Analysis of oxygen exchange between arterioles and surrounding capillary-perfused tissue.

A theoretical model is used to analyze oxygen transport in a three-dimensional tissue region containing an arteriole surrounded by an array of capillaries in planes perpendicular to the arteriole. Convective removal of oxygen from the vicinity of the arteriole by nearby capillaries is shown to increase diffusive oxygen loss from the arteriole. This effect depends on the locations of the capillaries, particularly those nearest to the arteriole. The arteriolar oxygen efflux is comparable to that predicted by a previous model which used a continuum approach, but the efflux does not increase with increasing perfusion as rapidly as predicted by the continuum model. Even a small capillary flow rate strongly influences the oxygen field surrounding the arteriole.     

Diffusion exchange between a membrane-bounded sphere and its surrounding

The diffusion equation is solved for a membrane-bounded sphere situated in an infinite medium with different diffusion properties. The formal solution is obtained through Laplace transformation in the time variable. It is not possible to find a closed form solution in terms of analytical functions, and therefore a numerical inversion technique is applied to obtain the final solution. The application on a biological problem is discussed.     

A mathematical model of airway and pulmonary arteriole smooth muscle

Airway hyperresponsiveness is a major characteristic of asthma and is believed to result from the excessive contraction of airway smooth muscle cells (SMCs). However, the identification of the mechanisms responsible for airway hyperresponsiveness is hindered by our limited understanding of how calcium (Ca²⁺), myosin light chain kinase (MLCK), and myosin light chain phosphatase (MLCP) interact to regulate airway SMC contraction. In this work, we present a modified Hai-Murphy cross-bridge model of SMC contraction that incorporates Ca²⁺ regulation of MLCK and MLCP. A comparative fit of the model simulations to experimental data predicts 1), that airway and arteriole SMC contraction is initiated by fast activation by Ca²⁺ of MLCK; 2), that airway SMC, but not arteriole SMC, is inhibited by a slower activation by Ca²⁺ of MLCP; and 3), that the presence of a contractile agonist inhibits MLCP to enhance the Ca²⁺ sensitivity of airway and arteriole SMCs. The implication of these findings is that murine airway SMCs exploit a Ca²⁺-dependent mechanism to favor a default state of relaxation. The rate of SMC relaxation is determined principally by the rate of release of the latch-bridge state, which is predicted to be faster in airway than in arteriole. In addition, the model also predicts that oscillations in calcium concentration, commonly observed during agonist-induced smooth muscle contraction, cause a significantly greater contraction than an elevated steady calcium concentration.     

A mechanism for oxygen exchange between ligated oxometalloporphinates and bulk water

Oxygen exchange between high-valent metal-oxo complexes and bulk water has been monitored for nonligated model porphyrins (hemin, FeTDCPPS, MnTMPyP) and the axially ligated microperoxidase-8 (MP-8). Exchange extents up to 90% were measured for MP-8 in spite of the presence of an axial histidine ligand and accompanied by the formation of nonlabelled H(2)O(2) from H(2)(18)O(2). These results point to the existence of a mechanism for oxygen exchange between the high-valent iron-oxo complex and the solvent different from the so-called "oxo-hydroxo tautomerism." Regeneration of the primary oxidant, H(2)O(2), and oxygen exchange by axially ligated porphyrins can be explained by a mechanism involving the reversibility of compound I formation.     

A mathematical model of the myogenic response to systolic pressure in the afferent arteriole

Elevations in systolic blood pressure are believed to be closely linked to the pathogenesis and progression of renal diseases. It has been hypothesized that the afferent arteriole (AA) protects the glomerulus from the damaging effects of hypertension by sensing increases in systolic blood pressure and responding with a compensatory vasoconstriction (Loutzenhiser R, Bidani A, Chilton L. Circ Res 90: 1316-1324, 2002). To investigate this hypothesis, we developed a mathematical model of the myogenic response of an AA wall, based on an arteriole model (Gonzalez-Fernandez JM, Ermentrout B. Math Biosci 119: 127-167, 1994). The model incorporates ionic transport, cell membrane potential, contraction of the AA smooth muscle cell, and the mechanics of a thick-walled cylinder. The model represents a myogenic response based on a pressure-induced shift in the voltage dependence of calcium channel openings: with increasing transmural pressure, model vessel diameter decreases; and with decreasing pressure, vessel diameter increases. Furthermore, the model myogenic mechanism includes a rate-sensitive component that yields constriction and dilation kinetics similar to behaviors observed in vitro. A parameter set is identified based on physical dimensions of an AA in a rat kidney. Model results suggest that the interaction of Ca(2+) and K(+) fluxes mediated by voltage-gated and voltage-calcium-gated channels, respectively, gives rise to periodicity in the transport of the two ions. This results in a time-periodic cytoplasmic calcium concentration, myosin light chain phosphorylation, and cross-bridge formation with the attending muscle stress. Furthermore, the model predicts myogenic responses that agree with experimental observations, most notably those which demonstrate that the renal AA constricts in response to increases in both steady and systolic blood pressures. The myogenic model captures these essential functions of the renal AA, and it may prove useful as a fundamental component in a multiscale model of the renal microvasculature suitable for investigations of the pathogenesis of hypertensive renal diseases.     

A stochastic model for facilitated transport of oxygen through tissue slices

Longmuir and co-workers have reported that respiration of certain tissue slices is approximated by Michaelis-Menten kinetics. From this and other experimental findings, Longmuir proposed that a carrier is involved in tissue oxygen transport. Gold developed a deterministic model to examine this hypothesis. This report presents a stochastic model for a fixed site carrier in a more general framework that includes the stochastic counter-part to Gold's deterministic model as a special case. The kinetics of tissue oxygen consumption predicted by the model are examined for various cases.     

Kinetics of water exchange between a mite,Laelaps echidnina,and the surrounding air

The temporal dependence of water exchange between an arthropod and its surroundings fits a mathematical model based on diffusion theory. The model requires that the mass change rate of L. echidnina results from a zeroorder component consisting primarily of water sorption and a first-order component made up largely of water loss. Tentatively, transpiration of water is associated with primarily the tracheal system, and sorption of water primarily with other surfaces. Placing mites in a CO₂ atmosphere greatly increased their water loss, but had little effect on sorption of water. The effect of increase in temperature on the sorption rate ($\text{m}\text{?}{}_{\mathrm{s}}$) and transpiration rate constant (k_T) was to increase them. The influence of the activity of the water in the vapour phase in the ambient air (a_v) was primarily on sorption.     

Analysis of oxygen delivery and uptake relationships in the Krogh tissue model

Normally, tissue O2 uptake (VO2) is set by metabolic activity rather than O2 delivery (QO2 = blood flow X arterial O2 content). However, when QO2 is reduced below a critical level, VO2 becomes limited by O2 supply. Experiments have shown that a similar critical QO2 exists, regardless of whether O2 supply is reduced by progressive anemia, hypoxemia, or reduction in blood flow. This appears inconsistent with the hypothesis that O2 supply limitation must occur by diffusion limitation, since very different mixed venous PO2 values have been seen at the critical point with hypoxic vs. anemic hypoxia. The present study sought to begin clarifying this paradox by studying the theoretical relationship between tissue O2 supply and uptake in the Krogh tissue cylinder model. Steady-state O2 uptake was computed as O2 delivery to tissue representative of whole body was gradually lowered by anemic, hypoxic, or stagnant hypoxia. As diffusion began to limit uptake, the fall in VO2 was computed numerically, yielding a relationship between QO2 and VO2 in both supply-independent and O2 supply-dependent regions. This analysis predicted a similar biphasic relationship between QO2 and VO2 and a linear fall in VO2 at O2 deliveries below a critical point for all three forms of hypoxia, as long as intercapillary distances were less than or equal to 80 microns. However, the analysis also predicted that O2 extraction at the critical point should exceed 90%, whereas real tissues typically extract only 65-75% at that point. When intercapillary distances were larger than approximately 80 microns, critical O2 extraction ratios in the range of 65-75% could be predicted, but the critical point became highly sensitive to the type of hypoxia imposed, contrary to experimental findings. Predicted gas exchange in accord with real data could only be simulated when a postulated 30% functional peripheral O2 shunt (arterial admixture) was combined with a tissue composed of Krogh cylinders with intercapillary distances of less than or equal to 80 microns. The unrealistic efficacy of tissue O2 extraction predicted by the Krogh model (in the absence of postulated shunt) may be a consequence of the assumed homogeneity of tissues, because real tissues exhibit many forms of heterogeneity among capillary units. Alternatively, the failure of the original Krogh model to fully predict tissue O2 supply dependency may arise from basic limitations in the assumptions of that model.     

The specificity of the high endothelial venule in bronchus-associated lymphoid tissue (BALT)

By using an in vitro binding assay, the specificity of T and B cell adherence on high endothelial venules (HEV) of bronchus-associated lymphoid tissue (BALT) was studied in the rat and the guinea pig. It was found that the adherence specificity of the BALT HEV is different from that found in Peyer's patches and more closely resembles the specificity of the HEV in mesenteric lymph nodes. The data are discussed in view of a common mucosal immune system.     

A note on Gutierrez's kinetics model for oxygen delivery to tissue.

The problems associated with Gutierrez model (1986, Resp. Physiol. 63, 79-96) on O2 delivery to tissue are discussed. He has used a dimensionally incorrect function for the oxygen dissociation curve (ODC). The dimensionally correct function for the ODC has been used in the analysis and the correct results are given for normoxic, hypoxic and anaemic conditions.     

Changes in oxygen partial pressure of brain tissue in an animal model of obstructive apnea

Background

Prolonged weaning from mechanical ventilation has a major impact on ICU bed occupancy and patient outcome, and has significant cost implications. There is evidence in patients around the period of extubation that helium-oxygen leads to a reduction in the work of breathing. Therefore breathing helium-oxygen during weaning may be a useful adjunct to facilitate weaning. We hypothesised that breathing helium-oxygen would reduce carbon dioxide production during the weaning phase of mechanical ventilation.

Materials/patients and methods

We performed a prospective randomised controlled single blinded cross-over trial on 19 adult intensive care patients without significant airways disease who fulfilled criteria for weaning with CPAP. Patients were randomised to helium-oxygen and air-oxygen delivered during a 2 hour period of CPAP ventilation. Carbon dioxide production (VCO₂) was measured using a near patient main stream infrared carbon dioxide sensor and fixed orifice pneumotachograph.

Results

Compared to air-oxygen, helium-oxygen significantly decreased VCO₂ production at the end of the 2 hour period of CPAP ventilation; there was a mean difference in CO₂ production of 48.9 ml/min (95% CI 18.7-79.2 p = 0.003) between the groups. There were no significant differences in other respiratory and haemodynamic parameters.

Conclusion

This study shows that breathing a helium-oxygen mixture during weaning reduces carbon dioxide production. This physiological study supports the need for a clinical trial of helium-oxygen mixture during the weaning phase of mechanical ventilation with duration of weaning as the primary outcome.

Trial registration

ISRCTN56470948     

Chromosome aberrations and sister chromatid exchange in the inhabitants of an area surrounding a large metallurgical plant

The aim of the study was to examine the level of chromosome aberrations and sister chromatid exchanges in lymphocytes of subjects living in the close vicinity of a large metallurgical plant and to compare it with the results obtained in the inhabitants of central Kraków and of a village located 40 km away from the city and the plant. An increased incidence of chromosomal abnormalities and thus an increased genetic hazard was found in the group living near the steel foundry.     

Ultrastructural features of the interrelationship between nerve fibers and the surrounding tissue in the major arteries of rabbits

The fine structure of nerve plexus in the rabbit abdominal aorta, ear and coronary arteries has been studied. Four types of the nerve fibre organization corresponding to different levels of sectioning their preterminal and terminal zones have been determined. Axons form large bundles which lose Schwann sheathes and divide into smaller and even single axons as they approach the distal end. Single axons make up contacts with effector cells without forming special synaptic structures. The smalles distance found between axon membranes and smooth muscle cells is 20 nm and 50 nm for the ear and coronary arteries, respectively. In the abdominal aorta, axons lie at a distance of several microns from the muscle sheath. Such arrangement supports the hypothesis of a "distant" nervous influence on the smooth muscle and indicates that the space of nervous influence comprises the tissue surrounding the blood vessel