I am a Professor in the Department of Mathematics
where I teach a range of courses, primarily in numerical analysis.
Specific course information is available on ICON.
I have a secondary appointment in the Department of Orthopaedics & Rehabilitation in the Carver College of Medicine, and an affiliate appointment in the Applied Mathematical and Computational Sciences (AMCS) program of the Graduate College.
I have a secondary appointment in the Department of Orthopaedics & Rehabilitation in the Carver College of Medicine, and an affiliate appointment in the Applied Mathematical and Computational Sciences (AMCS) program of the Graduate College.
Within the Department of Mathematics, I am part of the Mathematical & Computational Biology and Numerical Analysis research groups.
Current Group Members: Melissa Adrian (Undergraduate Honors Thesis 2020) Her thesis was on a mathematical model of threespecies 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, 20142017).
 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 histomorphometrybased 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.
Osteoarthritis.
I have worked on a number of problems with the Martin Lab in UIHC
Orthopaedics and Rehabilitation on osteoarthritis. Our work was
partially supported by NIH NIAMS grant p50
AR055533.
Applied Numerical Mathematics.
The backbone of my research has been in physiologically structured
multiscale modeling and simulation, including the development of
numerical methods and software. Earlier stages of research in this area
were partially supported by the NSF under awards DMS0609854, DMS0802609,
and DMS0914514.
Publications:
 Bruce P. Ayati, Considerations for Modeling Proteus mirabilis Swarming, in Proteus mirabilis: Methods and Protocols, Humana Press, NY, 2019, pp. 285296.
[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. 110.
[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. 118.
[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 posttraumatic osteoarthritis,
J. Orthopaedic Research, 35(3), 2017, pp. 566572.
[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
posttraumatic osteoarthritis, J. Orthopaedic Research,
35(3), 2017, pp. 515523.
[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 Antiinflammatory 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. 927941.
[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,
CDROM Proceedings of the 6th European Congress on Computational
Methods in Applied Sciences and Engineering (ECCOMAS 2012), September
1014, 2012, Vienna, Austria, Eds.: Eberhardsteiner, J.; Böhm, H.J.;
Rammerstorfer, F.G., ISBN: 9783950248197.
[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.
22672271.
[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. 281295.
[pdf, link, arXiv] © 2012 by the authors  Jason M. Graham, Bruce P. Ayati, Lei Ding,
Prem S. Ramakrishnan and James A. Martin, ReactionDiffusionDelay
Model for EPO/TNFα 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. 493511.
[link, arXiv] © 2012 International Press  Bruce P. Ayati, Microbial
Dormancy in Batch Cultures as a Function of SubstrateDependent
Mortality, J. Theoretical Biology, 243, 2012, pp. 3440.
[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 NaturalAgeGrid Galerkin Methods for AgeStructured
Biological Systems, Nonlinearity, 22(8), 2009, pp. 19831995.
[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
TumorHost Interaction: Application of Chemotherapy,
Mathematical Biosciences and Engineering, 6(3), 2009, pp. 521546.
[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(34), 2009, pp. 487494.
[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. 36233630.
[link, arXiv] © 2007 Society for General Microbiology  Bruce P. Ayati and Isaac
Klapper, A
Multiscale Model of Biofilm as a SenescenceStructured Fluid,
Multiscale Modeling & Simulation, 6(2), 2007, pp. 347365.
[pdf, link, arXiv] © 2007 Society for Industrial and Applied Mathematics  Bruce P. Ayati, Modeling
the Role of the Cell Cycle in Regulating Proteus
mirabilis SwarmColony
Development, Applied Mathematics Letters, 20(8), 2007, pp.
913918.
[link, arXiv] © 2007 Elsevier Ltd.  Bruce P. Ayati, Modeling
and Simulation of Age and SpaceStructured Biological Systems,
in Current Developments in Mathematical Biology, World Scientific
Publishing, 2007, pp. 107130.
[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. 120.
[pdf, link, arXiv] © 2006 Society for Industrial and Applied Mathematics  Bruce P. Ayati, A
StructuredPopulation Model of Proteus
mirabilis SwarmColony
Development, J. Mathematical Biology, 52(1), 2006, pp. 93114.
[link, arXiv] © SpringerVerlag 2005  Bruce P. Ayati and Todd
F. Dupont, Convergence
of a Stepdoubling Galerkin Method for Parabolic Problems,
Mathematics of Computation, 74(251), 2005, pp. 10531065.
[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. 10641076.
[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 1113, 2001, pp. 140148.
[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.123133.
[link] © 2001 Springer (formerly Kluwer)  Bruce
P. Ayati, A Variable Time
Step Method for an Agedependent Population
Model with Nonlinear Diffusion, SIAM J. Numerical Analysis, 37(5), 2000, pp. 15711589.
[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.
337347.
[ 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 CS9618, 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 CS9611, 1996.
[pdf, link] © 1996 Bruce P. Ayati  Bruce
P. Ayati, gridIt 1.0 User
Manual, University of Chicago Technical Report CS9601, 1996.
[pdf, link] © 1996 Bruce P. Ayati
Contact Information:

Department of Mathematics
University of Iowa
Iowa City, IA 522421419 
bruceayati@uiowa.edu

(319) 3350787
Office: 25G MacLean Hall
Last Revision: 20200417