The classical wetting models, such as the Wenzel and Cassie-Baxter have been extensively used to quantify the wettability of laser-textured surfaces. However, these models do not provide any description of the corresponding droplet dynamics. In this work, we propose a detailed continuum-level modelling to study the wetting dynamics of a water droplet on Ti-6Al-4V alloy. The calculations are performed for flat surfaces and surfaces with various reliefs. The calculated evolutions of the droplet spreading parameter for flat surfaces, surfaces with triangular reliefs and one with two different periods and heights not only provide explanations of several experimental results but also underline the perspectives of using complex reliefs for efficient wettability control. Thus, such simulations are shown to be useful in relief design and laser texturing for a wide range of applications, for example, laser treatment of artificial implants and prostheses.