Model-Based ECG Fiducial Points Extraction Using a Modified EKF

Structure

Presented by: Omid Sayadi

Biomedical Signal and Image Processing Lab (BiSIPL),Biomedical Signal and Image Processing Lab (BiSIPL),Sharif University of Technology, Tehran, IranSharif University of Technology, Tehran, Iran

2

Contents:

Introduction and Problem Statement Theoretical Background Model-Based Approaches Modified EKF Structure Simulation and Results Conclusion & Future Work

3

Introduction

Heart: a hollow muscular organ which through a coordinated muscle contraction generates the force to circulate blood throughout the body.

Electrocardiogram: a graph representing the electrical activity of heart, also called ECG.

5 dominant characteristic waveforms and FPs, Single/Multiple beat features, including:

Amplitude features, Time intervals, Wave durations.

Pamp

Pdur

QRSdur

QRS-amp

STelevation

PRint

QRS+amp

RRint

QTpint

QTint

Tamp

TPint

4

Problem Statement

Arrhythmia Investigation, detection, diagnosis and treatment:

0 100 200 300 400 500 600 700 800 900-1.8

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plitu

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mV

]

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Major Problems: Decision Dependency,

Variability,

Noise and Drifts,

Ischemia Sinus Bradycardia Wolf Parkinson White Branch Bundle Block (BBB) Ventricular Tachycardia (VT) Ventricular Bigeminy/Trigeminy Atrial/Ventricular Flutter (AFL/VFL) Premature Atrial Contraction (APC) Atrial/Ventricular Fibrillation (AF/VF) Premature Ventricular Contraction (PVC)

Lack of sufficient morphological information.

5

Problem Statement

Goal:

Adaptive usage of the underlying ECG dynamical mechanism. Accuracy achievement for Arrhythmia Investigation:

Beat Detection,Beat Classification,Fiducial Points Extraction, Interval Timing Calculation,Feature Generation.

6

Contents:

Introduction and Problem Statement Theoretical Background Model-Based Approaches Modified EKF Structure Simulation and Results Conclusion & Future Work

7

Theoretical Background

ECG Dynamical Model (EDM):

},,,,{02

2)(

2exp

TSRQPi i

iii zz

baz

xyy

yxx

221 yx

2mod)( ii

),(2 xyanat

-2

-1

0

1

2

-1.5-1

-0.50

0.51

1.5-0.5

0

0.5

1

1.5

xy

z [m

V]

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

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0

0.2

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0.8

1

1.2

Samples

Am

p [

mV

]

-1.5 -1 -0.5 0 0.5 1 1.5-1.5

-1

-0.5

0

0.5

1

1.5

X

Y

250 300 350 400 450 500 550 600 650-0.4

-0.2

0

0.2

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1

1.2

Time/Index

Am

plitu

de [m

V]

8

Theoretical Background

EDM fit to an arbitrary ECG cycle:A prior estimate of the 5 Gaussian functionsNonlinear fit with Least Squares Error (LSE)

0 50 100 150 200 250 300 350 400 450 500-1

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Am

plit

ud

e [m

V]

P

Q

R

S

T

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-1

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1

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Am

plit

ud

e [m

V]

P fitQ fitR fitS fitT fit

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plit

ud

e [m

V]

Org.fiterror

For an ECG waveform:Cycle to Cycle fit.

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0

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Samples

Am

p [m

V]

ECG P(on) P(center) P(off) Q R S T(on) T(center) T(off)

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p [

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Org. Fit Error

9

Contents:

Introduction and Problem Statement Theoretical Background Model-Based Approaches Modified EKF Structure Simulation and Results Conclusion & Future Work

10

Model-Based Approaches

Mathematical Nonlinear Modeling:

Least Square Error Fit:

If we integrate the last equation of EDM, we conclude that:

i iiiiiii bbatbaz )2/exp(),,( 222

},,,,{02

2)(

2exp

TSRQPi i

iii zz

baz

xyy

yxx

An Optimization Problem: 2

2,,)()(min tztsE

iii ba

where,

s : Recorded ECG

z : ECG generated by EDM

-1.5

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0.51

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1

1.2

xy

N

R

P

Q S

T

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Model-Based Approaches

Adaptive Tracking:

Considering the nonlinear underlying dynamics for estimation → Extended Kalman Filter (EKF=linearized KF)

The discrete polar form of EDM:

kTSRQPi i

ii

i

ik

kk

zbb

z

odm

},,,,{2

2

21

1

)2

exp(

)2()(

random white noise which represents the baseline wander effects and models other additive

sources of process noise

sampling period (discretization step)

result of discrete derivation:

kk

kk

xx

xx

dt

dx

...1

1

12

Model-Based Approaches

EKF formulation:

kTSRQPi i

ii

i

ik

kk

zbb

z

odm

},,,,{2

2

21

1

)2

exp(

)2()(

)ˆ()ˆ(),ˆ,ˆ(

),,(

)ˆ()ˆ(),ˆ,ˆ(

),,(1

kkkkkkkk

kkk

kkkkkkkk

kkk

vvGxxCkvxg

kvxgy

wwFxxAkwxf

kwxfx

kk ww

kk

xx

kk w

kwxfF

x

kwxfA

ˆˆ

),,ˆ(),ˆ,(

kk vv

kk

xx

kk v

kvxgG

x

kvxgC

ˆˆ

),,ˆ(),ˆ,(

kkkkk

kTkkk

Tkkk

vkkkkk

Tkkk

Tkkkk

wkk

PCKPP

GCPCCPK

kvxgyKxx

FQFAPAP

kwxfx

1

0

1

01

][

]),,ˆ([ˆˆ

,

),,ˆ(ˆ

13

Contents:

Introduction and Problem Statement Theoretical Background Model-Based Approaches Modified EKF Structure Simulation and Results Conclusion & Future Work

14

Modified EKF Structure

Remember the ECG Dynamical Model (EDM):

},,,,{02

2)(

2exp

TSRQPi i

iii zz

baz

xyy

yxx

EKF2 (Sameni et al 2005)

ECG and wrapped Phase of ECG → states, Gaussian parameters, angular frequency and baseline → noises,

kTSRQPi i

ii

i

ik

kk

zbb

z

odm

},,,,{2

2

21

1

)2

exp(

)2()(

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5-4

-3

-2

-1

0

1

2

3

4

Time (sec)

Am

plit

ud

e (m

V)

ECGPhase

TTPTPTPk

Tkkk

bbw

zx

],,,,,,,,,,[

][

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Modified EKF Structure

EKF17 (Sayadi and Shamsollahi, IEEE TBME, 2008)

ECG, wrapped Phase and the Gaussian parameters → states, Angular frequency, baseline and the associated noises to the

Gaussian parameters model → noises,

Advantages: GMM parameters are considered as the states, Ability to reconstruct ECG (i.e. for compression tasks), Ability to show the features related to the fiducial points.

Tk

TTPPPkkk

uuw

bzx

],,,,[

],,,,,,,[

151

TTPTPTPk

Tkkk

bbw

zx

],,,,,,,,,,[

][

EKF2

EKF17

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Modified EKF Structure

AR(1) GMM parameters → Modified EKF (EKF17)

),,(][][]1[

),,(][][]1[

),,,,,,(][

)][2

][exp(][.

][

][.]1[

),,(.][]1[

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131

2

},,,,{2

2

2

1

kuFkukk

kuFkukk

kNbzFkz

kb

kk

kb

kkz

kFkk

k

k

kkk

TTT

PPP

iiikk

TSRQPi i

ii

i

i

k

Process equations:

Observation equations:

k

k

v

vx

s kk

k

2

1

0010

0001

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Modified EKF Structure

Linearized state-space model at each time instant around the most recent state estimation:

),2

exp(]2

1[

),2

exp(]2

1[2

),2

exp(

),2

exp(]1[

2

2

2

2

22

2

2

2

2

32

2

2

22

2

2

},,,,{2

2

22

i

i

i

i

i

i

ki

i

i

i

ii

i

i

ki

i

ii

iki

i

i

TSRQPi i

i

i

i

k

bbb

F

bbbb

F

bb

F

bbb

F

.1

,1

,1

1716151413

12111098

2176543

kTkSkRkQkP

kTkSkRkQkP

kkkTkSkRkQkP

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b

F

b

F

b

F

b

F

b

F

z

FFFFFFF

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Modified EKF Structure

Interpretation of GMM parameters of EDM: FP extraction

),3max(

),3min(

),3max(

),3min(

),3max(

),3min(

offTTToff

onTTTon

offSsSoff

onQQQon

offPPPoff

onPPPon

fbT

fbT

fbQRS

fbQRS

fbP

fbP

Tachogram (RR-interval variability) extraction

RpeakR

fluctuative parts of the estimations

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Contents:

Introduction and Problem Statement Theoretical Background Model-Based Approaches Modified EKF Structure Simulation and Results Conclusion & Future Work

20

Results

Estimated Gaussians’ parameters with EKF17 for record 231

(MIT-BIH database)

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0

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1

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Time (sec)

Am

p. (

mV

)

ECG

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3-1

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0

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1

Time (sec)

Am

p. (

mV

)

P

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 30

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1

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Time (sec)

Am

p. (

mV

)

Q

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 34

4.2

4.4

4.6

4.8

5

5.2

Time (sec)

Am

p. (

mV

)

R

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3-3

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0

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Time (sec)

Am

p. (

mV

)

S

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2

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3

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Time (sec)

Am

p. (

mV

)

T

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Am

p. (

mV

)

ECG

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Am

p. (

mV

)

ECG

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3-2

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0

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1

Time (sec)

Am

p. (

Rad

)

bP

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0

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Time (sec)

Am

p. (

Rad

)

bQ

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 39

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Time (sec)

Am

p. (

Rad

)

T

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p. (

Rad

)

S

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

-0.25

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0

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Time (sec)

Am

p. (

Rad

)

R

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3-0.5

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0

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Time (sec)

Am

p. (

Rad

)

Q

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3-10

-9.9

-9.8

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Time (sec)

Am

p. (

Rad

)

P

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3-1

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0

0.5

1

1.5

2

Time (sec)

Am

p. (

Rad

)

bT

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Time (sec)

Am

p. (

Rad

)

bS

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3-0.5

-0.4

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-0.1

0

0.1

Time (sec)

Am

p. (

Rad

)

bR

TP TPb TP

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Results

Fiducial points extraction results for records 106 and 117:

(MIT-BIH database)

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2

2.5

Time (sec)

Am

plitu

de (

mV

)

Input ECG EKF17 Output Fiducial Points

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plitu

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mV

)

Input ECG Fiducial Points

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Results

Numerical performance evaluation:

FNTP

TPSn

FPTN

TNSp

FPTP

TPP

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Contents:

Introduction and Problem Statement Theoretical Background Model-Based Approaches Modified EKF Structure Simulation and Results Conclusion & Future Work

24

Conclusion

An EDM-based ECG fiducial points extraction scheme was proposed. In summary: It is very simple, very precise and has a low computational cost,

It needs a non-accurate initial estimate for the KF,

It uses the underlying dynamics for ECG signal, so it can be adapted to any ECG having five major PQRST waveforms,

No thresholding is used in determination of FPs,

There is an intrinsic denoising using the EDM, The method guarantees adaptive tracking of the morphological

characteristics of the ECG signal.

The AR(1) models provides a simple dynamics for the newly introduced state variables (i.e. GMM parameters),

The modification is applied to the process, not the observations,

25

Future Work

Fitting the model to highly abnormal ECGs such as bundle blocks,

Modifications of the model: Using more than 5 Gaussians, Modifications of the model: Using a lag-normal function, Improving the method using more precise dynamics for the

GMM parameters, instead of the AR(1), Incorporating the effects of baseline drifts.

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Thank You ☺