Maithili Sharan

A compartmental model for oxygen transport in brain microcirculation

A compartmental model is formulated for oxygen transport in the cerebrovascular bed of the brain. The model considers the arteriolar, capillary and venular vessels. The vascular bed is represented as a series of compartments on the basis of blood vessel diameter. The formulation takes into account such parameters as hematocrit, vascular diameter, blood viscosity, blood flow, metabolic rate, the nonlinear oxygen dissociation curve, arterial PO2, P50 (oxygen tension at 50% hemoglobin saturation with O2) and carbon monoxide concentration. The countercurrent diffusional exchange between paired arterioles and venules is incorporated into the model. The model predicts significant longitudinal PO2 gradients in the precapillary vessels. However, gradients of hemoglobin saturation with oxygen remain fairly small. The longitudinal PO2 gradients in the postcapillary vessels are found to be very small. The effect of the following variables on tissue PO2 is studied: blood flow, PO2 in the arterial blood, hematocrit, P50, concentration of carbon monoxide, metabolic rate, arterial diameter, and the number of perfused capillaries. The qualitative features of PO2 distrbution in the vascular network are not altered with moderate variation of these parameters. Finally, the various types of hypoxia, namely hypoxic, anemic and carbon monoxide hypoxia, are discussed in light of the above sensitivity analysis.

Visibility and incidence of respiratory diseases during the 1998 haze episode in Brunei Darussalam

— Air pollution episodes as a result of forest fires in Brunei Darussalam and neighbouring regions have reached hazardous levels in recent years. Such episodes are generally associated with poor visibility and air quality conditions. In the present study, data on PM10 (particulate matter of size less than 10 microns) and CO in Brunei Darussalam have been considered to study the incidence of respiratory diseases whereas data on relative humidity (RH) in addition to PM10 have been used to explain the visibility with a particular emphasis on haze episode during 1998.¶Initial exploratory analysis indicates significant correlation of visibility with PM10 and RH. An attempt has been made to explain visibility on the basis of PM10 and RH using multiple linear regression analysis. The regression model shows that PM10 and RH are two significant factors affecting the visibility at a given site. Further, canonical correlation, a multivariate method of analysis, has been used to explain the incidence of respiratory diseases as a function of air quality during the haze period. The results indicate that PM10 and CO levels during the haze period have a significant bearing on the incidence of respiratory diseases (Asthma, Acute Respiratory Infections and Influenza (ARII)).

Experimental and theoretical studies of oxygen gradients in rat pial microvessels

Using modified oxygen needle microelectrodes and intravital videomicroscopy, measurements were made of tissue oxygen tension (PO2) profiles near cortical arterioles and transmural PO2 gradients in the pial arterioles of the rat. Under control conditions, the transmural PO2 gradient averaged 1.17 ± 0.06 mm Hg/μm (mean ± s.e., n = 40). Local arteriolar dilation resulted in a marked decrease in the transmural PO2 gradient to 0.68 ± 0.04 mm Hg/μm (P < 0.001, n = 38). The major finding of this study is a dependence of the transmural PO2 gradient on the vascular tone of the pial arterioles. Using a model of oxygen transport in an arteriole and experimental PO2 profiles, values of radial perivascular and intravascular O2 fluxes were estimated. Our theoretical estimates show that oxygen flux values at the outer surface of the arteriolar wall are approximately 10−5mL O2/cm2 per sec, independent of the values of the arteriolar wall O2 consumption within a wide range of consumption values. This also means that PO2 transmural gradients for cerebral arterioles are within the limits of 1 to 2 mm Hg/μm. The data lead to the conclusion that O2 consumption of the arteriolar wall is within the range for the surrounding tissue and O2 consumption of the endothelial layer appears to have no substantial impact on the transmural PO2 gradient.

An inversion technique for the retrieval of single-point emissions from atmospheric concentration measurements

The aim of the study is to propose a technique for the retrieval of point sources of atmospheric trace species from concentration measurements. The inverse problem of identifying the parameters of a point source is addressed within the assimilative framework of renormalization recently proposed for the identification of distributed emissions. This theory has been extended for the point sources based on the property that these are associated with the maximum of the renormalized estimate computed from the observations. This approach along with an analytic dispersion model is used for point source identification, and the sensitivity of the samplers is described by the same model in backward mode. The proposed technique is illustrated not only with synthetic measurements but also with seven sets of observations, corresponding to convective conditions, taken from the low-wind tracer diffusion experiment conducted at the Indian Institute of Technology Delhi in 1991. The position and intensity of the source are retrieved exactly with the synthetic measurements in all the sets validating the technique. The position of the source is retrieved with an average error of 17 m, mostly along wind; its intensity is estimated within a factor 2 for all the sets of real observations. From a theoretical point of view, the link established between point and distributed sources clarifies new concepts for the exploitation of monitoring networks. In particular, the influence of the noise on the identification of a source is related to the relative visibility of the various regions described with a renormalizing weight function. The geometry of the environment modified according to the weights is interpreted as an apparent geometry. It is analogous to the apparent flatness of the starry sky in eyes view, usually considered an impression rather than a scientific fact.

An inversion technique to retrieve the source of a tracer with an application to synthetic satellite measurements

An increasing number of satellites are being launched to observe the atmospheric concentrations of a variety of trace species. They cover a wide area at once and are expected to provide more extensive information than the rare ground-based concentration measurements. The paper introduces an adjoint technique to retrieve the emissions based on a recent concept of renormalization. This technique is used with a set of synthetic column-averaged measurements for an idealized satellite corresponding to a prescribed ground-level source. The Indian region is considered with two contrast meteorological conditions in the months of January and July, corresponding to winter and monsoon season. Since it is not feasible to handle a large volume of satellite data in the inversion due to the time involved in the computation of the matrices, a preprocessing is suggested to extract the manageable data set as a representative of the whole data. Considering a limited number of observations, it is shown that the emissions are underestimated without and with the renormalization procedure. The degree of underestimation is relatively more with non-renormalized estimates. The non-renormalized estimate is degraded further by a refined resolution of the model, whereas the renormalized estimate is not altered appreciably. The preprocessing based on aggregation of data is found to retrieve the prescribed emissions up to 75% in the month of January and 90% in the month of July. The relatively computationally expensive renormalization may be avoided except in the case of partial visibility of the area of interest, due to cloud cover or a technical constraint. A simple criterion for the optimum design of a monitoring network is suggested.

A mathematical model for the computation of the oxygen dissociation curve in human blood

The mathematical relations developed by various researchers for the oxygen dissociation curve are reviewed. Using well-known mechanisms of chemical kinetics of various species in the blood, we have developed a mathematical formula to compute the oxygen dissociation curve in the blood showing its dependence on the pH and PCO2. The functional form, proposed here, is much simpler in comparison to those available in the literature for use in the mathematical modelling of O2 transport in the pulmonary and systemic circulations. In the process, the well-known Hills equation has been generalized showing an explicit dependence on PCO2 and pH. It is shown that the oxygen dissociation curve computed from our comparatively simpler equation, fits in fairly well with the documented data and shows realistic shift with PCO2 and pH.

An analytical model for dispersion of pollutants from a continuous source in the atmospheric boundary layer

For the dispersion of a pollutant released from a continuous source in the atmospheric boundary layer (ABL), a generalized analytical model describing the crosswind-integrated concentrations is presented. An analytical scheme is described to solve the resulting two-dimensional steady-state advection–diffusion equation for horizontal wind speed as a generalized function of vertical height above the ground and eddy diffusivity as a function of both downwind distance from the source and vertical height. Special cases of this model are deduced and an extensive analysis is carried out to compare the model with the known analytical models by taking the particular forms of wind speed and vertical eddy diffusivity. The proposed model is evaluated with the observations obtained from Copenhagen diffusion experiments in unstable conditions and Hanford and Prairie Grass experiments in stable conditions. In evaluation of the model, a recently proposed formulation for the wind speed in the entire ABL is used. It is concluded that the present model is performing well with the observations and can be used to predict the short-range dispersion from a continuous release. Further, it is shown that the accurate parameterizations of wind speed and eddy diffusivity provide a significant improvement in the agreement between computed and observed concentrations.

Comparative Evaluation of Eddy Exchange Coefficients for Strong and Weak Wind Stable Boundary Layer Modeling

Abstract Five local K-closure formulations and a TKE closure were incorporated in a one-dimensional version of the Pielke’s model, and a comparative evaluation of the closure schemes was made for strong and weak wind stable boundary layer (SBL). The Cabauw (Netherlands) and EPRI-Kincaid site (United States) observations were used for this purpose. The results indicate that for the strong wind case study, the profiles of turbulent diffusivities in terms of shape, depth of significant mixing, and the height above the surface where diffusion reaches a maximum are more or less the same for the various closure schemes. Only the magnitudes of mixing produced by various closure schemes are different. This difference produced by various closure formulations causes minor but noticeable changes in the mean wind field and thermodynamic structure of the model SBL. However, although the profiles of turbulent diffusivities become weak, variable, and poorly defined under weak wind conditions, the mean profiles become in...

Inverse Modelling for Identification of Multiple-Point Releases from Atmospheric Concentration Measurements

An inverse modelling methodology is proposed for the identification of multiple-point sources releasing similar tracer, in which influences from the various emissions are merged in each detector’s measurement. The identification is addressed from a limited merged set of atmospheric concentration measurements. The methodology is blended with the natural information provided by the geometry of the monitoring network in terms of the weight functions that interpret the associated visibility/illumination of the monitoring network. The release parameters, locations and intensities of the multiple-point sources are estimated by minimizing the objective function within the least squares framework. The methodology has been successfully applied to identify the two- and three- point simultaneous emissions from synthetic measurements generated by the model without noise or with controlled noise artificially added, and from pseudo-real measurements generated from the Indian Institute of Technology low wind diffusion experiment by combining several of single-point release runs. With the synthetic measurements, all the release parameters are retrieved exactly as those prescribed in all the runs. With the pseudo-real measurements, the release locations are retrieved with an average error of 13 m and intensities are estimated on an average within a factor of 1.5. In a sensitivity analysis, it is shown that the incurred errors in the retrieval of the two- and three-point sources with the pseudo-real data correspond to the 10–30 % Gaussian distributed random noise in the observations. Theoretical and computational comparisons are given between the weighted and non-weighted classical formulations. In addition, an alternative strategy is proposed in order to reduce the computational time required in the source estimation.

An analysis of hypoxia in sheep brain using a mathematical model

AbstractCerebral blood flow (CBF) increases as arterial oxygen content falls with hypoxic (low PO2), anemic (low hemoglobin) and carbon monoxide (CO) (high carboxyhemoglobin) hypoxia. Despite a higher arterial PO2, CO hypoxia provokes a greater increase in CBF than hypoxic hypoxia. We analyzed published data using a compartmental mathematical model to test the hypothesis that differences in PO2 in tissue, or a closely related vascular compartment, account for the greater response to CO hypoxia. Calculations showed that tissue, but not arteriolar, PO2 was lower in CO hypoxia because of the increased oxyhemoglobin affinity with CO hypoxia. Analysis of studies in which oxyhemoglobin affinity was changed independently of CO supports the conclusion that changes in tissue PO2 (or closely related capillary or venular PO2) are predictive of alterations in CBF. We then sought to determine the role of tissue PO2 in anemic hypoxia, with no change in arterial and little, if any, change in venous PO2. Calculations predict a small fall in tissue PO2 as hematocrit decreases from 55% to 20%. However, calculations show that changes in blood viscosity can account for the increase in CBF in anemic hypoxia over this range of hematocrits.