Cardiovascular

disease (CVD) is the leading cause

of global mortality. An estimated 17.7 million

people died from CVDs in 2015, representing 31% of all global deaths. Therefore

it is necessary to bring about better treatment outcomes through early risk

analysis, diagnosis and intervention. Machine learning methods have been

successfully implemented for automation of risk stratification and diagnosis of

cardiovascular diseases. However, the existing applications of machine

learning in assisting interventional procedures are limited. Intelligent

guidance using machine learning techniques could reduce the burden on experts

during surgical procedures and also reduce inconsistency in surgical

performance by providing real-time assistance. A strategy for providing

real-time guidance to electrophysiologist during cardiac voltage mapping

procedure has been proposed (1).

2

Introduction

The

treatment of cardiac arrhythmia involves radiofrequency catheter ablation to

destroy dysfunctional tissues of the myocardium that are responsible for inducing

arrhythmia. The voltage map of the chamber of the heart is obtained prior to

the ablation procedure to identify the trigger points of arrhythmia. Real time

guidance during the voltage mapping procedure could help the electrophysiologists

to reduce the total time taken for the procedure and improve accuracy of the

obtained voltage map. The proposed strategy meets two main requirements: (i)

ensure maximum coverage of the chamber of the heart being mapped and (ii) focus

on regions of high electrical gradients. The existing geometry-based method

meets only the first requirement. Hence a new strategy is proposed based on

active learning in conjunction with Gaussian process regression.

Figure

1: Activation map of left ventricle

2

3

Active Learning Strategy

Active

learning is a type of semi-supervised machine learning. In this approach the

model is capable of interactively querying the user for output values or labels

of specific new data points. The model tries to extract maximum information

through minimum number of queries and it tries to simultaneously improve its

accuracy and find the best query point. Active learning overcomes the problem

of disparity between availability of labelled and unlabelled data. Although

unlabelled data is usually available in vast quantities, labelled data is

scarce and the task of labelling them requires a lot of effort.

In

the cardiac voltage mapping task, the cost of labelling is associated with the

total procedure time, which needs to be minimised. In order to maximise the

knowledge about the target region, the operator must obtain voltage values of

as many points on the target location as possible. However, this will lead to

prolonged procedure duration which could endanger the patient. The active

learning approach addresses this problem by requesting labels for only a few

chosen data points.

3.1

Query Strategies

All

active learning approaches are based on estimating the information content of

unlabelled data points which provides the basis for selection of the query

points. Several methods have been proposed as query strategy for active

learning approach.

i.

Uncertainty Sampling: The model selects

the data point about which it is least confident as the query point.

Implementation of this method is straightforward in probabilistic models. One

of the common approaches for uncertainty sampling is entropy estimation. The

most informative query point is the one which has maximum information entropy.

Here

represents the data point with highest

information entropy and

varies over the possible labels or output

values.

ii.

Query-By-Committee: A set of competing

hypotheses derived from the same training dataset are made to vote for

selecting the best query point. The data point about which they most disagree

is considered to be the most informative query point.

iii.

Expected Error Reduction: The expected

error of trained model is estimated from the pool of unlabelled data points and

the query point is chosen such that it has least future error. The aim is to

minimize the total number of incorrect predictions. However, this method is

computationally expensive as it involves error estimation of each possible

query point.

4

Gaussian Processes

Gaussian

process is by definition a collection of random variables that are jointly

Gaussian distributed. Gaussian process regression is a non-parametric machine

learning method because instead of trying to find a target function the model

measures the correlation between data points and uses similarity between data

points to predict the output values of unknown or unobserved instances. Here,

the model predicts the voltage values of unmapped points on the myocardium

using their correlation with previously observed points. A Gaussian process is

fully defined by a mean function and covariance function. The covariance

function measures the correlation between the data points and also encodes the

similarity of their output values.

Here

is the mean

function and

represents the covariance function. On

assuming zero mean the above expression can be written as

Here y is the observed value,

is the predicted output,

represents the input observed points and

represents the set of query points. The

Gaussian process model gives probability estimates for its prediction and it

can also approximate a smooth function by choosing different covariance

functions or kernel form. In the cardiac voltage mapping problem, the Gaussian

process model is used as a surrogate model. It strives to determine the best

mapping point, while getting updated towards the true voltage distribution

pattern on the chamber of the heart.

5

Implicit Exploration

An

implicit exploration (IE) approach, based on uncertainty sampling is used to

select the best mapping point. The best mapping point is the unobserved point

about which the Gaussian process model is most uncertain. This is the point

that gives the highest value for the entropy estimation of the Gaussian process

model. In this approach the best mapping point is determined and also the hyper-parameters

(

of the model are updated during each

iteration. In addition to the implicit exploration method, a pure exploitation

(PE) method was also used for determining the mapping point. In contrast to the

implicit exploration method, in pure exploitation the initial hyper parameters

of the model are assumed to be accurate and therefore capable of reflecting the

ground truth. However, it is important that the hyper-parameters are updated

because the electrical patterns of each patient are different, especially in

the case of patients suffering from congenital heart defects. The implicit

exploration method selects the best mapping point with maximum posterior entropy

and also updates the probability distribution of the model hyper-parameters.

Figure

2: Comparison of IE and PE approaches 1

6

Data Export and pre-processing

Data

from the electro anatomical mapping system (EAMS) combines with pre-operative

mesh obtained by CT or MRI scan using nearest neighbour search. The training

data consisted of 3D positions of the points on the chamber of the heart and

their respective voltage values. A total of 25 datasets were available and out

of these 24 datasets were used to train the model and the remaining dataset was

used test the performance of the model.

7

In Silico Voltage Mapping

The

different guidance strategies were compared first by a simulation experiment.

Leave-one-out experiments were carried using the 25 patient datasets. Different

mapping sequences were produced by the three different mapping strategies under

consideration. The performances of the different algorithms were compared by

estimating the mean L1 distance between the predicted voltage values and the

actual voltage values in the patient dataset.

7.1

Results

Figure 3: Regression

error and uncertainty curves, (a)

Mean regression error over observed points (b) Maximum covariance over

unobserved points (c) Median covariance over unobserved points 1

It

was observed that implicit exploration approach based mapping strategy produced

the voltage map with least regression error. The IE and PE methods were also

able to achieve faster reduction in model uncertainty compared to the existing

geometry-based method of guidance.

8

Phantom Model Experiment

Simulation

of patient’s right ventricle was done using a 3D printed phantom model and

pre-collected voltage data. The voltage mapping procedure was done on the

phantom model using a manually operated robotic catheter. Guidance was provided

during the mapping procedure using a magnetic navigation system. Voltage

mapping was done on 52 points by both expert and novice operators using

different mapping strategies.

8.1

Results

Mapping Sequence

Total time (s)

Total travel distance (mm)

Total robot operations

Implicit Exploration

579.658

1036.90938

344,030

Geometry-based method

579.027

1038.5505

378,841

Expert mapping

627.028

1329.7556

487,416

Table

2: Procedure Duration, travel cost and operation cost 1

The

implicit exploration method performed better compared to the existing

geometry-based method and expert mapping done without guidance. The operation

cost of the robotic catheter was reduced by 9.18% compared to the

geometry-based method. The operators were able to achieve a more even

distribution of mapping points when real-time assistance was provided using

active learning strategy.

9 ConclusionCardiovascular

disease (CVD) is the leading cause

of global mortality. An estimated 17.7 million

people died from CVDs in 2015, representing 31% of all global deaths. Therefore

it is necessary to bring about better treatment outcomes through early risk

analysis, diagnosis and intervention. Machine learning methods have been

successfully implemented for automation of risk stratification and diagnosis of

cardiovascular diseases. However, the existing applications of machine

learning in assisting interventional procedures are limited. Intelligent

guidance using machine learning techniques could reduce the burden on experts

during surgical procedures and also reduce inconsistency in surgical

performance by providing real-time assistance. A strategy for providing

real-time guidance to electrophysiologist during cardiac voltage mapping

procedure has been proposed (1).

2

Introduction

The

treatment of cardiac arrhythmia involves radiofrequency catheter ablation to

destroy dysfunctional tissues of the myocardium that are responsible for inducing

arrhythmia. The voltage map of the chamber of the heart is obtained prior to

the ablation procedure to identify the trigger points of arrhythmia. Real time

guidance during the voltage mapping procedure could help the electrophysiologists

to reduce the total time taken for the procedure and improve accuracy of the

obtained voltage map. The proposed strategy meets two main requirements: (i)

ensure maximum coverage of the chamber of the heart being mapped and (ii) focus

on regions of high electrical gradients. The existing geometry-based method

meets only the first requirement. Hence a new strategy is proposed based on

active learning in conjunction with Gaussian process regression.

Figure

1: Activation map of left ventricle

2

3

Active Learning Strategy

Active

learning is a type of semi-supervised machine learning. In this approach the

model is capable of interactively querying the user for output values or labels

of specific new data points. The model tries to extract maximum information

through minimum number of queries and it tries to simultaneously improve its

accuracy and find the best query point. Active learning overcomes the problem

of disparity between availability of labelled and unlabelled data. Although

unlabelled data is usually available in vast quantities, labelled data is

scarce and the task of labelling them requires a lot of effort.

In

the cardiac voltage mapping task, the cost of labelling is associated with the

total procedure time, which needs to be minimised. In order to maximise the

knowledge about the target region, the operator must obtain voltage values of

as many points on the target location as possible. However, this will lead to

prolonged procedure duration which could endanger the patient. The active

learning approach addresses this problem by requesting labels for only a few

chosen data points.

3.1

Query Strategies

All

active learning approaches are based on estimating the information content of

unlabelled data points which provides the basis for selection of the query

points. Several methods have been proposed as query strategy for active

learning approach.

i.

Uncertainty Sampling: The model selects

the data point about which it is least confident as the query point.

Implementation of this method is straightforward in probabilistic models. One

of the common approaches for uncertainty sampling is entropy estimation. The

most informative query point is the one which has maximum information entropy.

Here

represents the data point with highest

information entropy and

varies over the possible labels or output

values.

ii.

Query-By-Committee: A set of competing

hypotheses derived from the same training dataset are made to vote for

selecting the best query point. The data point about which they most disagree

is considered to be the most informative query point.

iii.

Expected Error Reduction: The expected

error of trained model is estimated from the pool of unlabelled data points and

the query point is chosen such that it has least future error. The aim is to

minimize the total number of incorrect predictions. However, this method is

computationally expensive as it involves error estimation of each possible

query point.

4

Gaussian Processes

Gaussian

process is by definition a collection of random variables that are jointly

Gaussian distributed. Gaussian process regression is a non-parametric machine

learning method because instead of trying to find a target function the model

measures the correlation between data points and uses similarity between data

points to predict the output values of unknown or unobserved instances. Here,

the model predicts the voltage values of unmapped points on the myocardium

using their correlation with previously observed points. A Gaussian process is

fully defined by a mean function and covariance function. The covariance

function measures the correlation between the data points and also encodes the

similarity of their output values.

Here

is the mean

function and

represents the covariance function. On

assuming zero mean the above expression can be written as

Here y is the observed value,

is the predicted output,

represents the input observed points and

represents the set of query points. The

Gaussian process model gives probability estimates for its prediction and it

can also approximate a smooth function by choosing different covariance

functions or kernel form. In the cardiac voltage mapping problem, the Gaussian

process model is used as a surrogate model. It strives to determine the best

mapping point, while getting updated towards the true voltage distribution

pattern on the chamber of the heart.

5

Implicit Exploration

An

implicit exploration (IE) approach, based on uncertainty sampling is used to

select the best mapping point. The best mapping point is the unobserved point

about which the Gaussian process model is most uncertain. This is the point

that gives the highest value for the entropy estimation of the Gaussian process

model. In this approach the best mapping point is determined and also the hyper-parameters

(

of the model are updated during each

iteration. In addition to the implicit exploration method, a pure exploitation

(PE) method was also used for determining the mapping point. In contrast to the

implicit exploration method, in pure exploitation the initial hyper parameters

of the model are assumed to be accurate and therefore capable of reflecting the

ground truth. However, it is important that the hyper-parameters are updated

because the electrical patterns of each patient are different, especially in

the case of patients suffering from congenital heart defects. The implicit

exploration method selects the best mapping point with maximum posterior entropy

and also updates the probability distribution of the model hyper-parameters.

Figure

2: Comparison of IE and PE approaches 1

6

Data Export and pre-processing

Data

from the electro anatomical mapping system (EAMS) combines with pre-operative

mesh obtained by CT or MRI scan using nearest neighbour search. The training

data consisted of 3D positions of the points on the chamber of the heart and

their respective voltage values. A total of 25 datasets were available and out

of these 24 datasets were used to train the model and the remaining dataset was

used test the performance of the model.

7

In Silico Voltage Mapping

The

different guidance strategies were compared first by a simulation experiment.

Leave-one-out experiments were carried using the 25 patient datasets. Different

mapping sequences were produced by the three different mapping strategies under

consideration. The performances of the different algorithms were compared by

estimating the mean L1 distance between the predicted voltage values and the

actual voltage values in the patient dataset.

7.1

Results

Figure 3: Regression

error and uncertainty curves, (a)

Mean regression error over observed points (b) Maximum covariance over

unobserved points (c) Median covariance over unobserved points 1

It

was observed that implicit exploration approach based mapping strategy produced

the voltage map with least regression error. The IE and PE methods were also

able to achieve faster reduction in model uncertainty compared to the existing

geometry-based method of guidance.

8

Phantom Model Experiment

Simulation

of patient’s right ventricle was done using a 3D printed phantom model and

pre-collected voltage data. The voltage mapping procedure was done on the

phantom model using a manually operated robotic catheter. Guidance was provided

during the mapping procedure using a magnetic navigation system. Voltage

mapping was done on 52 points by both expert and novice operators using

different mapping strategies.

8.1

Results

Mapping Sequence

Total time (s)

Total travel distance (mm)

Total robot operations

Implicit Exploration

579.658

1036.90938

344,030

Geometry-based method

579.027

1038.5505

378,841

Expert mapping

627.028

1329.7556

487,416

Table

2: Procedure Duration, travel cost and operation cost 1

The

implicit exploration method performed better compared to the existing

geometry-based method and expert mapping done without guidance. The operation

cost of the robotic catheter was reduced by 9.18% compared to the

geometry-based method. The operators were able to achieve a more even

distribution of mapping points when real-time assistance was provided using

active learning strategy.

9 Conclusion

The

surrogate model based on Gaussian process regression was able to utilize

knowledge from the available expert mapping procedure and provide intelligent

guidance during voltage mapping process. Real-time assistance for the cardiac

voltage mapping procedure using active learning approach produced more accurate

cardiac voltage maps and reduced the procedure duration. The active learning

approach for real-time guidance in conjunction with robotic catheter

manipulation has the potential to conduct automated cardiac voltage mapping

procedure.

The

surrogate model based on Gaussian process regression was able to utilize

knowledge from the available expert mapping procedure and provide intelligent

guidance during voltage mapping process. Real-time assistance for the cardiac

voltage mapping procedure using active learning approach produced more accurate

cardiac voltage maps and reduced the procedure duration. The active learning

approach for real-time guidance in conjunction with robotic catheter

manipulation has the potential to conduct automated cardiac voltage mapping

procedure.