A bi-parametric model for the tumour angiogenesis and antiangiogenesis therapy

Robust positive control of tumour growth using angiogenic inhibition

In practice, many physical systems, including physiological ones, can be considered whose input can take only positive quantities. However, most of the conventional control methods do not support the positivity of the main input data to the system. Furthermore, the parameters of these systems, similar to other non-linear systems, are either not accurately identified or may change over time. Therefore, it is reasonable to design a controller that is robust against system uncertainties. A robust positive-input control method is proposed for the automatic treatment of targeted anti-angiogenic therapy implementing a recently published tumour growth model based on experiments conducted on mouse models. The backstepping (BS) approach is applied to design the positive input controller using sensory data of tumour volume as feedback. Unlike previous studies, the proposed controller only requires the measurement of tumour volume and does not require the measurement of inhibitor level. The exponential stability of the controlled system is proved mathematically using the Lyapunov theorem. As a result, the convergence rate of the tumour volume can be controlled, which is an important issue in cancer treatment. Moreover, the robustness of the system against parametric uncertainties is verified mathematically using the Lyapunov theorem. The real-time simulation results-based (OPAL-RT) and comparisons with previous studies confirm the theoretical findings and effectiveness of the proposed method.

Effect of treatment on the global dynamics of delayed pathological angiogenesis models

For three different types of angiogenesis models with variable delays, we consider either continuous or impulse therapy that eradicates tumor cells and suppresses angiogenesis. For the cancer-free solution, explicit conditions of global stability for the continuous and impulsive systems are obtained, together with delay-dependent estimates for the rates of decay for the tumor volume and pathological angiogenesis.

Model-based angiogenic inhibition of tumor growth using modern robust control method

Cancer is one of the most destructive and lethal illnesses of the modern civilization. In the last decades, clinical cancer research shifted toward molecular targeted therapies which have limited side effects in comparison to conventional chemotherapy and radiation therapy. Antiangiogenic therapy is one of the most promising cancer treatment methods. The dynamical model for tumor growth under angiogenic stimulator/inhibitor control was posed by Hahnfeldt et al. in 1999; it was investigated and partly modified many times. In this paper, a modified version of the originally published model is used to describe a continuous infusion therapy. In order to generalize individualized therapies a robust control method is proposed using H(∞) methodology. Uncertainty weighting functions are determined based on the real pathophysiological case and simulations are performed on different tumor volumes to demonstrate the robustness of the proposed method.