  Coronary arteries and their branches supply blood to myocardium. The
obstruction of coronary arteries results in significant loss of myocardium,
called acute myocardial infarction, and the number one cause of death globally.
Hence, quantification of the regional amount of heart muscle subtended by
obstructed coronary arteries is of critical value in clinical medicine.
However, the conventional methods are inaccurate and frequently disagree with
clinical practices. This study proposes a novel algorithm to segment regional
myocardium-at-risk subtended by any potentially obstructed coronary artery.
Assuming the geometric triangular mesh models of coronary artery and myocardium
derived from an individual cardiac computed tomography image, the proposed
algorithm performs (i) computation of the medial axis of the coronary artery
and (ii) segmentation of the coronary artery and myocardium using the medial
axis. The algorithm provides the fused segmentation of coronary artery and
myocardium via the medial axis. The computed result provides a robust
mathematical linkage between myocardium-at-risk and supplying coronary arteries
so that ischemic myocardial regions can be accurately identified, and both the
extent and severity of myocardial ischemia can be quantified effectively and
efficiently. Furthermore, the correspondence between segmented coronary artery
and myocardium can be more importantly used for building optimization models of
cardiac systems for various applications. We believe that the proposed
algorithm and implemented VoroHeart program, which is freely available at
http://voronoi.hanyang.ac.kr/software/voroheart, will be an invaluable tool for
patient-specific risk predictions and the treatment of obstructed coronary
artery disease in clinical medicine. The algorithmic accuracy and efficiency
are theoretically asserted and experimentally verified.
