method and apparatus are provided to treat atherosclerosis wherein the artery is partially closed by dilating the artery while preserving the vital and sensitive endothelial layer thereof . microwave energy having a frequency from 3 ghz to 300 ghz is propagated into the arterial wall to produce a desired temperature profile therein at tissue depths sufficient for thermally necrosing connective tissue and softening fatty and waxy plaque while limiting heating of surrounding tissues including the endothelial layer and / or other healthy tissue , organs , and blood . the heating period for raising the temperature a potentially desired amount , about 20 ° c . within the atherosclerotic lesion may be less than about one second . in one embodiment of the invention , a radically beveled waveguide antenna is used to deliver microwave energy at frequencies from 25 ghz or 30 ghz to about 300 ghz and is focused towards a particular radial sector of the artery . because the atherosclerotic lesions are often asymmetrically disposed directable or focussed heating preserves healthy sectors of the artery and applies energy to the asymmetrically positioned lesion faster than a non - directed beam . a computer simulation predicts isothermic temperature profiles for the given conditions and may be used in selecting power , pulse duration , beam width , and frequency of operation to maximize energy deposition and control heat rise within the atherosclerotic lesion without harming healthy tissues or the sensitive endothelium cells .