Unseen Branch model based on physiologic principles for perfusion simulation of coronary arteries

Epicardial coronary arteries bifurcate to small vessels and transport blood to the heart tissue. As some of these vessel sizes are below the image resolution of typical imaging modalities, they are often missed when segmenting coronary arteries. These vessels, however, transport blood to the myocardium and pressure loss can be overestimated when they are not modeled in the coronary arteries as they generally taper after vessels bifurcate. We developed methods to model vessels below image resolution using the assumption that healthy epicardial coronary arteries transport blood while minimizing pressure loss. Ideal pressure loss was computed using the Poiseuille pressure loss when the vessel has no tapering while maintaining an input flow rate along the vessel path. Pressure loss of an actual vessel without diseases is computed and continually updated as unseen branches are added until the same pressure loss as in the ideal vessel is obtained. Flow to the added unseen branches is computed using scaling laws. The unseen branch model was validated using ideal cylinder models with various tapering ratios and image-based patient-specific coronary artery models. Further, perfusion simulation was performed by incorporating the unseen branch models and blood pressure and perfusion territories were compared against the ones without them.