A two-fluid model for tissue growth within\ud a dynamic flow environment

We study the growth of a tissue construct in a perfusion bioreactor, focussing on its response to the mechanical environment. The bioreactor system is modelled as a two-dimensional channel containing a tissue construct through which a flow of culture medium is driven. We employ a multiphase formulation of the type presented by G. Lemon, J. King, H. Byrne, O. Jensen and K. Shakesheff in their study (Multiphase modelling of tissue growth using the theory of mixtures. J. Math. Biol. 52(2), 2006, 571–594) restricted to two interacting fluid phases, representing a cell population (and attendant extracellular matrix) and a culture medium, and employ the simplifying limit of large interphase viscous drag after S. Franks in her study (Mathematical Modelling of Tumour Growth and Stability. Ph.D. Thesis, University of Nottingham, UK, 2002) and S. Franks and J. King in their study (Interactions between a uniformly proliferating tumour and its surrounding: Uniform material properties. Math. Med. Biol. 20, 2003, 47–89).\ud \ud The novel aspects of this study are: (i) the investigation of the effect of an imposed flow on the growth of the tissue construct, and (ii) the inclusion of a mechanotransduction mechanism regulating the response of the cells to the local mechanical environment. Specifically, we consider the response of the cells to their local density and the culture medium pressure. As such, this study forms the first step towards a general multiphase formulation that incorporates the effect of mechanotransduction on the growth and morphology of a tissue construct. The model is analysed using analytic and numerical techniques, the results of which illustrate the potential use of the model to predict the dominant regulatory stimuli in a cell population

Modelling crystal aggregation and deposition\ud in the catheterised lower urinary tract

Urethral catheters often become encrusted with crystals of magnesium struvite and calcium phosphate. The encrustation can block the catheter, which can cause urine retention in the bladder and reflux into the kidneys. We develop a mathematical model to investigate crystal deposition on the catheter surface, modelling the bladder as a reservoir of fluid and the urethral catheter as a rigid channel. At a constant rate, fluid containing crystal particles of unit size enters the reservoir, and flows from the reservoir through the channel and out of the system. The crystal particles aggregate, which we model using Becker–Döring coagulation theory, and are advected through the channel, where they continue to aggregate and are deposited on the channel’s walls. Inhibitor particles also enter the reservoir, and can bind to the crystals, preventing further aggregation and deposition. The crystal concentrations are spatially homogeneous in the reservoir, whereas the channel concentrations vary spatially as a result of advection, diffusion and deposition. We investigate the effect of inhibitor particles on the amount of deposition. For all parameter values, we find that crystals deposit along the full length of the channel, with maximum deposition close to the channel’s entrance

Prospects for reduced energy transports: A preliminary analysis

The recent energy crisis and subsequent substantial increase in fuel prices have provided increased incentive to reduce the fuel consumption of civil transport aircraft. At the present time many changes in operational procedures have been introduced to decrease fuel consumption of the existing fleet. In the future, however, it may become desirable or even necessary to introduce new fuel-conservative aircraft designs. This paper reports the results of a preliminary study of new near-term fuel conservative aircraft. A parametric study was made to determine the effects of cruise Mach number and fuel cost on the optimum configuration characteristics and on economic performance. For each design, the wing geometry was optimized to give maximum return on investment at a particular fuel cost. Based on the results of the parametric study, a nominal reduced energy configuration was selected. Compared with existing transport designs, the reduced energy design has a higher aspect ratio wing with lower sweep, and cruises at a lower Mach number. It has about 30% less fuel consumption on a seat-mile basis

On the predictions and limitations of the BeckerDoring model for reaction kinetics in micellar surfactant solutions

We investigate the breakdown of a system of micellar aggregates in a surfactant solution following an order-one dilution. We derive a mathematical model based on the Becker–Döring system of equations, using realistic expressions for the reaction constants fit to Molecular Dynamics simulations. We exploit the largeness of typical aggregation numbers to derive a continuum model, substituting a large system of ordinary differential equations for a partial differential equation in two independent variables: time and aggregate size. Numerical solutions demonstrate that re-equilibration occurs in two distinct stages over well-separated time-scales, in agreement with experiment and with previous theories. We conclude by exposing a limitation in the Becker–Döring theory for re-equilibration and discuss potential resolutions

Micron-sized forsterite grains in the pre-planetary nebula of IRAS 17150-3224 - Searching for clues on the mysterious evolution of massive AGB stars

We study the grain properties and location of the forsterite crystals in the circumstellar environment of the pre-planetary nebula (PPN) IRAS 17150-3224 in order to learn more about the as yet poorly understood evolutionary phase prior to the PPN. We use the best-fit model for IRAS 17150-3224 of Meixner et al. (2002) and add forsterite to this model. We investigate different spatial distributions and grain sizes of the forsterite crystals in the circumstellar environment. We compare the spectral bands of forsterite in the mid-infrared and at 69 micrometre in radiative transport models to those in ISO-SWS and Herschel/PACS observations. We can reproduce the non-detection of the mid-infrared bands and the detection of the 69 micrometre feature with models where the forsterite is distributed in the whole outflow, in the superwind region, or in the AGB-wind region emitted previous to the superwind, but we cannot discriminate between these three models. To reproduce the observed spectral bands with these three models, the forsterite crystals need to be dominated by a grain size population of 2 micrometre up to 6 micrometre. We hypothesise that the large forsterite crystals were formed after the superwind phase of IRAS 17150-3224, where the star developed an as yet unknown hyperwind with an extremely high mass-loss rate (10^-3 Msol/yr). The high densities of such a hyperwind could be responsible for the efficient grain growth of both amorphous and crystalline dust in the outflow. Several mechanisms are discussed that might explain the lower-limit of 2 micrometre found for the forsterite grains, but none are satisfactory. Among the mechanisms explored is a possible selection effect due to radiation pressure based on photon scattering on micron-sized grains.Comment: Accepted by A&

The interplay between tissue growth and scaffold degradation in engineered tissue constructs

In vitro tissue engineering is emerging as a potential tool to meet the high demand for replacement tissue, caused by the increased incidence of tissue degeneration and damage. A key challenge in this field is ensuring that the mechanical properties of the engineered tissue are appropriate for the in vivo environment. Achieving this goal will require detailed understanding of the interplay between cell proliferation, extracellular matrix (ECM) deposition and scaffold degradation.\ud \ud In this paper, we use a mathematical model (based upon a multiphase continuum framework) to investigate the interplay between tissue growth and scaffold degradation during tissue construct evolution in vitro. Our model accommodates a cell population and culture medium, modelled as viscous fluids, together with a porous scaffold and ECM deposited by the cells, represented as rigid porous materials. We focus on tissue growth within a perfusion bioreactor system, and investigate how the predicted tissue composition is altered under the influence of (i) differential interactions between cells and the supporting scaffold and their associated ECM, (ii) scaffold degradation, and (iii) mechanotransduction-regulated cell proliferation and ECM deposition.\ud \ud Numerical simulation of the model equations reveals that scaffold heterogeneity typical of that obtained from μCT scans of tissue engineering scaffolds can lead to significant variation in the flow-induced mechanical stimuli experienced by cells seeded in the scaffold. This leads to strong heterogeneity in the deposition of ECM. Furthermore, preferential adherence of cells to the ECM in favour of the artificial scaffold appears to have no significant influence on the eventual construct composition; adherence of cells to these supporting structures does, however, lead to cell and ECM distributions which mimic and exaggerate the heterogeneity of the underlying scaffold. Such phenomena have important ramifications for the mechanical integrity of engineered tissue constructs and their suitability for implantation in vivo

An asymptotic theory for the re-equilibration of a micellar surfactant solution

Micellar surfactant solutions are characterized by a distribution of aggregates comprised predominantly of pre-micellar aggregates (monomers, dimers, trimers, etc.) and a region of proper micelles close to the peak aggregation number, connected by an intermediate region containing a very low concentration of aggregates. Such a distribution gives rise to a distinct two-timescale re-equilibration following a system dilution, known as the 1 and 2 processes, whose dynamics may be described by the Becker–Döring equations. We use a continuum version of these equations to develop a reduced asymptotic description that elucidates the behavior during each of these processes

Infrared High-Resolution Spectroscopy of Post-AGB Circumstellar Disks. I. HR 4049 - The Winnowing Flow Observed?

High-resolution infrared spectroscopy in the 2.3-4.6 micron region is reported for the peculiar A supergiant, single-lined spectroscopic binary HR 4049. Lines from the CO fundamental and first overtone, OH fundamental, and several H2O vibration-rotation transitions have been observed in the near-infrared spectrum. The spectrum of HR 4049 appears principally in emission through the 3 and 4.6 micron region and in absorption in the 2 micron region. The 4.6 micron spectrum shows a rich 'forest' of emission lines. All the spectral lines observed in the 2.3-4.6 micron spectrum are shown to be circumbinary in origin. The presence of OH and H2O lines confirm the oxygen-rich nature of the circumbinary gas which is in contrast to the previously detected carbon-rich material. The emission and absorption line profiles show that the circumbinary gas is located in a thin, rotating layer near the dust disk. The properties of the dust and gas circumbinary disk and the spectroscopic orbit yield masses for the individual stars, M_AI~0.58 Msolar and M_MV~0.34 Msolar. Gas in the disk also has an outward flow with a velocity of $\gtrsim$ 1 km/s. The severe depletion of refractory elements but near-solar abundances of volatile elements observed in HR 4049 results from abundance winnowing. The separation of the volatiles from the grains in the disk and the subsequent accretion by the star are discussed. Contrary to prior reports, the HR 4049 carbon and oxygen isotopic abundances are typical AGB values: 12C/13C=6^{+9}_{-4} and 16O/17O>200.Comment: 42 pages, 14 figures, Accepted by Ap

The problematically short superwind of OH/IR stars - Probing the outflow with the 69 {\mu}m spectral band of forsterite

Spectra of OH/IR stars show prominent spectral bands of crystalline olivine (Mg$_{(2-2x)}$Fe$_{(2x)}$SiO$_{4}$). To learn more about the timescale of the outflows of OH/IR stars, we study the spectral band of crystalline olivine at 69 {\mu}m. The 69 {\mu}m band is of interest because its width and peak wavelength position are sensitive to the grain temperature and to the exact composition of the crystalline olivine. With Herschel/PACS, we observed the 69 {\mu}m band in the outflow of 14 OH/IR stars. By comparing the crystalline olivine features of our sample with those of model spectra, we determined the size of the outflow and its crystalline olivine abundance. The temperature indicated by the observed 69 {\mu}m bands can only be reproduced by models with a geometrically compact superwind ($R_{\rm{SW}}\lesssim$ 2500 AU = 1400 R$_{*}$).This means that the superwind started less than 1200 years ago (assuming an outflow velocity of 10 km/s). The small amount of mass lost in one superwind and the high progenitor mass of the OH/IR stars introduce a mass loss and thus evolutionary problem for these objects, which has not yet been understood.Comment: Accepted by A&

A Parameter Study of Classical Be Star Disk Models Constrained by Optical Interferometry

We have computed theoretical models of circumstellar disks for the classical Be stars $\kappa$ Dra, $\beta$ Psc, and $\upsilon$ Cyg. Models were constructed using a non-LTE radiative transfer code developed by \citet{sig07} which incorporates a number of improvements over previous treatments of the disk thermal structure, including a realistic chemical composition. Our models are constrained by direct comparison with long baseline optical interferometric observations of the H$\alpha$ emitting regions and by contemporaneous H$\alpha$ line profiles. Detailed comparisons of our predictions with H$\alpha$ interferometry and spectroscopy place very tight constraints on the density distributions for these circumstellar disks.Comment: 10 figures,28 pages, accepted by Ap