Four‐dimensional analysis of cyclic changes in coronary artery shape

Abstract

The objective of this study was to derive a method for quantifying the dynamic geometry of coronary arteries. Coronary artery geometry plays an important role in atherosclerosis. Coronary artery geometry also influences the performance of coronary interventions. Conversely, implantation of stents may alter coronary artery geometry. Clinical tools to define vessel shape have not been readily available. Using a Frenet-Serret curvature analysis applied to 3D reconstruction data derived from standard coronary angiograms, 21 coronary arteries were analyzed at end-diastole (ED) and end-systole (ES). Vessels were divided anatomically: type 1 consisted of vessels lying in the AV groove (left circumflex, right coronary) and type 2 consisted of vessels overlying actively contracting myocardium (left anterior descending, diagonal, obtuse marginal, right ventricular marginal, posterior descending, posterolateral). Vessel segments were analyzed by assessing the changes in curvature, torsion, and discrete flexion points (FPs), areas of systolic bending in the arterial contour. The curvature from ED to ES of type 1 vessels was unchanged (-0.02 +/- 0.03 cm(-1)), while the curvature change of type 2 vessels showed a 38% increase (0.33 +/- 0.04 cm(-1); P < 0.001). Type 1 vessels had fewer FPs per vessel than type 2 vessels (0.38 +/- 0.18 and 2.40 +/- 0.23 FP/vessel, respectively; P < 0.001). FPs were more common in distal segments and branch vessels. A method to quantify cyclic changes in coronary artery shape was applied to 3D data sets derived from standard coronary angiograms. Coronary arteries undergo a cyclic change in shape resulting in changes in overall curvature as well as formation of discrete flexion points. These changes in vessel shape are asymmetrically distributed in coronary arteries.

Methods for Quantifying Three-Dimensional Deformation of Arteries due to Pulsatile and Nonpulsatile Forces: Implications for the Design of Stents and Stent Grafts

“…For the coronary artery, curvature range of the LAD in this study was within those reported in previous studies 13,23,28 although individual anatomic variation along the length would have a greater effect on the numerical values. We also observed a greater curvature change in the distal LAD than the proximal portion which is consistent with the literature.…”

“…According to this formula, curvature and torsion are defined as j ¼ a 0 Â a 00 k k= a 0 k k 3 and s ¼ ða 0 Â a 00 Þ Á a 000 = a 0 Â a 00 k k 2 , respectively, where a indicates a position vector in space. 9,28,29,33,35,53 By definition, this curvature metric measures an infinitesimal rate of change in the tangent vector at each point of the curve, whereas the torsion metric measures the infinitesimal rate of change in the orientation (binormal vector of the curve) of the osculating plane. While curvature is well appreciated because of its reciprocal relation to the radius of curvature, the torsion metric is less frequently used in practice because of its susceptibility to error in calculations associated with higher-order derivatives.…”

“…6,34,42,44,50,53 Various methods and quantification metrics have been proposed to characterize the aforementioned types of in vivo arterial deformations. 5,7,9,10,14,20,28,29,33,[41][42][43][44]49,50,53 For example, the ''distance factor,'' which is defined as the ratio between the vessel path length and the distance between two endpoints, is a simple metric commonly used to measure nonlinearity of vessels, i.e., tortuosity. 7,53 This metric lumps 3D information into a one-dimensional (1D) metric and hence does not clearly differentiate local curvature changes, especially when the vessel maintains the same distance factor.…”

Role of Epicardial Fat to Buffer Deformation and Vibration in Coronary Arteries

“…8 The cyclic change in coronary artery shape not only alters coronary artery curvature but also produces discrete flexion points. 9 Another unique feature of coronary arteries is that phasic pressure and blood flow are not synchronous as the maximum pressure is in systole and most coronary blood flow occurs during diastole (although there are rare exceptions). [10][11][12] This unique relationship is responsible for a highly negative stress phase angle between coronary artery circumferential strain and wall shear.…”

Three-Dimensional Geometry of the Human Carotid Artery

“…In three-dimensional analysis tortuosity of the artery is best described by the well-known Frenet formulas which define the tortuosity of the spatial curve (arterial centerline) through its curvature and torsion [11,[23][24][25]. The Frenet frame is formed by three vectors: tangent, normal, and binormal that form the orthonormal basis.…”