Backstepping Based Automatically Controlled Angiogenic Inhibition Therapy

In this work, we present an automatically controlled angiogenic inhibition therapy where the variation profile of the inhibitory agent is generated by a control law that is derived using a back-stepping based control methodology. The angiogenic inhibition is described by a second order model representing the dynamics of tumor and supporting vasculature volumes. Backstepping control recursively stabilizes that dynamics and generates automatic control laws that allows the tumor volume to stay at a desired value. The desired value will be kept at one thousandth of its initial value. This will lead to a very small injection at the steady state. This is important as zero injection may lead to regrow of the tumor. The results will be presented in tabular and graphical forms. Tabular results present the variation of maximum injection rate and setup time. Graphical results present the variation of tumor and supporting vasculature volumes, injection rate and the tracking error between the reference and actual tumor volumes. In addition, we will also perform a simulation to test the capability of the closed loop to accomodate the parametric uncertainties in the rate constants. The uncertainties are represented by a random deviation in the range {+/-}10% times the nominal value of the effected parameter. The control laws will be kept the same and the simulations will be repeated by 1000 times and each result will be superimposed on the graph. The area occupied by the curves will show the relative capability of the designs.