Table 1:

Mass transfer terms for vascular tumor growth

Entity	Symbol	Term
Extracellular matrix	${\sum }_{\kappa \in {\mathcal{J}}_{\text{c}s}}\stackrel{\kappa \to s}{M}$	= 0
Healthy cells	${\sum }_{\kappa \in {\mathcal{J}}_{\text{c}h}}\stackrel{\kappa \to h}{M}$	= 0
Tumor cells	${\sum }_{\kappa \in {\mathcal{J}}_{\text{c}l}}\stackrel{\kappa \to t}{M}$	= ${\stackrel{l\to t}{M}}_{\text{growth}}$
Interstitial fluid	${\sum }_{\kappa \in {\mathcal{J}}_{\text{c}l}}\stackrel{\kappa \to l}{M}$	= ${\stackrel{l\to t}{M}}_{\text{growth}}+{\stackrel{v\to l}{M}}_{\text{leak}}-{\stackrel{l\to ly}{M}}_{\text{drainage}}$
Necrotic tumor cells	${\sum }_{\kappa \in {\mathcal{J}}_{\text{c}t}}\stackrel{N\kappa \to Nt}{M}+{\epsilon }^t{r}^{Nt}-{\omega }^{N\overline{t}}{\sum }_{\kappa \in {\mathcal{J}}_{\text{c}t}}\stackrel{\kappa \to t}{M}$	= ${\epsilon }^t{r}^{Nt}-{\omega }^{N\overline{t}}{\stackrel{l\to t}{M}}_{\text{growth}}$
Oxygen	${\sum }_{\kappa \in {\mathcal{J}}_{\text{c}l}}\stackrel{n\kappa \to nl}{M}+{\epsilon }^l{r}^{nl}-{\omega }^{n\overline{l}}{\sum }_{\kappa \in {\mathcal{J}}_{\text{c}l}}\stackrel{\kappa \to l}{M}$	= $\stackrel{nl\to t}{M}+\stackrel{nv\to nl}{M_{\text{tc}}}-{\omega }^{n\overline{l}}\left({\stackrel{v\to l}{M}}_{\text{leak}}-{\stackrel{l\to t}{M}}_{\text{growth}}\right)$
Tumor angiogenic factors	${\sum }_{\kappa \in {\mathcal{J}}_{\text{c}l}}\stackrel{TAF\kappa \to TAFl}{M}+{\epsilon }^l{r}^{TAFl}-{\omega }^{TAF\overline{l}}{\sum }_{\kappa \in {\mathcal{J}}_{\text{c}l}}\stackrel{\kappa \to l}{M}$	= $\stackrel{TAFt\to TAFl}{M}-{\omega }^{TAF\overline{l}}\left({\stackrel{v\to l}{M}}_{\text{leak}}-{\stackrel{l\to t}{M}}_{\text{growth}}\right)$