Within the Department of Mathematics, I am part of the Mathematical & Computational Biology and Numerical Analysis research groups.

• Melissa Adrian (Undergraduate Honors Thesis 2020) Her thesis was on a mathematical model of three-species interaction in the gut microbiota.

• Ruqiah Muhammad (AMCS Ph.D. 2019). Her dissertation was on a mathematical model of nonviral gene delivery systems for bone regeneration.
• Georgi Kapitanov (Visiting Assistant Professor of Mathematics, 2014-2017).
• Julia Walk (AMCS Ph.D. 2016). Her dissertation was on a mathematical model of the effects of multiple myeloma on renal function.
• Catherine Patterson (AMCS Ph.D. 2016). Her dissertation was on histomorphometry-based modeling and simulation of multiple myeloma bone disease.
• Xiayi Wang (AMCS Ph.D. 2015). Her dissertation was on the modeling and simulation of articular cartilage lesion formation.
• Jason Graham (AMCS Ph.D. 2012). His dissertation was on mathematical representations of various systems in orthopaedics and collective cell motility.
• Stephanie Schmidt (AMCS Ph.D. 2010). Her dissertation work was on models of Nafion fuel cells, in collaboration with the Leddy Lab.

• Bruce P. Ayati, Considerations for Modeling Proteus mirabilis Swarming, in Proteus mirabilis: Methods and Protocols, Humana Press, NY, 2019, pp. 285-296.
  [link] © 2019 Springer.
• Julia C. Walk, Bruce P. Ayati, Sarah A. Holstein, Modeling the Effects of Multiple Myeloma on Kidney Function, Scientific Reports, 9:1726, 2019, pp. 1-10.
  [pdf,  link, arXiv] © 2019 by the authors.
• Georgi I. Kapitanov, Bruce P. Ayati, James A. Martin, Modeling the Effect of Blunt Impact on Mitochondrial Dysfunction in Cartilage: Implications for Development of Osteoarthritis , PeerJ, 5:e3468, 2017, pp. 1-18.
  [pdf, link, supplement, arXiv] © 2017 by the authors.
• Bruce P. Ayati, Georgi I. Kapitanov, Mitchell C. Coleman, Donald D. Anderson, and James A. Martin, Mathematics as a conduit for translational research in post-traumatic osteoarthritis, J. Orthopaedic Research, 35(3), 2017, pp. 566-572.
  [link] © 2016 Orthopaedic Research Society.
• J.A. Martin, D.D. Anderson, J.E. Goetz, D. Fredericks, D.R. Pedersen, B.P. Ayati, J.L. Marsh, and J.A. Buckwalter, Complementary models reveal cellular responses to contact stresses that contribute to post-traumatic osteoarthritis, J. Orthopaedic Research, 35(3), 2017, pp. 515-523.
  [link] © 2016 Orthopaedic Research Society.
• Georgi I. Kapitanov, Xiayi Wang, Bruce P. Ayati, Marc J. Brouillette, James A. Martin, Linking Cellular and Mechanical Processes in Articular Cartilage Lesion Formation: A Mathematical Model, Frontiers in Bioengineering and Biotechnology, 4(80), 2016.
  [pdf, link, supplement, arXiv] © 2016 by the authors.
• Xiayi Wang, Marc J. Brouillette, Bruce P. Ayati, and James A. Martin, A Validated Model of the Pro- and Anti-inflammatory Cytokine Balancing Act in Articular Cartilage Lesion Formation, Frontiers in Bioengineering and Biotechnology, 3(25), 2015.
  [pdf, link, corrigendum] © 2015 by the authors.
• Catherine E. Patterson, Bruce P. Ayati, Sarah A. Holstein, Modeling the Multiple Myeloma Vicious Cycle: Signaling Across the Bone Marrow Microenvironment, arXiv, 2015.
  [arXiv] © 2015 by the authors.
• Xiayi Wang, Bruce P. Ayati, Marc J. Brouillette, Jason M. Graham, Prem S. Ramakrishnan, and James A. Martin, Modeling and Simulation of the Effects of Cyclic Loading on Articular Cartilage Lesion Formation, Intl. J. for Numerical Methods in Biomedical Engineering, 30(10), 2014, pp. 927-941.
  [pdf, link, arXiv] © 2014 John Wiley & Sons, Ltd.
• Jason M. Graham, Bruce P. Ayati, Sarah A. Holstein and James A. Martin, The Role of Osteocytes in Targeted Bone Remodeling: A Mathematical Model, PLoS ONE, 8(5), 2013, e63884.
  [pdf, link, arXiv] © 2013 by the authors.
• Bruce P. Ayati, Jason M. Graham and Sarah A. Holstein, Using a Level Set to Model Multiple Myeloma Induced Bone Loss, CD-ROM Proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), September 10-14, 2012, Vienna, Austria, Eds.: Eberhardsteiner, J.; Böhm, H.J.; Rammerstorfer, F.G., ISBN: 978-3-9502481-9-7.
  [pdf] © 2012 Vienna University of Technology
• Jason M. Graham and Bruce P. Ayati, A Unified Term for Directed and Undirected Motility in Collective Cell Invasion, Applied Mathematics Letters, 25(12), 2012, pp. 2267-2271.
  [link, arXiv] © 2012 Elsevier Ltd.
• Jason M. Graham, Bruce P. Ayati, Prem S. Ramakrishnan and James A. Martin, Towards a New Spatial Representation of Bone Remodeling, Mathematical Biosciences and Engineering, 9(2), 2012, pp. 281-295.
  [pdf, link, arXiv] © 2012 by the authors
• Jason M. Graham, Bruce P. Ayati, Lei Ding, Prem S. Ramakrishnan and James A. Martin, Reaction-Diffusion-Delay Model for EPO/TNF-α Interaction in Articular Cartilage Lesion Abatement, Biology Direct, 7:9, 2012.
  [pdf, link, arXiv] © 2012 by the authors
• Bruce P. Ayati and Isaac Klapper, Models of Microbial Dormancy in Biofilms and Planktonic Cultures, Communications in Mathematical Sciences, 10(2), 2012, pp. 493-511.
  [link, arXiv] © 2012 International Press
• Bruce P. Ayati, Microbial Dormancy in Batch Cultures as a Function of Substrate-Dependent Mortality, J. Theoretical Biology, 243, 2012, pp. 34-40.
  [link] © 2011 Elsevier Ltd.
• Bruce P. Ayati, Claire M. Edwards, Glenn F. Webb, and John P. Wikswo, A Mathematical Model of Bone Remodeling Dynamics for Normal Bone Cell Populations and Myeloma Bone Disease, Biology Direct, 5:28, 2010.
  [pdf, link] © 2010 by the authors
• Bruce P. Ayati and Todd F. Dupont, Mollified Birth in Natural-Age-Grid Galerkin Methods for Age-Structured Biological Systems, Nonlinearity, 22(8), 2009, pp. 1983-1995.
  [pdf, link] © 2009 IOP Publishing Ltd and London Mathematical Society.
• P. Hinow, P. Gerlee, L.J. McCawley, V. Quaranta, M. Ciobanu, S. Wang, J.M. Graham, B.P. Ayati, J. Claridge, K.R. Swanson, M. Loveless and A.R.A. Anderson, A Spatial Model of Tumor-Host Interaction: Application of Chemotherapy, Mathematical Biosciences and Engineering, 6(3), 2009, pp. 521-546.
  [link] © 2009 AIMS.
• Bruce P. Ayati, A Comparison of the Dynamics of the Structured Cell Population in Virtual and Experimental Proteus mirabilis Swarm Colonies, Applied Numerical Mathematics, 59(3-4), 2009, pp. 487-494.
  [link] © 2008 IMACS.
• Isaac Klapper, Peter Gilbert, Bruce P. Ayati, Jack Dockery and Philip S. Stewart, Senescence Can Explain Microbial Persistence, Microbiology, 153(11), 2007, pp. 3623-3630.
  [link, arXiv] © 2007 Society for General Microbiology
• Bruce P. Ayati and Isaac Klapper, A Multiscale Model of Biofilm as a Senescence-Structured Fluid, Multiscale Modeling & Simulation, 6(2), 2007, pp. 347-365.
  [pdf, link, arXiv] © 2007 Society for Industrial and Applied Mathematics
• Bruce P. Ayati, Modeling the Role of the Cell Cycle in Regulating Proteus mirabilis Swarm-Colony Development, Applied Mathematics Letters, 20(8), 2007, pp. 913-918.
  [link, arXiv] © 2007 Elsevier Ltd.
• Bruce P. Ayati, Modeling and Simulation of Age- and Space-Structured Biological Systems, in Current Developments in Mathematical Biology, World Scientific Publishing, 2007, pp. 107-130.
  [link] © 2007 World Scientific Publishing
• Bruce P. Ayati, Glenn F. Webb, and Alexander R.A. Anderson, Computational Methods and Results for Structured Multiscale Models of Tumor Invasion, Multiscale Modeling & Simulation, 5(1), 2006, pp. 1-20.
  [pdf, link, arXiv] © 2006 Society for Industrial and Applied Mathematics
• Bruce P. Ayati, A Structured-Population Model of Proteus mirabilis Swarm-Colony Development, J. Mathematical Biology, 52(1), 2006, pp. 93-114.
  [link, arXiv] © Springer-Verlag 2005
• Bruce P. Ayati and Todd F. Dupont, Convergence of a Step-doubling Galerkin Method for Parabolic Problems, Mathematics of Computation, 74(251), 2005, pp. 1053-1065.
  [pdf, link] © 2004 American Mathematical Society
• Bruce P. Ayati and Todd F. Dupont, Galerkin Methods in Age and Space for a Population Model with Nonlinear Diffusion, SIAM J. Numerical Analysis, 40(3), 2002, pp. 1064-1076.
  [pdf, link] © 2002 Society for Industrial and Applied Mathematics
• Bruce P. Ayati and Paul D. Massatt, Feasibility of Managing a Dynamic Constellation to a Fixed Constellation Definition, Proceedings of the Institute of Navigation 57th Annual Meeting, Albuquerque, New Mexico, June 11-13, 2001, pp. 140-148.
  [pdf, link] © 2001 Institute of Navigation
• Bruce P. Ayati and Claudia Neuhauser, A Markov Embedding Approximation for a Stochastic Population Model with Exogenous Disturbances, Methodology and Computing in Applied Probability, 3(2), 2001, pp.123-133.
  [link] © 2001 Springer (formerly Kluwer)
• Bruce P. Ayati, A Variable Time Step Method for an Age-dependent Population
  Model with Nonlinear Diffusion, SIAM J. Numerical Analysis, 37(5), 2000, pp. 1571-1589.
  [pdf, link] © 2000 Society for Industrial and Applied Mathematics
• Bruce P. Ayati, Todd F. Dupont and Thomas Nagylaki, The Influence of Spatial Inhomogeneities on Neutral Models of Geographical Variation IV. Discontinuities in the Population Density and Migration Rate, Theoretical Population Biology, 56(3), 1999, pp. 337-347.
  [ link] © 1999 Academic Press
• Bruce P. Ayati, Methods for Computational Population Dynamics, University of Chicago Department of Mathematics Doctoral Dissertation, 1998.
  [pdf] © 1998 Bruce P. Ayati
• Bruce P. Ayati, BuGS 1.0 User Guide, University of Chicago Technical Report CS-96-18, 1996.
  [pdf, link] © 1996 Bruce P. Ayati
• Sauro Succi, Bruce P. Ayati and A. E. Hosoi, A Six Lecture Primer on Parallel Computing, University of Chicago Technical Report CS-96-11, 1996.
  [pdf, link] © 1996 Bruce P. Ayati
• Bruce P. Ayati, gridIt 1.0 User Manual, University of Chicago Technical Report CS-96-01, 1996.
  [pdf, link] © 1996 Bruce P. Ayati

• Department of Mathematics
  University of Iowa 
  Iowa City, IA 52242-1419

• bruce-ayati@uiowa.edu

• (319) 335-0787

  Office: 25G MacLean Hall