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Basal when used in a medical sense refers to a minimal level that is necessary for health or life. As used by diabetics and health care professionals, it describes a low, continuous dosage of insulin (either as a basal rate from an insulin pump or a slow-acting insulin injection) intended to "cover" the glucose output of the liver.
This works together with a bolus of insulin, which is a dosage of insulin intended to "cover" a meal or to make a large glucose level correction.