Mechanisms of myocardium-coronary vessel interaction

Abstract

The mechanisms by which the contracting myocardium exerts extravascular forces (intramyocardial pressure, IMP) on coronary blood vessels and by which it affects the coronary flow remain incompletely understood. Several myocardium-vessel interaction (MVI) mechanisms have been proposed, but none can account for all the major flow features. In the present study, we hypothesized that only a specific combination of MVI mechanisms can account for all observed coronary flow features. Three basic interaction mechanisms (time-varying elasticity, myocardial shortening-induced intracellular pressure, and ventricular cavity-induced extracellular pressure) and their combinations were analyzed based on physical principles (conservation of mass and force equilibrium) in a realistic data-based vascular network. Mechanical properties of both vessel wall and myocardium were coupled through stress analysis to simulate the response of vessels to internal blood pressure and external (myocardial) mechanical loading. Predictions of transmural dynamic vascular pressure, diameter, and flow velocity were determined under each MVI mechanism and compared with reported data. The results show that none of the three basic mechanisms alone can account for the measured data. Only the combined effect of the cavity-induced extracellular pressure and the shortening-induced intramyocyte pressure provides good agreement with the majority of measurements. These findings have important implications for elucidating the physical basis of IMP and for understanding coronary phasic flow and coronary artery and microcirculatory disease.

Fig. 1.

Block diagram of the simulation platform. The main blocks are anatomic reconstruction (A), in vivo vessel mechanics (B), myocardium-vessel interaction (MVI) mechanisms (C and D), and the flow simulation (E). The model predictions under each MVI mechanism are evaluated in terms of transmural distribution of flow, velocity, intravascular pressures (P_IV), and diameters. The sarcomere stretch ratio (SSR), myocardium activation, and left ventricle, inlet, and outlet pressures (LVP, P_A, and P_V, respectively) are dynamic inputs (see Online Data Supplement I). The extravascular pressure (P_EV) and vessel dynamic axial stretch (λ_z) are determined for each tested MVI using Eqs. 2.

Fig. 2.

Schematic of network reconstruction based on the morphometric data of Kassab et al. (–33). Top left: a general layout of representative microvascular networks (rectangles) at 4 representative transmural layers interconnected through arterial and venous trees. P_A and P_V are the inlet and outlet boundary pressures, respectively. Top right: a symmetric arterial transmural tree. Length, diameter, and outlet flow conditions of both daughter vessels (denoted by asterisks) are mutually equal, except when daughter vessels feed different wall layers and are subject to different myocardial loading (bifurcations 1–3). Middle: a single microvascular network. A and V denote the microvascular arterial inlet and two venous outlets, respectively. Thin lines indicate capillaries, whereas thicker lines indicate arterioles and venules; broken lines are the perfused area boundaries. Thin arrows and solid and open circles represent capillaries that branch out in the network plane and in the upward and downward directions, respectively. Bottom: analog circuit for flow analysis in a single vessel segment. P_in and P_out are the segmental inlet and outlet pressures, respectively. ℜ and C are the vessel (nonlinear) resistance and capacitance, respectively.

Fig. 3.

Vessel loading configurations. A: casting configuration as determined from measurements. Vessel and myocardium cylinders are exposed to in situ axial stretch and transluminal pressure. B: externally unloaded configuration. The cylinders are closed and share a common length due to tethering. C: untethered configuration. Both cylinders are closed but allowed to freely stretch/contract. D: stress-free configuration. The residual stresses in both cylinders are released by a radial cut. OA, opening angle. E: loaded configuration. As described in A, but stretch and pressure depend on the specific MVI mechanism studied. F: predicted and measured pressure-diameter relations of coronary artery. Measured diameters in the passive heart (□; Ref. 19) were normalized against diameters under zero pressure and stretch. Model-predicted diameters were similarly normalized, using passive (solid line) and active (broken line) myocardium material laws.

Fig. 4.

The studied MVI mechanisms. A: varying elasticity (VE). Flow is affected by the activation-mediated changes in myocardial stiffness (represented by a spring). B: shortening-induced intracellular pressure (SIP). Flow is regulated by the difference between intravascular and contraction-induced myocyte intracellular pressures (arrows). C: cavity-induced extracellular pressure (CEP). P_EV is the interstitial pressure that varies linearly (20) from cavity pressure (LVP) at the endocardium to atmospheric pressure (P_atm) at the epicardium.

Fig. 5.

Predicted total flow (top) and subendocardial-to-subepicardial perfusion ratio (endo/epi perfusion ratio; bottom) under different MVI mechanisms. Heart rate (HR) is 90 beats/min and vessels are nonregulated. Baseline (dark gray bars) systolic/diastolic inlet pressure is 100/70 mmHg; inlet pressure waveforms lower (light gray bars) and higher (white bars) by 20 mmHg are also shown. Asterisks and diamonds indicate predictions under HR of 60 and of 120 beats/min, respectively. Horizontal lines denote the range of reported endo/epi ratios (23). Under CEP + VE, contractility (defined in this study as systolic myocardial stiffening) is predicted to slightly augment total flow (top, dashes), whereas under CEP + SIP, contractility (elevated intracellular pressure) is predicted to attenuate total flow (top, dots). Under mechanisms that do not include CEP, endo/epi ratio is unaffected by cardiac contraction, thus out of the measured (23) range. When CEP is included, 1) predicted endo/epi ratio is reduced to values closer to unity, 2) elevated HR attenuates total flow, and 3) endo/epi ratio varies with P_A.

Fig. 6.

Predicted P_IV waveform under MVI mechanisms that include VE (top) and under other mechanisms (bottom). Pressure is for a 30-μm subepicardial arteriole. Contrary to observations (62), VE and CEP + VE waveforms do not follow the input aortic pressure waveform (inset). The predicted pressure is attenuated in midsystole.

Fig. 7.

Predicted and measured systolic/diastolic diameter differences at various myocardial layers. A: arteriolar diameter differences predicted under CEP (continuous line), CEP + VE (dot-dashed line), and CEP + SIP mechanisms (dashed line), respectively. Diameter data: ■ and □, pig, 45–235 μm (22) and 50–250 μm (73), respectively; ♦, turtle, 28 μm (61); ▴, dog, 28 μm (61); ●, rabbit, 4–10 μm (14); ○, dog, 25 ± 11 μm (2). B: venous diameter differences predicted under CEP (continuous line), CEP + VE (dot-dashed line), and CEP + SIP (dashed line), respectively. Diameter data: ■ and □, pig, 25–150 μm (22) and 50–300 μm (73), respectively; ♦, turtle, 17 μm (61); ▴, dog, 22 μm (61); ○, dog, 28 ± 12 μm (2). All MVI mechanisms that include CEP are in agreement with the data.

Fig. 8.

Comparison of data [modified from Toyota et al. (63)] to predicted average blood velocity (solid line, scale at right) and lumen diameters (dashed line, scale at left) for subepicardium (top) and subendocardium (bottom). All graphs feature a common time scale. A: comparison of data and predictions under interaction mechanisms excluding CEP. From left to right: in vivo data in the canine heart (63), followed by predictions under no MVI (except for the dynamic vessels stretch; none), VE, and SIP mechanisms. B: same as at A but under interactions that include the CEP mechanism. From left to right: same data as at top, followed by predictions under CEP, CEP + VE, and CEP + SIP. Note that mechanisms that do not include CEP do not generate a significant subendocardial early systolic flow impediment. Observed subendocardial retrograde flow at early systole is predicted only by CEP and CEP + SIP.