Sensor-based Modeling and Control of Nonlinear …Sensor-based Modeling and Control of Nonlinear...

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


Research Roadmap


Outline

1 Overview




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


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


Research Motivation

Total deaths for the 10 leading causes in United States [CDC]


Modeling Rationale


Research Motivation

Discrete-event simulation vs. Continuous-flow simulation


Background

Action Potential: Net change of transmembrane potentials


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−/−).


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


Outline

1 Overview




Research Methodology


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


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)


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∗)


Outline

1 Overview




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.


Sequential Design


(T−E{f (x∗)}std{f (x∗)}



Sequential Design


(T−E{f (x∗)}std{f (x∗)}



Outline

1 Overview




Significance Test


Data Modeling

Steady state activation and inactivationRecovery from fast inactivation


Model Validation

Current density-voltage relationships


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


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


Broad Applications


Outline

1 Overview




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)


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


Distributed Sensor Network

Environment, Healthcare, Defense, Manufacturing

USF Marine - sensing Tampa Bay BSN - surface ECG potentials


Sensor-based Informatics and Control


Challenges

Space-time dynamics

Pollution Dynamics Cardiac Electrical Dynamics


ChallengesSpatially-temporally big data

DimensionalityVelocity - sampling in millisecondsVeracity - sensor reliability


Challenges

Stochastic Sensor network - A subset of sensors at temporally-varyinglocations within the network to transmit dynamic informationintermittently.


State of the Art

Limited number of sensorsReliable sensor readingsIncomplete space-time information


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


Outline

1 Overview




Sensor-based Modeling of Space-time Dynamics


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


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.


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.


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)


Submodular Optimization

Objective function: w∗ ⊆ V such that w∗ = argmin|W |<N

H(W )


∑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)


Minimizing Submodular Functions

Objective function: w∗ = argmin H(W )s.t. w∗ ⊆ V and |W | < N


∑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?


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})


Outline

1 Overview




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.


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.



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].


Outline

1 Overview




Optimal Kernel Placement






Performance ComparisonPrediction Comparison:

Model Comparison:


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


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


Model Performance - Stochastic Sensor Network


Outline

1 Overview




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


Acknowledgements

NSF CMMI-1454012NSF IIP-1447289NSF CMMI-1266331NSF IOS-1146882Florida Department of HealthJames A. Haley Veterans’ Hospital


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/


http://www.personal.psu.edu/huy25/

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