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A key aim of the cardiac Physiome Project is to develop theoretical models to simulate the functional behaviour of the heart under physiological and pathophysiological conditions. Heart function is critically dependent on the delivery of an adequate blood supply to the myocardium via the coronary vasculature. Key to this critical function of the coronary vasculature is system dynamics that emerge via the interactions of the numerous constituent components at a range of spatial and temporal scales. Here, we focus on several components for which theoretical approaches can be applied, including vascular structure and mechanics, blood flow and mass transport, flow regulation, angiogenesis and vascular remodelling, and vascular cellular mechanics. For each component, we summarise the current state of the art in model development, and discuss areas requiring further research. We highlight the major challenges associated with integrating the component models to develop a computational tool that can ultimately be used to simulate the responses of the coronary vascular system to changing demands and to diseases and therapies.

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The unsteady dispersion of a solute in a Casson fluid flowing in a conduit (pipe/channel) is studied using the generalized dispersion model of Gill and Sankarasubramanian. With this approach, the entire dispersion process is described appropriately in terms of a simple diffusion process with the effective diffusion coefficient as a function of time, in addition to its dependence on the yield stress of the fluid. The results are accurate up to a first approximation for small times, but verified with Sharp to be exact for large times. The model brings out mainly the effect of yield stress, or equivalently, the plug flow region on the overall dispersion process. It is found that the rate of dispersion is reduced (i.e., the effective diffusivity decreases) due to the yield stress of the fluid, or equivalently, the plug flow region in the conduit. Also, the effective diffusivity increases with time, but eventually attains its steady state value below a critical time [0.48(a2/Dm) for dispersion in a pipe and 0.55(a2/Dm) for dispersion in a channel-the critical transient time for a Newtonian fluid-where "a" is the radius of the pipe and Dm is the molecular diffusivity]. At steady state, for dispersion in a pipe with the plug flow radius one tenth of the radius of the pipe, the effective diffusivity is reduced to about 0.78 times of the corresponding value for a Newtonian fluid at equivalent flow rates; for dispersion in a channel, the reduction factor is about 0.73 confirming the earlier result of Sharp. Further, the location of the center of mass of a passive species over a cross section is found to remain unperturbed during the course of dispersion and for different values of the plug flow parameter (i.e., the yield stress of the fluid). The study can be used as a starting first approximate solution for studying the dispersion in the cardiovascular system or blood oxygenators.

The study focuses on assessing the status of respiratory morbidity in Delhi over a four years period from 2000-2003. An attempt was made to investigate the role of important pollutants (SO(2), NO(2), SPM and RSPM) and various meteorological factors (temperature minimum & maximum, relative humidity at 0830 and 1730 hrs. and wind speed) in being responsible for respiratory admissions on account of COPD, asthma and emphysema. The study showed that winter months had greater exposure risk as pollutants often get trapped in the lower layers of atmosphere resulting in high concentrations. Statistical analysis revealed that two pollutants have significant positive correlation with the number of COPD cases viz., SPM (r = 0.474; p < 0.01) and RSPM (r = 0.353; p < 0.05), while a meteorological factor temperature (minimum) has a significant negative correlation (r = -0.318; p < 0.05) with COPD. Stepwise multiple regression analysis was performed for COPD as dependent variable and R(2) value of 0.33 was obtained indicating that SPM and RH(1730) were able to explain 33 percent variability in COPD. The partial correlation of SPM and RH(1730) on COPD was higher than any other combination and therefore they can be regarded as important contributing variables on COPD.

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