A rigorous analysis of blood flow must be based on the branching pattern and vascular geometry of the full vascular circuit of interest. It is experimentally difficult to reconstruct the entire vascular circuit of any organ because of the enormity of the vessels. The objective of the present study was to develop a novel method for the reconstruction of the full coronary vascular tree from partial measurements. Our method includes the use of data on those parts of the tree that are measured to extrapolate the data on those parts that are missing. Specifically, a two-step approach was employed in the reconstruction of the entire coronary arterial tree down to the capillary level. Vessels > 40 microm were reconstructed from cast data while vessels < 40 microm were reconstructed from histological data. The cast data were reconstructed one-bifurcation at a time while histological data were reconstructed one-sub-tree at a time by "cutting" and "pasting" of data from measured to missing vessels. The reconstruction algorithm yielded a full arterial tree down to the first capillary bifurcation with 1.9, 2.04 and 1.15 million vessel segments for the right coronary artery (RCA), left anterior descending (LAD) and left circumflex (LCx) trees, respectively. The node-to-node connectivity along with the diameter and length of every vessel segment was determined. Once the full tree was reconstructed, we automated the assignment of order numbers, according to the diameter-defined Strahler system, to every vessel segment in the tree. Consequently, the diameters, lengths, number of vessels, segments-per-element ratio, connectivity and longitudinal matrices were determined for every order number. The present model establishes a morphological foundation for future analysis of blood flow in the coronary circulation.
A hemodynamic analysis of coronary blood flow must be based on the measured branching pattern and vascular geometry of the coronary vasculature. We recently developed a computer reconstruction of the entire coronary arterial tree of the porcine heart based on previously measured morphometric data. In the present study, we carried out an analysis of blood flow distribution through a network of millions of vessels that includes the entire coronary arterial tree down to the first capillary branch. The pressure and flow are computed throughout the coronary arterial tree based on conservation of mass and momentum and appropriate pressure boundary conditions. We found a power law relationship between the diameter and flow of each vessel branch. The exponent is ϳ2.2, which deviates from Murray's prediction of 3.0. Furthermore, we found the total arterial equivalent resistance to be 0.93, 0.77, and 1.28 mmHg ⅐ ml Ϫ1 ⅐ s Ϫ1 ⅐ g Ϫ1 for the right coronary artery, left anterior descending coronary artery, and left circumflex artery, respectively. The significance of the present study is that it yields a predictive model that incorporates some of the factors controlling coronary blood flow. The model of normal hearts will serve as a physiological reference state. Pathological states can then be studied in relation to changes in model parameters that alter coronary perfusion. vascular reconstruction; coronary morphometry; flow simulation; flow resistance; transit time THE CORONARY VASCULAR SYSTEM constitutes the specialized channels that conduct oxygenated blood throughout the myocardium. The function of this network is to continuously supply blood to meet the requirements of the beating heart. Numerous attempts have been made at simulation of blood flow through these specialized channels to understand the spatial and temporal distribution of blood flow. Much of the modeling of the coronary circulation, however, has centered around lumped-parameter models in which the coronary vasculature or subgroup of vessels are treated as single entities whose whole behavior is characterized by a limited number of parameters. Despite the usefulness of such models, they are generally limited to global aspects of coronary blood flow (10, 21). For example, lumped models cannot be used to predict the significant spatial distribution of coronary blood flow.Over a decade ago, a program was initiated to provide the necessary details of the coronary vascular anatomy (vascular geometry and branching pattern) to enable anatomically based modeling of coronary circulation. In this approach, the vascular system comprised of millions of distensible vessel branches, strategically distributed and mostly embedded within the myocardium, must be modeled in as much detail as possible rather than "lumped." Although we are still several years away from accomplishing this goal, some important strides have been made. As a first step, Kassab and colleagues (13,(15)(16)(17)(18) reconstructed the entire vascular anatomy of the porcine heart in the framework of a ma...
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