One of the highest stakes moments of my life was the time in graduate school when I was (badly) playing Donkey Kong at Pinball Pete’s Arcade, and a very, very good Donkey Kong player came over to watch me play in silence. I’d just spent six dollars worth in quarters dying repeatedly on the first floor of the first level, but something about his judging, appraising eyes summoned the fireball-hopper within. I made it past the first level, then the second, then the third—an absolute record for me—and I had almost cleared the fourth when the pressure finally got the best of me. Still, it felt like a tremendous achievement. I like to think the good player and I shared a nod of mutual respect as he elbowed me out of the way and proceeded to spend the next forty-five minutes on an uninterrupted victory run.
Besides letting everyone know that I need to get out more, this story is an opportunity to talk about a kind of math that should be more integrated into clinical care, and isn’t— yet. There was a model of physics deciding what happened in that game, a system of differential equations for converting my button mashing into movement across a screen. And just like the inputs I gave the system could be transformed into outputs that captured the physics of motion, so too can the inputs we give our bodies be transformed by a realistic biophysics model to give us outputs that capture the ways our bodies work without the need for invasive tests.
Let’s back up: At a very high level, what’s going on in a video game is that you’ve got prescribed rules for how to update all the positions of all the moving pieces from one frame to the next. In the next blink of an eye, where should Mario go? If I’m pushing the joystick to the left in that instant, nudge him a little to the left. If I’ve just hit the jump button, nudge him a little bit upwards. If I’m mid-jump, make the force of gravity and the speed he took off the ground fight it out to see if he should be nudged a little up or a little down.
The whole set of rules for making these decisions on how to nudge can be called a physics engine. Passing the history of my joystick spins and button presses into this physics engine gets you an output that describes how Mario moves, how he jumps, and how far I make it in the game before an untimely demise. This type of math is all over the place in games, CGI, and user interaction elements (like views that scroll and bounce). But there’s no reason a physics engine has to be restricted to visuals, or video games, or the physics of movement. You can have a physics engine that captures ion channels open and close, for instance, or how neurons talk to each other in the brain.
Which brings us to your body’s internal clock. Circadian rhythms are a massive pain to measure experimentally; it’s one of their defining properties. It’s hard to know what’s going on in the brain without looking at it, and it’s hard to get a glimpse of it without getting pretty invasive. But if you know the rules for how the clock part of your brain works— “the differential equations describing the suprachiasmatic nucleus”— you can pass through a history of inputs to the system, and get out an output that describes how the neurons are communicating with each other at a specific point in time. Pass in what my lighting history has looked like over the last four weeks, and I can tell you what time my brain would cue melatonin to start rising in my body tonight.
So here’s why I think we should be using differential equations in medicine more: they can help you see things you otherwise wouldn’t be able to see. You can use a system of differential equations to track how the brain would react to the inputs you give it, even if you can’t readily experimentally measure brain state, just how a person with access to Donkey Kong’s code could track how far I got on my amazing run, even if someone blocked off the console screen with a tarp. Knowing the rules means you can measure things in the dark.
And there’s another reason, too—personalization. By tweaking the rules of your video game physics engine, you can change the way the gameplay works. Cut gravity in half, and suddenly Mario’s soaring with every jump. Double it, and he’s a sitting duck for everything Donkey Kong throws at him. As the importance of individual differences in light sensitivity and fatigue management become better understood, biophysics engines are ready-made for customization. Want to better fit the data of someone who’s hyper-sensitive to light? Crank up the light sensitivity parameters. Got genetic data on them? Plug that into a molecular model of their rhythms.
Biophysics engines can be the key to a true digital twin, helping us look inside a simulation of ourselves in ways we can’t look inside our real selves. There’s potential for these quantitative methods in medicine beyond sleep and circadian rhythms, too. Who knows? Maybe someday a model of this kind could be useful for understanding how the (fun) stress of my epic Donkey Kong run affected my mood and memory. Or at the very least, how my body processed the enormous bubble tea I drank in triumph right after.
Want to learn why we don’t think the answer to circadian estimation in the real world is to just throw an artificial neural net at it? Check out this blog post by CTO Kevin Hannay.