Xiaoming Zheng

Associate Professor of mathematics

Contact Information

Office phone:

Pearce Hall 201 E
Department of Mathematics,
Central Michigan University
Mount Pleasant, MI 48859

My Pic in Summer

2014-2015 Colloquium Schedule of Mathematics Department


Great Lakes SIAM 2013 conference: Computational Mathematics: Modeling, Algorithms and Applications.
at Central Michigan Unviersity.
Saturday, April 20, 2013

Research Interests:

    Mathematical and Computational Biology

    Numerical Methods for Free Boundary Problems

Demonstrations:   A movie of interface-aligned mesh simulation of tumor growth

Research related:
  1. Angiogenesis page
  2. Conference:  ECMTB2011: 8th European Conf on Math and Theor Biol, Krokow, June 28-July 2, 2011
  3. Matlab files related to the submission "A viscoelastic model of capillary growth: derivation, analysis, and simulation" by X. Zheng and C. Xie
  4. A movie demonstrating the pull and push behaviors of a developing sprout, January 03, 2012.


Journal Publications
  1. X. Zheng, Y. Kim, L. Rakesh, E.-B. Lin. A conservative and variation preserving finite volume method for non-overlapping meshes of reaction and diffusion in angiogenesis. J. Comput. Appl. Math., 275,183-196, 2015.
  2. X. Zheng and C. Xie. A viscoelastic model of blood capillary extension and regression: derivation, analysis, and simulation. Journal of Mathematical Biology, 68(1-2), 57-80, 2014.
  3. X. Zheng, G.Y. Koh, T. Jackson, A continuous model of angiogenesis: initiation, extension, and maturation of new blood vessels modulated by vascular endothelial growth factor, angiopoietins, platelet-derived growth factor-B, and pericytes. Discrete and Continuous Dynamical Systems - Series B (DCDS-B) (special issue on cancer modeling, analysis and control), 18(4), 1109-1154, 2013.
  4. F. Li and X. Zheng. Singularity analysis of a reaction-diffusion equation with a solution-dependent Dirac delta source. Applied Mathematics Letters, 25(12), 2179-2183, 2012
  5. T. Jackson and X. Zheng. A Cell-Based Model of Endothelial Cell Elongation, Proliferation and Maturation During Corneal Angiogenesis. Bull. Math. Biol. 72(4):830-868, 2010.
  6. J.P. Sinek, S. Sanga, X. Zheng, H. B. Frieboes, M. Ferrari and V. Cristini. Predicting drug pharmacokinetics and effect in vascularized tumors using computer simulation. Journal of Mathematical Biology, 58, 485-510 (2009).
  7. S. Sanga, H. B. Frieboes, X. Zheng, R. Gatenby, E. L. Bearer and V. Cristini. Predictive oncology: A review of multidisciplinary, multiscale in silico modeling linking phenotype, morphology and growth. NeuroImage, 37, S120-S134 (2007)
  8. H. Frieboes, J.S. Lowengrub, S. Wise, X. Zheng, P. Macklin, E.L. Bearrer and V. Cristini. Computer simulation of glioma growth and morphology. Neuroimage, 37, S59-S70(2007).
  9. H. Frieboes, X. Zheng, C.-H. Sun, B. Tromberg, R. Gatenby and V. Cristini. An integrated experimental/computational model of tumor invasion. Cancer Res., 66,1597-1604(2006).
  10. C. Lee, J. Lowengrub, J. Rubinstein and X. Zheng. Phase reconstruction by the weighted least action principle. Journal of Optics A: Pure and Applied Optics, 8,279-289(2006).
  11. X. Yang, A. James, J. Lowengrub, X. Zheng and V. Cristini. An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids. J. Comp. Phys., 217, 364-394(2006).
  12. A. Anderson, X. Zheng and V. Cristini. Adaptive unstructured volume remeshing-I: the method. J. Comp. Phys. 208, 616-625(2005).
  13. X. Zheng, J. Lowengrub, A. Anderson and V. Cristini. Adaptive unstructured volume remeshing-I: Applications to two- and three-dimensional levelset simulations of multiphase flow. J. Comp. Phys. 208, 625-650(2005).
  14. X. Zheng, S.M. Wise and V. Cristini. Nonlinear simulation of tumor necrosis, neo-vascularization and tisse invasion via an adaptive finite-element/level-set method. Bull. Math. Biol. 67, 211-259(2005).
  15. J. Sinek, H. Frieboes, X. Zheng and V. Cristini. Two-dimensional simulations of chemotherapy involving nanoparticles demonstrate fundamental transport and tumor response limitations. Biomedical Microdevices 6, 297-309(2004).
  16. P. Zhang and X. Zheng. Numerical studies of 2D free surface waves with fixed bottom. J. Comput. Math. 20, no. 4, 391-412(2002).

Book Chapters
  1. Book: "Modeling Tumor Vasculature:Molecular, Cellular, and Tissue Level Aspects and Implication", editor: T. Jackson, ISBN: 978-1-4614-0051-6 (Print) 978-1-4614-0052-3 (Online), Springer, 2011.
    Chapter: "A Cell-Based Model of Endothelial Cell Elongation, Proliferation and Maturation in Corneal Angiogenesis", by T. Jackson and X. Zheng.
  2. Book: "INTERFACE PROBLEMS AND METHODS IN BIOLOGICAL AND PHYSICAL FLOWS", editors: Khoo, Li, Lin. Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore - Vol. 17. 2009 World Scientific Publishing Co. Pte. Ltd.
    Chapter: "Lecture Notes on Nonlinear Tumor Growth: Modeling and Simulation" (J S Lowengrub et al.)
  3. Book "Selected Topics in Cancer Modeling. Genesis, Evolution, Immune Competition, and Therapy", editors: Bellomo, Chaplain and De Angelis. 2008 Birkhauser Boston.
    Chapter: "Nonlinear modeling and Simulation of tumor growth". Authors: V. Cristini, H. B. Frieboes, X. Li, J. S. Lowengrub, P. Macklin, S. Sanga, S. M. Wise, and X. Zheng.


    General applied mathemtics courses, including numerical analysis, scientific computing, and mathematical biology.

Miscellaneous items

1. Use special values and inverse function to solve trigonometric equations. (pre-calculus and calculus material)