Memory-Controlled Diffusion

Memory effects require for their incorporation into random-walk models an extension of the conventional equations. The linear Fokker-Planck equation for the probability density $p(\vec r, t)$ is generalized to include non-linear and non-local spatial-temporal memory effects. The realization of the memory kernels are restricted due the conservation of the basic quantity $p$. A general criteria is given for the existence of stationary solutions. In case the memory kernel depends on $p$ polynomially the transport is prevented. Owing to the delay effects a finite amount of particles remains localized and the further transport is terminated. For diffusion with non-linear memory effects we find an exact solution in the long-time limit. Although the mean square displacement shows diffusive behavior, higher order cumulants exhibits differences to diffusion and they depend on the memory strength

Assessment of Hyperbolic Heat Transfer Equation in Theoretical Modeling for Radiofrequency Heating Techniques

Theoretical modeling is a technique widely used to study the electrical-thermal performance of different surgical procedures based on tissue heating by use of radiofrequency (RF) currents. Most models employ a parabolic heat transfer equation (PHTE) based on Fourier’s theory, which assumes an infinite propagation speed of thermal energy. We recently proposed a one-dimensional model in which the electrical-thermal coupled problem was analytically solved by using a hyperbolic heat transfer equation (HHTE), i.e. by considering a non zero thermal relaxation time. In this study, we particularized this solution to three typical examples of RF heating of biological tissues: heating of the cornea for refractive surgery, cardiac ablation for eliminating arrhythmias, and hepatic ablation for destroying tumors. A comparison was made of the PHTE and HHTE solutions. The differences between their temperature profiles were found to be higher for lower times and shorter distances from the electrode surface. Our results therefore suggest that HHTE should be considered for RF heating of the cornea (which requires very small electrodes and a heating time of 0.6 s), and for rapid ablations in cardiac tissue (less than 30 s)

Physical activity differences between children from migrant and native origin

BACKGROUND: Children from migrant origin are at higher risk for overweight and obesity. As limited physical activity is a key factor in this overweight and obesity risk, in general, the aim of this study is to assess to what degree children from migrant and native Dutch origin differ with regard to levels of physical activity and to determine which home environment aspects contribute to these differences. METHODS: A cross-sectional survey among primary caregivers of primary school children at the age of 8–9 years old (n = 1943) from 101 primary schools in two urban areas in The Netherlands. We used bivariate correlation and multivariate regression techniques to examine the relationship between physical and social environment aspects and the child’s level of physical activity. All outcomes were reported by primary caregivers. Outcome measure was the physical activity level of the child. Main independent variables were migrant background, based on country of birth of the parents, and variables in the physical and social home environment which may enhance or restrict physical activity: the availability and the accessibility of toys and equipment, as well as sport club membership (physical environment), and both parental role modeling, and supportive parental policies (social environment). We controlled for age and sex of the child, and for socio-economic status, as indicated by educational level of the parents. RESULTS: In this sample, physical activity levels were significantly lower in migrant children, as compared to children in the native population. Less physical activity was most often seen in Turkish, Moroccan, and other non-western children (p < .05). CONCLUSIONS: Although traditional home characteristics in both the physical, and the social environment are often associated with child’s physical activity, these characteristics provided only modest explanation of the differences in physical activity between migrant and non-migrant children in this study. The question arises whether interventions aimed at overweight and obesity should have to focus on home environmental characteristics with regard to physical activity