ecg imaging of ventricular activity multi-parametric ... · l e.g. a linear model n y: dependent...

ECG Imaging of Ventricular Activity in Clinical ApplicationsWalther Schulze

INSTITUTE OF BIOMEDICAL ENGINEERING

www.ibt.kit.eduKIT – University of the State of Baden-Württemberg and National Research Center of the Helmholtz Association

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Multi-Parametric Measurements and Data Analysis in Electrophysiology

Olaf Dössel

Institute of Biomedical Engineering12.12.2017 Multi-parametric Measurements and Data Analysis in Electrophysiology

The Team of Olaf Dössel at IBT Karlsruhe

2

Tobias Oesterlein

Axel Loewe

Lukas Baron

Stefan Pollnow

Michael Kircher

Yannick Lutz

Nicolas Pilia

Tobias Gerach Ekaterina Kovacheva

Laura UngerSteffen Schuler


Multi-Parametric Measurements in Life Sciences

Multi-parametric measurements in flow cytometry Multi-parametric analysis of immunoassay results Cell microscopy with various biomarkers

Multi-parametric MRI imaging Multi-channel ECG data, blood pressure, oxygenation,… Voltage clamp protocol measurements for ion channel modelling … and hundreds more

3

Uncover hidden values/characteristics/parameters of

cells/tissue/patients from a variety of measured data


Outline

Multi-parametric measurements in life sciences Basics of multivariate data analysis Example 1: Classification of Complex Fractionated Atrial Signals Example 2: Finding the best ion-channel model parameters for genetic diseases Quantification of uncertainty

Personalization of patient models by merging imaging, biosignals, biomarkers and genetics

4




Multivariate Data Analysis Clustering, Classification, Modelling: Find a Quantitative Input-Output Relation

Clustering: Find an appropriate type and number of classes, so that each subject belongs to just one class.

Classification: find the right class for the each subject put the cells of cell cytometry into the right box (cell sorter) predict whether a drug will have positive or negative effect on a patient is this melanoma benign or malign? is this ECG signal a normal beat, a ventricular extrasystole or an atrial extrasystole goodness of classification: specificity and selectivity

Uncover relations in the data to better understand - a qualitative approach

Modelling: find a quantitative (thus mathematical) input-output relation identify the appropriate „input“ data, that can be measured, find the best model, that can describe all relations in the measured data, goodness of prediction, boundaries of confidence, statistical significance of model parameters

5

modelling

classification


Our Objective in Medicine: Predict what will happen, if…

What will happen, if we do not do anything? risk of sudden ventricular fibrillation >> implant a defibrillator?

What will happen, if we do A or B (decision points in guidelines) is drug A better than drug B or the other way around?

What will happen, if we do more or less of A the best dosage of a drug? the best field and dosage of radiation therapy?

6

Can we trust the result? What will happen, if our input data have an error? What will happen, if the parameters of our model were erroneous? What will happen, if we go beyond the boundaries of the model? What will happen, if we did not take important other aspects into account?

So we use computer assisted data analysis. But….

classificationmodelling


Clustering

7

Y1 = y11 , y12 ,..... , y1M( )Y2 = y21 , y22 ,..... , y2M( ).....YN = yN1 , yN2 ,..... , yNM( )

given: N examples Y of M measurements y find: the best number and type of cluster

Y3Y9Y7

Y1Y6Y5

Y2 Y8Y4

A

B

C

define a „distance“ Euklidian distance, covariance based dis. Mahalanobis distance

find an appropriate algorithm k-means algorithm ….. silhouette coefficient

solve the problem


Classification

8

Y1 = y11 , y12 ,..... , y1M( )Y2 = y21 , y22 ,..... , y2M( ).....YN = yN1 , yN2 ,..... , yNM( )

YN+1 = yN+1,1 , yN+1,2 ,..... , yN+1,M( )

N examples Y of M measurements y

?

A

B

C

Recipe: select a set of good features, set up a feature space, find the right class…

train

ing

data

with

kno

wn

clas

scl

assi

ficat

ion

our job: find the right class for object N+1


Classification - some famous algorithms

Decision Tree Random Forest Bayesian Network Support Vector Machine SVM Neural Network Logistic Regression

9

Support Vector Machine wikipedia


Modelling: Quantitative Input-Output Relations

10

Y1 = f x11 ,x12 ,..... ,x1Q( ) + e1Y2 = f x21 ,x22 ,..... ,x2Q( )+ e2.....YN = f xN1 ,xN2 ,..... ,xNQ( )+ eN

YN+1 = f xN+1,1 ,xN+1,2 ,..... ,xN+1,Q( )+ eN+1

Y1 = a1x11 +a2x12 + .... aPx1Q +bY2 = a1x21 +a2x22 + .... aPx2Q +b.....YN = a1xN1 +a2xN2 + .... aPxNQ +b

YN+1 = a1xN+1,1 +a2xN+1,2 + .... aPxN+1,Q +ba) select a model b) define an error function c) adjust the parameters

e.g. a linear model

data

to a

djus

t the

mod

elpr

edic

tion

y: dependent variable=output x: independent variable=input


Quantitative Input-Output Relation

linear model >> linear regression polynomial regression sine-cosine model (Fourier expansion) sum of exponentials …..

Gaussian mixture model Kernel regression Support vector regression….

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physics driven models versus data driven models

polynomial regression wikipedia CI:confidence interval

y1y2...yn

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

=

1 x1 x12 ...

1 x2 x22 ...

... ... ... ...1 xn xn

2 ...

⎡

⎣

⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥

⋅

β0β1...βm

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

+

ε1ε2...εm

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

!̂β = XTX( )−1 XT !y


How to find the best model parameters? Optimization!

linear regression, polynomial regression,

Simplex / Nelder-Mead, Newton methods,

gradient decent, conjugate gradient, Levenberg Marquart, trust region… simulated annealing, genetic algorithms, particle swarm, ….

12

define an error function solve the problem of „optimization“

Is it a convex error function? Or are there any local minima? How to find the best free parameters of the algorithm?

Downhill-Simplex, wikipedia


Optimization of the Optimization Parameters

Example: find the location of a ventricular extrasystole from multichannel ECG using support vector regression Parameters of the Support Vector Regression: C and s

s is the bandwidth of the Gaussian Kernel C takes care of the tradeoff between flatness and error

Within the training dataset the ground truth is known. Try out all combinations of and C and s and take the best.

13


Software Packages

MATLAB

14

… and many more

Facebook Open Source


Example 1: Classification of

Complex Fractionated Atrial Signals CFAEs

15


Classification of Complex Fractionated Atrial Electrograms (CFAEs)

Many patients suffer from Atrial Flutter or Atrial Fibrillation. An RF-Ablation could solve the problem. Where are the areas in the atria, that drive the arrhythmia?

16

Zeit (s)

0 1 2 3 4 5

C3

C2

C1

C0

some electrograms measured in the atria


Descriptors (Features) of CFAEs

17

Segmentation

−1 −0.5 0 0.5 1−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1CFAE 5

f(x)

f(1) (x

)

f(x)

f‘(x)

Phase Space

Harmonics

CF1CF2 = DF

Frequenz

Frequency Domain

−0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5 0.60

50

100

150

200

250

300CFAE 5

Signalamplitude

Anz

ahl

Signalamplitude

Anz

ahl

Kurtosis =E{(X � µ)4}

�

4=

µ4

µ

22

Histogram

...

0 500 1000 1500 2000 25000

500

1000

1500

2000

t [samples]

NLEO [(mV)

2 ]

0 500 1000 1500 2000−150

−100

−50

0

50

100

t [samples]

Signal [mV]

NLEO

Signal

NLEO

1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4

CFAE5

CFAE4

Common CFAEs

Zeit in Sekunden

1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4

CFAE5

CFAE4

Common CFAEs

Zeit in Sekunden

Time Domain

1120 1130 1140 1150 1160 1170

−2

−1

0

1

2

3

4

5

6

x 10−5

Zeit / ms

0 5 10 15 20 25−1

−0.5

0

0.5

1

1.5coif4

Coiflet 4

Wavelet Features

CFAE 0

CFAE 1

CFAE 2

CFAE 3

{

{

C0

C1

C2

C3


Classification using a Fuzzy Decision Tree

18

The fuzzy decision tree delivers a probability of class membership

Correct rate: 86,1% C0: 92,9%C1: 83,3%C2: 69,3%C3: 100%

D5

D7

D14

D10

D1

D4

D18

D1D14

0:0.001:0.162:0.743:0.10

0:0.001:0.092:0.853:0.06

0:0.951:0.052:0.003:0.00

0:0.021:0.002:0.103:0.88

0:0.061:0.942:0.003:0.00

0:0.001:0.002:0.773:0.23

0:0.001:0.002:0.293:0.71

0:0.771:0.222:0.013:0.00

0:0.041:0.872:0.093:0.00

0:0.131:0.782:0.093:0.00

C1

C2

C3

C0

{

{C3

C2

C1

C0


Left Atrium with Annotated CFAE classes

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No Data

CFAE 0

CFAE 1

CFAE 2

CFAE 3

C3

C2

C1

C0

No DataSchilling, C.; Keller, M.; Scherr, D.; Oesterlein, T.; Haissaguerre, M.; Schmitt, C.; Dössel, O.; Luik, A., Fuzzy decision tree to classify complex fractionated atrial electrograms, Biomedizinische Technik. Biomedical Engineering, 60, 245-255, 2015


Example 2: Find the best ion-channel model parameters for

genetic diseases

20


body surface

r · ((�i + �e)r�e) =

�r · (�irVm)

Poisson’s equation to compute body surface potentials

Multi-scale Modeling of Cardiac Electrophysiology

21

myocyte ion channels

ordinary differential equations (ODEs)

Ix

= gx

Y

i

�i

(Vm

� Ex

)

d�idt

=�i1(Vm)� �i

⌧�i(Vm)

dVm

dt= �

PIx

+ Istim

Cm

coupled ODEs

tissue / organ

r · (�irVm) =

�

✓C

m

dVm

dt+

XIx

◆

COO–NH3+

S3 S4 S5 S6S2S1

��

��

��

��

��

��

��

��

��

��

��

��

Reaction-diffusion model (monodomain)

COO–NH3+

S3 S4 S5 S6S2S1

Gunnar Seemann, Axel Loewe, IBT Karlsruhe


Benchmarking Models of Human Atrial Electrophysiology

22

Ito IKur IKr IKs IK1IKACh If

INa ICaL IbCa IbNa IbCl ICl(Ca)

NCX

NKA

PMCA[Cl2-]i

[K+]i

[Na+]i

[Ca2+]i

Common to allmodelsGrandi et al. only

Maleckar et al. only

Koivumäki et al. only

SR

IKp B

C

-100-80-60-40-20

0 20 40 60

0 50 100 150 200 250 300 350 400

volta

ge (m

V)

time (ms)

Courtemanche et al.Nygren et al.

Maleckar et al.Koivumäki et al.

Grandi et al.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 100 200 300 400 500 600

[Ca2+

] i ( µ

M)

time (ms)

D

A

extracleft

dyad

IleakItr

Irel

Idi

IrelIup

Itr IrelIup

Nygren et al.Maleckar et al. Koivumäki et al.

Courtemanche et al.

subintra

extra

ICaLICaL

intra

Iup

ICaL

extraintra

Iup

intra

extrasub

cleft

ICaL

Irel Itr

Grandi et al.

Wilhelms, M.; Hettmann, H.; Maleckar, M. M. C.; Koivumäki, J. T.; Dössel, O.; Seemann, G., Benchmarking electrophysiological models of human atrial myocytes, Frontiers in Physiology, 3, 1-16, 2013


Voltage Clamp Protocol for Characterization of Chanellopathies

Adapting the IKr channel due to hERG mutations

23

I Kr (µA

)

t (s)

-10-8-6-4-2 0 2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

N588K400 ms 200 ms15 ms

-80 mV -80 mV

+50 mV

400 ms-120 mV

-70 mV

-10-8-6-4-2 0 2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

WT K897T

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

simuliertgemessen xI K

r (µA

)

t (s)

WT

simulatedmeasured

L532P

COO–NH3+

S3 S4 S5 S6S2S1

Voltage clamp protocolLoewe, A.; Wilhelms, M.; Fischer, F.; Scholz, E. P.; Dössel, O.; Seemann, G., Arrhythmic potency of human ether-a-go-go-related gene mutations L532P and N588K in a computational model of human atrial myocytes, Europace, 16, 435-443, 2014


The parameters of the Ion Channel IKr

24

I

Kr

=g

Kr

x

r

(Vm

�E

K

)

1+ exp

⇣V

m

+g

Kr1g

Kr2

⌘

axr

= Xr

a1V

m

+Xr

a2

1� exp

⇣V

m

+Xr

a2Xr

a3

⌘

bxr

= 7.3898e�5V

m

+Xr

b1

exp

⇣V

m

+Xr

b1Xr

b2

⌘�1

txr

= [Xr

KQ10(axr

+bxr

)]�1

x

r• =

1+ exp

✓�V

m

+Xr

m1

Xr

m2

◆��1

E

K

=RT

F

log

[K+]o

[K+]i

Find 12 model parameters, so that all voltage clamp measurements can be reproduced.

Particle Swarm Algorithm

Lutz, 2008

3.1. Mathematical Modeling of Cardiac Cells 17

Ib,Ca Ib,Na INa

ICa,L

INaCa Ip,Ca Ca2+

Ca2+

3Na+

2K+

3Na+ INaK Ito IKur IKr IKs

IK1

Iup Itr

Irel

NSR JSR

Cytosol

Extracellular Space

Ileak

Fig. 3.2. Schematic of the atrial cell modeled by Courtemanche et al..

ion concentrations are not included in the model nor are processes of intracellular Ca

2+

di↵usion.

3.1.4 Nygren, Fiset, Firek, Clark, Lindblad, Clark, Giles 1998

In 1998, Nygren et al. [3] published a mathematical model of atrial myocytes with its

focus on the importance of potassium currents for the shape of the action potential.

To improve the reconstruction of human action potentials, the model described in the

following, which is a further development of the LMCG model of rabbit atrial cells [22],

concentrates on electrophysiological di↵erences between human and rabbit myocytes.

Fig. 3.3. Schematic of the atrial cell modeled by Nygren et al..

wikipedia

even better: Hybrid Optimization Approach: start with particle swarm and precede with trust region reflective!


Effect on the Action Potential and Generation of Arrhythmias

Adapting the IKr channel

25

I Kr (µA

)

t (s)

-10-8-6-4-2 0 2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

N588K400 ms 200 ms15 ms

-80 mV -80 mV

+50 mV

400 ms-120 mV

-70 mV

-10-8-6-4-2 0 2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

WT K897T

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

N588K400 ms 200 ms15 ms

-80 mV -80 mV

+50 mV

400 ms-120 mV

-70 mV

simuliertgemessen xI K

r (µA

)

t (s)

-80

-60

-40

-20

0

0 100 200 300 400

V m (m

V)

Time (ms)

ControlN588KL532P

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 100 200 300 400

I Kr (

pA/p

F)

Time (ms)Loewe et al., Europace, 2014

WT N588KL532P

dVm

dt= �

PIx

+ Istim

Cm

Loewe, A.; Wilhelms, M.; Schmid, J.; Krause, M. J.; Fischer, F.; Thomas, D.; Scholz, E. P.; Dössel, O.; Seemann, G., Parameter estimation of ion current formulations requires hybrid optimization approach to be both accurate and reliable, Frontiers in Bioengineering and Biotechnology, 3, 209, 2016

Institute of Biomedical EngineeringAxel Loewe - In Silico Assessment of Dynamic Drug Effects on Human Atrial Patho-Electrophysiology07.05.2015

Predict the Arrhythmogeneity: Effect on rotor inducability and lifetime

26

-2 +2 +10 +350 +6 +20

0 0.2

0.4

0.6

0.8

1

Zeit (s)

Time (s)0 521 43

Control

N588K-1:1

L532P-1:1

4 cm

Stimulation time with respect to end of refractory phase

Loewe et al., Europace, 2014


Quantification of Uncertainty

27


Evaluate the Quality of a Classification Problem

Train the method with data A, evaluate with data B Measure sensitivity, selectivity, ….

If there are only few data, where the ground truth is known? cross validation

exhaustive, leave-p-out … leave-one-out non-exhaustive, f-fold-cross-validation

28

confusion matrix for binary classification problems

Statistical significance? Is the p-value below the limit?


Quantification of Uncertainty for Mathematical Modelling

29

propagation of measurement errors of the input data

influence of errors of model parameters on the result interindividual variability of model parameters errors due to application with variables outside of the recommended boundaries

errors due to using the wrong model, errors due to neglecting important variables.

easy model - easy solution non-linear model - not so easy…

sensitivity analysis - time consuming…

???

???

???

latin hypercube sampling


Quantification of Uncertainty

s1

s2

s1 and s2 : vector in state space

prediction of the mathematical model

uncertainty of the model

uncertainty of the initial

state

uncertainty of prediction

s3

s3 uncertainty by omitting one dimension in state space

30

A good mathematical model of uncertainties is better than intuition.


Personalization of patient models by merging imaging, biosignals, biomarkers and genetics.

31




Atrial Electrogram

32

[PentaRay Mapping Catheter, Biosense]

[Constellation, Boston Scientific] and FIRMap, Topera

2.4. CATHETER ABLATION OF ATRIAL FIBRILLATION 21

(a) A typical 4-pole ablation catheter with equidistantspaced electrodes. The tip electrode at the distalend of the catheter is 4 mm, all other electrodes are2 mm. The inter-electrode spacing is 2 mm.

(b) A multi-polar circular mapping catheter. The elec-trodes have a width of 1 mm and the inter-electrodespacing is 1 mm and 4 mm, respectively.

Fig. 2.13: Two examples of common catheters used during catheter ablation. The straight catheter on theleft is used for ablation as well as for analyzing EGMs. The circular catheter on the right is atypical analyzing catheter that gives spatial information about the tachycardia.

Therefore, tip temperature and impedance are constantly monitored during the ab-lation process. To avoid local temperature peaks at the electrode tip, irrigated tipelectrodes are used [65]. To ensure not only superficial but also transmural lesions,ablation currents are typically applied for 60 s to set an ablation point.

(a) The ablation catheter is pushed via the inferiorvena cava into the right atrium.

(b) Crossing the intra-atrial septum, irregular tis-sue can be destroyed by use of electrical en-ergy.

Fig. 2.14: Radio-frequency catheter ablation. Displayed is a typical ablation catheter with four electrodes.

[Orbiter, Boston Scientific] and: Lasso, Biosense

[Inquiry AFocusII, St. Jude Medical]

[Rhythmia Orion, Boston Scientific]


Steps to Personalized Modeling of Atrial Tachycardia

33

70 year old female, persistent atrial flutter, cycle length ≈460ms Macro-Reentry passing roof and posterior wall Critical substrate: slow conducting region at central anterior wall


Steps to Personalized Modeling of Atrial Tachycardia

34

individual geometry of the atria imported LAT pattern imported to MATLAB

Manual initialization: Lines of block, refractory tissue, trigger

CV estimated using FaMaS

Resulting excitation in agreement with clinical data:

Region of slow conduction correctly identified Cycle length corresponds to clinical data

… opens the door to computer assisted personalized therapy optimization.


The Integrated Heart Model

35

0 1 2 3 4 5 6 7 8

B

A

�A

Time [s]0 1 2 3 4 5 6 7 8

B

A

�V

Time [s]


Algorithms and Software for Medical Applications

… give a soft advice ("second opinion“)

36

… give a strong advice (follow the guide lines!)

… are part of a closed circle

… will need a CE mark „medical device“ and an FDA approval

open questions: There are too many input / output options to test them all! How can we validate a computer model? How can we validate a „machine learning“ algorithm that ist changing every day? Do we have to approve the „learning dataset“?

ecg imaging of ventricular activity multi-parametric ... · l e.g. a linear model n y: dependent...

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