Uncertainty through polynomial chaos in the EEG problem

A sensitivity and correlation analysis of EEG sensors influenced by uncertain conductivity is conducted. We assume a three layer spherical head model with different and random layer conductivities. This randomness is modeled by Polynomial Chaos (PC). On average, we observe the least influenced electrodes along the great longitudinal fissure. Also, sensors located closer to a dipole source, are of greater influence to a change in conductivity -- this is in agreement with previous research. The highly influenced sensors were on average located temporal. This was also the case in the correlation analysis, which was made possible by our approach with PC. Sensors in the temporal parts of the brain are highly correlated. Whereas the sensors in the occipital and lower frontal region, though they are close together, are not so highly correlated as in the temporal regions

Bayesian Inference with Combined Dynamic and Sparsity Models: Application in 3D Electrophysiological Imaging

Data-driven inference is widely encountered in various scientific domains to convert the observed measurements into information that cannot be directly observed about a system. Despite the quickly-developing sensor and imaging technologies, in many domains, data collection remains an expensive endeavor due to financial and physical constraints. To overcome the limits in data and to reduce the demand on expensive data collection, it is important to incorporate prior information in order to place the data-driven inference in a domain-relevant context and to improve its accuracy. Two sources of assumptions have been used successfully in many inverse problem applications. One is the temporal dynamics of the system (dynamic structure). The other is the low-dimensional structure of a system (sparsity structure). In existing work, these two structures have often been explored separately, while in most high-dimensional dynamic system they are commonly co-existing and contain complementary information. In this work, our main focus is to build a robustness inference framework to combine dynamic and sparsity constraints. The driving application in this work is a biomedical inverse problem of electrophysiological (EP) imaging, which noninvasively and quantitatively reconstruct transmural action potentials from body-surface voltage data with the goal to improve cardiac disease prevention, diagnosis, and treatment. The general framework can be extended to a variety of applications that deal with the inference of high-dimensional dynamic systems

Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography

This work addresses the inverse problem of electrocardiography from a new perspective, by combining electrical and mechanical measurements. Our strategy relies on the defini-tion of a model of the electromechanical contraction which is registered on ECG data but also on measured mechanical displacements of the heart tissue typically extracted from medical images. In this respect, we establish in this work the convergence of a sequential estimator which combines for such coupled problems various state of the art sequential data assimilation methods in a unified consistent and efficient framework. Indeed we ag-gregate a Luenberger observer for the mechanical state and a Reduced Order Unscented Kalman Filter applied on the parameters to be identified and a POD projection of the electrical state. Then using synthetic data we show the benefits of our approach for the estimation of the electrical state of the ventricles along the heart beat compared with more classical strategies which only consider an electrophysiological model with ECG measurements. Our numerical results actually show that the mechanical measurements improve the identifiability of the electrical problem allowing to reconstruct the electrical state of the coupled system more precisely. Therefore, this work is intended to be a first proof of concept, with theoretical justifications and numerical investigations, of the ad-vantage of using available multi-modal observations for the estimation and identification of an electromechanical model of the heart

An interferometric technique for B/A measurement

An isentropic phase method is described for measuringin vitro the acoustic nonlinearity parameterB/A of several aqueous buffers, protein solutions, lipid oils, and emulsions. The technique relies upon the use of an acoustic interferometer to measure the small changes in sound speed that accompany a rapid hydrostaticpressure change of between one and two atmospheres. Average accuracies of 0.85% are attainable with this method

Liver function as an engineering system

Process Systems Engineering has tackled a wide range of problems including manufacturing, the environment, and advanced materials design. Here we discuss how tools can be deployed to tackle medical problems which involve complex chemical transformations and spatial phenomena looking in particular at the liver system, the body's chemical factory. We show how an existing model has been developed to model distributed behavior necessary to predict the behavior of drugs for treating liver disease. The model has been used to predict the effects of suppression of de novo lipogenesis, stimulation of β-oxidation and a combination of the two. A reduced model has also been used to explore the prediction of behavior of hormones in the blood stream controlling glucose levels to ensure that levels are kept within safe bounds using interval methods. The predictions are made resulting from uncertainty in two key parameters with oscillating input resulting from regular feeding

Biological control of the chestnut gall wasp with \emph{T. sinensis}: a mathematical model

The Asian chestnut gall wasp \emph{Dryocosmus kuriphilus}, native of China, has become a pest when it appeared in Japan, Korea, and the United States. In Europe it was first found in Italy, in 2002. In 1982 the host-specific parasitoid \emph{Torymus sinensis} was introduced in Japan, in an attempt to achieve a biological control of the pest. After an apparent initial success, the two species seem to have locked in predator-prey cycles of decadal length. We have developed a spatially explicit mathematical model that describes the seasonal time evolution of the adult insect populations, and the competition for finding egg deposition sites. In a spatially homogeneous situation the model reduces to an iterated map for the egg density of the two species. While the map would suggest, for realistic parameters, that both species should become locally extinct (somewhat corroborating the hypothesis of biological control), the full model, for the same parameters, shows that the introduction of \emph{T. sinensis} sparks a traveling wave of the parasitoid population that destroys the pest on its passage. Depending on the value of the diffusion coefficients of the two species, the pest can later be able to re-colonize the empty area left behind the wave. When this occurs the two populations do not seem to attain a state of spatial homogeneity, but produce an ever-changing pattern of traveling waves

A "well-balanced" finite volume scheme for blood flow simulation

We are interested in simulating blood flow in arteries with a one dimensional model. Thanks to recent developments in the analysis of hyperbolic system of conservation laws (in the Saint-Venant/ shallow water equations context) we will perform a simple finite volume scheme. We focus on conservation properties of this scheme which were not previously considered. To emphasize the necessity of this scheme, we present how a too simple numerical scheme may induce spurious flows when the basic static shape of the radius changes. On contrary, the proposed scheme is "well-balanced": it preserves equilibria of Q = 0. Then examples of analytical or linearized solutions with and without viscous damping are presented to validate the calculations. The influence of abrupt change of basic radius is emphasized in the case of an aneurism.Comment: 36 page

Near wall hemodynamics: Modelling the glycocalyx and the endothelial surface

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.In this paper a coarse-grained model for blood flow in small arteries is presented. Blood is modelled as a two-component incompressible fluid: the plasma and corpuscular elements dispersed in it. The latter are modelled as deformable liquid droplets having greater density and viscosity. Interfacial surface tension and membrane effects are present to mimic key properties and to avoid droplets’ coalescence. The mesoscopic model also includes the presence of the wavy wall, due to the endothelial cells and incorporates a representation of the glycocalyx, covering the vessel wall. The glycocalyx is modelled as a porous medium, the droplets being subjected to a repulsive elastic force when approaching it, during their transit. Preliminary simulations are intended to show the influence of the undulation on the wall together with that of the glycocalyx