Alternatives to a liver biopsy?

[Missypea]

The doctor is scheduling a liver biopsy and I was wondering what, if any, alternatives exist.  I think this may be cancer rather than liver disease. Should I opt for a PET scan or other scan that would show if cancer exists and be less invasive?
Medical History:  Upper endoscopy in January showed stage 2 varices.  All blood work for liver disease came back negative (not showing disease).  An ultrasound showed abnormal liver tissue.
Symptoms:  Pain in right side of abdomon (specific area) over the last year (thought it was a muscle pain).
Hair loss (thought I wasn't getting enough vitamins) over the last year
Dark urine (last 4 months)
Increasing fatigue (last year)