Following the steps of spanish mathematical analysis: from Cauchy to Weierstrass between 1880 and 1914

[EN] Rigorous Mathematical Analysis in the Cauchy style was not accepted in a straightforward manner by the European mathematical community of the central years of the 19th Century. In average, only around forty years after the 1821 Cours d'Analyse did Cauchy's treatment become a standard in the more mathematically advanced countries, as a paradigm that remained in use until the arithmetisation of Analysis by Weierstrass replaced it before the end of the century. ln this paper the authors show how rigorous Mathematical Analysis à la Cauchy was adopted in Spain quite late -around 1880- and how in sorne more forty years, the Weierstrassian formulation became the usual presentation in Spanish texts

The lactate paradox revisited in lowlanders during acclimatization to 4100 m and in high-altitude natives

[EN] Chronic hypoxia has been proposed to induce a closer coupling in human skeletal muscle between ATP utilization and production in both lowlanders (LN) acclimatizing to high altitude and high-altitude natives (HAN), linked with an improved match between pyruvate availability and its use in mitochondrial respiration. This should result in less lactate being formed during exercise in spite of the hypoxaemia. To test this hypothesis six LN (22-31 years old) were studied during 15 min warm up followed by an incremental bicycle exercise to exhaustion at sea level, during acute hypoxia and after 2 and 8 weeks at 4100 m above sea level (El Alto, Bolivia). In addition, eight HAN (26-37 years old) were studied with a similar exercise protocol at altitude. The leg net lactate release, and the arterial and muscle lactate concentrations were elevated during the exercise in LN in acute hypoxia and remained at this higher level during the acclimatization period. HAN had similar high values; however, at the moment of exhaustion their muscle lactate, ADP and IMP content and Cr/PCr ratio were higher than in LN. In conclusion, sea-level residents in the course of acclimatization to high altitude did not exhibit a reduced capacity for the active muscle to produce lactate. Thus, the lactate paradox concept could not be demonstrated. High-altitude natives from the Andes actually exhibit a higher anaerobic energy production than lowlanders after 8 weeks of acclimatization reflected by an increased muscle lactate accumulation and enhanced adenine nucleotide breakdown.

Prediction of clinical toxicity in localized cervical carcinoma by radio-induced apoptosis study in peripheral blood lymphocytes (PBLs)

[EN] Background: Cervical cancer is treated mainly by surgery and radiotherapy. Toxicity due to radiation is a limiting factor for treatment success. Determination of lymphocyte radiosensitivity by radio-induced apoptosis arises as a possible method for predictive test development. The aim of this study was to analyze radio-induced apoptosis of peripheral blood lymphocytes. Methods: Ninety four consecutive patients suffering from cervical carcinoma, diagnosed and treated in our institution, and four healthy controls were included in the study. Toxicity was evaluated using the Lent-Soma scale. Peripheral blood lymphocytes were isolated and irradiated at 0, 1, 2 and 8 Gy during 24, 48 and 72 hours. Apoptosis was measured by flow cytometry using annexin V/propidium iodide to determine early and late apoptosis. Lymphocytes were marked with CD45 APC-conjugated monoclonal antibody. Results: Radiation-induced apoptosis (RIA) increased with radiation dose and time of incubation. Data strongly fitted to a semi logarithmic model as follows: RIA = βln(Gy) + α. This mathematical model was defined by two constants: α, is the origin of the curve in the Y axis and determines the percentage of spontaneous cell death and β, is the slope of the curve and determines the percentage of cell death induced at a determined radiation dose (β = ΔRIA/Δln(Gy)). Higher β values (increased rate of RIA at given radiation doses) were observed in patients with low sexual toxicity (Exp(B) = 0.83, C.I. 95% (0.73-0.95), p = 0.007; Exp(B) = 0.88, C.I. 95% (0.82-0.94), p = 0.001; Exp(B) = 0.93, C.I. 95% (0.88-0.99), p = 0.026 for 24, 48 and 72 hours respectively). This relation was also found with rectal (Exp(B) = 0.89, C.I. 95% (0.81-0.98), p = 0.026; Exp(B) = 0.95, C.I. 95% (0.91-0.98), p = 0.013 for 48 and 72 hours respectively) and urinary (Exp(B) = 0.83, C.I. 95% (0.71-0.97), p = 0.021 for 24 hours) toxicity. Conclusion: Radiation induced apoptosis at different time points and radiation doses fitted to a semi logarithmic model defined by a mathematical equation that gives an individual value of radiosensitivity and could predict late toxicity due to radiotherapy. Other prospective studies with higher number of patients are needed to validate these results.