A new description of spin tunneling in magnetic molecules

A new approach is used that allows to describe the magnetic molecules main properties in a direct and simple way. Results obtained for the Fe8 cluster show good agreement with the experimental data.Comment: 7 pages, 2 figure

Calculation of Volterra kernels for solutions of nonlinear differential equations

We consider vector-valued autonomous differential equations of the form x' = f(x) + phi with analytic f and investigate the nonanticipative solution operator phi bar right arrow A(phi) in terms of its Volterra series. We show that Volterra kernels of order > 1 occurring in the series expansion of the solution operator A are continuous functions, and establish recurrence relations between the kernels allowing their explicit calculation. A practical tensor calculus is provided for the finite-dimensional case. In addition to analytically calculating the kernels, we present an algorithm to numerically obtain them from the output x(t) through sampling the input space by linear combinations of delta functions. We call this "differential sampling". It is a nonlinear analogue of the classical method of impulse response. We prove a continuity theorem stating that, in the finite-dimensional case, approximate delta functions give rise to approximate Volterra kernels and that continuity holds in the sense of weak convergence. Finally, we discuss a practical implementation of differential sampling and relate it to the Wiener method

Periodic Instanton and Phase Transition in Quantum Tunneling of Spin Systems

The quantum-classical transitions of the escape rates in a uniaxial spin model relevant to the molecular magnet Mn$_{12}$Ac and a biaxial anisotropic ferromagnetic particle are investigated by applying the periodic instanton method. The effective free energies are expanded around the top of the potential barrier in analogy to Landau theory of phase transitions. We show that the first-order transitions occur below the critical external magnetic field $h_x = 1/4$ for the uniaxial spin model and beyond the critical anisotropy constant ratio $\lambda = 1/2$ for the biaxial ferromagnetic grains, which are in good agreement with earlier works.Comment: 14 pages, revtex, 5 postscript figure

Xenon depresses aEEG background voltage activity whilst maintaining cardiovascular stability in sedated healthy newborn pigs

Changes in electroencephalography (EEG) voltage range are used to monitor the depth of anaesthesia, as well as predict outcome after hypoxia-ischaemia in neonates. Xenon is being investigated as a potential neuroprotectant after hypoxic-ischaemic brain injury, but the effect of Xenon on EEG parameters in children or neonates is not known. This study aimed to examine the effect of 50% inhaled Xenon on background amplitude-integrated EEG (aEEG) activity in sedated healthy newborn pigs.Five healthy newborn pigs, receiving intravenous fentanyl sedation, were ventilated for 24 h with 50%Xenon, 30%O2 and 20%N2 at normothermia. The upper and lower voltage-range of the aEEG was continuously monitored together with cardiovascular parameters throughout a 1 h baseline period with fentanyl sedation only, followed by 24 h of Xenon administration.The median (IQR) upper and lower aEEG voltage during 1 h baseline was 48.0 μV (46.0-50.0) and 25.0 μV (23.0-26.0), respectively. The median (IQR) aEEG upper and lower voltage ranges were significantly depressed to 21.5 μV (20.0-26.5) and 12.0 μV (12.0-16.5) from 10 min after the onset of 50% Xenon administration (p=0.002). After the initial Xenon induced depression in background aEEG voltage, no further aEEG changes were seen over the following 24h of ventilation with 50% xenon under fentanyl sedation. Mean arterial blood pressure and heart rate remained stable.Mean arterial blood pressure and heart rate were not significantly influenced by 24h Xenon ventilation. 50% Xenon rapidly depresses background aEEG voltage to a steady ~50% lower level in sedated healthy newborn pigs. Therefore, care must be taken when interpreting the background voltage in neonates also receiving Xenon

Xenon combined with therapeutic hypothermia is not neuroprotective after severe hypoxia-ischemia in neonatal rats

Therapeutic hypothermia (TH) is standard treatment following perinatal asphyxia in newborn infants. Experimentally, TH is neuroprotective after moderate hypoxia-ischemia (HI) in seven-day-old (P7) rats. However, TH is not neuroprotective after severe HI. After a moderate HI insult in newborn brain injury models, the anesthetic gas xenon (Xe) doubles TH neuroprotection. The aim of this study was to examine whether combining Xe and TH is neuroprotective as applied in a P7 rat model of severe HI.120 P7 rat pups underwent a severe HI insult; unilateral carotid artery ligation followed by hypoxia (8% O2 for 150min at experimental normothermia (NT-37: Trectal 37°C). Surviving pups were randomised to immediate NT-37 for 5h (n = 36), immediate TH-32: Trectal 32°C for 5h (n = 25) or immediate TH-32 plus 50% inhaled Xe for 5h (n = 24). Pups were sacrificed after one week of survival. Relative area loss of the ligated hemisphere was measured, and neurons in the subventricular zone of this injured hemisphere were counted, to quantify brain damage.Following the HI insult, median (interquartile range, IQR) hemispheric brain area loss was similar in all groups: 63.5% (55.5-75.0) for NT-37 group, 65.0% (57.0-65.0) for TH-32 group, and 66.5% (59.0-72.0) for TH-32+Xe50% group (not significant). Correspondingly, there was no difference in neuronal cell count (NeuN marker) in the subventricular zone across the three treatment groups.Immediate therapeutic hypothermia with or without additional 50% inhaled Xe, does not provide neuroprotection one week after severe HI brain injury in the P7 neonatal rat. This model aims to mimic the clinical situation in severely asphyxiated neonates and treatment these newborns remains an ongoing challenge

Treatment temperature and insult severity influence the neuroprotective effects of therapeutic hypothermia

Therapeutic hypothermia (HT) is standard care for moderate and severe neonatal hypoxic-ischaemic encephalopathy (HIE), the leading cause of permanent brain injury in term newborns. However, the optimal temperature for HT is still unknown, and few preclinical studies have compared multiple HT treatment temperatures. Additionally, HT may not benefit infants with severe encephalopathy. In a neonatal rat model of unilateral hypoxia-ischaemia (HI), the effect of five different HT temperatures was investigated after either moderate or severe injury. At postnatal-day seven, rat pups underwent moderate or severe HI followed by 5 h at normothermia (37 °C), or one of five HT temperatures: 33.5 °C, 32 °C, 30 °C, 26 °C, and 18 °C. One week after treatment, neuropathological analysis of hemispheric and hippocampal area loss, and CA1 hippocampal pyramidal neuron count, was performed. After moderate injury, a significant reduction in hemispheric and hippocampal loss on the injured side, and preservation of CA1 pyramidal neurons, was seen in the 33.5 °C, 32 °C, and 30 °C groups. Cooling below 33.5 °C did not provide additional neuroprotection. Regardless of treatment temperature, HT was not neuroprotective in the severe HI model. Based on these findings, and previous experience translating preclinical studies into clinical application, we propose that milder cooling should be considered for future clinical trials

Spin tunnelling in mesoscopic systems

We study spin tunnelling in molecular magnets as an instance of a mesoscopic phenomenon, with special emphasis on the molecule Fe8. We show that the tunnel splitting between various pairs of Zeeman levels in this molecule oscillates as a function of applied magnetic field, vanishing completely at special points in the space of magnetic fields, known as diabolical points. This phenomena is explained in terms of two approaches, one based on spin-coherent-state path integrals, and the other on a generalization of the phase integral (or WKB) method to difference equations. Explicit formulas for the diabolical points are obtained for a model Hamiltonian.Comment: 13 pages, 5 figures, uses Pramana style files; conference proceedings articl

Variability and sex-dependence of hypothermic neuroprotection in a rat model of neonatal hypoxic-ischaemic brain injury:a single laboratory meta-analysis

Therapeutic hypothermia (HT) is standard care for term infants with hypoxic–ischaemic (HI) encephalopathy. However, the efficacy of HT in preclinical models, such as the Vannucci model of unilateral HI in the newborn rat, is often greater than that reported from clinical trials. Here, we report a meta-analysis of data from every experiment in a single laboratory, including pilot data, examining the effect of HT in the Vannucci model. Across 21 experiments using 106 litters, median (95% CI) hemispheric area loss was 50.1% (46.0–51.9%; n = 305) in the normothermia group, and 41.3% (35.1–44.9%; n = 317) in the HT group, with a bimodal injury distribution. Median neuroprotection by HT was 17.6% (6.8–28.3%), including in severe injury, but was highly-variable across experiments. Neuroprotection was significant in females (p < 0.001), with a non-significant benefit in males (p = 0.07). Animals representing the median injury in each group within each litter (n = 277, 44.5%) were also analysed using formal neuropathology, which showed neuroprotection by HT throughout the brain, particularly in females. Our results suggest an inherent variability and sex-dependence of the neuroprotective response to HT, with the majority of studies in the Vannucci model vastly underpowered to detect true treatment effects due to the distribution of injury