Analysis of Time-Varying Biological Data Using Rainflow Cycle Counting

A wide range of biological investigations lead to time-history data. The characterization of such data can be difficult particularly in the presence of signal noise or superimposed signals. Several methods are described which can be brought to bear including FFT, thresholding, peak counting, and range counting. However, each of these approaches has significant disadvantages. In this paper we describe a novel method, known as rainflow cycle counting, for characterizing time varying biological time-history data in terms of spiking or oscillation amplitude and frequency. Rainflow counting is a straightforward algorithm for identifying complete cycles in the data and determining their amplitudes. The approach is simple, reliable, easily lends itself to automation, and robust even in the presence of superimposed signals or background noise. After describing the method, its use and behavior are demonstrated on three sample histories of intracellular calcium concentration in chondrocytes exposed to fluid shear stress. The method is also applied to a more challenging data set that has had an artificial random error included. The results demonstrate that the rainflow counting algorithm identifies signal oscillations and appropriately determines their amplitudes even when superimposed or distorted by background noise. These attractive properties make rainflow counting a powerful approach for quantifying and characterizing biological time histories.     

Few-sweep estimation of evoked potential based on a generalized subspace approach

A generalized subspace approach is proposed for single channel brain evoked potential (EP) extraction from background electroencephalogram (EEG) signal. The method realizes the optimum estimate of EP signal from the observable noisy signal. The underlying principle is to project the signal and noise into signal and noise coefficient subspace respectively by applying projection matrix at first. Secondly, coefficient weighting matrix is achieved based on the autocorrelation matrices of the noise and the noisy signal. With the coefficient weighting matrix, we can remove the noise projection coefficients and estimate the signal ones. EP signal is then obtained by averaging the signals estimated with the reconstruction matrix. Given different signal-to-noise ratio (SNR) conditions, the algorithm can estimate the EP signal with only two sweeps observable noisy signals. Our approach is shown to have excellent capability of estimating EP signal even in poor SNR conditions. The interference of spontaneous EEG has been eliminated with significantly improved SNR. The simulation results have demonstrated the effectiveness and superior performance of the proposed method.     

Adaptive processing techniques based on hidden Markov models for characterizing very small channel currents buried in noise and deterministic interferences.

Techniques for characterizing very small single-channel currents buried in background noise are described and tested on simulated data to give confidence when applied to real data. Single channel currents are represented as a discrete-time, finite-state, homogeneous, Markov process, and the noise that obscures the signal is assumed to be white and Gaussian. The various signal model parameters, such as the Markov state levels and transition probabilities, are unknown. In addition to white Gaussian noise, the signal can be corrupted by deterministic interferences of known form but unknown parameters, such as the sinusoidal disturbance stemming from AC interference and a drift of the base line owing to a slow development of liquid-junction potentials. To characterize the signal buried in such stochastic and deterministic interferences, the problem is first formulated in the framework of a Hidden Markov Model and then the Expectation Maximization algorithm is applied to obtain the maximum likelihood estimates of the model parameters (state levels, transition probabilities), signals, and the parameters of the deterministic disturbances. Using fictitious channel currents embedded in the idealized noise, we first show that the signal processing technique is capable of characterizing the signal characteristics quite accurately even when the amplitude of currents is as small as 5-10 fA. The statistics of the signal estimated from the processing technique include the amplitude, mean open and closed duration, open-time and closed-time histograms, probability of dwell-time and the transition probability matrix. With a periodic interference composed, for example, of 50 Hz and 100 Hz components, or a linear drift of the baseline added to the segment containing channel currents and white noise, the parameters of the deterministic interference, such as the amplitude and phase of the sinusoidal wave, or the rate of linear drift, as well as all the relevant statistics of the signal, are accurately estimated with the algorithm we propose. Also, if the frequencies of the periodic interference are unknown, they can be accurately estimated. Finally, we provide a technique by which channel currents originating from the sum of two or more independent single channels are decomposed so that each process can be separately characterized. This process is also formulated as a Hidden Markov Model problem and solved by applying the Expectation Maximization algorithm. The scheme relies on the fact that the transition matrix of the summed Markov process can be construed as a tensor product of the transition matrices of individual processes.     

Denoising two-photon calcium imaging data

Two-photon calcium imaging is now an important tool for in vivo imaging of biological systems. By enabling neuronal population imaging with subcellular resolution, this modality offers an approach for gaining a fundamental understanding of brain anatomy and physiology. Proper analysis of calcium imaging data requires denoising, that is separating the signal from complex physiological noise. To analyze two-photon brain imaging data, we present a signal plus colored noise model in which the signal is represented as harmonic regression and the correlated noise is represented as an order autoregressive process. We provide an efficient cyclic descent algorithm to compute approximate maximum likelihood parameter estimates by combing a weighted least-squares procedure with the Burg algorithm. We use Akaike information criterion to guide selection of the harmonic regression and the autoregressive model orders. Our flexible yet parsimonious modeling approach reliably separates stimulus-evoked fluorescence response from background activity and noise, assesses goodness of fit, and estimates confidence intervals and signal-to-noise ratio. This refined separation leads to appreciably enhanced image contrast for individual cells including clear delineation of subcellular details and network activity. The application of our approach to in vivo imaging data recorded in the ferret primary visual cortex demonstrates that our method yields substantially denoised signal estimates. We also provide a general Volterra series framework for deriving this and other signal plus correlated noise models for imaging. This approach to analyzing two-photon calcium imaging data may be readily adapted to other computational biology problems which apply correlated noise models.     

Fast, automated implementation of temporally precise blind deconvolution of multiphasic excitatory postsynaptic currents

Records of excitatory postsynaptic currents (EPSCs) are often complex, with overlapping signals that display a large range of amplitudes. Statistical analysis of the kinetics and amplitudes of such complex EPSCs is nonetheless essential to the understanding of transmitter release. We therefore developed a maximum-likelihood blind deconvolution algorithm to detect exocytotic events in complex EPSC records. The algorithm is capable of characterizing the kinetics of the prototypical EPSC as well as delineating individual release events at higher temporal resolution than other extant methods. The approach also accommodates data with low signal-to-noise ratios and those with substantial overlaps between events. We demonstrated the algorithm's efficacy on paired whole-cell electrode recordings and synthetic data of high complexity. Using the algorithm to align EPSCs, we characterized their kinetics in a parameter-free way. Combining this approach with maximum-entropy deconvolution, we were able to identify independent release events in complex records at a temporal resolution of less than 250 μs. We determined that the increase in total postsynaptic current associated with depolarization of the presynaptic cell stems primarily from an increase in the rate of EPSCs rather than an increase in their amplitude. Finally, we found that fluctuations owing to postsynaptic receptor kinetics and experimental noise, as well as the model dependence of the deconvolution process, explain our inability to observe quantized peaks in histograms of EPSC amplitudes from physiological recordings.     

Unravelling gene networks from noisy under-determined experimental perturbation data

Systems biology aims to study the properties of biological systems in terms of the properties of their molecular constituents. This occurs frequently by a process of mathematical modelling. The first step in this modelling process is to unravel the interaction structure of biological systems from experimental data. Previously, an algorithm for gene network inference from gene expression perturbation data was proposed. Here, the algorithm is extended by using regression with subset selection. The performance of the algorithm is extensively evaluated on a set of data produced with gene network models at different levels of simulated experimental noise. Regression with subset selection outperforms the previously stated matrix inverse approach in the presence of experimental noise. Furthermore, this regression approach enables us to deal with under-determination, that is, when not all genes are perturbed. The results on incomplete data sets show that the new method performs well at higher number of perturbations, even when noise levels are high. At lower number of perturbations, although still being able to recover the majority of the connections, less confidence can be placed in the recovered edges.     

Automatic signal classification in fluorescence in situ hybridization images

BACKGROUND: Previous systems for dot (signal) counting in fluorescence in situ hybridization (FISH) images have relied on an auto-focusing method for obtaining a clearly defined image. Because signals are distributed in three dimensions within the nucleus and artifacts such as debris and background fluorescence can attract the focusing method, valid signals can be left unfocused or unseen. This leads to dot counting errors, which increase with the number of probes. METHODS: The approach described here dispenses with auto-focusing, and instead relies on a neural network (NN) classifier that discriminates between in and out-of-focus images taken at different focal planes of the same field of view. Discrimination is performed by the NN, which classifies signals of each image as valid data or artifacts (due to out of focusing). The image that contains no artifacts is the in-focus image selected for dot count proportion estimation. RESULTS: Using an NN classifier and a set of features to represent signals improves upon previous discrimination schemes that are based on nonadaptable decision boundaries and single-feature signal representation. Moreover, the classifier is not limited by the number of probes. Three classification strategies, two of them hierarchical, have been examined and found to achieve each between 83% and 87% accuracy on unseen data. Screening, while performing dot counting, of in and out-of-focus images based on signal classification suggests an accurate and efficient alternative to that obtained using an auto-focusing mechanism.     

Characterization of single channel currents using digital signal processing techniques based on Hidden Markov Models.

Techniques for extracting small, single channel ion currents from background noise are described and tested. It is assumed that single channel currents are generated by a first-order, finite-state, discrete-time, Markov process to which is added 'white' background noise from the recording apparatus (electrode, amplifiers, etc). Given the observations and the statistics of the background noise, the techniques described here yield a posteriori estimates of the most likely signal statistics, including the Markov model state transition probabilities, duration (open- and closed-time) probabilities, histograms, signal levels, and the most likely state sequence. Using variations of several algorithms previously developed for solving digital estimation problems, we have demonstrated that: (1) artificial, small, first-order, finite-state, Markov model signals embedded in simulated noise can be extracted with a high degree of accuracy, (2) processing can detect signals that do not conform to a first-order Markov model but the method is less accurate when the background noise is not white, and (3) the techniques can be used to extract from the baseline noise single channel currents in neuronal membranes. Some studies have been included to test the validity of assuming a first-order Markov model for biological signals. This method can be used to obtain directly from digitized data, channel characteristics such as amplitude distributions, transition matrices and open- and closed-time durations.     

Noise-invariant Neurons in the Avian Auditory Cortex: Hearing the Song in Noise

Given the extraordinary ability of humans and animals to recognize communication signals over a background of noise, describing noise invariant neural responses is critical not only to pinpoint the brain regions that are mediating our robust perceptions but also to understand the neural computations that are performing these tasks and the underlying circuitry. Although invariant neural responses, such as rotation-invariant face cells, are well described in the visual system, high-level auditory neurons that can represent the same behaviorally relevant signal in a range of listening conditions have yet to be discovered. Here we found neurons in a secondary area of the avian auditory cortex that exhibit noise-invariant responses in the sense that they responded with similar spike patterns to song stimuli presented in silence and over a background of naturalistic noise. By characterizing the neurons'' tuning in terms of their responses to modulations in the temporal and spectral envelope of the sound, we then show that noise invariance is partly achieved by selectively responding to long sounds with sharp spectral structure. Finally, to demonstrate that such computations could explain noise invariance, we designed a biologically inspired noise-filtering algorithm that can be used to separate song or speech from noise. This novel noise-filtering method performs as well as other state-of-the-art de-noising algorithms and could be used in clinical or consumer oriented applications. Our biologically inspired model also shows how high-level noise-invariant responses could be created from neural responses typically found in primary auditory cortex.     

Recovering motifs from biased genomes: application of signal correction

A significant problem in biological motif analysis arises when the background symbol distribution is biased (e.g. high/low GC content in the case of DNA sequences). This can lead to overestimation of the amount of information encoded in a motif. A motif can be depicted as a signal using information theory (IT). We apply two concepts from IT, distortion and patterned interference (a type of noise), to model genomic and codon bias respectively. This modeling approach allows us to correct a raw signal to recover signals that are weakened by compositional bias. The corrected signal is more likely to be discriminated from a biased background by a macromolecule. We apply this correction technique to recover ribosome-binding site (RBS) signals from available sequenced and annotated prokaryotic genomes having diverse compositional biases. We observed that linear correction was sufficient for recovering signals even at the extremes of these biases. Further comparative genomics studies were made possible upon correction of these signals. We find that the average Euclidian distance between RBS signal frequency matrices of different genomes can be significantly reduced by using the correction technique. Within this reduced average distance, we can find examples of class-specific RBS signals. Our results have implications for motif-based prediction, particularly with regards to the estimation of reliable inter-genomic model parameters.     

Online control of evaluation algorithms of the image applied to identification of deglutition function]

Comprehensive software and hardware have been developed for the processing of biosignals. Such automatic signal processing, however not only has advantages, but also drawbacks. The question as to the reliability of the evaluation algorithm arises when the signal is modified, in the presence of interindividual differences, and in particular when noise is superimposed. This is of great interest for long-term recording when the original signal can no longer be inspected visually. The aim of our work was to display the signals on the screen of a monitor simultaneously with lines marking the points (start, end, extreme value, etc.) processed by the specific signal processing algorithm. The program package permits the on-line recording and monitoring of signals, the parallel processing and marking of detected events on the monitor, as well as storage of the parameters extracted. It is a very effective tool for developing, improving and monitoring of algorithms and their efficiency for signal processing.     

Assessing marine ecosystem acoustic diversity across ocean basins

Concurrent with the elevation of the concern over the state of sound in the ocean, advances in terrestrial acoustic monitoring techniques have produced concepts and tools that may be applicable to the underwater world. Several index values that convey information related to acoustic diversity with a single numeric measurement made from acoustic recordings have been proposed for rapidly assessing community biodiversity. Here we apply the acoustic biodiversity index method to low frequency recordings made from three different ocean basins to assess its appropriateness for characterizing species richness in the marine environment. Initial results indicated that raw acoustic entropy (H) values did not correspond to biological patterns identified from individual signal detections and classification. Noise from seismic airgun activity masked the weaker biological signals and confounded the entropy calculation. A simple background removal technique that subtracted an average complex spectrum characteristic of seismic exploration signals from the average spectra of each analysis period that contained seismic signals was applied to compensate for salient seismic airgun signals present in all locations. The noise compensated (H_N) entropy index was more reflective of biological patterns and holds promise for the use of rapid acoustic biodiversity in the marine environment as an indicator of habitat biodiversity and health.     

Your attention please: increasing ambient noise levels elicits a change in communication behaviour in humpback whales (Megaptera novaeangliae)

High background noise is an important obstacle in successful signal detection and perception of an intended acoustic signal. To overcome this problem, many animals modify their acoustic signal by increasing the repetition rate, duration, amplitude or frequency range of the signal. An alternative method to ensure successful signal reception, yet to be tested in animals, involves the use of two different types of signal, where one signal type may enhance the other in periods of high background noise. Humpback whale communication signals comprise two different types: vocal signals, and surface-generated signals such as ‘breaching’ or ‘pectoral slapping’. We found that humpback whales gradually switched from primarily vocal to primarily surface-generated communication in increasing wind speeds and background noise levels, though kept both signal types in their repertoire. Vocal signals have the advantage of having higher information content but may have the disadvantage of loosing this information in a noisy environment. Surface-generated sounds have energy distributed over a greater frequency range and may be less likely to become confused in periods of high wind-generated noise but have less information content when compared with vocal sounds. Therefore, surface-generated sounds may improve detection or enhance the perception of vocal signals in a noisy environment.     

Facilitating joint chaos and fractal analysis of biosignals through nonlinear adaptive filtering

Background

Chaos and random fractal theories are among the most important for fully characterizing nonlinear dynamics of complicated multiscale biosignals. Chaos analysis requires that signals be relatively noise-free and stationary, while fractal analysis demands signals to be non-rhythmic and scale-free.

Methodology/Principal Findings

To facilitate joint chaos and fractal analysis of biosignals, we present an adaptive algorithm, which: (1) can readily remove nonstationarities from the signal, (2) can more effectively reduce noise in the signals than linear filters, wavelet denoising, and chaos-based noise reduction techniques; (3) can readily decompose a multiscale biosignal into a series of intrinsically bandlimited functions; and (4) offers a new formulation of fractal and multifractal analysis that is better than existing methods when a biosignal contains a strong oscillatory component.

Conclusions

The presented approach is a valuable, versatile tool for the analysis of various types of biological signals. Its effectiveness is demonstrated by offering new important insights into brainwave dynamics and the very high accuracy in automatically detecting epileptic seizures from EEG signals.     

Automated detection of elementary calcium release events using the á trous wavelet transform

We developed an algorithm for the automated detection and analysis of elementary Ca2+ release events (ECRE) based on the two-dimensional nondecimated wavelet transform. The transform is computed with the "à trous" algorithm using the cubic B-spline as the basis function and yields a multiresolution analysis of the image. This transform allows for highly efficient noise reduction while preserving signal amplitudes. ECRE detection is performed at the wavelet levels, thus using the whole spectral information contained in the image. The algorithm was tested on synthetic data at different noise levels as well as on experimental data of ECRE. The noise dependence of the statistical properties of the algorithm (detection sensitivity and reliability) was determined from synthetic data and detection parameters were selected to optimize the detection of experimental ECRE. The wavelet-based method shows considerably higher detection sensitivity and less false-positive counts than previously employed methods. It allows a more efficient detection of elementary Ca2+ release events than conventional methods, in particular in the presence of elevated background noise levels. The subsequent analysis of the morphological parameters of ECRE is reliably reproduced by the analysis procedure that is applied to the median filtered raw data. Testing the algorithm more rigorously showed that event parameter histograms (amplitude, rise time, full duration at half-maximum, and full width at half-maximum) were faithfully extracted from synthetic, "in-focus" and "out-of-focus" line scan sparks. Most importantly, ECRE obtained with laser scanning confocal microscopy of chemically skinned mammalian skeletal muscle fibers could be analyzed automatically to reproducibly establish event parameter histograms. In summary, our method provides a new valuable tool for highly reliable automated detection of ECRE in muscle but can also be adapted to other preparations.     

A common goodness-of-fit framework for neural population models using marked point process time-rescaling

The noisy threshold regime, where even a small set of presynaptic neurons can significantly affect postsynaptic spike-timing, is suggested as a key requisite for computation in neurons with high variability. It also has been proposed that signals under the noisy conditions are successfully transferred by a few strong synapses and/or by an assembly of nearly synchronous synaptic activities. We analytically investigate the impact of a transient signaling input on a leaky integrate-and-fire postsynaptic neuron that receives background noise near the threshold regime. The signaling input models a single strong synapse or a set of synchronous synapses, while the background noise represents a lot of weak synapses. We find an analytic solution that explains how the first-passage time (ISI) density is changed by transient signaling input. The analysis allows us to connect properties of the signaling input like spike timing and amplitude with postsynaptic first-passage time density in a noisy environment. Based on the analytic solution, we calculate the Fisher information with respect to the signaling input’s amplitude. For a wide range of amplitudes, we observe a non-monotonic behavior for the Fisher information as a function of background noise. Moreover, Fisher information non-trivially depends on the signaling input’s amplitude; changing the amplitude, we observe one maximum in the high level of the background noise. The single maximum splits into two maximums in the low noise regime. This finding demonstrates the benefit of the analytic solution in investigating signal transfer by neurons.     

A comparison of three noise reduction procedures applied to bird vocal signals

ABSTRACT.   Recordings of avian vocal signals in natural habitats include ambient noise. Often this background noise corrupts across all frequencies and is of substantial amplitude. Reducing this ambient noise to prepare vocal signals for playback stimuli or to remove habitat-specific noise signatures prior to analyzing a signal's acoustic characteristics can be useful. We conducted experimental evaluations of three noise reduction procedures to determine their effectiveness. We embedded two bird vocalizations ("clean" signals) in four kinds of natural noise, resulting in eight noise-signal combinations. We then applied three noise reduction procedures (Noise Profile, Band Pass, and Noise Estimate) to each of the embedded signals and compared the recovered signals to the original (clean) signals. Noise Profile filtering was effective in reducing noise and returning fairly high-quality signals from even severe levels of masking noise. The other two noise reduction procedures did not perform as well. For the two most corrupting maskers, however, Noise Profile filtering also altered the signal properties by reducing signal amplitude at those frequencies containing high levels of noise. Apart from this loss of amplitude, the quantitative features of the filtered signals were similar to those of the original model sounds. We conclude that Noise Profile filtering produces good results for cases where noise is approximately constant over the signal duration and the signal intensity exceeds noise intensity over the frequencies of interest.     

Comparison of different methods of time shift measurement in EEG

Digital signal processing techniques are often used for measurement of small time shifts between EEG signals. In our work we tested properties of linear cross-correlation and phase/coherence method. The last mentioned method was used in two versions. The first version used fast Fourier transform (FFT) algorithm and the second was based on autoregressive modeling with fixed or adaptive model order. Methods were compared on several testing signals mimicking real EEG signals. The accuracy index for each method was computed. Results showed that for long signal segments all methods bring comparably good results. Accuracy of FFT phase/coherence method significantly decreased when very short segments were used and also decreased with an increasing level of the additive noise. The best results were obtained with autoregressive version of phase/coherence. This method is more reliable and may be used with high accuracy even in very short signals segments and it is also resistant to additive noise.     

Restoration of single-channel currents using the segmental k-means method based on hidden Markov modeling

Patch-clamp recording provides an unprecedented means for study of detailed kinetics of ion channels at the single molecule level. Analysis of the recordings often begins with idealization of noisy recordings into continuous dwell-time sequences. Success of an analysis is contingent on accuracy of the idealization. I present here a statistical procedure based on hidden Markov modeling and k-means segmentation. The approach assumes a Markov scheme involving discrete conformational transitions for the kinetics of the channel and a white background noise for contamination of the observations. The idealization is sought to maximize a posteriori probability of the state sequence corresponding to the samples. The approach constitutes two fundamental steps. First, given a model, the Viterbi algorithm is applied to determine the most likely state sequence. With the resultant idealization, the model parameters are then empirically refined. The transition probabilities are calculated from the state sequences, and the current amplitudes and noise variances are determined from the ensemble means and variances of those samples belonging to the same conductance classes. The two steps are iterated until the likelihood is maximized. In practice, the algorithm converges rapidly, taking only a few iterations. Because the noise is taken into explicit account, it allows for a low signal/noise ratio, and consequently a relatively high bandwidth. The approach is applicable to data containing subconductance levels or multiple channels and permits state-dependent noises. Examples are given to elucidate its performance and practical applicability.     

Background noise from a natural chorus alters female discrimination of male calls in a Neotropical frog

Many animals communicate in environments with high levels of background noise. Although it is a fundamental prediction of signal detection theory that noise should reduce both detection and discrimination of signals, little is known about these effects in animal communication. Female treefrogs, Hyla ebraccata, in Costa Rica choose mates in large noisy multispecies choruses. We tested gravid females for preferences between computer-synthesized calls with carrier frequencies of 3240 and 2960 Hz (values near the mode and the fifth percentile of the population, respectively) in four levels of background noise from a natural chorus. In the absence of noise (signal/noise ratio >25 dB), females preferred the lower frequency. With moderate signal/noise ratios (6 and 9 dB), they did not discriminate between these frequencies. With low signal/noise ratios (3 dB), females preferred the frequency near the mode for the population. Similar experiments had previously demonstrated that females can detect the presence of a male's calls with signal/noise ratios of 3 dB or greater. Thus moderate levels of natural background sound reduced a female's ability to discriminate between males' calls even when she could detect them. In high levels of background sound, females abandoned discrimination for low-frequency calls and reverted to the task of detecting signals with modal properties for the population. These results justify recent theoretical analyses of the importance of receivers' errors in the evolution of communication.