Boundary value problems for second order linear difference equations: application to the computation of the inverse of generalized Jacobi matrices

We have named generalized Jacobi matrices to those that are practically tridiagonal, except for the two final entries and the two first entries of its first andits last row respectively. This class of matrices encompasses both standard Jacobiand periodic Jacobi matrices that appear in many contexts in pure and appliedmathematics. Therefore, the study of the inverse of these matrices becomes ofspecific interest. However, explicit formulas for inverses are known only in a fewcases, in particular when the coefficients of the diagonal entries are subjected tosome restrictions.We will show that the inverse of generalized Jacobi matrices can be raisedin terms of the resolution of a boundary value problem associated with a secondorder linear difference equation. In fact, recent advances in the study of lineardifference equations, allow us to compute the solution of this kind of boundaryvalue problems. So, the conditions that ensure the uniqueness of the solution ofthe boundary value problem leads to the invertibility conditions for the matrix,whereas that solutions for suitable problems provide explicitly the entries of theinverse matrix.Peer ReviewedPostprint (author's final draft

Towards an alternative testing strategy for nanomaterials used in nanomedicine: lessons from NanoTEST.

In spite of recent advances in describing the health outcomes of exposure to nanoparticles (NPs), it still remains unclear how exactly NPs interact with their cellular targets. Size, surface, mass, geometry, and composition may all play a beneficial role as well as causing toxicity. Concerns of scientists, politicians and the public about potential health hazards associated with NPs need to be answered. With the variety of exposure routes available, there is potential for NPs to reach every organ in the body but we know little about the impact this might have. The main objective of the FP7 NanoTEST project ( www.nanotest-fp7.eu ) was a better understanding of mechanisms of interactions of NPs employed in nanomedicine with cells, tissues and organs and to address critical issues relating to toxicity testing especially with respect to alternatives to tests on animals. Here we describe an approach towards alternative testing strategies for hazard and risk assessment of nanomaterials, highlighting the adaptation of standard methods demanded by the special physicochemical features of nanomaterials and bioavailability studies. The work has assessed a broad range of toxicity tests, cell models and NP types and concentrations taking into account the inherent impact of NP properties and the effects of changes in experimental conditions using well-characterized NPs. The results of the studies have been used to generate recommendations for a suitable and robust testing strategy which can be applied to new medical NPs as they are developed

Eulerian modelling of lung deposition with sectional representation of aerosol dynamics

A dynamical model of respiratory deposition is developed based on an Eulerian approach. The model simulates detailed lung deposition along all generations of the respiratory tract by solving numerically the aerosol general dynamics equation (GDE). All deposition mechanisms are described mechanistically, without using any empirical correlations. The GDE is solved in a one-dimensional form using a sectional method to describe the aerosol size distribution. To describe lung geometry the classical Weibel's morphometric model is used, employing a time-varying alveolar geometry to accommodate inhalation dynamics. A computationally efficient methodology is implemented based on a time-step splitting and subcycling approach, combined with a moving grid method for the growth process. The model is validated by comparing extensively with experimental and numerical results. The simulation results show that aerosol dynamics, in particular condensational growth, significantly influence respiratory deposition of fine hygroscopic particles. Instead, the effect of coagulation was found to be negligible. Particle deposition in terms of number, surface, or mass is addressed, which is of interest to current inhalation toxicology studies. © 2004 Published by Elsevier Ltd

Particulate matter exposure and dose relationships derived from realistic exposure scenarios

Day-averaged outdoor aerosol concentrations from fixed ambient air monitoring stations are associated with the daily lung dose of an individual and the consequent health effects in most studies. The applicability of such measurements for dose assessment is evaluated in this study by comparing the estimated total and regional lung doses using the above concentrations, continuous (hourly) or day-averaged, to the dose derived from actual exposure. Dosimetric calculations are performed using experimentally determined indoor and outdoor concentrations during realistic exposure under variant physical exertion in both environments. The results show that the daily dose can be closely estimated by day-averaged data. © SAGE Publications 2008