A Kalman filter-based approach to reduce the effects of geometric errors and the measurement noise in the inverse ECG problem

In this article, we aimed to reduce the effects of geometric errors and measurement noise on the inverse problem of Electrocardiography (ECG) solutions. We used the Kalman filter to solve the inverse problem in terms of epicardial potential distributions. The geometric errors were introduced into the problem via wrong determination of the size and location of the heart in simulations. An error model, which is called the enhanced error model (EEM), was modified to be used in inverse problem of ECG to compensate for the geometric errors. In this model, the geometric errors are modeled as additive Gaussian noise and their noise variance is added to the measurement noise variance. The Kalman filter method includes a process noise component, whose variance should also be estimated along with the measurement noise. To estimate these two noise variances, two different algorithms were used: (1) an algorithm based on residuals, (2) expectation maximization algorithm. The results showed that it is important to use the correct noise variances to obtain accurate results. The geometric errors, if ignored in the inverse solution procedure, yielded incorrect epicardial potential distributions. However, even with a noise model as simple as the EEM, the solutions could be significantly improved

Spectral analysis of T wave alternans signal

T wave alternans signal was obtained from a patient who recently recovered from ventricular fibrillation. The power spectrum of the T wave alternans is computed using an Autoregressive model based technique. The signal is found to be a sinusoid at a frequency equal to the half of the heart rate and amplitude modulated with another sinusoid at a lower frequency. Relation between the spectrums of the T wave alternance signal and the RR variation signal is also discussed

Lanczos bidiagonalization-based inverse solution methods applied to electrical imaging of the heart by using reduced lead-sets: A simulation study

In inverse problem of electrocardiography (ECG), electrical activity of the heart is estimated from body surface potential measurements. This electrical activity provides useful information about the state of the heart, thus it may help clinicians diagnose and treat heart diseases before they cause serious health problems. For practical application of the method, having fewer number of electrodes for data acquisition is an advantage. Additionally, inverse problem of ECG is ill-posed due to attenuation and smoothing within the body. Therefore, the solution of ECG inverse problem has to be regularized. In this study, we constrain ourselves to two Lanczos-bidiagonalization-based inverse solution methods, namely, Lanczos least-squares QR (L-LSQR) factorization and Lanczos truncated total least-squares (L-TTLS). Tikhonov regularization is also implemented as a base for comparison for these methods. We use body surface measurements simulated using epicardial potentials measured from the surface of canine hearts. In these experiments, the hearts are stimulated from the ventricles at various sites, mimicking ectopic beats. Torso potentials are obtained from these epicardial measurements by multiplying them with the forward transfer matrix and adding Gaussian distributed noise. We solve the inverse problem using different number of leads on the body surface (771, 192, 64, and 32 leads), and assess the performances of these regularization methods for the reduced lead-sets. These reduced lead-sets are selected from the primary 771-lead configuration by using two main approaches. The first approach is manually selecting appropriate leads, and the second one uses the inverse problem approach to select leads sequentially. The results show that the L-TTLS method is more successful in reconstructing epicardial potentials than the L-LSQR method. The L-TTLS method is faster than the Tikhonov regularization, since it benefits from bidiagonal form of the forward matrix. Reducing the number of electrodes to 64 has a small effect on the solutions, but with 32 leads, inverse solutions get less precise, and the difference between the results of Tikhonov regularization and L-TTLS method becomes less significant

Nf2–Yap signaling controls the expansion of DRG progenitors and glia during DRG development

AbstractMolecular mechanisms governing the maintenance and proliferation of dorsal root ganglia (DRG) progenitors are largely unknown. Here we reveal that the Hippo pathway regulates the expansion of DRG progenitors and glia during mammalian DRG development. The key effectors of this pathway, transcriptional coactivators Yap and Taz, are expressed in DRG progenitors and glia during DRG development but are at least partially inhibited from activating transcription. Aberrant YAP activation leads to overexpansion of DRG progenitor and glial populations. We further show that the Neurofibromatosis 2 (Nf2) tumor suppressor inhibits Yap during DRG development. Loss of Nf2 leads to similar phenotypes as does YAP hyperactivation, and deleting Yap suppresses these phenotypes. Our study demonstrates that Nf2–Yap signaling plays important roles in controlling the expansion of DRG progenitors and glia during DRG development

Implications of Price Dispersions in Producers Markets

In this paper, 'snore regularity' is studied in terms of the variations of snoring sound episode durations, separations and average powers in simple snorers and in obstructive sleep apnoea (OSA) patients. The goal was to explore the possibility of distinguishing among simple snorers and OSA patients using only sleep sound recordings of individuals and to ultimately eliminate the need for spending a whole night in the clinic for polysomnographic recording. Sequences that contain snoring episode durations (SED), snoring episode separations (SES) and average snoring episode powers (SEP) were constructed from snoring sound recordings of 30 individuals (18 simple snorers and 12 OSA patients) who were also under polysomnographic recording in Gülhane Military Medical Academy Sleep Studies Laboratory (GMMA-SSL), Ankara, Turkey. Snore regularity is quantified in terms of mean, standard deviation and coefficient of variation values for the SED, SES and SEP sequences. In all three of these sequences, OSA patients' data displayed a higher variation than those of simple snorers. To exclude the effects of slow variations in the base-line of these sequences, new sequences that contain the coefficient of variation of the sample values in a 'short' signal frame, i.e., short time coefficient of variation (STCV) sequences, were defined. The mean, the standard deviation and the coefficient of variation values calculated from the STCV sequences displayed a stronger potential to distinguish among simple snorers and OSA patients than those obtained from the SED, SES and SEP sequences themselves. Spider charts were used to jointly visualize the three parameters, i.e., the mean, the standard deviation and the coefficient of variation values of the SED, SES and SEP sequences, and the corresponding STCV sequences as two-dimensional plots. Our observations showed that the statistical parameters obtained from the SED and SES sequences, and the corresponding STCV sequences, possessed a strong potential to distinguish among simple snorers and OSA patients, both marginally, i.e., when the parameters are examined individually, and jointly. The parameters obtained from the SEP sequences and the corresponding STCV sequences, on the other hand, did not have a strong discrimination capability. However, the joint behaviour of these parameters showed some potential to distinguish among simple snorers and OSA patients