sensor-based modeling and control of nonlinear …sensor-based modeling and control of nonlinear...
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Sensor-based Modeling and Control of NonlinearDynamics in Complex Cardiovascular Systems
Better Heart Beats Through Engineering
Dr. Hui Yang
杨 徽
Associate ProfessorComplex Systems Monitoring, Modeling and Control Lab
The Pennsylvania State UniversityUniversity Park, PA 16802
November 6, 2017
Yang, Hui (PSU) Simulation Modeling and Sensor Informatics November 6, 2017 1 / 62
Outline
1 Overview
2 Simulation ModelingIntroductionStatistical MetamodelingSequential Design of Computer ExperimentsExperimental Results
3 Sensor InformaticsIntroductionSensor-based Modeling of Space-time DynamicsSparse Particle FilteringExperimental ResultsSummary
Yang, Hui (PSU) Simulation Modeling and Sensor Informatics November 6, 2017 2 / 62
Research Roadmap
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Outline
1 Overview
2 Simulation ModelingIntroductionStatistical MetamodelingSequential Design of Computer ExperimentsExperimental Results
3 Sensor InformaticsIntroductionSensor-based Modeling of Space-time DynamicsSparse Particle FilteringExperimental ResultsSummary
Yang, Hui (PSU) Simulation Modeling and Sensor Informatics November 6, 2017 4 / 62
Physical-Statistical Modeling and Simulation
D. Du, H. Yang, A. Ednie, and E. Bennett, “Computer experiments and optimization ofcardiac models,” placed first in the CIEADH Doctoral Colloquium poster competition,ISERC 2014, Montreal, Quebec, Canada, May 31-June 3, 2014
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Relevant Work
D. Du, H. Yang*, A. Ednie, and E. Bennett, “In-silico modeling of the functional role ofreduced sialylation in sodium and potassium channel gating of mouse ventricularmyocytes,”IEEE Journal of Biomedical and Health Informatics, 2017. DOI:10.1109/JBHI.2017.2664579D. Du, H. Yang*, A. Ednie, and E. Bennett, “Statistical metamodeling and sequentialdesign of computer experiments to model glyco-altered gating of sodium channels incardiac myocytes,”IEEE Journal of Biomedical and Health Informatics, (Posterpresentation received the 1st place in the CIEADH Doctoral Colloquium postercompetition), Vol. 20, No. 5, p1439-1452, 2016, DOI: 10.1109/JBHI.2015.2458791D. Du, H. Yang*, S. Norring, and E. Bennett, “In-silico modeling of glycosylationmodulation dynamics in hERG channels and cardiac electrical signaling,”IEEE Journal ofBiomedical and Health Informatics (Feature Article highlighted in the homepage of IEEEjournal website), Vol. 18, No. 1, p205-214, 2013, DOI: 10.1109/JBHI.2013.2260864S. Norring, T. Schwetz, A. Ednie, D. Du†, H. Yang, and E. Bennett, “Channel Sialic AcidsLimit hERG Channel Activity During the Ventricular Action Potential,”FASEB Journal(IF-5.712), Vol. 27, No. 2, p622-631, 2012, DOI: 10.1096/fj.12-214387D. Du, H. Yang*, S. Norring, and E. Bennett, “Multi-scale modeling of glycosylationmodulation dynamics in cardiac electrical signaling,”Proceedings of 2011 IEEEEngineering in Medicine and Biology Society Conference (EMBC)(Placed first in IBMBest Paper Competition), p. 104-107, September 2, 2011, Boston, MA. DOI:10.1109/IEMBS.2011.6089907
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Research Motivation
Total deaths for the 10 leading causes in United States [CDC]
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Modeling Rationale
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Research Motivation
Discrete-event simulation vs. Continuous-flow simulation
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Background
Action Potential: Net change of transmembrane potentials
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BackgroundGlycosylation:The enzymatic process that attaches glycans to proteins,lipids, or other organic molecules.Research objectives:
To determine whether and how aberrant glycosylation modifiescardiac electrical function.To model mechanistic details of glycosylation-altered cardiac electricalsignaling.
Physical experiments: Datasets under control (physiological, wild-type)and reduced glycosylation (pathology, ST3Gal4−/−).
Yang, Hui (PSU) Simulation Modeling and Sensor Informatics November 6, 2017 11 / 62
ChallengesMarkov model of Na+ channel
dP(t)dt = f (t, v ,A,P(t))
where P = [PIC3,PIC2,PIF ,PI1,PI2,PC3,PC2,PC1,PO], A is the transitionmatrix,e.g., A1,1 = −(α31 + α111), α31 = 1
2.5exp(θ1 + v
7.0
)+8.0exp
(θ2 + v
7.0
)
Nonlinear differential equationsHigh dimensional design space, e.g., full factorial experiments - 225
(approximately 33.5 million) design pointsYang, Hui (PSU) Simulation Modeling and Sensor Informatics November 6, 2017 12 / 62
Challenges
Experimental protocols: steady state activation (SSA); steady stateinactivation (SSI); recovery from fast inactivation (REC).Functional responses
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Outline
1 Overview
2 Simulation ModelingIntroductionStatistical MetamodelingSequential Design of Computer ExperimentsExperimental Results
3 Sensor InformaticsIntroductionSensor-based Modeling of Space-time DynamicsSparse Particle FilteringExperimental ResultsSummary
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Research Methodology
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Space-filling Design
Generate design points in the space of control variables (θ)Maximin Latin Hypercube Design (LHD)
dij = ‖xi − xj‖maxX∈[0,1]d mini 6=jdij
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Statistical Metamodeling
Gaussian Process: a collection of random variables, any finitenumber of which have joint Gaussian Distribution.Assume that the prior of f is a GP, i.e.,
f (x) ∼ N(f (x), k(x, x′))
)we then can prove that[
fobsf (x∗)
]∼ N
([f(X)f (x∗)
],
[K (X,X) + σ2
nI K (X, x∗)K (x∗,X) k(x∗, x∗)
])
wherefobs =
(f 1obs , . . . , f N
obs)T
X = {x1, . . . , xN}f(X)i = f (xi )K (X,X)ij = k(xi , xj)
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Statistical MetamodelingPosterior distribution:
f (x∗) ∼ N (E{f (x∗)}, var{f (x∗)})where
E{f (x∗)} = f (x∗)︸ ︷︷ ︸prior
+K (x∗,X)[K (X,X) + σ2
nI]−1
(fobs − f(X))
var{f (x∗)} = k(x∗, x∗)︸ ︷︷ ︸prior
−K (x∗,X)[K (X,X) + σ2
nI]−1
K (X, x∗)
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Outline
1 Overview
2 Simulation ModelingIntroductionStatistical MetamodelingSequential Design of Computer ExperimentsExperimental Results
3 Sensor InformaticsIntroductionSensor-based Modeling of Space-time DynamicsSparse Particle FilteringExperimental ResultsSummary
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Sequential Design
Probability of Improvement:ProbI = Φ
(T−E{f (x∗)}std{f (x∗)}
)where E{f (x∗)} and std{f (x∗)} are mean and standard error ofpredictions, Φ (·) is the Normal CDF function.
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Sequential Design
Probability of Improvement:ProbI = Φ
(T−E{f (x∗)}std{f (x∗)}
)where E{f (x∗)} and std{f (x∗)} are mean and standard error ofpredictions, Φ (·) is the Normal CDF function.
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Sequential Design
Probability of Improvement:ProbI = Φ
(T−E{f (x∗)}std{f (x∗)}
)where E{f (x∗)} and std{f (x∗)} are mean and standard error ofpredictions, Φ (·) is the Normal CDF function.
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Outline
1 Overview
2 Simulation ModelingIntroductionStatistical MetamodelingSequential Design of Computer ExperimentsExperimental Results
3 Sensor InformaticsIntroductionSensor-based Modeling of Space-time DynamicsSparse Particle FilteringExperimental ResultsSummary
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Significance Test
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Data Modeling
Steady state activation and inactivationRecovery from fast inactivation
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Model Validation
Current density-voltage relationships
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Model Validation
Refractory periods of ST3Gal4−/− and WT cellsComputer experiments: WT: 138.0ms, ST3Gal4−/−: 109.5msPhysical experiments: WT: 139.8±8.6ms, ST3Gal4−/−: 110.2±10.0ms
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Summary
ChallengesDiscrete-event simulation vs. continuous-flow simulationNonlinear differential equationsHigh-dimensional design spaceExperimental protocols and functional responses
Methodological and Biomedical MeritsStatistical metamodeling and sequential design of experimentsComputer experiments and calibration of large-scale cardiac modelsImprove fundamental knowledge about the functional role ofglycosylation in cardiac electrical signalingNew pharmaceutical designs to correct aberrant glycosylation
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Broad Applications
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Outline
1 Overview
2 Simulation ModelingIntroductionStatistical MetamodelingSequential Design of Computer ExperimentsExperimental Results
3 Sensor InformaticsIntroductionSensor-based Modeling of Space-time DynamicsSparse Particle FilteringExperimental ResultsSummary
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Sensor-based System Informatics and Control
Y. Chen and H. Yang, “Sparse Particle Filtering for Modeling Space-Time Dynamics inDistributed Sensor Networks,” Proceedings of the 10th Annual IEEE Conference onAutomation Science and Engineering (CASE), August 18-22, 2014, Taipai, Taiwan.(Finalist in the Best Student Paper Competition)
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Relevant Work
Y. Chen and H. Yang*, “Sparse modeling and recursive prediction of space-time dynamicsin stochastic sensor networks,”IEEE Transactions on Automation Science andEngineering, Vol. 13, No. 1, p215-226, 2016, DOI: 10.1109/TASE.2015.2459068Y. Chen and H. Yang*, “Sparse Particle Filtering for Modeling Space-Time Dynamics inStochastic Sensor Networks,”Proceedings of 2015 Industrial and Systems EngineeringResearch Conference (ISERC), May 30, 2015, Nashville, Tennessee (Best Paper Award inComputer and Information Systems)Y. Chen and H. Yang*, “Sparse Particle Filtering for Modeling Space-Time Dynamics inDistributed Sensor Networks,”Proceedings of the 10th Annual IEEE Conference onAutomation Science and Engineering (CASE), August 18-22, 2014, Taipai, Taiwan.(Finalist in the Best Student Paper Competition)B. Yao, R. Zhu, and H. Yang*, “Characterizing the Location and Extent of MyocardialInfarctions with Inverse ECG Modeling and Spatiotemporal Regularization,”IEEE Journalof Biomedical and Health Informatics, page 1-11, 2017, DOI:10.1109/JBHI.2017.2768534B. Yao and H. Yang*, “Physics-driven spatiotemporal regularization for high-dimensionalpredictive modeling,”Scientific Reports 6, 39012, 2016. DOI:www.nature.com/articles/srep39012
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Distributed Sensor Network
Environment, Healthcare, Defense, Manufacturing
USF Marine - sensing Tampa Bay BSN - surface ECG potentials
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Sensor-based Informatics and Control
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Challenges
Space-time dynamics
Pollution Dynamics Cardiac Electrical Dynamics
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ChallengesSpatially-temporally big data
DimensionalityVelocity - sampling in millisecondsVeracity - sensor reliability
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Challenges
Stochastic Sensor network - A subset of sensors at temporally-varyinglocations within the network to transmit dynamic informationintermittently.
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State of the Art
Limited number of sensorsReliable sensor readingsIncomplete space-time information
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Problem Fomulation
Software algorithms to support the design of stochastic sensor networkand realize a highly resilient cyber-physical system:
Reduce the requirement in sensor reliability (veracity)Robust and resilientWearable and comfortableFast and recursive predictionSpace-time information
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Outline
1 Overview
2 Simulation ModelingIntroductionStatistical MetamodelingSequential Design of Computer ExperimentsExperimental Results
3 Sensor InformaticsIntroductionSensor-based Modeling of Space-time DynamicsSparse Particle FilteringExperimental ResultsSummary
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Sensor-based Modeling of Space-time Dynamics
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Spatial Model
Y (s) = M(s;β) + ε, ε ∼ N(0, σ2)
Y (s) =
y(s1)y(s2)
...y(sk)
M(s;β) =
∑Ni=1 wi (s)f ′i (s)βi
=
w1f11|s1 · · · w1f1p|s1 · · · wN fN1|s1 · · · wN fNp|s1
w1f11|s2 · · · w1f1p|s2 · · · wN fN1|s2 · · · wN fNp|s2... . . . ... · · ·
... . . . ...w1f11|sK · · · w1f1p|sK · · · wN fN1|sK · · · wN fNp|sK
β11β12
...βNp
Weighting Kernel: wi (s) ∝ |Σi |−1/2 exp
(− (s−µi )
′ )Σ−1i (s−µi )
2
)Basis function: fi (s) = [fi1(s), . . . , fip(s)]T e.g ., (1, x , y)T
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Spatioptemporal Model
Y (s, t) = M(s;β(t)) + ε, ε ∼ N(0, σ2)
β(t) = g(β(t − 1), γ)g(.) is the nonlinear evolution model.γ is the noise.
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Model Structure
Weighting Kernel: wi (s) ∝ |Σi |−1/2 exp(− (s−µi )
′ )Σ−1i (s−µi )
2
)µi is the center.Σi is the covariance function.
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Submodular Optimization
Objective function: w∗ ⊆ V such that w∗ = argmin|W |<N
H(W )
V - finite set of kernels.H(W ) = ‖y(s, t)−
∑Ni=1 wi (s)f ′i (s)βi (t)‖.
Set function H on V is submodular ifFor A ⊆ B and w /∈ B,H(A)− H (A ∪ {w}) ≥ H(B)− H (B ∪ {w})
Submodularity (diminishing returns)
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Submodular Optimization
Objective function: w∗ ⊆ V such that w∗ = argmin|W |<N
H(W )
V - finite set of kernels.H(W ) = ‖y(s, t)−
∑Ni=1 wi (s)f ′i (s)βi (t)‖.
Set function H on V is submodular ifFor A ⊆ B and w /∈ B,H(A)− H (A ∪ {w}) ≥ H(B)− H (B ∪ {w})
Submodularity (diminishing returns)
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Minimizing Submodular Functions
Objective function: w∗ = argmin H(W )s.t. w∗ ⊆ V and |W | < N
V - finite set of kernels.H(W ) = ‖y(s, t)−
∑Ni=1 wi (s)f ′i (s)βi (t)‖.
Theorem [Iwata and Orlin,2009]There is a fully combinatorial, strongly polynomial algorithm forminimizing SFs, that runs in time O(n8logn).
Polynomial-time = Practical?
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Greedy Algorithm
Start with W = ∅For i=1 to N
w∗ := argminw
H(W ∪ {w})W := W ∪ {w∗}
End
Theorem [Nemhauser et al., 78]The greedy algorithm guarantees(1-1/e) optimal approximation formonotone SFs, i.e.,F (Wgreedy ) ≥ (1− 1/e)F (Wopt)(1− 1/e) ∼ 63%
Near-optimal solutions!
H = ‖y(s, t)−∑N
i=1 wi (s)f ′i (s)βi (t)‖
Marginal benefit:H(A)− H (A ∪ {w})
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Outline
1 Overview
2 Simulation ModelingIntroductionStatistical MetamodelingSequential Design of Computer ExperimentsExperimental Results
3 Sensor InformaticsIntroductionSensor-based Modeling of Space-time DynamicsSparse Particle FilteringExperimental ResultsSummary
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State Space Model
Spatiotemporal model:Y (s, t) = M(s;β(t)) + ε, ε ∼ N(0, σ2)
β(t) = g(β(t − 1), γ)g(.) is the nonlinear evolution model.γ is the noise.
Estimation: p(βt |Y1:t) = p(Yt |βt)p(Yt |Y1:t−1)p(βt |Y1:t−1)
Prediction: p(βt+1|Y1:t) =∫
p(βt+1|βt)p(βt |Y1:t)dβt
Challenges:
Nonlinear and non-Gaussian properties.Curse of dimensionality: overfitting and ill-posed estimation.
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Sparse Particle Filtering
General discrete-time nonlinear and non-Gaussian dynamical system:
Process model: zt = ht(zt−1, θ, ωt−1)
Measurement model: βt = g(zt , γ)
States follow a first order Markov process.p(zt |zt−1, zt−2, . . . , z0) = p(zt |zt−1)Observations are independent given states.
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Sparse Particle Filtering
High-dimensional parameters βt ← Latent state variables zt
Nonlinear PCA generalizes principal components of linear PCA fromstraight lines to nonlinear curves [Scholz et al., 2007].
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Outline
1 Overview
2 Simulation ModelingIntroductionStatistical MetamodelingSequential Design of Computer ExperimentsExperimental Results
3 Sensor InformaticsIntroductionSensor-based Modeling of Space-time DynamicsSparse Particle FilteringExperimental ResultsSummary
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Optimal Kernel Placement
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Sparse Particle Filtering
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Sparse Particle Filtering
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Performance ComparisonPrediction Comparison:
Model Comparison:
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Stochastic Sensor Network
Real-world data: ECG data for 352 torso-surface sites, 2kHz.Simulation design: stochastic Kronecker graph [Leskovec, 2007].
Kronecker product: C = A⊗ B =
a11B . . . a1mB... . . . ...
an1B . . . anmB
Create a N × N probability matrix KCompute the nth Kronecker power K n
K n = K ⊗ K ⊗ · · · ⊗ K︸ ︷︷ ︸n
For each entry of K n include the edge with probability kij
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Stochastic Sensor Network
Stochastic Kronecker graph [Leskovec, 2007].Generate a realistic sequence of graphs that will obey patterns:
Static PatternsPower Law Degree DistributionPower Law eigenvalue and eigenvector distributionSmall Diameter
Dynamic PatternsGrowth Power LawShrinking/Stabilizing Diameters
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Model Performance - Stochastic Sensor Network
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Outline
1 Overview
2 Simulation ModelingIntroductionStatistical MetamodelingSequential Design of Computer ExperimentsExperimental Results
3 Sensor InformaticsIntroductionSensor-based Modeling of Space-time DynamicsSparse Particle FilteringExperimental ResultsSummary
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Summary
ChallengesSpatially-temporally big data (dimensionality, velocity and veracity)Stochastic sensor network
MethodologySpatiotemporal modelOptimal kernel placementSparse particle filtering
SignificanceBroad applications - stochastic sensor networkHighly wearable and resilient body area sensing systemBig data analytics in CPS: from IoT to real-time control
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Acknowledgements
NSF CMMI-1454012NSF IIP-1447289NSF CMMI-1266331NSF IOS-1146882Florida Department of HealthJames A. Haley Veterans’ Hospital
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Contact Information
Hui Yang, PhDAssociate Professor
Complex Systems Monitoring Modeling and Control LaboratoryHarold and Inge Marcus Department of Industrial and Manufacturing
EngineeringThe Pennsylvania State University
Tel: (814) 865-7397Fax: (814) 863-4745
Email: [email protected]: http://www.personal.psu.edu/huy25/
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Questions?
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