Nonlinear analysis of the EEG of schizophrenics with optimal embedding dimension

We estimated the correlation dimensions of EEGs in patients with schizophrenia to investigate the dynamical properties underlying the EEG. We employed a new method, proposed by Kennel et al. (Kennel MB, Brown R, Abarbanel HDI. Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys Rev A 1992;45:3403-11), to calculate the correlation dimension D2. That method determined the proper minimum embedding dimension by looking at the behaviour of nearest neighbours under a change in the embedding dimension d from d to d + 1. We demonstrated that for limited noisy data, our algorithm was strikingly faster and more accurate than previous ones. We estimated the D2 of EEGs from 16 channels in patients with schizophrenia according to DSM-IV whereas previous studies, which estimated chaoticity of EEG in schizophrenia, recorded EEG only in a limited number of channels. Schizophrenic patients had a lower correlation dimension in the left inferior frontal and anterior temporal regions compared with controls. Our finding of decreased left frontal and temporal chaotic activity in schizophrenics is in line with the findings of a hypofrontality and hypotemporality reported in previous clinical studies such as EEG, blood flow, brain MRI and positron emission tomography studies in schizophrenia. This result suggests that chaos analysis may be a useful tool in analysing EEG data to explore the brain mechanism of schizophrenia.

Quantification of emotion by nonlinear analysis of the chaotic dynamics of electroencephalograms during perception of 1/f music

The goal of this study is to quantify and determine the way in which the emotional response to music is reflected in the electrical activities of the brain. When the power spectrum of sequences of musical notes is inversely proportional to the frequency on a log-log plot, we call it 1/f music. According to previous research, most listeners agree that 1/f music is much more pleasing than white (1/f0) or brown (1/f2) music. Based on these studies, we used nonlinear methods to investigate the chaotic dynamics of electroencephalograms (EEGs) elicited by computer-generated 1/f music, white music, and brown music. In this analysis, we used the correlation dimension and the largest Lyapunov exponent as measures of complexity and chaos. We developed a new method that is strikingly faster and more accurate than other algorithms for calculating the nonlinear invariant measures from limited noisy data. At the right temporal lobe, 1/f music elicited lower values of both the correlation dimension and the largest Lyapunov exponent than white or brown music. We observed that brains which feel more pleased show decreased chaotic electrophysiological behavior. By observing that the nonlinear invariant measures for the 1/f distribution of the rhythm with the melody kept constant are lower than those for the 1/f distribution of melody with the rhythm kept constant, we could conclude that the rhythm variations contribute much more to a pleasing response to music than the melody variations do. These results support the assumption that chaos plays an important role in brain function, especially emotion.

Non-linear dynamical analysis of the EEG in Alzheimer's disease with optimal embedding dimension

We used non-linear analysis to investigate the dynamical properties underlying the EEG in patients with Alzheimer's disease. We calculated the correlation dimension D2 and the first positive Lyapunov exponent L1. We employed a new method, which was proposed by Kennel et al., to calculate the non-linear invariant measures. That method determined the proper minimum embedding dimension by looking at the behavior of nearest neighbors under a change in the embedding dimension d from d to d + 1. We demonstrated that for limited noisy data, our algorithm was strikingly faster and more accurate than previous ones. Also, we found that, in almost all channels, patients with Alzheimer's disease had significantly lower D2 and L1 values than those for age-approximated healthy controls. These results suggest that brains afflicted by Alzheimer's disease show behaviors which are less chaotic than those of normal healthy brains. In this paper, we show that non-linear analysis can provide a fruitful tool for detecting relative changes, which cannot be detected by conventional linear analysis, in the complexity of brain dynamics. We propose that non-linear dynamical analyses of the EEGs from patients with Alzheimer's disease will be a diagnostic modality in the appropriate clinical setting.

A study on the cost-effectiveness of coronary revascularization: introducing the simultaneous mimic health status model

An econometric model is presented to compare the cost-effectiveness of two alternative procedures, percutaneous transluminal coronary angioplasty (PTCA) and coronary artery bypass surgery (CABG), for the treatment of multivessel coronary artery disease. This study utilizes the MIMIC (multiple indicator multiple cause) health model in a simultaneous equation system to analyse Emory Angioplasty Surgery Trial (EAST) data. This method eliminates the possibility of endogeneity bias, which may have affected the results of previous cost-effectiveness analyses on this topic. The empirical results indicate that neither procedure proves more cost-effective at 3 year follow-up.

Developmental regulation and phytochrome-mediated induction of mRNAs encoding a proline-rich protein, glycine-rich proteins, and hydroxyproline-rich glycoproteins in Phaseolus vulgaris L

We have studied developmental and light regulation of mRNAs encoding a putative cell wall proline-rich protein (PvPRP1), cell wall glycine-rich proteins (GRPs), and cell wall hydroxyproline-rich glycoproteins (HRGPs) in bean (Phaseolus vulgaris). Light increases the levels of these mRNAs 2- to 150-fold in highly spatially regulated patterns during seedling development. These mRNA changes include differential regulation of transcripts derived from the GRP and HRGP multigene families. In 6-day-old light-grown seedlings, the PvPRP1 and GRP1.0 mRNAs were most abundant in the apical region of hypocotyls, epicotyls, and roots. In contrast, several HRGP transcripts were most abundant in the mature region of hypocotyls and roots in light-grown seedlings. When etiolated 6-day-old seedlings were illuminated with white light for 8 hr, maximal accumulation of PvPRP1 and GRP1.0 mRNAs occurred in the apical hook, whereas HRGP and GRP1.8 mRNAs accumulated in the mature region of hypocotyls. Etiolated seedlings subjected to a pulse of red light accumulated PvPRP1, GRP, and HRGP mRNAs in the hypocotyls. Far-red light inhibited red light induction of these mRNAs, indicating a phytochrome-mediated process. The possible roles of PRPs, GRPs, and HRGPs in cell differentiation and photomorphogenesis are discussed.