Bending and twisting of an in vivo coronary artery at a bifurcation

Dynamic changes in the geometric shape and dimensions of a left coronary artery tree were extracted from the computer-tomographically reconstructed three-dimensional images of an in situ beating heart of an anesthetized dog. Wireframe models of the left coronary artery tree at 16 different instants of a cardiac cycle were constructed for the study of its flexing motion. For quantifying the local bending and twisting of the left coronary artery tree, the anatomic landmarks of the bifurcation points are selected as focussed locations. At these points, the space curves of the tree at different cardiac instants were first derived in parametric forms. Curvature and torsion expressions are next obtained in terms of the derivatives with respect to the parameter. This analysis revealed that during the initial contraction of the heart wall, a 2% reduction per millisecond in the radius of curvature occurred near the bifurcation point where the left circumflex coronary artery descends toward the apex of the heart. When the left ventricular chamber reached a maximum value, the radius of curvature was found to decrease at a rate of 2.3% ms^-1. At the end of diastole, an increase in the radius of curvature at a rate of 5.7% ms^-1 was observed. The twisting rates per unit length of artery near the bifurcation point of the selected artery were found to range from -0.62 to 0.63° ms^-1.