Taylor dispersion of gyrotactic swimming micro-organisms in a linear flow

The theory of generalized Taylor dispersion for suspensions of Brownian particles is developed to study the dispersion of gyrotactic swimming micro-organisms in a linear shear flow. Such creatures are bottom-heavy and experience a gravitational torque which acts to right them when they are tipped away from the vertical. They also suffer a net viscous torque in the presence of a local vorticity field. The orientation of the cells is intrinsically random but the balance of the two torques results in a bias toward a preferred swimming direction. The micro-organisms are sufficiently large that Brownian motion is negligible but their random swimming across streamlines results in a mean velocity together with diffusion. As an example, we consider the case of vertical shear flow and calculate the diffusion coefficients for a suspension of the alga <i>Chlamydomonas nivalis</i>. This rational derivation is compared with earlier approximations for the diffusivity

Dispersion of biased swimming microorganisms in a fluid flowing through a tube

Classical Taylor-Aris dispersion theory is extended to describe the transport of suspensions of self-propelled dipolar cells in a tubular flow. General expressions for the mean drift and effective diffusivity are determined exactly in terms of axial moments, and compared with an approximation a la Taylor. As in the Taylor-Aris case, the skewness of a finite distribution of biased swimming cells vanishes at long times. The general expressions can be applied to particular models of swimming microorganisms, and thus be used to predict swimming drift and diffusion in tubular bioreactors, and to elucidate competing unbounded swimming drift and diffusion descriptions. Here, specific examples are presented for gyrotactic swimming algae.Comment: 20 pages, 4 figures. Published version available at http://rspa.royalsocietypublishing.org/content/early/2010/02/09/rspa.2009.0606.short?rss=

Influence of flowing fluid property through an elastic tube on various deformations along the tube length

The study of fluid flow characteristics in collapsible elastic tubes is useful to understand biofluid mechanics encountered in the human body. The research work presented here is aimed at thoroughly investigating the influence of both Newtonian and/or non-Newtonian fluids (low and high shear thinning) during steady flow through an elastic tube on various tube deformations, which enables understanding of the interaction between wall motion, fluid flow, and intestinal transmembrane mass transfer as a crucial contribution to a mechanistic understanding of bioaccessibility/bioavailability. It is observed that for a given steady volume flow rate, the tube is buckled from an elliptical shape to a line or area contacted two lobes as the critical external pressure is increased. The downstream transmural pressure is found to get more negative than that at the upstream as the outlet pressure decreased due to stronger tube collapse resulting in a reduced cross-sectional area. The experimental results depict that the tube cross-sectional area decreased by only about a factor of one for PEG (polyethylene glycol) and about a factor of six for both CMC (carboxymethyl cellulose) and PAA (polyacrylamide) from the undeformed one under an applied external pressure of 105 mbar. The corresponding maximum velocity increased by a factor of two during steady flow of shear-thinning fluids. The shear-thinning behavior of both CMC and PAA solutions is clearly observed at a constant flow rate of 17 ml/s as the tube cross-sectional area decreased due to an increase in compressive transmural pressure. In addition, the viscosity of PAA is drastically decreased due to its high shear-thinning behavior than that of the CMC under the same applied external pressure

Dosimetric evaluation and radioimmunotherapy of anti-tumour multivalent Fab́ fragments

We have been investigating the use of cross-linked divalent (DFM) and trivalent (TFM) versions of the anti-carcinoembryonic antigen (CEA) monoclonal antibody A5B7 as possible alternatives to the parent forms (IgG and F(ab́)2) which have been used previously in clinical radioimmunotherapy (RIT) studies in colorectal carcinoma. Comparative biodistribution studies of similar sized DFM and F(ab́)2 and TFM and IgG, radiolabelled with both 131I and 90Y have been described previously using the human colorectal tumour LS174T nude mouse xenograft model (Casey et al (1996) Br J Cancer 74: 1397–1405). In this study quantitative estimates of radiation distribution and RIT in the xenograft model provided more insight into selecting the most suitable combination for future RIT. Radiation doses were significantly higher in all tissues when antibodies were labelled with 90Y. Major contributing organs were the kidneys, liver and spleen. The extremely high absorbed dose to the kidneys on injection of 90Y-labelled DFM and F(ab́)2 as a result of accumulation of the radiometal would result in extremely high toxicity. These combinations are clearly unsuitable for RIT. Cumulative dose of 90Y-TFM to the kidney was 3 times lower than the divalent forms but still twice as high as for 90Y-IgG. TFM clears faster from the blood than IgG, producing higher tumour to blood ratios. Therefore when considering only the tumour to blood ratios of the total absorbed dose, the data suggests that TFM would be the most suitable candidate. However, when corrected for equitoxic blood levels, doses to normal tissues for TFM were approximately twice the level of IgG, producing a two-fold increase in the overall tumour to normal tissue ratio. In addition RIT revealed that for a similar level of toxicity and half the administered activity, 90Y-IgG produced a greater therapeutic response. This suggests that the most promising A5B7 antibody form with the radionuclide 90Y may be IgG. Dosimetry analysis revealed that the tumour to normal tissue ratios were greater for all 131I-labelled antibodies. This suggests that 131I may be a more suitable radionuclide for RIT, in terms of lower toxicity to normal tissues. The highest tumour to blood dose and tumour to normal tissue ratio at equitoxic blood levels was 131I-labelled DFM, suggesting that 131I-DFM may be best combination of antibody and radionuclide for A5B7. The dosimetry estimates were in agreement with RIT results in that twice the activity of 131I-DFM must be administered to produce a similar therapeutic effect as 131I-TFM. The toxicity in this therapy experiment was minimal and further experiments at higher doses are required to observe if there would be any advantage of a higher initial dose rate for 131I-DFM. © 1999 Cancer Research Campaig

Interplay between geometry and flow distribution in an airway tree

Uniform fluid flow distribution in a symmetric volume can be realized through a symmetric branched tree. It is shown here, however, that the flow partitioning can be highly sensitive to deviations from exact symmetry if inertial effects are present. This is found by direct numerical simulation of the Navier-Stokes equations in a 3D tree geometry. The flow asymmetry is quantified and found to depend on the Reynolds number. Moreover, for a given Reynolds number, we show that the flow distribution depends on the aspect ratio of the branching elements as well as their angular arrangement. Our results indicate that physiological variability should be severely restricted in order to ensure uniform fluid distribution in a tree. This study suggests that any non-uniformity in the air flow distribution in human lungs should be influenced by the respiratory conditions, rest or hard exercise

Model validation for a noninvasive arterial stenosis detection problem

Copyright @ 2013 American Institute of Mathematical SciencesA current thrust in medical research is the development of a non-invasive method for detection, localization, and characterization of an arterial stenosis (a blockage or partial blockage in an artery). A method has been proposed to detect shear waves in the chest cavity which have been generated by disturbances in the blood flow resulting from a stenosis. In order to develop this methodology further, we use both one-dimensional pressure and shear wave experimental data from novel acoustic phantoms to validate corresponding viscoelastic mathematical models, which were developed in a concept paper [8] and refined herein. We estimate model parameters which give a good fit (in a sense to be precisely defined) to the experimental data, and use asymptotic error theory to provide confidence intervals for parameter estimates. Finally, since a robust error model is necessary for accurate parameter estimates and confidence analysis, we include a comparison of absolute and relative models for measurement error.The National Institute of Allergy and Infectious Diseases, the Air Force Office of Scientific Research, the Deopartment of Education and the Engineering and Physical Sciences Research Council (EPSRC)