We study the repeatedfolding of a two-parameterfamily of quadrilaterals abouttheir successively transformeddiagonalsby examiningthe evolutionof thediagonal lengths.Successivelymappedpairs of squaredlengthslie on an elliptic curve on which folding acts as translationunderthe group law. We prove the rotation numberattainsall possiblevaluesand anyvaluedeterminesa uniquecurvein parameter space.For rational parameters we give an algorithmto determineif the folding map is periodic. This gives a partial explanationfor the diversity and intricacy of the curvestracedout by the pathsof the verticesof the transformedquadrilaterals.
Background: Neonatal asphyxia can be complicated by myocardial dysfunction with secondary alterations in pulmonary and regional hemodynamics. Levosimendan is a calcium-sensitizing inotrope that may support cardiac output, but little is known regarding its differential hemodynamic effects in asphyxiated neonates. Methods: Mixed breed piglets (1–4 days old, weight 1.6–2.3 kg) were acutely instrumented. Normocapnic alveolar hypoxia (10–15% oxygen) was induced for 2 h, followed by reoxygenation with 100% (1 h) and then 21% oxygen (3 h). At 2 h of reoxygenation, after volume loading (Ringer’s lactate 10 ml/kg), either levosimendan (0.1 or 0.2 µg/kg/min) or D5W (placebo) was infused for 2 h in a blinded, block-randomized fashion (n = 7–8/group). The systemic, pulmonary and regional (carotid, superior mesenteric and renal) hemodynamics were compared. Results: At 0.1 and 0.2 µg/kg/min, levosimendan significantly increased cardiac output (121 and 123% of pretreatment, respectively) and heart rate, and decreased systemic vascular resistance without causing hypotension. Pulmonary arterial pressure and estimated pulmonary vascular resistance were significantly increased from pretreatment baseline in 0.1 but not 0.2 µg/kg/min levosimendan. Levosimendan infusion had no effects on regional hemodynamics. Myocardial efficiency but not oxygen consumption increased with 0.1 µg/kg/min levosimendan without significant effects on plasma troponin and myocardial lactate levels. Conclusions: In newborn piglets following hypoxia-reoxygenation injury, levosimendan improves cardiac output but has no marked effects in carotid, superior mesenteric and renal perfusion. It appears that various doses of levosimendan increase the cardiac output through different mechanisms. Further investigations are needed to examine the effectiveness of levosimendan as a cardiovascular supportive therapy either alone or in conjunction with other inotropes in asphyxiated neonates.
We examined whether or not coherence between chest wall intercostal and oblique muscles changed as a function of lung volume excursion, alveolar pressure, and muscular demand. We also assessed the effects of acute expiratory threshold loading (ETL) on chest wall muscular control. A total of 15 healthy adults (7 males; average age = 28 years) completed maximum performance and ETL tasks. Chest wall surface electromyographic and kinematic recordings were made. Participants also performed a session of acute ETL. We showed that corticomuscular control of the chest wall varied as a function of lung volume excursion and muscular effort. Acute ETL had some effect on respiratory kinematics but not coherence.
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