Comparison of entropy-based regularity estimators: application to the fetal heart rate signal for the identification of fetal distress

Linear and nonlinear measures of fetal heart rate patterns evaluated on very short fetal magnetocardiograms

We analyzed the effectiveness of linear short- and long-term variability time domain parameters, an index of sympatho-vagal balance (SDNN/RMSSD) and entropy in differentiating fetal heart rate patterns (fHRPs) on the fetal heart rate (fHR) series of 5, 3 and 2 min duration reconstructed from 46 fetal magnetocardiograms. Gestational age (GA) varied from 21 to 38 weeks. FHRPs were classified based on the fHR standard deviation. In sleep states, we observed that vagal influence increased with GA, and entropy significantly increased (decreased) with GA (SDNN/RMSSD), demonstrating that a prevalence of vagal activity with autonomous nervous system maturation may be associated with increased sleep state complexity. In active wakefulness, we observed a significant negative (positive) correlation of short-term (long-term) variability parameters with SDNN/RMSSD. ANOVA statistics demonstrated that long-term irregularity and standard deviation of normal-to-normal beat intervals (SDNN) best differentiated among fHRPs. Our results confirm that short- and long-term variability parameters are useful to differentiate between quiet and active states, and that entropy improves the characterization of sleep states. All measures differentiated fHRPs more effectively on very short HR series, as a result of the fMCG high temporal resolution and of the intrinsic timescales of the events that originate the different fHRPs.

Advances in monitoring cardiovascular signals. Contribution of nonlinear signal processing

Monitoring procedures are the basis to evaluate the clinical state of patients and to assess changes in their status, thus providing necessary interventions in time. To obtain this important objective it is necessary to integrate technological development with systems performing biomedical knowledge extraction and classification. Methods extracting non linear characteristics from HRV signal are presented and discussed to stress that integrated and multiparametric signal processing approaches can contribute to new diagnostic and classification indices. Examples report heart rate variability analysis in long periods in patients with cardiovascular disease. Fetal ECG monitoring is another example. In this case, coupling nonlinear parameters and linear time and frequency techniques increases diagnostic power and reliability of the monitoring. The paper shows that integrated signal analysis is very helpful to describe pathophysiological mechanisms involved in the cardiovascular and neural system control. It is a reliable basis to set up knowledge-based monitoring systems.

Fetal phonocardiography--past and future possibilities

The paper presents an overview of the 15 year long development of fetal phonocardiography including the works on the applied signal processing methods for identification of sound components. Based on the improvements achieved on this field, the paper shows that beyond the traditional CTG test the phonocardiography may be successfully applied for long-term fetal measurements and home monitoring. In addition, by indication of heart murmurs based on a comprehensive analysis of the recorded heart sound congenital heart defects can also be detected together with additional features in the third trimester. This makes an early widespread screening possible combined with the prescribed CTG test even at home using a telemedicine system.

Comparative study of approximate entropy and sample entropy robustness to spikes

OBJECTIVE

There is an ongoing research effort devoted to characterize the signal regularity metrics approximate entropy (ApEn) and sample entropy (SampEn) in order to better interpret their results in the context of biomedical signal analysis. Along with this line, this paper addresses the influence of abnormal spikes (impulses) on ApEn and SampEn measurements.

METHODS

A set of test signals consisting of generic synthetic signals, simulated biomedical signals, and real RR records was created. These test signals were corrupted by randomly generated spikes. ApEn and SampEn were computed for all the signals under different spike probabilities and for 100 realizations.

RESULTS

The effect of the presence of spikes on ApEn and SampEn is different for test signals with narrowband line spectra and test signals that are better modeled as broadband random processes. In the first case, the presence of extrinsic spikes in the signal results in an ApEn and SampEn increase. In the second case, it results in an entropy decrease. For real RR records, the presence of spikes, often due to QRS detection errors, also results in an entropy decrease.

CONCLUSIONS

Our findings demonstrate that both ApEn and SampEn are very sensitive to the presence of spikes. Abnormal spikes should be removed, if possible, from signals before computing ApEn or SampEn. Otherwise, the results can lead to misunderstandings or misclassification of the signal regularity.

The effect of orthostatic stress on multiscale entropy of heart rate and blood pressure

Cardiovascular control acts over multiple time scales, which introduces a significant amount of complexity to heart rate and blood pressure time series. Multiscale entropy (MSE) analysis has been developed to quantify the complexity of a time series over multiple time scales. In previous studies, MSE analyses identified impaired cardiovascular control and increased cardiovascular risk in various pathological conditions. Despite the increasing acceptance of the MSE technique in clinical research, information underpinning the involvement of the autonomic nervous system in the MSE of heart rate and blood pressure is lacking. The objective of this study is to investigate the effect of orthostatic challenge on the MSE of heart rate and blood pressure variability (HRV, BPV) and the correlation between MSE (complexity measures) and traditional linear (time and frequency domain) measures. MSE analysis of HRV and BPV was performed in 28 healthy young subjects on 1000 consecutive heart beats in the supine and standing positions. Sample entropy values were assessed on scales of 1-10. We found that MSE of heart rate and blood pressure signals is sensitive to changes in autonomic balance caused by postural change from the supine to the standing position. The effect of orthostatic challenge on heart rate and blood pressure complexity depended on the time scale under investigation. Entropy values did not correlate with the mean values of heart rate and blood pressure and showed only weak correlations with linear HRV and BPV measures. In conclusion, the MSE analysis of heart rate and blood pressure provides a sensitive tool to detect changes in autonomic balance as induced by postural change.

Biomedical signal and image processing

Generally, physiological modeling and biomedical signal processing constitute two important paradigms of biomedical engineering (BME): their fundamental concepts are taught starting from undergraduate studies and are more completely dealt with in the last years of graduate curricula, as well as in Ph.D. courses. Traditionally, these two cultural aspects were separated, with the first one more oriented to physiological issues and how to model them and the second one more dedicated to the development of processing tools or algorithms to enhance useful information from clinical data. A practical consequence was that those who did models did not do signal processing and vice versa. However, in recent years,the need for closer integration between signal processing and modeling of the relevant biological systems emerged very clearly [1], [2]. This is not only true for training purposes(i.e., to properly prepare the new professional members of BME) but also for the development of newly conceived research projects in which the integration between biomedical signal and image processing (BSIP) and modeling plays a crucial role. Just to give simple examples, topics such as brain–computer machine or interfaces,neuroengineering, nonlinear dynamical analysis of the cardiovascular (CV) system,integration of sensory-motor characteristics aimed at the building of advanced prostheses and rehabilitation tools, and wearable devices for vital sign monitoring and others do require an intelligent fusion of modeling and signal processing competences that are certainly peculiar of our discipline of BME.

Prototype of a wearable system for remote fetal monitoring during pregnancy

Fetal Heart Rate (FHR) monitoring gives important information about the fetus health state during pregnancy. This paper presents a new prototype for remote fetal monitoring. The device will allow to monitor FHR in a domiciliary context and to send fetal ECG traces to a hospital facility, where clinicians can interpret them. In this way the mother could receive prompt feedback about fetal wellbeing. The system is characterized by two units: (i) a wearable unit endowed with textile electrodes for abdominal ECG recordings and with a Field Programmable Gate Array (FPGA) board for fetal heart rate (FHR) extraction; (ii) a dock station for the transmission of the data through the telephone line. The system will allow to reduce costs in fetal monitoring, improving the assessment of fetal conditions. The device is actually in development state. In this paper, the most crucial aspects behind its fulfillment are discussed.

Adaptive multiscale complexity analysis of fetal heart rate

Per partum fetal asphyxia is a major cause of neonatal morbidity and mortality. Fetal heart rate monitoring plays an important role in early detection of acidosis, an indicator for asphyxia. This problem is addressed in this paper by introducing a novel complexity analysis of fetal heart rate data, based on producing a collection of piecewise linear approximations of varying dimensions from which a measure of complexity is extracted. This procedure specifically accounts for the highly non-stationary context of labor by being adaptive and multiscale. Using a reference dataset, made of real per partum fetal heart rate data, collected in situ and carefully constituted by obstetricians, the behavior of the proposed approach is analyzed and illustrated. Its performance is evaluated in terms of the rate of correct acidosis detection versus the rate of false detection, as well as how early the detection is made. Computational cost is also discussed. The results are shown to be extremely promising and further potential uses of the tool are discussed. MATLAB routines implementing the procedure will be made available at the time of publication.

Mutual information in natural position order of electroencephalogram is significantly increased at seizure onset

Epilepsy affects an estimated 60 million people worldwide. As many as 50% of people with epilepsy will continue to have seizures despite therapeutic dosages of appropriately selected antiepileptic drugs. Among proposed treatment modalities for persons with medication refractory epilepsy are implantable devices that rapidly detect and abort seizures. Computational resources in these devices are limited and much effort is directed to improving the efficiency of seizure detection. The goal of this study is to determine if electroencephalogram (EEG) may be reduced by the method of natural position order in a way that increases computation speed and reduces system memory requirements while preserving features relevant to detecting seizure onset. In this study we show increased mutual information (MI) at seizure onset in simultaneous channels of EEG reduced by natural position order with a 40-fold reduction in computation time and a fivefold reduction in system memory requirements. The trade-offs to EEG reduction by natural position order include decreased bandwidth and increased noise sensitivity.

A new, phonocardiography-based telemetric fetal home monitoring system

The purpose of this article is to describe a new, phonocardiography-based fetal telemonitoring system, which, due to its passive nature, allows long-term measurements even at the home of the pregnant woman. The input element of the system was the home monitor with two sensors for recording the trans-abdominal fetal heart signal and the uterine contractions. The recorded signal was transmitted by mobile network and Internet to an Evaluation Center, where it was analyzed in detail to obtain information about possible dysfunction of the fetal heart. The investigations on this system made clear that by advanced processing of the recorded signal the system captured many additional cardiac features compared with the traditional ultrasound-based cardiotocographic procedure.

Infant's emotional variability associated to interactive stressful situation: a novel analysis approach with Sample Entropy and Lempel-Ziv Complexity

This study examined to which extent the lack of the mother's communicative input is associated to the variability of the infant's behavioral and emotional states at a microtemporal level. Two novel non-linear signal-processing metrics were used as regularity indexes during both normal and stressful mother-infant interactions (Face-to-Face Still-Face paradigm): (1) Sample Entropy estimates the presence of epochs of similar states in a data-series, according to a moment-to-moment analysis; (2) Lempel-Ziv Complexity evaluates the occurrence and recurrence of the patterns of analogous states along the data sequence. Fourteen mothers and their healthy full-term 7-month-old infants were videotaped and the infants' socio-emotional behaviors were micro-analytically coded off-line using a .20s time sampling method. During the maternal still-face episodes, when infants were confronted with the perturbation of their caregiver remaining unresponsive, both regularity indexes were lower than in normal interactions. Evidence is provided that non-linear techniques are suitable to detect variability in the infant's states.

Measuring body temperature time series regularity using Approximate Entropy and Sample Entropy

Approximate Entropy (ApEn) and Sample Entropy (SampEn) have proven to be a valuable analyzing tool for a number of physiological signals. However, the characterization of these metrics is still lacking. We applied ApEn and SampEn to body temperature time series recorded from patients in critical state. This study was aimed at finding the optimal analytical configuration to best distinguish between survivor and non-survivor records, and at gaining additional insight into the characterization of such tools. A statistical analysis of the results was conducted to support the parameter and metric selection criteria for this type of physiological signal.

Complexity analysis of the fetal heart rate variability: early identification of severe intrauterine growth-restricted fetuses

The main goal of this work is to suggest new indices for a correct identification of the intrauterine growth-restricted (IUGR) fetuses on the basis of fetal heart rate (FHR) variability analysis performed in the antepartum period. To this purpose, we analyzed 59 FHR time series recorded in early periods of gestation through a Hewlett Packard 1351A cardiotocograph. Advanced analysis techniques were adopted including the computation of the Lempel Ziv complexity (LZC) index and the multiscale entropy (MSE), that is, the entropy estimation with a multiscale approach. A multiparametric classifier based on k-mean cluster analysis was also performed to separate pathological and normal fetuses. The results show that the proposed LZC and the MSE could be useful to identify the actual IUGRs and to separate them from the physiological fetuses, providing good values of sensitivity and accuracy (Se = 77.8%, Ac = 82.4%).

Fetal distress evaluation using and analyzing the variables of antepartum computerized cardiotocography

OBJECTIVE

In this study, we tried to establish cut-off values for more than one parameters of computerized cardiotocography (c CTG) in the prediction of fetal distress during labor, using a group of pregnant women with low-risk pregnancies.

METHOD

A retrospective study was performed. Data were collected from 167 patients for measurements of fetal heart rate (FHR) variables and perinatal outcome. Computerized CTG was performed with an Oxford Sonicaid monitor with connection to a 8000 system for CTG spontaneous analysis. The following c CTG variables were considered: FHR, number of accelerations, the presence and the number of episodes of high and low variation, the number of decelerations, short-term variation (STV), peaks of contractions (per hour) and fetal movements assessed by maternal perception (per hour). Computerized CTG recordings started not earlier than the beginning of week 38 of gestation. Immediately after delivery, blood sample was collected from umbilical artery for umbilical artery blood gas analysis (UBGA). The main UBGA parameter in cord umbilical artery that was considered for analysis was pH. pH values<7.25 were considered as suspicious for acidemia and pH values>or=7.25 as normal.

RESULTS

Women suspicious for fetal distress during labor presented significantly lower fetal movements (P=0.026), accelerations (P=0.018), variability (P<0.001), number of high episodes (P<0.001), higher values of FHR baseline (P<0.001) and low episodes (P<0.001). Only the number of decelerations did not differ significantly between the two groups (P=0.545). The cut-off points of 5.00 for STV and 3.00 for high episodes were determined to classify women with fetal distress, which yielded high sensitivities (34 and 52%) and specificities (96.6 and 94.9%), with positive predictive values of 81.0 and 81.3% and negative predictive values of 77.4 and 82.2%, respectively.

CONCLUSIONS

In conclusion, we believe that not only STV but also other components of the cCTG, mainly the presence and the number of episodes of high variation, are related to pregnancy's outcome as measured by an umbilical artery pH.

Entropy analysis on EEG signal in a case study of focal myoclonus

Electrophysiological studies provide useful information for diagnosis and classification of myoclonus, and for the investigation of its generative mechanisms, due to association of myoclonus with abnormally increased excitability of cortical structures. In this work we analyzed the polygraphic data of a 7-year old girl affected by continuous partial epilepsy with focal myoclonus both related and not related with epileptiform discharges on EEG. We applied Sample Entropy (SampEn) and Lempel-Ziv complexity (LZ) methods to investigate the regularity and complexity content of EEG recordings and to find possible analogies in the behaviour of non-parametric complexity measures in epilepsy and in myoclonus. Our results show that these algorithms succeeded in finding a significant difference between the hypothesized focus on C3 electrode and the contralateral electrode C4, for EEG correlated myoclonus. A significant difference between the two contralateral electrodes (C3-C4) was also found for non EEG correlated myoclonus, but only by means of SampEn. This preliminary study confirmed the ability of entropic methods in discriminating myoclonic events. Indeed, near the myoclonic focus location both SampEn and LZ methods showed below average values.

A comparison of fetal and neonatal heart rate variability at similar post-menstrual ages

Substantial differences of heart rate variability (HRV) were found between fetuses and prematurely born neonates in the high-frequency band of the power spectrum. The range of post-menstrual ages of the fetuses and neonates were closely matched in this study. Growth of HRV was observed in low-frequency and high-frequency bands, reflecting maturation of the autonomic nervous system. The higher level of fetal HRV in the high-frequency band persisted even after accounting for age-related changes. Multiscale entropy was also higher in fetuses than in prematurely born neonates. These results suggest that the autonomic balance is poorer among neonates born prematurely than in fetuses of identical post-menstrual age.

Influence of noise on the sample entropy algorithm

We study the effect of static additive noise on the sample entropy (SampEn) algorithm [J. S. Richman and J. R. Moorman, Am. J. Physiol. Heart Circ. Physiol. 278, 2039 (2000); R. B. Govindan et al., Physica A 376, 158 (2007)] for analyzing time series. Using surrogate data tests, we empirically investigate the ability of the SampEn index to detect nonlinearity in simulated time series corrupted by increased amounts of noise. Discrete and continuous chaotic and nonchaotic systems are included in the numerical experiments. Both Gaussian and uniformly distributed noises are considered. The results indicate that the SampEn statistic is a robust index for detecting nonlinearity in time series corrupted by observational noise.

Age-related variation in EEG complexity to photic stimulation: a multiscale entropy analysis

OBJECTIVE

This study was intended to examine variations in electroencephalographic (EEG) complexity in response to photic stimulation (PS) during aging to test the hypothesis that the aging process reduces physiologic complexity and functional responsiveness.

METHODS

Multiscale entropy (MSE), an estimate of time-series signal complexity associated with long-range temporal correlation, is used as a recently proposed method for quantifying EEG complexity with multiple coarse-grained sequences. We recorded EEG in 13 healthy elderly subjects and 12 healthy young subjects during pre-PS and post-PS conditions and estimated their respective MSE values.

RESULTS

For the pre-PS condition, no significant complexity difference was found between the groups. However, a significant MSE change (complexity increase) was found post-PS only in young subjects, thereby revealing a power-law scaling property, which means long-range temporal correlation.

CONCLUSIONS

Enhancement of long-range temporal correlation in young subjects after PS might reflect a cortical response to stimuli, which was absent in elderly subjects. These results are consistent with the general "loss of complexity/diminished functional response to stimuli" theory of aging.

SIGNIFICANCE

Our findings demonstrate that application of MSE analysis to EEG is a powerful approach for studying age-related changes in brain function.

Interpretation of the auto-mutual information rate of decrease in the context of biomedical signal analysis. Application to electroencephalogram recordings

The mutual information (MI) is a measure of both linear and nonlinear dependences. It can be applied to a time series and a time-delayed version of the same sequence to compute the auto-mutual information function (AMIF). Moreover, the AMIF rate of decrease (AMIFRD) with increasing time delay in a signal is correlated with its entropy and has been used to characterize biomedical data. In this paper, we aimed at gaining insight into the dependence of the AMIFRD on several signal processing concepts and at illustrating its application to biomedical time series analysis. Thus, we have analysed a set of synthetic sequences with the AMIFRD. The results show that the AMIF decreases more quickly as bandwidth increases and that the AMIFRD becomes more negative as there is more white noise contaminating the time series. Additionally, this metric detected changes in the nonlinear dynamics of a signal. Finally, in order to illustrate the analysis of real biomedical signals with the AMIFRD, this metric was applied to electroencephalogram (EEG) signals acquired with eyes open and closed and to ictal and non-ictal intracranial EEG recordings.

Change in complexity of fetal heart rate variability

In a pilot study of fetal heart rate variability using magnetocardiograms it was found that substantial changes occur in complexity as the fetus matures. The self-similarity parameter increased sharply from 26 weeks to 30 weeks gestational age, while the relationship of entropy to timescale reversed during the same period. This suggests that there is distinct maturation of the autonomic nervous system during this period.

New indexes from the fetal heart rate analysis for the identification of severe intra uterine growth restricted fetuses

This study proposes new indexes extracted from fetal heart rate signal in order to identify intrauterine growth restricted (IUGR) fetuses and separate them from healthy small for gestational age ones (SGA). Unfortunately evidence-based guidelines for clinical surveillance are poor and lack of reliable indexes. Therefore we proposed new parameters: the Lempel Ziv complexity (LZC) and the multiscale entropy (MSE). The results show that the LZ complexity is able to significantly discriminate the severe IUGR (preterm delivered) from moderate IUGR (at term delivered) and healthy fetuses. Moreover the k-mean cluster analysis applied to these indexes was able to gather the severe IUGRs and to separate them from both not severe IUGRs and normal fetuses, which were included in the same cluster. The cluster analysis provides good values of sensitivity and accuracy.

Nonlinear analysis of heart rate variability signal for the characterization of cardiac heart failure patients

The purpose of this work is to characterize the heart rate variability (HRV) of patients affected by congestive heart failure (CHF) and to find out the main difference between this pathological condition and the physiological state. Parameters adopted in this work are: the detrended fluctuation analysis (DFA) and the Higuchi exponent to assess long correlations and self-similarity; the regularity estimators, approximate entropy (ApEn) and sample entropy (SampEn) and the multiscale entropy (MSE). Furthermore we proposed a new regularity index, the Gaussian entropy (GaussEn) which is a modification of the previous ApEn and SampEn. The results show the proposed parameters do an effective separation of physiological and pathological subject conditions. These results are part of a study evaluating the nonlinear index prognostic value toward cardiac death.

Experiences with fetal phonocardiographic telemonitoring and future possibilities

Phonocardiography (PCG) makes possible the examination of some fetal cardiac anomalies which otherwise usually remain undetected during pregnancy. The application of PCG in a telemonitoring system enhances its diagnostic capabilities, allowing long-term measurements even at home. The paper summarizes the intensive fetal monitoring campaign carried out in Hungary during the last three years that yielded useful experience regarding recent and future possibilities of fetal monitoring. Results collected from a large number of measurements suggest that PCG home monitoring may be a suitable screening method for fetal congenital heart diseases, even if surgical intervention in this phase of pregnancy is not easy.

Entropy-based automated classification of independent components separated from fMCG

Fetal magnetocardiography (fMCG) is a noninvasive technique suitable for the prenatal diagnosis of the fetal heart function. Reliable fetal cardiac signals can be reconstructed from multi-channel fMCG recordings by means of independent component analysis (ICA). However, the identification of the separated components is usually accomplished by visual inspection. This paper discusses a novel automated system based on entropy estimators, namely approximate entropy (ApEn) and sample entropy (SampEn), for the classification of independent components (ICs). The system was validated on 40 fMCG datasets of normal fetuses with the gestational age ranging from 22 to 37 weeks. Both ApEn and SampEn were able to measure the stability and predictability of the physiological signals separated with ICA, and the entropy values of the three categories were significantly different at p <0.01. The system performances were compared with those of a method based on the analysis of the time and frequency content of the components. The outcomes of this study showed a superior performance of the entropy-based system, in particular for early gestation, with an overall ICs detection rate of 98.75% and 97.92% for ApEn and SampEn respectively, as against a value of 94.50% obtained with the time-frequency-based system.

Analysis of electroencephalograms in Alzheimer's disease patients with multiscale entropy

The aim of this study was to analyse the electroencephalogram (EEG) background activity of Alzheimer's disease (AD) patients using multiscale entropy (MSE). MSE is a recently developed method that quantifies the regularity of a signal on different time scales. These time scales are inspected by means of several coarse-grained sequences formed from the analysed signals. We recorded the EEGs from 19 scalp electrodes in 11 AD patients and 11 age-matched controls and estimated the MSE profile for each epoch of the EEG recordings. The shape of the MSE profiles reveals the EEG complexity, and it suggests that the EEG contains information in deeper scales than the smallest one. Moreover, the results showed that the EEG background activity is less complex in AD patients than control subjects. We found significant differences between both subject groups at electrodes F3, F7, Fp1, Fp2, T5, T6, P3, P4, O1 and O2 (p-value < 0.01, Student's t-test). These findings indicate that the EEG complexity analysis performed on deeper time scales by MSE may be a useful tool in order to increase our knowledge of AD.

Self-similarity behavior characterization of fetal heart rate signal in healthy and intrauterine growth retarded fetuses

In this paper we deal with the problem of the interpretation of the fetal heart rate (FHR) signal. From literature is known that FHR contains both linear and non linear components. Starting from this consideration we analyzed FHR as a fractal time series and we evaluated its self similarity behavior using the Hurst's coefficient (H). We first evaluated the stationarity of FHR time series and then we estimated H with Detrend fluctuation analysis (DFA) method. We calculated Hurst's coefficient for healthy fetuses and for fetuses affected by Intrauterine grow retardation (IUGR). Results provided H = 0.350 +/- 0.064 (avg +/- std) for healthy patients and H = 0.461 +/- 0.059 for IUGR. It is also shown that IUGR patients exhibit a "less non-stationary" and longer-memory behavior than normals with a reduced information content of FHR signal. We propose for this phenomenon a physiological explanation connected with the abnormal autonomic nervous system development of IUGR patients.

Robustness of support vector machine-based classification of heart rate signals

In this study, we discuss the use of support vector machine (SVM) learning to classify heart rate signals. Each signal is represented by an attribute vector containing a set of statistical measures for the respective signal. At first, the SVM classifier is trained by data (attribute vectors) with known ground truth. Then, the classifier learnt parameters can be used for the categorization of new signals not belonging to the training set. We have experimented with both real and artificial signals and the SVM classifier performs very well even with signals exhibiting very low signal to noise ratio which is not the case for other standard methods proposed by the literature.