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Since Noble adapted in 1962 the model of Hodgkin and Huxley to fit Purkinje fibres, the refinement of models for cardiomyocytes has continued. Most of these models are high-dimensional systems of coupled equations so that the possible mathematical analysis is quite limited, even numerically. This has inspired the development of reduced, phenomenological models that preserve qualitatively the main feature of cardiomyocyte's dynamics. In this paper, we present a systematic comparison of the dynamics between two notable low-dimensional models, the FitzHugh-Nagumo model (FitzHugh in Bull Math Biophys 17:257-269, 1955, J Gen Physiol 43:867-896, 1960, Biophys J 1:445-466, 1961) as a prototype of excitable behaviour and a polynomial version of the Karma model (Karma in Phys Rev Lett 71(7):16, 1993, Chaos 4:461, 1994) which is specifically developed to fit cardiomyocyte's behaviour well. We start by introducing the models and considering their pure ODE versions. We analyse the ODEs employing the main ideas and steps used in the setting of geometric singular perturbation theory. Next, we turn to the spatially extended models, where we focus on travelling wave solutions in 1D. Finally, we perform numerical simulations of the 1D PDE Karma model varying model parameters in order to systematically investigate the impact on wave propagation velocity and shape. In summary, our study provides a reference regarding key similarities as well as key differences of the two models.

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In recent decades, many studies have been developed in psychoneuroimmunology that associate stress, arising from multiple different sources and situations, to changes in the immune system, from the medical or immunological point of view as well as from the biochemical one. In this paper, we identify important behaviors of this interplay between the immune system and stress from medical studies and seek to represent them qualitatively in a paradigmatic, yet simple, mathematical model. To that end, we develop an ordinary differential equation model with two equations, for infection level and immune system, respectively, which integrates the effects of stress as an independent parameter. In addition, we perform a geometric analysis of the model for different stress values as well as the corresponding bifurcation analysis. In this context, we are able to reproduce a stable healthy state for little stress, an oscillatory state between healthy and infected states for high stress, and a "burn-out" or stable sick state for extremely high stress. The mechanism between the different dynamical regimes is controlled by two saddle-node in cycle bifurcations. Furthermore, our model is able to capture an induced infection upon dropping from moderate to low stress, and it predicts increasing infection periods upon increasing stress before eventually reaching a burn-out state.

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The objective of this narrative review is to provide updated evidence, based on data from experimental and clinical studies, of the prominent role of omega-3 polyunsaturated fatty acids (n-3 PUFAs) for a number of crucial mechanisms involved in counteracting cell damage induced by oxidative stress in eye diseases. This article is focused on the antioxidant and neuroprotective effects of docosahexaenoic acid (DHA), which have been assessed in different experimental models and clinical studies, particularly in proliferative diabetic retinopathy, age-related macular degeneration and glaucoma that are the most common eye diseases leading to severe vision loss. The mechanisms involved in the role of DHA in protecting human retinal pigment epithelial cells from oxidative stress as well as the interaction with glutathione (GSH) are also described. The review is intended to provide novel and salient findings supporting the rationale of the use of dietary supplementation with high-dose DHA (1050 mg/day) in the form of triglyceride as a potent antioxidant compound for improving the eye health. However, the overall clinical evidence for the use of dietary strategies based on supplementation with n-3 PUFAs in eye diseases linked to oxidative stress other than high-dose DHA triglyceride is both limited and inconsistent.

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Inherited photoreceptor degenerations are not treatable diseases and a frequent cause of blindness in working ages. In this study we investigate the safety, integration and possible rescue effects of intravitreal and subretinal transplantation of adult human bone-marrow-derived mononuclear stem cells (hBM-MSCs) in two animal models of inherited photoreceptor degeneration, the P23H-1 and the Royal College of Surgeons (RCS) rat. Immunosuppression was started one day before the injection and continued through the study. The hBM-MSCs were injected in the left eyes and the animals were processed 7, 15, 30 or 60 days later. The retinas were cross-sectioned, and L- and S- cones, microglia, astrocytes and Müller cells were immunodetected. Transplantations had no local adverse effects and the CD45+ cells remained for up to 15 days forming clusters in the vitreous and/or a 2-3-cells-thick layer in the subretinal space after intravitreal or subretinal injections, respectively. We did not observe increased photoreceptor survival nor decreased microglial cell numbers in the injected left eyes. However, the injected eyes showed decreased GFAP immunoreactivity. We conclude that intravitreal or subretinal injection of hBM-MSCs in dystrophic P23H-1 and RCS rats causes a decrease in retinal gliosis but does not have photoreceptor neuroprotective effects, at least in the short term. However, this treatment may have a potential therapeutic effect that merits further investigation.

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OBJECTIVE: There is little evidence of real-life outcomes of dietary supplementation with high-dose docosahexaenoic acid (DHA) and carotenoids in patients with diabetic retinopathy (DR). We assessed the effect of supplementation with DHA triglyceride (1,050 mg/d) + xanthophyll carotenoid multivitamin on macular function in nonproliferative DR. METHODS: Asymptomatic patients with nonproliferative DR were included in a prospective controlled study and assigned (1:1) to the DHA supplementation group or the control group. Macular sensitivity and macular integrity area were the main outcome measures. Functional vision measures (macular function [MAIA™ CenterVue], best-corrected visual acuity), structural retinal measures (central subfield macular thickness), and biochemical parameters (plasma total antioxidant capacity, DHA content of the erythrocyte membrane, and plasma IL-6) were evaluated at baseline and after 45 and 90 days of DHA supplementation. RESULTS: The study included 24 patients (48 eyes) (12 patients, 24 eyes in each group). Baseline clinical characteristics of patients in both groups were similar. Macular sensitivity increased from a mean (SD) of 25.9 (2.4) dB at baseline to 27.3 (2.3) dB at 90 days (P=0.030) in the DHA group only (between-group differences P<0.19). The macular integrity index decreased from 71.2 (33.2) at baseline to 63.5 (36.4) at 45 days and to 51.6 (35.9) at 90 days (P=0.002) in the DHA group only (between-group differences P<0.05). Best-corrected visual acuity and central subfield macular thickness did not vary significantly in any of the comparisons and in none of the groups. DHA content of erythrocyte membrane and total antioxidant capacity levels increased significantly only in the DHA group. Plasma IL-6 levels decreased significantly only in the DHA group. CONCLUSION: In an early stage of DR, supplementation with high-dose DHA plus xanthophyll carotenoid multivitamin during 90 days was associated with a progressive and significant improvement of macular function measured by microperimetry. Biochemical changes supported the effect of DHA.

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El presente trabajo estudia los efectos de una metodología cooperativa en el aula de matemáticas centrándose en las interacciones entre tratamiento y contenido. Los autores parten de los resultados que obtienen otros investigadores que defienden la idea de que los métodos de aprendizaje cooperativo son más efectivos en tareas complejas y, centrándose en un aula de 4º de ESO, desarrollan las actividades a partir de una metodología mixta (cooperativo-individualista), dividiendo el contenido del curso académico en tres grandes bloques. El primer bloque hace referencia a la operatividad numérica, el segundo bloque es el de álgebra y, el tercero, es el de los contenidos que hacen referencia explícita a esquemas operacionales formales (combinatoria, probabilidad, etc.). Los resultados confirman que las diferencias en rendimiento, aunque son siempre a favor de la cooperación, son más acusadas en los contenidos más novedosos y complejos, incluso aunque estos contenidos estén directamente vinculados a los instrumentos cognitivos (esquemas) del sujeto

The present work studies the effects of a cooperative method-ology in mathematics classes focusing on the interactions between processing and content. The authors start from the results obtained by other researchers that support the idea of cooperative learning methods been more effective in complex tasks, and focusing on a class of the 4th course of Compulsory Secondary Education (ESO), they develop the activities starting from a mix methodology (cooperative-individualistic), they divide academic content into three large-scale sections. The first block refers to the numerical operativity, the second segment is the one that belongs to algebra, and the third one corresponds to the contents that refer closely to the operational scheme (combinatory, probability, etc.). The results confirm that the dissimilarities in performance, however they are always in favour of cooperation, they are more noticeable in more innovative and complex contents, even though this contents are straight away linked to the cognitive tool (scheme) of the individual

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