Kubios HRV--heart rate variability analysis software.

Kubios HRV is an advanced and easy to use software for heart rate variability (HRV) analysis. The software supports several input data formats for electrocardiogram (ECG) data and beat-to-beat RR interval data. It includes an adaptive QRS detection algorithm and tools for artifact correction, trend removal and analysis sample selection. The software computes all the commonly used time-domain and frequency-domain HRV parameters and several nonlinear parameters. There are several adjustable analysis settings through which the analysis methods can be optimized for different data. The ECG derived respiratory frequency is also computed, which is important for reliable interpretation of the analysis results. The analysis results can be saved as an ASCII text file (easy to import into MS Excel or SPSS), Matlab MAT-file, or as a PDF report. The software is easy to use through its compact graphical user interface. The software is available free of charge for Windows and Linux operating systems at http://kubios.uef.fi.

Tracking single-trial evoked potential changes with Kalman filtering and smoothing.

A mathematical way to describe trial-to-trial variations in evoked potentials (EPs) is given by state-space modeling. Linear estimators optimal in the mean square sense can then be obtained through Kalman filter and smoother algorithms. Of importance are the parametrization of the problem and the selection of an observation model for estimation. In this paper, we introduce a general way for designing a model for dynamical estimation of EPs. The observation model is constructed based on a finite impulse response (FIR) filter and can be used for different kind of EPs. We also demonstrate that for batch processing the use of the smoother algorithm is preferable. The method is demonstrated with measurements obtained from an experiment with visual stimulation.

Estimation of single-trial fMRI BOLD responses using combined EEG and fMRI measurements.

In this paper, we present a method for modeling human brain response using combined fMRI and EEG measurements. A subspace is formed using the eigenvectors of data correlation matrix of augmented measurements. This subspace is then used for regularization of the fitting of parametric model to fMRI BOLD signal. The approach is utilized for single-trial estimation of blood oxygenation level dependent (BOLD) responses in fMRI time series.

A subspace method for dynamical estimation of evoked potentials.

It is a challenge in evoked potential (EP) analysis to incorporate prior physiological knowledge for estimation. In this paper, we address the problem of single-channel trial-to-trial EP characteristics estimation. Prior information about phase-locked properties of the EPs is assesed by means of estimated signal subspace and eigenvalue decomposition. Then for those situations that dynamic fluctuations from stimulus-to-stimulus could be expected, prior information can be exploited by means of state-space modeling and recursive Bayesian mean square estimation methods (Kalman filtering and smoothing). We demonstrate that a few dominant eigenvectors of the data correlation matrix are able to model trend-like changes of some component of the EPs, and that Kalman smoother algorithm is to be preferred in terms of better tracking capabilities and mean square error reduction. We also demonstrate the effect of strong artifacts, particularly eye blinks, on the quality of the signal subspace and EP estimates by means of independent component analysis applied as a prepossessing step on the multichannel measurements.

Time-varying analysis of heart rate variability signals with a Kalman smoother algorithm.

A time-varying parametric spectrum estimation method for analysing non-stationary heart rate variability signals is presented. As a case study, the dynamics of heart rate variability during an orthostatic test is examined. In this method, the non-stationary signal is first modelled with a time-varying autoregressive model and the model parameters are estimated recursively with a Kalman smoother algorithm. The benefit of using the Kalman smoother is that the lag error present in a Kalman filter, as well as in all other adaptive filters, can be avoided. The spectrum estimates for each time instant are then obtained from the estimated model parameters. Statistics of the obtained spectrum estimates are derived using the error propagation principle. The obtained spectrum estimates can further be decomposed into separate components and, thus, the time variation of low- and high-frequency components of heart rate variability can be examined separately. By using the presented method, high resolution time-varying spectrum estimates with no lag error can be produced. Other benefits of the method are the straightforward procedure for evaluating the statistics of the spectrum estimates and the option of spectral decomposition.

Relationship of P300 single-trial responses with reaction time and preceding stimulus sequence.

Variation of single-trial P300 responses was studied both in relation to reaction times and to the preceding stimulus sequence in an auditory oddball paradigm. Single-trial responses were estimated with the Subspace regularization method that is based on Bayesian estimation and linear modeling. The results of the single-trial method were compared to those of averaging. Both methods showed that the latency of the P300 was shorter and its amplitude larger for faster than slower reaction times. The P300 latency was shorter for target tones that were preceded by a large number of standard tones compared to those preceded by a small number of standard tones. The P300 amplitude was statistically significantly affected by the stimulus sequence only when analyzed with conventional averaging. In-depth analysis of standard deviations showed that the variability of the P300 single-trial latencies could explain the differences between the two methods. Specifically, the regression analysis showed that the latency correlated negatively with the number of preceding standard tones and positively with the reaction time, whereas the P300 amplitude correlated positively with the number of the preceding standard stimuli and negatively with the reaction time. The analysis of the single-trial responses gives information about the behavior of the P300 component that is lost with conventional averaging. The method used in this study is independent of subjective decision making and can be used to model changes in the dynamical behavior of the P300 component objectively.

Single-trial dynamical estimation of event-related potentials: a Kalman filter-based approach.

A method for single-trial dynamical estimation of event-related potentials (ERPs) is presented. The method is based on recursive Bayesian mean square estimation and the estimators are obtained with a Kalman filtering procedure. We especially focus on the case that previous trials contain prior information of relevance to the trial being analyzed. The potentials are estimated sequentially using the previous estimates as prior information. The performance of the method is evaluated with simulations and with real P300 responses measured using auditory stimuli. Our approach is shown to have excellent capability of estimating dynamic changes form stimulus to stimulus present in the parameters of the ERPs, even in poor signal-to-noise ratio (SNR) conditions.

High-resolution QRS fiducial point corrections in sparsely sampled ECG recordings.

A model based high-resolution QRS fiducial point correction algorithm, which is suitable for sparsely sampled electrocardiogram (ECG) recordings, is presented. The presented method can be divided into three steps. First, the initial QRS fiducial points are estimated by using ordinary interpolation methods. Then, the data points of each QRS are extracted and centered in time and the shape of the QRS complex is estimated by nonlinearly fitting a double exponential function to the extracted data points. Finally, the estimated model and its derivative are linearly fitted to the data points of each QRS complex separately and new fiducial point estimates are obtained. The proposed method is tested with simulations and real ECG data. As a result, it is observed that the proposed method is also suitable for asymmetric QRS complexes unlike, e.g., the commonly used cubic spline interpolation method.

Software for advanced HRV analysis.

A computer program for advanced heart rate variability (HRV) analysis is presented. The program calculates all the commonly used time- and frequency-domain measures of HRV as well as the nonlinear Poincaré plot. In frequency-domain analysis parametric and nonparametric spectrum estimates are calculated. The program generates an informative printable report sheet which can be exported to various file formats including the portable document format (PDF). Results can also be saved as an ASCII file from which they can be imported to a spreadsheet program such as the Microsoft Excel. Together with a modern heart rate monitor capable of recording RR intervals this freely distributed program forms a complete low-cost HRV measuring and analysis system.

Estimation of nonstationary EEG with Kalman smoother approach: an application to event-related synchronization (ERS).

An adaptive spectrum estimation method for nonstationary electroencephalogram by means of time-varying autoregressive moving average modeling is presented. The time-varying parameter estimation problem is solved by Kalman filtering along with a fixed-interval smoothing procedure. Kalman filter is an optimal filter in the mean square sense and it is a generalization of other adaptive filters such as recursive least squares or least mean square. Furthermore, by using the smoother the unavoidable tracking lag of adaptive filters can be avoided. Due to the properties of Kalman filter and benefits of the smoothing the time-frequency resolution of the presented Kalman smoother spectra is extremely high. The presented approach is applied to estimation of event-related synchronization/desynchronization (ERS/ERD) dynamics of occipital alpha rhythm measured from three healthy subjects. With the Kalman smoother approach detailed spectral information can be extracted from single ERS/ERD samples.

An advanced detrending method with application to HRV analysis.

An advanced, simple to use, detrending method to be used before heart rate variability analysis (HRV) is presented. The method is based on smoothness priors approach and operates like a time-varying finite-impulse response high-pass filter. The effect of the detrending on time- and frequency-domain analysis of HRV is studied.