Fractional Flow Reserve Evaluated as Metric of Coronary Stenosis — A Mathematical Model Study

Abstract

<b>Introduction:</b> Coronary arterial stenosis may impair myocardial perfusion with myocardial ischemia and associated morbidity and mortality as result. The myocardial fractional flow reserve (<i>FFR</i>) is clinically used as a stenosis-specific index. <b>Aim:</b> This study aims to identify the relation between the <i>FFR</i> and the degree of coronary arterial stenosis using a simple mathematical model of the coronary circulation. <b>Methods:</b> A mathematical model of the coronary circulation, including an arterial stenosis of variable degree, was developed. The relation between the <i>FFR</i> and the degree of stenosis (defined as the fractional cross sectional area narrowing) was investigated, including the influence of the aortic and venous pressures and the capillary resistance. An additional study concerning 22 patients with coronary artery disease permits comparison of clinical data and <i>in silico</i> findings. <b>Results:</b> The <i>FFR</i> shows an S-shaped relationship with the stenosis index. We found a marked influence of venous and aortic pressure and capillary resistance. The <i>FFR</i> is accompanied by a clinically relevant co-metric (<i>FFR</i> _<i>C</i> ), defined by the Pythagorean sum of the two pressures in the definition formula for <i>FFR</i>. In the patient group the <i>FFR</i> _<i>C</i> is strongly related to the post-stenotic pressure (<i>R</i> = 0.91). The <i>FFR</i> _<i>C</i> requires establishment of a validated cut-off point using future trials. <b>Conclusion:</b> The S-shaped dependence of <i>FFR</i> on the severity of the stenosis makes the <i>FFR</i> a measure of the ordinal scale. The marked influences of the aortic and venous pressures and the capillary resistance on the <i>FFR</i> will be interpreted as significant variations in intra- and inter-individual clinical findings. These fluctuations are partly connected to the neglect of considering the <i>FFR</i> _<i>C</i> . At otherwise identical conditions the <i>FFR</i> as measured at baseline differs from the value obtained during hyperemic conditions. This expected observation requires further investigation, as the current hyperemia based evaluation fails to take advantage of available baseline data.