Xiaoming Zheng

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              2011


Research Interests:

•    Mathematical and Computational Biology

•    Numerical Methods for Free Boundary Problems


Research related:

  1. Angiogenesis page.
  2. Conference:  ECMTB2011: 8th European Conf on Math and Theor Biol, Krokow, June 28-July 2, 2011.
  3. Great Lakes SIAM 2013 conference: Computational Mathematics: Modeling, Algorithms and Applications, at Central Michigan University, Saturday, April 20, 2013.
  4. Matlab files,  related to the paper  "A viscoelastic model of blood capillary" by X. Zheng and C. Xie, 2014.
  5. A movie demonstrating the pull and push behaviors of a developing sprout. This is related to "A viscoelastic model of blood capillary".
  6. Demonstration:   A movie of interface-aligned mesh simulation of tumor growth. This is related to "An interface-fitted adaptive mesh method".



Journal Publications

  1. M. Moore, Y. Zhang and X. Zheng, Steady state and sensitivity analysis of a Notch-Delta signaling system of one single cell interacting with fixed environment, Journal of Biological Systems, 28(337–363), 2019.
  2. X. Zheng and M. Sweidan, Analysis of Ghost-Fluid Method with cubic extrapolation for two-point boundary value problems, International Journal of Numerical Methods and Applications, 18(19–58), 2019.
  3. X. Zheng and M. Sweidan, A mathematical model of angiogenesis and tumor growth: analysis and application in anti-angiogenesis therapy, Journal of Mathematical Biology, 77(1589–1622), 2018.
  4. C. Doering, J. Wu, K. Zhao, X. ZhengLong time behavior of the two-dimensional Boussinesq equations without buoyancy diffusion. Physics D: Nonlinear Phenomena, 2018.
  5. F. Li and X. Zheng, Comparison of several reaction and diffusion models of growth factors in angiogenesis, Communications in Mathematical Sciences, 15(1), 1-26, 2017.
  6. X. Zheng and J. Lowengrub. An interface-fitted adaptive mesh method for elliptic problems and its application in free interface problems with surface tension. Advances in Computational Mathematics, 42(5), 1225-1257, 2016.
  7. 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.
  8. 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.
  9. 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.
  10. 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
  11. 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.
  12. 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).
  13. 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)
  14. 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).
  15. 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).
  16. 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).
  17. 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).
  18. A. Anderson, X. Zheng and V. Cristini. Adaptive unstructured volume remeshing-I: the method. J. Comp. Phys. 208, 616-625(2005).
  19. 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).
  20. 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).
  21. 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).
  22. 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)