A model for the study of diffusion and perfusion limitation

On the basis of a very simple model for the association of diffusion and perfusion, an association common to many respiratory gas transfers, a simple equation is described that defines gas partial pressure equilibration in diffusion-perfusion-limited systems as a function of the ratio of D to beta bQ(D = diffusing capacity, beta b = blood capacitance coefficient, Q = perfusion). The equation applies to steady-state conditions and assumes D, beta b, and Q to be independent of gas partial pressures. In spite of the fact that this assumption may represent a gross simplification, the equation can be regarded as a powerful conceptual tool in the analysis of most gas exchange systems.     

Influence of blood flow on cutaneous permeability to inert gas

A thermally regulated Plexiglas chamber was designed for investigation of transcutaneous diffusion of N2 and helium (He) in the human hand. Influence of cutaneous blood flow in this process was studied simultaneously with gas diffusion measurements. Changes in cutaneous blood flow (Q, in ml X min-1 X 100 ml tissue-1) were effected by altering ambient temperature (T) from 20 to 40 degrees C (Q = 0.08 X 100.07T). We found that the rate of inert gas diffusion through human skin, expressed as conductance (G, in ml STPD X h-1 X m-2 X atm-1), increases exponentially as a function of blood flow, and was indistinguishable between He and N2 (G = 21.19 X 100.0124Q). The permeability, diffusion coefficient per unit diffusion distance (D/h, in cm/h), also rose exponentially as a function of blood flow. But permeability for He (D/h = 0.1748 X 100.0203Q) was greater than that for N2 (D/h = 0.1678 X 100.0114Q). As cutaneous blood flow rises, because of increased temperature, the apparent diffusion distance falls linearly for both N2 and He. The change is more prominent for He than for N2 diffusion. Estimated replacement time for the body stores of N2 by transcutaneous diffusion alone was shortened from 26.8 h at 31 degrees C to 15.1 h at 37 degrees C. It is suggested from this study that beneficial results may be derived during decompression procedure 1) by maintaining an appropriate transcutaneous pressure gradient of inert gases, and 2) by elevating ambient temperature.     

Mass transfer resistance of sterile plugs in shaking bioreactors

One of the mass transfer resistances for the gas exchange of shaking flasks is the sterile plug. The gas exchange through the sterile plug is described by an extended model of Henzler and Schedel [Bioprocess Eng. 7 (1991) 123]. Based on this model, a new method was developed to obtain the mass transfer resistance of various sterile closures. It consists of measuring the water evaporation rate of the shaking flask and is therefore very easily applied. Sterile plugs made of cotton, wrapped paper, urethane foam and fibreglass and caps made out of aluminium and silicone have been examined. Instead of the oxygen transfer coefficient (k(O(2))), which is commonly found in the literature, the carbon dioxide diffusion coefficient (D(CO(2))) is used to describe the mass transfer resistance of the sterile plug. The investigation revealed that this resistance is mainly dependent on the neck geometry and to a lesser extent on the plug material and density. The gas exchange of aluminium-caps was not reproducible.     

Function of Nicotiana tabacum aquaporins as chloroplast gas pores challenges the concept of membrane CO2 permeability

Photosynthesis is often limited by the rate of CO(2) diffusion from the atmosphere to the chloroplast. The primary resistances for CO(2) diffusion are thought to be at the stomata and at photosynthesizing cells via a combination resulting from resistances of aqueous solution as well as the plasma membrane and both outer and inner chloroplast membranes. In contrast with stomatal resistance, the resistance of biological membranes to gas transport is not widely recognized as a limiting factor for metabolic function. We show that the tobacco (Nicotiana tabacum) plasma membrane and inner chloroplast membranes contain the aquaporin Nt AQP1. RNA interference-mediated decreases in Nt AQP1 expression lowered the CO(2) permeability of the inner chloroplast membrane. In vivo data show that the reduced amount of Nt AQP1 caused a 20% change in CO(2) conductance within leaves. Our discovery of CO(2) aquaporin function in the chloroplast membrane opens new opportunities for mechanistic examination of leaf internal CO(2) conductance regulation.     

Gene delivery of l-caldesmon protects cytoskeletal cell membrane integrity against adenovirus infection independently of myosin ATPase and actin assembly

The cytoskeleton is critical to the viral life cycle. Agents like cytochalasin inhibit viral infections but cannot be used for antiviral therapy because of their toxicity. We report the efficacy, safety, and mechanisms by which gene delivery of human wild-type low-molecular-weight caldesmon (l-CaD) protects cell membrane integrity from adenovirus infection in a DF-1 cell line, an immortalized avian fibroblast that is null for l-CaD. Transfection with an adenovirus (Ad)-controlled construct mediated a dose-dependent decline in transcellular resistance. In accordance with a computational model of cytoskeletal membrane properties, Ad disturbed cell-cell and cell-matrix adhesion and membrane capacitance. Transfection with the Ad-l-CaD construct attenuated adenovirus-mediated loss in transcellular resistance. Quantitation of vinculin-stained plaques revealed an increase in total focal contact mass in monolayers transfected with the Ad-l-CaD construct. Expression of l-CaD protected transcellular resistance through primary effects on membrane capacitance and independently of actin solubility and effects on prestress, as measured by the decline in isometric tension in response to cytochalasin D. Expression of l-CaD exhibited less Trypan blue cell toxicity than cytochalasin, and, unlike cytochalasin, it did not interfere with wound closure or adversely effect transcellular resistance. These findings demonstrate the gene delivery of wild-type human l-CaD as a potentially efficacious and safe agent that inhibits some of the cytopathic effects of adenovirus. adhesion; motility; computational modeling; focal contact; quantitation     

Quantifying the Role of Nanotubes in Nano:Nano Composite Supercapacitor Electrodes

Many promising supercapacitor electrode materials have high resistivity and require conductive additives to function effectively. However, the detailed role of the additive is not understood. Here, this question is resolved by applying a quantitative model for resistance‐limited supercapacitor electrodes to Co(OH)₂‐nanosheet/carbon nanotube composites. Without nanotubes, theory predicts and experiments show that while the low‐rate capacitance increases linearly with electrode thickness, the high rate capacitance decreases with thickness due to slow charging. Experiments supported by theory show that nanotube addition has two effects. First, the nanotube network effectively distributes charge, increasing the intrinsic electrode performance to the limit associated with its accessible surface area. Second, at high‐rate, the increased electrode conductivity shifts the rate‐limiting resistance from electrode to electrolyte, thus removing the thickness‐dependent capacitance falloff. Furthermore, the analysis quantifies the out‐of‐plane conductivity of the nanotube network, identifies the cross‐over from resistance‐limited to diffusion‐limited behavior, and allows full electrode modeling, facilitating rational design.     

Effect of breath-hold time on DLCO(SB) in patients with airway obstruction

The single-breath diffusing capacity of the lung for CO [DLCO(SB)] is considered a measure of the conductance of CO across the alveolar-capillary membrane and its binding with hemoglobin. Although incomplete mixing of inspired gas with alveolar gas could theoretically influence overall diffusion, conventional calculations of DLCO(SB) spuriously overestimate DLCO(SB) during short breath-holding periods when incomplete mixing of gas within the lung might have the greatest effect. Using the three-equation method to calculate DLCO(SB) which analytically accounts for changes in breath-hold time, we found that DLCO(SB) did not change with breath-hold time in control subjects but increased with increasing breath-hold time in both patients with asthma and patients with emphysema. The increase in DLCO(SB) with increasing breath-hold time correlated with the phase III slope of the single-breath N2 washout curve. We suggest that in patients with ventilation maldistribution, DLCO(SB) may be decreased for the shorter breath-hold maneuvers because overall diffusion is limited by the reduced transport of CO from the inspired gas through the alveolar gas prior to alveolar-capillary gas exchange.     

A Model of the Regulation of Nitrogenase Electron Allocation in Legume Nodules (II. Comparison of Empirical and Theoretical Studies in Soybean)

In N2-fixing legumes, the proportion of total electron flow through nitrogenase (total nitrogenase activity, TNA) that is used for N2 fixation is called the electron allocation coefficient (EAC). Previous studies have proposed that EAC is regulated by the competitive inhibition of H2 on N2 fixation and that the degree of H2 inhibition can be affected by a nodule's permeability to gas diffusion. To test this hypothesis, EAC was measured in soybean (Glycine max L. Merr.) nodules exposed to various partial pressures of H2 and N2, with or without changes in TNA or nodule permeability to gas diffusion, and the results were compared with the predictions of a mathematical model that combined equations for gas diffusion and competitive inhibition of N2 fixation (A. Moloney and D.B. Layzell [1993] Plant Physiol 103: 421-428). The empirical data clearly showed that decreases in EAC were associated with increases in external pH2, decreases in external pN2, and decreases in nodule permeability to O2 diffusion. The model predicted similar trends in EAC, and the small deviations that occurred between measured and predicted values could be readily accounted for by altering one or more of the following model assumptions: K1(H2) of nitrogenase (range from 2-4% H2), Km(N2) of nitrogenase (range from 4-5% N2), the allocation of less than 100% of whole-nodule respiration to tissues within the diffusion barrier, and the presence of a diffusion pathway that is open pore versus closed pore. The differences in the open-pore and closed-pore versions of the model suggest that it may be possible to use EAC measurements as a tool for the study of legume nodule diffusion barrier structure and function. The ability of the model to predict EAC provided strong support for the hypothesis that H2 inhibition of N2 fixation plays a major role in the in vivo control of EAC and that the presence of a variable barrier to gas diffusion affects the H2 and N2 concentration in the infected cell and, therefore, the degree of H2 inhibition.     

A new technique for measurement of water permeability of stomatous cuticular membranes isolated from Hedera helix leaves

Transpiration of cuticular membranes isolated from the lower stomatous surface of Hedera helix (ivy) leaves was measured using a novel approach which allowed a distinction to be made between gas phase diffusion (through stomatal pores) and solid phase diffusion (transport through the polymer matrix membrane and cuticular waxes) of water molecules. This approach is based on the principle that the diffusivity of water vapour in the gas phase can be manipulated by using different gases (helium, nitrogen, or carbon dioxide) while diffusivity of water in the solid phase is not affected. This approach allowed the flow of water across stomatal pores ('stomatal transpiration') to be calculated separately from the flow across the cuticle (cuticular transpiration) on the stomatous leaf surface. As expected, water flux across the cuticle isolated from the astomatous leaf surface was not affected by the gas composition since there are no gas-filled pores. Resistance to flux of water through the solid cuticle on the stomatous leaf surface was about 11 times lower than cuticular resistance on the astomatous leaf surface, indicating pronounced differences in barrier properties between cuticles isolated from both leaf surfaces. In order to check whether this difference in resistance was due to different barrier properties of cuticular waxes on both leaf sides, mobility of 14C-labelled 2,4-dichlorophenoxy-butyric acid 14C-2,4-DB) in reconstituted cuticular wax isolated from both leaf surfaces was measured separately. However, mobility of 14C-2,4-DB in reconstituted wax isolated from the lower leaf surface was 2.6 times lower compared with the upper leaf side. The significantly higher permeability of the ivy cuticle on the lower stomatous leaf surface compared with the astomatous surface might result from lateral heterogeneity in permeability of the cuticle covering normal epidermal cells compared with the cuticle covering the stomatal cell surface.     

Modeling of Gas Production from Shale Reservoirs Considering Multiple Transport Mechanisms

Gas transport in unconventional shale strata is a multi-mechanism-coupling process that is different from the process observed in conventional reservoirs. In micro fractures which are inborn or induced by hydraulic stimulation, viscous flow dominates. And gas surface diffusion and gas desorption should be further considered in organic nano pores. Also, the Klinkenberg effect should be considered when dealing with the gas transport problem. In addition, following two factors can play significant roles under certain circumstances but have not received enough attention in previous models. During pressure depletion, gas viscosity will change with Knudsen number; and pore radius will increase when the adsorption gas desorbs from the pore wall. In this paper, a comprehensive mathematical model that incorporates all known mechanisms for simulating gas flow in shale strata is presented. The objective of this study was to provide a more accurate reservoir model for simulation based on the flow mechanisms in the pore scale and formation geometry. Complex mechanisms, including viscous flow, Knudsen diffusion, slip flow, and desorption, are optionally integrated into different continua in the model. Sensitivity analysis was conducted to evaluate the effect of different mechanisms on the gas production. The results showed that adsorption and gas viscosity change will have a great impact on gas production. Ignoring one of following scenarios, such as adsorption, gas permeability change, gas viscosity change, or pore radius change, will underestimate gas production.     

Modeling tree water flow as an unsaturated flow through a porous medium

The electric circuit analogy has had a profound influence on how tree physiologists measure, model and think about tree water flow. For example, previous models that attempt to account for changes in saturation use the electric circuit analogy to define capacitance as the change in saturation per change in pressure. Given that capacitance is constant, this relationship implies that subjecting a block of wood to a pressure of -2.5 MPa for 2 min results in the same change in saturation as subjecting the same block to the same pressure for 2 days. Given the definition of capacitance, it is unclear how the electric circuit analogy could be used to predict changes in saturation separately from changes in pressure. The inadequacies in the electric circuit analogy discussed in this paper necessitate a new theory of tree water flow that recognizes the sapwood as being a porous medium and explicitly deals with the full implications of the unsaturated flow occurring in the sapwood. The theory proposed in this paper combines the Cohesion theory with a mathematical theory of multiphase flow through porous media. Based on this theory, both saturated and unsaturated tree water flow models are presented. Previous partial differential equation models of tree water flow based on the electric circuit analogy are shown to be mathematically equivalent to the model of saturated porous flow. The unsaturated model of tree water flow explicitly models the pressure profile and the rates of change in saturation and specific interfacial area (a measure of how the water in the unsaturated sapwood is partitioned between mobile and immobile components). The unsaturated model highlights the differences between saturated and unsaturated flow and the need to measure the variables governing tree water flow at higher spatial and temporal resolutions.     

Development of a spark sustained by charging the stray capacitance of the external circuit in atmospheric-pressure nitrogen

Results are presented from experimental studies and numerical simulations of a spark discharge excited in a short point-plane gap filled with atmospheric-pressure nitrogen. The discharge was powered from a high-voltage source connected to the discharge gap through a large ballast resistance. In this case, a short-term spark develops only due to the charging of the stray capacitance of the external circuit; therefore, the energy released by the spark and its intensity are both low. Rapid current growth in a weak spark is accompanied by the contraction of the current channel rather than by its gasdynamic expansion, as it occurs in long-duration kiloampere sparks. Simulations show that, because of the very short spark lifetime, the plasma in a weak spark is substantially nonequilibrium and the gas temperature is fairly high.     

The effect of changing the gaseous diffusion coefficient on the mass loss pattern of Hyalophora cecropia pupae

The importance of gas phase diffusion in insect gas exchange remains unclear. The role of diffusion in gas exchange of developing Hyalophora cecropia pupae was examined by altering the gaseous diffusion coefficient in the breathing mixture. Gaseous diffusion coefficients were manipulated by substituting helium or sulfur hexafluoride for the nitrogen usually present in air. Sensitive mass loss recordings were employed to monitor gas exchange activity. Mass loss recordings showed a two-phase cycle, open and closed-flutter. Mass loss rates during the open and closed-flutter periods were not altered in proportion to the changes induced in the rate of diffusion. Open-phase duration was inversely and proportionally related to the diffusion coefficient. These results are consistent with changes in spiracle resistance or convective flow during the open period in response to a change in the diffusion coefficient. In addition, they indicate a significant gas phase diffusive resistance within the pupal tracheal system. This previously unreported gas phase resistance appears to be a major determinant of the duration of the open period and thus of overall water loss rates in these pupae.     

面向血液葡萄糖测量的生物组织阻抗模型

本文推导了细胞膜电容与血糖浓度之间的关系,并将这种关系应用到Pauly和Schwan提出的弛豫模型中,再将弛豫模型应用于多重Cole-Cole介电模型,最后通过介电模型得出阻抗模型,建立起人体血糖浓度与组织介电谱,阻抗谱之间的联系。通过分析发现,细胞膜电容随着血糖浓度增加而增大,且当血糖浓度趋于无穷大时,细胞膜电容等于血糖浓度为0时细胞膜电容的1.53倍。对介电谱的仿真得出,当外加信号频率小于1 MHz时,介电常数实部随着葡萄糖浓度改变而发生明显变化。阻抗谱的研究结果表明,随着葡萄糖浓度的升高,阻抗的实部减小,阻抗虚部模增大,且分别在频率为1.48 MHz和0.55 MHz时变化得最快。本文建立的模型为血糖无创检测提供了一种新的方法和手段。     

Ozone concentration in leaf intercellular air spaces is close to zero

Transpiration and ozone uptake rates were measured simultaneously in sunflower leaves at different stomatal openings and various ozone concentrations. Ozone uptake rates were proportional to the ozone concentration up to 1500 nanoliters per liter. The leaf gas phase diffusion resistance (stomatal plus boundary layer) to water vapor was calculated and converted to the resistance to ozone multiplying it by the theoretical ratio of diffusion coefficients for water vapor and ozone in air (1.67). The ozone concentration in intercellular air spaces calculated from the ozone uptake rate and diffusion resistance to ozone scattered around zero. The ozone concentration in intercellular air spaces was measured directly by supplying ozone to the leaf from one side and measuring the equilibrium concentration above the other side, and it was found to be zero. The total leaf resistance to ozone was proportional to the gas phase resistance to water vapor with a coefficient of 1.68. It is concluded that ozone enters the leaf by diffusion through the stomata, and is rapidly decomposed in cell walls and plasmalemma.     

Diffusion in gas exchange of insects

The air-filled tracheal system constitutes the organ for gas exchange in terrestrial insects-its finest branches, the tracheoles, contacting individual cells. In the pupal stage, in which the animal lacks significant ventilatory movement, diffusion in the gas phase of the tracheal system constitutes the only mechanism for gas transfer between the environment and the tissues, transport in the hemolymph being insignificant. We have attempted to identify the main sites of diffusional resistance in the tracheal gas system by measuring the evolution of inert gases of low solubility from the pupa of the giant silkworm moth (Hyalophora cecropia). The results are compatible wih a single model in which the resistance to diffusional gas transfer in the tracheal system is concentrated at its opening at the body surface (spiracle).     

Diffusion and partition of solutes in cartilage under static load

We describe experimental apparatus, methodology and mathematical algorithms to measure diffusion and partition for typical small ionic solutes and inulin (a medium size solute) in statically loaded cartilage. The partition coefficient based on tissue water (K(H(2)O)) of Na(+) increased from 1.8 to 4.5 and for SO(4)(-2) decreased from 0.5 to 0.1, when the applied pressure was raised from zero to 22 atm K(H(2)O) of inulin decreased from 0.3 to 0.05, for an increase in pressure from zero to 11 atm. Our theoretical interpretation of the results is that the partition coefficient can be expressed as a function of fixed charge density (FCD) for both loaded and unloaded cartilage. The partition coefficient shows good agreement with the ideal Gibbs-Donnan equilibrium, particularly when FCD is based on extrafibrillar water (EFW). The diffusion coefficients, D also decreased with an increase in applied pressure; raising the pressure from 0 to 22 atm resulted in the following changes in the values of D: for Na(+) from 2.86 x 10(-6) to 1.51 x 10(-6) cm(2)/s, for SO(4)(-2) from 1.58 x 10(-6) to 7.5 x 10(-7) cm(2)/s, for leucine from 1.69 x 10(-6) to 8.30 x 10(-7) cm(2)/s and for inulin from 1.80 x 10(-7) to 3.30 x 10(-8) cm(2)/s. For the three small solutes (two charged and one neutral) the diffusion coefficient D is highly correlated with the fraction of fluid volume in the tissue. These experimental results show good agreement with the simple model of Mackie and Meares: hence solute charge does not affect the diffusion of small solutes under load. For inulin D & K show some agreement with a modified Ogston model based on two major components, viz., glycosaminoglycans (GAG) and core protein. We conclude that the changes in the partition and diffusion coefficients of small and medium size solutes in statically loaded cartilage can be interpreted as being due to the reduction in hydration and increase in FCD. The change in the latter affects the partition of small ionic solutes and the partition and diffusion of larger molecules. Our results throw light on the ionic environment of chondrocytes in loaded cartilage as well as on the transport of solutes through the matrix.     

Diffusion barriers limit the effect of mobile calcium buffers on exocytosis of large dense cored vesicles

Fast exocytosis in melanotropic cells, activated by calcium entry through voltage-gated calcium channels, is very sensitive to mobile calcium buffers (complete block at 800 microM ethylene glycol bis(beta-aminoethyl ether)-N,N,N'N'-tetraacetic acid (EGTA)). This indicates that calcium diffuses a substantial distance from the channel to the vesicle. Surprisingly, 1, 2-bis(2-aminophenoxy)ethane-N,N,N',N'-tetraacetic acid (BAPTA), having a similar KD for calcium as EGTA but a approximately 100 times faster binding rate, blocked exocytosis only twice as effectively as EGTA. Using computer simulations, we demonstrate that this result cannot be explained by free diffusion and buffer binding rates. We hypothesized that local saturation of calcium buffers is involved. A diffusion barrier for both calcium and buffer molecules, located 50-300 nm from the membrane and reducing diffusion 1000 to 10,000 times, generated similar calcium concentrations for specific concentrations of EGTA and BAPTA. With such barriers, calcium rise phase kinetics upon short step depolarizations (2-20 ms) were faster for EGTA than for BAPTA, implying that short depolarizations should allow exocytosis with 50 microM EGTA but not with 25 microM BAPTA. This prediction was confirmed experimentally with capacitance measurements. Coupling exocytosis to calcium dynamics in the model, we found that a barrier with a approximately 3000 times reduced diffusion at approximately 130 nm beneath the membrane best explains the experimentally observed effects of EGTA and BAPTA on block and kinetics of release.     

Diffusion of bacteriophages through artificial biofilm models

The simple two-chamber diffusion method was improved to study the diffusion properties of bacteriophage (phage) T4 through a model biofilm agarose gel membrane (AGM) embedded with dead host Escherichia coli K12 cells. The apparent diffusion coefficient (D(app) ) of phage T4 was calculated to be 2.4 × 10(-12) m(2) /s in 0.5% AGM, which was lower than the coefficient of 4.2 × 10(-12) m(2) /s in 0.5% AGM without host cells. The phage adsorption process by dead host cells slowed the apparent phage diffusion. The Langmuir adsorption equation was used to simulate phage adsorption under different multiplicity of infections (MOIs); the maximum adsorbed phage MOI was calculated to be 417 PFU/CFU, and the Langmuir adsorption constant K(L) was 6.9 × 10(-4) CFU/PFU. To evaluate the effects of phage proliferation on diffusion, a simple syringe-based biofilm model was developed. The phage was added into this homogenous biofilm model when the host cells were in an exponential growth phase, and the apparent diffusion coefficient was greatly enhanced. We concluded that D(app) of phages through biofilms could be distinctly affected by phage adsorption and proliferation, and that the idea of D(app) and these methods can be used to study diffusion properties through real biofilms.