A Computer Reconstruction of the Entire Coronary Arterial Tree Based on Detailed Morphometric Data

Abstract

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 hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree

“…The impedance boundary conditions are computed through a Womersley-type model at every flow outlet. Both models are based on the measured morphometric data of Kassab et al (15,20). This is the first investigation to implement the time-domain model coupled with the frequencydomain model in the entire coronary arterial tree on the basis of experimentally measured morphometric data of the entire coronary arterial tree.…”

Pulsatile blood flow in the entire coronary arterial tree: theory and experiment

“…The morphometric and mechanical parameters used for the computation of the pulsatile flow through the arterial tree were adopted from our previous publications (13,19,22). The length and diameter of every vessel segment were assigned to the entire coronary arterial tree (22), on the basis of detailed morphometric data. The blood flow density () in the coronary arterial tree was assumed to be 1.23 g/cm 3 (8).…”

“…Figure 14 shows a comparison of the measured pressure-crosssectional area (pressure-CSA) relationship between these two models. Figure 7 shows a comparison of the flow waves when these two models are implemented in the entire coronary arterial trees (22). Although there is a phase angle and amplitude difference between the results, it is found the mean flow rates are similar.…”

“…Kassab et al (17,18,20) have previously measured the morphometric data of the coronary vasculature. Recently, a computer model of the entire coronary arterial tree has been developed by Mittal et al (22) based on measured morphometric data of Kassab et al (20). This model will serve as the platform for the present systematic pulse pressure and flow wave transmission analysis.…”

“…Here, we shall use the platform of the entire coronary arterial tree (22) to carry out a Womersley-type numerical analysis of pulse wave transmission. The constitutive equation that relates pressure to cross-sectional area for the several largest orders is based on experimental data (19).…”