4 weeks ago

Imagine that you and hundreds of millions of people were simultaneously imprisoned in an iron can of more than a thousand meters in diameter. There was no air, no light, only water. In a corner of the jar, only a small hole can lead to the outside, whoever can find this small mouth can escape. Once someone successfully escapes, the exit will be sealed and the rest will never be able to go out again. Even more frightening is that the shape of the cans is a bit irregular, and everyone can only carry one oxygen cylinder.

This terrible scene is not from science fiction movies, but a competition that every one of us has ever experienced. Iron cans are analogous to the mother's womb, and each of us has "is" one of hundreds of millions of sperm players, trying to find an exit to the egg in the mother's womb. The moment the sperm finds the egg is the moment when our life begins.

The human uterus grows a bit like an inverted pear, about 5 cm wide and 7.5 cm long. There are two openings about 0.3 mm wide on either side of the uterus, connected to a pair of fallopian tubes, and the mother's eggs appear randomly at one of the fallopian tubes. To escape from the father's hundreds of millions of sperm and escape from birth, you have to touch the black quickly into the fallopian tube and find the egg.

Although many scientists have observed the movement of sperm in the endoscope, it is still unclear how the sperm finds the egg in the uterus, because the endoscope can detect only a few microns. In order to clarify this problem, Yang Jing, a post-doctoral fellow in Paris, decided to carry out research in theory and establish a two-dimensional mathematical model of sperm movement in the uterus.

Yang Jing hypothesized that the trajectory of sperm is a bit like a marble on the table. If it does not hit the boundary, the sperm will swim in a straight line at a speed of about 75 microns per second. If you hit the boundary, the sperm will randomly bounce off at an angle and then continue to swim along a straight line.

A two-dimensional model of human uterus and fallopian tube openings.

After a lot of formula derivation and numerical simulation, Yang Jing found that in the two-dimensional model of the human mother's uterus, the average time for the sperm to enter the oviduct with the egg is about 17 hours, which is basically consistent with the previous experimental data. Moreover, they found that the shape of the uterus seriously affected the average time of sperm escape. In a narrow uterus or a flat uterus, the average time for sperm to escape is relatively short. In a rounded uterus, the average time for sperm to escape may be extended several times.

The relationship between the aspect ratio ρ of the uterus and the average escape time <τ> of the sperm.

Yang Jing pointed out that the process of sperm looking for eggs plays an important evolutionary role in the reproduction of animals. Statistics show that the number of sperm in Western men has been declining over the past 40 years. There is evidence that sperm concentration can cause infertility when it drops to 25%. Therefore, it is of great practical significance to study the mathematical theory that sperm search for eggs.

In recognition of their quantitative efforts to accurately reinvent humans, we decided to award them the 2018 Pineapple Science Award for Mathematics.

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