A Microstructurally-Motivated Framework to Study Autoregulation in the Coronary Circulation

Abstract Coronary autoregulation maintains relatively constant myocardial flow over a wide range of perfusion pressures through myogenic, shear-dependent, and metabolic control mechanisms. Understanding this phenomenon is challenging due to the coupled nature of these mechanisms and their heterogeneous effects throughout the coronary tree. In this study we developed a novel microstructurally-motivated model of coronary autoregulation based on constrained mixture theory, with anatomical and structural parameters calibrated through a homeostatic optimization framework. Autoregulation was simulated at three myocardial depths (subepicardium, midwall, and subendocardium), with the calibrated model accurately reproducing baseline hemodynamics and autoregulatory responses. For changes in epicardial pressure, our model reproduced experimentally measured subendocardium-to-subepicardium flow ratios (ENDO/EPI) and changes in vessel diameter, demonstrating its predictive capability. Furthermore, we extended Womersley’s theory to simulate phasic coronary hemodynamics with a time-varying intramyocardial pressure. This microstructurally-motivated framework provides a mechanistic foundation for investigating coronary autoregulation and long-term vascular growth and remodeling in pathphysiological conditions. Summary Coronary autoregulation is defined as the capability of the coronary circulation to maintain the blood supply to the heart over a range of perfusion pressures. This phenomenon is facilitated through intrinsic mechanisms that control the vascular resistance by regulating the mechanical function of smooth muscle cells. Understanding the mechanisms involved in coronary autoregulation is one of the most fundamental questions in coronary physiology. This paper presents a structurally-motivated coronary autoregulation model that uses a nonlinear continuum mechanics approach to account for the morphometry and vessel wall composition in two coronary trees in the subepicardial and subendocardial layers. The model is calibrated against diverse experimental data from literature and is used to study heterogeneous autoregulatory response in the coronary trees. This model drastically differs from previous models, which relied on lumped parameter model formulations, and is suited to the study of long-term pathophysiological growth and remodeling phenomena in coronary vessels. Competing Interest Statement The authors have declared no competing interest. Nomenclature - a - Autoregulatory scaling coefficient - A - SMC activation - c - Pulse wave velocity - c1 - Elastin material parameter - c2 - Collagen material parameter - c3 - Collagen dimensionless material parameter - c4 - SMCs material parameter - c5 - SMCs dimensionless material parameter - CEP - Cavity-induced pressure - D - Internal vessel diameter - G - Tissue constituent pre-stretch - H - Wall thickness - i - J - Bessel functions - L - Vessel length - L0 - Metabolic characteristic length - Lp - Path length - LV - Left ventricle - M - Mass per unit reference area of a tissue constituent - MVO2 - Myocardial oxygen consumption - NO - Nitric oxide - p - Lumen pressure - pim - Intramyocardial pressure - pLV - Left ventricle pressure - ptv - Transvascular pressure - q - Flow rate - s - Autoregulatory stimulus - Smax - Maximum SMC activation stress - SIP - Shortening-induced pressure - SMC - Smooth muscle cells - Tθθ - Circumferential wall tension - w - Strain energy density - Y - Vessel admittance - z - Longitudinal spatial coordinate - αWom - Womersley number - αmyo - Myogenic scaling coefficient - αmeta - Metabolic scaling coefficient - ατ - Shear-dependent scaling coefficient - β - Normalized myocardial depth - θ - Circumferential spatial coordinate - λ0 - Zero stretch - λM - Maximum active tension stretches - λz - Axial stretch - λθ - Circumferential stretch - μ - Blood viscosity - v - Tissue constituent mass fraction - ξ - Bifurcation diameter exponent - ρblood - Blood density - ρwall - Density of the vascular wall - σ - Hoop stress - τ - Wall shear stress - ϕ - Normalized autoregulatory response - ω - Angular frequency