Morphometry of Coronary Vasculature

Abstract

The morphological (i.e., geometric) features (e.g., diameter, length, vessel wall thickness, branching pattern) of the coronary vasculature (i.e., arteries, capillaries, and veins) are necessary to understand the circulation, to predict the pressure–flow relationship, to determine the longitudinal pressure and flow distribution, to understand the distensibility of the blood vessels, to study atherogenesis or restenosis, and to determine the effect of hypertension, hypertrophy, flow-overload, and tissue remodeling on the coronary circulation. This is analogous to the need to know the structure of the circuitry as well as the distribution of the resistors, capacitors, and inductors in an electric circuit if one wishes to analyze an electric instrument. Trying to understand the coronary circulation without the morphometric data is like exploring a continent without a map. Specifically, in a network analysis of coronary blood flow, the circuit must agree with the anatomical data on the branching pattern and geometry of the coronary vasculature, and the basic hemodynamic equations and boundary conditions must be satisfied.

Appendices

Appendix 1: Diameters, Lengths, and S/E for Segments and Elements of Arteries and Veins

Table 2.1 Diameters and lengths of vessel segments and elements in each order of vessels in pig RCA

Table 2.2 Diameters and lengths of vessel segments and elements of each order in pig LAD

Table 2.3 Diameters and lengths of vessel segments and elements of each order in pig LCx

Table 2.4 S/E in pig RCA, LAD, and LCx

Table 2.5 Major axis, major-to-minor axis ratio, and lengths of vessel segments and elements in each order of vessels in pig coronary sinusal veins

Table 2.7 Segment-to-element numbers ratio for each order of vessels in sinusal and coronary Thebesian veins of pig

Table 2.6 Major axis, major-to-minor axis ratio, and lengths of vessel segments and elements in each order of vessels in pig Thebesian veins

Appendix 2: Connectivity Matrix of Arteries and Veins

Table 2.8 Connectivity matrix of pig RCA

Table 2.9 Connectivity matrix of pig LAD

Table 2.10 Connectivity matrix of pig LCx

Table 2.11 Connectivity matrix C(m, n) for coronary sinusal veins of pig

Table 2.12 Connectivity matrix C(m, n) for Thebesian veins of pig

Appendix 3: Longitudinal Position Matrix of Arteries and Veins

Tables 2.13, 2.14, 2.15, 2.16, and 2.17 reprinted with permission from Kassab, Schatz, Imoto, and Fung (2000).

Table 2.13 Longitudinal position matrix of pig right coronary arterial tree

Table 2.14 Longitudinal position matrix of pig left anterior descending arterial tree

Table 2.15 Longitudinal position matrix of pig left circumflex arterial tree

Table 2.16 Longitudinal position matrix of pig coronary sinusal venous tree

Table 2.17 Longitudinal position matrix of pig coronary Thebesian venous tree

Appendix 4: Diameter and Length Asymmetry Ratios of Arteries and Veins

Tables 2.18, 2.19, 2.20, 2.21 and 2.22 Reprinted with permission from Kalsho and Kassab (2004)

Table 2.18 Asymmetry ratios of diameters and lengths of daughter vessels in each order of mother vessels in the RCA and its branches of the pig

Table 2.19 Asymmetry ratios of diameters and lengths of daughter vessels in each order of mother vessels in the LAD artery and its branches of the pig

Table 2.20 Asymmetry ratios of diameters and lengths of daughter vessels in each order of mother vessels in the LCx artery and its branches of the pig

Table 2.21 Asymmetry ratios of major diameters and lengths of daughter vessels in each order of mother vessels in the coronary sinus vein and its branches of the pig

Table 2.22 Asymmetry ratios of major diameters and lengths of daughter vessels in each order of mother vessels in the Thebesian veins and their branches of the pig

Appendix 5: Asymmetry Ratio Matrix

Tables 2.23, 2.24, and 2.25 reprinted with permission from Kaimovitz et al. (2008)

Table 2.23 Mean ± SD values for D_s/D_m for the left anterior descending (LAD) artery where D_m and D_s are the diameters of the mother and smaller daughters, respectively

Table 2.24 Mean ± SD values for D_s/D_m for the left circumflex (LCx) artery where D_m and D_s are the diameters of the mother and smaller daughters, respectively

Table 2.25 Mean ± SD values for D_s/D_m for the right coronary artery (RCA) where D_m and D_s are the diameters of the mother and smaller daughters, respectively

Appendix 6: Numbers for segments and elements

Table 2.26 Total no. of vessel elements in each order of pig RCA, LAD, LCx, and LCCA

Table 2.27 Total number of vessel elements in each order of sinusal and coronary Thebesian veins of pig

Appendix 7: Connectivity Matrix for Venous Arcades

Tables 2.28 and 2.29 reprinted with permission from Kassab et al. (1994b).

Table 2.28 Tree/arcade connectivity in veins of pig

Table 2.29 Morphometry and connectivity of tree/anastomoses in veins of pig

Appendix 8: Connectivity Matrix of Capillaries

Table 2.30 Connectivity of C_0a and C_0v to arteries and veins in RV and LV

Appendix 9: Diameters and Lengths of Capillary Segments

Tables 2.31 and 2.32 reprinted with permission by Kassab and Fung (1994).

Table 2.31 Segment diameters and lengths of pig coronary capillaries in RV free wall

Table 2.32 Segment diameters and lengths of pig coronary capillaries in LV free wall

Appendix 10: Sample Input File for the Arteriolar Tree Shown in Fig. 2.16

Table 2.33 Sample input file for the arteriolar tree shown in Fig. 2.16