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Quantification of pressure drop across stenotic arteries is a major element in the functional assessment of occlusive arterial disease. Accurate estimation of the pressure drop with a numerical model allows the calculation of Fractional Flow Reserve (FFR), which is a haemodynamic index employed for guiding coronary revascularisation. Its non-invasive evaluation would contribute to safer and cost-effective diseases management. In this work, we propose a new formulation of a reduced-order model of trans-stenotic pressure drop, based on a consistent theoretical analysis of the Navier-Stokes equation. The new formulation features a novel term that characterises the contribution of turbulence effect to pressure loss. Results from three-dimensional computational fluid dynamics (CFD) showed that the proposed model produces predictions that are significantly more accurate than the existing reduced-order models, for large and small symmetric and eccentric stenoses, covering mild to severe area reductions. FFR calculations based on the proposed model produced zero classification error for three classes comprising positive (≤ 0.75), negative (≥ 0.8) and intermediate (0.75 − 0.8) classes.

Interruptions in nonlinear wave propagation, commonly referred to as wave breaks, are typical of many complex excitable systems. In the heart they lead to lethal rhythm disorders, the so-called arrhythmias, which are one of the main causes of sudden death in the industrialized world. Progress in the treatment and therapy of cardiac arrhythmias requires a detailed understanding of the triggers and dynamics of these wave breaks. In particular, two very important questions are: 1) What determines the potential of a wave break to initiate re-entry? and 2) How do these breaks evolve such that the system is able to maintain spatiotemporally chaotic electrical activity? Here we approach these questions numerically using optogenetics in an in silico model of human atrial tissue that has undergone chronic atrial fibrillation (cAF) remodelling. In the lesser studied sub-threshold illumination régime, we discover a new mechanism of wave break initiation in cardiac tissue that occurs for gentle slopes of the restitution characteristics. This mechanism involves the creation of conduction blocks through a combination of wavefront-waveback interaction, reshaping of the wave profile and heterogeneous recovery from the excitation of the spatially extended medium, leading to the creation of re-excitable windows for sustained re-entry. This finding is an important contribution to cardiac arrhythmia research as it identifies scenarios in which low-energy perturbations to cardiac rhythm can be potentially life-threatening., Author summary Electric turbulence in the heart is associated with complex spatiotemporal dynamics of nonlinear excitation waves. This life-threatening state is initiated by wavebreaks and maintained by self-organized vortices of abnormal excitation. Control over this state is achieved via defibrillation, a method whose efficacy relies on understanding the role of electric vortices in the onset and perpetuation of the turbulent state. However, in biological tissue, these vortices remain largely elusive in experiments due to limitations of visualisation. In order to study the spatiotemporal evolution of vortices in the heart precisely, reversibly and in real-time, we apply computational cardiac optogenetics on a mathematical model for human atrial tissue. Our study demonstrates a heretofore unidentified mechanism of wavebreak initiation, in the absence of standard markers of excitable medium vulnerability. This finding is an important contribution to cardiac arrhythmia research as it identifies how low-energy perturbations to cardiac rhythm can be potentially life-threatening, and render a defibrillation strategy to backfire.