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An Obstructive Sleep Apnea Detection Approach Using Kernel Density Classification Based on Single-Lead Electrocardiogram

  • Patient Facing Systems
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Abstract

Obstructive sleep apnea (OSA) is a common sleep disorder that often remains undiagnosed, leading to an increased risk of developing cardiovascular diseases. Polysomnogram (PSG) is currently used as a golden standard for screening OSA. However, because it is time consuming, expensive and causes discomfort, alternative techniques based on a reduced set of physiological signals are proposed to solve this problem. This study proposes a convenient non-parametric kernel density-based approach for detection of OSA using single-lead electrocardiogram (ECG) recordings. Selected physiologically interpretable features are extracted from segmented RR intervals, which are obtained from ECG signals. These features are fed into the kernel density classifier to detect apnea event and bandwidths for density of each class (normal or apnea) are automatically chosen through an iterative bandwidth selection algorithm. To validate the proposed approach, RR intervals are extracted from ECG signals of 35 subjects obtained from a sleep apnea database (http://physionet.org/cgi-bin/atm/ATM). The results indicate that the kernel density classifier, with two features for apnea event detection, achieves a mean accuracy of 82.07 %, with mean sensitivity of 83.23 % and mean specificity of 80.24 %. Compared with other existing methods, the proposed kernel density approach achieves a comparably good performance but by using fewer features without significantly losing discriminant power, which indicates that it could be widely used for home-based screening or diagnosis of OSA.

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Acknowledgments

The authors would like to thank Dr. Thomas Penzel of Phillips-University for providing the data and also thank Dr. Zhaoming Dong, Dr. Yanbin Zhao and Changyue Song for giving some useful advices.

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Correspondence to Xi Zhang.

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This article is part of the Topical Collection on Patient Facing Systems

Appendix

Appendix

The algorithm for one dimension can be extended to two dimensions for the estimation of a p.d.f f(x). Assume a Gaussian kernel

$$ \phi(\mathbf{x},\mathbf{y};t) = \frac{1}{2\pi t}e^{-(\mathbf{x}-\mathbf{y})^{T}(\mathbf{x}-\mathbf{y})/(2t)} $$
(11)

where x = [x 1, x 2]T and y = [y 1, y 2]T. The asymptotically optimal squared bandwidth is given by

$$ \ast t = (2\pi N(\psi_{0,2}+\psi_{2,0}+\psi_{1,1}))^{-1/3} $$
(12)

where

$$\begin{array}{@{}rcl@{}} \psi_{i,j}&=&(-1)^{i+j}{\int}_{\mathbb{R}^{2}} f(\mathbf{x})\frac{\partial^{2(i+j)}}{\partial x_{1}^{2i}\partial x_{2}^{2j}}f(\mathbf{x})d \mathbf{x} \\ &=&\int \left( \frac{\partial^{(i+j)}}{\partial {x_{1}^{i}}\partial {x_{2}^{j}}} f(\mathbf{x})\right)^{2}d\mathbf{x}, i,j \in \mathbb{N}^{+} \end{array} $$
(13)

Similar to the one-dimensional case, two plug-in estimators for ψ i, j are derived from two formulas of equation (11).

$$ \tilde{\psi}_{i,j}=\frac{(-1)^{i+j}}{N^{2}}\sum\limits_{k=1}^{N}\sum\limits_{m=1}^{N} \frac{\partial^{2(i+j)}}{\partial x_{1}^{2i}\partial x_{2}^{2j}} \phi(\mathbf{X}_{m},\mathbf{X}_{k}; t_{i,j})$$
(14)
$$ \hat{\psi}_{i,j}=\frac{(-1)^{i+j}}{N^{2}}\sum\limits_{k=1}^{N}\sum\limits_{m=1}^{N} \frac{\partial^{2(i+j)}}{\partial x_{1}^{2i}\partial x_{2}^{2j}} \phi(\mathbf{X}_{m},\mathbf{X}_{k}; 2t_{i,j}) $$
(15)

The asymptotic expansion of the squared bias of estimator \(\tilde {\psi }_{i,j}\) is given by

$$\begin{array}{@{}rcl@{}} &&\left(\mathbb{E}_{f}\left[\tilde{\psi}_{i,j}\right]-\psi_{i,j}\right)^{2} \\ &&\thicksim\left(\frac{q(i)q(j)}{Nt^{i+j+1}_{i,j}}+\frac{t_{i,j}}{2}\left(\psi_{i+1,j}+\psi_{i,j+1}\right)\right)^{2}, \\ &&\phantom{000000000000000000000000}N\rightarrow\infty \end{array} $$
(16)

where

$$\begin{array}{@{}rcl@{}} q(j) = \left\{\begin{array}{ll} (-1)^{j} \frac{1\times 3\times 5\times {\ldots} \times (2j-1)}{\sqrt{2\pi}} \qquad ,j\geq 1\\ \frac{1}{\sqrt{2\pi}} \qquad \qquad \qquad \qquad \qquad j=0 \end{array}\right. \end{array} $$
(17)

Thus, we have

$$\begin{array}{@{}rcl@{}} &&\left(\mathbb{E}_{f}\left[\hat{\psi}_{i,j}\right]-\psi_{i,j}\right)^{2} \\ &&\thicksim\left(\frac{q(i)q(j)}{N(2t_{i,j})^{i+j+1}}+t_{i,j}\left(\psi_{i+1,j}+\psi_{i,j+1}\right)\right)^{2} \\ &&\phantom{0000000000000000000000000}N\rightarrow\infty \end{array} $$
(18)

For both estimators the squared bias in the dominant term in the asymptotic mean squared error, it follows that both estimators will have the same leading asymptotic mean square error term provided that

$$ t_{i,j}=\left(\frac{1+2^{-i-j-1}}{3}\frac{-2q(i)q(j)}{N(\psi_{i+1,j}+\psi_{i,j+1})}\right)^{1/(2+i+j)} $$
(19)

So, t i, j is estimated via

$$ \hat{t}_{i,j}=\left(\frac{1+2^{-i-j-1}}{3}\frac{-2q(i)q(j)}{N(\hat{\psi}_{i+1,j}+\hat{\psi}_{i,j+1})}\right)^{1/(2+i+j)} $$
(20)

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Chen, L., Zhang, X. & Wang, H. An Obstructive Sleep Apnea Detection Approach Using Kernel Density Classification Based on Single-Lead Electrocardiogram. J Med Syst 39, 47 (2015). https://doi.org/10.1007/s10916-015-0222-6

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