Stress Response Analysis via Dynamic Entropy in EEG: Caregivers in View.

According to the World Health Organization (WHO), stress can be defined as any type of alteration that causes physical, emotional, or psychological tension. A very important concept that is sometimes confused with stress is anxiety. The difference between stress and anxiety is that stress usually has an existing cause. Once that activator has passed, stress typically eases. In this respect, according to the American Psychiatric Association, anxiety is a normal response to stress and can even be advantageous in some circumstances. By contrast, anxiety disorders differ from temporary feelings of anxiousness or nervousness with more intense feelings of fear or anxiety. The Diagnostic and Statistical Manual (DSM-5) explicitly describes anxiety as exorbitant concern and fearful expectations, occurring on most days for at least 6 months, about a series of events. Stress can be measured by some standardized questionnaires; however, these resources are characterized by some major disadvantages, the main one being the time consumed to interpret them; i.e., qualitative information must be transformed to quantitative data. Conversely, a physiological recourse has the advantage that it provides quantitative spatiotemporal information directly from brain areas and it processes data faster than qualitative supplies. A typical option for this is an electroencephalographic record (EEG). We propose, as a novelty, the application of time series (TS) entropies developed by us to inspect collections of EEGs obtained during stress situations. We investigated this database related to 23 persons, with 1920 samples (15 s) captured in 14 channels for 12 stressful events. Our parameters reflected that out of 12 events, event 2 (Family/financial instability/maltreatment) and 10 (Fear of disease and missing an important event) created more tension than the others. In addition, the most active lobes reflected by the EEG channels were frontal and temporal. The former is in charge of performing higher functions, self-control, self monitoring, and the latter is in charge of auditory processing, but also emotional handling. Thus, events E2 and E10 triggering frontal and temporal channels revealed the actual state of participants under stressful situations. The coefficient of variation revealed that E7 (Fear of getting cheated/losing someone) and E11 (Fear of suffering a serious illness) were the events with more changes among participants. In the same sense, AF4, FC5, and F7 (mainly frontal lobe channels) were the most irregular on average for all participants. In summary, by means of dynamic entropy analysis, the goal is to process the EEG dataset in order to elucidate which event and brain regions are key for all participants. The latter will allow us to easily determine which was the most stressful and on which brain zone. This study can be applied to other caregivers datasets. All this is a novelty.

Evaluation and Predictive Modeling of Removal Condition for Bioadsorption of Indigo Blue Dye by Spirulina platensis.

Among the different chemical and physical treatments used to remove the color of the textile effluents, bioremediation offers many benefits to the environment. In this study, we determined the potential of Spirulina platensis (S. platensis) for decolorizing indigo blue dye under different incubation conditions. The microalgae were incubated at different pH (from 4 to 10) to calibrate for the optimal discoloration condition; a pH of 4 was found to be optimal. The biomass concentration in all experiments was 1 g/L, which was able to decolorize the indigo blue dye by day 3. These results showed that S. platensis is capable of removing indigo blue dye at low biomass. However, this was dependent on the treatment conditions, where temperature played the most crucial role. Two theoretical adsorption models, namely (1) a first-order model equation and (2) a second-order rate equation, were compared with observed adsorption vs. time curves for different initial concentrations (from 25 to 100 mg/L). The comparison between models showed similar accuracy and agreement with the experimental values. The observed adsorption isotherms for three temperatures (30, 40, and 50 °C) were plotted, showing fairly linear behavior in the measured range. The adsorption equilibrium isotherms were estimated, providing an initial description of the dye removal capacity of S. platensis.

Understanding the evolution of pollutants via hierarchical complexity of space-time deterministic and stochastic dynamical systems.

This manuscript focuses on the implementation of the hierarchical complexity of space-time deterministic and stochastic dynamical systems to study the pollution dispersion behavior. Considering the concurrent environmental scope and requisites to understand the evolution of various types of environmentally related pollutants of high concern, herein, several suitable mathematical models are anticipated. Aiming to study the current pollution phenomenon at hand, we employed a lumped-linear or nonlinear structure and directly discussed in support of relevant equations. Up to some extent, by intuition, the researcher knows which model is more complex (suitable) than others, so the basic concepts are coated with linked references. Hence, the structural complexity features of the dynamical system are discussed in detail. The continuous dynamical system is discretized, and from the associated time series, a complexity measure can be obtained. There also exists a research gap on complexity theory, which generally deals with the behavior (solutions to the representing differential equations) in a system. Taking all these into account to cover the left behind literature gaps, herein, we propose to glimpse a family of classical models used to describe pollution and bacterial dispersion in the environment. From this review, we offer a qualitative complexity measure to each modeling paradigm by taking into account the underlying space of definition of the model and the key issue of the related differentiability. For instance, a lumped-linear set of differential equations is relatively simple with respect to its nonlinear counterpart because the former lives in the three-dimensional (3-D) real space R3, where the notion of differentiability shows up naturally. However, the latter needs to translate such conception to a manifold by means of differential geometry. Going further, we reflected on this issue for random systems where the notion of differentiability is transformed into an integral equivalence by means of Ito's lemma and so on for more exotic modeling perspectives. Moreover, the study presents a qualitative measure of complexity in terms of underlying sets and feasibility of differentiability.

Dynamic complexity measures and entropy paths for modelling and comparison of evolution of patients with drug resistant epileptic encephalopathy syndromes (DREES).

Epileptic encephalopathies (EE) is a term coined by the International League Against Epilepsy (ILAE) to refer to a group of epilepsies in which the ictal and interictal abnormalities may contribute to progressive cerebral dysfunction. Among them, two affect mainly children and are very difficult to deal with, Doose and Lennox-Gastaut syndromes, (DS and LGS, respectively). So far (Zavala-Yoe et al., J Integr Neurosci 15(2):205-223, 2015a and works of ours there), quantitative analysis of single case studies of EE have been performed. All of them are manifestations of drug resistant epileptic encephalopathies (DREES) and as known, such disorders require a lot of EEG studies through all patient's life. As a consequence, dozens of EEG records are stored by parents and neurologists as time goes by. However, taking into account all this massive information, our research questions (keeping colloquial wording by parents) arise: a) Which zone of the brain has been the most affected so far? b) On which year was the child better? c) How bad is our child with respect to others? We must reflect that despite clinical assessment of the EEG has undergone standardization by establishment of guidelines such as the recently published guidelines of the American Clinical Neurophysiology Society (Tsuchida et al., J Clin Neurophysiol 4(33):301-302, 2016), qualitative EEG will never be as objective as quantitative EEG, since it depends largely on the education and experience of the conducting neurophysiologist (Grant et al., Epilepsy Behav 2014(32):102-107, 2014, Rating, Z Epileptologie, Springer Med 27(2):139-142, 2014). We already answered quantitatively the above mentioned questions in the references of ours given above where we provided entropy curves and an entropy index which encompasses the complexity of bunches of EEG making possible to deal with massive data and to make objective comparisons among some patients simultaneously. However, we have refined that index here and we also offer another two measures which are spatial and dynamic. Moreover, from those indices we also provide what we call a temporal dynamic complexity path which shows in a standard 10-20 system head diagram the evolution of the lowest complexity per brain zone with respect to the EEG period. These results make it possible to compare quantitatively/graphically the progress of several patients at the same time, answering the questions posed above. The results obtained showed that we can associate low spatio-temporal entropy indices to multiple seizures events in several patients at the same time as well as tracking seizure progress in space and time with our entropy path, coinciding with neurophysiologists observations.

Entropy measures to study and model long term simultaneous evolution of children in Doose and Lennox-Gastaut syndromes.

Doose and Lennox-Gastaut (syndromes) are rare generalized electroclinical affections of early infancy of variable prognosis which manifest with very diverse kinds of seizures. Very frequently, these types of epilepsy become drug resistant and finding reliable treatment results is very difficult. As a result of this, fighting against these syndromes becomes a long term (or endless) event for the little patient, the neurologist and the parents. A lot of Electroencephalographic (EEG) records are so accumulated during the child's life in order to monitor evolution and correlate it with medications. So, given a bunch of EEG, three questions arise: (a) On which year was the child healthier (less affected by seizures)? (b) Which area of the brain has been the most affected? (c) What is the status of the child with respect to others (which also have a bunch of EEG, each)? Answering these interrogations by traditional scrutinizing of the whole database becomes subjective, if not impossible. We propose to answer these questions objectively by means of time series entropies. We start with our modified version of the Multiscale Entropy (MSE) in order to generalize it as a Bivariate MSE (BMSE) and from them, we compute two indices. All were tested in a series of patients and coincide with medical conclusions. As far as we are concerned, our contribution is new.

Novel way to investigate evolution of children refractory epilepsy by complexity metrics in massive information.

Epilepsy demands a major burden at global levels. Worldwide, about 1% of people suffer epilepsy and 30% of them (0.3%) are anticonvulsants resistant. Among them, some children epilepsies are peculiarly difficult to deal with as Doose syndrome (DS). Doose syndrome is a very complicated type of children cryptogenic refractory epilepsy (CCRE) which is traditionally studied by analysis of complex electrencephalograms (EEG) by neurologists. CCRE are affections which evolve in a course of many years and customarily, questions such as on which year was the kid healthiest (less seizures) and on which region of the brain (channel) the affection has been progressing more negatively are very difficult or even impossible to answer as a result of the quantity of EEG recorded through the patient's life. These questions can now be answered by the application of entropies to massive information contained in many EEG. CCRE can not always be cured and have not been investigated from a mathematical viewpoint as far as we are concerned. In this work, a set of 80 time series (distributed equally in four yearly recorded EEG) is studied in order to support pediatrician neurologists to understand better the evolution of this syndrome in the long term. Our contribution is to support multichannel long term analysis of CCRE by observing simple entropy plots instead of studying long rolls of traditional EEG graphs. A comparative analysis among aproximate entropy, sample entropy, our versions of multiscale entropy (MSE) and composite multiscale entropy revealed that our refined MSE was the most convenient complexity measure to describe DS. Additionally, a new entropy parameter is proposed and is referred to as bivariate MSE (BMSE). Such BMSE will provide graphical information in much longer term than MSE.