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.     

Hemoglobin‐based oxygen carrier and convection enhanced oxygen transport in a hollow fiber bioreactor

A mathematical model was developed to study O₂ transport in a convection enhanced hepatic hollow fiber (HF) bioreactor, with hemoglobin‐based O₂ carriers (HBOCs) present in the flowing cell culture media stream of the HF lumen. In this study, four HBOCs were evaluated: PEG‐conjugated human hemoglobin (MP4), human hemoglobin (hHb), bovine hemoglobin (BvHb) and polymerized bovine hemoglobin (PolyBvHb). In addition, two types of convective flow in the HF extra capillary space (ECS) were considered in this study. Starling flow naturally occurs when both of the ECS ports are closed. If one of the ECS ports is open, forced convective flow through the ECS will occur due to the imposed pressure difference between the lumen and ECS. This type of flow is referred to as cross‐flow in this work, since some of the fluid entering the HF lumen will pass across the HF membrane and exit via the open ECS port. In this work, we can predict the dissolved O₂ concentration profile as well as the O₂ transport flux in an individual HF of the bioreactor by solving the coupled momentum and mass transport equations. Our results show that supplementation of the cell culture media with HBOCs can dramatically enhance O₂ transport to the ECS (containing hepatocytes) and lead to the formation of an in vivo‐like O₂ spectrum for the optimal culture of hepatocytes. However, both Starling flow and cross‐flow have a very limited effect on O₂ transport in the ECS. Taken together, this work represents a novel predictive tool that can be used to design or analyze HF bioreactors that expose cultured cells to defined overall concentrations and gradients of O₂. Biotechnol. Bioeng. 2009;102: 1603–1612. © 2008 Wiley Periodicals, Inc.     

Determinants of oxygen tension in normal and tumour tissues: A theoretical study

The partial pressure of O₂ (pO₂) at any point within the tissue surrounding a blood capillary is obtained through a modified version of the Erlang-Krogh model, in which the details of the intracapillary pressure profile and the axial diffusion of oxygen have been taken into consideration. The model is analytically solvable and contains only a single free parameter. A search for the major determinants of tissue O₂ tension reveals that the parameters influencing the pO₂ profile within the capillaries are the most sensitive factors. Experimentally obtained pO₂ histograms of various normal and tumour tissues can be reproduced fairly accurately from the model.     

Perfluorocarbon facilitated O2 transport in a hepatic hollow fiber bioreactor

A mathematical model describing O₂ transport in a hepatic hollow fiber (HF) bioreactor supplemented with perfluorocarbons (PFCs) in the circulating cell culture media was developed to explore the potential of PFCs in properly oxygenating a bioartificial liver assist device (BLAD). The 2‐dimensional model is based on the geometry of a commercial HF bioreactor operated under steady‐state conditions. The O₂ transport model considers fluid motion of a homogeneous mixture of cell culture media and PFCs, and mass transport of dissolved O₂ in a single HF. Each HF consists of three distinct regions: (1) the lumen (conducts the homogeneous mixture of cell culture media and PFCs), (2) the membrane (physically separates the lumen from the extracapillary space (ECS), and (3) the ECS (hepatic cells reside in this compartment). In a single HF, dissolved O₂ is predominantly transported in the lumen via convection in the axial direction and via diffusion in the radial direction through the membrane and ECS. The resulting transport equations are solved using the finite element method. The calculated O₂ transfer flux showed that supplementation of the cell culture media with PFCs can significantly enhance O₂ transport to the ECS of the HF when compared with a control with no PFC supplementation. Moreover, the O₂ distribution and subsequent analysis of ECS zonation demonstrate that limited in vivo‐like O₂ gradients can be recapitulated with proper selection of the operational settings of the HF bioreactor. Taken together, this model can also be used to optimize the operating conditions for future BLAD development that aim to fully recapitulate the liver's varied functions. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

Optimum capillary number for oxygen delivery to tissue in man

The optimum number of total capillaries in the whole human body was estimated from the analysis of the efficiency for oxygen (O₂) transport in the vascular-tissue system. We used a tissue model composed of uniform spheres in which O₂ diffuses from the capillary located at the centre of each sphere towards the surrounding tissue consuming O₂ at a constant rate. The tissue mass supplied by a single capillary was estimated as the area of positive O₂ concentration under a given condition of capillary flow and O₂ consumption rate. Total tissue mass was determined as the function of the capillary numbern and the total blood flow. On the other hand, the energy cost required to maintain the vascular system withn terminals was assessed by using the minimum volume model (Kamiya and Togawa,Bull. math. Biophys. 34, 431–438, 1972). The efficiency of the entire vascular-tissue system was evaluated by calculating the ratio of total tissue mass/cost function. The result of the calculation using physiological data of cardiac output and O₂ consumption for an average human adult during a heavy exercise revealed the maximum efficiency occurring at the capillary number 3.7×10¹⁰ which coincided well with its normal range of physiological estimates (3.2×10¹⁰–4.2×10¹⁰). We concluded that the entire vascular-tissue system is constructed so as to attain the highest efficiency in O₂ transport at its maximum activity.     

Venular endothelium-derived NO can affect paired arteriole: a computational model

Venular endothelial cells can release nitric oxide (NO) in response to intraluminal flow both in isolated venules and in vivo. Experimental studies suggest that venular endothelium-released NO causes dilation of the adjacent paired arteriole. In the vascular wall, NO stimulates its target hemoprotein, soluble guanylate cyclase (sGC), which relaxes smooth muscle cells. In this study, a computational model of NO transport for an arteriole and venule pair was developed to determine the importance of the venular endothelium-released NO and its transport to the adjacent arteriole in the tissue. The model predicts that the tissue NO levels are affected within a wide range of parameters, including NO-red blood cell reaction rate and NO production rate in the arteriole and venule. The results predict that changes in the venular NO production affected not only venular endothelial and smooth muscle NO concentration but also endothelial and smooth muscle NO concentration in the adjacent arteriole. This suggests that the anatomy of microvascular tissue can permit the transport of NO from arteriolar to venular side, and vice versa, and may provide a mechanism for dilation of proximal arterioles by venules. These results will have significant implications for our understanding of tissue NO levels in both physiological and pathophysiological conditions.     

Mixtures of hemoglobin‐based oxygen carriers and perfluorocarbons exhibit a synergistic effect in oxygenating hepatic hollow fiber bioreactors

Hepatic hollow fiber (HF) bioreactors are being developed for use as bioartificial liver assist devices (BLADs). In general, BLADs suffer from O₂ limited transport, which reduces their performance. This modeling study seeks to investigate if O₂ carrying solutions consisting of mixtures of hemoglobin‐based oxygen carriers (HBOCs) and perfluorocarbons (PFCs) can enhance O₂ transport to hepatocytes cultured in the extra capillary space (ECS) of HF bioreactors. We simulated supplementing the circulating cell culture media stream of the HF bioreactor with a mixture containing these two types of oxygen carriers (HBOCs and PFCs). A mathematical model was developed based on the dimensions and physical characteristics of a commercial HF bioreactor. The resulting set of partial differential equations, which describes fluid transport; as well as, mass transport of dissolved O₂ in the pseudo‐homogeneous PFC/water phase and oxygenated HBOC, was solved to yield the O₂ concentration field in the three HF domains (lumen, membrane and ECS). Our results show that mixtures of HBOC and PFC display a synergistic effect in oxygenating the ECS. Therefore, the presence of both HBOC and PFC in the circulating cell culture media dramatically improves transport of O₂ to cultured hepatocytes. Moreover, the in vivo O₂ spectrum in a liver sinusoid can be recapitulated by supplementing the HF bioreactor with a mixture of HBOCs and PFCs at an inlet pO₂ of 80 mmHg. Therefore, we expect that PFC‐based oxygen carriers will be more efficient at transporting O₂ at higher O₂ levels (e.g., at an inlet pO₂ of 760 mmHg, which corresponds to pure O₂ in equilibrium with aqueous cell culture media at 1 atm). Biotechnol. Bioeng. 2010; 105: 534–542. © 2009 Wiley Periodicals, Inc.     

Placental blood flows and oxygen transfer during uterine contractions: A mathematical model

Theoretical calculations have been performed on the effects of changes in intrauterine pressure on maternal and fetal placental blood flows and pressures and transplacental O₂ exchange. Initial conditions and contraction profiles may be “assumed normal” or abnormal. The model predicts that the fetal O₂ deficit is most sensitive to the maximum intensity of the contraction and maternal mean arterial blood pressure, less sensitive to the duration of the contraction and far less sensitive to the value of maternal arterial PO₂. The umbilical venous PO₂ falls to a minimum at the peak of a contraction. Its level is most sensitive to contraction intensity and maternal blood pressure; while the value of maternal arterial PO₂ has less effect and the duration of contraction has essentially no effect. There is interaction between factors so that the effect of simultaneous changes is not necessarily in proportion to the effects of individual changes.     

A role for iron and oxygen chemistry in preserving soft tissues,cells and molecules from deep time

The persistence of original soft tissues in Mesozoic fossil bone is not explained by current chemical degradation models. We identified iron particles (goethite-αFeO(OH)) associated with soft tissues recovered from two Mesozoic dinosaurs, using transmission electron microscopy, electron energy loss spectroscopy, micro-X-ray diffraction and Fe micro-X-ray absorption near-edge structure. Iron chelators increased fossil tissue immunoreactivity to multiple antibodies dramatically, suggesting a role for iron in both preserving and masking proteins in fossil tissues. Haemoglobin (HB) increased tissue stability more than 200-fold, from approximately 3 days to more than two years at room temperature (25°C) in an ostrich blood vessel model developed to test post-mortem ‘tissue fixation’ by cross-linking or peroxidation. HB-induced solution hypoxia coupled with iron chelation enhances preservation as follows: HB + O₂ > HB − O₂ > −O₂ ≫ +O₂. The well-known O₂/haeme interactions in the chemistry of life, such as respiration and bioenergetics, are complemented by O₂/haeme interactions in the preservation of fossil soft tissues.     

Analysis of coupled intra- and extraluminal flows for single and multiple capillaries

Matched asymptotic expansions are used to study a model of the coupled fluid flow in the capillaries and tissue of the microcirculation. These capillaries are long, narrow cylindrical tubes embedded in a uniform tissue space. The capillary, or intraluminal, flow is assumed to be that of an incompressible Navier-Stokes fluid wherein colloids are represented as dilute solute; the extraluminal flow in the tissue is according to Darcy's law. Central to this fluid exchange is the boundary condition on the fluid radial velocity at the semipermeable wall of the capillary. This boundary condition, involving the local hydrostatic and colloidal osmotic pressures in both the capillary and the tissue, together with the radial gradient of the tissue hydrostatic pressure, couples the intra- and extraluminal flow fields. With this model we investigate the relationship between transport properties, hydrostatic pressures, and flow exchange for a single capillary, and describe the fluid transport in the tissue space produced by an array of such capillaries.     

Respiration and oxygen transport functions of the blood from an intertidal fish,Helcogramma medium (Tripterygiidae)

Synopsis Aquatic and aerial oxygen uptake (̇O₂), ventilation frequency, and oxygen transport properties of the blood were determined for the intertidal fish Helcogramma medium. Ventilation frequency increased in response to decreased environmental PO₂ and aquatic ̇O₂ was maintained down to a critical PO₂ of 30–40 mm Hg. Below PO₂ 30 mm Hg fish intermittently gulped air and finally emerged into air at PO₂ 18 mm Hg. After 1 h exposure to air ̇O₂ decreased to 60% of the aquatic rate and this was accompanied by an increase in blood lactate. Aerobic expansibility was reduced in air (×1.2) compared to water (× 5.5). The Hb concentration was 0.47 ± 0.13 mmol 1^–1 and hematocrit 11.55 ± 3.61% indicating a moderate O₂-carrying capacity. Oxygen affinity was not especially high (P₅₀ = 19 mm Hg at pH 7.7 and 15°C) and ATP was the predominant acid-soluble phosphate regulating P₅₀. The equilibrium curve was essentially hyperbolic (Hill's n = 1.2) with a marked Bohr effect = –1.06) and Root effect (saturation depressed by 50% at pH7.1). The pattern of respiration and the respiratory properties of the blood together with observations of the behaviour of the fish during aerial exposure indicated that Helcogramma is adapted to living in a well-aerated environment yet can adequately tolerate short term exposure to low aquatic PO₂ or air.     

Trabeculae carneae as models of the ventricular walls: implications for the delivery of oxygen

Trabeculae carneae are the smallest naturally arising collections of linearly arranged myocytes in the heart. They are the preparation of choice for studies of function of intact myocardium in vitro. In vivo, trabeculae are unique in receiving oxygen from two independent sources: the coronary circulation and the surrounding ventricular blood. Because oxygen partial pressure (PO₂) in the coronary arterioles is identical in specimens from both ventricles, whereas that of ventricular blood is 2.5-fold higher in the left ventricle than in the right ventricle, trabeculae represent a “natural laboratory” in which to examine the influence of “extravascular” PO₂ on the extent of capillarization of myocardial tissue. We exploit this advantage to test four hypotheses. (1) In trabeculae from either ventricle, a peripheral annulus of cells is devoid of capillaries. (2) Hence, sufficiently small trabeculae from either ventricle are totally devoid of capillaries. (3) The capillary-to-myocyte ratios in specimens from either ventricle are identical to those of their respective walls. (4) Capillary-to-myocyte ratios are comparable in specimens from either ventricle, reflecting equivalent energy demands in vivo, driven by identical contractile frequencies and comparable wall stresses. We applied confocal fluorescent imaging to trabeculae in cross section, subsequently using semi-automated segmentation techniques to distinguish capillaries from myocytes. We quantified the capillary-to-myocyte ratios of trabeculae from both ventricles and compared them to those determined for the ventricular free walls and septum. Quantitative interpretation was furthered by mathematical modeling, using both the classical solution to the diffusion equation for elliptical cross sections, and a novel approach applicable to cross sections of arbitrary shape containing arbitrary disposition of capillaries and non-respiring collagen cords.     

Optimization of the photodynamic inactivation of prions by a phthalocyanine photosensitizer: The crucial involvement of singlet oxygen

Prion disorders are fatal neurodegenerative diseases caused by the autocatalytic conversion of a natively occurring prion protein (PrP^C) into its misfolded infectious form (PrP^TSE). The proven resistance of PrP^TSE to common disinfection procedures increases the risk of prion transmission in medical settings. Herein, we present the effective photodynamic inactivation (PDI) of prions by disulfonated hydroxyaluminum phthalocyanine (AlPcOH(SO₃)₂) utilizing two custom‐built red light sources. The treatment eliminates PrP^TSE signal in infectious mouse brain homogenate with efficiency that depends on light intensity but has a low effect on the overall protein content. Importantly, singlet oxygen (O₂(¹Δ_g)) is the only species significantly photogenerated by AlPcOH(SO₃)₂, and it is responsible for the PDI of prions. More intensive light conditions show not only higher O₂(¹Δ_g) production but also decreases in AlPcOH(SO₃)₂ photostability. Our findings suggest that PDI by AlPcOH(SO₃)₂‐generated O₂(¹Δ_g) represents a promising approach for prion inactivation that may be useful in future decontamination strategies for delicate medical tools.     

Spatial heterogeneity and short‐term oxygen dynamics in the rhizosphere of Vallisneria spiralis: Implications for nutrient cycling

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Effects of prolonged bed rest on cardiovascular oxygen transport during submaximal exercise in humans

The hypothesis was tested that prolonged bed rest impairs O₂ transport during exercise, which implies a lowering of cardiac output Q˙ _c and O₂ delivery (_aO₂). The following parameters were determined in five males at rest and at the steady-state of the 100-W exercise before (B) and after (A) 42-day bed rest with head-down tilt at −6°: O₂ consumption (V˙O₂), by a standard open-circuit method; Q˙ _c, by the pressure pulse contour method, heart rate ( f _c), stroke volume (Q _h), arterial O₂ saturation, blood haemoglobin concentration ([Hb]), arterial O₂ concentration (C _aO₂), and Q˙ _aO₂. The V˙O₂ was the same in A and in B, as was the resting f _c. The f _c at 100 W was higher in A than in B (+17.5%). The Q _h was markedly reduced (−27.7% and −22.2% at rest and 100 W, respectively). The Q˙ _c was lower in A than in B [−27.6% and −7.8% (NS) at rest and 100 W, respectively]. The C _aO₂ was lower in A than in B because of the reduction in [Hb]. Thus also Q˙ _aO₂ was lower in A than in B (−32.0% and −11.9% at rest and at 100 W, respectively). The present results would suggest a down-regulation of the O₂ transport system after bed rest. Accepted: 22 April 1998     

Treatment of hypoxia‐dependent cardiovascular diseases by myo‐inositol trispyrophosphate (ITPP)‐enhancement of oxygen delivery by red blood cells

Heart failure is a consequence of progression hypoxia‐dependent tissue damages. Therapeutic approaches to restore and/or protect the healthy cardiac tissue have largely failed and remain a major challenge of regenerative medicine. The myo‐inositol trispyrophosphate (ITPP) is a modifier of haemoglobin which enters the red blood cells and modifies the haemoglobin properties, allowing for easier and better delivery of oxygen by the blood. Here, we show that this treatment approach in an in vivo model of myocardial infarction (MI) results in an efficient protection from heart failure, and we demonstrate the recovery effect on post‐MI left ventricular remodelling in the rat model. Cultured cardiomyocytes used to study the molecular mechanism of action of ITPP in vitro displayed the fast stimulation of HIF‐1 upon hypoxic conditions. HIF‐1 overexpression was prevented by ITPP when incorporated into red blood cells applied in a model of blood‐perfused cardiomyocytes coupling the dynamic shear stress effect to the enhanced O₂ supply by modification of haemoglobin ability to release O₂ in hypoxia. ITPP treatment appears a breakthrough strategy for the efficient and safe treatment of hypoxia‐ or ischaemia‐induced injury of cardiac tissue.     

Noninvasive estimation of human tissue respiration with wavelet-analysis of oxygen saturation and blood flow oscillations in skin microvessels

Laser Doppler flowmetry, laser spectrophotometry of oxygen saturation, and the fluorescence determination of the NADH/FAD ratio were carried out in 30 subjects in the upper limb skin zones with and without arteriolovenular anastomoses (AVAs). It was demonstrated that the wavelet-analysis of oxygen saturation and blood flow oscillations in microvessels was an efficient approach to noninvasive estimation of the skin oxygen extraction (OE) and oxygen consumption (OC) rates. OE = (SaO₂ ? SvO₂)/SaO₂, where SaO₂ (%) and SvO₂ (%) are the oxygen saturations of arterial and venular blood, respectively. If the cardiac (A_c, perfusion units, p.u.) to respiratory rhythm amplitude (A_r, p.u.) ratio A_c/A_r ?? 1, SvO₂ = SO₂. If A_c/A_r > 1, SvO₂ = SO₂/(A_c/A_r). OC = M _nutr (SaO₂ ?? SvO₂) in p.u. · %O₂, where M _nutr is the nutritive blood flow value in p.u. M _nutr = M/SI, where SI is the shunting index of blood flow in microvessels. The perfusion, OE, and OC values were higher in the skin with AVAs than in the skin without AVAs. The perfusion and oxygen saturation values were more variable in the skin with AVAs. The oxygen diffusing from the tiniest arterioles and capillaries is the most important for tissue metabolism. The contribution of the total perfusion and the oxygen diffusion from arterioles to tissue metabolism increased under the tissue ischemia conditions.     

Diffusion and seasonal dynamics of O2 in woody debris from the Pacific Northwest,USA

O₂ is an important regulator of physiological processes involved in the decomposition of woody debris, yet O₂ levels and diffusion rates within decomposing logs are largely unknown. We examined how O₂ diffusion rates in decayed and sound wood varied with moisture and density, and we compared predicted with observed seasonal changes in oxygen concentration in logs in a Pacific Northwest old-growth Pseudotsuga menziesii forest. In the laboratory, the oxygen diffusion coefficient (D_O2) was determined in the longitudinal and radial (or tangential) directions on wood cores of varying moisture content and density. In the field, O₂ was measured in tubes inserted to three radial depths (2, 6 and 15 cm) within logs of two species (Pseudotsuga menziesii and Tsuga heterophylla) and five decay classes (where class 5 = most decayed). In both the radial and longitudinal directions, D_O2 increased exponentially as the air filled pore space (AFPS) increased and as density decreased. In the field, mean O₂ concentrations in logs were not significantly different between species. Mean O₂ concentrations were significantly lower in the least decayed logs as compared to the most decayed logs. Mean O₂ concentrations decreased with radial depth only in decay class two logs. Seasonal O₂ levels did not consistently vary with log moisture, respiration, or air temperature. The comparison of the results from a model that assumes oxygen diffuses only in the radial direction to field data indicates that laboratory measurements of oxygen diffusion may underestimate field oxygen concentrations. Cracks, insect galleries and other passages in decayed logs, and longitudinal oxygen diffusion may account for this discrepancy. In the field, log oxygen concentrations were rarely as low as 2%, indicating anaerobic conditions may not be as common in logs as we previously thought. Oxygen limitations on decomposition may occur in relatively sound and/or water soaked wood, but probably not in decayed logs in a terrestrial setting.