Virtual FFR Quantified with a Generalized Flow Model Using Windkessel Boundary Conditions

Figures

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  Figure 1. (a) The original angiography image (the coronary tree of interest is framed with red). (b) The black and white original image. (c) The resulting multistenotic coronary tree.

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  Figure 2. The 2D geometry considered. Arrows indicate the isoline orientation.

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  Figure 3. (a) Spline function approaching left coronary blood flow. (b) The flow function prescribed at the inlet I(t).

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  Figure 4. Windkessel electrical analogy.

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  Figure 5. (a) Schema of the invasive FFR technique. (b) A typical example of FFR measurement. Automated calculation of FFR (yellow) corresponds to the ratio of mean distal coronary pressure (green) to mean aortic pressure (red) during maximal hyperemia.

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  Figure 6. FFR calculation. The mutlistenotic coronary tree contains two lesions: 56% stenosis and 68% stenosis.

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  Figure 7. Velocity fields at peak diastole using generalized fluid model with Windkessel outlet BCs (a), free outlet BCs (c), and mixed outlet BCs (e). Corresponding pressure fields: Windkessel outlet BCs (b), free outlet BCs (d), and mixed outlet BCs (f).

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  Figure 8. Velocity field using generalized fluid model at peak systole (a) and peak diastole (b). Velocity field using Navier–Stokes model at peak systole (c) and peak diastole (d).

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  Figure 9. Velocity distributions near stenosis with the two flow models at different times of the cardiac cycle. (a) Peak diastole—generalized flow model. (c) Peak systole—generalized flow model. (b) Peak diastole—Navier–Stokes model. (d) Peak systole—Navier–Stokes model.

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  Figure 10. Distal sensor displacement according to the normal and tangential positions.

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  Figure 11. (a) Comparison between FFR values for Navier–Stokes model and non-Newtonian flow model obtained by moving the sensor in the normal direction. (b) Comparison between FFR values for Navier–Stokes model and non-Newtonian flow model obtained by moving the sensor in the tangential direction. The grey area represents critical FFR values.

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  Figure 12. (a) Comparison between FFR values for Navier–Stokes model and non-Newtonian flow model combined with free outlets or Windkessel BC obtained by moving the sensor in the normal direction. (b) Comparison between FFR values for Navier–Stokes model and non-Newtonian flow model combined with free outlets or Windkessel BC obtained by moving the sensor in the tangential direction.