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CPS from EU-Science Perspective. Radu Grosu Vienna University of Technology. 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-Free System . Error-Prone System. - PowerPoint PPT Presentation
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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!
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