University of Houston

Department of Mathematics

Motion of Blood Cells


Particulate Flow Research Group
Department of Mathematics
University of Houston
Houston, TX 77204
We acknowledge the support of the NSF grants (DMS-0443826, DMS-0707602, and DMS-0914788) for developing the immersed boundary (IB) methods to investigate the blood cell motion in microvessels and micro-channels and the distributed Lagrange multiplier/fictitious domain/immersed boundary (DLM/FD/IB) methods for simulating the interaction of many red blood cells and rigid particles in Poiseuille flows.

Numerical Results in 3D flows obtained via an immersed boundary method with finite element method and operator splitting method:

  1. Snapshots of the changing from a sphere to a biconcave RBC shape when getting the initial shape of RBC.

  2. A red blood cell migrating in a 3D slit Poiseuille flow (published in Int. J. Numer. Methods Fluids 76 (2014), 397-415).

  3. A red blood cell either tumbles or tank-treads in 3D shear flow:

Numerical Results in 2D flows obtained via an immersed boundary method with finite element method and operator splitting method:

  1. Initial shape of a 2D membrane:
  2. Intermittent behavior of an RBC in a shear flow (2D result; published in Biomechanics and Modeling in Mechanobiology 14 (2015), 865-876):
  3. Multi-cell interaction behind a moving interface (published in Numerical Mathematics: Theory, Methods and Applications 7 (2014), 499-511):
  4. Multi-cell interaction (published in Int. J. Numer. Methods Fluids 68 (2012), 1393-1408):
  5. Multi-cell and particle interaction (published in Chinese Annals of Mathematics, Series B 31 (2010), 975-990):

    Research Funding

    1. NSF DMS-0914788: Computational Mathematics (the PI is T.-W. Pan, CO-PIs are R. Glowinski and R. Hoppe).
      Grant title: Computational methods for the suspensions of deformable and rigid particles and their applications to modelling of blood flows.
      Grant amount and duration: $340,454, 07/15/2009 - 07/30/2013.
    2. NSF DMS-0707602: Applied Mathematics (the PI was R. Hoppe, CO-PIs are R. Glowinski and T.-W. Pan).
      Grant title: Modeling, Analysis and Simulation of Surface Acoustic Wave Driven Microfluidic Biochips.
      Grant amount and duration: $209,384, 08/01/2007 - 07/31/2010.
    3. NSF DMS-0443826: NIGMS (the PI was S. Canic, and CO-PIs were R. Glowinski and T.-W. Pan).
      Grant title: Collaborative research: Modeling the growth and adhesion of auricular chondrocytes under controlled flow conditions.
      Grant amount and duration: $740,000, 05/15/2005 - 04/30/2010.

    Publications:

    1. Shihai Zhao, Yao Yu, T.-W. Pan, R. Glowinski
      A DLM/FD/IB method for simulating compound cell Interacting with red blood cells in a microchannel
      Chinese Annals of Mathematics, Series B, 39 (2018), 535-552.

    2. Lingling Shi, Suncica Canic, Annalisa Quaini, T.-W. Pan
      A study of self-propelled elastic cylindrical micro-swimmers using modeling and computation
      J. Comput. Phys. 314 (2016), 264–286.

    3. T.-W. Pan, Shihai Zhao, Xiting Niu, R. Glowinski
      A DLM/FD/IB method for simulating compound vesicle motion under creeping flow condition
      J. Comput. Phys. 300 (2015), 241-253.

    4. Xiting Niu, Lingling Shi, T.-W. Pan, R. Glowinski
      Numerical simulation of the motion of inextensible capsules in shear flow under the effect of the nature state
      Communications in Computational Physics 18 (2015), 787-807.

    5. Xiting Niu, T.-W. Pan, R. Glowinski
      The dynamics of inextensible capsules in shear flow under the effect of the natural state
      Biomechanics and Modeling in Mechanobiology 14 (2015), 865-876.

    6. Shihai Zhao, T.-W. Pan
      Numerical simulation of red blood cell suspensions behind a moving interface in a capillary
      Numerical Mathematics: Theory, Methods and Applications 7 (2014), 499-511.

    7. Lingling Shi, T.-W. Pan, R. Glowinski
      Three-dimensional numerical simulation of red blood cell motion in Poiseuille flows
      Int. J. Numer. Methods Fluids 76 (2014), 397-415.

    8. Lingling Shi, Yao Yu, T.-W. Pan, R. Glowinski
      Oscillating motions of neutrally buoyant particle and red blood cell in Poiseuille flow in a narrow channel
      Physics of Fluids 26 (2014) 041904.

    9. T. Franke, R.H.W. Hoppe, C. Linsenmann, K. Zeleke
      Numerical simulation of surface acoustic wave actuated cell sorting
      Central European Journal of Mathematics 11 (2013), 760-778.

    10. R.H.W. Hoppe and C. Linsenmann
      The finite element immersed boundary method for the numerical simulation of the motion of red blood cells in microfluidic flows
      In: Numerical Methods for Differential Equations, Optimization, and Technological Problems (S. Repin, T. Tiihonen, T. Tuovinen; eds.),
      Springer Series 'Computational Methods in Applied Sciences', Springer, Berlin-Heidelberg-New York, 2013.

    11. Lingling Shi, T.-W. Pan, R. Glowinski
      Lateral migration and equilibrium shape and position of a single red blood cell in bounded Poiseuille flows
      Physical Review E 86 (2012), 056308.

    12. Shih-Di Chen, T-W Pan, Chien-Cheng Chang
      The motion of a single and multiple neutrally buoyant elliptical cylinders in plane Poiseuille flow
      Physics of Fluids 24 (2012), 103302.

    13. R.H.W. Hoppe, C. Linsenmann
      An adaptive newton continuation strategy for the fully implicit finite element immersed boundary methods
      Journal of Computational Physics 231 (2012), 4676-4693.

    14. Lingling Shi, T.-W. Pan, R. Glowinski
      Numerical simulation of lateral migration of red blood cells in Poiseuille flows
      Int. J. Numer. Methods Fluids 68 (2012), 1393-1408.

    15. T. Franke, R.H.W. Hoppe, C. Linsenmann, L. Schmid, C. Willbold, A. Wixforth
      Numerical simulation of the motion and deformation of red blood cells and vesicles in microfluidic flows
      Computing and Visualization in Science 14 (2012), 167-180.

    16. Lingling Shi, T.-W. Pan, R. Glowinski
      Deformation of a single blood cell in bounded Poiseuille flows
      Physical Review E 85 (2012), 016307.

    17. R. Glowinski, Q. He
      A least-squares/fictitious domain method for linear elliptic problems with Robin boundary conditions
      Commun. Comput. Phys. 9 (2011), p.587.

    18. T.-W. Pan, Lingling Shi, R. Glowinski
      A DLM/FD/IB method for simulating cell/cell and cell/particle interaction in microchannels
      Chinese Annals of Mathematics, Series B 31 (2010), 975-990.

    19. Tong Wang, T.- W. Pan, Z. Xing, R. Glowinski
      Numerical simulation of rheology of red blood cell rouleaux in micro-channels
      Physical Review E 79 (2009), 041916

    20. T.-W. Pan, Tong Wang
      Dynamical simulation of red blood cell rheology in microvessels
      International Journal of Numerical Analysis and Modeling 6 (2009), 455-473.