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Table 1 Model parameters.

From: A 3D multiscale model of cancer stem cell in tumor development

Parameter Symbol

Parameter Annotation

Parameter Value

Reference

D n

Diffusion rate of Nutrient

1.0

P. Macklin et al. (2009)

D c

Diffusion rate of TAF

100

Estimated

D m

Diffusion rate of MDE

1.0

P. Macklin et al. (2009)

λ u n

Uptake rate of Nutrient

[0.2, 0.5, 0.33, 0.67, 1, 1]

X. Zheng et al. (2005); Estimated

λ b n

Binding rate of nutrient

2.5·e-3

Estimated

λ p a n

Nutrient transfer rate from neo-vasculature

0.05

X. Zheng et al. (2005); Estimated

λ p p n

Nutrient transfer rate from existing vessel

0.01

Estimated

λ p N c

TAF secretion rate by dying cells

0.05

Estimated

λ p V c

TAF secretion rate by viable cells

0.004

Estimated

λ d c

TAF degradation rate

0.01

P. Macklin et al. (2009)

λ u c

TAF uptake rate by endothelial cells

0.025

P. Macklin et al. (2009)

λ p m

MDE secretion rate by viable cells

{50, 100, 150}

P. Macklin et al. (2009); Estimated

λ s p m

MDE secretion rate by endothelial cells

1.0

P. Macklin et al. (2009)

λ d m

MDE degradation rate

10

P. Macklin et al. (2009)

λ p f

ECM secretion rate by viable cells

0.1

P. Macklin et al. (2009)

λ s p f

ECM secretion rate by endothelial cells

0.01

Estimated

λ d f

ECM degradation rate

0.01

P. Macklin et al. (2009)

λ a

Volume loss rate due to apoptosis

0~0.00013

Estimated

λ N

Volume loss rate due to necrosis

0.25

X. Zheng et al. (2005)

θ a

Nutrient dose for cell survival

{0.1, 0.17, 0.25}

X. Zheng et al. (2005); Estimated

θ d

Maximum drug concentration for cell survival

{0.25, 0.27, 0.375}

Estimated

[K CC , K CCP , K CP , K CT ]

CSC proliferation probabilities

{0.6, 0.25, 0.1, 0.05}

Estimated

[K PP , K PT ]

PC proliferation probabilities

{0.25, 0.75}

Estimated

[K TT , d T ]

TC proliferation probability

[1- λ a , λ a ]

Estimated

A p

Relative proliferation ages

[1, 0.4, 1, 0.2]

Estimated

G m

Maximum generations a cell can divide

[250, 50, 25]

Estimated

C s

Constant for cell size scaling

10·e-5

Estimated

  1. NOTE:
  2. P. Macklin et al. (2009): Macklin, P., et al., Multiscale modelling and nonlinear simulation of vascular tumour growth. J Math Biol, 2009. 58(4-5): p. 765-98.
  3. X. Zheng et al. (2005): Zheng, X., S.M. Wise, and V. Cristini, Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method. Bull Math Biol, 2005. 67(2): p. 211-59.