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Circadian science Sleeping troubles Technology

One Simple* Rule for Understanding Your Sleep

My friend sent this to me the other day:

“If I go to bed at 10:30 pm, I often wake up at 4:30 or 5:30 am and can’t go back to sleep. But if I go to bed at 1:00 am, I fall asleep easily and can sleep until 9:00 am. Throughout the work week I’m running on 5-6 hours of sleep, and only on the weekend do I get to recover. Could it be that my natural cycle is just different from what social norms say?”

Reader, I pushed my glasses up my nose so fast and so hard that they are now deeply embedded into my face. A small price to pay for this gift of a question.

But before I can get into why I was so excited about my friend’s pain and suffering, I need to tell you about the two-process model of sleep.

The Two-Process Model, 10,000-ft-View Edition.

When you’re awake, you build up a “hunger” for sleep. This is your sleep homeostat, and it grows when you’re awake and drains when you’re asleep.

Two days of wake and sleep. Purple line goes up, you’re awake. Purple line goes down, you’re asleep. Shaded purple regions show sleep windows.

At the same time, you’ve got a circadian drive for alertness, which for day-adjusted folks tends to send its strongest signal for sleep in the middle of the night. The effect of both of these together is your sleep drive.

When the sleep drive hits an upper threshold, your body switches into “wants sleep” mode and tries to get you to go to bed. When it drops below a threshold, your body switches into “wants wake” mode and tries to get you to wake up. You can visualize this phenomenon as the zig-zag of the homeostat bopping between time-varying upper and lower thresholds set by the circadian clock. Hit the upper limit, fall asleep. Hit the lower limit, wake up.

Visualizing the two processes—homeostatic (purple) and circadian (orange/red).

Still with me? Ok, here’s the most important picture you’ll see in this whole blog post:

Ta-da.

Well, there you have it! My friend’s sleep problems in a nutshell. No further explanation needed.

I showed this graph to another friend of my mine, and he sent back this:

Okay, so maybe a little more explanation needed.

Simple model. Complex phenomena.

Let’s talk about the two-process model in the real world. For one, people don’t instantly pass out when they hit the upper threshold for sleep. People can push sleep back in a lot of ways— staying out of bed, keeping the lights on, or, as was the case in one old sleep study, repeatedly dunking their heads in ice water. We can call this a “wake effort”—making an effort to stay awake in the face of the tyrannical rule of the two-process model. In fact, it might not really feel like that much effort if you’re having fun on the internet.

The blue-dashed line in the plot below shows what would happen if my friend stayed up a couple hours later than her body necessarily wanted to, moving her bedtime from roughly 10:00 pm (no wake effort) to a bit after midnight (with wake effort). The blue shaded region shows her sleep when she delays her bedtime in this way.

Purple line: falling asleep right when the two-process model says to. Blue line: Staying awake a little longer. Two different choices, two different sleep durations (blue vs. purple shaded area.)

Here’s the thing: That blue shaded sleep area, the one that starts a little after hour 24 (midnight) and goes until a little bit after 8:00 am? It’s wider than the shaded purple sleep area, which starts around 10:00 pm (hour 22) and goes until maybe 4:30 am. In other words, she’s sleeping more by staying up later—almost two hours longer.

You can eyeball it if you look where the lines are hitting the red waveform on the bottom. The purple and blue curves are chasing it as it’s going down, and the “stay up later” blue curve is hitting it at a significantly later point. That means more sleep overall (“good,” in theory), despite a later bedtime (“bad,” in theory).

What does this mean? Well, for starters, it hints at the enormous complexity you can start to get at when you mix two waveforms and thresholding conditions. The wiggly line of circadian sleep drive and the zig-zag line of homeostatic sleep drive, while deceptively simple, can interact to generate some wild phenomena.

Let’s explore a bit. I’m starting my friend’s sleep homeostat at a fairly high value, because she told me she tends to need an alarm to wake up during the work week (and feels pretty tired all of the time). If I started her at a lower sleep homeostat (waking up better rested), the difference between the two sleep durations becomes a lot smaller (purple: 7.7 hours of sleep, blue: 7.9 hours).

Starting my friend at a low homeostatic value. Now there’s really not a difference in sleep duration between her staying up a few extra hours or not—both the purple and blue shaded regions have the same duration.

Give her a higher starting homeostat, on the other hand, and the no-resistance-to-sleep-drive curve (purple) has her falling asleep around 7:30pm, waking up at midnight, and staying awake all night until she passes out again in the early morning, while the “wake effort” curve in blue mostly stays the same:

Now there’s a huge difference in sleep between the two options! They’re basically complements of each other.

These are wildly different scenarios, and they’re arising from me gently nudging a number up or down a little bit. Imagine what happens if we make those upper and lower thresholds—representing the circadian drive for alertness—act the way a real circadian rhythm does: shifting, stretching, and bending in response to the signals you give it during the day. Imagine weakening the signal from the body’s clock, or adding the effects of noise:

Circadian madness

Mathematicians who study this kind of stuff have done some pretty great work looking at just how much complexity can arise from the simple rules of a sleep homeostat and a circadian rhythm. In my own life, I think of the two process model most often when I wake up in the middle of the night. Ok, I tell myself. My circadian sleep drive is probably running a bit late. If I hang out in the dark a while, it’ll swing in and kick me back into sleep. And what’s great is that it reliably does.

“Are my natural cycles just different from social norms?”

But let’s get back to my friend’s question. If I had to make a guess as to what was going on with her based on the two-process model, I’d say her circadian clock is delayed relative to where she wants it to be (and that she’s often waking up in the morning with a high sleep homeostat due to the chronic sleep restriction from her work.)

That might seem to be a vote for her natural rhythms just not jiving with her work hours, and there’s probably some merit to this. She’s described herself as light sensitive, which may be a trait that predisposes you to being more of a night owl. That could be shifting her rhythms later, and making it so her circadian clock isn’t where it needs to be when her sleep homeostat drops to a low value.

Yet one of the great things about circadian rhythms is that they can change. If they didn’t, we’d never get over jet lag. We’d stay on our starting time zone schedule for all time, regardless of where we went, when we slept, or when we went outside. The fact that our clocks can be disrupted also means they can be fixed.

Another way of thinking about it: My friend’s weekend rhythms would make her a pretty darn early bird if we abruptly transplanted her three time zones west to California. What’s the difference between living in California versus her home city on the East Coast? Well, a lot of things, but the most important one for her circadian clock is the difference in her light exposure.

So I’ve got her trying out a new circadian regimen to help herself sleep during the work week. My hope is that the two-process model, along with the fancier flavors of it that have spun up in research and at our company, can help people in the real world understand their sleep better. Simple rules can interact to make complicated behaviors happen, but at the end of the day they’re still simple rules. And simple rules might just have straightforward solutions, too.