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...
Abstract-It has been shown that right ventricle (RV) hypertrophy involves significant compensatory vascular growth and remodeling. The objective of the present study was to determine the functional implications of the vascular growth and remodeling through a full flow analysis of arterial tree down to first capillary segments. A computer reconstruction of RV branches including the proximal right coronary artery to the posterior descending artery was established based on measured morphometric data in arrested, vasodilated porcine heart. The flows were computed throughout the reconstructed trees based on conservation of mass and momentum and appropriate pressure boundary conditions. It was found that the flow rate was significantly increased in large epicardial coronary arteries in hypertrophic as compared with control hearts but normalized in the intramyocardial coronary arteries and smaller vessels in RV hypertrophy primarily because of the significant increase in number of arterioles. Furthermore, the wall shear stress was restored to nearly homeostatic levels throughout most of the vasculature after 5 weeks of RV hypertrophy. The compensatory remodeling in RV hypertrophy functionally restores the perfusion at the arteriolar and capillary level and wall shear stress in most of larger vessels. This is the first full analysis of coronary arterial tree, with millions of vessels, in cardiac hypertrophy that reveals the compensatory adaptation of structure to function. With the availability of detailed morphometric data on vascular geometry and branching pattern of RV branches in control and RV hypertrophy, a systematic hemodynamic analysis can be performed to investigate the adaptation of structure to function (perfusion). To facilitate the structure/ function analysis, our group has recently developed a computer algorithm 10 that allows full reconstruction of the entire coronary arterial tree down to the arterial capillaries (first capillary segments) from morphological cast and histological data. 1 The computer model facilitates the analysis of the coronary arterial circulation based on detailed anatomical data.Here, a computer reconstruction of the RV branches was implemented down to the capillary level in the right coronary artery (RCA) proximal to the posterior descending artery of control and RV hypertrophy. The detailed morphometric data (ie, vessel diameters, lengths, and numbers) were used to determine the flow throughout the vascular network as well as the wall shear stress. The blood flow was calculated under steady state in arrested, vasodilated pig hearts. The distribution of wall shear stress was studied in the entire coronary arterial tree. One major finding is that RCA flow is significantly increased because of a decrease in vascular resistance primarily attributable to the increase in number of small vessels. Although the flow is increased in large vessels (eg, epicardial), it is normalized in smaller vessels (eg, arterial capillaries and arterioles). The wall shear stress in the majority of vascu...
A new method to denude the endothelium without damage to media: structural, functional, and biomechanical validation. Am J Physiol Heart Circ Physiol 286: H1889-H1894, 2004; 10.1152/ ajpheart.00863.2003.-The intimial thickening that occurs in human and animal atherogenesis can be induced by mechanical injury to the endothelium. The objective of the present study was to develop a new method to induce arterial endothelial injury without damage to the media for future investigations of mechanisms of intimal thickening and atherogenesis. A specifically designed catheter was inserted into the common femoral artery of Wistar rats (n ϭ 9) through an arteriotomic mouth. After application of Tyrode solution containing 0.14 M KCl on the surface of the vessel, the vessel contracted onto the catheter. The catheter was then moved back and forth to scrape away the endothelium. The left common femoral artery of the same rat was subjected to the standard balloon injury model. The two models were evaluated structurally, functionally, and biomechanically. Structurally, we verified that both techniques remove the endothelium, but the balloon method damages the media. Functionally, we examined the contractile response of the artery to [K ϩ ] and norepinephrine 2 days after the denudation. We found that the right femoral artery underwent contraction in response to [K ϩ ], whereas the left artery did not. Furthermore, neither artery responded to norepinephrine. Biomechanically, we measured the pressure-diameter relationship and the zero-stress state of the vessel and computed the stress-strain relation. The circumferential stretch ratios at 120 mmHg were 1.38 Ϯ 0.08 for the control, 1.41 Ϯ 0.08 (P Ͼ 0.05) for the new method, and 1.56 Ϯ 0.09 for the balloon injury (P Ͻ 0.05). The opening angles at the zero-stress state were 113 Ϯ 21°for the control, 102 Ϯ 18°for the new method (P Ͼ 0.05), and 8 Ϯ 13°for the balloon injury (P Ͻ 0.001). In conclusion, the new method removes the endothelium while maintaining the structure, contractile function, and biomechanical properties of the vessel. injury; zero-stress state; balloon injury; endothelin THE ENDOTHELIAL CELLS that line the lumen of the blood vessel are extremely important for the normal function of the vessel. The endothelium is the largest autocrine, paracrine, and endocrine organ that regulates vessel tone, monocyte adhesion, platelet activation, thrombogenesis, inflammation, lipid metabolism, vessel growth, and remodeling (21, 23). Because endothelial injury is an important risk factor for atherosclerosis, numerous models of endothelial injury have appeared in the literature (10,12,13). Previous investigations have induced endothelial injury mechanically (via balloon distension, microsurgical instrument, or air desiccation) or chemically (via hydrochloric acid or Triton X-100) (2, 12). The most widely used model, however, is injury induced by a balloon overinflated into the lumen of the vessel and dragged along the lumen to scrape off the endothelium. Unfortunately, this technique...
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