Validation in principal components analysis applied to EEG data.

The well-known multivariate technique Principal Components Analysis (PCA) is usually applied to a sample, and so component scores are subjected to sampling variability. However, few studies address their stability, an important topic when the sample size is small. This work presents three validation procedures applied to PCA, based on confidence regions generated by a variant of a nonparametric bootstrap called the partial bootstrap: (i) the assessment of PC scores variability by the spread and overlapping of "confidence regions" plotted around these scores; (ii) the use of the confidence regions centroids as a validation set; and (iii) the definition of the number of nontrivial axes to be retained for analysis. The methods were applied to EEG data collected during a postural control protocol with twenty-four volunteers. Two axes were retained for analysis, with 91.6% of explained variance. Results showed that the area of the confidence regions provided useful insights on the variability of scores and suggested that some subjects were not distinguishable from others, which was not evident from the principal planes. In addition, potential outliers, initially suggested by an analysis of the first principal plane, could not be confirmed by the confidence regions.

Assessing the combined performance of texture and morphological parameters in distinguishing breast tumors in ultrasound images.

PURPOSE: This work aims to investigate the combination of morphological and texture parameters in distinguishing between malignant and benign breast tumors in ultrasound images. METHODS: Linear discriminant analysis was applied to sets of up to five parameters, and then the performances were assessed using the area A(z) (± standard error) under the receiver operator characteristic curve, accuracy (Ac), sensitivity (Se), specificity (Sp), positive predictive value, and negative predictive value. RESULTS: The most relevant individual parameter was the normalized residual value (nrv), calculated from the convex polygon technique. The best performance among all studied combinations was achieved by two morphological and three texture parameters (nrv, con, std, R, and asm(i)), which correctly distinguished nearly 85% of the breast tumors. CONCLUSIONS: This result indicates that the combination of morphological and texture parameters may be useful to assist physicians in the diagnostic process, especially if it is associated with an automatic classification tool.

Multiple Coherence vs Multiple Component Synchrony Measure for somatosensory evoked response detection.

This work aims at comparing the performance of two Multivariate Objective Response Detection (MORD) techniques in the frequency domain, the Multiple Coherence (MC) and the Multiple Component Synchrony Measure (MCSM), for tibial nerve somatosensory evoked potential (SEP) detection. Electroencephalographic (EEG) signals during somatosensory stimulation were collected from forty adult volunteers using the 10-20 International System. The stimulation was carried out throughout current pulses (200 µs width) applied to the right posterior tibial nerve (motor threshold intensity level) at the rate of 5 Hz. The response detection was based on rejecting the null hypothesis of response absence (M = 100 and M = 800 epochs and significance level α = 0.05). The MORD techniques were applied to the pairs of derivations [Cz][Fz] and [C3][C4]. The MC outperforms the MCSM, regardless the pair of derivations or the number of epochs used for the estimates calculation. Hence, the MC should be used, if two derivations are available for SEP recording.

A non-linear morphometric feature selection approach for breast tumor contour from ultrasonic images.

Ultrasound breast images have been used to improve diagnostics and decrease the number of unneeded biopsies. Malignant breast tumors tend to present irregular and blurred contours while benign ones are usually round, smooth and well-defined. Accordingly, investigating the tumor contour may help in establishing diagnosis. Herein, Mutual Information and Linear Discriminant Analysis were implemented to rank morphometric features in discriminating breast tumors in ultrasound images. Seven features were extracted from Convex Polygon and the Normalized Radial Length techniques. By applying a Mutual Information based approach, it was possible to identity features with possibly non-linear contributions to the outcome.

Assessing the performance of morphological parameters in distinguishing breast tumors on ultrasound images.

This work aims at investigating seven morphological parameters in distinguishing malignant and benign breast tumors on ultrasound images. Linear discriminant analysis was applied to sets of up to five parameters and then the performances were assessed using the area Az (+/- standard error) under the ROC curve, accuracy (Ac), sensitivity (Se), specificity (Sp), positive predictive value and negative predictive value. The most relevant individual parameters were the normalized residual value (nrv) and overlap ratio (RS), both calculated from the convex polygon technique, and the circularity (C). When nrv and C were taken together with roughness (R), calculated from normalized radial length (NRL), a performance slightly over 83% in distinguishing malignant and benign breast tumors was achieved.

Multiple correspondence analysis in predictive logistic modelling: application to a living-donor kidney transplantation data.

This work deals with the use of multiple correspondence analysis (MCA) and a weighted Euclidean distance (the tolerance distance) as an exploratory tool in developing predictive logistic models. The method was applied to a living-donor kidney transplant data set with 109 cases and 13 predictors. This approach, followed by backward and forward selection procedures, yielded two models, one with four and another with two predictors. These models were compared to two other models, ordinarily built by backward and forward stepwise selection, which yielded, respectively, five and two predictors. After internal validation, the models performance statistics showed similar results. Likelihood ratio tests suggested that backward approach achieved a better fit than the forward modelling in both methods and the Vuong's non-nested test between backward-built models suggested that these were undistinguishable. We conclude that the tolerance distance, in combination with MCA, could be a feasible method for variable selection in logistic modelling, when there are several categorical predictors.

A heuristic index for selecting similar categories in multiple correspondence analysis applied to living donor kidney transplantation.

This work introduces a heuristic index (the "tolerance distance") to define the "closeness" of two variable categories in multiple correspondence analysis (MCA). This index is a weighted Euclidean distance where weightings are based on the "importance" of each MCA axis, and variable categories were considered to be associated when their distances were below the tolerance distance. This approach was applied to a renal transplantation data. The analysed variables were allograft survival and 13 of its putative predictors. A bootstrap-based stability analysis was employed for assessing result reliability. The method identified previously detected associations within the database, such as that between race of donors and recipients, and that between HLA match and Cyclosporine use. A hierarchical clustering algorithm was also applied to the same data, allowing for interpretations similar to those based on MCA. The defined tolerance distance could thus be used as an index of "closeness" in MCA, hence decreasing the subjectivity of interpreting MCA results.

A multiple coherence-based detector for evoked responses in the EEG during sensory stimulation.

The sampling distribution of the multiple coherence estimate between a periodic signal and a set of filtered versions of evoked responses embedded in additive noise signals is derived for the zero-coherence case. For a fixed number of signals used in the estimation, the probability density function varies with the number of data segments. Analytical expressions for both bias and variance of the estimate were derived and together with the critical values constitute the statistical apparatus for the detector based on this multiple coherence estimate. An illustration of the technique as applied to detect evoked responses in the Electroencephalogram during sensory stimulation is also provided.

Evaluating the event-related synchronization and desynchronization by means of a statistical frequency test.

In the present work, a commonly used index for evaluating the Event-Related Synchronization and Desynchronization (ERS/ERD) in the EEG was expressed as a function of the Spectral F-Test (SFT), which is a statistical test for assessing if two sample spectra are from populations with identical theoretical spectra. The sampling distribution of SFT has been derived, allowing hence ERS/ERD to be evaluated under a statistical basis. An example of the technique was also provided in the EEG signals from 10 normal subjects during intermittent photic stimulation.

Evaluating the relationship of non-phase locked activities in the electroencephalogram during intermittent stimulation: a partial coherence-based approach.

Partial coherence estimate between two signals removing the contribution of a periodic, deterministic one is proposed for measuring the coherence between two ongoing eletroencephalografic (EEG) activities collected at distinct cortical regions under sensory stimulation. The estimator expression was derived and shown to be independent of the stimulating signal. Simulations were used for obtaining the critical values for this coherence estimate. The technique was also evaluated throughout simulations and next applied to the EEG from 12 subjects under intermittent photic stimulation at 4 and 6 Hz. In both simulation and EEG data, major differences between partial and simple coherences occurred at the stimulation frequency and harmonics, except for those falling within the alpha band. These findings suggest that the technique is highly selective in removing the contribution of the periodic source. They also indicate high coherence values of the ongoing EEG within the alpha band.

Complexity curve and grey level co-occurrence matrix in the texture evaluation of breast tumor on ultrasound images.

This work aims at investigating texture parameters in distinguishing malign and benign breast tumors on ultrasound images. A rectangular region of interest (ROI) containing the tumor and its neighboring was defined for each image. Five parameters were extracted from the complexity curve (CC) of the ROI. Another five parameters were calculated from the grey-level co-occurrence matrix (GLCM) also for the ROI. The same was carried out for internal tumor region, hence, totaling 20 parameters. The linear discriminant analysis was applied to sets of up to five parameters and then the performances were assessed. The most relevant individual parameters were the contrast (con) (from the GLCM over the ROI) and the maximum value (mvi) from the CC just for the tumor internal region). When they were taken together, a correct classification slightly over 80% of the breast tumors was achieved. The highest performance (accuracy=84.2%, sensitivity=87.0%, and specificity=78.8%) was obtained with mvi, con, the standard deviation of the pixel pairs and the entropy, both for GLCM, and the internal region contrast also from GLCM. Parameters extracted from the internal region generally performed better and were more significant than those from the ROI. Moreover, parameters calculated only from CC or GLCM resulted in no statistically significant performance difference. These findings suggest that the texture parameters can be useful to help radiologist in distinguishing between benign or malign breast tumors on ultrasound images.

Spectral F-test power evaluation in the EEG during intermittent photic stimulation.

Intermittent photic stimulation (IPS) is an important functional test, which can induce the photic driving in the electroencephalogram (EEG). It is capable of enhancing latent oscillations manifestations not present in the resting EEG. However, for adequate quantitative evaluation of the photic driving, these changes should be assessed on a statistical basis. With this aim, the sampling distribution of spectral F test was investigated. On this basis, confidence limits of the SFT-estimate could be obtained for different practical situations, in which the signal-to-noise ratio and the number of epochs used in the estimation may vary. The technique was applied to the EEG of 10 normal subjects during IPS, and allowed detecting responses not only at the fundamental IPS frequency but also at higher harmonics. It also permitted to assess the strength of the photic driving responses and to compare them in different derivations and in different subjects.

Spectral F-Test power evaluation in the EEG during intermittent photic stimulaton

A fotoestimulação intermitente (FEI) é um importante teste functional, que pode induzir o fotorecrutamento no eletroencefalograma (EEG), sendo capaz de realçar manifestações latentes de oscilações não observadas no EEG de repouso. Entretanto, para uma análise quantitativa adequada do fotorecrutamento, tais alterações devem ser avaliadas com base estatística. Assim, a distribuição de probabilidade do teste-F espectral (TFE) foi investigada. Neste sentido, limites de confiança para a estimativa do TFE puderam ser obtidos para diferentes situações práticas, nas quais a razão sinal-ruído e o número de épocas usadas na estimação podem variar. A técnica foi aplicada ao EEG de 10 sujeitos normais durante FEI, e permitiu a detecção de respostas não somente na freqüência fundamental da FEI como também em seus harmônicos. Além disso, permitiu avaliar o grau de fotorecrutamento entre derivações distintas e entre diferentes sujeitos.

A coherence-based technique for separating phase-locked from non-phase-locked power spectrum estimates during intermittent stimulation.

In addition to evoked responses, which are phase-locked to the stimuli, the stimulation may also change the ongoing EEG in a time-locked manner. This change has been investigated in event-related synchronization/desynchronization (ERS/ERD) studies by comparing the spectra before and during stimulation or alternatively by using the intertrial variance method (IVM). In the present work, a technique based on the coherence estimate (kappa(y)(2)(f)) between the stimulation signal and the EEG is proposed for separating the ongoing EEG activity spectrum from that of the evoked responses. Furthermore, a statistical criterion is applied to reduce spurious spectral peaks. The performance of this procedure was assessed through simulation and illustrated with EEG during photic stimulation. For simulated data (signal-to-noise-ratio of 0.995 within 10-12.5 Hz) kappa(y)(2)(f) led to a non-phase-locked spectrum estimate with an average normalized error of 12.4%, which is reduced to only 0.2% after applying the statistical criterion. The methodology proposed is asymptotically equivalent to the IVM but it does not require previous filtering the EEG data. Kappa(y)(2)(f) together with the statistical correction criterion allows investigating the entrainment within a narrow-band range, particularly in frequencies close to that of the alpha peak. Hence it is useful in ERS/ERD studies. Moreover, it can be also used for characterizing frequencies within the gamma band.

Estimation of coherence between blood flow and spontaneous EEG activity in neonates.

Blood flow to the brain responds to changes in neuronal activity and, thus, metabolic demand. In earlier work, we observed correlation between cerebral blood flow and spontaneous electroencephalogram (EEG) activity in neonates. Using coherence, we now found that during Tracé Alternant EEG activity in quiet sleep of normal term neonates, this correlation is strongest at frequencies around 0.1 Hz, reaching statistical significance (p < 0.05) in six of the nine subjects studied (p < 0.07 in eight subjects). Due to noise, artifact, and spontaneous changes in the subjects' EEG patterns, the signals investigated included epochs of missing samples. We, therefore, developed a novel algorithm for the estimation of coherence in such data and applied a Monte Carlo (surrogate data) method for its statistical analysis. This process provides a test for the statistical significance of the maximum coherence within a selected frequency band. In addition to permitting further insight into the mechanisms of cerebral blood flow control, these algorithms are potentially of great benefit in a wide range of biomedical applications, where interrupted (gapped) recordings are often a problem.

A matrix-based algorithm for estimating multiple coherence of a periodic signal and its application to the multichannel EEG during sensory stimulation.

The coherence between the stimulation signal and the electroencephalogram (EEG) has been used in the detection of evoked responses. The detector's performance, however, depends on both the signal-to-noise ratio (SNR) of the responses and the number of data segments (M) used in coherence estimation. In practical situations, when a given SNR occurs, detection can only be improved by increasing M and hence the total data length. This is particularly relevant when monitoring is the objective. In the present study, we propose a matrix-based algorithm for estimating the multiple coherence of the stimulation signal taking into account a set of N EEG channels as a way of increasing the detection rate for a fixed value of M. Monte Carlo simulations suggest that thresholds for such multivariate detector are the same as those for multiple coherence of Gaussian signals and that using more than six signals is not advisable for improving the detection rate with M = 10. The results with EEG from 12 normal subjects during photic stimulation at 10 Hz showed a maximum detection for N greater than 2 in 58% of the subjects with M = 10, and hence suggest that the proposed multivariate detector is valuable in evoked responses applications.

Artificial neural networks for infant mortality modelling.

This work aims to investigate a simple to use and easy to interpret methodology for assessing the relative importance of input variables in artificial neural networks (ANNs) applied to epidemiological modelling. The independent variables were 43 variables of the social, economic, environmental and health sector of 59 Brazilian municipalities, and the outcomes were infant mortality rates from these municipalities. Two assays were developed for the ANN modelling. On the first, all 43 variables were taken as input; and on the second, input variables were chosen with the help of factor analysis (FA). The relative importance of the input variables was investigated by means of bootstrap replications of the ANN model on the second assay. Further, multiple linear regression models (LRMs) were developed with the same data set and compared to the ANN models. The FA analysis allowed the selection of eight variables for the second assay. The percent of explained variance R(2) on the ANNs was in the range 0.74-0.80, while linear models had R(2)=0.4-0.5. These findings were validated by the bootstrap replications, in which the ANN models remained with higher R(2) and lower mean square error than the LRMs. The analysis of the best (second) ANN model indicated the highest ranking of importance for the variables literacy, agricultural and livestock sector jobs, number of commercial establishments and telephones. The approach presented here successfully integrated a data-oriented model with expert knowledge, indicating the potentiality of ANN modelling in the prediction, planning and assessment of public health actions.

Resoluçäo espacial em mapas cerebrais após derivaçäo da fonte / Spatial resolution in brain map after source derivation

As interpolações, planar spline (PS) e 4-vizinhos-mais-próximos (NN), foram investigadas para o mapeamento cerebral após Derivação da Fonte. Distribuições simuladas com componentes de alta freqüência espacial (dipolos próximos ao scalpo) e 28 eletrodos resultaram em melhor localização de dipolos ao empregar-se a NN, em paarticipar para dipolos subjacentes aos pontos de captação. Entretanto, aumento na confiabilidade da localização de fontes depende de uma maior densidade de eletrodos.

Comparaçäo de técnicas de interpolaçäo para mapeamento topográfico cerebral / Comparison between interpolationfot brain for brain topography mapping

Utilizando distribuição de potencial simulada, técnicas de interpolação (4-vizinhos, Spline Planar e Spline Esférica) foram usadas na reconstrução de mapas topográficos cerebrais. Os resultados quantitativos indicam que o desempenho destas técnicas depende fortemente da profundidade das fontes cerebrais e de sua localização em relação aos eletrodos.

Estudo comparativo entre a coerência parcial e a derivaçäo da fonte no EEG / Comparative study between partial coherence and the EEG source derivation

Tanto a correlação/coerência após a Derivação da Fonte (DP) quanto a Coerência Parcial (CP) têm sido empregadas na quantificação da similaridade entre dois sinais EEG de regiões cerebrais distintas, após remoção da contribuição de regiões vizinhas. Apesar de poderem ser aplicadas para fins semelhantes, estas técnicas diferem conceitualmente, podendo levar a resultados diferentes. Este trabalho objetiva mostrar algumas das diferenças destas técnicas na análise do EEG.