Multiscale angiogenesis modeling

Shuyu Sun*, Mary F. Wheeler, Mandri Obeyesekere, Charles Patrick

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

Abstract

We propose a deterministic two-scale tissue-cellular approach for modeling growth factor-induced angiogenesis. The bioreaction and diffusion of capillary growth factors (CGF) are modeled at a tissue scale, whereas capillary extension, branching and anastomosis are modeled at a cellular scale. The capillary indicator function is used to bridge these two scales. To solve the equation system numerically, we construct a two-grid algorithm that involves applying a mixed finite element method to approximate concentrations of CGF on a coarse mesh and a point-to-point tracking method to simulate sprout branching and anastomosis on a fine grid. An analysis of the algorithm establishes optimal error bounds for each of the processes - CGF reaction-diffusion, capillary extension, sprout branching and anastomosis - and overall error bounds for their coupled nonlinear interactions.

Original languageEnglish (US)
Pages (from-to)96-103
Number of pages8
JournalLecture Notes in Computer Science
Volume3516
Issue numberIII
DOIs
StatePublished - Jan 1 2005
Event5th International Conference on Computational Science - ICCS 2005 - Atlanta, GA, United States
Duration: May 22 2005May 25 2005

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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