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 and the specified responsible blood vessel are depicted, together with information indicative of the responsible stenosis and the responsible blood vessel, wherein the extracted coronary arteries supply nutrition to the dominance territory, and the responsible blood vessel is inherently responsible for supply of the nutrition to the ischemic region, and wherein the dominance map is predetermined, and associates the dominance territory of a cardiac muscle with the extracted coronary arteries being inherently responsible for supply of the nutrition to the dominance territory.