By observing the perfect geometry of a tricuspid aortic valve, a team of cardiac surgeons speculated that an approximation to the golden ratio might be present between its components, and the Fibonacci spiral would fit into the valve, representing a very interesting way to describe its fascinating symmetry.
The ratio a+ b/a=a/b=1.618 was dubbed the “golden section” in the nineteenth century, but it was known to Euclid as the mean and extreme ratio. During the 13th century, the brilliant mathematician Leonardo Bonacci, better known as Fibonacci, detailed his famous sequence in the Liber Abaci, in which the ratio of each subsequent number approaches the value of 1.618. This sequence may be used to produce a spiral that is inscribed in a rectangle composed of squares with sides generated by the same sequence.
![Fig. 1. The golden perfection of the aortic valve. The golden hexagon is a set of six points, which is projectively equivalent to the vertices of a regular pentagon togetherwith its center [4]. A Fibonacci spiral is composed of quarter-circle arcs inscribed in squares of integer Fibonacci-number side, shown for square sizes 1, 1, 2, 3, 5, 8 (Fig. 1a). The figure shows the fascinating symmetry of the aortic valve that ultimately can be represented by six Fibonacci spirals inscribed in regular hexagon that includes golden pentagons, squares, rectangles and triangleswith the same aspect ratio of 1.618 (Fig. 1m).](https://d3i71xaburhd42.cloudfront.net/57d936e36deb3559029065a90f8a0a716887689e/2-Figure1-1.png)
The team developed a six-step process:
1) A trans-esophageal short axis view of the aortic valve was obtained, and three golden rectangles with a+b/a=a/b=1.618 were created from the internal edge to the external edge, approximating the two-dimensional silhouette of the sinuses of Valsalva, and a golden hexagon was then generated from the union of the rectangles (Fig. 1b/c).
2) The free edges of the aortic leaflets were highlighted in red, and the valve center was approximated to the center of the hexagon formed by the three golden rectangles (Fig. 1d/e).
3) To make the Fibonacci spirals for each leaflet, divide each rectangle into four golden rectangles and squares with the same aspect ratio (Fig. 1f/g).
4) Following the Fibonacci sequence, six Fibonacci spirals were drawn (Fig. 1h/i).
5) The six spirals were emphasized (Fig. 1).
6) The hexagon, which comprises golden pentagons, rectangles, squares, and triangles with the same aspect ratio of 1.618 and resembles the aortic valve’s “golden perfection,” was then finished (Fig. 1).
The aortic valve may have a geometry that approximates apredetermined ratio of 1.618. Applying the Fibonacci series to our current understanding of the aortic valve may better explain its fascinating anatomy
Marco Moscarelli
The golden perfection of the aortic valve, Marco Moscarelli
Ruggero De Paulis
Published: December 2015
DOI: https://doi.org/10.1016/j.ijcard.2015.12.018