Discrete Antiangiogenic Therapy for Cancer
by Mike Martin
On this page, you can vary the parameters in a model for continuous dosing of antiangiogenic drug for an established tumor. Submit real values for all of the parameters to obtain graphical solutions of the system as functions of time and in the phase plane. A numeric solution on the interval [0, T] is produced using Mathematica's numerical ODE solver, NDSolve. A constant dosing is administered over an interval of length m and then their is no treatment for an interval of length m. Tstop is the maximum time value when treatment is discontinued. D is the dosage strength. Initial values for both the tumor volume, V, and vasculature volume, K, must be input. Also, a variety of model parameters must be input which are detailed below the model. The first plot is that of the dosage or treatment; that is, a plot of g (t). The second plot is that of the response -- the volume of the tumor (in purple) and the volume of the tumor's vasculature (in red). The last plot is the phase plane with the vasculature volume on the x-axis and the tumor volume on the y-axis. Note that since the system explicitly involves time, the trajectory in the phase plane can intersect with itself.
The model equations are:
Enter in the value of the parameters and select the plotting bounds, then press the "Plot" button.
Hahnfeldt, P., D. Panigrahy, J. Folkman and L. Hlatky, Tumor Development Under Angiogenic Signaling: A Dynamical Theory of Tumor Growth, Treatment Response, and Postvascular Dormancy, Cancer Research, 59, (1999), pp. 4770-4775