1. A medical image processing apparatus comprising: a first extraction unit implemented by processing circuitry configured to extract a plurality of coronary arteries depicted in data of images of a plurality of time phases relating to the heart, and to extract at least one stenosed part depicted in each of the extracted coronary arteries; a calculation unit implemented by processing circuitry configured to calculate a pressure gradient of each of the extracted coronary arteries, based on tissue blood flow volumes of the plurality of extracted coronary arteries; a second extraction unit implemented by processing circuitry configured to extract an ischemic region depicted in the images; a specifying unit implemented by processing circuitry configured to specify a responsible blood vessel of the ischemic region by referring to a dominance map, in which each of the extracted coronary arteries and a dominance territory are associated, for the extracted ischemic region, and to specify a responsible stenosis, based on the pressure gradient corresponding to a stenosed part in the specified responsible blood vessel; and a display configured to display an image in which the specified responsible stenosis is depicted, together with information indicative of the responsible stenosis.