This is a pilot single arm study with the primary endpoints of feasibility and preliminary estimates of safety and efficacy. This protocol builds on over 25 years of experience with high dose liver RT (Radiation Therapy), and in particular adaptive RT aimed at adjusting the global radiation dose based on a patient's measured sensitivity to treatment. This current protocol uses functional imaging and specialized radiation planning techniques to spare highly functional portions of the liver to preserve function. The investigators feel this will further improve the safety and efficacy of RT for all patients by customizing treatments to each. If this approach is promising, the investigators will proceed to a phase II randomized study of standard versus spatially and dosimetrically adapted RT.

Inclusion Criteria:

• Patients must have hepatocellular carcinoma.
• Patients must not have extrahepatic cancer.
• Patients must not be eligible for a curative liver resection or have refused resection
• Patients must have recovered from the acute effects of prior liver-directed therapy and 4 weeks must have passed since the last procedure and protocol therapy.
• Patients must have a Zubrod performance status of less than or equal to 2 (Zubrod performance status is a measure that attempts to quantify a cancer patients' general well-being. Scores run from 0 to 5 where 0 denotes normal activity and 5 denotes death).
• Patients must be 18 years of age or older.
• Patients must have adequate organ function.
• Patients must understand and be willing to sign an IRB (Institutional Review Board) approved informed consent form.

Exclusion Criteria:

• Patients with known allergies to intravenous iodinated contrast agents.
• Patients with a contraindication to contrast-enhanced MRI are excluded.

All adverse event data (serious and non-serious) collected from the time of the initial study treatment administration through 2 years after last dose of study treatment. Data was collected over 6 years.