Rapidly acting antitumoral antiangiogenic therapies

We deal with a biophysical description of antitumor antiangiogenic therapies. In particular, by means of some simple models, we study the possible effects of the delay between the drug consumption by endothelial cells and their death on the outcome of the therapy. We have found that this time lag implies an increase in the minimal dose guaranteeing tumor eradication and, if the delay is greater than a meaningful threshold, it may preclude the total regression. These results might be of interest in better understanding the causes underlying the contradictory literature on the clinical trials of antiangiogenic therapies.

Figure 1

Simulations of the time course of the tumor volume under boli-based therapy with $q<b$ and increasing values of the dose (from top to bottom, $D=20,40,80,160,320,640,1280\mathrm{mg}∕\mathrm{kg}$). Simulated drug: endostatin, $c=1.7{\text{day}}^{-1}$. Tumor volume $V$ $\left({\mathrm{mm}}^3\right)$, time $t$ (days). $F\left(u\right)=\alpha \ln \left(u\right)$, $\alpha =0.192{\text{day}}^{-1}$, $T=2\text{days}$, $b=5.85{\text{day}}^{-1}$, $d=0.00873{\text{day}}^{-1}{\mathrm{mm}}^{-2}$, $\eta =0.66{\text{day}}^{-1}\mathrm{kg}∕\mathrm{mg}$.

Figure 2

Simulations of the time course of the tumor volume under boli-based therapy with angiostatin ($c=0.38{\text{day}}^{-1}$, $\eta =0.66{\text{day}}^{-1}\mathrm{kg}∕\mathrm{mg}$) with $q=3b>b$ and two values of the dose: $D=42\mathrm{mg}∕\mathrm{kg}<D_{\mathit{min}}^{\mathit{\text{Boli}}}$ (upper curve: no eradication) and $D=43\mathrm{mg}∕\mathrm{kg}>D_{\mathit{min}}^{\mathit{\text{Boli}}}$ (lower curve: eradication). Other parameters values as in Fig. 1. Tumor volume $V$ $\left({\mathrm{mm}}^3\right)$, time $t$ (days).