. Garikipati, K. Grosh, E. M. Arruda
Cellular, Molecular and Tissue Mechanics
IUTAM Symposium Bookseries
Vol. 16, pp. 3–17, 2010 
“Collaborative computational frameworks and the growth problem”
[postprint]
[preprint]
H. Narayanan, K. Garikipati, A. Logg
The Mathematics of Growth and Remodelling of Soft Biological Tissues
Mathematisches Forschungsinstitut Oberwolfach Reports
Vol. 5(3), pp. 2247–2249, 2008 
“Mathematical modelling of solid tumor growth”
[postprint]
[preprint]
K. Garikipati, H. Narayanan, K. Grosh, E. M. Arruda
The Mathematics of Growth and Remodelling of Soft Biological Tissues
Mathematisches Forschungsinstitut Oberwolfach Reports
Vol. 5(3), pp. 2235–2238, 2008
Other academic writing

“A continuum theory of multiphase mixtures for modelling biological growth”
[postprint]
[preprint]
[source]
H. Narayanan
Doctoral Dissertation, University of Michigan
2007 
“Variational level sets in shape reconstruction from unorganised data sets”
[preprint]
H. Narayanan
Project Report, University of Michigan
2005
Selected talks at conferences

“A continuum model for the active mechanical response of the myocardium”
[slides]
Tenth World Congress on Computational Mechanics
São Paulo, Brazil, July 2012 
“The role of K+ channels in human articular chondrocyte electrophysiology”
[slides]
Cardiac Modelling Seminar at Simula Research Laboratory
Oslo, Norway, July 2011 
“An automated computational framework for hyperelasticity”
[slides]
Fourth European Conference on Computational Mechanics
Paris, France, May 2010 
“A goaloriented errorcontrolled solver for biomedical flows”
[slides]
Fifth M.I.T. Conference on Computational Fluid and Solid Mechanics
Cambridge, MA, June 2009 
“Collaborative computational frameworks and the growth problem”
[slides]
Workshop on the Mathematics of Growth and Remodelling of Soft Biological Tissues
Mathematisches Forschungsinstitut Oberwolfach, Germany, September 2008 
“Reshaping tumour growth”
[slides]
University of Michigan Engineering Graduate Student Symposium
Ann Arbor, MI, November 2007 
“A continuum theory of multiphase mixtures for modelling biological growth”
[slides]
Doctoral Dissertation Defence
Ann Arbor, MI, October 2007 
“The numerical implications of multiphasic mechanics assumptions underlying growth models”
[slides]
Ninth U.S. National Congress on Computational Mechanics
San Fransisco, CA, July 2007 
“Finite element methods in general relativity”
[slides]
University of Michigan Engineering Graduate Student Symposium
Ann Arbor, MI, November 2006 
“Viscoelastic and growth mechanics in engineered and native tendons”
[slides]
43^{rd} Annual Technical Meeting of the Society of Engineering Science
University Park, PA, August 2006 
“The numerical implications of fluid incompressibility in multiphasic modelling of soft tissue growth”
[slides]
Seventh World Congress on Computational Mechanics
Los Angeles, CA, July 2006 
“Tendon growth and healing: The roles of reaction, transport and mechanics”
[slides]
15^{th} U.S. National Congress on Theoretical and Applied Mechanics
Boulder, CO, June 2006 
“Computational modelling of mechanics and transport in growing tissue”
[slides]
Eighth U.S. National Congress on Computational Mechanics
Austin, TX, July 2005 
“Simulations of coupled mechanics and transport in growing soft tissue”
[slides]
Third M.I.T. Conference on Computational Fluid and Solid Mechanics
Cambridge, MA, June 2005 
“Multiscale simulations of the mechanics of transport and growth in soft tissue”
[slides]
41^{st} Annual Technical Meeting of the Society of Engineering Science
Lincoln, NE, October 2004 
“Material forces in the context of biological tissue remodelling”
[slides]
Seventh U.S. National Congress on Computational Mechanics
Albuquerque, NM, July 2003 
“A continuum treatment of growth in tissue”
[slides]
Second M.I.T. Conference on Computational Fluid and Solid Mechanics
Cambridge, MA, June 2003