Aging Impact on Thoracic Aorta 3D Morphometry in Intermediate-Risk Subjects: Looking Beyond Coronary Arteries with Non-Contrast Cardiac CT

Abstract

An increasing number of intermediate risk asymptomatic subjects benefit from measures of atherosclerosis burden like coronary artery calcification studies with non-contrast heart computed tomography (CT). However, additional information can be derived from these studies, looking beyond the coronary arteries and without exposing the patients to further radiation. We report a semi-automatic method that objectively assesses ascending, arch and descending aorta dimension and shape from non-contrast CT datasets to investigate the effect of aging on thoracic aorta geometry. First, the segmentation process identifies the vessel centerline coordinates following a toroidal path for the curvilinear portion and axial planes for descending aorta. Then, reconstructing oblique planes orthogonal to the centerline direction, it iteratively fits circles inside the vessel cross-section. Finally, regional thoracic aorta dimensions (diameter, volume and length) and shape (vessel curvature and tortuosity) are calculated. A population of 200 normotensive men was recruited. Length, mean diameter and volume differed by 1.2 cm, 0.13 cm and 21 cm³ per decade of life, respectively. Aortic shape uncoiled with aging, reducing its tortuosity and increasing its radius of curvature. The arch was the most affected segment. In conclusion, non-contrast cardiac CT imaging can be successfully employed to assess thoracic aorta 3D morphometry.

Appendix

The curvilinear portion of the thoracic aorta was analyzed reconstructing oblique planes that turned around the mid-point between centerline coordinates C _A and C _D as shown in Fig. 1b. Starting from an axial plane P ₀, that contain C _A and C _D, the algorithm makes a fixed translation-rotation and a subsequent dynamic rotation pivoting around the center of the aortic arch.

The plane P ₀ was defined as:

$$ P_{0} = \lambda \cdot \hat{x} + \varepsilon \cdot \hat{y} + z_{{C_{\text{A}} ,C_{\text{D}} }} \cdot \hat{z} $$

where $\hat{x}, \hat{y}$ and $\hat{z}$ are the unit vectors of the 3D euclidean space along the coronal, sagital and axial directions of the CT volume, $z_{{C_{\text{A}} ,C_{\text{D}} }}$ is the z-coordinate of the slice containing C _A and C _D and parameters λ, ɛ are such that:

$$ \lambda ,\varepsilon \in N^{0} /\{ \lambda < 512 \wedge \varepsilon < 512\} $$

P ₀ was first translated and rotated with the following transformation

$$ rtP_{0} = R_{{\alpha ,\hat{z}}} \left( {P_{0} - \left\langle {P_{0} } \right\rangle } \right) $$

where $\left\langle {P_{0} } \right\rangle$ is the center-point of the plane P ₀ and $R_{{\alpha ,\hat{z}}}$ is the rotation matrix

$$ R_{{\alpha ,\hat{z}}} = \left[ {\begin{array}{*{20}c} {\cos \alpha } & { - \sin \alpha } & 0 \\ {\sin \alpha } & {\cos \alpha } & 0 \\ 0 & 0 & 1 \\ \end{array} } \right] $$

that aligns P ₀ with the vector connecting C _A and C _D. Accordingly, angle α was calculated as:

$$ \alpha = a\cos \left( {\frac{{\hat{x} \cdot (C_{\text{A}} - C_{\text{D}} )}}{{\left\| {C_{\text{A}} - C_{\text{D}} } \right\|}}} \right) $$

Finally, the resulting plane was sequentially rotated in 2° steps, using the transformation

$$ P_{i} = R_{{\theta_{i} ,u}} \cdot rtP_{0} $$

where $R_{{\theta_{i},u}}$ is the rotation matrix:

$$ R_{\theta ,u} = \left[ {\begin{array}{*{20}c} {\cos \theta + u_{x}^{2} (1 - \cos \theta )} & {u_{x} u_{y} (1 - \cos \theta ) - u_{z} \sin \theta } & {u_{x} u_{z} (1 - \cos \theta ) + u_{y} \sin \theta } \\ {u_{y} u_{x} (1 - \cos \theta ) + u_{z} \sin \theta } & {\cos \theta + u_{y}^{2} (1 - \cos \theta )} & {u_{y} u_{z} (1 - \cos \theta ) - u_{x} \sin \theta } \\ {u_{z} u_{x} (1 - \cos \theta ) - u_{y} \sin \theta } & {u_{z} u_{y} (1 - \cos \theta ) + u_{x} \sin \theta } & {\cos \theta + u_{z}^{2} (1 - \cos \theta )} \\ \end{array} } \right] $$

which performs a rotation of θ degrees around the axis u, orthogonal to the segment $\overline{{C_{\text{A}} - C_{\text{D}} }}$ and the unit vector $\hat{z}$, calculated from the following a vector product:

$$ u = \frac{{(C_{\text{A}} - C_{\text{D}} ) \otimes \hat{z}}}{{\left\| {C_{\text{A}} - C_{\text{D}} } \right\|}} $$

The curvilinear path of the thoracic aorta was covered assigning values of θ _i angle from 0° to 240°.