The determination of myocardial volume at risk distal to coronary stenosis provides important information for prognosis and treatment of coronary artery disease. In this paper, we present a novel computational framework for estimating the myocardial volume at risk in computed tomography angiography (CTA) imagery. Initially, epicardial and endocardial surfaces, and coronary arteries are extracted using an active contour method. Then, the extracted coronary arteries are projected onto the epicardial surface, and each point on this surface is associated with its closest coronary artery using the geodesic distance measurement. The likely myocardial region at risk on the epicardial surface caused by a stenosis is approximated by the region in which all its inner points are associated with the sub-branches distal to the stenosis on the coronary artery tree. Finally, the likely myocardial volume at risk is approximated by the volume in between the region at risk on the epicardial surface and its projection on the endocardial surface, which is expected to yield computational savings over risk volume estimation using the entire image volume. Furthermore, we expect increased accuracy since, as compared to prior work using the Euclidean distance, we employ the geodesic distance in this work. The experimental results demonstrate the effectiveness of the proposed approach on pig heart CTA datasets.