An analytical, mathematical annuloplasty ring curvature model for planning of valve-in-ring transcatheter mitral valve replacement

Figures

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  Modeling and analysis of annuloplasty ring geometry before and after balloon dilation.

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  Figure 1. Curvature formula and derivation. Labeled image describing our mathematical model and parameter definition. Δα is the angle between the curve differential derivatives and Δs is the differential arc length.

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  Figure 2. Calibration geometries with corresponding curvature plots. The red circles indicate from which point curvature was calculated and correspond with the red circles in the plots below. Note that greater circularity corresponds to reduced variance levels and corners correspond to peaks in y-axis curvature. A perfect circle would be plotted as a zero-slope line as seen in the far left figure.

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  Figure 3. Curvature plot interpretation for annuloplasty rings. A, Data from dilation of a custom, 3-dimensional-printed, semi-rigid ring. This condition illustrates the result interpretation for a deformable, semi-rigid ring. B, Images describing the procedure of ring dilation for a Carpentier-Edwards Physio II M24 ring. Data were recorded for 3 separate conditions: the initial state, the final state (immediately postdilation), and the relaxed state (10 minutes after dilation). Curvature is plotted below with reported variance changes for this representative example.

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  Figure 4. Composite averaged curvature results for (A) Carpentier-Edwards Physio II, (B) Carpentier-Edwards Physio, (C) LivaNova Annuloflex, and (D) Edwards Geoform rings plotted against curve progress. Solid lines indicate initial state, dot slashed lines indicate final dilated state (after 30-second balloon dilation) and dotted lines indicate relaxed state (10 minutes after final dilated state). Blue and red coloring in A and B represent unique ring sizes for the given ring type.

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  Figure 5. Bar plot of curvature variance for all tested annuloplasty rings before balloon dilation (initial), after 30 seconds of dilation (final), and after 10 minutes of relaxation (relaxed). Relative curvature variance reduction between conditions indicates an increase in circularity for the given ring. Rings tested were Carpentier-Edwards Physio II and Physio, Edwards Geoform, and LivaNova Annuloflex.

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  Figure 6. An analytical, mathematical annuloplasty ring curvature model for planning of valve-in-ring transcatheter mitral valve replacement.