bifurcation

According to recent guidelines, endovascular angioplasty is the standard treatment for TASC A and B primary aorto-iliac occlusive (AIOD) disease, and the first-line approach for TASC C lesions [1,2]. Extended TASC D occlusive disease is usually treated by open surgery yielding excellent patency rates at a cost of a higher mortality (2%-4%) and a severe morbidity (up to 10%) [3]. However, several studies have reported promising results after endovascular treatment of extensive AIOD and full reconstruction of the aortic bifurcation [4,5]. In a recent meta-analysis, Jongkind et al., concluded that endovascular treatment of extensive AIOD can be performed successfully by experienced interventionists in selected patients [6]. Although primary patency rates seem to be lower than those reported for surgical revascularization, reinterventions can often be performed percutaneously yielding a secondary patency comparable to surgical repair.

The dynamics of the glucose-insulin regulatory system are highly nonlinear and must be understood to be controlled effectively. Bifurcation analysis and multiobjective nonlinear model predictive control (MNLMPC) are performed on a glucose-insulin dynamic model. MATCONT was used for the bifurcation analysis, and for the MNLMPC calculations, the optimization language PYOMO is used in conjunction with the solvers IPOPT and BARON. The bifurcation analysis revealed a Hopf bifurcation point and a limit point. A Hopf bifurcation point is a tipping point where a system that was behaving steadily suddenly starts to oscillate or cycle on its own, like a machine that begins to vibrate instead of staying still. A limit point is a tipping point at which pushing a system a little further suddenly causes it to jump to a completely different state, rather than changing smoothly. MNLMC converged on the Utopia solution. The Hopf bifurcation point, which leads to an unwanted limit cycle, is eliminated by an activation factor. A limit cycle is a repeating pattern of behavior that a system naturally settles into over time, like a steady heartbeat or a clock that keeps ticking. The limit point (which causes multiple steady-state solutions from a singular point enables the Multiobjective nonlinear model predictive control calculations to converge to the Utopia point (the best possible solution) in the model. A Utopia solution in multi-objective nonlinear model predictive control is an ideal operating point at which all goals are simultaneously perfectly optimized.