Thank you.

Thank Senator thank you for

this train extra lection is one of my
students I guess you have to do I.

Put the good stuff well thank you so
much for coming this morning.

So it's a pleasure to be here talking when
you hear a few times kind of your early

in the morning so I have missed a few but
I've been having a few of these but

really there are a lot of fun I like them
so again anytime you have a question is

placing through interrupt me we thank you
but Kushal So today I will talk a little

bit about the hired killers in the heights
or actually how to fix what sibling done

the same things you do to us for us but
perfect thank you he was perfect.

Perfect for food for
today I guess anyway so

what I want to add them to my talking
I'll talk about all salacious and

complex systems in general then how this.

Spyware So
then how they write it in the heart and

then some which they will it is
that we've seen the heart and

then I talk about some
methods that we have used.

To try to terminate or even us.

Using low energy so some up
occasions of all the theory that we.

Through the years and
application reining in into the Kleenex.

So when we talk about
complex systems in my lab

we work with things that isolate
anything that isolates I like.

And when you say complex he said
there's a need to be very complicated

very simple systems can have very complex
dynamics so I run a simple example that at

that time that we were working in the lab
with one of my undergrad smell and

one of my poster Greg if
you take a candle and

you put a stick through the center of
the kind of you can balance the candle and

it can be basically the way to
really the center of mass and

you can buy less it will be static
that you can burn it from both ends so

if you start burning that the color
from both ends is going to

say dripping wax so it's never going to
be exactly symmetric one box one is going

to believe in my wife's and then when
she's going to tilt and I see two it's

then that the flame is I was going to be
perpendicular this is Gov property so

I see two that's the low end is
going to have touching the flame

the lower one is going to touch more
wacks than the one on the higher one so

the other one is going to lose
my weight than the higher one so

then it's going to change center of
mass and is going to oscillate and

of the change here then
it's going to get so

let me show you the movie it's a simple
and this is actually a very nice and

simple toy that he was a vice
in in last century in France so

that a couple of examples and how they
use it that you have to use it was one of

the nice things to play with at night so
you can see how the solution starts and

goes very complicated very very wide now
from only one of the next we know that any

system that has three or more the grease
of freedom can actually have chaos so

in these cases this is kind of
like similar to out of pendulum

because the time to talk about so
those are trying to do that yourself for

them but the other one is the center
of mass that is changing so

there must be three three degrees of
freedom that can in principle give

you chaos how would you do then
the simulation it was not producing

chaos you can produce really
a lot of answer a lot of.

Well you figure it has
a lot of the nations but

in previous chaos one of
the things that we tried to do is

easy we figure out that there was a level
of damping there was some friction and

just on the post that opera was damping So
we took out the friction we put some.

Barbells into the system so
my on the drive to the center.

She sent a much more professional
device where you can put.

Through the printer so you can have
a section where you can put them in a bad

moment when the friction and in that case
now becomes chaotic You can rotate and

it actually can go all around one time so

here is going to say you can see it's
going to go almost all around and

he seems going to stop but
he actually is going to flip.

So he flips and then he can come
back again and becomes chaotic

now he has a complex and i'm so you see
that you follow the trail of these steep

function of time he just becomes
complicated just like your existence so

I'm sure that he said very simple system
that oscillates we're going to have

to clean Amex and
dynamic simply means that you have to

if you study the system we just a small
initial condition difference then I'm

mixing things space is going to be in time
and space is going to change eventually So

this is a very sort of two of two points
at the same time that we started it

in face space but it's function
of time the third diverting and

that's basically what is chaotic that just
one initial conditions change initial

conditions will have eventually
different dynamics in time and space.

So these are solutions when we put
in space they can produce waves so

it's kind of like this is like the ways
that we seen in the stadiums when when

they have the they when they wave.

You can have these ways of
property now when these waves.

In your solution they go up
in a space can produce a wave

now sometimes when you break they they
they they the symmetry of these of the.

The propagation of these waves
they can produce spider waves and

it's probably their family
many many systems so

what happens is you have a way front
that propagates following a way back and

when you break it then the front and the
back they have to meet at some point and.

The front.

OK so the front on the back they're
following when they break they have to

the front has and

I will have a lot of the going in this
direction the box is direction when you

break it the front is going this way
the back is going this way the separates

where the meat where there's going to be
left a changing face the normal rest it

is going to be zero right because
because he's lost it's like that and

at some point there's going to be certain
number of losses the celebs waste and he

said the point that people point four four
out for us probably two or three so this

is one of the reasons how many of these
systems that have solutions can produce.

Spider waves let me just
show you an example.

That we need here I do you think so
many fields of you were part of it we have

learned to use in a row we try to the
another year we have done this one with

Andrea so she she's the one in she's
been working with me on these things so

they used to put.

So we could collect C I want six
hundred students we put them in

you know green we give an initial
condition and stuff it for sick.

So we need an initial condition here of
a way kind of similar like the way even

in the stadium but you know we were
stadium you have a way that propagates and

just finishes and that's it here we
stand there with initial condition

that they wave that's only
only started this action here.

You will excite on one side but the first
time we're not excited on the opposite

side so we're providing this erection so
now you have the wave on the way back and

I say because he was back in here he would
people think it was like this by the way

and then he showed it again.

So here's the wave.

And stuff that they think so for
this is very nice is probably.

What is probably says from
is basically just stable and

will continue rotating as well as long as
a system keeps pollution oscillations.

Now one of the things that happen when one
touch the boundary can that it touches

the boundary and he waits and you just
end up there way now one of things that

happens is that the spiral waves very
little it takes very little actually to

break us by the way this another another
on another experiment that I really want

to try so we did here because not all of
the students and just but for a second.

That evolution basically their
response you get excited.

Then if you're going to decide if you want
to know any of your four neighbors case is

excited so
basically if one of your neighbors

is get excited then you're going to get
excited and that's how the way propagates.

Because not everybody is completely
following that rule sometimes people see

the way many of us sooner so
the next I think you'll soon or so

might actually just not looking and
then they see their way coming and

then they excite that you're too late so
they said you'll be the coupling so

that's an off sometimes to
produce way to break and

when he breaks then producers want to
pull waves then we show you again.

So in this case there was a spiral
he was rotating here then I could

see this really got excited a little
trailer too late and he broke that way and

it just becomes now become chaotic so
instead of one spot where you don't

have a lot of multiple spider waves
I mean to me I say just becomes so

it shows you how quickly how it is
actually to stop ISIS by the way.

To break up and when you have multiple
spider ways then you have chaos

because you have fast frequencies but
out of face so

then the system is completely
Yeah you know any.

So spammers actually can happen
to to us not only in this in

that we were part of nature so
there are a lot of sea.

That actually can be spyware so
there are some that are not dangerous

this is everything under Laurie and
everything of the skin similar to our.

Two.

Like at least food when
you have it is food but

on the other parts of your skin a squirrel
ring worm so you have to ring worm but

rewarm just propagates and he continues to
get in excited everything under a lot or

even taste but
he hears behind the relation so

because of that he can produce spider
waves so this imitation can in time

in a couple of they see keeps If you spot
a gate in a key producing spot waves.

So this is just a tradition of the skin
another one he said you got forgotten.

That actually when you have it when you
get sick sometimes your tongue gets

a little white gets that direction so
that actually can produce these waves

that if they break thinking
pretty spry we see the tongue.

Now let's just spy with what
happened in the inn in the skin on

the on the tissue but are not dangerous.

Now in the heart actually we can have
these waves that actually can form but

it before I show you this by wishing
the heart I'm sure the red heart.

So this is a back heart so

this is the it's real this is a ventricle
this is producing the contraction and

we always follow the contraction of
the heart following the C.G. So they C.G.

in this other has a people wave which is
a contraction of the it's where you see

the edges much smaller than the ventricle
So that's where the center of the P.

wave is much smaller then you have
the activation of events recall which is

the Q R S which is activation and that he
waves they are the activation of the heart

so when you have these.

We have these C.G. you have the next
evolution of the atria which tracks but

he contracts because there's an electrical
signal that propagates with a through

the X. ray so that's where you get you
can can measure an action potential and

you can measure the sum of the action but
they show the H.

I give you these people
wait on the on the cue.

Rests on a C.G. and then you have
a curious use activation of the ventricles

and activation.

So you know how you can have
normal the normal rhythm

will be produced by
an activation of the waves

repeating through the heart making
that the high contract that once

when these forward these ways break
they can produce a spiral waves.

Now so you everything you perturb on
one wave and produce a spot away.

It will it will produce a frequency that
is faster than the natural pacemaker

this despite always when the from the
heart they rotate with a frequency that is

faster than it was not as a not so
they take control over the heart and

they make it contract faster and then
the C. you know that you get on the C.G.

will be much faster so you know just
the rotation now of the show you with

it with example with a with
the students will find a spot where

the Starlight said that many make a nice
in the spot a way to show you a couple and

they're in the talk so
one is the Copley company because pink and

star like the waist I can
produce multiple spiral waves.

That it produces a chaos so
these one when you measuring the C.G.

he just basically very complicated just a.

Very small signal because
just selective ation and

in this case how can a contract any
more than a pump plant and that's.

That's what it produces so
that I think that.

Any questions of are.

OK So let me show you an example here say
I have anything ventricle I think idea so

this constructed very fast because I think
very fast because we have a spine wave

actually driving the heart so if you
assure the simulation of us happening

here.

So you have you have what happened here
with a high this sort of thing very

very fast because it's written by.

I spy a way that he's very sexually.

Driving this dysfunction traction right so
that's just for the for

the bench for the for the now is
to say very often they style ice.

And then the brake and then the produce So

now this is a hard after after
that Kerry went to tribulation so

now you see just shivering he's not
contracting any more because he has

someone just a bunch of little spiral
waves running through the heart.

Let me show you.

And make a simulation for these.

So now you have.

You have multiple spider ways driving
the heart to these more irregular rhythm

right.

And the same so you have each and
you have the ventricles so

you can they say well you can have
tribulation in the event because you have

a relation of yours so now here the atria
are the ones with the spinal waves

now the activation goes from the edges to
the ventricle through the A.V. node so

when you have a relation in the area you
have the iteration is just she wearing but

then activation goes to the ventricle
because very regularly through the essay

not using the sort of the A.V. know it's a
filter so none of the Activation is going

to give you know go through
the ventricle just every other so so

now the activation of the Eventually still
contracts but it's not very regularly so

when you have a spider we see the kind
of intercourse is there really

almost instantaneously you have to get
within them within within seconds or

within minutes if you happen in
the area now you can leave you can

you can have a high life of but
but but then if.

You always tire you you're going to
feel well and it's a major cause for

strokes so this is not that right away but
of course it will be the only in.

In time but if it happens in the
ventricles then that's when we have to do

basically be connected shock
which is sure by the end of the.

Talk.

So so

how this is one of the leading causes of
death in the cell ask Well that's a recent

want to research we study them Iraq's
number one in the stressed countries.

About one third of all the total
deaths in the United States has to

do heart disease this is the same amount
of the next two causes of higher than that

which is cancer and.

Brain brain problems.

So let me just talk a little bit about how
we select you can see that happening in.

The heart so the heart contract is
the same because there's an energy kind of

wave that propagates So
the salute you can see that we see

he said Change event that she actually
hears normalized but in general.

The kind of access they had this
construct of cells which I read

one hundred microns in length
they're like more like rods or

hundred markers in length
by ten microns in radius.

They produce what is called an action
potential the voltage changes

from minus thirty five million votes
to about twenty min of all it's.

And so these change in voltage produced
by a change in brain tissue between

the inside and the outside of the cells so
the says they follow the membrane.

In the concentrations of values
between inside and outside the cell.

These membrane has some proteins that
go across the membrane these proteins

they open and close it's function of
voltage and it's function of time so

this is where the not only know the nomics
of the problem comes from and what we do

we use mathematical models to try to
understand the dynamics of the cells so

the opening and closing of these these
these channels they there are different

types of channels depending on
their I own that I answer that.

China's for so.

And for potassium for calcium.

There are also some cultural exchanges.

About that shrimp so
the mix changes as well so for

each one of these you have to write any
fresh equation the source that I mix of

the is going through them in reality
just mostly it's I'm slow it

gives you the current that goes through
is proportional to the voltage.

Conductance Now the problem
is that this conductance is.

Basically how much I use can be allowed to
pass through the internals because these

are in China's open and close and they're
not normally nearly the open across

as a function of what is but its function
of time the amount of current it is G.

is viable and these G. surely has to be
written by any financial equation that

the explicit than a mix of these
of these open your close so

that's where the complication
comes from for these channels

you have a family like these but you have
to have a very complicated equation for G.

that solves this this time the planets So
I mean you have to do it for

all the channels that you have on
the membrane so that's why simulations

of kind of economics can become very
complicated because you have a lot of

equations just for one cell you have to
account for a lot of the front currents

that are happening here in the cell so
you can how many of those something

suspiciously some of them additions
we try to construct a simple model so

I forgot about the lease enough to
reproduce one of the basic dynamics but

if you want to go into detail with all the
other different characters that you have

a for the ion channels I there
most that have up to one hundred

hundred equations for oneself so
now you have hundred equations

that have to solve with a lot of
different parameters for oneself and

if you go to scale the fence
become very complicated to solve.

So as I say in the later see you
know actually produces a contraction

the contraction is produced because as the
as it went the changes in the membrane.

Inside the cell gets release.

Assume then balance between
the Miocene and the acting and for

this is a contraction.

So so this construction is produced
first by unit you can see that it

releases constant and
it produces a contraction.

As a species The nice thing about
the heart is that we can study the need

different levels we can have we can
study like single cell will be like and.

See all there then I mean it's just
that I mix of all this in prime

because it's on a single cell we can go
inside because when you open a ventricle

the activation from the outer to the
ventricle goes very quickly through a path

called the perky fibers so you can see
here this is you know this is this is

a part we stain the the heart staying
with Lugar so you can see actually

the staining of the well the speck you
fibers so that is that emission course

from the answer to the ventricle you want
to actively the ventricle very quickly so

these propagation along the fibers is
actually three hundred reconnaissance with

this perception so activation goes
very quickly into the ventricle So

the winters can interact contract very
quickly so these these packages fibers

sometimes they go across them they feel so
you can actually cut them and

how basically try lots of tissue
connected by a person you five or so

it's a very nice system to study
when the mission and they now mix so

you can have a very one thing so
we can study single cell a few

of the we can study one
the mission of people.

We can take the atria some might and
yet they can be actually very thin

there are some sections where the X. ray
can be so thin that it's only a few a few

a few cells in thickness you can see
translucent it through the tree so

that counts for simulations of
experiments that we can do in.

Question to the and of course in three D.

The structure of the Heart disease
is more complicated right.

Then I think that is very nice
about the heart is the scaling so

we can call that leaf and if in fact
it's a finding myself since I saw.

Heights this is a mouse hut which is about

you not to actually send it on my
site he said about half a centimeter.

This is a mouse heart which
is about one centimeter.

And this is a horse cart.

So horse hired that actually they're
done for their mates for running so

when you open up a horse basically just
you just long long and hard it's just so

hard so by the size.

So.

So they finish because you have but

also you can have the nice
thing about the heart.

Is a very robust machine when you take
it out of an animal you can actually

keep it alive you can profuse and
you can profuse the.

So this is I would have been
profuse I mean kept alive so

now you see the a trick on track
in the ventricle contracting.

This is she refused charts.

So she refused I thought
about one quite a millimeter.

And he says.

This is one of the other horse hides that
I that I did when I was in Cornell So

this is this is just yes yes so when you
take out the attributes is the size so

we can keep it profuse we close and
you can keep it a life.

So the nice thing is that then you can
do nice explain as you can to make

a simulation we can do also experiments
directly on the heart so you can actually

try to understand the dynamics from both
point of views from the micro simulations

to do the experiments so many simulations
we try to do the simulations has the same

first result being that they only channels
in equations for they only channels for

one cell and then we have to connected
it in tissue so they connect

basically as a resource so you have every
cell will have their own dynamics and

then connected by bike up junctions
which are basically legacy stores and

you can have access
a little media money to.

Siller medium.

And then the membrane
conductance in between so

basically what you had to do is he's right
all these differential equations for

the currents all these arms
little equations for one cell and

then coupled to all the other cells and
the couple by the fusion so

he's actually right the questions of the
voltage propagation in height is actually

very simple to write he just basically
say the change of ownership time

is going to be the sum of then
channels the existence of plus or

the fusion term accomplice Now
the problem is these races are right

now in reality these I don't channel
this is some of all these ions for

each one of the cells and then there's
the fusion term here he's actually and

I through the mission a structure that
gives you information of the the heart and

the five percent on the hard because
I was saying there's SAS are I don't

know get it right are we sure that it
was about a hundred microns bye bye

bye by ten microns so
propagation along the Fiver's is

three things faster than across
the fibers on the part of your five or so

I was telling you if I could if I were
the preparations piece about three hundred

centimeters per second
in normal cardiac P.S.U.

normal cells he says about less you he
said about eighty something at this for

second so eighty something is for
sex along the five years but

across across the fibers it's about thirty
centimeters per second so it's an order of

three to one so that that effect and then
five S. as they go from the ventricle they

they rotate the five S S S these fibers
sheets as you go from the inside to

the outside of the heart they were
at eight hundred eighty degrees so

there's an isotope either you had to count
when you saw these differential equations

that comes into these if you
sometimes there some here.

So anyway so it's just easy to write
we sell you a little complicated and

to solve it that's just my
point that I want to say but

I want to do it simulations are going to
simulations of propagation of a wave.

So you can stimulate a tissue when you
stimulate that's a piece of tissue.

Going away.

And so you can stimulate and you have
a way that propagates through the tissue.

And as I was saying so
the structure had to account for

these new fusion in the structure of these
disease fission tensor accounts for.

Ten to one which Occulus to the to that
one too because that efficient process

they were lost because the square root of
the diffusion That's why I tend to want to

get changed between of of one to three.

So different we have we have a different
structures we can do simulations of

different types of structures we have
seen rabbit kind and we can always get

the higher that you know experiments we
can try to bring it to our micro city or

and in my right to get the structure and
to get information of the fibers so

I was mentioning as you go from the air
because into the in the car the in

this one hundred eighty degree rotation
of the fibers is because the fibers they

follow their six and this is your
this is a from a legal concept you're

going to the ventricle So that's where
you go from the set of the out so

you see these what they should and
they realize that when you want to do it

is very nice very nice paper from
a mathematician in the current Institute

which see the rise of the structure of the
structure just from first principles and

they realize that if you want to have a
very strong pump that when you contract it

pushes you know only one to two to
squeeze but you want to squeeze and

twist so you get by the twisting
you get no more strain by the more

force by the by the amount of contraction.

So so that's that's just function to
to make it much better contraction but

then simulations of course get more
complicated because we're talking for

this and I sort of.

Well there's a some other stuff that I
want to you when you go when you don't

include contraction but for now you're
going to consider only the efficacy know

when studying cousin dynamics that
to the front types of groups.

People who just concentrate
on the electrical signal and

people who concentrate on the contraction
both are important but then so so

they're We divided into electricians and
plumbers and and

then so so I'm not an electrician so

I work more on the electric outside
driving than the everything else but

there are people here in the department
who also work on construction and.

Unfairly dynamics.

So anyway for the money of the little
guy sitting on houses saying you can do

YOU CAN DO THE from models you can how
mellows with all these between four

to one hundred four for each cell so
you seen equations for the ion channels

between four which is a minimal amount
to produce a similar action potential

to the to what you see experimentally
the more realistic mother that account for

one hundred miles out to solve this
information equations you have to use so

this could say any time of point zero
one milli second because every shot

the officer connection potentially is very
very it happens when you know about five

minutes seconds so I would just in the
scene of the say it gets activated within

five minutes seconds it goes from C. minus
thirty five to twenty million volts and

finally seconds is very sharp and then the
last about two hundred milliseconds before

it comes back to rest so that's right
numerically you have to account for

that using point zero one many seconds.

And then also simulated if you have to
account for this good fish in the space so

that means some are two
hundred microns for

in any time step when you go a simulation.

So that requires that if you are doing
a simulation of a four by four centimeters

tissue you require two hundred by two
hundred elements the micron stands for.

Times so if you want to sit on
a sixty thousand or the equations for

four miles if you have one hundred
miles you require four million of these

every time step if you use some other
they sell even more complicated something

between the two twenty nine
via was this model one really

one second simulation into
the would require basically.

Ten to eleven differential equations.

If you want to the one second
of simulation it really they

require a twenty three million or these to
be solved so this is actually an amount of

large enough that you have to use computer
supercomputers so people over the last

few hours they can say we haven't used in
supercomputers to run these these these

these these problems the nice thing
about these problems is that they.

Because of the question that the form of
the questions that we have the diffusion

they need their eyes very nicely so
there are processors to use basically just

if you use two processors just be there by
two you will use four processors people

buy four summers niña there are more
processes you've got in there the faster

you get the solution and it's almost
linear which is very nice for this kind of

problems now one of the nice things is
that over the last few years not only

supercomputers and I will but also how
many of you have heard there were G.P.S..

So you POS is now he's saying that is
a graphic cards in the computer we

always run everything in the C.P.U.
on but now there's the graphic card which

displays has a lot of legal processes
that can be used to compute

there they have many more than less
powerful but they have a lot so

if you use these graphic cards too to
solve now it's very cheap nowadays and

you can actually paralyze very quickly and
solve this season much faster so

we're using G.P.S. now actually these
mileage you can actually even sort them

into in your cell phone so the cell phone
has a graphic card because of course it is

press so you can recruit the graphic cards
to produce simulations for these for

these biases and we show you here so
this is my cell phone

running running is in this running in this
NG when in the cell phone this is a simple

matter with a spy wave that please
are we activated you can put us now and

you can do a simulation here in three D.
Yes well.

So that's one of the nice things are now
we're in the we're reaching the time that

we can actually do simulations
on the three hearts.

Even Of course you know their stock
computer but also you might think if

you can read on the cell phone how
much faster you can do on things and

on the phone on a computer all right.

So let's just right now for the modelling
I'll come back and read one more thing but

in the show you once we do the monitor
we have to compete with experiments so

hard that we can verify and understand
the dynamics that we see experimentally

within America by the ricer versa so
we need to be so

I selected a scene or scene and heart.

So over the last.

Twenty years people have developed
what is called article mapping so

in the lab we would work with up to come
up with my present kill yourself and

corner he's also working the laughter
in some of the experiments so

the idea is that you.

Know you can once you have
the heart perfuse and

keep it a life you can stain the membrane
with certain dice that actually that

that gets into the membrane and then they
florescence us function of the voltage.

So what happens is that they they have
sort of like that one frequency and

then it can be that if and frequency and
their mission can change a little bit us

function of the voltage so they their
structure can change a little bit as

function of the voltage such that they
metion of the photons that they meet

can change a little bit the frequency
as a function of the voltage so

this race is so they get excited when
one from one frequency they have

an expectation sorry and of social.

And of social frequency and
they have an animation frequency.

So they have some of these lights and
then they meter these like.

I'm not but the trick is that the mission
the mission peak uses function

of the voltage so I use a rather she's
minus if I mean if the pic is here

you know want to she's twenty
million votes in the pic here so

if she has a pic now the pic that's fifty
is very small it's a few nanometers So

here I'm just showing you big but
you see only a few nanometers so steady.

The shift here is so mostly near you so
it's almost in there mentally so

then the nice thing is
that then you can't so

this admission changes suspension
of the motor change but

the nice thing is that you can you can
excite the tissue with a light of the.

Suction spectrum which in this case for
these voltage.

Membrane.

The i Phone apps in this case is called
for and apps you say run for fifty so

you excited one for fifty then you
can put a filter on six hundred so

you only visualize light coming
about six hundred so it is going to

shift the voltage is going to shift and
as it shifts the amount of light that you

are going to get the intensity is going to
change and is going to change the nearly

the proportion of the voltage so the idea
is to utilize these and these change and

this change is going to really really
proportional to the voltage so

as it as a as this one to shifts the
amount of light that you see eclipses So

the creases in this case because he shifts
to the left is inversely proportional.

Proportional but it negatively so you have
an actual potential and I see changes

you're going to get this is a signal
that you're going to see obviously.

So so that I think you have a piece of
tissue you can profusely you keep alive

you profusely these drugs you
are you excited with a rap for

a knee in this case which is in
the green you put the filter for

about six hundred which is in the red and
this is what you see.

So this is a piece of tissue that gets
sustain and then you can just change

the you're recording time
with a high speed camera and

any small changes in intensities are going
to be reflected to the voltage so

this is an actual position measuring
a single cell and this is of others

if you will in from an optical mapping so
the signal is a little bit more noisy but

the thing is that this one out
the signal we can see especially ever.

Where because we record from the camera so

we can see everywhere in the tissue
the cells on the surface the signal so

we can put a color we can put when it is
just minus eighty five many of us we can

see these block when he's twenty min of
also we can say he's yellow so that way we

can actually visualize the scene S. We
can also do the same thing for costume so

in the system we can have one one die for
want there's one there for counseling and

we can switch the lights and we can switch
then and we can be so nice both seen us at

the same thing with one camera so
let me show you example now this is.

Right ventricle and RIGHT RIGHT RIGHT
RIGHT Atria So now this is activation

coming from the a C. note this is
actually what we can we shall I say.

She see the lights because you know
going through the through the entry

that same way the seven circle this
is elliptical we pacing from here so

you see this electrical signal
now passing through the vents.

So that we can actually read
what I just by the waves so

this is a spot away disappear heart and
this is part of we want to you know

going around of the ventricle and then
after a few seconds as I say they're very

honest they when they break and
now becomes chaotic.

And you have all that on
the on the spot waves right.

So what I think we're trying to study
is that the name is what produces

a spiral wave.

Front from a stable spot a wave
to kill someone to pull waves.

So we saw there were you know
the top one case was coupling

the coupling can actually affect any of
the probation of the waves can destabilize

the only mechanisms let me show
you quickly one example of of that

before that let me show you
exactly how spot which can form.

It's all about timing when you're excited
because Excel you produce an action

potential and before you can produce
another excitation that the system has to

go back to rest to go back to you
some time to go to recover so

if you stimulate an action but they shall.

You try to stimulate again.

Either it's not enough or the Chinese
have not open again and cannot open still

remain close over a factory so there's
no activation like if you wait long

enough then that says open again and then
you can have another action potential So

what happens is that if you
have a stimulus coming.

And then I stimulate in the back and the
Says have a quarter then I have another

activation right so this is this is an
actual petition provided I stimulate and

then a stimulate it provides Now if I
stimulate too soon on the back of a wave

when the tissues refractory then he
will die out so I stimulate and ice out.

Because he was too soon
behind the way right so

if I am very soon behind the wave it will
die out because she's refractory you found

back a little farther away than you
activate right so in between this there's

a window when I really think between part
of that issue can be excitable but part of

the show will be refractory So that means
that if I stimulate at that point part

of that wave propagating one direction but
we get a block on the other direction and

that's what produces the so now in this
case he was probably one direction but

blocking the other one direction so
that he sees this part way so

let me show you again we see many hear
us properly think one direction but

blocks in the other direction so
this is one of the mechanisms to initiate

the spider waves by conduction block.

Well you have a spiral wave we always
think of a spa break flowing like

a circular sequence right for the right
kind of like a chameleon spiral way.

But it turns out that the dynamics
of the spiral way this rotation it

depends on the excitability of the system
and the wavelength of the direction

of the activation so by changing climate
there is you know a model in a similar

we can go from a circular core.

To.

The cyclo that's rectory.

With.

Where is call in in a near inner petals.

Close up directory which
completely just cycloid.

To the to the P.C.
clothes now with the partners outside.

You got to know higher for the frequencies
when you have high premium there so

the dynamics of this by the way
would more complicated.

And all the way up to waste calling
your territory with a wavelength is so

fast that it is so

large that he blocks itself until finally
has enough time to to activate again and

turns around so all this I makes as you
go from from circular quarterly not

core either based on the site every day of
the system the higher the realty the more

the leaner Courtrai through the lower
the Excite that will be this case except I

mean it is related to increase when
hard with oxygen so if you have a hard

day scheming takes loosing oxygen you're
going to get this kind of spider waves you

know how it's excited when he's high high
when we don't suggest he's going to start

with the spider waves so that way you know
when you have a spot reforming the House

will start the form and we time it
was developing to those ones and

also this in doing this straight
through their source or the other.

All the things that can happen
that can stop when I spy weeks and

make them break so let me show you are.

Well an example of Koreans in.

Experiment and also for
the next point an experiment so

this is just following
the inner core to me.

So one of the examples I'll share quickly
so that we can use mathematics to explain

that we need is a spot of waste
he said that is what is called.

Afternoons.

So I answer Nancy it's a peer diary but
for creation explain you quickly what he

did this I said was saying you
have an actual potential when

excited sell you an action but they show
you wait long enough you accept again you

have another action but then show similar
to the first one you wait long enough we.

Call.

They call the time between
activations they call it the eye for

the stomach interval their time
the duration of the exact nation they call

action but
they share the ration of a P.D. So

if you stimulate sooner you make that
isolate interval smaller the A.P. will

start becoming a little smaller because
it has not time time to recover right so

you start pacing faster and faster
the actual position becomes smaller and

smaller and smaller until you
finally reach a small there so

you can try when there's no activation
right refractory period so you can create

a curve of that static interval that gives
you the A.P.'s function of the static

interval right I'd love its allows us
to look into about your good action but

they sure there are basically the same
right as you the creases I started to run

the action potential become smaller and
smaller until you finally reach a point

and there's no activation so this
curve is just a response function that

tells you how the hard to access function
of pacing and this carries rain but

very important for the nomics because
you can do what is called a mop so

I won't bore you quickly with a dynamic
but you can create that when the mission

and mop function you can do some analysis
is there some ways cleaner several

of the analysis and
it will tell you that any path to ration

will grow as function of what is
called a function of that they are.

The only thing that wakes up one body
with it with a mass but basically

what happens is that if the cause of this
curve has a slope greater than one so

I see changes in France very
very steep becomes very steep.

Then then if you place a cycling's
where this this curve is steep is

going to produce about creation and
let me show you how this actually.

So let me just show you the example here.

These things.

So here this is that they come from this
is the rest of the pacing that's very.

Five degree pacing a constant cycling
sideline at forty five degrees so

I wasn't around so no medically what I
was just showing you is calculating this

is the meat of this point I said change
the period I get I get a fixed point

yes met one to one solution but once you
got this part here when the slope is

greater than one was telling companies
that there's going to be produced.

And this is very nice because it just
comes from the pure mathematics of

the system you just tells you that
if you have these kind of function

then it's going to if you do
a division you produce a return map

he's going to act on it between
two points so he has a so

it's a solution a one to one but at some
point when you place at a constant cycling

you're not going to have a one to one
response you can have a long response and

a short response so the action potential
is going to be long short long short so

that's actually very cool right
because now you have you have these.

You happen you start pacing a tissue
when you start placing very fast it

will develop so the Early this period of
a bifurcation and the Senate's payment so

this is we've pacing faster
the pace in cycling is constant so

you see that activation is based on
a constant cycling but now the response is

along actual position a short section
of action so it produces these.

Activation and that actually
eventually will produce tribulation.

And the reason is because well this is
going to tell you more to you how this

period I mean bifurcation you go and
you go from two to two then he goes to

thirty four then he goes to eight to eight
sixteen to sixteen to you got to kill us

so this is some other experiment and then
we can make sure of this distance ition.

How and how time to show you quickly but

basically what happens is that in America
I want I was able to show experimentally

where you have these days
after announcing in the ration

imagine the same way that propagates and
I see propagates the long way if.

And the next thing is the short wave and
the long wave and

a short wave now I see propagates
conduction velocity changes too and

that actually well does is that they were
long way was the propagation is going to

become short and the short want
to see purpose becomes long and

that actually produces of these waves to
oscillate as they propagate and that can

produce the special offer factoring is in
the tissue that can produce relation so

let me show you this
example of this movie.

Yes and.

Yes.

Most of us are so this is.

So this is a really hard it's space a
difference actually this is three hundred

fifty milliseconds two hundred one eighty
one seventy one sixty one fifty one forty

six and the cycle length there's no
utterance the way propagates nicely so

everywhere propagates and this is
very interesting this is causing So

the well this propagates So
we simulate from somewhere here so the way

propagates through the through through
the through the through the ventricle

you see the popping is very nicely on
the beat but I just second increases

now as I show you these waves a good
long short as they propagate so

the duration of activation becomes very
complicated and which different so

let me show the movie.

So here first look at and look at these
when you just a way that propagates and

then the next one follows and
it's not too complicated.

But as you go farther and faster now the
population is not the same right he just

gets long and short and he just is not
continually going in every nice try to

rewrite sharing.

So here he.

Rocks and then the proxy any
propping specs this fire.

And the next time.

Using inverse right so when he was
short he's going to be long and

when he was long he's going to be short.

So you see the way he's propriety now not
only genius the right he started to become

around like wondering and that's what
produces this initiation of our reading us

so as you pace faster and faster you
produce this this actor and I think other

waves that we conduction velocity they
change to a space and then after this is

that there are genius waves appropriation
and eventually can block and produce.

And produce relation.

So for example here this is a power wave
that is doing the solution of the wave

service telling you so you get slung short
at some point it gets too soon too long to

shore that we call the next
we actually call lights.

And it produces a start position breakup.

So this is a make one of the mechanism
that can produce the study and

he's very nice so you can you can first
proven mathematically where he comes from

you can do the simulations and

you can do experimentally you can see this
this this transition actually occurring.

Another thing is that it makes life more
complicated too is that all this by which

I was showing you sense into the when you
got to really spiral is that have actually

a three dimensional information so that
they stop ology involving three the so

we usually spiral we seem to the you can
put a color to the voltage in three D.

cellular higher because you have X.
Y. and Z.

and you can put a college for the voltage
so the result ISIS by waving three D.

when we do this we look for the this point
we see the normal velocity that's the face

to face the singularity and this by
the way that people this by the way so

the tip of the spiral wave in three D.
becomes of all text filament So

if you have a cube and I thank God through
the cube through the different levels of

the other killed I can
see the spiral way for

I see it for a second follow
the Tiptronic three the tip of the so

the greater the teep in space and that's
going to form from a vortex filament.

And by following this for

this filament I can I can if I know
the horse in the twist in the curvature

every time I know where the curve of
this problem is he's he said every time.

So it becomes complicated because now you
have the political effect now you can have

a spiral way that forms inside like
a ring and then disappears you can have

one that appears and
can fuse or one by several So

that can can expand and can pinch.

And so now dynamics of the school we see
in three D. because more complicated so

this is a simulation of failure.

So this is a front view up back
to you off of a lot of ventricle

the view from the apex and

he said trust me don't you when you
have the vortex filaments driving the.

The relation so
now you have the fact that he's

not only the rotation of
the fivers the coupling on the.

Self but also.

Also the three dimensionality of
this feeling is that makes life

very complicated for
these Remus to terminate and

that's what they've been doing you see.

All right so so how we can terminate
the Serenus I'll just finish

quickly with an example of terminations.

To determine it I mean if you had
to draw a big electric shock and

the Selectric shock basically
you have a spider wave you have

this is a relation you have sparred with
here the only way you can terminate them

is by a plane electric shock that strong
enough that excites everywhere and

then basically then yes all
the ways right so you want to do is

is a strong electric field that excites
all the cells and kills the waves so

he's going to be example again we excite
now but he's strong enough that everybody

find it gets excited and he just I saw
them in the Hulk and go back to normal

you know to do that you have to apply
at least five percent the meter inside.

Inside the heart and
to do that if your external shock

you had to do between hundred to three
hundred sixty euros that's a lot

that's that's a thousand volts there
in pairs for about two milliseconds but

that's a lot of current That's a cell or
it's very strong I mean but today but

I know they have time but but
it takes only point zero one.

Point zero zero one Jules to make you
crack to make your arm move if I apply.

A current that has points or
one million pairs I can I can make you or

I move so say magine the main three
hundred sixty joules is actually very

painful if you see in turn all you can
lower to seven Joules but it still is very

painful and there's the really painful but
actual shock and really damage short so

they can burn some of
the tension in the ventricle.

So so what are we going to do when we're
trying when we decide if we start doing

one big shock we can then want to pull
shocks try to synchronize the system to

terminate it to a new frequency so I don't
have time to show you this point here but

I'm sorry.

I just saw the theory behind that but
let me show you an example

where we actually this is this is and I
remain in and it's here where we shot with

one.

So we the one big shock.

And it to me is that reading it so

now the big shock is strong enough that
eventually everybody gets excited so

this is violent this is amount of
the shock side that's function of time.

So you see late in the very near you shock
and eventually everybody gets excited so

that you can tell me that
right now in this case.

We're going to do fine
with the bull sharks.

Each one with very low energy but

little by little what we
doing you see Christ in this.

Into the new frequency went to
we everybody gets excited and

then you terminate you think there are you
ready for the signal it's basically this

is going to station so just tell you
that every time you shock you start

synchronizing more and more tissue to
the new frequency Well everybody responds

to that frequency you stop pacing and
then the tissue goes back to normal so

that that requires only ten percent of
the energy compared to the one shock so

that's actually very very nice
because then we can train him evil so

we try that in we were in the gate area so
we can have this.

Catheters inside the gates
one in each right and

left at three where we can
produce an electric field.

So this is an example off so this is the
right ventricle this is the right Atria So

this is the only scene A.F..

You see in A.F. we're going to do
one big shock determination and

then they're in the air.

And it goes back to normal but the shock
was enough to tell me there is nobody

strong enough to actually engage
all the nerves never system and

then makes anyone move right and jump and
that's where you would expect that

that's what you see that's what you very
painful because it recreate it is a strong

enough elect if you're there across all
the nerves and makes the muscles contract

now and show you the same thing.

But now you see if I
process you see the same.

You know Nischelle.

I.

Know what happened to me before.

We were playing in.

You know us so I was going to be
fine Persis then present the energy.

Recovers a normal activation and

I was slowing off the need to recruit
the nervous system so it was not painful.

For me to show you one more scene
a half week of the five process.

The same every.

So anyway so
we show these when actually both.

Have to go mapping and in vivo in vitro
and we can get the same frequency so

we can show from the optical mapping
that he's actually what we're doing here

Secretary connection the system and
that's basically what we wanted to show

that from the we did on these one of
with initial conditions when by and

we don't know make assimilations First
the theory and then the experiments and

then we managed to succeed on these
things so my point here one story is that

there's a lot of theory behind it a lot
of the make us images we can do and

eventually we can actually
apply it to maybe seen and and

this is we working out to try to do
the same thing for the ventricles But so

the meantime I just want to
thank you guys for for but

then even some of my collaborators in the
seventy and I was star some of those looks

a lot of my students Andrea and
many of my students and Connor and

I think UNICEF has been very kind to us
over the years so thanks and open for

questions.

No not that we we have a patent for
it but it's but he still.

Is He's very complicated to work with
the with the with the industry because

they don't care about lowering the energy
they they have all their other concerns

right now for them this is thing works so
they're fine the the color problems like

the leads where they connect and problems
like that so those are some of the things

that they're concerned the lower
the energy is good for the patient but

he's not the critical importance from
there right now so he's not he's not.

And still if we have a profile
concept that we have done it but

still it has to work for
larger I mean most of us too.

I say for the atria but there.

Are some problems when you try to that for
the ventricle that he and talk and

sometimes if you do multiple shocks.

In reality when you're when you're
doing in the year if you keep

the wave on the during
the during the game they C.G.

you can actually initiate and I read me in
the ventricles So it's not completely safe

to do this actually has to become one
hundred percent safe so there are a lot

of things I need to be actually
improving or to to do to have these.

Yeah but at least we have a profile
concept and we can work with it but

yes there was a long way
to the having to clean.

Things think.

Yes So
this one was we we need we stimulate the.

Living on Earth so we can keep it up.

So you want us healthy healthy animal but
just used by stimulation of the of

the vegan Norton Nohant we
can induce a C.-H. and and

then that that state of
relation on the answer.

Yeah so
we work in actually trying to work with.

Three three three three three three.

Laps to do some a allegation and.

Geishas on the hearts and try to do heart

failure.

Thank you.