Convection-enhanced delivery (CED)is used as a method to deliver a direct infusion oftherapeutic agents to the central nervous centre thuscircumventing the blood-blood barrier. A non-PEGylatedliposomal composition comprising at least onesaturated neutral phospholipid and at least one saturatedanionic phospholipid and a therapeutic or diagnosticagent encapsulated therein is used to overcometoxicity associated with high peak drug concentrationdelivered locally CED as well as to increasetissue distribution volume for an improvedsustained drug release. In one embodiment, the liposomecomposition comprises a molar ratio ofDSPC:DSPG:CHOL of 7:2:1 and the therapeutic ordiagnostic agent is selected from topotecan, conotoxin,gadodiamide or rhodamine, and is used in thetreatment of epilepsy