Table 6.

Dimensionless Constants.

Dimensionless Constant	Biological Representation	Scaling Factors*	Value Assigned
${\stackrel{\mathbf{\sim }}{\mathit{\epsilon }}}_{\mathit{T}}$	Interaction strength for tumor cells	$\overline{\overline{\epsilon }}$	0.05
${\stackrel{\mathbf{\sim }}{\mathit{\epsilon }}}_{\mathit{E}}$	Interaction strength for ECM	$\overline{\overline{\epsilon }}$	0.05
${\stackrel{\mathbf{\sim }}{\mathit{\epsilon }}}_{\mathit{T}\mathit{E}}$	Interaction strength between tumor cells and ECM	$\overline{\overline{\epsilon }}$	0.02
${\stackrel{\mathbf{\sim }}{\mathit{\epsilon }}}_{\mathit{e}}$	Strain energy coefficient	${\overline{\overline{\epsilon }}}_e$	0.001
${\stackrel{\mathbf{\sim }}{\mathit{n}}}_{\mathit{h}}$	Hypoxic level of O2	n∞	0.3
${\stackrel{\mathbf{\sim }}{\mathit{n}}}_{\mathit{C}}$	O2 level in capillaries	n∞	1.0
${\stackrel{\mathbf{\sim }}{\mathit{g}}}_{\mathit{C}}$	Glucose level in capillaries	g∞	1.0
${\stackrel{\mathbf{\sim }}{\mathit{w}}}_{\mathit{C}}$	CO2 level in capillaries	n∞	0.0
${\stackrel{\sim }{\ell }}_{\mathit{C}}$	Lactate level in capillaries	n∞	0.0
${\stackrel{\mathbf{\sim }}{\mathit{n}}}_{\mathit{v}\mathbf{,}\mathit{V}}$	O2 viability limit of viable tumor cells	n∞	0.21
${\stackrel{\mathbf{\sim }}{\mathit{n}}}_{\mathit{v}\mathbf{,}\mathit{B}}$	O2 viability limit of ECs	n∞	0.1
${\stackrel{\mathbf{\sim }}{\mathit{n}}}_{\mathit{v}\mathbf{,}\mathit{L}}$	O2 viability limit of LECs	n∞	0.1
${\stackrel{\mathbf{\sim }}{\mathit{n}}}_{\mathit{v}\mathbf{,}\mathit{F}}$	O2 viability limit of MFCs	n∞	0.21
${\stackrel{\mathbf{\sim }}{\mathit{a}}}_{\mathit{v}\mathbf{,}\mathit{V}}$	H+ viability limit of viable tumor cells	n∞	0.7
${\stackrel{\mathbf{\sim }}{\mathit{a}}}_{\mathit{v}\mathbf{,}\mathit{F}}$	H+ viability limit of MFCs	n∞	0.7
${\stackrel{\mathbf{\sim }}{\mathit{g}}}_{\mathit{v}\mathbf{,}\mathit{V}}$	Glucose viability limit of viable tumor cells	g∞	0.1
${\stackrel{\mathbf{\sim }}{\mathit{g}}}_{\mathit{v}\mathbf{,}\mathit{F}}$	Glucose viability limit of myofibroblast-like cells	g∞	0.1
${\stackrel{\mathbf{\sim }}{\mathit{g}}}_{\mathit{d}\mathit{e}\mathbf{,}\mathit{V}}$	Threshold level of glucose leading to the onset of autophagy for viable tumor cells	g∞	0.3
${\stackrel{\sim }{\ell }}_{\mathit{s}\mathit{a}\mathit{t}}$	Saturation level of lactate in tissues	n∞	1.0
${\stackrel{\sim }{\ell }}_{\mathit{t}\mathit{g}\mathit{f}}$	Threshold lactate level for tgf upregulation	n∞	0.8
${\stackrel{\sim }{\ell }}_{\mathit{t}\mathit{a}\mathit{f}}$	Threshold lactate level for taf upregulation	n∞	0.8
${\stackrel{\mathbf{\sim }}{\mathit{z}}}_{\ell }$	Charge of a lactate ion	za	−1.0
${\stackrel{\mathbf{\sim }}{\mathit{z}}}_{\mathit{b}}$	Charge of a bicarbonate ion	za	−1.0
${\stackrel{\mathbf{\sim }}{\mathit{z}}}_{\mathit{s}}$	Charge of Na+	za	1.0
${\stackrel{\mathbf{\sim }}{\mathit{z}}}_{\mathit{r}}$	Charge of Cl−	za	−1.0
${\stackrel{\sim }{\mathit{t}\mathit{g}\mathit{f}}}_{\mathit{F}\mathit{E}}$	Threshold level of corresponding to the onset of the upregulation of myofibroblastic cell proliferation	tgfsat	0.1
${\stackrel{\sim }{\mathit{t}\mathit{a}\mathit{f}}}_{\mathit{B}\mathit{n}}$	Threshold level of taf corresponding to the onset of EC proliferation	tafsat	0.2
${\stackrel{\sim }{\mathit{t}\mathit{a}\mathit{f}}}_{\mathit{L}\mathit{n}}$	Threshold level of corresponding to the onset of LEC proliferation	tafsat	0.2
${({\stackrel{\mathbf{\sim }}{\mathit{\epsilon }}}_{\mathit{E}}^{\ast })}_{\mathit{i}\mathit{j}}$	Eigenstrain for the ECM component	$\overline{\overline{\epsilon }}$	1.0
${({\stackrel{\mathbf{\sim }}{\mathit{\epsilon }}}_{\mathit{C}}^{\ast })}_{\mathit{i}\mathit{j}}$	Eigenstrain for the cell components	$\overline{\overline{\epsilon }}$	0.0
${\stackrel{\mathbf{\sim }}{\mathit{L}}}_1^{\mathit{E}}$	Lamé constants for ECM component	$L_2^E$	1.0
${\stackrel{\mathbf{\sim }}{\mathit{L}}}_1^{\mathit{C}}$	Lamé constants for cell components	$L_2^E$	1.0
${\stackrel{\mathbf{\sim }}{\mathit{L}}}_2^{\mathit{C}}$	Lamé constants for cell components	$L_2^E$	1.0
${({\stackrel{\sim }{\varphi }}_{\mathit{E}})}_{\mathit{m}\mathit{i}\mathit{n}\mathbf{,}\mathit{B}\mathit{n}}$	Concentration of ECM macromolecules corresponding to the minimum EC haptotaxis strength	${\stackrel{\sim }{\varphi }}_{\alpha }$	0.2
${({\stackrel{\sim }{\varphi }}_{\mathit{E}})}_{\mathit{m}\mathit{a}\mathit{x}\mathbf{,}\mathit{B}\mathit{n}}$	Concentration of ECM macromolecules corresponding to the maximum EC haptotaxis strength	${\stackrel{\sim }{\varphi }}_{\alpha }$	0.8
${({\stackrel{\sim }{\varphi }}_{\mathit{E}})}_{\mathit{m}\mathit{i}\mathit{n}\mathbf{,}\mathit{L}\mathit{n}}$	Concentration of ECM macromolecules corresponding to the minimum LEC haptotaxis strength	${\stackrel{\sim }{\varphi }}_{\alpha }$	0.2
${({\stackrel{\sim }{\varphi }}_{\mathit{E}})}_{\mathit{m}\mathit{a}\mathit{x}\mathbf{,}\mathit{L}\mathit{n}}$	Concentration of ECM macromolecules corresponding to the maximum LEC haptotaxis strength	${\stackrel{\sim }{\varphi }}_{\alpha }$	0.8
${\stackrel{\mathbf{\sim }}{\mathit{k}}}_{\mathit{c}\mathit{h}\mathit{e}\mathbf{,}\mathit{B}\mathit{n}\mathit{E}}$	Positive chemotaxis constant for ECs	tafsat	1.0
${\stackrel{\mathbf{\sim }}{\mathit{k}}}_{\mathit{c}\mathit{h}\mathit{e}\mathbf{,}\mathit{L}\mathit{n}\mathit{E}}$	Positive chemotaxis constant for LECs	tafsat	1.0
${\stackrel{\mathbf{\sim }}{\mathit{p}}}_{\mathit{t}\mathbf{,}\mathit{B}}$	Threshold pressure corresponding to the onset of blood vessel loss	$\mathcal{P}$	0.6
${\stackrel{\mathbf{\sim }}{\mathit{p}}}_{\mathit{t}\mathbf{,}\mathit{L}}$	Threshold pressure corresponding to the onset of lymphatic vessel loss	$\mathcal{P}$	0.6
${\stackrel{\mathbf{\sim }}{\mathit{p}}}_{\mathit{c}\mathbf{,}\mathit{B}\mathit{n}}$	Threshold pressure corresponding to the maximum rate of neo-blood vessel loss	$\mathcal{P}$	0.8
${\stackrel{\mathbf{\sim }}{\mathit{p}}}_{\mathit{c}\mathbf{,}\mathit{L}\mathit{n}}$	Threshold pressure corresponding to the maximum rate of neo-lymphatic vessel loss	$\mathcal{P}$	0.8

^*For example, ${\stackrel{\sim }{n}}_h=n_h/n_{\infty }$.

Nondimensionalized Eigenstrain ${({\stackrel{\sim }{\epsilon }}_E^{\ast })}_{ij}$ and all Lamé constants are set to 1 as an initial value in this study. A wider range of values will be tested and analyzed in future work.