8,409 research outputs found
A mathematical model for breath gas analysis of volatile organic compounds with special emphasis on acetone
Recommended standardized procedures for determining exhaled lower respiratory
nitric oxide and nasal nitric oxide have been developed by task forces of the
European Respiratory Society and the American Thoracic Society. These
recommendations have paved the way for the measurement of nitric oxide to
become a diagnostic tool for specific clinical applications. It would be
desirable to develop similar guidelines for the sampling of other trace gases
in exhaled breath, especially volatile organic compounds (VOCs) which reflect
ongoing metabolism. The concentrations of water-soluble, blood-borne substances
in exhaled breath are influenced by: (i) breathing patterns affecting gas
exchange in the conducting airways; (ii) the concentrations in the
tracheo-bronchial lining fluid; (iii) the alveolar and systemic concentrations
of the compound. The classical Farhi equation takes only the alveolar
concentrations into account. Real-time measurements of acetone in end-tidal
breath under an ergometer challenge show characteristics which cannot be
explained within the Farhi setting. Here we develop a compartment model that
reliably captures these profiles and is capable of relating breath to the
systemic concentrations of acetone. By comparison with experimental data it is
inferred that the major part of variability in breath acetone concentrations
(e.g., in response to moderate exercise or altered breathing patterns) can be
attributed to airway gas exchange, with minimal changes of the underlying blood
and tissue concentrations. Moreover, it is deduced that measured end-tidal
breath concentrations of acetone determined during resting conditions and free
breathing will be rather poor indicators for endogenous levels. Particularly,
the current formulation includes the classical Farhi and the Scheid series
inhomogeneity model as special limiting cases.Comment: 38 page
Single-Phase Flow of Non-Newtonian Fluids in Porous Media
The study of flow of non-Newtonian fluids in porous media is very important
and serves a wide variety of practical applications in processes such as
enhanced oil recovery from underground reservoirs, filtration of polymer
solutions and soil remediation through the removal of liquid pollutants. These
fluids occur in diverse natural and synthetic forms and can be regarded as the
rule rather than the exception. They show very complex strain and time
dependent behavior and may have initial yield-stress. Their common feature is
that they do not obey the simple Newtonian relation of proportionality between
stress and rate of deformation. Non-Newtonian fluids are generally classified
into three main categories: time-independent whose strain rate solely depends
on the instantaneous stress, time-dependent whose strain rate is a function of
both magnitude and duration of the applied stress and viscoelastic which shows
partial elastic recovery on removal of the deforming stress and usually
demonstrates both time and strain dependency. In this article the key aspects
of these fluids are reviewed with particular emphasis on single-phase flow
through porous media. The four main approaches for describing the flow in
porous media are examined and assessed. These are: continuum models, bundle of
tubes models, numerical methods and pore-scale network modeling.Comment: 94 pages, 12 figures, 1 tabl
Mathematical models for chemotaxis and their applications in self-organisation phenomena
Chemotaxis is a fundamental guidance mechanism of cells and organisms,
responsible for attracting microbes to food, embryonic cells into developing
tissues, immune cells to infection sites, animals towards potential mates, and
mathematicians into biology. The Patlak-Keller-Segel (PKS) system forms part of
the bedrock of mathematical biology, a go-to-choice for modellers and analysts
alike. For the former it is simple yet recapitulates numerous phenomena; the
latter are attracted to these rich dynamics. Here I review the adoption of PKS
systems when explaining self-organisation processes. I consider their
foundation, returning to the initial efforts of Patlak and Keller and Segel,
and briefly describe their patterning properties. Applications of PKS systems
are considered in their diverse areas, including microbiology, development,
immunology, cancer, ecology and crime. In each case a historical perspective is
provided on the evidence for chemotactic behaviour, followed by a review of
modelling efforts; a compendium of the models is included as an Appendix.
Finally, a half-serious/half-tongue-in-cheek model is developed to explain how
cliques form in academia. Assumptions in which scholars alter their research
line according to available problems leads to clustering of academics and the
formation of "hot" research topics.Comment: 35 pages, 8 figures, Submitted to Journal of Theoretical Biolog
A New Approach to Model Confined Suspensions Flows in Complex Networks: Application to Blood Flow
The modeling of blood flows confined in micro-channels or micro-capillary beds depends on the interactions between the cell-phase, plasma and the complex geometry of the
network. In the case of capillaries or channels having a high aspect ratio (their longitudinal size is much larger than their transverse one), this modeling is much simplified from the use of a continuous description of fluid viscosity as previously proposed in the literature. Phase separation or plasma skimming effect is a supplementary mechanism responsible for the relative distribution of the red blood cell’s volume density in each branch of a given bifur-
cation. Different models have already been proposed to connect this effect to the various hydrodynamics and geometrical parameters at each bifurcation. We discuss the advantages and drawbacks of these models and compare them to an alternative approach for modeling phase distribution in complex channels networks. The main novelty of this new formulation is to show that albeit all the previous approaches seek for a local origin of the phase segre-
gation phenomenon, it can arise from a global non-local and nonlinear structuration of the flow inside the network. This new approach describes how elementary conservation laws
are sufficient principles (rather than the complex arametric models previously proposed) to provide non local phase separation. Spatial variations of the hematocrit field thus result from the topological complexity of the network as well as nonlinearities arising from solving a new
free boundary problem associated with the flux and mass conservation. This network model approach could apply to model blood flow distribution either on artificial micro-models, micro-fluidic networks, or realistic reconstruction of biological micro-vascular networks
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