In this guided research report, I present the results of investigating the new time-dependent variational principle method with controlled bond expansion to time-evolve open quantum systems, specifically the spin-boson model. The model was first formulated in the hierarchy of matrix product states before time-evolving it. The results are compared with the two-site version results because it has a higher accuracy than the one-site version, from which the controlled bond expansion version is based. The results prove that the controlled bond expansion version can expand and grow its bond dimensions while still having the running time of the one-site version in an open quantum system setting. Although the accuracy changes depending on the complexity of the model, the method can still get the two-site results by tweaking its hyperparameters and enabling an additional orthogonalization process. The method holds much promise and it should be tested in more complex scenarios.