Inclusion Criteria:

1. Patients with newly diagnosed pathologically confirmed WHO Grade III or Grade IV glioma (anaplastic astrocytoma, anaplastic oligodendroglioma, anaplastic mixed glioma, gliosarcoma and glioblastoma multiforme);
2. Patients must be 18 years of age or older at the time of informed consent;
3. Karnofsky performance status 60% and a life expectancy of at least 6 months;
4. The patient is at least 48 hours after craniotomy or stereotactic biopsy but no later than four weeks from the last surgical procedure;
5. Adequate hematologic function as demonstrated by laboratory values performed within 14 days: platelet count > 100,000, prothrombin time (PT) 1.2 x control, inactivated partial thromboplastin time (aPTT) 1.2 x control;
6. Signed informed consent prior to patient registration.

Exclusion Criteria:

1. Presence of a coagulopathy, as defined by laboratory parameters including a platelet count < 100,000, PT > 1.2 x control or a PTT > 1.2 x control.
2. Symptomatic intracranial bleeding, which includes inter- or intratumor bleeding and causes mass effect or neurological disability control;
3. The presence of acute or chronic deep venous thrombosis demonstrated by ultrasonography or venography. A baseline screening ultrasound or venogram is not required;
4. Active systemic bleeding, such as gastrointestinal bleeding or gross hematuria;
5. Excessive risk of bleeding as defined by stroke within the prior 6 months, history of CNS or intraocular bleed, or septic endocarditis;
6. Prior history of documented DVT or PE;
7. History of immune mediated heparin induced thrombocytopenia, as documented by a platelet count < 50,000 and positive heparin-induced platelet aggregation test;
8. Contraindication to tinzaparin or other heparins, including allergy or hypersensitivity to heparin or pork products, sulfite allergy, benzyl alcohol allergy or have or had had an epidural catheter or traumatic spinal puncture within 7 days prior to screening;
9. Serum creatinine >3.0 mg/dl;
10. Patient or partner of childbearing potential and not using adequate contraception;
11. Pregnant or nursing (women of childbearing potential may have a screening pregnancy test at the discretion of the investigator);
12. Medical condition requiring long-term anticoagulants such as atrial fibrillation or a mechanical heart valve;
13. Inability to give informed consent;
14. Inability to comply with study procedures, including subcutaneous injections and diagnostic procedures;
15. Participating in another study of an investigational agent at the time of enrollment. The use of an experimental or investigational regimen of an approved product is not cause for exclusion.