###### Abstract  
BackgroundThe treatment of coronary stenosis is decided by performing high risk invasive surgery to generate the fractional flow reserve diagnostics index, a ratio of distal to proximal pressures in respect of coronary atherosclerosis. Non-invasive methods are a need of the times that necessitate the use of mathematical models of coronary hemodynamic physiology. This study proposes an extensible mathematical description of the coronary vasculature that provides an estimate of coronary fractional flow reserve. _Methods._ By adapting an existing computational model of human coronary blood flow, the effects of large vessel stenosis and microvascular disease on fractional flow reserve were quantified. Several simulations generated flow and pressure information, which was used to compute fractional flow reserve under several conditions including focal stenosis, diffuse stenosis, and microvascular disease. Sensitivity analysis was used to uncover the influence of model parameters on fractional flow reserve. The model was simulated as coupled non-linear ordinary differential equations and numerically solved using our implicit higher order method. _Results._ Large vessel stenosis affected fractional flow reserve. The model predicts that the presence, rather than severity, of microvascular disease affects coronary flow deleteriously. _Conclusions._ The model provides a computationally inexpensive instrument for future in silico coronary blood flow investigations as well as clinical-imaging decision making. A combination of focal and diffuse stenosis appears to be essential to limit coronary flow. In addition to pressure measurements in the large epicardial vessels, diagnosis of microvascular disease is essential. The independence of the index with respect to heart rate suggests that computationally inexpensive steady state simulations may provide sufficient information to reliably compute the index. coronary vasculature; lumped parameter model; fractional flow reserve; computational cardiology +
Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([[https://creativecommons.org/licenses/py/4.0/](https://creativecommons.org/licenses/py/4.0/)]([https://creativecommons.org/licenses/py/4.0/](https://creativecommons.org/licenses/py/4.0/))). Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([[https://creativecommons.org/licenses/py/4.0/0](https://creativecommons.org/licenses/py/4.0/0)]([https://creativecommons.org/licenses/py/4.0/0](https://creativecommons.org/licenses/py/4.0/0))). Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons. diagnostics [4; 5; 6]. FFR is clinically measured by determination of the ratio of blood flow through a stenosed vessel to that in the same vessel in the absence of stenosis [7]. In recent times, non-invasive computed tomography angiography combined with computational fluid dynamics (CFD) have become increasingly prevalent in estimating FFR, and aim at reducing the significant risks associated with invasive pressure wire measurements [8]. However, multiple complex physiological processes render uncertain FFR estimation [9]. In particular, the clinical literature suggests that micro-vascular dysfunction and stenosis morphology play a significant role in the estimated FFR. In addition, surgical and pharmacological sensitivity remains limited where adverse events often occur in critically ill patients, such as those with renal failure [10], where diagnostics are sub-optimal. As such, the use of FFR to determine clinical intervention depends on quantification of the vascular structure and function. _A brief overview of FFR modelling:_ Computed tomography angiography-driven computational estimation of FFR is now an advanced technology [11].