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Altered glymphatic function is observed for many neurological diseases. Glioma, one of the most common brain cancers, is known to have altered fluid dynamics in terms of edema and blood-brain barrier breakdown, both features potentially impacting the glymphatic function. To study glioma and its fluid dynamics, we propose a flexible mathematical model, including the tumor, the peri-tumoral edema and the healthy tissue. From a mechanical point of view, we consider the brain as a multicompartment porous medium and model both the fluid movement and the clearance of solutes within the brain. Our results indicate that the impairment of the glymphatic system due to glioma growth is two-fold. First, edema resulting from the leakage of fluid at the blood-brain barrier and/or the occlusion of the interstitial fluid exit routes (notably the perivascular spaces) due to migratory tumor cells result in a slight localized increase of pressure, consequently impairing negatively glymphatic clearance. Second, local changes of porosity (i.e. the volume fraction of certain compartments such as perivascular or extracellular spaces), result in a disruption of the transport of solutes in the brain. Our results indicate that an effect similar to the enhanced permeability and retention is obtained using biologically relevant changes of parameter values of our model. Our mathematical model is the first step towards a digital twin for drug or contrast product delivery within the cerebro-spinal fluid directly (e.g. from intrathecal injection) for patients suffering from gliomas.