[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.