This is a multi-center, non-randomized pharmacokinetically-guided optimal dosing study of intraventricular topotecan in children with neoplastic meningitis. Topotecan will be administered daily for five consecutive days utilizing the schema shown in the Schema below. Concomitant chemotherapy to control systemic disease or bulk CNS disease is allowable provided that the systemic chemotherapy is not an investigational agent or one of the following: high-dose methotrexate (> 1g/m2), high-dose cytarabine (> 1g/m2), 5-fluorouracil, capecitabine, thiotepa, a nitrosourea, or topotecan. The starting dose for this trial was derived from pharmacokinetic simulations that utilized data from a prior phase I study of intrathecal topotecan. The simulations were performed to estimate the length of time that ventricular CSF concentrations of topotecan lactone would remain above an optimal "target level" of 1 ng/mL. One of the primary objectives of this study is to estimate the dose of intrathecal topotecan that will result in CSF lactone concentrations exceeding 1 ng/mL for at least eight hours after an intrathecal injection. Dose escalations for patient cohorts will be conducted following the traditional phase 1 design in order to determine the maximum tolerated dose (MTD). The MTD will be called pharmacokinetically optimal if that dose achieves the targeted PK parameter in at least 23 of 25 patients treated at that dose level.