### Abstract

A high-resolution fast boundary-integral method is developed for simulating red blood cell motion in complex geometries. The algorithm employs a particle-mesh-Ewald method (PME) to achieve computational efficiency superior to that of standard boundary-element implementations. The computational expense scales with O(N logN), where N is the number of collocation points distributed over the cell membranes. The no-slip boundary condition on vessel walls with complex geometry is enforced implicitly in terms of a linear system for unknown forces required to stop the flow at the walls. In the numerical implementation, cell shapes are represented by spherical harmonic functions interpolated through collocation points. Because the resolution of the global spectral basis functions is perfect in some sense, accurate solutions can be obtained efficiently and error-free interpolation can be achieved for switching resolutions. The procedure facilitates the control of aliasing error and circumvents explicit filtering and implicit numerical dissipation; both would degrade the numerical accuracy. The resolution of the scheme can be set based on desired accuracy, unconstrained by stability considerations. The overall approach, motivation, advantages, and drawbacks of the numerical scheme are discussed in detail. The solver is demonstrated for case studies involving the motion of a red blood cell through a constriction, the computation of the effective blood viscosity in tube flow, the transport of a leukocyte in a microvessel, and flow in a model network. Considering the simplicity of the finite-deformation elastic constitutive model used to describe the cell membrane, the calculated effective viscosity reproduces remarkably well the well-known non-monotonic dependence on vessel diameter.

Original language | English (US) |
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Title of host publication | Computational Hydrodynamics of Capsules and Biological Cells |

Publisher | CRC Press |

Pages | 71-111 |

Number of pages | 41 |

ISBN (Electronic) | 9781439820063 |

ISBN (Print) | 9781439820056 |

DOIs | |

State | Published - Jan 1 2010 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Medicine(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Physics and Astronomy(all)

### Cite this

*Computational Hydrodynamics of Capsules and Biological Cells*(pp. 71-111). CRC Press. https://doi.org/10.1201/EBK1439820056

**A high-resolution fast boundary-integral method for multiple interacting blood cells.** / Freund, J. B.; Zhao, H.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Computational Hydrodynamics of Capsules and Biological Cells.*CRC Press, pp. 71-111. https://doi.org/10.1201/EBK1439820056

}

TY - CHAP

T1 - A high-resolution fast boundary-integral method for multiple interacting blood cells

AU - Freund, J. B.

AU - Zhao, H.

PY - 2010/1/1

Y1 - 2010/1/1

N2 - A high-resolution fast boundary-integral method is developed for simulating red blood cell motion in complex geometries. The algorithm employs a particle-mesh-Ewald method (PME) to achieve computational efficiency superior to that of standard boundary-element implementations. The computational expense scales with O(N logN), where N is the number of collocation points distributed over the cell membranes. The no-slip boundary condition on vessel walls with complex geometry is enforced implicitly in terms of a linear system for unknown forces required to stop the flow at the walls. In the numerical implementation, cell shapes are represented by spherical harmonic functions interpolated through collocation points. Because the resolution of the global spectral basis functions is perfect in some sense, accurate solutions can be obtained efficiently and error-free interpolation can be achieved for switching resolutions. The procedure facilitates the control of aliasing error and circumvents explicit filtering and implicit numerical dissipation; both would degrade the numerical accuracy. The resolution of the scheme can be set based on desired accuracy, unconstrained by stability considerations. The overall approach, motivation, advantages, and drawbacks of the numerical scheme are discussed in detail. The solver is demonstrated for case studies involving the motion of a red blood cell through a constriction, the computation of the effective blood viscosity in tube flow, the transport of a leukocyte in a microvessel, and flow in a model network. Considering the simplicity of the finite-deformation elastic constitutive model used to describe the cell membrane, the calculated effective viscosity reproduces remarkably well the well-known non-monotonic dependence on vessel diameter.

AB - A high-resolution fast boundary-integral method is developed for simulating red blood cell motion in complex geometries. The algorithm employs a particle-mesh-Ewald method (PME) to achieve computational efficiency superior to that of standard boundary-element implementations. The computational expense scales with O(N logN), where N is the number of collocation points distributed over the cell membranes. The no-slip boundary condition on vessel walls with complex geometry is enforced implicitly in terms of a linear system for unknown forces required to stop the flow at the walls. In the numerical implementation, cell shapes are represented by spherical harmonic functions interpolated through collocation points. Because the resolution of the global spectral basis functions is perfect in some sense, accurate solutions can be obtained efficiently and error-free interpolation can be achieved for switching resolutions. The procedure facilitates the control of aliasing error and circumvents explicit filtering and implicit numerical dissipation; both would degrade the numerical accuracy. The resolution of the scheme can be set based on desired accuracy, unconstrained by stability considerations. The overall approach, motivation, advantages, and drawbacks of the numerical scheme are discussed in detail. The solver is demonstrated for case studies involving the motion of a red blood cell through a constriction, the computation of the effective blood viscosity in tube flow, the transport of a leukocyte in a microvessel, and flow in a model network. Considering the simplicity of the finite-deformation elastic constitutive model used to describe the cell membrane, the calculated effective viscosity reproduces remarkably well the well-known non-monotonic dependence on vessel diameter.

UR - http://www.scopus.com/inward/record.url?scp=84969726892&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84969726892&partnerID=8YFLogxK

U2 - 10.1201/EBK1439820056

DO - 10.1201/EBK1439820056

M3 - Chapter

AN - SCOPUS:84969726892

SN - 9781439820056

SP - 71

EP - 111

BT - Computational Hydrodynamics of Capsules and Biological Cells

PB - CRC Press

ER -