A universal mathematical model applied to the congenital ventral penile curvature

The macroscopic dynamic of fetal penis development presents a pattern resembling the unfolding of a spiral, so congenital ventral penile curvature could indicate that this natural sequence has been interrupted. Our aim in this article is to offer a mathematical model of congenital ventral curvature of the penis.

Five individuals who presented with congenital ventral penile curvature and three who presented with acquired penile ventral curvature due to Peyronie's disease were evaluated. The penises were photographed during an induced erection test and the penile curvature patterns were compared with an equiangular spiral. When an association was found, a potential relationship to the golden spiral-a type of equiangular spiral-was also assessed. The mathematical spiral relationships were analyzed using Wolfram CDF Player® (Logarithmic Spiral) and PhiMatrix® software. The Wolfram software generated logarithmic spirals equivalent to the penile curvature with appropriate mathematical values. The PhiMatrix software, which builds any golden spirals from golden rectangles, was used to check whether the spiral was golden as well as equiangular.

An equiangular spiral that was also golden was found in all cases of congenital ventral penile curvature. In contrast, none of the acquired penile ventral curvature cases showed a specific pattern.

Congenital ventral penile curvature has the mathematical pattern of a golden spiral. Our results offer a mathematical algorithm for potential use in surgical reconstruction procedures, regenerative medicine, tissue engineering, robotics, and body-machine interfaces.