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Like a column collapsing under the burden of a heavy roof, erectile dysfunction is a classical mechanical engineering problem, says a US urologist. Using mathematical models of penis geometry and hydrostatic pressure, doctors can predict when penises will fail – and in which vagina – he says.

The most widely investigated parameter of penile rigidity is intracavernosal pressure (ICP) – the fluid pressure achieved by blood build up in the two expandable "caverns" of the penis. For a healthy man, the erect ICP is between 60 and 90 millimetres of mercury (mmHg), but can drop to just 30 mmHg, in men with erectile dysfunction (ED).

Anti-impotence drugs, such as Viagra, work by relaxing arterial muscles and allowing more blood, and hence more pressure, to build up in the penis.

But Daniel Udelson, a research urologist and professor of aerospace engineering at Boston University, thought that penis geometry - specifically the ratio of width to length - ought to play a significant role in the robustness of an erection against the force of sexual intercourse.
Ancient formula

So Udelson developed a model that would predict the buckling force, based on penis length, circumference and the ease of expandability over a range of ICPs - it is a direct adaptation of 200-year-old column buckling research by Swiss mathematician Leonard Euler.

Udelson tested the model against 57 men with erectile dysfunction. Each was measured by slowly injecting their penises with saline solution until erect. Udelson then applied a force to the tip of the penis until it started to bend, the first sign of buckling.

The model correctly predicted the buckling forces for 80% of patients - forces ranged from about 2 kilograms to just 0.3 kg given a pressure of 50 mmHg. But the buckling force during intercourse doesn't just rely a man's blood flow and penis shape, it also depends on his partner's vagina.

Previous studies have found that the force required enter a vagina, which depends on a vaginal diameter and lubrication, ranges from 1.5 to 2.5 kg. So, "an individual male may exhibit ED with one partner but not with another," says Udelson ... (more)

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