CPP, INI, Cambridge, July 2009

Integrative System Framework for Noninvasive Understanding of

Myocardial Tissue Electrophysiology

Linwei Wang, Ken C.L. Wong, Pengcheng Shi

Computational System Biomedicine LaboratoryB. Thomas Golisano College of Computing and Information Sciences

Rochester Institute of Technology

• Noninvasive observations on specific patient:– Structural: tomographic image– Functional: projective ECG/BSPM

• In clinical settings, it really has been a sophisticated pattern recognition process to decipher the information.

• How can models offer help?– Better models lead to more appropriate constraints in

data analysis.• Physiological plausibility vs. algorithmic/computational

feasibility• Volumetric?

– Ultimately, models have to be personalized to be truly meaningful.

From patient observations to personalized electrophysiology

Integrative system perspective

Patient Observations

• Subject-specific information

• Noisy, sparse, incomplete

Prior Knowledge: Models

• Built up over many years

• General population

Data Acquisition

• BSP sequence• Tomographic

images

System Modeling

• System dynamics• System

observations

Personalized Information Recovery

• Electrical function• Tissue property• Latent substrate

Individual Subject

Wang et al. IEEE-TBME, 2009 (in press).

Physiological model constrained statistical framework

• System perspective to recover personalized cardiac electrophysiology – (phenomenal)

Model constrained data analysis: prior knowledge guides a physiologically-meaningful understanding of personal data

– Data driven model personalization: patient data helps to identifies parameter changes in specific system models

Information Recovery

Data Acquisitio

n

System Modeling

Volumetric myocardial representation

• Ventricular wall: point cloud

• Fiber structure: mapped from Auckland model

Slice segmentation

Surface mesh

Volume representation

Surface registration

Surface fiber structure

3D fiber structure

Surface body torso representation

• (Isotropic and homogeneous volume conductor)

Patient’s images

Surface model

Cardiac electrophysiological system

Personalized 3D-BEM mixed

heart-torso model

Volumetric TMP

dynamics model

TMP-to-BSP mapping

System dynamics: volumetric TMP activity

• Diffusion-reaction system: 2-variable ordinary differential equation

• Meshfree representation and computation

u

t (Du) f1(u,v)

v

t f2(u,v)

U

t M 1KU f1(U,V)

V

t f2(U,V)

- u: excitation variable: TMP- v: recovery variable: current- D: diffusion tensor

System observation: TMP-to-BSP mapping

• Quasi-static electromagnetism Poisson’s equation

• Mixed meshfree and boundary element methodsGoverning equation

Direct solution method

Meshfree+BEM

2(r) (D(r)u(r))

c()() (r)q*(t ,r)dt

(r)

r n

*(t ,r)dt

1

4(

Di(r)

| r |

u(r)

r n t

dt 1

| r | (Di(r)u(r))

t dt )

HU

Surface integral: BEM

Volume integral: meshfree

State space system representation

Ut

M 1KU f1(U,V,)

V

t f2(U,V,)

HU

X UT VT T

Y Uncertainty:

,

Nonlinear dynamic model Local linearization Temporal discretization

Large-scale & high-dimensional system U,V is of dimension 2000-3000

Monte Carlo

integration

✗Predictio

nCorrectio

n

TMP activity:

TMP-to-BSP

mapping:

Xk Fd (Xk 1,k 1) kState equation:

Yk HXk kMeasurement equation:

k k 1 kParameter:

Sequential data assimilation

• Combination of unscented transform (UT) and Kalman filter: unscented Kalman filter

Correction: KF update

Computational feasibility

Prediction: UT(MC integration + deterministic sampling)

Preserve intact model nonlinearity

Black-box discretization

Ensemble generation (unscented transform)

Prediction (MC integration)

Filter Gain

Correction (KF update)

k 1,i 0

n ˆ U k 1

ˆ U k 1 (n

2 ) ˆ P uk 1

( k|k 1,i, k|k 1,i) ˜ F d ( k 1,i,V k 1)

U k W i

m k|k 1,ii0

n ,V k W i

m k|k 1,ii0

n

Puk

W ic ( k|k 1,i U k

)( k|k 1,i U k )T Q

ku

i0

n

K ku Puk

HT (HPuk

HT Rvk) 1

ˆ U k U k K k

u(Yk HU k )

ˆ P uk(I K k

uH)Puk

Initialization

ˆ U 0 ˆ P u0 k = k+1

TMP estimator: reconstructing TMP from BSP

Ensemble generation (unscented transform)

Prediction (MC integration)

Filter Gain

Correction (KF update)

k 1,i 0

2n ˆ k 1

ˆ k 1 (n ) ˆ P k 1

k |k 1,i

˜ F d ( ˆ U k 1,k 1,i)

k|k 1,i ˜ H

k|k 1,i

P k

ˆ P k 1 Qk

Y k W i

mk|k 1,ii0

2n

Pyk

W ic (k|k 1,i

Y k )(k|k 1,i

Y k )T R ki0

2n

P k yk W i

c (k 1,i ˆ k 1)(k|k 1,i Y k

)T

i0

2n

K k P k yk

Pyk

1

ˆ k ˆ k 1 K k(Yk Y k

)

ˆ P kP k

K kPyk

K kT

Initialization

ˆ 0 ˆ P 0

k = k+1

Nonlinear measurement

model

Parameter estimator: reconstructing model parameters

BSP

Gd-enhanced MRI

MRI personalized heart-torso structures

gold standard

Cardiac: 1.33×1.33×8mmWhole-body: 1.56×1.56×5mm

123 electrodes, QRST @ 2KHz sampling

Experiments (PhysioNet.org): electrocardiographic imaging of myocardial infarction

• Four post-MI patients

Goals and procedures

• Quantitative reconstruction of tissue property and electrical functioning

Tissue excitability TMP dynamics

Procedures Initialization – TMP estimation with general normal model Simultaneous estimation of TMP and excitability

Identify arrhythmogenic substrates (imaging + quantitative evaluation)

Localize abnormality in TMP and excitability

Investigate the correlation of local abnormality between TMP and excitability

Result: case II

• Infarct location: septal-inferior basal-middle LV

Simulated normal TMP dynamics

Estimated TMP dynamics

Result: case II

• Location, extent, and 3D complex shape of infarct tissues• Correlation of abnormality between electrical functions

and tissue property– Abnormal electrical functioning occurs within infarct zone– Border zone exhibits normal electrical functioning

-Black contour: abnormal TMP dynamics-Color: recovered tissue excitability

Delay enhanced MRI registered with epicardial electrical signals

Delayed activation: 4-9

Infarct: 3-14

H. Ashikaga, Am J Physiol Heart Circ Physiol, 2005

Result: case II

Result: case I

• Infarct: septal-anterior basal LV, septal middle LV

Result: case III

• Infarct: inferior basal-middle LV, lateral middle-apical LV

Result: case V

• Infarct: anterior basal LV, septal middle-apical LV

Quantitative validation

- EP: Percentage of infarct in ventricular mass- CE: Center of infarct, labeled by segment- Segments: A set of segments which contain infarct- SO: Percentage of correct identification compared to gold standard

Comparison with existent results

- Dawoud et al: epicardial potential imaging- Farina et al: optimization of infarct model- Mneimneh et al: pure ECG analysis

- EPD: difference of EP from gold standard- CED: difference of CE from gold standard

Conclusion

• Personalized noninvasive imaging of volumetric cardiac electrophysiology

Noninvasive observations

Personalized volumetric

cardiac electrophysiolo

gy

Latent substrates