Fast Virtual Fractional Flow Reserve Based Upon Steady-State Computational Fluid Dynamics Analysis

Figure 1. Processing Raw Clinical Data Angiograms of a diseased right coronary artery (left) have been segmented, and the reconstructed vessel is shown (middle) alongside the processed pressure data (right) within the VIRTUheart workflow environment.

Figure 2. Sample Finite Element Mesh Used for Simulations Mesh shown is produced from the angiogram shown in Figure 1. Details of the wall (blue) and inlet (green) are shown. The near-wall region is refined using prism elements.

Figure 3. Models for Computing vFFR The imaging and pressure input data for both novel models are those collected during routine coronary angiography (image data in yellow and aortic pressure data in green). The parameters of CMV physiology must be estimated (red). The type of simulation used to calculate vFFR values are shown in the blue boxes. vFFRps-trns is a function of 9 parameters, whereas vFFRsteady is a function of 4. Pseudotransient flow can be reconstructed using a 1D flow model representing the 3D vessel geometry coupled to the 0-dimensional Windkessel model. C = compliance; CMV = coronary microvasculature; R = resistance; vFFR = virtual fractional flow reserve; Z = impedance.

Figure 4. A Pseudotransient Pressure Result From an LAD Arterial Case Invasively measured FFR was 0.350 and the computed vFFR was 0.346. The pseudotransient result closely matches the invasively measured result (RMS norm: 0.026), despite no transient data being used in its computation. RMS = root mean square; other abbreviations as in Figure 3.

Figure 5. Bland-Altman Plots Demonstrating Agreement Between vFFR and Measured FFR The solid line indicates bias (mean delta), and the interrupted lines represent the upper and lower limits of agreement (SD: ±1.96). (A) Agreement for vFFRps-trns, and (B) agreement for vFFRsteady. Note the high number of cases in the clinically important FFR range from 0.7 to 0.9.

Figure 6. Pie Chart Demonstrates Relative Effect of Each Individual Model Input Parameter on Model Output (vFFR) Variance See Supplemental Appendix D.

Figure 7. Sensitivity Index Heatmap The main sensitivity indices (Si), total sensitivity indices (SiT), and interaction effects are displayed for the 4 input parameters: RCMV, geometry parameters (z1 and z2), and average proximal pressure (Pa). The axis on the right indicates the magnitude of the influence on output (vFFR) result, with higher values having a stronger influence on result. CMV resistance is the dominant influence on vFFR result. CMV = coronary microvascular; RCMV = CMV resistance; other abbreviations as in Figure 3.

Figure 8. Total and Interaction Model Input Effects Bar chart demonstrating the magnitude of the total (direct and interactions) effect on vFFR caused by the input parameters CMV resistance (RCMV), geometry parameters (z1 and z2) and average proximal pressure (Pa). Abbreviations as in Figure 7.