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Golden ratio and fractals in mitral valve geometry: Potential implications for valve imaging assessment

Luca Deorsola, Alessandra Bellone

Nowadays, the procedure of choice to manage a diseased Mitral Valve is represented by conservative treatment. Geometrical references are fundamental to perform a correct evaluation on a diseased valve, to plan the best repair strategy and to assess its results, both during the procedure and at follow-up. In the last decades, the number and the precision of these references have widely grown, due to a significant amount of research, as well as to a rapid empowering of imaging software and devices. Therefore, the routine measurements now obtainable from the different imaging techniques allow an extensive and deep spatial evaluation of valve geometry. Similarly, both repair techniques and devices have undergone a consistent improvement in the last years, adding to traditional surgery a wide series of percutaneous and hybrid procedures. In this scenario, an accurate geometrical analysis of the whole valve is actually mandatory, particularly when a hybrid or percutaneous approach is chosen and imaging is the only available eye. In two recently published papers, we hypothesized that the healthy Mitral Valve could have a geometrical structure based on Golden Ratio, Fibonacci Series and Fractals, a scalar 3D model where all components are related one another by defined proportions and fit together like the pieces of a puzzle. Such a model, with the use of very simple calculations, can describe every geometrical reference of the Mitral Valve and seems to predict their expected normal values.

After a brief summary about the results of our previous research, we have reviewed literature concerning the most common geometrical references retrievable from imaging and currently employed to evaluate the Mitral Valve. Published data and normality ranges have been compared with the values obtained from the 3D model, showing how it seems to produce the same results and give them a logical interpretation.