[Prof Liz Bradley:] Okay,
I'd like to introduce you to my colleague Sriram,
who is in the Department of Computer Science
here at the University of Colorado Boulder.
And, I'm going to ask him to tell the camera
a little bit about his interests.
We've been talking about ODE models in my MOOC a lot
and I know that you are interested in particular
in modeling the human insulin system,
and the idea is to build a controller that can replace the pancreas,
so I'm going to let you tell the class a little bit more about that.
[Prof Sriram Sankaranarayanan:] Thank you, thank you Liz for inviting me.
It's a pleasure to talk to people who are interested in
the same things as you are.
My interest in modeling the human insulin-glucose system
comes from this project that's ongoing these days -
it's called the "Artificial Pancreas Project."
It concerns people who have type 1 diabetes.
So, type 1 diabetes is actually a really... interesting condition.
It actually places a lot of burden on people who have it
and it's characterized by the inability of the human body to secrete insulin -
so it's a hormone that helps us take up glucose.
In our human body, we ingest glucose typically in the form of food.
This is digested, and what the food ends up as...
it ends up being stored up -
the energy from the food in the form of glucose -
it ends up being stored up in fat cells in the liver.
It ends up being taken up by the brain - we think - all the time,
so that requires glucose of course,
and, by the musculoskeletal cells when you do exercise - you walk around.
Now, there's a key hormone here called "insulin,"
and insulin actually regulates the uptake of glucose.
So, physiologically, if you have insulin,
it forces the fat cells, the liver and the muscle cells
to take up the glucose in your blood.
Strangely enough for some reason, do not ask me why -
it's not needed for your central nervous system,
but it's needed for pretty much everything else.
And, the physiology of this is very interesting.
Together, it forms a very interesting closed loop system.
This is the kind of closed loop system we talked about,
where the insulin control in the body is done by the pancreas.
Now, the pancreas is a wonderful organ, and - if it works -
it actually keeps your blood glucose level in a very narrow range.
And, the interesting thing about the pancreas is -
it's a closed loop control system.
It's very beautiful - it's beautifully tuned.
And it - when it works - it keeps us healthy,
and it keeps us on our feet all day.
In people with type 1 diabetes, the pancreas goes out of action,
or specifically, the cells that produce insulin are compromised,
so they either lose it completely or they are deficient in these cells.
So, when that happens,
insulin needs to be administered externally through an insulin pump.
And, this is an example of a pump that has a syringe with insulin in it,
and this pump infuses insulin into the patient.
And, on the other side there is a glucose sensor,
and this is a continuous glucose sensor - a common brand by Dexcom.
Now, together there is an insulin control
that's now implemented outside the human body
that compensates for the missing pancreas,
and this is called the "artificial pancreas."
So, for people whose natural pancreas lacks the ability to synthesize insulin,
we would like this artificial pancreas system to somehow take the place.
The dynamics of this closed loop are really interesting
and they are really key to understanding this artificial pancreas.
So, there are many kinds of artificial pancreas -
it's actually a project that's currently ongoing.
Many stages of it are in clinical trials.
The FDA, for very good reasons,
has kept these from coming to the market because there are safety concerns.
During the daytime, the patient is awake - active -
so it's... in control systems,
we call it a "disturbance" to the closed loop,
but alerting the patient if something goes wrong is easier.
So, there are trade-offs, and people are considering
all these points of trade-offs when building an artificial pancreas.
So, it's not a single device, it's actually a class of devices
that understand the dynamics of insulin-glucose action
on the human body, and perform control.
So, there are many challenges, and these are the challenges
that make it interesting from a dynamic point of view.
First of all, it's safety critical - excess insulin can kill a person.
And, in terms of the dynamics, it exhibits very complicated dynamics
because the control-loop has numerous time lags.
So, the way I think of the artificial pancreas
is a very common scenario.
When you drive across on a highway, you are following a car in front of you
and you would like to keep a distance from that car in front of you.
Now, suppose you imagine I blind your windshields completely
and the only way you can see the car in front is through a camera.
Now I take this camera, and I time-lapse the image
so you can see what was on the road 15 minutes before -
so you cannot see the road right now.
I time-lapse the video, so you can see it only 15 minutes ahead.
Then I make it even harder - I take away the accelerators.
You only have brakes and you are going on a downslope.
And, I make it even harder.
If you apply the brakes now,
the brakes will take effect 20 minutes from now,
and somehow the brakes will keep taking effects for the next seven hours.
Now, if you understand all of this,
and if you know how to keep a constant distance from the car in front of you,
that's exactly the same problem - the same dynamics
that the artificial pancreas has to contend with.
And, it's nonlinear,
which is a very important thing in dynamics.
If dynamics were linear,
we could solve many of these problems that are well-known techniques.
But, human response to insulin happens to be nonlinear,
so this makes it even harder to design such a system
and even more challenging.
These are challenges that make it really hard
and the resulting controllers that you produce
become extremely complicated as a result of these challenges.
[Prof Bradley:] What are the roles of ODEs in all of this?
[Prof Sankaranarayanan:] That's a great question.
So, I'm now coming to ODEs
because it's really central to modeling these systems.
And, one of the ways you model the human insulin-glucose action
is through ordinary differential equations.
Without such a model,
it's going to be really difficult to design controllers,
and once you have designed controllers, to verify controllers.
ODEs play the role of forming the mathematical dynamics model
for the human body's insulin-glucose regulation system.
ODEs are the most natural formalism for modeling this,
and once you model this through an ODE,
you also have a nice model of the entire closed loop dynamics.
So, the alternative is not easy.
The alternative would be to take a controller and test it.
Usually, this is done with animal testing,
using animals like guinea pigs, monkeys or dogs.
And, what ODEs have done in this space
is completely eliminated - to some extent - animal testing.
So, the FDA is allowed certain models of human insulin-glucose regulation
ordinary differential equation models to stand in for animals.
So, ODEs have been a great revolution
in this space of designing and verifying control systems for insulin.
So, ODEs - there are many ODE models here,
starting from work that was started by Bergman in the 70s and 80s.
And, Bergman built a model called a "Minimal Model"
or the "Bergman Minimal Model."
There's no straightforward mapping between the variables in these models
and physical quantities inside the human body.
So, those... those kinds of models are called "Minimal Models,"
whereas the kind of modeling approach that we take
are models like the Hovorka Model or the Dalla-Man Model.
These are physiological models... these are actually models
where there are terms for how much glucose is in my brain -
there are terms for how much glucose is stored in my liver.
So, it models the physiology to a large extent
and comes up with these differential equations
that talk about the different terms in this physiology.
So, the slide shows you the differential equations.
And, here is the whole closed loop model
at the end of the day that we are forced to study.
So, it's not just the human dynamics model,
which is a differential equation -
we also have stochastic models of meals and exercises,
and for this we have been using data collected by the NIH.
There's ARMA models, and these are called "autoregressive moving average models."
These are models which are not differential equations,
but they are stochastic - they are usually discrete-time.
And, they model the noise that enters the system because of the sensors.
The insulin controller is a computer program.
So, our modeling framework puts all of these together.
But the central part which you will definitely recognize
is the differential equation and the simulation
of the differential equation.
But, it's not just the differential equation.
When you build a full closed loop model of this form
you have to account for many different modeling frameworks.
But, that's what we do,
and that's part of what makes this whole project very interesting.
We also have tools that allow us to actually reason about these models.
One example of a tool which we have developed
jointly with Arizona State is a tool called "S-Taliro."
It tries to adapt from its simulations
to learn where problems could be made to come forth.
And, this is in simulation - we are not hurting or harming anyone,
which makes simulation very interesting.
Another example is a formal - symbolic - verification tool,
and this uses an idea called "set-valued flowpipe construction."
Our tool is called "Flow*."
As you can imagine, it's a very hard computation.
So, doing it for 9 to 10 variable ODEs itself is extremely challenging -
it can take up to weeks.
But, we have tools that can enable us
to reason about what we call this "model soup"
of a large number of modeling paradigms.
I would remind you at the end that -
"all models are wrong, but some are useful."
This is a very inspirational quote I came across
from a statistician - George Box.
One of the reasons here... I mentioned this is -
at the end of the day, we are modeling these systems,
and we are coming up with some scenarios that could be problematic.
But, we have a collaboration with engineers and clinical researchers,
so it's not just differential equations and modeling -
we value this collaboration a lot with clinical researchers.
After all, human insulin-glucose system is way more complicated
than what the nine state ODE can tell us about the human glucose system.
Currently we have two systems under analysis.
These are actual systems that are running on patients in clinical trials.
But, we are still trying to analyze this
and we are hoping to use the results of our analysis
to move it along and convince the FDA
that these systems are actually safer,
so they can be moved along to the next stage of the clinical trials.
[Prof Bradley:] Thank you so much Sriram.
[Prof Sankaranarayanan:] Thank you Liz - this was great.
[Prof Bradley:] One of the fields that both Sriram and I work in
is what's called "control theory."
And, that's designing things -
like speed controls for cars or thermostats for buildings...
like the thermostat on my office wall is a closed loop controller.
So, it has a loop - it measures the temperature of the room.
Then, depending on if that temperature is above or below where you want it to be,
it either turns the heat up for down.
And, if the heat is... sorry--
If the temperature is too high, it turns the heat down;
if the temperature is too low, it turns the heat up.
That's what's called "negative feedback."
Cruise control in the car is the same way.
If you set your cruise control for 100 Km/h,
the cruise control device measures the actual speed of the car
and adjusts the pressure on the accelerator
to keep the speed at 100 Km/h.
Those are much, much simpler things than what Sriram is doing.
Incidentally, Sriram has more experience...
Incidentally, Sriram also teaches a MOOC -
he teaches a MOOC through Coursera on programming languages,
and I'll put a link to his MOOC
on the supplementary materials page for our course.
He's a great teacher - I hope you enjoyed the visit with him.