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Go to Brilliant.org/SciShow to learn how you can take today's lessons even deeper with their Physics of the Everyday course! [♩INTRO]. If you've ever strolled through a pharmacy in search of over-the-counter meds, you might have noticed that lots of drugs have special children's formulas.

And you might think that's because smaller people need smaller doses. But you'd be wrong. Because kids aren't just tiny adults.

In fact, children sometimes need larger doses of medicine! Welcome to the weird science of allometry. Allometry simply refers to the study of how physiology changes with size, and it plays a big part in understanding how much medicine kids should get.

You might think bigger bodies would need larger doses of medicine since they have more of whatever tissue or cells the drug is targeting. And there are a lot of medications that are prescribed based on a patient's weight what's sometimes referred to as a weight-based dose. For instance, an adult might be prescribed five milligrams of medicine for every kilogram they weigh.

But what's really weird is that this dose isn't constant throughout a person's lifetime. You often can't take the dose per weight an adult would take and simply multiply it by the child's weight to figure out how much they should get. And that's largely because a person's cells use less energy as their body grows.

In other words, bigger people have lower mass-specific metabolic rates than smaller ones. Even at the cellular and sub-cellular level, oxygen and calorie consumption is just slower in larger bodies. Not only that, but it's a nonlinear relationship so as bodies get smaller, metabolism increases fast.

And that matters when it comes to medicines because it impacts how fast your body processes drugs. Generally speaking, the faster the metabolism, the faster you break down a drug and that means, even if you're small, you might need to take more to have the amount you need stick around long enough for it to work. Let's consider acetaminophen, which you might know as Tylenol.

It's an over the counter drug you can take to reduce pain and fevers. The regular adult dose for acetaminophen is 650 milligrams. So an adult weighing roughly 80 kilograms the average mass for adults in North America would generally take that amount every four to six hours as needed.

If you'd never heard of allometry, you might think a child one-quarter that weight, 20 kilograms or so, would get 162.5 milligrams. But that's way too little. The child will metabolize it super quickly, so the drug won't really have the chance to be effective.

With junior strength tablets, the recommended dose is actually 240 milligrams. And for a 44 kilogram child, the recommended amount is 640 milligrams. That's basically the same as what's recommended for adults, even though the child is about half the weight!

And if you calculate the weight-based doses for everyone, the children actually take about two times as much. Other drugs can be even more extreme. The adult dose of oseltamivir, which is an antiviral used to treat influenza infections, is 150 milligrams a day.

So, a little under two milligrams per kilogram per day for our 80 kilogram adult. But pediatric doses range from three to six milligrams per kilogram per day! As for why metabolic rate scales with mass in this strange, nonlinear way, well… physiologists don't know for sure.

But by looking at people and animals of all sizes, they have come up with some good hypotheses! The first and perhaps most obvious is that little bodies belong to individuals that are still growing, and it takes more energy to build tissues than to maintain them. So, that's probably part of it.

But there has to be more going on, because the allometric pattern holds across different sized adults, too. That's where the shapes of smaller and larger bodies might be coming into play. Because a smaller body has a larger surface area relative to its tiny volume, it loses core heat faster.

That means it needs to burn more energy and, therefore, run a higher metabolic rate, to stay warm. But even that still doesn't fully explain the allometric scaling of metabolic rate seen in nature, because it only makes sense in so-called “warm blooded” species like us that strictly regulate their internal temperature with the heat they produce. And this metabolic rate scaling occurs in reptiles and other so-called “cold-blooded” species, as well.

There may be another way that overall shape impacts all this, though, which helps explain that. Some mathematical work suggests metabolic rates in large animals are limited by their internal plumbing. See, branching blood vessels have to strike a balance between their width, the pressure of the blood moving against their walls, and the force it takes to move that blood around.

In a bigger animal with a larger, longer, and branchier circulatory system, blood flow ends up being slower. Since it's slower and the body is larger, it takes longer for blood and the oxygen it carries to get places. And the animal can't beat its heart faster or harder to speed things up, because if it tried, its heart would fail.

So as an animal grows in size, its cells simply can't keep using oxygen at the same rate. More work is needed to sort out how all these ideas apply to humans specifically. But whatever the reason for children's elevated metabolisms, the effect on drug dosing can be pretty dramatic.

So, ultimately, it's not that there are separate formulations because kids always need less medicine. If anything, it's so that a patient, or their caregiver can more carefully adjust the dose they need for their body size. Liquid medications in particular can be carefully tailored to a child's weight.

And there are other reasons to have special formulas for kids, too. Like that pills can be hard to swallow or even a choking hazard, especially for younger children. So lots of kid's medicines avoid the issue by using chewables or liquids instead.

Plus, not all medications are recommended for children of all ages. They might be ineffective or have more severe side effects in smaller kids. Or they just haven't been thoroughly tested yet.

The bottom line is, if it isn't sold in a separate children's version, it shouldn't be given to a child without consulting a pediatrician. And you should always stick to the children's formulations when treating kids because that's the best way to ensure they get the right amount even though it may be more than what you'd take. The allometric scaling of metabolism also helps explain why we can't usually give our pets and other animals weight-adjusted doses of medicine.

And it has a really strong impact on what they eat which you can learn all about in the mammalian eating portion of Brilliant's Physics of the Everyday course! While physiology is complicated, all that loss of heat stuff comes from fundamental physics principles. Which means you can actually learn how to calculate how much heat differently-sized animals lose, and from that, how much of their body mass they would need to eat simply to stay warm.

And even though you make some entertaining assumptions, like that animals are spherically shaped, the theoretical calculation lines up really well with how much biologists observe animals eating. Which is pretty cool, right? In addition to mammal diets, the course examines the science behind everything from household items to forensics.

So it's a fun way to learn about your world and refresh your science knowledge. And right now, the first 200 people to sign up at Brilliant.org/SciShow will get 20% off the annual Premium subscription. Which is a great deal!

So if you're interested, check it out. And as always, thanks for watching SciShow! [♩OUTRO].