Derivation and sensitivity analysis of a novel one-dimensional model of coronary blood flow accounting for vessel taper & boundary slip

Computational models of coronary flow allow quantification of virtual fractional flow reserve (vFFR) and absolute flow, reducing the need for invasive testing in supporting a diagnosis of ischaemic heart disease (IHD). One-dimensional (1D) models of coronary flow are an emerging tool, which provide rapid assessment of coronary physiology. However, they currently do not fully account for side branch flow, the importance of which for clinically indeterminate cases is disputed. In the current study, we derive a novel 1D model of coronary flow from the Navier-Stokes equations, which accounts for vessel taper, convective acceleration and boundary slip. Using 15 idealised coronary arterial anatomies derived from patient data, we compared vFFR results from our model with those from a pre-existing 1D model of coronary flow. The techniques showed strong correlation (r=0.99, p < 0.001) with close agreement. Through a novel output-constrained global sensitivity analysis (GSA), we demonstrated that anatomical parameters, particularly the magnitude of simulated side branches significantly influences vFFR in the diagnostic grey zone (0.75 - 0.85) and absolute coronary flow regardless of stenosis severity. This challenges the commonly accepted dominance of stenosis parameters. We present a more mathematically and anatomically consistent 1D system for modelling coronary flow, which demonstrated modest differences with established models. GSA highlighted the influence of the flow diameter (Murray) scaling exponent in all cases when computing flow and in intermediate epicardial stenoses when quantifying vFFR. This work highlights the importance of accurately quantifying side branch flow when computing virtual coronary physiology.