PLoS One

Quantitative analysis of the vascular network anatomy is critical for the understanding of the vasculature structure and function. In this study, we have combined microcomputed tomography (microCT) and computational analysis to provide quantitative three-dimensional geometrical and topological characterization of the normal kidney vasculature, and to investigate how 2 core genes of the Wnt/planar cell polarity, Frizzled4 and Frizzled6, affect vascular network morphogenesis. Experiments were performed on frizzled4 (Fzd4-/-) and frizzled6 (Fzd6-/-) deleted mice and littermate controls (WT) perfused with a contrast medium after euthanasia and exsanguination. The kidneys were scanned with a high-resolution (16 μm) microCT imaging system, followed by 3D reconstruction of the arterial vasculature. Computational treatment includes decomposition of 3D networks based on Diameter-Defined Strahler Order (DDSO). We have calculated quantitative (i) Global scale parameters, such as the volume of the vasculature and its fractal dimension (ii) Structural parameters depending on the DDSO hierarchical levels such as hierarchical ordering, diameter, length and branching angles of the vessel segments, and (iii) Functional parameters such as estimated resistance to blood flow alongside the vascular tree and average density of terminal arterioles. In normal kidneys, fractal dimension was 2.07±0.11 (n = 7), and was significantly lower in Fzd4-/- (1.71±0.04; n = 4), and Fzd6-/- (1.54±0.09; n = 3) kidneys. The DDSO number was 5 in WT and Fzd4-/-, and only 4 in Fzd6-/-. Scaling characteristics such as diameter and length of vessel segments were altered in mutants, whereas bifurcation angles were not different from WT. Fzd4 and Fzd6 deletion increased vessel resistance, calculated using the Hagen-Poiseuille equation, for each DDSO, and decreased the density and the homogeneity of the distal vessel segments. Our results show that our methodology is suitable for 3D quantitative characterization of vascular networks, and that Fzd4 and Fzd6 genes have a deep patterning effect on arterial vessel morphogenesis that may determine its functional efficiency

A Novel Method for Visualization of Entire Coronary Arterial Tree

The complexity of the coronary circulation especially in the deep layers largely evades experimental investigations. Hence, virtual/computational models depicting structure-function relation of the entire coronary vasculature including the deep layer are imperative. In order to interpret such anatomically based models, fast and efficient visualization algorithms are essential. The complexity of such models, which include vessels from the large proximal coronary arteries and veins down to the capillary level (3 orders of magnitude difference in diameter), is a challenging visualization problem since the resulting geometrical representation consists of millions of vessel segments. In this study, a novel method for rendering the entire porcine coronary arterial tree down to the first segments of capillaries interactively is described which employs geometry reduction and occlusion culling techniques. Due to the tree-shaped nature of the vasculature, these techniques exploit the geometrical topology of the object to achieve a faster rendering speed while still handling the full complexity of the data. We found a significant increase in performance combined with a more accurate, gap-less representation of the vessel segments resulting in a more interactive visualization and analysis tool for the entire coronary arterial tree. The proposed techniques can also be applied to similar data structures, such as neuronal trees, airway structures, bile ducts, and other tree-like structures. The utility and future applications of the proposed algorithms are explored

Biophysical Model of the Spatial Heterogeneity of Myocardial Flow

The blood flow in the myocardium has significant spatial heterogeneity. The objective of this study was to develop a biophysical model based on detailed anatomical data to determine the heterogeneity of regional myocardial flow during diastole. The model predictions were compared with experimental measurements in a diastolic porcine heart in the absence of vessel tone using nonradioactive fluorescent microsphere measurements. The results from the model and experimental measurements showed good agreement. The relative flow dispersion in the arrested, vasodilated heart was found to be 44% and 48% numerically and experimentally, respectively. Furthermore, the flow dispersion was found to have fractal characteristics with fractal dimensions (D) of 1.25 and 1.27 predicted by the model and validated by the experiments, respectively. This validated three-dimensional model of normal diastolic heart will play an important role in elucidating the spatial heterogeneity of coronary blood flow, and serve as a foundation for understanding the interplay between cardiac mechanics and coronary hemodynamics

Biophysical Model of the Spatial Heterogeneity of Myocardial Flow

The blood flow in the myocardium has significant spatial heterogeneity. The objective of this study was to develop a biophysical model based on detailed anatomical data to determine the heterogeneity of regional myocardial flow during diastole. The model predictions were compared with experimental measurements in a diastolic porcine heart in the absence of vessel tone using nonradioactive fluorescent microsphere measurements. The results from the model and experimental measurements showed good agreement. The relative flow dispersion in the arrested, vasodilated heart was found to be 44% and 48% numerically and experimentally, respectively. Furthermore, the flow dispersion was found to have fractal characteristics with fractal dimensions (D) of 1.25 and 1.27 predicted by the model and validated by the experiments, respectively. This validated three-dimensional model of normal diastolic heart will play an important role in elucidating the spatial heterogeneity of coronary blood flow, and serve as a foundation for understanding the interplay between cardiac mechanics and coronary hemodynamics

A Novel Method for Visualization of Entire Coronary Arterial Tree

The complexity of the coronary circulation especially in the deep layers largely evades experimental investigations. Hence, virtual/computational models depicting structure-function relation of the entire coronary vasculature including the deep layer are imperative. In order to interpret such anatomically based models, fast and efficient visualization algorithms are essential. The complexity of such models, which include vessels from the large proximal coronary arteries and veins down to the capillary level (3 orders of magnitude difference in diameter), is a challenging visualization problem since the resulting geometrical representation consists of millions of vessel segments. In this study, a novel method for rendering the entire porcine coronary arterial tree down to the first segments of capillaries interactively is described which employs geometry reduction and occlusion culling techniques. Due to the tree-shaped nature of the vasculature, these techniques exploit the geometrical topology of the object to achieve a faster rendering speed while still handling the full complexity of the data. We found a significant increase in performance combined with a more accurate, gap-less representation of the vessel segments resulting in a more interactive visualization and analysis tool for the entire coronary arterial tree. The proposed techniques can also be applied to similar data structures, such as neuronal trees, airway structures, bile ducts, and other tree-like structures. The utility and future applications of the proposed algorithms are explored