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
Feb 23, 2016
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!