IDW shows the best performance at any degree of reduction ... {dianaorrego,catalinatobon,beatrizvaldes}@itm.edu.co, {migb2b,jpmurillo22}@gmail.com,.
Reconstruction of Multi Spatial Resolution Feature Maps on a 2D Model of Atrial Fibrillation: Simulation Study Juan Murillo-Escobar1, Miguel A. Becerra1, Esteban A. Cardona2, Catalina Tobón2, Laura C. Palacio2, B.E. Valdés2, and Diana A. Orrego2 1
Institución Universitaria Salazar y Herrera, Grupo de Investigación GEA, Medellín, Colombia 2 Instituto Tecnológico Metropolitano, Grupo de Investigación GI2B, Medellín, Colombia {dianaorrego,catalinatobon,beatrizvaldes}@itm.edu.co, {migb2b,jpmurillo22}@gmail.com, {estebanac,laura-sarca116}@hotmail.com Abstract— Catheter ablation is a technique used as treatment for atrial fibrillation, this procedure is guided using 3D electro anatomic mapping systems. Ablation is one of the treatments for AF whose effectiveness depend on the location of the rotor tip and this depend of the quality of mapping obtained from a reduced set of real signals. This paper presents a comparison study between three approaches for reconstruction of features maps of a 2D model of simulated atrial fibrillation. The model was characterized using the mean, Shannon entropy and approximate entropy of the electrograms (EGM). The model is made up of 22500 EGM and reductions of 75%, 93.5% and 97.3% in the spatial resolution of the model was conducted. Thereupon a reconstruction of the feature maps was realized using inverse distance weighted (IDW), inverse distance weighted-median filter (IDW-MF) and backpropagation artificial neural networks (BPANN), the performance of the techniques was analyzed using the root mean square error (RMSE) and the peak signal to noise ratio (PSNR). IDW shows a general RSME of 4.2% and a PSNR of 27.5dB, IDW-MF exhibited a RSME of 17.5% and a PSNR of 21.8 dB, finally BPANN shows a RSME of 9% and PSNR of 22.8 dB. IDW shows the best performance at any degree of reduction while IDW-MF represent the best approach for Shannon entropy and mean maps reconstruction and IDW has the best performance for approximate entropy maps reconstruction.
because the CFAEs areas have been reported as promise targets for AF ablation [5]. Systems for CFAEs areas identifications based on dominant frequency [6], Shannon entropy [7] and approximate entropy [8], have been proposed, however algorithms based on dominant frequency shows 93% of error in the identification of the CFAE’s areas [6] while systems based on Shannon entropy and approximate entropy show promising results although they only have been tested on simulated environments. This approach needs to obtain a high number of EGMs, and such a thing is not possible with the current available mapping systems. On [9] a system for EGM reconstruction based on an inverse solution to Laplace’s equation was developed, however that system is limited by its incapacity to determine the sources of error and lacks of a method comparison.
In this work a comparative study between different interpolation techniques for features maps reconstruction was conducted. First, the characterization of the 2D simulated model of permanent AF was carried out using the Shannon entropy, approximate entropy and the mean of the 22500 EGM from the model; subsequently we realize a reduction on the spatial resolution of Keywords— IDW, Median filter, ANN, EGM, Approximate the 75%, 93.5% and 97.3% of the obtained EGMs of the model entropy, Shannon entropy keeping a uniform distribution. Then a reconstruction of the whole model was realized using the inverse distance weighted (IDW), IDW median filter (IDW-MF) and back propagation I. INTRODUCTION artificial neural networks (BPANN). The performance of the Catheter ablation is an approach used as a treatment for su- techniques was conducted using the measurement of root mean praventricular arrhythmias such as atrial fibrillation (AF) [1], square error (RMSE) and peak signal to noise ratio (PSNR) which is a prevalence in middle age population, representing between the reconstructed features maps and the original one. 2.5% of them [2]. AF ablation has as objective to stop or prevent the AF, suppressing the triggers that start AF and/or II. MATERIALS Y METHODS modifying the arrhythmogenic substrate, the principal triggers in AF are ectopic focus, rotors, spiral waves and the ligament of A. 2D model of simulated human atrial tissue under chronic Marshall [3]. Catheter ablation procedures are guided using 3D AF conditions electro anatomic mapping systems contributing electrophysioThe 2D computational model used in this study simulates a 6 logical information as voltage and activation from the electrox 6 cm atrial human tissue using the electrophysiological model grams (EGM) [4]. The developed systems for complex fractionproposed in [10], on this model a permanent AF is simulated. ated atrial electrogram (CFAE) mapping are being studied 22500 unipolar EGM were obtained from the model through virtual electrodes distributed over the surface of the model to a © Springer International Publishing Switzerland 2015 A. Braidot and A. Hadad (eds.), VI Latin American Congress on Biomedical Engineering CLAIB 2014, Paraná, Argentina 29, 30 & 31 October 2014, IFMBE Proceedings 49, DOI: 10.1007/978-3-319-13117-7_159
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ii) ( ⃗ ) is a vector of m points:
400 µm distance among them. The model provides simple EGMs, EGMs with double potentials and CFAEs which lasted 5 seconds each one. B. Theoretical Background 1) Inverse distance weighted (IDW) is an interpolation method used to estimate unknown data point values, based on the assumption that this will be the weighted average of his neighbor values. IDW assumes that the closest values have a largest weight than those further, in other words the weight of a value is inverse to the distance from the point that want to be interpolate [11].
(⃗)
,(⃗)
iii) [( ⃗ ) ( ⃗ )] denotes the distance between the vector ( ⃗ ) to ( ⃗ ). [( ⃗ ) ( ⃗ )]
(⃗
)| (5)
iv) Calculate as the number of ( ) that for a given ( ⃗ ) satisfied [( ⃗ ) ( ⃗ )] r is the tolerance parameter.
, where
Thus, the weights calculation is defined by the equation (1) where de index i represents the points which values are known and j represents the points with unknown values, nj is the points number with unknown values related to the point j and is the distance from the j point to the i point [12].
|( ⃗
)
v) Estimate the frequency of similar pattern: ( )
(6)
vi) Compute the average of the natural algorithm of (1)
∑
Thereupon, the interpolated value ̅ in the point j which is calculated using the equation (2), where is the value of the known point i. ̅
∑
Let X be a data array and be a sub data array of X with size M x N centered in the point (x,y), the MF calculate the median value of X in the area. ̅(
( )
)
(
)
(3)
∑
( )
(
)
( )
∑
( )
( )
(4)
4) Approximate entropy (ApEn) is an indicator of the complexity and irregularity of a time series. Mathematically ApEn is defined as [15, 16]: i) Let a time series
contain N data points as:
( )
(8)
5) Root square mean error (RSME) is calculated via the equation (9), where M is the number of elements, and are the original and the reconstructed features respectively [17]. [ ∑
(
) ]
(9)
6) Peak signal to noise ratio (PSNR) is a measure of the noise level in a data array. PSNR is widely used in the field of image and video processing and is an indicator of quality image [18]. The PSNR is defined as:
3) Shannon entropy quantify the randomness of a time series, measuring the inequality of its probability distribution p. Shannon entropy is calculated using the equation (4) [14]. ( )
(7)
vii) Finally the ApEn is calculated using the equation (8):
(2)
2) Median filter (MF) is the most popular statistic filter, this one generate a new data array replacing its values by the median of the neighborhood values in the old data array [13].
( )
as:
(
√
)
(10)
Where is the maximum value in the data array and MSE is the mean square error and is defined as: ∑
(
)
(11)
7) Back propagation artificial neural network (BPANN) is a kind of artificial neural network this one assume the function of a common and complex nervous system, BPANN is
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3.8 4.9
28.2 25.1
16.8 17.9
23.6 19.2
8.9 12.1
22.4 19.9
IV. CONCLUSIONS
A comparison analysis between IDW, IDW-MF and BPANN was carried out for feature maps reconstruction of 2D model of simulated human atrial tissue under chronic AF conditions with multiple spatial resolution reduction. IDW shows the best performance at any degree of reduction and any feature, however the best performance to reconstruction of mean and ShanEn maps is obtained using IDW-MF at any spatial resolution reduction, for ApEn map reconstruction IDW represent the best approach for any level of reduction. BPANN has an intermediate overall performance, but in ShanEn maps reconstruction its performance is significantly lowest than other techniques, similarly IDW-MF performance in ApEn maps reconstruction is critically lower compared with IDW and BPANN performance. Despite this, is necessary assessed the reconstructed features maps in systems for CFAEs and/or rotor tips identification to determinate which one of this techniques is the best approach for this task.
ACKNOWLEDGMENT This work was supported by the research project identify with the code 250 at the Institución Universitaria Salazar y Herrera and the Instituto Tecnológico Metropolitano of Medellín, Colombia.
CONFLICT OF INTEREST The authors declare that they have no conflict of interest.
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