Picture of Jeff Heys 2011


Department Head

Email: jeffrey.heys@montana.edu

Office Phone: 406-994-7902
Cell Phone: 406-600-6491
Office: COBH 310


  • EGEN 102
  • ECHM 201
  • ECHM 451
  • EBIO 411

Chemical and Biomedical Calculations Using PythonBackground

Research Interests

  • Development of mathematical models for nanoparticle synthesis and radiation detection.
  • Using systems biology and dynamical system modeling to understand productivity in microbial consortia.
  • Implicit Discontinuous Galerkin Methods for advection-diffusion problems and the Navier-Stokes equation
  • Biofilm-fluid interaction and quorum sensing
  • Using the higher-order finite elements and the spectral element methods to predict particle deposition in the human airways
  • The modeling of biological systems in which there is a mechanical coupling between a moving fluid and tissues. Problems of current interest include the cricket sensory system and biofilms.
  • Using a first-order system least-squares (FOSLS) and algebraic multigrid (AMG) to solve the Navier-Stokes equations with additional boundary data (i.e., data assimilation).
  • I've developed a parallel, high-order least-squares finite element code that uses "hypre" by LLNL and a high-order discontinuous Galerkin finite element code that uses Trilinos by SNL.
  • Group website


  • Heys, J.J. (2017) "Chemical and Biomedical Engineering Calculations Using Python", John Wiley & Sons, Hoboken, NJ.
  • Ray, L., J.J. Iliff, and J.J. Heys (2019), “Analysis of convective and diffusive transport in the brain interstitium”,

    Fluids and Barriers of the CNS, 16 (1), 6

  • Schepens, D., R.P. Carlson, J. Heys, A.E. Beck, T. Gedeon (2019) “Role of resource allocation and transport in emergence of cross-feeding in microbial consortia”,  Journal of theoretical biology 467, 150-163

  • Heys, J.J., (2018) “Machine Learning as a Tool to Identify Critical Assignments”, Chemical Engineering Education, 52(4): 243-250

  • Carlson, R.P., A.E. Beck, P. Phalak, M.W. Fields, T. Gedeon, L. Hanley, W.R. Harcombe, M.A. Henson, J.J. Heys, (2018) “Competitive resource allocation to metabolic pathways contributes to overflow metabolisms and emergent properties in cross-feeding microbial consortia”, Biochemical Society Transactions, BST20170242

  • Akar, B. , K. Subramaniam, E. Narayanan, K. Rege and J.J. Heys, (2018) “Mechanistic investigation of radiolysis-induced gold nanoparticle formation for radiation dose prediction”, Biomedical Physics & Engineering Express

  • Mushaben, M., R. Urie, T. Flake, K. Rege, and J.J. Heys, (2018) “Spatiotemporal Modeling for the Optimization of Laser Tissue Soldering”, Lasers Surg. Med., 50(2): 143-152

  • Schepens, D., A.E. Beck, J.J. Heys, T. Gedeon, and R.P. Carlson, (2017) "The Benefits of Resource Partitioning and Division of Labor in Microbial Consortia", Advances in Systems and Synthetic Biology

  • Rajaraman, P.K, G.D. Vo, G. Hansen, and J.J. Heys, (2017) "Comparison of Continuous and Discontinuous Galerkin Finite Element Methods for Parabolic Differential Equations Employing Implicit Time Integration", Int. J. Comp. Meth. Eng. Sci. and Mech., 18(2-3): 182-190
  • Venters, M., R.P. Carlson, T. Gedeon, and J.J. Heys, (2017) “Effects of Spatial Localization on Microbial Consortia Growth”, PLoS One, 12(1): e0168592
  • Rajaraman, P.K., T.A. Manteuffel, M. Belohlavek, and J.J. Heys, (2017) “Combining Existing Numerical Models with Data Assimilation using Weighted Least-Squares Finite Element Methods”, Int. J. Num. Meth. Biomed. Eng., 33(1), 1-16
  • Heys, J.J., A.M. Richards, and J.Seymour (2016), "Chemical Engineering at Montana State University.", Chem Eng Educ
  • Gosney, J. and J.J. Heys (2016), "Numerical Prediction of Microbubble Attachment in Biological Flows." Am J Undergrad Res, 13(1), 21-30
  • Heys, J.J. (2015), "Chemical and Biological Engineering Calculations using Python" Preliminary Edition. John Wiley & Sons, Hoboken, NJ.
  • Rajaraman, P.K., and J.J. Heys (2014), “Echocardiographic Data Assimilation Using Least-Squares Finite Element Method.” Comput & Math Appl, 68(11), 1569-1580
  • Harvey, E., J.J. Heys, and T. Gedeon (2014) “Quantifying the Effects of the Division of Labor in Metabolic Pathways”, J Theo Biol, 360, 222-242
  • Rajaraman, P.K., and J.J. Heys, (2014) “Simulation of Nanoparticles Transport in Airways Using Petrov-Galerkin Finite Element Methods”, Int. J. Num. Meth. Biomed. Eng., 30(1), 103-116
  • Borazjani, I., J. Westerdale, E. McMahon, P.K. Rajaraman, J.J. Heys, and M. Belohlavek, (2013) “Left Ventricular Flow Analysis: Recent Advances in Numerical Methods and Applications in Cardiac Ultrasound”, Comp Math Methods Medicine, n. 395081
  • Heys, J.J., P.K. Rajaraman, T. Gedeon, and J.P. Miller, (2012) “A Model of Filiform Hair Distribution on the Cricket Cercus”, PLoS One, 7(10): e46588
  • Gedeon, T., G. Cummns, and J. Heys, (2012) “Effect of model selection on prediction of periodic behavior in gene regulatory networks”, Bull. Math. Biol.,, 74(8): 1706-1726
  • Wei, F., J. Westerdale, M. Belohlavek, and J.J. Heys, (2012) “Weighted Least-Square Finite Element Method for Cardiac Blood Flow Simulation with Echocardiographic Data”, Comp. Math. Methods Medicine, n. 371315
  • Miller, J.P., S. Krueger, J.J. Heys, and T. Gedeon, (2011) “Quantitative Characterization of the Filiform Mechanosensory Hair Array on the Cricket Cercus”, PLoS One, 6(11): e2787
  • Wininger, C.W., and J.J. Heys (2011) “Particle Transport Modeling in Pulmonary Airways with High-order Elements”, Mathematical Biosciences, 232(1): 11-19.
  • Vo, G., and J.J. Heys, (2011) “Biofilm Deformation in Response to Fluid Flow in Capillaries”, Biotech. Bioeng., 108(8): 1893-1899.
  • Adams, J.C., P. Jiamsripong, M. Belohlavek, E.M. McMahon, V. Marupakula, J.J. Heys, and H.P. Chaliki, (2011) “Potential Role of Reynolds Number in Resolving Doppler- and Catheter-Based Transvalvular Gradient Discrepancies in Aortic Stenosis.”, J Heart Valve Disease, 20(2):159-164.
  • Westerdale, J., M. Belohlavek, E.M. McMahon, P. Jiamsripong, J.J. Heys, and M. Milano, (2011) “Flow Velocity Vector Fields by Ultrasound Particle Imaging Velocimetry: In Vitro Comparison to Optical Flow Velocimetry”, J. Ultrasound Med., 30(2): 187-195
  • Jiamsripong, P., M.S. Alharthi, A.M. Calleja, E.M. McMahon, M. Katayama, J. Westerdale, M. Milano, J.J. Heys, F. Mookadam, M. Belohlavek, (2010) “Impact of Pericardial Adhesions on Diastolic Function as Assessed by Vortex Formation Time, a Parameter of Transmitral Flow Efficiency.” Cardio. Ultrasound , 8(42): 1-6
  • J.J. Heys, N. Holyoak, A.M. Callega, M. Belohlavek, H.P. Chalikim, (2010) “Revisiting the Simplified Bernoulli Equation”, TOBEJ, 4(6): 123-128
  • Vo, G., E. Brindle, and J.J. Heys, (2010) “An Experimentally Validated Immersed Boundary Model of Fluid-Biofilm Interaction”, Water Sci. Tech., 61(12): 3033-3040
  • Haung, H.C., K. Rege, and J.J. Heys, (2010) “Spatiotemporal Temperature Distribution and Cancer Cell Death in Response to Extracellular Hyperthermia Induced by Gold Nanorods”, ACS Nano, 4(5): 2892-2900
  • Heys, J.J., T.A. Manteuffel, S.F. McCormick, M. Milano, and M. Belohlavek, (2010) “Weighted Least-Squares Finite Elements for Particle Imaging Velocimetry Analysis”, J. Comp. Physics 229(1): 107-118
  • Heys, J.J., E. Lee, T.A. Manteuffel, and S.F. McCormick, (2009) “Enhanced Mass Conservation in Least-Squares Methods for Navier-Stokes Equations.” SIAM J. Sci. Comput., 31(3): 2303-2321
  • Jiamsripong, P., A.M. Callega, M.S. Alharthi, M. Dzsinich, E.M. McMahon, J.J. Heys, M. Milano, P.P. Sengupta, B.K. Khandheria, M. Belohlavek, (2009) “Impact of Acute Moderate Elevation in Left Ventricular Afterload on Diastolic Transmitral Flow Efficiency: Analysis by Vortex Formation Time.” J. Am. Soc. Echocard., 22(4): 427-431
  • Jiamsripong, P., A.M. Callega, M.S. Alharthi, E.J. Cho, E.M. McMahon, J.J. Heys, M. Milano, P.P. Sengupta, B.K. Khandheria, M. Belohlavek, (2009) “Increase in the Late Diastolic Filling Force Is Associated With Impaired Transmitral Flow Efficiency in Acute Moderate Elevation of Left Ventricular Afterload.” J. Ultrasound Med., 28(2): 175-182
  • Wong, S.S., J. Vargas, A. Thomas, C. Fastje, M. McLaughlin, R. Camponovo, R. C. Lantz, J. Heys, and M.L. Witten, (2008) “In Vivo Comparison of Epithelial Responses for S-8 versus JP-8 Jet Fuels Below Permissible Exposure Limit.”Toxicology, 254(1-2): 106-111
  • Heys, J.J., B. Knott, T. Gedeon, and Y. Kim, (2008) “Modeling Arthropod Filiform Hair Motion using the Penalty Immersed Boundary Method.” J. Biomech Eng., 41(5): 977-984
  • Stukel, J.M., J.J. Heys, and M.R. Caplan, (2008) “Optimizing Delivery of Multivalent Constructs for Detection of Secondary Tumors.”Ann. Biomed. Eng., 36(7):1291-1304
  • Heys J.J., (2008) “Group Projects in Chemical Engineering Using a Wiki.”, Chem. Eng. Ed., 42(2):91-104
  • Merchant, B.M., and J.J. Heys, (2008) “Effects of Variable Permeability on Aqueous Humor Outflow.” Appl. Comp. Math., 196:371-380
  • Heys, J.J., E. Lee, T.A. Manteuffel, and S.F. McCormick, (2007) “An Alternative Least-Squares Formulation of the Navier-Stokes Equations with Improved Mass Conservation.”, J. Comp. Physics, 226:994-1006
  • Heys, J.J., E. Lee, T.A. Manteuffel, and S.F. McCormick, (2006) “On Mass-Conserving Least-Squares Methods.” SIAM J. Sci. Comput.,28(5) 1675-1693
  • De Sterck, H., U. M. Yang, and J.J. Heys, (2006) "Reducing Complexity in Parallel Algebraic Multigrid Preconditioners." SIAM J. Matrix Anal., 27: 1019 - 1039
  • Heys, J.J., C.G. DeGroff, T.A. Manteuffel, and S.F. McCormick, (2006) “First-Order System Least Squares (FOSLS) for Modeling Blood Flow.”Medical Eng. & Physics, 28(6): 495-503
  • Heys, J.J., T.A. Manteuffel, S.F. McCormick, and L.N. Olson, (2005)“Algebraic Multigrid (AMG) for Higher-Order Finite Elements.”J. Comp. Physics, 204: 520-532
  • Heys, J.J., T.A. Manteuffel, S.F. McCormick, and J.W. Ruge, (2004)“First-Order System Least Squares (FOSLS) for Coupled Fluid-Elastic Problems.” J. Comp. Physics, 195(2): 560-575
  • Heys, J.J., C.G. DeGroff, W.W. Orlando, T.M. Manteuffel, and S.F. McCormick, (2002) “First-order system least squares for elastohydrodynamics with application to flow in compliant blood vessels.” Biomed. Sci. Instr., 38:277-282.
  • Heys, J.J. and V.H. Barocas, (2002), "A Boussinesq Model of Natural Convection in the Human Eye and the Formation of Krukenberg's Spindle.", Ann. Biomed. Eng. , 30:392-401.
  • Heys, J.J. and V.H. Barocas, (2002), "Computational Evaluation of the Role of Accommodation in Pigmentary Glaucoma.", Inv. Opthalmol. Vis. Sci., 43(3): 700-708.
  • Heys, J., V.H. Barocas, and M.J. Taravella (2001), "Modeling Passive Mechanical Interaction between the Aqueous Humor and Iris."J. Biomech. E., 123(6): 540-547.
  • Xu, J., J.J. Heys, V. H. Barocas, and T.W. Randolph (1999), "Permeability and Diffusion in Vitreous Humor: Implications for Drug Delivery." Pharmaceut. Res., 17(6): 664-669.
  • Heys, J. and V.H. Barocas (1998), "Mechanical Characterization of the Bovine Iris." J. Biomech. 32: 999-1003.