Recent research shows that liquid crystals can be used to report the presence of different types of substances through optical amplication of ligand-receptor binding. In this work, simulations based on a coarse-grained method have been performed to study a class of liquid-crystal-based sensors. A tensor order parameter was used to model the liquid crystalline system and the Beris-Edwards formulation was employed to obtain the time evolution of a liquid crystal medium containing particles. The simulation cases are built using three-dimensional unstructured meshes and the simulation geometries studied include simple models involving spheres as well as detailed modeling for a protein. The dynamics of a liquid crystal medium confined between two solid walls has been studied in the presence of spherical particles and a representative biological macromolecule. Comparisons of steady state and transient solutions from the present study with corresponding results from molecular dynamics based simulations in the literature yield good agreements.