Thermodynamic analogies for the characterization of 3D human coronary arteries

The thermodynamics of three-dimensional curves is explored through numerical simulations, providing room for a broader range of applications. Such approach, which makes use of elements of information theory, enables the processing of parametric as well as non-parametric data distributed along the curves. Descriptors inspired in thermodynamic concepts are derived to characterize such three-dimensional curves. The methodology is applied to characterize a sample of 48 human coronary arterial trees and compared with standard geometric descriptors. As an application, the usefulness of the thermodynamic descriptors is tested by assessing statistical associations between arterial shape and diseases. The feature space defined by arterial descriptors is analyzed using multivariate kernel density classification methods. A two-tailed U-test with 95% confidence interval showed that some of the proposed thermodynamic descriptors have different mean values for healthy/diseased left anterior descending (LAD) and left circumflex (LCx) arteries. Specifically: in the LAD, the temperatures based on mean number of intersection points and curvature are larger in healthy arteries (p < 0.05); in the LCx, the intersection counting pressure is larger in healthy arteries (p < 0.05). Moreover, the shape of the right coronary artery is thoroughly characterized by these descriptors. Specifically: intersection count thermodynamics, i.e. entropy, temperature and pressure are larger in Σ-Shape RCAs, in turn curvature based entropy and pressure are larger in C-Shape RCAs (p < 0.05).