Cardiovascular the cost of labelling is associated with

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

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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.