. Author manuscript; available in PMC: 2018 Oct 7.

Published in final edited form as: J Theor Biol. 2017 May 18;430:245–282. doi: 10.1016/j.jtbi.2017.05.013

Table 3.

Dimensionless Diffusivities.

Dimensionless Parameter

Biological Representation

Scaling Factor^*

Value Assigned

{\tilde{D}}_{n}

Effective diffusivity of O₂

D_n,T

computed

{\tilde{D}}_{n, E}

Diffusivity of O₂ through ECM regions

D_n,T

1.0

{\tilde{D}}_{n, T}

Diffusivity of O₂ through tumor regions

D_n,T

1.0

{\tilde{D}}_{n, H}

Diffusivity of O₂ through host regions

D_n,T

1.0

{\tilde{D}}_{g}

Effective diffusivity of glucose

D_n,T

computed

{\tilde{D}}_{g, E}

Diffusivity of glucose through ECM regions

D_n,T

1.0

{\tilde{D}}_{g, T}

Diffusivity of glucose through tumor regions

D_n,T

1.0

{\tilde{D}}_{g, H}

Diffusivity of glucose through host regions

D_n,T

1.0

{\tilde{D}}_{w}

Effective diffusivity of CO₂

D_n,T

computed

{\tilde{D}}_{w, E}

Diffusivity of CO₂ through ECM regions

D_n,T

1.0

{\tilde{D}}_{w, T}

Diffusivity of CO₂ through tumor regions

D_n,T

1.0

{\tilde{D}}_{w, H}

Diffusivity of CO₂ through host regions

D_n,T

1.0

{\tilde{D}}_{ℓ}

Effective diffusivity of lactate

D_n,T

computed

{\tilde{D}}_{ℓ, E}

Diffusivity of lactate through ECM regions

D_n,T

1.0

{\tilde{D}}_{ℓ, T}

Diffusivity of lactate through tumor regions

D_n,T

1.0

{\tilde{D}}_{ℓ, H}

Diffusivity of lactate through host regions

D_n,T

1.0

{\tilde{D}}_{b}

Effective diffusivity of bicarbonate

D_n,T

computed

{\tilde{D}}_{b, E}

Diffusivity of bicarbonate through ECM regions

D_n,T

1.0

{\tilde{D}}_{b, Τ}

Diffusivity of bicarbonate through tumor regions

D_n,T

1.0

{\tilde{D}}_{b, H}

Diffusivity of bicarbonate through host regions

D_n,T

1.0

{\tilde{D}}_{a}

Effective diffusivity of H⁺ ions

D_n,T

computed

{\tilde{D}}_{a, E}

Diffusivity of H⁺ through ECM regions

D_n,T

1.0

{\tilde{D}}_{a, T}

Diffusivity of H⁺ ions through tumor regions

D_n,T

1.0

{\tilde{D}}_{a, H}

Diffusivity of H⁺ ions through host regions

D_n,T

1.0

{\tilde{D}}_{s}

Effective diffusivity of Na⁺ ions

D_n,T

computed

{\tilde{D}}_{s, E}

Diffusivity of Na⁺ through ECM regions

D_n,T

1.0

{\tilde{D}}_{s, T}

Diffusivity of Na⁺ ions through tumor regions

D_n,T

1.0

{\tilde{D}}_{s, H}

Diffusivity of Na+ ions through host regions

D_n,T

1.0

{\tilde{D}}_{r}

Effective diffusivity of Cl⁻ ions

D_n,T

computed

{\tilde{D}}_{r, E}

Diffusivity of Cl⁻ through ECM regions

D_n,T

1.0

{\tilde{D}}_{r, T}

Diffusivity of Cl⁻ ions through tumor regions

D_n,T

1.0

{\tilde{D}}_{r, H}

Diffusivity of CE ions through host regions

D_n,T

1.0

{\tilde{D}}_{t g f}

Effective diffusivity of TGFs

D_n,T

computed

{\tilde{D}}_{t g f, E}

Diffusivity of TGFs through ECM regions

D_n,T

1.0

{\tilde{D}}_{t g f, T}

Diffusivity of TGFs through tumor regions

D_n,T

1.0

{\tilde{D}}_{t g f, H}

Diffusivity of TGFs through host regions

D_n,T

1.0

{\tilde{D}}_{t a f}

Effective diffusivity of TAFs

D_n,T

computed

{\tilde{D}}_{t a f, E}

Diffusivity of TAFs through ECM regions

D_n,T

1.0

{\tilde{D}}_{t a f, T}

Diffusivity of TAFs through tumor regions

D_n,T

1.0

{\tilde{D}}_{t a f, H}

Diffusivity of TAFs through host regions

D_n,T

1.0

{\tilde{D}}_{m}

Effective diffusivity of MDEs

ℒ^{2} / T

computed

{\tilde{D}}_{m, E}

Diffusivity of MDEs through ECM regions

ℒ^{2} / T

0.05

{\tilde{D}}_{m, T}

Diffusivity of MDEs through tumor regions

ℒ^{2} / T

0.01

{\tilde{D}}_{m, H}

Diffusivity of MDEs through host regions

ℒ^{2} / T

0.01

{\tilde{D}}_{F}

Effective diffusivity of Myofibroblastic cells (MFC)

{\bar{\bar{D}}}_{F}

computed

{\tilde{D}}_{F, E}

Diffusivity of MFCs through ECM regions

{\bar{\bar{D}}}_{F}

1.0

{\tilde{D}}_{F, T}

Diffusivity of MFCs through tumor regions

{\bar{\bar{D}}}_{F}

0.0

{\tilde{D}}_{F, H}

Diffusivity of MFCs through host regions

{\bar{\bar{D}}}_{F}

0.0

{\tilde{D}}_{B n E}

Effective diffusivity of ECS

ℒ^{2} / T

computed

{\tilde{D}}_{B n E, E}

Diffusivity of ECs through ECM regions

ℒ^{2} / T

1.0

{\tilde{D}}_{B n E, T}

Diffusivity of ECs through tumor regions

ℒ^{2} / T

0.0

{\tilde{D}}_{B n E, H}

Diffusivity of ECs through host regions

ℒ^{2} / T

0.0

{\tilde{D}}_{L n E}

Effective diffusivity of LECs

ℒ^{2} / T

computed

{\tilde{D}}_{L n E, E}

Diffusivity of LECs through ECM regions

ℒ^{2} / T

1.0

{\tilde{D}}_{L n E, T}

Diffusivity of LECs through tumor regions

ℒ^{2} / T

0.0

{\tilde{D}}_{L n E, H}

Diffusivity of LECs through host regions

ℒ^{2} / T

0.0

For example, ${\tilde{D}}_{n} = D_{n} / D_{n, T}$

Most diffusivities are assumed to be on the same order of magnitude as D_n,T, hence the nondimensionalized values are set to 1. A wider range of values will be tested and analyzed in future work.