- Georgi I. Kapitanov, Bruce P. Ayati, James A. Martin,
*Modeling the Effect of Blunt Impact on Mitochondrial Dysfunction in Cartilage*, Preprint, 2016.

[arXiv] © 2016 by the authors. - Julia C. Walk, Bruce P. Ayati, Sarah A. Holstein,
*Modeling the Effects of Multiple Myeloma on Kidney Function*, Preprint, 2016.

[arXiv] © 2016 by the authors. - Catherine E. Patterson, Bruce P. Ayati, Sarah A. Holstein,
*Modeling the Multiple Myeloma Vicious Cycle: Signaling Across the Bone Marrow Microenvironment*, Preprint, 2015.

[arXiv] © 2015 by the authors. - 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. - 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, 2016.

[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, 2016.

[link] © 2016 Orthopaedic Research Society. - 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. - 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*, 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*, SIAM J. Numerical Analysis, 37(5), 2000, pp. 1571-1589.

Model with Nonlinear Diffusion

[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

Last Revision: 2016-12-12