Polytopal finite element methods for partial differential equations (PDEs) have recently attracted increasing attention due to their flexibility in handling complex geometries, heterogeneous media, and adaptively refined meshes. Among them, the Polytopal Discontinuous Galerkin (PolyDG) method offers a robust and high-order accurate framework for simulating problems characterized by strong anisotropies and sharp solution gradients. This talk focuses on the numerical simulation of transmembrane potential dynamics in brain electrophysiology, a multiscale process characterized by rapid ion concentration fluctuations and steep wavefronts propagating through heterogeneous, anisotropic tissues. While high-order PolyDG methods are well suited to capture these phenomena, their computational cost remains significant. To address this, we develop a p-adaptive strategy that exploits the traveling wave-like nature of the solution: by identifying localized regions of high activity, we can locally increase the polynomial degree where needed and reduce it elsewhere. This adaptivity is driven by efficient a-posteriori error indicators tailored to the PolyDG framework. To perform local polynomial adaptivity, we apply a k-means clustering technique to group elements based on the local error indicator, allowing a robust and fully automatic classification of regions requiring refinement, by reducing the total number of degrees of freedom of the system and the computational costs. We present numerical results that validate the approach and highlight its effectiveness in simulating epileptic seizures across complex brain domains, such as the interface between grey and white matter. Our findings show that the proposed p-adaptive PolyDG method maintains high-order accuracy while significantly reducing the number of degrees of freedom and overall computational costs. This work contributes to the broader landscape of polytopal methods by showcasing their potential in real-world applications involving wave propagation in complex biological systems.