Introduction:
Hydrodynamic theory predicts fluid approaches a point orifice with accelerating velocity in hemispheric shells, forming the basis for the proximal isovelocity surface area (PISA) method to quantify valve regurgitation. Previous CFD and in vitro work has shown that with a finite, non-point orifice, there is a small, systematic underestimation of flow that is approximately the ratio of contour velocity (va) to maximal orifice velocity (vo), e.g., roughly an 8% error if a 40 cm/s contour is used with a 5 m/s jet. The PISA method is further questioned in the setting of noncircular orifices, with concerns of further underestimation. We sought to quantify this impact with CFD.
Hypothesis:
Application of standard PISA analysis to an elliptical orifice leads to further flow underestimation, but the magnitude is negligible.
Methods:
Mathematical modeling of flow through a finite elliptical orifice was computed using the open-source incompressible flow solver Nalu. Forty-five permutations of valve flow were characterized by varying valve orifice area (0.1, 0.3 and 0.5 cm^2), ellipse axis ratios (1:1, 2:1, 3:1, 5:1, and 10:1), and max velocity (400, 500 and 600 cm/s). Computed hemispherical flow contours scaled to true orifice flow (Qc/Qo) and scaled computed area to true orifice area (Ac/Ao) were plotted against distance from the orifice scaled to a circular orifice with equivalent orifice area.
Results:
Qc/Qo and Ac/Ao for each ellipse axis ratio when plotted against normalized orifice distance produced the same curves for each permutation of valve orifice area and max velocity. Plotting Qc/Qo (or Ac/Ao) against va/vo reveals marginal underestimation of flow with physiologic elliptical axis ratios of 2:1 and 3:1 against a circular orifice with axis ratios of 1:1 (Figure 1).
Conclusions:
The added error in using PISA to approximate flow through an elliptical mitral valve orifice area is minimal compared to traditional assumptions of a circular mitral valve orifice.
Anterior Mitral Valve Orifice in a Dog
