Diffusion of active ingredients in textiles: a three step multiscale model

Most practical textile models are based on a two scale approach: a one-dimensional fiber model and a fabric model. No meso-level is used in between, i.e. the yarn scale is neglected in this setup. For dense textile substrates this seems appropriate as the yarns connect everywhere, but for loose fabrics or scrims this approach cannot be kept. Specifically when one is interested in tracking an active component released by the fibers, the yarn level plays an important role. This is because the saturation vapor pressure will influence the release rate from the fibers, and its value will vary over the yarn cross-section. Therefore, in this work we present a three step multiscale model: the active component is tracked in the fiber, the yarn, and finally at the fabric level. At the fiber level a one-dimensional reduction to a non-linear diffusion equation is performed, and solved on a as needed basis. At the yarn level both a two-dimensional or a one-dimensional model can be applied, and finally the yarn result is upscaled to the fabric level

Characteristic times for multiscale diffusion of active ingredients in coated textiles

A three-scale approach for textile models was given in [1]: a one-dimensional fiber model and a room model, with a meso-level in between, which is the yarn scale. To analyse and simplify the model, its characteristic times are investigated here. At these times the fiber and yarn model, and the yarn and room model, respectively, tend to reach an equilibrium concentration. The identification of these characteristic times is key in reducing the model to its variously scaled components when simplifying it

Polynomial chaos and Bayesian inference in RPDE's: a biomedical application

The electroencephalograph (EEG) is one of the most influential tools in the diagnosis of epilepsy and seizures. It measures electrical discharges of neurons in the human brain. The latter consists of many regions, all with a different electrical conductivity. Unfortunately one cannot measure this non invasively, e.g. preoperatively. In this paper, we investigate the uncertainty induced on the location of EEG current dipoles. A Bayesian framework is used, so as to include modeling error and noise, but combined with Polynomial Chaos expansions to represent random variables, speeding up computations. We evaluate this technique on a spherical head model with a standard clinical 27 sensor positioning

Regional sensitivity analysis of the EEG sensors through polynomial chaos

We study the sensitivity with respect to an uncertain conductivity in the electroencephalography (EEG) forward problem. A three layer spherical head model with different and random layer conductivities is considered. The randomness is modeled by Legendre Polynomial Chaos. We introduce a (regional) sensitivity index to quantify the sensitivity of sensors with regard to subregions of the brain. As an example the cerebrum and cerebellum are compared together with the whole head as reference