Heart Sound Localization in Respiratory Sound Based on a New Computationally Efficient Entropy Bound.

A new entropy bound with low computational complexity for differential Shannon entropy estimation with kernel density approach is proposed in this study, which is based on defining a bound for the Kullback-Leibler divergence between two Gaussian mixture models. The proposed entropy bound is derived to provide computational efficiency without decreasing the accuracy in detecting heart sound segments in respiratory sound. It is shown both theoretically and experimentally that using the proposed bound in an adaptive threshold-based detection method gives very similar performance compared to that obtained by a nonparametric kernel based approach, while its computational cost is much lower. The performance of the proposed method is shown and compared with the three methods in the literature by means of experiments utilizing a database of 20 subjects. The results show that the false negative rate values for the proposed method are 1.45±1.50 % and 1.98±1.81 % for low and medium flow rates, respectively. These average values are similar to the results obtained by the alternative methods. Moreover, the average elapsed time of the proposed method for a piece of data with a length of 20 s is 0.05 s, which is significantly lower than that of the other methods.

A robust method for online heart sound localization in respiratory sound based on temporal fuzzy c-means.

This work presents a detailed framework to detect the location of heart sound within the respiratory sound based on temporal fuzzy c-means (TFCM) algorithm. In the proposed method, respiratory sound is first divided into frames and for each frame, the logarithmic energy features are calculated. Then, these features are used to classify the respiratory sound as heart sound (HS containing lung sound) and non-HS (only lung sound) by the TFCM algorithm. The TFCM is the modified version fuzzy c-means (FCM) algorithm. While the FCM algorithm uses only the local information about the current frame, the TFCM algorithm uses the temporal information from both the current and the neighboring frames in decision making. To measure the detection performance of the proposed method, several experiments have been conducted on a database of 24 healthy subjects. The experimental results show that the average false-negative rate values are 0.8 ± 1.1 and 1.5 ± 1.4 %, and the normalized area under detection error curves are 0.0145 and 0.0269 for the TFCM method in the low and medium respiratory flow rates, respectively. These average values are significantly lower than those obtained by FCM algorithm and by the other compared methods in the literature, which demonstrates the efficiency of the proposed TFCM algorithm. On the other hand, the average elapsed time of the TFCM for a data with length of 0.2 ± 0.05 s is 0.2 ± 0.05 s, which is slightly higher than that of the FCM and lower than those of the other compared methods.

Robust heart sound detection in respiratory sound using LRT with maximum a posteriori based online parameter adaptation.

This paper investigates the utility of a likelihood ratio test (LRT) combined with an efficient adaptation procedure for the purpose of detecting the heart sound (HS) with lung sound and the lung sound only (non-HS) segments in a respiratory signal. The proposed detection method has four main stages: feature extraction, training of the models, detection, and adaptation of the model parameter. In the first stage, the logarithmic energy features are extracted for each frame of respiratory sound. In the second stage, the probabilistic models for HS and non-HS segments are constructed by training Gaussian mixture models (GMMs) with an expectation maximization algorithm in a subject-independent manner, and then the HS and non-HS segments are detected by the results of the LRT based on the GMMs. In the adaptation stage, the subject-independent trained model parameter is modified online using the observed test data to fit the model parameter of the target subject. Experiments were performed on the database from 24 healthy subjects. The experimental results indicate that the proposed heart sound detection algorithm outperforms two well-known heart sound detection methods in terms of the values of the normalized area under the detection error trade-off curve (NAUC), the false negative rate (FNR), and the false positive rate (FPR).

Heart sound localization in chest sound using temporal fuzzy C-means classification.

Most of heart sound cancellation algorithms to improve the quality of lung sound use information about heart sound locations. Therefore, a reliable estimation of heart sound localizations within chest sound is a key issue to enhance the performance of heart sound cancellation algorithms. In this paper, we present a new technique to estimate locations of heart sound segments in chest sound using the temporal fuzzy c-means (TFCM) algorithm. In applying the method, chest sound is first divided into frames and then for each frame, the entropy feature is calculated. Next, by means of these features, the TFCM algorithm is applied to classify a chest sound into two classes: heart sound (heart sound containing lung sound) and non-heart sound (only lung sound). The proposed method was tested on the database used in the liteature and experimetal results are compared with the baseline which is a well-known method in the literature. The experimental results show that the proposed method outperforms the baseline method interms of false negative rate (FNR), false positive rate (FPR) and accuracy (ACC).

Anomalous transport and nonlinear reactions in spiny dendrites.

We present a mesoscopic description of the anomalous transport and reactions of particles in spiny dendrites. As a starting point we use two-state Markovian model with the transition probabilities depending on residence time variable. The main assumption is that the longer a particle survives inside spine, the smaller becomes the transition probability from spine to dendrite. We extend a linear model presented in Fedotov [Phys. Rev. Lett. 101, 218102 (2008)] and derive the nonlinear Master equations for the average densities of particles inside spines and parent dendrite by eliminating residence time variable. We show that the flux of particles between spines and parent dendrite is not local in time and space. In particular the average flux of particles from a population of spines through spines necks into parent dendrite depends on chemical reactions in spines. This memory effect means that one cannot separate the exchange flux of particles and the chemical reactions inside spines. This phenomenon does not exist in the Markovian case. The flux of particles from dendrite to spines is found to depend on the transport process inside dendrite. We show that if the particles inside a dendrite have constant velocity, the mean particle's position increases as t(µ) with µ<1 (anomalous advection). We derive a fractional advection-diffusion equation for the total density of particles.