Nonlinear dynamic modeling of MS to investigate the effect of monophasic and biphasic DBS stimulation on PPMS and RRMS.

In this study, a nonlinear dynamic model has been presented to investigate the behavior of the brain in multiple sclerosis (MS) and the dynamics of healthy cells, infected cells and harmful agents under different parameter conditions have been analyzed. First, the stability of healthy equilibrium states and instability of the system have been investigated using numerical simulation and eigenvalue analysis and its relation with clinical types of MS including healthy state, primary progressive (PPMS) and relapsing-remitting (RRMS) has been shown. Then, the effect of deep brain stimulation (DBS) including monophasic, symmetric biphasic and asymmetric biphasic stimulation in different frequency and pulse width ranges on the dynamics of the system has been studied. To evaluate the neural function, power spectral density (PSD) analysis has been considered in the alpha band and the changes in the total power of this band have been investigated under different conditions. Finally, using bifurcation diagrams, the chaotic behavior of the system and the role of DBS stimulation types in suppressing instability and chaos have been analyzed. The results show that the type and parameters of DBS stimulation have a significant impact on improving the stability of the system; monophasic stimulation shows the highest spectral similarity to the healthy state and also, it has the highest ability to suppress the dynamic chaos of the system.