A couple, returning from vacation, turns on the air-conditioning. The wife is overwhelmed by a terrible stench coming from the ductwork and is convinced that an animal must have died in the house. She tells her husband that they need to hire somebody to get rid of it.

His response? “I don’t smell anything.”

Both the husband and wife were patients of mine in 2004 in Poolesville, Maryland, but their experience is not so unusual. What I explained to them was that the sense of smell differs between women and men. It’s entirely plausible that a woman could perceive an odor which is — for the woman — overpoweringly awful, while a man doesn’t smell anything.

In research published in 2002 in the journal Nature Neuroscience, Pamela Dalton of the Monell Chemical Senses Center and her colleagues exposed men and women to smells in the laboratory. Not just once, but over and over again. Dalton and her team found that with repeated exposure, the women’s ability to detect the odors improved 100,000-fold: The women were able to detect the odor at a concentration 1/100,000th of the concentration they needed at the beginning of the study.

But the male subjects, on average, showed no improvement at all in their ability to detect the odor.

How is that possible? What’s going on in the anatomy of the olfactory system — the system we use to smell — that can account for such huge differences between women and men?

Quick anatomy lesson: Smell receptors in the nose send their signals via the olfactory nerve to the olfactory bulb. The olfactory bulb is the first stop in the brain for information about smell.

There are two basic kinds of brain cells: Neurons are considered the most important, because they seem to play the biggest role in sending information via electrical signals. But glial cells are essential too, because they provide structure and may also modulate information processing in the brain.

On all counts, women beat men. Women have more cells in the olfactory bulb: 16.2 million cells total in the average woman, compared with 9.2 million total cells in the average man. In 2014 research published in PLOS One, researchers at the University of São Paulo compared the noses of 18 subjects aged 55 to 94 shortly after their deaths. They found that the women had 6.9 million neurons, double the 3.5 million in the men. When they counted glial cells, women again had more: 9.3 million compared with 5.7 million in the men.

And outside the lab, those differences can have a significant impact on relationships, as in the case of my patients, who hired a service to clean out their ductwork. They found two rats that had died in a puddle of water inside their house.

Here’s what I think happened. The rats must have died a few days before the couple left on vacation: The woman said there was a trace of the smell before she left. Each time she came into the house before she left, she was being exposed to the odor, something like the subjects in Dalton’s study. With each successive exposure, she was becoming more sensitive to the odor. Then they went away. When she came back, the stink was much stronger because the rats had been rotting in the ductwork. But her husband didn’t smell anything.

The differences in their perceptions could make each feel that the other must be crazy. Was she imagining the smell? Was he lying and pretending he didn’t smell it?

Knowing that the differences in male and female noses can be so extreme, the best approach may be for each family member to agree to respect and trust the other’s report of sensory experiences. Does the milk smell sour? Does the dog stink? These could be cases where women are biologically more sensitive than men.

This also applies to the stereotypical teenage boy who leaves heaps of dirty laundry and sports gear in his room. If you are a woman living in the same household with such a young man, perhaps your own son, explain that good hygiene means keeping the room clean, even if he doesn’t think it smells bad. It’s not entirely his fault — maybe he just doesn’t have enough neurons sending scent messages to his brain.

Leonard Sax is a psychologist and a family physician in West Chester, Pennsylvania.

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