Self-adaptive model-based ECG denoising using features extracted by mean shift algorithm

Denoising of electrocardiogram (ECG) is the fundamental technique for manual or automatic ECG diagnosis. Model-based denoising has attracted initial studies since the ECG dynamical model was established in 2003 and been demonstrated to outperform most model-less denoising methods. The focus of this paper is robust denoising of abnormal ECG signals, which do not satisfy the assumption in previous model-based studies that morphological or physiological variations are small from one beat to another. A mean shift based initializer is proposed to provide a much more robust estimation of initial model parameters for each heart beat. Together with physiological knowledge based wave sub-segmentation and enhanced strategies, the novel initializer has been demonstrated to achieve satisfactory performance for both normal and abnormal heart beats under both white and pink noises. Utilizing records from Massachusetts Institute of Technology (MIT)-Beth Israel Hospital (BIH) database, this paper also applies various filters to denoise noisy signals and the denoising performances verify the availability and efficacy of the proposed denoising method.     

A data-driven framework to model the organism–environment system

Organisms modify their development and function in response to the environment. At the same time, the environment is modified by the activities of the organism. Despite the ubiquity of such dynamical interactions in nature, it remains challenging to develop models that accurately represent them, and that can be fitted using data. These features are desirable when modeling phenomena such as phenotypic plasticity, to generate quantitative predictions of how the system will respond to environmental signals of different magnitude or at different times, for example, during ontogeny. Here, we explain a modeling framework that represents the organism and environment as a single coupled dynamical system in terms of inputs and outputs. Inputs are external signals, and outputs are measurements of the system in time. The framework uses time-series data of inputs and outputs to fit a nonlinear black-box model that allows to predict how the system will respond to novel input signals. The framework has three key properties: it captures the dynamical nature of the organism–environment system, it can be fitted with data, and it can be applied without detailed knowledge of the system. We study phenotypic plasticity using in silico experiments and demonstrate that the framework predicts the response to novel environmental signals. The framework allows us to model plasticity as a dynamical property that changes in time during ontogeny, reflecting the well-known fact that organisms are more or less plastic at different developmental stages.     

A generating model of realistic synthetic heart sounds for performance assessment of phonocardiogram processing algorithms

A new model which is capable of generating realistic synthetic phonocardiogram (PCG) signals is introduced based on three coupled ordinary differential equations. The new PCG model takes into account the respiratory frequency, the heart rate variability and the time splitting of first and second heart sounds. This time splitting occurs with each cardiac cycle and varies with inhalation and exhalation. Clinical PCG statistics and the close temporal relationship between events in ECG and PCG are used to deduce values of PCG model parameters.In comparison with published PCG models, the proposed model allows a larger number of known PCG features to be taken into consideration. Moreover it is able to generate both normal and abnormal realistic synthetic heart sounds. Results show that these synthetic PCG signals have the closest features to those of a conventional heart sound in both time and frequency domains. Additionally, a sound quality test carried out by eight cardiologists demonstrates that the proposed model outperforms the existing models.This new PCG model is promising and useful in assessing signal processing techniques which are developed to help clinical diagnosis based on PCG.     

Quantitative analysis of the phonocardiogram for detection of murmurs

A method is proposed for quantification of the phonocardiogram (PCG) signal into two parameters representing time and frequency domain characteristics of the signal. For this purpose the energy curve and power spectrum of the signal are used. Results of application of the method to PCG signals of 8 normal and 39 pathological cases are presented. The study shows that the parameters of PCG signals with murmurs differ from those of normal signals and hence aid detection of murmurs. The algorithms involved are simple and a microprocessor-based automatic PCG analysis system using the proposed technique is being contemplated.     

Methods of weighted averaging of ECG signals using Bayesian inference and criterion function minimization

Averaging signals in time domain is one of the main methods of noise attenuation in biomedical signal processing in case of systems producing repetitive patterns such as electrocardiographic (ECG) acquisition systems. This paper presents a comprehensive study of weighted averaging of ECG signal. Presented methods use criterion function minimization, partitioning of input set of data in the time domain as well as Bayesian and empirical Bayesian framework. The existing methods are described together with their extensions. Performance of all presented methods is experimentally evaluated and compared with the traditional averaging by using arithmetic mean and well-known weighted averaging methods based on criterion function minimization (WACFM).     

Variational learning for Generalized Associative Functional Networks in modeling dynamic process of plant growth

This paper presents a new statistical techniques — Bayesian Generalized Associative Functional Networks (GAFN), to model the dynamical plant growth process of greenhouse crops. GAFNs are able to incorporate the domain knowledge and data to model complex ecosystem. By use of the functional networks and Bayesian framework, the prior knowledge can be naturally embedded into the model, and the functional relationship between inputs and outputs can be learned during the training process. Our main interest is focused on the Generalized Associative Functional Networks (GAFNs), which are appropriate to model multiple variable processes. Three main advantages are obtained through the applications of Bayesian GAFN methods to modeling dynamic process of plant growth. Firstly, this approach provides a powerful tool for revealing some useful relationships between the greenhouse environmental factors and the plant growth parameters. Secondly, Bayesian GAFN can model Multiple-Input Multiple-Output (MIMO) systems from the given data, and presents a good generalization capability from the final single model for successfully fitting all 12 data sets over 5-year field experiments. Thirdly, the Bayesian GAFN method can also play as an optimization tool to estimate the interested parameter in the agro-ecosystem. In this work, two algorithms are proposed for the statistical inference of parameters in GAFNs. Both of them are based on the variational inference, also called variational Bayes (VB) techniques, which may provide probabilistic interpretations for the built models. VB-based learning methods are able to yield estimations of the full posterior probability of model parameters. Synthetic and real-world examples are implemented to confirm the validity of the proposed methods.     

Integrating the niche and neutral perspectives on community structure and dynamics

Elucidating the mechanisms underlying the assembly and dynamics of ecological communities is a fundamental goal of ecology. Two conceptual approaches have emerged in this respect: the niche-assembly view and the neutral perspective. The debate as to which approach best explains the biodiversity patterns observed in nature is becoming outdated, as ecologists increasingly agree on the existence of a niche-neutral continuum of community dynamical behaviors. However, attempts to make the continuum idea operational and measurable remain sparse. Here, we propose a model-based approach to achieving this. The proposed methodology consists of separating out fluctuations in species abundances into niche-mediated and stochastic factors, linking the niche configuration to community dynamics through competition, and adding demographic stochasticity. This results in a comprehensive framework including neutrality and strict niche segregation as extreme cases. We develop an index of departure from neutral drift as a surrogate for community position on the niche-neutral continuum. We evaluate the performance of our modeling approach with simulated data, and subsequently use the model to analyze rodent web-trapping data from a real-world system. The model fitting is carried out with a Bayesian approach using Markov chain Monte Carlo simulation methods.     

Bayesian restoration of ion channel records using hidden Markov models

Hidden Markov models have been used to restore recorded signals of single ion channels buried in background noise. Parameter estimation and signal restoration are usually carried out through likelihood maximization by using variants of the Baum-Welch forward-backward procedures. This paper presents an alternative approach for dealing with this inferential task. The inferences are made by using a combination of the framework provided by Bayesian statistics and numerical methods based on Markov chain Monte Carlo stochastic simulation. The reliability of this approach is tested by using synthetic signals of known characteristics. The expectations of the model parameters estimated here are close to those calculated using the Baum-Welch algorithm, but the present methods also yield estimates of their errors. Comparisons of the results of the Bayesian Markov Chain Monte Carlo approach with those obtained by filtering and thresholding demonstrate clearly the superiority of the new methods.     

Identifying differentially expressed genes in meta-analysis via Bayesian model-based clustering

A Bayesian model-based clustering approach is proposed for identifying differentially expressed genes in meta-analysis. A Bayesian hierarchical model is used as a scientific tool for combining information from different studies, and a mixture prior is used to separate differentially expressed genes from non-differentially expressed genes. Posterior estimation of the parameters and missing observations are done by using a simple Markov chain Monte Carlo method. From the estimated mixture model, useful measure of significance of a test such as the Bayesian false discovery rate (FDR), the local FDR (Efron et al., 2001), and the integration-driven discovery rate (IDR; Choi et al., 2003) can be easily computed. The model-based approach is also compared with commonly used permutation methods, and it is shown that the model-based approach is superior to the permutation methods when there are excessive under-expressed genes compared to over-expressed genes or vice versa. The proposed method is applied to four publicly available prostate cancer gene expression data sets and simulated data sets.     

Stimulus design for model selection and validation in cell signaling

Mechanism-based chemical kinetic models are increasingly being used to describe biological signaling. Such models serve to encapsulate current understanding of pathways and to enable insight into complex biological processes. One challenge in model development is that, with limited experimental data, multiple models can be consistent with known mechanisms and existing data. Here, we address the problem of model ambiguity by providing a method for designing dynamic stimuli that, in stimulus–response experiments, distinguish among parameterized models with different topologies, i.e., reaction mechanisms, in which only some of the species can be measured. We develop the approach by presenting two formulations of a model-based controller that is used to design the dynamic stimulus. In both formulations, an input signal is designed for each candidate model and parameterization so as to drive the model outputs through a target trajectory. The quality of a model is then assessed by the ability of the corresponding controller, informed by that model, to drive the experimental system. We evaluated our method on models of antibody–ligand binding, mitogen-activated protein kinase (MAPK) phosphorylation and de-phosphorylation, and larger models of the epidermal growth factor receptor (EGFR) pathway. For each of these systems, the controller informed by the correct model is the most successful at designing a stimulus to produce the desired behavior. Using these stimuli we were able to distinguish between models with subtle mechanistic differences or where input and outputs were multiple reactions removed from the model differences. An advantage of this method of model discrimination is that it does not require novel reagents, or altered measurement techniques; the only change to the experiment is the time course of stimulation. Taken together, these results provide a strong basis for using designed input stimuli as a tool for the development of cell signaling models.     

Efficient Optimization of Stimuli for Model-Based Design of Experiments to Resolve Dynamical Uncertainty

This model-based design of experiments (MBDOE) method determines the input magnitudes of an experimental stimuli to apply and the associated measurements that should be taken to optimally constrain the uncertain dynamics of a biological system under study. The ideal global solution for this experiment design problem is generally computationally intractable because of parametric uncertainties in the mathematical model of the biological system. Others have addressed this issue by limiting the solution to a local estimate of the model parameters. Here we present an approach that is independent of the local parameter constraint. This approach is made computationally efficient and tractable by the use of: (1) sparse grid interpolation that approximates the biological system dynamics, (2) representative parameters that uniformly represent the data-consistent dynamical space, and (3) probability weights of the represented experimentally distinguishable dynamics. Our approach identifies data-consistent representative parameters using sparse grid interpolants, constructs the optimal input sequence from a greedy search, and defines the associated optimal measurements using a scenario tree. We explore the optimality of this MBDOE algorithm using a 3-dimensional Hes1 model and a 19-dimensional T-cell receptor model. The 19-dimensional T-cell model also demonstrates the MBDOE algorithm’s scalability to higher dimensions. In both cases, the dynamical uncertainty region that bounds the trajectories of the target system states were reduced by as much as 86% and 99% respectively after completing the designed experiments in silico. Our results suggest that for resolving dynamical uncertainty, the ability to design an input sequence paired with its associated measurements is particularly important when limited by the number of measurements.     

Transfer Functions for Protein Signal Transduction: Application to a Model of Striatal Neural Plasticity

We present a novel formulation for biochemical reaction networks in the context of protein signal transduction. The model consists of input-output transfer functions, which are derived from differential equations, using stable equilibria. We select a set of “source” species, which are interpreted as input signals. Signals are transmitted to all other species in the system (the “target” species) with a specific delay and with a specific transmission strength. The delay is computed as the maximal reaction time until a stable equilibrium for the target species is reached, in the context of all other reactions in the system. The transmission strength is the concentration change of the target species. The computed input-output transfer functions can be stored in a matrix, fitted with parameters, and even recalled to build dynamical models on the basis of state changes. By separating the temporal and the magnitudinal domain we can greatly simplify the computational model, circumventing typical problems of complex dynamical systems. The transfer function transformation of biochemical reaction systems can be applied to mass-action kinetic models of signal transduction. The paper shows that this approach yields significant novel insights while remaining a fully testable and executable dynamical model for signal transduction. In particular we can deconstruct the complex system into local transfer functions between individual species. As an example, we examine modularity and signal integration using a published model of striatal neural plasticity. The modularizations that emerge correspond to a known biological distinction between calcium-dependent and cAMP-dependent pathways. Remarkably, we found that overall interconnectedness depends on the magnitude of inputs, with higher connectivity at low input concentrations and significant modularization at moderate to high input concentrations. This general result, which directly follows from the properties of individual transfer functions, contradicts notions of ubiquitous complexity by showing input-dependent signal transmission inactivation.     

Time-frequency analysis of phonocardiogram signals using wavelet transform: a comparative study

Analysis of phonocardiogram (PCG) signals provides a non-invasive means to determine the abnormalities caused by cardiovascular system pathology. In general, time-frequency representation (TFR) methods are used to study the PCG signal because it is one of the non-stationary bio-signals. The continuous wavelet transform (CWT) is especially suitable for the analysis of non-stationary signals and to obtain the TFR, due to its high resolution, both in time and in frequency and has recently become a favourite tool. It decomposes a signal in terms of elementary contributions called wavelets, which are shifted and dilated copies of a fixed mother wavelet function, and yields a joint TFR. Although the basic characteristics of the wavelets are similar, each type of the wavelets produces a different TFR. In this study, eight real types of the most known wavelets are examined on typical PCG signals indicating heart abnormalities in order to determine the best wavelet to obtain a reliable TFR. For this purpose, the wavelet energy and frequency spectrum estimations based on the CWT and the spectra of the chosen wavelets were compared with the energy distribution and the autoregressive frequency spectra in order to determine the most suitable wavelet. The results show that Morlet wavelet is the most reliable wavelet for the time-frequency analysis of PCG signals.     

Bayesian modeling of dynamic motion integration

The quality of the representation of an object's motion is limited by the noise in the sensory input as well as by an intrinsic ambiguity due to the spatial limitation of the visual motion analyzers (aperture problem). Perceptual and oculomotor data demonstrate that motion processing of extended objects is initially dominated by the local 1D motion cues, related to the object's edges and orthogonal to them, whereas 2D information, related to terminators (or edge-endings), takes progressively over and leads to the final correct representation of global motion. A Bayesian framework accounting for the sensory noise and general expectancies for object velocities has proven successful in explaining several experimental findings concerning early motion processing [Weiss, Y., Adelson, E., 1998. Slow and smooth: a Bayesian theory for the combination of local motion signals in human vision. MIT Technical report, A.I. Memo 1624]. In particular, these models provide a qualitative account for the initial bias induced by the 1D motion cue. However, a complete functional model, encompassing the dynamical evolution of object motion perception, including the integration of different motion cues, is still lacking. Here we outline several experimental observations concerning human smooth pursuit of moving objects and more particularly the time course of its initiation phase, which reflects the ongoing motion integration process. In addition, we propose a recursive extension of the Bayesian model, motivated and constrained by our oculomotor data, to describe the dynamical integration of 1D and 2D motion information. We compare the model predictions for object motion tracking with human oculomotor recordings.     

Recognition of cognitive load with a stacking network ensemble of denoising autoencoders and abstracted neurophysiological features

The safety of human–machine systems can be indirectly evaluated based on operator’s cognitive load levels at each temporal instant. However, relevant features of cognitive states are hidden behind in multiple sources of cortical neural responses. In this study, we developed a novel neural network ensemble, SE-SDAE, based on stacked denoising autoencoders (SDAEs) which identify different levels of cognitive load by electroencephalography (EEG) signals. To improve the generalization capability of the ensemble framework, a stacking-based approach is adopted to fuse the abstracted EEG features from activations of deep-structured hidden layers. In particular, we also combine multiple K-nearest neighbor and naive Bayesian classifiers with SDAEs to generate a heterogeneous classification committee to enhance ensemble’s diversity. Finally, we validate the proposed SE-SDAE by comparing its performance with mainstream pattern classifiers for cognitive load evaluation to show its effectiveness.     

Mixed Signal Learning by Spike Correlation Propagation in Feedback Inhibitory Circuits

The brain can learn and detect mixed input signals masked by various types of noise, and spike-timing-dependent plasticity (STDP) is the candidate synaptic level mechanism. Because sensory inputs typically have spike correlation, and local circuits have dense feedback connections, input spikes cause the propagation of spike correlation in lateral circuits; however, it is largely unknown how this secondary correlation generated by lateral circuits influences learning processes through STDP, or whether it is beneficial to achieve efficient spike-based learning from uncertain stimuli. To explore the answers to these questions, we construct models of feedforward networks with lateral inhibitory circuits and study how propagated correlation influences STDP learning, and what kind of learning algorithm such circuits achieve. We derive analytical conditions at which neurons detect minor signals with STDP, and show that depending on the origin of the noise, different correlation timescales are useful for learning. In particular, we show that non-precise spike correlation is beneficial for learning in the presence of cross-talk noise. We also show that by considering excitatory and inhibitory STDP at lateral connections, the circuit can acquire a lateral structure optimal for signal detection. In addition, we demonstrate that the model performs blind source separation in a manner similar to the sequential sampling approximation of the Bayesian independent component analysis algorithm. Our results provide a basic understanding of STDP learning in feedback circuits by integrating analyses from both dynamical systems and information theory.     

Dynamic detection of rhythmic oscillations in heart-rate tracings: a state-space approach based on fourth-order cumulants

 This paper presents a new procedure specifically aimed at providing a dynamical detection of the oscillations occurring in long-term heart-rate (HR) tracings. The procedure is based on a time-variant state-space modelling of the fourth-order cumulants of the HR signal. The state-space estimator was selected because of its demonstrated capability to distinguish between deterministic and stochastic components of the signal, while the fourth-order cumulants of the signal were used as input of the model to further reduce adverse effects of coloured, white and 1/f Gaussian noise possibly present in the input data. The procedure was tested by the analysis of simulated signals and its performance was compared with the results obtained by state-space modelling applied directly on the test signals (instead of on the fourth-order cumulants of the signals) and by the more traditional auto-regressive modelling. The comparison has shown a clear superiority of the proposed procedure over the other techniques in discriminating deterministic oscillations from coloured noise. Finally, the applicability of the procedure to biological data was verified by analysing five experimental HR tracings recorded in normal subjects during laboratory and daily life conditions. Received: 17 May 1996 / Accepted in revised form: 29 November 1996     

A Bayesian Outlier Criterion to Detect SNPs under Selection in Large Data Sets

Background

The recent advent of high-throughput SNP genotyping technologies has opened new avenues of research for population genetics. In particular, a growing interest in the identification of footprints of selection, based on genome scans for adaptive differentiation, has emerged.

Methodology/Principal Findings

The purpose of this study is to develop an efficient model-based approach to perform Bayesian exploratory analyses for adaptive differentiation in very large SNP data sets. The basic idea is to start with a very simple model for neutral loci that is easy to implement under a Bayesian framework and to identify selected loci as outliers via Posterior Predictive P-values (PPP-values). Applications of this strategy are considered using two different statistical models. The first one was initially interpreted in the context of populations evolving respectively under pure genetic drift from a common ancestral population while the second one relies on populations under migration-drift equilibrium. Robustness and power of the two resulting Bayesian model-based approaches to detect SNP under selection are further evaluated through extensive simulations. An application to a cattle data set is also provided.

Conclusions/Significance

The procedure described turns out to be much faster than former Bayesian approaches and also reasonably efficient especially to detect loci under positive selection.     

Modeling compositional heterogeneity

Compositional heterogeneity among lineages can compromise phylogenetic analyses, because models in common use assume compositionally homogeneous data. Models that can accommodate compositional heterogeneity with few extra parameters are described here, and used in two examples where the true tree is known with confidence. It is shown using likelihood ratio tests that adequate modeling of compositional heterogeneity can be achieved with few composition parameters, that the data may not need to be modelled with separate composition parameters for each branch in the tree. Tree searching and placement of composition vectors on the tree are done in a Bayesian framework using Markov chain Monte Carlo (MCMC) methods. Assessment of fit of the model to the data is made in both maximum likelihood (ML) and Bayesian frameworks. In an ML framework, overall model fit is assessed using the Goldman-Cox test, and the fit of the composition implied by a (possibly heterogeneous) model to the composition of the data is assessed using a novel tree-and model-based composition fit test. In a Bayesian framework, overall model fit and composition fit are assessed using posterior predictive simulation. It is shown that when composition is not accommodated, then the model does not fit, and incorrect trees are found; but when composition is accommodated, the model then fits, and the known correct phylogenies are obtained.