The Golden Proportion in the scallop geometry of normal mitral valves. When nature plays with jigsaw puzzles.

INTRODUCTION: The Golden Proportion is a particular geometric ratio between two segments. It results in an irrational number, commonly rounded to 1.618, or 0.618, and showing unique geometrical/mathematical properties. Its presence has been documented in a huge amount of natural settings, as well as the human body and the heart. In light of a previous research of ours, about its presence in the Coaptation Triangle, we investigated the dimensions of both mitral leaflets in healthy mitral valves and then compared our results to literature data, in order to search whether this proportional pattern could be extended to other valve aspects. METHODS AND RESULTS: Forty-one adults, with healthy mitral valves, underwent 2D echocardiography. Adequate long-axis three-chamber view images were chosen, at mid-diastole, where the central scallop of both the anterior and posterior leaflets (A2 and P2, respectively) could be well identified and measured. We then investigated these measurements, calculating their ratio and comparing our findings to literature data on normal mitral anatomy. The ratio between the two scallop heights appeared very close to the Golden Ratio. Literature data supported our results and, apparently, showed the mitral leaflets to be like a jigsaw puzzle of components highly interconnected each other with an extremely simple geometry, based on the Golden Proportion. CONCLUSION: The Golden Proportion looks to determine the geometry of normal mitral scallops. Studying such a pattern of anatomical proportions could improve surgical techniques for conservative surgery, as well as innovate the design of mitral repair rings and valve prostheses.

Coaptation Triangle and Golden Proportion in mitral valve anatomy. Does nature play with geometry?

INTRODUCTION: The Coaptation Triangle, or Tenting Area, can be identified on long-axis 2D images. Its assessment is a routine practice during echocardiographic mitral evaluation. The Golden Proportion is a particular geometric ratio between two segments. Its value is an irrational number, commonly rounded to 0.618 and showing unique geometrical/mathematical properties. Interestingly, its presence has been documented in an extremely variable number of natural settings. Hypothesizing the presence of the Golden Proportion in normal mitral anatomy, we examined the Coaptation Triangle of healthy valves to investigate such a theory. METHODS AND RESULTS: A total of 41 healthy adults, with normal mitral valves, underwent 2D echocardiography. Adequate images were chosen and loaded into custom software. Firstly, the Coaptation Triangle was manually drawn by the operator. Then, a second Coaptation Triangle, with the same base, but based on Golden Proportion, was automatically built by the software. Eventually, the two triangles were analyzed and compared. All retrieved measurements were investigated for differences and correlations. Ratios close to the Golden Proportion were found in several locations of the manually drawn Coaptation Triangle. On the other hand, comparing the manually drawn Coaptation Triangle with the automatically built one, no significant differences were revealed, and very strong correlations were demonstrated. CONCLUSION: The Golden Proportion appears present in the geometry of normal mitral valves. Studying such an aspect and identifying disruption in anatomical proportions could improve early diagnosis of mitral alterations, and allows a more standardized follow-up and help surgeons to plan a repair strategy, particularly quantifying the needed surgical modifications.