Approche électronique de la carte de comportement d'un environnement biologique soumis à la dynamique tumorale.

Abstract

We propose to characterize the evolution of cancer by analytical, numerical and electronic techniques, starting from interaction models and systems of equations describing the evolution of tumor dynamics in a tumor site. The delay is taken into account to model the activation time of effector immune cells. The stability of steady states is studied and results in relation to tumor development are also provided. It is analytically and numerically demonstrated by considering the dynamics without delay that the increase in the parameter associated with the elimination of tumor cells by the host cells does not influence the size of the tumor cells as long as this parameter remains below a threshold value. . When this parameter becomes greater than the threshold value, the system may intermittently degenerate into chaos via the node-saddle bifurcation indicating maximum tumor cell size. It is in these situations that we also study the conditions leading to a metastatic phase. The analyzes thus led to the following predictions : An equilibrium attractor with a population of non-zero tumor cells corresponding to a site where the tumor cells do not proliferate and remain in a dormant state ; a limit cycle attractor with osculation of tumor cells corresponding to a vascular tumor site associated with a proliferating shell can ; an equilibrium attractor with a population of null tumor cells corresponding to a healthy state of the patient ; a chaotic attractor indicating a maximum size of tumor cells corresponding to an angiogenic switch where the vascularization is quite significant with a saturation of the tumor site. As a result, these tumor cells begin to migrate to other sites to form metastases. The analysis of the effect of the delay shows that the delay acts as a destabilizer of the dynamics of the tumor site and not as a stabilizer. Small delays guarantee stability, but delays above a critical value can produce periodic solutions. Larger delays can even lead to chaotic attractors. An experimental study is carried out. An electrical circuit capable of reproducing the dynamics of cancer progression is proposed. Investigations using the electronic approach may be relevant for biomedical technology, in the context of the development of tumor dynamic simulators, with clinical and pharmaceutical applications.