Table 4.

Dimensionless Rate Constants.

Dimensionless Parameter	Biological Representation	Scaling Factor *	Value Assigned
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{M}\mathbf{,}\mathit{V}}$	Mitosis rate constant of viable tumor cells	λM,V	1.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{A}\mathbf{,}\mathit{V}}$	Apoptosis rate constant of viable tumor cells	λM,V	0.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{N}\mathbf{,}\mathit{V}}$	Necrosis rate constant of viable tumor cells	λM,V	3.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{B}\mathbf{,}\mathit{V}}$	Metastasis rate constant of viable tumor cells via blood vessels	λM,V	0.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{L}\mathbf{,}\mathit{V}}$	Metastasis rate constant of viable tumor cells via lymphatic vessels	λM,V	0.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{d}\mathit{e}\mathbf{,}\mathit{V}}$	Autophagy rate constant of viable tumor cells	λM,V	0.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{L}\mathbf{,}\mathit{D}}$	Lysis rate constant of dead tumor cells	λM,V	1.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{V}\mathbf{,}\mathit{E}}$	ECM rate of secretion by tumor viable cells	λM,V	0.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{B}\mathbf{,}\mathit{E}}$	ECM rate of secretion by ECs	${\stackrel{\sim }{\varphi }}_{\alpha }{\lambda }_{M,V}/B_{max}$	0.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{L}\mathbf{,}\mathit{E}}$	ECM rate of secretion by LECs	${\stackrel{\sim }{\varphi }}_{\alpha }{\lambda }_{M,V}/L_{max}$	0.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{F}\mathbf{,}\mathit{E}}$	ECM rate of secretion by myofibroblastic cells	${\stackrel{\sim }{\varphi }}_{\alpha }{\lambda }_{M,V}/F_{max}$	5.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{d}\mathit{e}\mathbf{,}\mathit{E}}$	Degradation rate of ECM	λM,V	1.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{d}\mathit{e}\mathbf{,}\mathit{C}}$	Degradation rate of ECM macromolecules catalyzed by MDEs	${\lambda }_{M,V}{\stackrel{\sim }{\varphi }}_{\alpha }{C}_E$	5.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{B}\mathbf{,}\mathit{n}}$	Apparent transfer coefficient of O2 via capillary network	λU,V,n	computed
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{B}\mathbf{,}\mathit{n}\mathbf{,}\mathit{E}}$	Transfer coefficient of O2 via capillary network in ECM regions	λU,V,n	0.1
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{B}\mathbf{,}\mathit{n}\mathbf{,}\mathit{T}}$	Transfer coefficient of O2 via capillary network in tumor regions	λU,V,n	0.001
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{B}\mathbf{,}\mathit{n}\mathbf{,}\mathit{H}}$	Transfer coefficient of O2 via capillary network in host regions	λU,V,n	0.01
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{U}\mathbf{,}\mathit{V}\mathbf{,}\mathit{n}}$	Uptake rate constant of O2 by viable tumor cells	λU,V,n	1.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{U}\mathbf{,}\mathit{H}\mathbf{,}\mathit{n}}$	Uptake rate constant of O2 by healthy host cells	λU,V,n	0.0001
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{B}\mathbf{,}\mathit{g}}$	Apparent transfer coefficient of glucose via capillary network	λU,V,n	computed
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{B}\mathbf{,}\mathit{g}\mathbf{,}\mathit{E}}$	Transfer coefficient of glucose via capillary network in ECM regions	λU,V,n	0.1
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{B}\mathbf{,}\mathit{g}\mathbf{,}\mathit{T}}$	Transfer coefficient of glucose via capillary network in tumor regions	λU,V,n	0.001
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{B}\mathbf{,}\mathit{g}\mathbf{,}\mathit{H}}$	Transfer coefficient of glucose via capillary network in host regions	λU,V,n	0.01
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{U}\mathbf{,}\mathit{V}\mathbf{,}\mathit{g}}$	Uptake rate constant of glucose by viable tumor cells	λU,V,n	1.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{U}\mathbf{,}\mathit{H}\mathbf{,}\mathit{g}}$	Uptake rate constant of glucose by healthy host cells	λU,V,n	0.0001
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{B},\mathit{w}}$	Apparent transfer coefficient of CO2 via capillary network	λU,V,n	computed
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{B},\mathit{w}\mathbf{,}\mathit{E}}$	Transfer coefficient of CO2 via capillary network in ECM regions	λU,V,n	1.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{B},\mathit{w}\mathbf{,}\mathit{T}}$	Transfer coefficient of CO2 via capillary network in tumor regions	λU,V,n	1.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{B},\mathit{w}\mathbf{,}\mathit{H}}$	Transfer coefficient of CO2 via capillary network in host regions	λU,V,n	1.0
${\stackrel{\mathbf{\sim }}{\mathit{k}}}_{\mathit{f}}$	Forward reaction rate of the dissolution of CO2 and H2O	λU,V,n	1.0
${\stackrel{\mathbf{\sim }}{\mathit{k}}}_{\mathit{r}}$	Backward reaction rate of the dissolution of CO2 and H2O	λU,V,n/n∞	1.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{B}\mathbf{,}\ell }$	Apparent transfer coefficient of lactate via capillary network	λU,V,n	computed
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{B}\mathbf{,}\ell \mathbf{,}\mathit{E}}$	Transfer coefficient of lactate via capillary network in ECM regions	λU,V,n	1.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{B}\mathbf{,}\ell \mathbf{,}\mathit{T}}$	Transfer coefficient of lactate via capillary network in tumor regions	λU,V,n	0.1
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{B}\mathbf{,}\ell \mathbf{,}\mathit{H}}$	Transfer coefficient of lactate via capillary network in host regions	λU,V,n	0.5
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{V}\mathbf{,}\mathit{t}\mathit{g}\mathit{f}}$	Production rate constant of TGFs by viable tumor cells	λU,V,n	0.2
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{B}\mathbf{,}\mathit{t}\mathit{g}\mathit{f}}$	Production rate constant of TGFs by ECs	λU,V,n	0.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{L}\mathbf{,}\mathit{t}\mathit{g}\mathit{f}}$	Production rate constant of TGFs by LECs	λU,V,n	0.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{F}\mathbf{,}\mathit{t}\mathit{g}\mathit{f}}$	Production rate constant of TGFs by MFCs	λU,V,n	0.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{d}\mathit{e}\mathbf{,}\mathit{t}\mathit{g}\mathit{f}}$	Degradation rate constant of TGFs	λU,V,n	0.05
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{U}\mathbf{,}\mathit{V}\mathbf{,}\mathit{t}\mathit{g}\mathit{f}}$	Uptake rate constant of TGFs by viable tumor cells	λU,V,n	0.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{V}\mathbf{,}\mathit{t}\mathit{a}\mathit{f}}$	Production rate constant of TAFs by viable tumor cells	λU,V,n	0.2
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{B}\mathbf{,}\mathit{t}\mathit{a}\mathit{f}}$	Production rate constant of TAFs by ECs	λU,V,n	0.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{L}\mathbf{,}\mathit{t}\mathit{a}\mathit{f}}$	Production rate constant of TAFs by LECs	λU,V,n	0.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{F}\mathbf{,}\mathit{t}\mathit{a}\mathit{f}}$	Production rate constant of TAFs by MFCs	λU,V,n	0.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{d}\mathit{e}\mathbf{,}\mathit{t}\mathit{a}\mathit{f}}$	Degradation rate constant of TAFs	λU,V,n	0.05
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{U}\mathbf{,}\mathit{B}\mathbf{,}\mathit{t}\mathit{a}\mathit{f}}$	Uptake rate constant of TAFs by proliferating ECs	λU,V,n/Bmax	0.0011574
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{U}\mathbf{,}\mathit{L}\mathbf{,}\mathit{t}\mathit{a}\mathit{f}}$	Uptake rate constant of TAFs by proliferating LECs	λU,V,n/Lmax	0.0011574
${\stackrel{\mathbf{\sim }}{\mathit{k}}}_{\mathit{c}\mathit{a}\mathit{t}\mathbf{,}\mathit{B}}$	Rate constant for the loss of TAFs to the production of MDEs by proliferating ECs	$\frac{{\lambda }_{U,V,n}ta{f}_{\mathit{sat}}}{B_{max}}$	1.0
${\stackrel{\mathbf{\sim }}{\mathit{k}}}_{\mathit{c}\mathit{a}\mathit{t}\mathbf{,}\mathit{L}}$	Rate constant for the loss of TAFs to the production of MDEs by proliferating LECs	$\frac{{\lambda }_{U,V,n}ta{f}_{\mathit{sat}}}{L_{max}}$	1.0
${\stackrel{\mathbf{\sim }}{\mathit{k}}}_{\mathit{m}\mathbf{,}\mathit{B}}$	Michaelis constant for the uptake of TAF by proliferating ECs	tafsat	1.0
${\stackrel{\mathbf{\sim }}{\mathit{k}}}_{\mathit{m}\mathbf{,}\mathit{L}}$	Michaelis constant for the uptake of TAF by proliferating LECs	tafsat	1.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{V}\mathbf{,}\mathit{m}}$	Production rate constant of MDEs by viable tumor cells	λM,V	0.2
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{F}\mathbf{,}\mathit{m}}$	Production rate constant of MDEs by MFCs	λM,V	0.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{d}\mathit{e}\mathbf{,}\mathit{m}}$	Decay rate constant of MDEs	λM,V	5.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{M}\mathbf{,}\mathit{F}\mathit{E}}$	Mitosis rate constant of MFCs	λM,V	0.1
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{A}\mathbf{,}\mathit{F}\mathit{E}}$	Apoptosis rate constant of MFCs	λM,V	0.1
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{N}\mathbf{,}\mathit{F}\mathit{E}}$	Necrosis rate constant of MFCs	λM,V	0.3
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{m}\mathbf{,}\mathit{B}\mathit{n}\mathit{E}}$	Maximum mitosis rate constant of ECs	λM,V	1.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{c}\mathit{r}\mathit{u}\mathit{s}\mathit{h}\mathbf{,}\mathit{B}\mathit{n}\mathit{E}}$	Maximum degradation rate constant of new blood vessels due to cell pressure	λM,V	1.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{d}\mathit{e}\mathbf{,}\mathit{B}\mathit{n}\mathit{E}}$	Remodeling rate constant of new blood vessels by MDEs	λM,V/msat	1.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{a}\mathit{s}\mathbf{,}\mathit{B}\mathit{n}\mathit{E}}$	Anastomosis rate constant (periodic) of the new blood vessels	λM,V	0.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{m}\mathbf{,}\mathit{L}\mathit{n}\mathit{E}}$	Maximum mitosis rate constant of LECs	λM,V	1.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{c}\mathit{r}\mathit{u}\mathit{s}\mathit{h}\mathbf{,}\mathit{L}\mathit{n}\mathit{E}}$	Maximum degradation rate constant of new lymphatic vessels due to cell pressure	λM,V	1.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{d}\mathit{e}\mathbf{,}\mathit{L}\mathit{n}\mathit{E}}$	Remodeling rate constant of new lymphatic vessels by MDEs	λM,V	1.0
${\stackrel{\mathbf{\sim }}{\mathbf{\lambda }}}_{\mathit{a}\mathit{s}\mathbf{,}\mathit{L}\mathit{n}\mathit{E}}$	Anastomosis rate constant (periodic) of the new lymphatic vessels	λM,V	0.0

^*For example, ${\stackrel{\sim }{\lambda }}_{N,V}={\lambda }_{N,V}/{\lambda }_{M,V}$.