Modeling cardiac microcirculation for the simulation of coronary flow and 3D myocardial perfusion

Purpose accurate modeling of blood dynamics in the coronary microcirculation is a crucial step towards the clinical application of in silico methods for the diagnosis of coronary artery disease (CAD). In this work, we present a new mathematical model of microcirculatory hemodynamics accounting for microvasculature compliance and cardiac contraction; we also present its application to a full simulation of hyperemic coronary blood flow and 3D myocardial perfusion in real clinical cases. Methods microvasculature hemodynamics is modeled with a compliant multi-compartment Darcy formulation, with the new compliance terms depending on the local intramyocardial pressure generated by cardiac contraction. Nonlinear analytical relationships for vessels distensibility are included based on experimental data, and all the parameters of the model are reformulated based on histologically relevant quantities, allowing a deeper model personalization. Results Phasic flow patterns of high arterial inflow in diastole and venous outflow in systole are obtained, with flow waveforms morphology and pressure distribution along the microcirculation reproduced in accordance with experimental and in vivo measures. Phasic diameter change for arterioles and capillaries is also obtained with relevant differences depending on the depth location. Coronary blood dynamics exhibits a disturbed flow at the systolic onset, while the obtained 3D perfusion maps reproduce the systolic impediment effect and show relevant regional and transmural heterogeneities in myocardial blood flow (MBF). Conclusion the proposed model successfully reproduces microvasculature hemodynamics over the whole heartbeat and along the entire intramural vessels. Quantification of phasic flow patterns, diameter changes, regional and transmural heterogeneities in MBF represent key steps ahead in the direction of the predictive simulation of cardiac perfusion. ### Competing Interest Statement The authors have declared no competing interest. * CAD : Coronary Artery Disease CBF : Coronary Blood Flow cCTA : coronary Computed Tomographic Angiography FFR : Fractional Flow Reserve LAD Left Anterior Descending MBF : Myocardial Blood Flow NS : Navier-Stokes RCA : Right Coronary Artery stress-CTP : stress Computed Tomographic Perfusion * p i : Pore pressure in Darcy compartment i K i Permeability of Darcy compartment i φ i : Fluid volume fraction of Darcy compartment i β i,j : Inter-compartment conductance between Darcy compartments i and j P LV Pressure in the left ventricular chamber P im : Intramyocardial pressure θ i : Mass source/sink term in Darcy compartment i γ Conductance of venous circulation p ra : Right atrium pressure ( nL ) i : Vessels length density of Darcy compartment i A i : Average cross section of vessels in Darcy compartment i C i : Compliance of vessels in Darcy compartment i μ : Blood dynamic viscosity κ : Specific permeability of cardiac tissue to blood flow δ i : Morphometry conductance factor of Darcy compartment i