Why is the subendocardium more vulnerable to ischemia? A new paradigm

Abstract

Myocardial ischemia is transmurally heterogeneous where the subendocardium is at higher risk. Stenosis induces reduced perfusion pressure, blood flow redistribution away from the subendocardium, and consequent subendocardial vulnerability. We propose that the flow redistribution stems from the higher compliance of the subendocardial vasculature. This new paradigm was tested using network flow simulation based on measured coronary anatomy, vessel flow and mechanics, and myocardium-vessel interactions. Flow redistribution was quantified by the relative change in the subendocardial-to-subepicardial perfusion ratio under a 60-mmHg perfusion pressure reduction. Myocardial contraction was found to induce the following: 1) more compressive loading and subsequent lower transvascular pressure in deeper vessels, 2) consequent higher compliance of the subendocardial vasculature, and 3) substantial flow redistribution, i.e., a 20% drop in the subendocardial-to-subepicardial flow ratio under the prescribed reduction in perfusion pressure. This flow redistribution was found to occur primarily because the vessel compliance is nonlinear (pressure dependent). The observed thinner subendocardial vessel walls were predicted to induce a higher compliance of the subendocardial vasculature and greater flow redistribution. Subendocardial perfusion was predicted to improve with a reduction of either heart rate or left ventricular pressure under low perfusion pressure. In conclusion, subendocardial vulnerability to a acute reduction in perfusion pressure stems primarily from differences in vascular compliance induced by transmural differences in both extravascular loading and vessel wall thickness. Subendocardial ischemia can be improved by a reduction of heart rate and left ventricular pressure.

Fig. 1.

Mechanisms of subendocardial vulnerability to ischemia. A: the observation that reduced perfusion pressure (P_perf) decreases the subendocardial-to-subepicardial perfusion ratio (Endo/Epi). B: simplified representation of the epicardial and endocardial coronary network. Under normal P_perf, the transmural distribution of flow is approximately homogeneous, implying that subepicardial and subendocardial time-averaged resistances (R_epi and R_endo, respectively) are approximately equal. The observed reduction in Endo/Epi must stem from a higher subendocardial resistance than the respective subepicardial resistance under reduced P_perf. Capacitors (representing vascular capacitance) are not considered as, according to circuit theory, they do not affect the time-averaged flow conditions. P_v, vascular pressure. C: physical interpretation of the resistance differences in B. Since vascular resistance highly depends on its diameter, a higher subendocardial resistance under reduced P_perf implies smaller diameters there. D_endo, endocardial diameter; D_epi, epicardial diameter. D: possible reasons for smaller subendocardial diameters under low P_perf. I: anatomic differences induce differences between the vessel diameter-pressure (D-P) relations in the subendocardium (Endo) versus the subepicardium (Epi), which result in higher subendocardial compliance (i.e., D-P slope). Hence, under similar transvascular pressures (ΔP), reductions (from shaded to open symbols) will induce a higher diameter decrease in subendocardial vessels (circles) than in subepicardial vessels (rectangles). II: functional differences. Differences between subendocardial and subepicardial time-averaged transvascular pressures (), when combined with vascular nonlinear D-P, result in higher subendocardial compliance and a consequent larger diameter reduction in subendocardial vessels, as long as the pressures are within the concave (high) range of the D-P curve.

Fig. 2.

Scheme of the simulation platform. A: network anatomy was reconstructed from statistical morphometric data of porcine coronaries (29–31). A, artery; V, vein. B: the nonlinear analog circuit used to analyze each vessel flow. P_IV, intravascular pressure; P_EV, extravascular pressures. R(t), vessel (time-varying) resistance; C(t), vessel (time-varying) capacitance. The entire network flow was analyzed based on the conditions of mass conservation both within each vessel and at each network junction (open circles). C: the vessel-in-myocardium micromechanical submodel. The in situ vessel D-P relationship was determined using a nonlinear finite deformation stress analysis of the vessel inside a cylinder of the myocardium. The analysis accounts for the measured stress-free (unloaded and free of residual stress) configuration of the two cylinders (left). Right, the submodel-predicted sigmoid (Eq. 2) D-P curve in an unpressurized 1.3-mm-diameter vessel (solid line) and comparison with coronary data (19) (error bars). x-axis, ΔP (equal to P_IV − P_EV, in mmHg); y-axis, diameter normalized relative to zero-pressure diameter (1.3 mm). D: each network vessel was subject to an P_EV, which was previously found (1) to stem from a combination of the effects of left ventricular cavity pressure (LVP; left) and contraction-induced intramyocyte pressure (38) (Eq. 3). P_atm, atmospheric pressure. E: heart rate (HR), contractility, hematocrit, LVP(t), P_perf(t), and P_v(t) are inputs to the flow analysis. F: predictions of the flow analysis in terms of transmural distribution of flow and dynamic ΔP were compared with experimental data.

Fig. 3.

Vessel D-P curves predicted by the model. A: differences between subendocardial (solid line) and subepicardial (dashed line) arterioles of ∼35 μm in diameter under baseline conditions. The arrow denotes the difference in diameters at diastolic pressure (see methods). Compliance is the curve slope. B: pressure-dependent (Eq. 2; solid line) versus constant (Eq. 4; dashed line) compliance in a ∼35-μm-diameter subendocardial arteriole. C: predicted effects of in situ vessel stretch on D-P curves. The diameter at vessel cast pressure (31) is an input to the vessel-in-myocardium submodel (Supplement III) and thus remains unchanged at different stretch values. Higher vessel axial stretch induces a lower slope of the vessel D-P curve (i.e., lower vessel compliance). x-Axis, ΔP (in mmHg); y-axis: vessel diameter (in μm).

Fig. 4.

Major determinants of the transmural difference in (_epi − _endo). A: predicted effects of myocardial contraction and of the vessel pressure-dependent (vs. constant) compliance. With contraction, levels of vessels that perfuse the subepicardium or drain it are substantially higher than the levels of the respective subendocardial vessels, whether vessel compliance is pressure dependent (solid line) or constant (dashed line). Without contraction (dashed-dotted line), the ΔP difference is considerably lower. B: predicted effects of systolic LVP. Low levels (60 mmHg, dashed-dotted line) are predicted to substantially decrease the ΔP difference compared with normal (120 mmHg, solid line) levels. C: predicted effects of vessel compliance. High compliance (dashed-dotted line), induced by a low level (1.0) of in situ stretch (see Fig. 3C), increases the predicted ΔP difference compared with normal (1.2, solid line) in situ stretch, although the effect is predicted to be lower compared with that of systolic LVP. D: predicted effects of a P_perf reduction. Lower P_perf levels (35 mmHg, dashed-dotted line) are predicted to moderately increase the ΔP difference compared with normal (95 mmHg; solid line) P_perf. x-Axis, vessel time-averaged diameter (in μm; veins on the left of 0 and arteries on the right of 0); y-axis, difference between values of the subepicardial vessels and respective subendocardial vessels (in mmHg).

Fig. 5.

Predicted sensitivity of Endo/Epi to major flow determinants. A: dependence of Endo/Epi on P_perf (x-axis, in mmHg). Under baseline conditions (Table 1), Endo/Epi is significantly affected by P_perf (solid line), whereas under constant compliance (linear D-P curves, Eq. 4, dashed-dotted line) or when the effect of myocardial contraction (dashed line) is ignored, the dependence is milder and baseline Endo/Epi is elevated. B: same as in A but with a focus on the effect of in situ stretch. Lower stretch (dashed-dotted line) induces a significant drop of Endo/Epi under a reduction of P_perf, whereas higher stretch (dashed line) induces the opposite effect. The data points are reproduced from Bache and Schwartz (2) (open squares), Chilian and Layne (9) (solid diamonds), and Boatwright et al. (3) (shaded circles). C: predicted sensitivity of Endo/Epi under baseline P_perf to perturbations (Table 1) in vessel compliance (CMP), HR, diastolic LVP (DLVP), systolic LVP (SLVP), cardiac contractility (CTR), and P_perf pulsatility (PPP). Solid and open columns indicate low and high values, respectively (Table 1). The horizontal solid line is the Endo/Epi level under the baseline level of the flow determinants. D: predicted sensitivity of the change of Endo/Epi under a reduction of P_perf from 95 to 35 mmHg (flow redistribution) to flow determinants. The solid horizontal line is the Endo/Epi change under baseline conditions. The effects on flow redistribution of vessel compliance (altered by varying the in situ vessel stretch between levels of 1.0 and 1.4; Table 1) can be seen to be substantial.

Fig. 6.

Anatomic determinants of subendocardial vulnerability in the beating heart. Shown are the predicted Endo/Epi under baseline (95 mmHg; Table 1) P_perf (open bars, left y-axis scale) and its change with a reduction (to 35 mmHg) of P_perf (solid bars, right y-axis scale) under the following anatomic conditions: 1) no transmural differences in diameter, vessel wall thickness, and vessel number density (D=,WT=,N = ); 2) thinner subendocardial vessel wall thickness (10), homogeneous diameters, and a higher number of subendocardial vessel (D=,WT↓,N↑); 3) thinner subendocardial vessel walls (10), homogeneous diameters, and no differences in vessel number (D=,WT↓,N = ); and 4) no transmural differences in vessel wall thickness and vessel numbers but larger subendocardial diameters (D↑,WT=,N = ). Under baseline anatomy (horizontal line), the subendocardial vessel wall is thinner and subendocardial vessel diameters are assumed to be larger than the respective subepicardial vessel diamters. The baseline vessel number is taken to be homogeneous (D↑,WT↓,N = ). The reported heterogeneity in wall thickness induces higher flow redistribution, i.e., a higher Endo/Epi decrease, as seen by the comparison of anatomic condition 4, solid bar, against the horizontal reference line. Transmural heterogeneity in diameters (anatomic condition 3 vs. the horizontal line) or in vessel numbers (anatomic condition 2 vs. 3) substantially affects Endo/Epi under baseline P_perf (open bars) but only modestly affects flow redistribution (solid bars).

Fig. 7.

Effect of contractility on coronary diameters. A: predicted diameters in representative subendocardial and subepicardial arterioles. Symbols indicate in each vessel as predicted by the flow analysis. Diameters were determined from the corresponding D-P curves in the subendocardium (solid line) and subepicardium (dashed line). Under baseline conditions (squares; Table 1), both subendocardial and subepicardial vessel diameters are 0.1 mm. Under high contractility (change of scale factor α in Eq. 2 from 140 to 280 mmHg/% shortening; diamonds), the vessel diameter decreases (compared with baseline; arrowheads) more prominently in the subendocardium than in the subepicardium due to the higher slope (i.e., compliance) of subendocardial D-P curve. Similar diameter changes occur under reduced P_perf (from 95 to 75 mmHg; circles). x-Axis, ΔP (in mmHg); y-axis, vessel diameter (in mm). B: predicted diameters in representative subendocardial and subepicardial venules. In the venules, high contractility reduces the predicted ΔP in both subepicardial and subendocardial veins. Subepicardial diameters decrease accordingly, whereas subendocardial diameters are hardly affected by the contractility-induced pressure change, due to the low slope of the D-P curve. In contrast, reduced P_perf hardly changes the predicted pressures and diameters since their ΔP is little affected by P_perf. C: longitudinal distribution of the transmural difference in diameter changes. The predicted decrease in arterial diameters due to contractility elevation (CTR; dashed line) is up to 5% higher in the subendocardium than in the subepicardium, whereas the reduction in subepicardial venous diameters is up to 10% higher than in subendocardial venous diameters. In contrast, after a P_perf reduction (solid line), the reduction in subepicardial venous diameters is only mildly lower than in subendocardial venous diameters. x-Axis, vessel time-averaged diameter (in μm; veins on the left of 0 and arteries on the right of 0); y-axis, difference between the predicted diameter change in vessels feeding the endocardium and epicardium (Endo_{D change} − Epi_{D change}).

Fig. 8.

Predicted dynamic flow waveforms in large arteries. A: flow waveform in a 450-μm-diameter artery perfusing the external half of the myocardial wall under normal and reduced (low) P_perf (from 95 to 35 mmHg; Table 1). B: flow waveform in a 450-μm-diameter artery perfusing the internal half of the myocardium under similar conditions. Both arteries share a common inlet. In the former vessel, the reduced P_perf attenuates flow during the entire cardiac cycle, whereas systolic flow in the latter hardly changes (arrows).