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.
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© 2005 Springer-Verlag Berlin Heidelberg
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Sun, S., Wheeler, M.F., Obeyesekere, M., Patrick, C. (2005). Multiscale Angiogenesis Modeling. In: Sunderam, V.S., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science – ICCS 2005. ICCS 2005. Lecture Notes in Computer Science, vol 3516. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11428862_13
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DOI: https://doi.org/10.1007/11428862_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26044-8
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