Feasibility Trial of the Modified Atkins Diet and Bevacizumab for Recurrent Glioblastoma

Inclusion Criteria: * Patients must have histologically or cytologically confirmed glioblastoma or other grade IV malignant glioma (i.e. gliosarcoma, small cell glioblastoma, etc.), recurrent after prior external beam fractionated radiotherapy and temozolomide chemotherapy. * Any number of prior recurrences are allowed * Karnofsky Performance status ≥60 * Patients must have normal organ and marrow function as defined below: * Hemoglobin ≥ 9.0 g/dl * Absolute neutrophil count ≥ 1.5 x 10\^9/L * Platelet count ≥ 100 x 10\^9/L * Total bilirubin ≤ 1.5 X institutional upper limit of normal * Aspartate aminotransferase (AST) (SGOT) ≤ 3.0x institutional upper limit of normal * Alanine aminotransferase (ALT) (SGPT) ≤ 3.0x institutional upper limit of normal * Serum Creatinine ≤ 1.5 X institutional upper limit of normal * Cr \<2, blood urea nitrogen (BUN) \< 100mg/dL * Blood coagulation parameters: international normalized ratio (INR) ≤ 1.5 * Minimum interval since last drug therapy; * 3 weeks since last non-cytotoxic therapy * 3 weeks must have elapsed since the completion of non-nitrosourea-containing chemotherapy regimen. * 6 weeks since the completion of a non-nitrosourea-containing therapy regimen. * Patients must have no concurrent malignancy except curatively treated basal or squamous cell carcinoma of the skin or carcinoma in situ of the cervix and breast, adequately treatment stage I or II cancer from which the patient is in complete remission. Patients with other malignancies must also be disease free for at least three years. * Patients must be maintained on a stable corticosteroid regimen from the time of their baseline scan until the start of the treatment and/or for at least 5 days before starting treatment. * Patients with the potential for pregnancy or impregnating their partners must agree to follow acceptable birth control methods to avoid conception. The effects of bevacizumab on the developing human fetus are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (double barrier method of birth control or abstinence prior to study entry, for the duration of study participation and after completing treatment. Should a woman become pregnant or suspect that she is pregnant while she or her partner is participating in this study, she should inform the treating physician immediately. * Subjects must have the ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Patients who have not recovered from adverse events due to agents administered more than 4 weeks earlier. * Patients who are receiving any other investigational agents. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to bevacizumab. * Patients who have had previous treatment with bevacizumab. * Patients with uncontrolled intercurrent illness including, but not limited to ongoing or active infection, active bowel instruction, diabetic (insulin dependent), Active or remote pancreatitis, Pancreatic insufficiency, symptomatic congestive heart failure (NYHA \> 2), unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Pregnant or breastfeeding women are excluded from this study because bevacizumab is an agent with the potential for teratogenic or abortifacient effects. Because there is an unknown, but potential risk for adverse events in nursing infants secondary to treatment of the mother with bevacizumab, breastfeeding should be discontinued if the mother is treated with bevacizumab. These potential risks may also apply to other agents used in this study. * Known diagnosis of human immunodeficiency virus (HIV). (HIV testing is not required). * Patients who have undergone major surgery (ie, intra-thoracic, intra abdominal or inra-pelvic), open biopsy or significant traumatic injury =\< 4 weeks prior to starting study drug, or patients who have had minor procedures, percutaneous biopsies or placement of vascular access device ≤ 1 week prior to starting study drug, or who have not recovered from side effects of previous procedure or injury. * Patients with cirrhosis, or active viral or nonviral hepatitis. * Implanted pacemaker, defibrillator, deep brain stimulator, or other implanted electronic devices in the brain or other documented clinically significant arrhythmias. * Evidence of increased intracranial pressure (clinically significant papilledema, vomiting, and nausea, or reduced level of consciousness). * Patients who are unwilling to comply with protocol. * Myocardial infarction within the last 6 months. * Symptomatic atrial fibrillation. * Patients with a body mass index (BMI) \>35, \< 20. * Patients with a genetic disorder of fat metabolism. * Patients who are allergic to milk. * Insulin dependent diabetes mellitus. * Patients with uncontrolled hypertension. Patients with a history of hypertension must be well controlled (\<160/90) on a regimen of hypertensive medication. * Patients with known inborn errors of metabolism of primary carnitine deficiency, carnitine palmitoyltransferase I or II deficiency, carnitine translocase deficiency, beta-oxidation defects, pyruvate carboxylase deficiency and porphyria.