Table 3 Summary of the equations used for the numerical simulation depicted in Figs. 2 and 3
From: Proposal of a hybrid approach for tumor progression and tumor-induced angiogenesis
Variable | Equation |
|---|---|
Proliferative tumor cells density | P t +∇·(vP)=Γ P+f QP Q−(f PQ +f PN )P |
Quiescent cells density | Q t +∇·(vQ)=f PQ P−(f QP +f QN )Q |
Necrotic tumor cells density | N t +∇·(vN)=f PN P+f QN Q |
Host cells density | S t +∇·(vS)=0 |
Endothelial cells density | ρ t +∇·(vρ)+∇·(g CH )=f ρ ρ ρ |
[O 2] | C t −∇·(D C ∇C)=−g C +h C |
[V E G F] | α t −∇·(D α ∇α)=−g α +h α |
Advection velocity | v=−k∇φ |
Pressure | −∇·(k∇φ)=Γ P+f ρ ρ ρ−∇·(g CH ) |