Table 5.

Additional parameters in the invasion model

	Description	Value	References
Diffusion coefficients
$D_t^1$	Tumor-associated proteinase (tissue)	1.67 × 10−12 cm2/s	TW
$D_t^2$	Tumor-associated proteinase (duct)	3.67 × 10−12 cm2/s	TW
$D_S^1$	Fibroblast-secreted proteinase (tissue)	1.02 × 10−7 cm2/s	(Saffarian et al. 2004; Sherratt and Murray 1990; Kim etal. 2009), TW
$D_s^2$	Fibroblast-secreted proteinase (duct)	1.08 × 10−8 cm2/s	(Saffarian et al. 2004; Sherratt and Murray 1990), TW
Degradation/Decay rates
λ1	ECM degradation rate by TAP	1.0 × 103cm 3g−1 s−1	TW
λ2	ECM remodeling	1.67 × 10−5 s−1	(Kim et al. 2009), TW
ρK	Carrying capacity of ECM	= ρ*	TW
λ3	Production rate of tumor cell-associated proteinase	2.32 × 10 −11 g cm−3 s−1	(Mercapide et al. 2003 ; Kim et al. 2009), TW
λ4	Decay rate of tumor cell associated proteinase	1.67 × 10 −5 s–1	(Kim et al. 2009), TW
λ5	Fibroblast-secreted proteinase production rate	3.15 × 10−9 gcm−3 s−1	TW
λ6	Decay rate of fibroblast-secreted proteinase	1.67 × 10−5 s−1	(Kim et al. 2009), TW
Reference values
ρ*	ECM	1.0 × 10−3 g/cm3	(Kaufman et al. 2005)
$P_t^{*}$	Tumor-associated proteinase	1.0 × 10−7 g/cm3	(Annabi et al. 2005)
$P_S^{*}$	Fibroblast-secreted proteinase (FSP)	1.0 × 10−7 g/cm3	TW
$P_S^{*,\text{th}}$	Threshold for activation of TECs by FSP	2.0 × 10−8 g/cm3	TW