K is potassium and I is Iodine - potassium iodide. it can be bought rather expensively as nuke pills - the kind you take in case of a nuclear incident to protect the thyroid. it is simply taken orally but can be taken in larger quantities than the I2 in lugols. some of the old prescriptions called for taking grams a day of KI in the form of SSKI (super saturated potassium iodide) solution. Lugols has 10 grams of KI and 5 grams of I2 per 100ml whereas SSKI has 100 grams of KI only per 100ml.