Bistability and chaotic behaviors in a 4D cancer oncolytic Virotherapy mathematical model: Pspice and FPGA implementations

Abstract

Oncolytic viruses (OVs) exploit characteristics of mass cells and tumor-related reaction of the body to the presence of antigen, to lyse malignant cells and modulate the tumor microenvironment. However, the effective clinical utilization of these powerful treatment modules necessitates their logical control, especially in order to prevent solid and metastatic outgrowths. Hence, it is imperative to develop methods to protect a virus from the annihilating surroundings from the bloodstream when traveling to tumor locations. Our article reports on bistability and chaotic behavior in a 4D cancer virotherapy model. We find that unstable, stable and chaotic behaviors can appear in the model when tuning some of its parameters. With the help of the chart of dynamic behaviors in parameter spaces, numerical investigations of the system’s characteristics are analyzed followed by a discussion of the obtained results. It appears that the local transition change from an invariant one-torus (IT1) to its two-torus (IT2) counterpart can be found in the system and this undergoes a Neimark-Saker (NS) change of direction. As the increasing rate of immune effector enhance, the immune cells amount increases and as a consequence, the virotherapy dynamics becomes chaotic with a pronounced Lyapunov exponent. This can result to the failure of the virotherapy due to the interference of the immune cells with viruses. We also focus our study on the deign of ad-hoc electronic and Field Programmable Gate Arrays (FPGA) implementations of the cancer virotherapy’s model, to illustrate the obtained results.