Sequential Melphalan for Use With Hepatic Delivery System Treatment Followed by Sorafenib in Patients With Unresectable HCC

Inclusion Criteria: 1. HCC diagnosed by tissue or imaging study 2. Unresectable HCC without extrahepatic disease based on CT 3. At least one target lesion. In patients with prior loco-regional therapy, the target lesion(s) must be located in area(s) outside previous treatment 4. Child-Pugh Class A in the absence of hepatoencephalopathy or clinically evident ascites 5. Barcelona Clinic Liver Cancer (BCLC) stage B 6. MELD Score \< 15 7. Eastern Cooperative Oncology Group Performance Status 0-1 8. No prior systemic therapy for HCC 9. No prior radiation therapy to the liver including Y90-, I131-based loco-regional therapy. Prior loco-regional therapy based on other technology for HCC, if any, must have been completed at least 4 weeks prior to baseline imaging 10. Age ≥ 18 years 11. Signed informed consent Exclusion Criteria: 1. Metastatic disease outside of liver 2. Greater than 50% tumor burden in the liver by imaging 3. History of orthotopic liver transplantation, clinical symptoms of portal hypertension, Whipple's procedure, hepatic artery anatomy incompatible with perfusion or known unresolved venous shunting 4. Evidence of ascites on imaging study, or the use of diuretics for ascites 5. Clinically significant encephalopathy 6. History of allergies or known hypersensitivity to any components of melphalan or the components of the Melphalan/HDS system 7. Known hypersensitivity to heparin or the presence of heparin-induced thrombocytopenia 8. Received an investigational agent for any indication within 30 days prior to first treatment 9. Not recovered from side effects of prior therapy to ≤ grade 1 (according to National Cancer Institute Common Terminology Criteria for Adverse Events version 4.03 \[NCI CTCAE v. 4.03\]). Certain side effects that are unlikely to develop into serious or life-threatening events (e.g. alopecia) are allowed at \> grade 1 10. Those with New York Heart Association functional classification II, III or IV; active cardiac conditions including unstable coronary syndromes (unstable or severe angina, recent myocardial infarction), worsening or new-onset congestive heart failure, significant arrhythmias and severe valvular disease must be evaluated for risks of undergoing general anesthesia 11. History or evidence of clinically significant pulmonary disease that precludes the use of general anesthesia 12. Uncontrolled diabetes mellitus, hypothyroidism, or hyperthyroidism 13. Active uncontrolled infection, including Hepatitis B, Hepatitis C infection. Patients with anti-HBc positive, or HBsAg but DNA negative are exception(s) 14. History of bleeding disorders 15. Brain lesions with a propensity to bleed 16. Known esophageal varices at risk of bleeding, including medium or large esophageal or gastric varices, or active peptic ulcer 17. Previous malignancy within 3 years prior to enrollment, except for curatively-treated basal cell or squamous cell carcinoma of the skin, cervical carcinoma in situ, bladder carcinoma in situ or breast cancer in situ 18. Inadequate hematologic function as evidenced by any of the following: * Platelets \< 125,000/µL * Hemoglobin ≤ 10 g/dL, independent of transfusion or growth factor support * Neutrophils \< 1,500/µL 19. Serum creatinine \> 1.5 mg/dL 20. Inadequate liver function as evidenced by any of the following: * Total serum bilirubin ≥ 2.0 mg/dL * Prothrombin time International Normalized Ratio (INR) \> 1.5 * Aspartate aminotransferase (AST) or alanine transaminase (ALT) \> 5 times ULN * Serum albumin \< 3.0 g/dL 21. Alcohol consumption within 30 days of first study treatment, or refusing to abstain from alcohol for the duration of study treatment 22. For female subjects of childbearing potential (i.e., have had a menstrual period within the past 12 months): a positive serum pregnancy test (β-human chorionic gonadotropin) within 7 days prior to enrollment; or unwilling or unable to undergo hormonal suppression to avoid menstruation during treatment 23. Sexually active females of childbearing potential and sexually active males with partners of reproductive potential: unwilling or unable to use appropriate contraception from screening until at least 30 days after last administration of study treatment