Poincaré maps are a time series analysis technique, that consists in a scattered plot that allows the visualization of the dynamics in a time series. This study aims to visualize and characterize the behavior of complex systems (human body) in disease (COVID-19 disease with lung involvement), according to prognosis outcome, stratified by two comparable groups. The potential use of our work lies in its possible application for identifying biomarkers of physiological health and predictive biomarkers in the prognosis against COVID-19 by changes in system dynamics. Results show that certain variables such as Diastolic blood pressure, PaO2/FiO2, average epicardial fat, direct bilirubin, and Triglyceride-Glucose Ratio/BMI can be inferred as important predictive markers of worse prognosis against COVID-19, with dynamic becoming deterministic.

Down syndrome, or trisomy 21 (T21), is a genetic neurodevelopmental disorder (NDD) often associated with various health challenges. In this population, physiological alterations remain poorly recognized, including dysregulated interactions among systems that play important roles in maintaining homeostasis. Common challenges include nutritional deficiencies, impaired metabolic detoxification, a hypoxia-like state, and gut dysbiosis. This study investigates the impact of dietary interventions and nutrient supplementation on the physiological profiles of individuals with T21. Using a database from the “Integración Down” Institute in Mexico City, we analyzed a panel of 121 biochemical markers before and after a 10-month intervention period. The interventions comprised dietary restriction alone (D) and dietary restriction with nutrient supplementation (D + S), aimed at modifying the participants’ physiological profiles. Our findings demonstrate changes in several physiological markers following the interventions, mainly in response to D + S. In particular, we observed changes in dysbiosis markers related to bacterial and fungal overgrowth; the D + S protocol reduced biomarkers associated with fungal overgrowth. Biomarkers related to nutritional deficiency and a hypoxia-like state (described for T21) showed changes, especially in the D + S group. Increases in red‑blood‑cell indices and decreases in markers of metabolic pathway disruption suggest improved energy metabolism. This research highlights the potential of dietary interventions to ameliorate T21-associated comorbidities and improve overall health outcomes in this population. Further research is needed to explore the long-term effects and optimal strategies for personalized nutritional management in individuals with T21.

Autism spectrum disorder (ASD) is associated with atypical brain network organization. Functional connectivity has been extensively studied using fMRI, which often reports reduced long-range connectivity alongside local hyperconnectivity. However, BOLD-based connectivity reflects neurovascular coupling and therefore provides an indirect estimate of neuronal activity. Complementary information may be obtained from [ ¹⁸ F]FDG microPET, which quantifies regional glucose uptake—an index of synaptic energy demand integrated over minutes—although FDG-derived network organization has been scarcely examined in ASD. Here, “metabolic connectivity” refers to between-subject covariance in regional [ ¹⁸ F]FDG uptake (group-level metabolic covariance networks), not within-subject temporal coupling as in BOLD-fMRI functional connectivity. We tested whether the C58/J mouse strain—an ASD-relevant model with social deficits and repetitive behaviors—recapitulates ASD-relevant metabolic network-level alterations. Using [ ¹⁸ F]FDG microPET, we constructed ROI-wise metabolic covariance networks by correlating uptake values across animals and compared C58/J mice with C57BL/6 controls. The C58/J network exhibited higher clustering and a more locally cohesive organization than the C57BL/6 network. Nodal degree/edge density was reduced in the olfactory bulb, hippocampus, and hypothalamus. In contrast, the motor-related regions—including the striatum, brainstem, and superior and inferior colliculi—showed a higher degree/denser covariance. These findings suggest that C58/J mice display FDG-derived metabolic covariance network features qualitatively consistent with those reported in ASD FDG-PET studies, supporting this strain as a tool to investigate ASD-relevant pathophysiological mechanisms and to evaluate candidate interventions.

The human body is a complex system where patterns emerge as a result of the interactions between multiple phys-iological systems. These interactions are affected by illnesses such as COVID-19. A potential treatment of COVID-19 patients is intramuscular administration of polymerized type I collagen (PTIC). In this work we evaluate the effect of the intramuscular administration of PTIC and placebo in the physiological network of patients with COVID-19. Furthermore, we investigated sex differences in the correlation between baseline and time evolution of experimental test.