Morphometric Reconstruction of Coronary Vasculature Incorporating Uniformity of Flow Dispersion

Figures

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  Figure 1. (A) Schematic of a single coronary vessel and the applied dynamic pressure boundary conditions. Pin is the inlet pressure, Pout is the outlet pressure, PT is the tissue pressure exerted by the myocardium, Pmid is the unknown intravascular pressure. (B) The vessel 3-element Windkessel model comprising two resistors R1, R2 and a capacitive element C that accounts for the vessel volume changes.

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  Figure 2. Comparison of the flow distribution in the terminal pre-capillary arterioles in the 400-vessel subtree under shear and myogenic controls prior vs. after diameter re-assignment. Each bin on the X-axis represents a 0.05 × 10−3 mm3/s range of terminal pre-capillary flows per cardiac cycle. The Y-axis is the pre-capillary frequency for each bin.

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  Figure 3. Comparison of the model-predicted time-averaged intravascular pressure distribution in the subtree after diameter re-assignment with the data sets of Chilian (1991) for pigs coronaries, of Tillmanns et al. (1981) for the epi-myocardium of rats and cats, of Fronek and Zweifach (1975) and Zweifach and Lipowsky (1977) for the cat mesentery, and of Davis et al. (1986), for the hamster cheek pouch. Model predictions and mesentery data show significant pressure drop in small micro-vessels.

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  Figure 4. Log-log plot of model prediction and data of flow dispersion (represented by CV = SD/Mean) vs. perfused sample mass. The slope of the linear fit equals 1–D, where D being the fractal dimension (Bassingthwaighte et al., 1989). The results yield D = 1.44 for the diameter-reassigned tree, D = 1.62 for the original reconstructed tree, D = 1.24 for the data of Matsumoto et al. (1999) in the sub-endocardial region. There is a close agreement between the data of Matsumoto et al. and the present model prediction for the diameter re-assigned tree, while predictions of the original reconstructed tree yields a CV of up to an order of magnitude higher than the data.

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  Figure 5. Flow spatial autocorrelation function between pairs of pre-capillary arterioles as a function of their spatial distance (Equation 4). Symbols are model estimates. The curves are single term exponentials of the form a · exp (−e/e0) + c fit to f(e) of the two subtrees. The parameter estimates are listed in Table 3.

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  Figure 6. The network longitudinal (downstream) pressure distribution under ±25% perturbations of the myogenic and flow parameters ρm (A), ϕm (B), Cm (C), and Fτmax(D), under ± 20 mmHg variations of the network outlet pressure Pout(E), and under ±50% variations of the terminal target flow rate qtarget (F). Depicted in each sub-figure are the pressure distribution in the reference case (solid line), and under positive (broken line) and negative (dash-dot line) perturbation.