Table 2.

Dimensionless Dependent Variables.

Dimensionless Dependent Variable	Biological Representation	Scaling Factor (e.g. ${\varphi }_V=\frac{{\stackrel{\sim }{\varphi }}_V}{{\stackrel{\sim }{\varphi }}_{\alpha }}$)
${\stackrel{\sim }{\varphi }}_{\mathit{V}}$	Viable tumor cells	${\stackrel{\sim }{\varphi }}_{\alpha }$ (fixed solid volume fraction)
${\stackrel{\sim }{\varphi }}_{\mathit{D}}$	Dead tumor cells	${\stackrel{\sim }{\varphi }}_{\alpha }$
${\stackrel{\sim }{\varphi }}_{\mathit{E}}$	Extracellular Matrix	${\stackrel{\sim }{\varphi }}_{\alpha }$
${\stackrel{\sim }{\varphi }}_{\mathit{H}}$	Healthy host cells	${\stackrel{\sim }{\varphi }}_{\alpha }$
$\stackrel{\mathbf{\sim }}{\mathit{n}}$	Oxygen	${\stackrel{\sim }{n}}_{\infty }$
$\stackrel{\mathbf{\sim }}{\mathit{g}}$	Glucose	${\stackrel{\sim }{g}}_{\infty }$
$\stackrel{\mathbf{\sim }}{\mathit{w}}$	Carbon dioxide	${\stackrel{\sim }{n}}_{\infty }$
$\stackrel{\sim }{\ell }$	Lactate	${\stackrel{\sim }{n}}_{\infty }$
$\stackrel{\mathbf{\sim }}{\mathit{b}}$	Bicarbonate	${\stackrel{\sim }{n}}_{\infty }$
$\stackrel{\mathbf{\sim }}{\mathit{a}}$	Hydrogen ion	${\stackrel{\sim }{n}}_{\infty }$
$\stackrel{\mathbf{\sim }}{\mathit{s}}$	Sodium ion	${\stackrel{\sim }{n}}_{\infty }$
$\stackrel{\sim }{r}$	Chloride ion	${\stackrel{\sim }{n}}_{\infty }$
$\stackrel{\sim }{\mathit{t}\mathit{g}\mathit{f}}$	Tumor growth factors	$tg{f}_{\mathit{sat}}$
$\stackrel{\sim }{\mathit{t}\mathit{a}\mathit{f}}$	Tumor angiogenic factors	$ta{f}_{\mathit{sat}}$
$\stackrel{\mathbf{\sim }}{\mathit{m}}$	MDEs	$m_{\mathit{sat}}$
$\stackrel{\mathbf{\sim }}{\mathit{F}}$	Myofibroblastic cells	$F_{\mathit{max}}$
${\stackrel{\mathbf{\sim }}{\mathit{B}}}_{\mathit{N}}^{\mathit{E}}$	New blood vessels	$B_{\mathit{max}}$
${\stackrel{\mathbf{\sim }}{\mathit{L}}}_{\mathit{n}}^{\mathit{E}}$	New lymphatic vessels	$L_{\mathit{max}}$
${\stackrel{\mathbf{\sim }}{\mathit{\mu }}}_{\mathit{T}}$	Tumor cell potential	$E_a^{\ast }$
${\stackrel{\mathbf{\sim }}{\mathit{\mu }}}_{\mathit{E}}$	Extracellular matrix potential	$E_a^{\ast }$
${\stackrel{\mathbf{\sim }}{\mathit{\mu }}}_{\mathit{H}}$	Healthy host cell potential	$E_a^{\ast }$
$\stackrel{\mathbf{\sim }}{\mathit{p}}$	Solid phase tumor cell pressure	$\mathcal{P}$
$\stackrel{\mathbf{\sim }}{\mathit{q}}$	Interstitial fluid phase pressure	$\mathcal{Q}$
${\stackrel{\mathbf{\sim }}{\mathit{u}}}_{\mathit{\beta }}$	Interstitial fluid velocity	$ℒ/\mathcal{T}$
${\stackrel{\mathbf{\sim }}{\mathit{u}}}_{\mathit{\alpha }}$	Solid cell velocity	$ℒ/\mathcal{T}$