title: Flow velocity is relatively uniform in the coronary sinusal venous tree: structure-function relation.
abstract: The structure and function of coronary venous vessels are different from those of coronary arteries and are much less understood despite the therapeutic significance of coronary sinus interventions. Here we aimed to perform a hemodynamic analysis in the entire coronary sinusal venous tree, which enhances the understanding of coronary venous circulation. A hemodynamic model was developed in the entire coronary sinusal venous tree reconstructed from casts and histological data of five swine hearts. Various morphometric and hemodynamic parameters were determined in each vessel and analyzed in the diameter-defined Strahler system. The findings demonstrate an area preservation between the branches of the coronary venous system that leads to relatively uniform flow velocity in different orders of the venous tree. Pressure and circumferential and wall shear stresses decreased abruptly from the smallest venules toward vessels of order -5 (80.4 ± 39.1 µm) but showed a more modest change toward the coronary sinus. The results suggest that vessels of order -5 denote a hemodynamic transition from the venular bed to the transmural subnetwork. In contrast with the coronary arterial tree, which obeys the minimum energy hypothesis, the coronary sinusal venous system complies with the area-preserving rule for efficient venous return, i.e., da Vinci's rule. The morphometric and hemodynamic model serves as a physiological reference state to test various therapeutic rationales through the venous route.
  
  
  
  A hemodynamic model is developed in the entire coronary sinusal venous tree of the swine heart. A key finding is that the coronary sinusal venous system complies with the area preservation rule for efficient venous return while the coronary arterial tree obeys the minimum energy hypothesis. This model can also serve as a physiological reference state to test various therapeutic rationales through the venous route.
authors: Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing, People's Republic of China.|State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, People's Republic of China.
authors: Hao
authors: H
authors: Wu
authors: California Medical Innovations Institute, San Diego, California.
authors: Ghassan S
authors: GS
authors: Kassab
authors: Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing, People's Republic of China; tanwch@pku.edu.cn.|State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, People's Republic of China.|Shenzhen Graduate School, Peking University, Shenzhen, People's Republic of China; and.
authors: Wenchang
authors: W
authors: Tan
authors: Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing, People's Republic of China.|State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, People's Republic of China.|College of Medicine, Hebei University, Baoding, People's Republic of China.
authors: Yunlong
authors: 0000-0003-4121-3224
authors: Y
authors: Huo
mesh_terms: D000818:Animals; D001783:Blood Flow Velocity / Q000502:physiology*; D003326:Coronary Circulation / Q000502:physiology*; D054326:Coronary Sinus / Q000502:physiology*; D003331:Coronary Vessels / Q000502:physiology*; D006439:Hemodynamics / Q000502:physiology; D008955:Models, Cardiovascular; D013552:Swine; D014680:Veins / Q000502:physiology*; D014699:Venules / Q000502:physiology*
keywords: area preservation; coronary venous circulation; hemodynamics; morphometry