Radu Grosu Vienna University of Technology

CPS from EU-Science Perspective

Joint work with

Ezio Bartocci, Flavio H. Fenton, James Glimm Ariful Islam, Abhishek Murthy, and Scott A. Smolka

Consider the Following CP-EM-Systems

Error-Prone SystemError-Free System

Whose problem is this to solve?

It is a Medical ProblemNational Vital Statistics Report, Vol.49, No.11, October 12, 2006

Deaths and percent of total deaths for the 10 leading causes of death: USA

Rank Cause of death Total Deaths PercentageAll causes 2,391,399 100.0

1 Diseases of heart 725,192 30.3 2 Malignant neoplasms 549,838 23.0 3 Cerebrovascular diseases 167,366 7.0 4 Chronic lower respiratory diseases 124,181 5.2 5 Accidents (unintentional injuries) 97,860 4.1 6 Diabetes mellitus 68,399 2.9 7 Influenza and pneumonia 63,730 2.7 8 Alzheimer’s disease 44,536 1.9 9 Nephritis, nephrotic syndrome and nephrosis 35,525 1.510 Septicemia 30,680 1.3

All other causes 484,092 20.2

http://www.cdc.gov/nchs/data/nvsr/nvsr57/nvsr57_14.pdf

What are the Fundamental Questions?

For cardiologists, pharmacologists and patients: • What is the risk of a patient to develop the disorder? • Under what circumstances will such a disorder arise?

Given a disorder-specification and a model of the ventricle: • What is the probability of the model to satisfy the specification? • For what parameter-ranges does it satisfy the specification?

Whose problem is this to solve?

It is a Communication-Structure Problem

5

Complicated structure

Pittsburgh NMR Center

Anatomy Fibers Vessels

MicroCT Cornell

Canine heart: slices (DTMRI @ 250 microns resolution)

4 Billion communication nodes (cells) linked in a very sophisticated way

Plateau

LateDepolarization

EarlyDepolarization

Upstroke

Resting Resting

lt is a Cellular Problem

Cell membraneselective ion permeability

⎛⎝⎜

⎞⎠⎟

INa

Na+

INa,b

Na+

ICa

Ca2+

ICa,b

Ca2+

Ca2+ INa,Ca

Na+

Ip(Ca)

Ca2+

BufferSubspace

JSR NSRBuffer Jrel

Jup

Jtrpn

Ca2+

Ca2+

Ca2+ Ca2+ Jtr

Jxfer

Ca2+

IKr

K+ K+

IKs IK1

K+ K+ Na+

INaK

Ca2+ K+

ICaK

K+

IKv1.4 IKv4.3

K+

Na+

Na+

Na+

K+

K+

V

FinalDepolarization

It is an Electrical Problem

&V=−( INa + ICa + ICaK + IK1 + INaCa + INaK + ICab + INab + IKr + IKs + IKv1.4 + IKv4.3 + Ip(Ca) + Istim )

Cell membraneselective ion permeability

⎛⎝⎜

⎞⎠⎟

IKr

K+ K+

IKs IK1

K+ K+ Na+

INaK

Ca2+ K+

ICaK

K+

IKv1.4 IKv4.3

K+

INa

Na+

INa,b

Na+

ICa

Ca2+

ICa,b

Ca2+

Ca2+ INa,Ca

Na+

Ip(Ca)

Ca2+

BufferSubspace

JSR NSRBuffer Jrel

Jup

Jtrpn

Ca2+

Ca2+

Ca2+ Ca2+ Jtr

Jxfer

Ca2+

Na+

Na+

Na+

K+

K+

V

Plateau

lt is an Abstraction Problem

Cell membraneselective ion permeability

⎛⎝⎜

⎞⎠⎟

V

LateDepolarization

EarlyDepolarization

Iso

Isi

Resting Resting

Upstroke

Ifi

FinalDepolarization

&V=−( Ifi + Isi + Iso + Istim )

Enough if only voltage V is of interest

It is a Molecular Problem

INa = gNa(V −VNa)

Na Channel Conductance

Nernst Potential

Sodium ionsLipid

bi-layerActivating

m-gateInactivating

h-gate

Extracellular space

Intracellular space

3 m-units 1 h-unit

=gNam3h(V −VNa)

C m am (V )

bm (V)

&m =am (V)(1 −m) − βm (V)m

h O ah(V)

bh(V)

&h =ah(V)(1−h) − βh (V)h

The sodium channel: Hodgkin-Huxley Nobel-Prize model

It is an Abstraction Problem

o(V)=O1(V )+O2 (V )

Approximate bisimulation

&m =am (V)(1 −m) − βm (V)m &h =ah(V)(1−h) − βh (V)h

C m am (V )

bm (V) h

O ah(V) bh(V)

o(V)=m 3 (V )h(V )

C00 C10

4a(V)

C01 C11

4a(V)a

bm (V)

b(V) /a

C20

3a(V)

C21

3a(V)a

2bm (V)

2b(V) /a

Cf Cn Cf / a Cna Cf /a2

C30

2a(V)

C31

2a(V)a

3bm (V)

3b(V) / a

Cna2 Cf /a

3 Cna3

C40

a(V)

C41

a(V)a

3bm (V)

4b(V) / a

Cf / a4

Cna4

O1

g(V)

I gg(V)

δ(V)

δδ(V)

Of On

O2

ω ε

h(V)

ν(V)

The sodium channel: Most recent Iyer-Mazhari-Winslow model

1111

3D Model of a Pig Heart (Fenton-Karma 3V Model)

3D Model of a Mouse Heart (Fenton-Karma 3V Model)

Web Graphics Language (Fenton-Karma 2V)

Runs in your Browser and Uses your own GPU

It is a Simulation Problem

12

Spiral Wave Induced by Unexcitable Myocytes

G(u <θv)Property to Check

go1 ∈[0,180], go2∈[0,10]

gsi ∈[0.1,100], gso ∈[0.9,50]

Uncertain Parameters

It is a Verification Problem

Computer simulation

Defibrillation with 90% energy reduction

1 Shock 5 Low Energy Shocks

It is a Control Problem

It is a EU-CPS Problem

This is a World-CPS Problem

We are on the brink of a paradigm shift in the Diagnosis and treatment of cardiac disorders

It is up to us in to make it happen!