Erratum to: 36th International Symposium on Intensive Care and Emergency Medicine: Brussels, Belgium. 15-18 March 2016

[This corrects the article DOI: 10.1186/s13054-016-1208-6.].

Acidic sweep gas with carbonic anhydrase coated hollow fiber membranes synergistically accelerates CO2 removal from blood

The use of extracorporeal carbon dioxide removal (ECCO2R) is well established as a therapy for patients suffering from acute respiratory failure. Development of next generation low blood flow (<500 mL/min) ECCO2R devices necessitates more efficient gas exchange devices. Since over 90% of blood CO2 is transported as bicarbonate (HCO3(-)), we previously reported development of a carbonic anhydrase (CA) immobilized bioactive hollow fiber membrane (HFM) which significantly accelerates CO2 removal from blood in model gas exchange devices by converting bicarbonate to CO2 directly at the HFM surface. This present study tested the hypothesis that dilute sulfur dioxide (SO2) in oxygen sweep gas could further increase CO2 removal by creating an acidic microenvironment within the diffusional boundary layer adjacent to the HFM surface, facilitating dehydration of bicarbonate to CO2. CA was covalently immobilized onto poly (methyl pentene) (PMP) HFMs through glutaraldehyde activated chitosan spacers, potted in model gas exchange devices (0.0151 m(2)) and tested for CO2 removal rate with oxygen (O2) sweep gas and a 2.2% SO2 in oxygen sweep gas mixture. Using pure O2 sweep gas, CA-PMP increased CO2 removal by 31% (258 mL/min/m(2)) compared to PMP (197 mL/min/m(2)) (P<0.05). Using 2.2% SO2 acidic sweep gas increased PMP CO2 removal by 17% (230 mL/min/m(2)) compared to pure oxygen sweep gas control (P<0.05); device outlet blood pH was 7.38 units. When employing both CA-PMP and 2.2% SO2 sweep gas, CO2 removal increased by 109% (411 mL/min/m(2)) (P<0.05); device outlet blood pH was 7.35 units. Dilute acidic sweep gas increases CO2 removal, and when used in combination with bioactive CA-HFMs has a synergistic effect to more than double CO2 removal while maintaining physiologic pH. Through these technologies the next generation of intravascular and paracorporeal respiratory assist devices can remove more CO2 with smaller blood contacting surface areas.

STATEMENT OF SIGNIFICANCE

A clinical need exists for more efficient respiratory assist devices which utilize low blood flow rates (<500 mL/min) to regulate blood CO2 in patients suffering from acute lung failure. Literature has demonstrated approaches to chemically increase hollow fiber membrane (HFM) CO2 removal efficiency by shifting equilibrium from bicarbonate to gaseous CO2, through either a bioactive carbonic anhydrase enzyme coating or bulk blood acidification with lactic acid. In this study we demonstrate a novel approach to local blood acidification using an acidified sweep gas in combination with a bioactive coating to more than double CO2 removal efficiency of HFM devices. To our knowledge, this is the first report assessing an acidic sweep gas to increase CO2 removal from blood using HFM devices.

Kinetics of CO2 exchange with carbonic anhydrase immobilized on fiber membranes in artificial lungs

Artificial lung devices comprised of hollow fiber membranes (HFMs) coated with the enzyme carbonic anhydrase (CA), accelerate removal of carbon dioxide (CO2) from blood for the treatment of acute respiratory failure. While previous work demonstrated CA coatings increase HFM CO2 removal by 115 % in phosphate buffered saline (PBS), testing in blood revealed a 36 % increase compared to unmodified HFMs. In this work, we sought to characterize the CO2 mass transport processes within these biocatalytic devices which impede CA coating efficacy and develop approaches towards improving bioactive HFM efficiency. Aminated HFMs were sequentially reacted with glutaraldehyde (GA), chitosan, GA and afterwards incubated with a CA solution, covalently linking CA to the surface. Bioactive CA-HFMs were potted in model gas exchange devices (0.0119 m(2)) and tested for esterase activity and CO2 removal under various flow rates with PBS, whole blood, and solutions containing individual blood components (plasma albumin, red blood cells or free carbonic anhydrase). Results demonstrated that increasing the immobilized enzyme activity did not significantly impact CO2 removal rate, as the diffusional resistance from the liquid boundary layer is the primary impediment to CO2 transport by both unmodified and bioactive HFMs under clinically relevant conditions. Furthermore, endogenous CA within red blood cells competes with HFM immobilized CA to increase CO2 removal. Based on our findings, we propose a bicarbonate/CO2 disequilibrium hypothesis to describe performance of CA-modified devices in both buffer and blood. Improvement in CO2 removal rates using CA-modified devices in blood may be realized by maximizing bicarbonate/CO2 disequilibrium at the fiber surface via strategies such as blood acidification and active mixing within the device.

Carbonic anhydrase immobilized on hollow fiber membranes using glutaraldehyde activated chitosan for artificial lung applications

Extracorporeal CO2 removal from circulating blood is a promising therapeutic modality for the treatment of acute respiratory failure. The enzyme carbonic anhydrase accelerates CO2 removal within gas exchange devices by locally catalyzing HCO3 (-) into gaseous CO2 within the blood. In this work, we covalently immobilized carbonic anhydrase on the surface of polypropylene hollow fiber membranes using glutaraldehyde activated chitosan tethering to amplify the density of reactive amine functional groups for enzyme immobilization. XPS and a colorimetric amine assay confirmed higher amine densities on the chitosan coated fiber compared to control fiber. Chitosan/CA coated fibers exhibited accelerated CO2 removal in scaled-down gas exchange devices in buffer and blood (115% enhancement vs. control, 37% enhancement vs. control, respectively). Carbonic anhydrase immobilized directly on hollow fiber membranes without chitosan tethering resulted in no enhancement in CO2 removal. Additionally, fibers coated with chitosan/carbonic anhydrase demonstrated reduced platelet adhesion when exposed to blood compared to control and heparin coated fibers.

Acute in vivo testing of an intravascular respiratory support catheter

Current treatment for acute respiratory failure (ARF) includes the use of mechanical ventilation and/or extracorporeal membrane oxygenation, both of which can exacerbate lung injury. Intravenous respiratory support, using hollow fiber membranes placed in the vena cava, represents an attractive potential treatment for ARF, which could help reduce or eliminate ventilator induced trauma and/or other problems. Our group has been developing a respiratory support catheter (the Hattler catheter [HC]) that consists of a constrained hollow fiber bundle with a centrally located balloon. The balloon can be pulsated rapidly to increase blood flow across the fibers and decrease diffusional transfer resistance there, thus increasing gas exchange. The purpose of this study was to evaluate the HC in acute animal implants and to compare performance with that achieved in previous ex vivo studies. The HC was implanted into four calves by means of the external jugular vein and placed in the superior and inferior vena cava spanning the right atrium. Gas exchange, hemodynamics, and hematologic parameters were assessed over a range of balloon pulsation rates from 30 to 300 beats/minute. A <10% reduction in cardiac output was associated with catheter insertion and operation. The maximum CO2 exchange rate occurred at the highest pulsation rate and averaged 56 +/- 3 ml/min, or 327 +/- 15 ml/min per m2 when averaged to catheter membrane area, a level comparable to that achieved in the previous ex vivo studies. Balloon pulsation did not produce significant levels of hemolysis, as plasma-free hemoglobin remained below 10-15 mg/dl.

Specific removal of anti-A and anti-B antibodies by using modified dialysis filters

Removal of anti-A and anti-B blood group antibodies from human blood has been shown to facilitate cross-matched kidney transplantation by preventing hyperacute rejection. Patients in these studies had anti-A and anti-B antibodies removed by using plasmapheresis, followed by immunoadsorption onto packed bead columns. We conducted a study to assess the feasibility of selectively removing anti-A and anti-B antibodies directly from blood by using modified dialysis filters. An anti-A and anti-B specific antigen was covalently attached to the lumenal surfaces of hollow fibers within selected commercial dialysis modules. The filters were able to reduce the anti-A and anti-B titers of 300 ml of blood to 2 or below. A low molecular weight fraction of our antigen system was found to have no antibody binding capacity. The standard antigen was purified by removal of the low molecular weight fraction and a dialysis filter was modified by using the purified antigen. This filter displayed a six-fold higher capacity than a dialysis filter modified with the same mass of standard antigen. We conclude that selective blood group antibody removal by antigen modified dialysis filters is feasible and may be a simpler system than plasmapheresis followed by immunoadsorption.

Ex vivo testing of the intravenous membrane oxygenator

Intravenous oxygenation represents a potential respiratory support modality for patients with acute respiratory failure or with acute exacerbations of chronic respiratory conditions. Our group has been developing an intravenous oxygenator, the IMO, which uses a constrained fiber bundle and a rapidly pulsating balloon within the fiber bundle. Balloon pulsation drives blood flow past the fibers at greater relative velocities than would otherwise exist within the host vessel, and gas exchange rates are enhanced. The purpose of this study was twofold: (1) to characterize the gas exchange performance of the current IMO in an extracorporeal mock vena cava vessel under conditions of known fixed vessel geometry and controlled blood flow rates; and (2) to compare the IMO gas exchange performance to that reported for the clinically tested IVOX device within a comparable ex vivo set-up. The ex vivo flow loop consisted of a 1 inch ID tube as a mock vena cava that was perfused directly from an anesthetized calf at blood flow rates ranging from 1 to 4 1/2 L/min. O2 and CO2 exchange rates were measured for balloon pulsation rates, which ranged from 0 to 180 bpm. Balloon pulsation significantly increased gas exchange, by 200-300% at the lowest blood flow rate and 50-100% at the highest blood flow rate. Balloon pulsation eliminated much if not all of the dependence of the gas exchange rate on blood flow rate as seen in passive oxygenators. This suggests that in clinical application the IMO may exhibit less gas transfer variability due to differences in cardiac output Over the entire flow rate range studied, the CO2 and O2 gas exchange rates of the IMO at maximal balloon pulsation varied from approximately 250 to 350 ml/min/m2. At maximum balloon pulsation the IMO exchanged CO2 and O2 at rates from 50-500% greater, depending upon the blood flow rate, than the exchange rates reported for the IVOX device in ex vivo tests.

Experimental evaluation of a model for oxygen exchange in a pulsating intravascular artificial lung

Intravascular oxygenation and carbon dioxide removal remains a potentially attractive means for respiratory support in patients with acute or chronic respiratory failure. Our group has been developing an intravascular hollow fiber artificial lung that uses a pulsating balloon located within the fiber bundle to augment gas transfer. We previously reported on a simple compartmental model for simulating O2 exchange in pulsating intravascular artificial lungs. In this study we evaluate the O2 exchange model with gas exchange and PO2 measurements performed on an idealized intravascular artificial lung (IIVAL) tested in a water perfusion loop. The IIVAL has well-defined bundle geometry and can be operated in balloon pulsation mode, or a steady perfusion mode for determining the mass transfer correlation required by the model. The O2 exchange rates and compartmental O2 tensions measured with balloon pulsation in the IIVAL are within 10% of model predictions for flow and pulsation conditions relevant to intravascular oxygenation. The experiments confirmed that a significant buildup of PO2 occurs within the fiber bundle, which reduces the O2 exchange rate. The agreement between experiments and predictions suggests that the model captures the cardinal processes dictating gas transfer in pulsating intravascular artificial lungs.

Validation of a model for flow-dependent carbon dioxide exchange in artificial lungs

The exchange rate of CO2 in artificial lungs depends on the sweep gas flow rate. Control of the amount of CO2 removed by an artificial lung requires quantitative knowledge of the flow dependence. A simple model of the dependence of CO2 exchange on sweep gas flow rate in artificial lungs has been previously presented (1). For a given partial pressure of CO2 in the blood phase, sweep gas flow rate, and CO2 exchange rate, the model indicates how close the CO2 exchange rate is to the maximum level attainable by the artificial lung. The focus of this study was to validate the model experimentally by testing 2 commercial artificial lungs in an in vitro test loop. The CO2 exchange rate for each artificial lung was measured over a range of sweep gas flow rates. Linear regression was used to fit the data to the model and estimate the maximum possible CO2 exchange rate and the average water-side PCO2 (PCO2w). The difference between the measured and regressed values of PCO2w was used as an indicator of the ability of the model to quantitatively predict the dependence of CO2 exchange on gas flow rate. This difference was less than 5% for each experiment, indicating that the model can be used to guide control of CO2 exchange rates in artificial lungs.

Effect of intraluminal thrombus thickness and bulge diameter on the oxygen diffusion in abdominal aortic aneurysm

The intraluminal thrombus (ILT) commonly found within abdominal aortic aneurysm (AAA) may serve as a barrier to oxygen diffusion from the lumen to the inner layers of the aortic wall. The purpose of this work was to address this hypothesis and to assess the effects of AAA bulge diameter (dAAA) and ILT thickness (delta) on the oxygen flow. A hypothetical, three-dimensional, axisymmetric model of AAA containing ILT was created for computational analysis. Commercial software was utilized to estimate the volume flow of O2 per cell, which resulted in zero oxygen tension at the AAA wall. Solutions were generated by holding one of the two parameters fixed while varying the other. The supply of O2 to the AAA wall increases slightly and linearly with dAAA for a fixed delta. This slight increase is due to the enlarged area through which diffusion of O2 may take place. The supply of O2 was found to decrease quickly with increasing delta for a fixed dAAA due to the increased resistance to O2 transport by the ILT layer. The presence of even a thin, 3 mm ILT layer causes a diminished O2 supply (less than 4 x 10(-10) mumol/min/cell). Normally functioning smooth muscle cells require a supply of 21 x 10(-10) mumol/min/cell. Thus, our analysis serves to support our hypothesis that the presence of ILT alters the normal pattern of O2 supply to the AAA wall. This may lead to hypoxic cell dysfunction in the AAA wall, which may further lead to wall weakening and increased potential for rupture.

A mathematical model of gas exchange in an intravenous membrane oxygenator

Acute respiratory distress syndrome (ARDS) is a pulmonary edemic condition which reduces respiratory exchange in 150,000 people per year in the United States. The currently available therapies of mechanical ventilation and extracorporeal membrane oxygenation are associated with high mortality rates, so intravenous oxygenation represents an attractive, alternative support modality. We are developing an intravenous membrane oxygenator (IMO) device intended to provide 50% of basal oxygen and carbon dioxide exchange requirements for ARDS patients. A unique aspect of the IMO is its use of an integral balloon to provide active mixing. This paper describes a mathematical model which was developed to quantify and optimize the gas exchange performance of the IMO. The model focuses on balloon activated mixing, uses a lumped compartment approach, and approximates the blood-side mass transfer coefficients with cross-flow correlations. IMO gas exchange was simulated in water and blood, for a variety of device geometries and balloon pulsation rates. The modeling predicts the following: (1) gas exchange efficiency is reduced by a buildup of oxygen in the fluid near the fibers; (2) the IMO gas exchange rate in blood is normally about twice that in water under comparable conditions; (3) a balloon diameter of about 1.5 cm leads to optimal gas exchange performance: and (4) in vivo positioning can affect gas exchange rates. The numerically predicted gas transfer rates correlate closely with those experimentally measured in vitro for current IMO prototypes.

Development of a low flow resistance intravenous oxygenator

A potentially attractive support device for patients with acute respiratory failure is an intravenous membrane oxygenator. One problem, however, is that the membrane surface area required for sufficient gas exchange can unduly increase vena caval pressure drop and impede venous return. The purpose of this study was to design and develop an intravenous oxygenator that would offer minimal venous flow resistance in situ. The device uses a constrained fiber bundle of smaller cross sectional size than the vena cava so as to effect an intentional shunt flow of venous blood around the fiber bundle and reduce the venous pressure drop caused by the device. A pulsating balloon within the fiber bundle redirects part of this shunt flow into reciprocating flow in and out of the fiber bundle. This offers dual advantages: 1) Blood flow through the fiber bundle is mainly perpendicular to the fibers; and 2) the requisite energy for driving flow comes largely from the pneumatic system pulsating the balloon, not from a venous pressure drop. In this mode a full length device with a 2 cm fiber bundle in a 2.5 cm blood vessel would offer a pressure drop of only a few millimeters of mercury. The use of constrained fiber bundles requires good uniformity of fiber spacing for effective gas exchange. Several prototypes have been fabricated, and CO2 and O2 exchange rates of up to 402 and 347 ml/min/m2 have been achieved during acute animal implantation.

Recent progress in engineering the Pittsburgh intravenous membrane oxygenator

The University of Pittsburgh intravenous membrane oxygenator (IMO) is undergoing additional engineering development and characterization. The focus of these efforts is an IMO device that can supply as much as one-half basal O2 consumption and CO2 elimination rates while residing within the inferior and superior vena cavae after peripheral venous insertion. The current IMO design consists of a bundle of hollow fiber membranes potted to manifolds at each end, with an intra-aortic type balloon integrally situated within the fiber bundle. Pulsation of the balloon using helium gas and a balloon pump console promotes fluid and fiber motion and enhances gas exchange. During the past year, more than 15 IMO prototypes have been fabricated and extensively bench tested to characterize O2 gas exchange capacity, balloon inflation/deflation over relevant frequency ranges, and the pneumatics of the sweep gas pathway through the device. The testing has led to several engineering changes, including redesign of the helium and sweep gas pathways within the IMO device. As a result, the maximum rate of balloon pulsation has increased substantially above the previous 70 bpm to 160 bpm, and the vacuum pressure required for sufficient sweep gas flow has been reduced. The recent IMO prototypes have demonstrated an O2 exchange capacity of as much as 90 ml/min/m2 in water, which appears within 70% of our design goal when extrapolated to scaled up devices in blood.

A novel method for measuring hollow fiber membrane permeability in a gas-liquid system

Designing an effective intravenous membrane oxygenator requires selecting hollow fiber membranes (HFMs) that present minimal resistance to gas exchange over extended periods of time. Microporous fiber membranes, as used in extracorporeal oxygenators, offer a minimal exchange resistance, but one that diminishes with time because of fiber wetting and subsequent serum leakage. Potentially attractive alternatives are composite HFMs, which inhibit fiber wetting and serum leakage by incorporating a true membrane layer within their porous walls. To evaluate composite and other HFMs, the authors developed a simple apparatus and method for measuring HFM permeability in a gas-liquid system under conditions relevant to intravenous oxygenation. The system requires only a small volume of liquid that is mixed with a pitched blade impeller driven by a direct current motor at controlled rates. Mass flux is measured from the gas flow exiting the fibers, eliminating the necessity of measuring any liquid side conditions. The authors measured the CO2 exchange permeabilities of Mitsubishi MHF 200L composite HFMs, KPF 280E microporous HFMs, and KPF 190 microporous HFMs. The membrane permeabilities to CO2 were 9.3 x 10(-5) ml/cm2/sec/cmHg for the MHF 200L fiber, 4.7 x 10(-4) ml/cm2/sec/cmHg for the KPF 280E fiber, and 2.8 x 10(-4) ml/cm2/sec/cmHg for the KPF 190 fiber. From these results it is concluded that 1) because of liquid-fiber surface interactions, the permeabilities of the microporous fibers are several orders of magnitude less than would be measured for completely gas filled pores, emphasizing the importance of measuring microporous fiber permeability in a gas-liquid system; and 2) the liquid diffusional boundary layer adjacent to the fibers generated by the pitched blade impeller is unique to each fiber, resulting in different boundary layer characterizations.

Acute in vivo studies of the Pittsburgh intravenous membrane oxygenator

The efficacy of an innovative intravenous membrane oxygenator (IMO) was tested acutely (6-8 hrs) in seven calves. The IMO prototypes consisted of a central polyurethane balloon within a bundle of hollow fibers with a membrane surface area of 0.14 m2. The IMO devices were inserted through the external jugular vein into the inferior vena cava of anesthetized calves (68.9 +/- 2.3 kg). Rhythmic balloon pulsation (60-120 bpm) was controlled with an intra-aortic balloon pump console. Oxygen sweep gas was delivered through the device at 3.0 L/min. Gas concentrations were monitored continuously by mass spectroscopy. The principal results were as follows: 1) oxygen and carbon dioxide exchange ranged from 125 to 150 ml/min/m2 and 150 to 200 ml/min/m2, respectively; 2) there was at least a 30-50% augmentation of gas exchange with balloon pulsation; 3) maximum exchange occurred with 60-90 bpm balloon pulsations; and 4) hemodynamic parameters remained unchanged. There were no device related complications, and the feasibility of insertion of the device by a cervical cut-down was established. These acute in vivo experiments show that the Pittsburgh IMO device can exchange oxygen and carbon dioxide gases in vivo at levels consistent with this current prototype design, and that intravenous balloon pulsation significantly enhances gas exchange without causing any end-organ damage.

Nitric oxide prevents human platelet adhesion to fiber membranes in whole blood

During cardiopulmonary bypass or long-term extracorporeal life support, foreign surface induced platelet deposition in the oxygenator causes deterioration of gas exchange. In this study, the authors evaluated the effectiveness of nitric oxide (NO) in reducing the adhesion of platelets in whole blood to the surface of hollow fiber membranes. For this purpose, a test chamber was designed consisting of a gas exchanger with ten mitsubishi multi-layered composite hollow fibers (MHF: 257 mm OD; 203 mm ID; 70 mm length) and a polypropylene tube (16 mm OD; 100 mm length). Pure N2 (control) or nitric oxide (NO) (100 ppm, 200 ppm in N2) were delivered into the test chamber previously filled with 13 ml human whole blood. Platelet counts and platelet factor 4 (PF4), as a measure of platelet activation, were measured before and after either 1 or 2 hr of testing, and fibers were observed under scanning electron microscopic study (SEM) after each experiment. In the control and 100 ppm NO groups, platelet counts decreased and the level of PF4 increased during the 1 hr period. In the 200 ppm NO group, almost no platelet deposition could be observed on the surface of fibers under SEM. In conclusion, NO flow through hollow fiber membranes can markedly reduce platelet adhesion. Additional quantitative studies should define the optimal concentration for this effect and determine if this finding could improve oxygenator function, especially under conditions of long-term support.

Sweep gas flowrate and CO2 exchange in artificial lungs

A simple analysis and graphic result are presented for characterizing the dependence of CO2 exchange on the sweep gas (ventilating gas) flowrate in artificial lungs. The analysis requires no knowledge of the device-specific mass transfer characteristics of an artificial lung, nor does it require detailed mathematical modeling or computer simulation. Rather, it uses appropriate normalization to establish generic features of the gas flow dependency of CO2 exchange that are applicable to all artificial lung devices. Principal results are that the transition from relatively gas flow-sensitive to gas flow-insensitive CO2 exchange occurs at sweep gas flowrates of approximately 40-60 times the CO2 exchange rate. Achieving a CO2 exchange rate within 85% of maximal (for a given oxygenator and blood-side conditions) requires a sweep gas flowrate of no less than approximately 50 times the nominal CO2 exchange rate. When the sweep gas flowrate is less than 20 times the CO2 exchange rate, CO2 exchange is highly gas flow dependent and less than one-half the maximal possible rate.

Model experiments on measuring flow in microvessels using tracers

Most techniques for measuring plasma or red cell flow velocity within microvessels rely on determining the transit time of a tracer to transverse the distance between two monitoring sites within a vessel. In principle, proper transit time determinations require flow-weighted sampling of the tracer at monitoring sites. In practical application of the tracer technique, however, trace sampling at monitoring sites is not flow-weighted but is area-weighted, and hence elapsed transient time can only be estimated from tracer data. We previously showed theoretically (Microvasc. Res. 40, 394-411, 1990) that the flow velocity determined under these conditions can differ appreciably from the actual mean flow velocity of the carrier fluid within the microvessel. Nevertheless, trace mean flow velocity does approach that of the fluid when tracer velocity is measured past a finite distance from the microvessel entrance. In this study, we examined the tracer measurement of flow experimentally using a physical model. We perfused single glass microvessels and simple fabricated microvessel networks with distilled water at physiological flow rates. Mean tracer velocity (Vd) was determined at several axial locations within the microvessels using injected Evans blue dye. At each location Vd was determined in a manner consistent with usual application of the tracer flow measurement technique. Actual mean flow velocity (Va) was determined from the measured effluent flow rates discharged from each microvessel. Our experimental results confirm the existence of an appreciable velocity measurement error (VME) associated with the tracer technique. The VME behavior was consistent with our original theoretical analysis. Vd was significantly smaller than Va within a finite length of vessel near the entrance, but approached and became equal to Va past this length. Furthermore, even under conditions where the VME was negligible at the end of a parent microvessel, a new and appreciable VME arose within the connecting downstream daughter microvessels. These results underscore that tracer mean flow velocity as obtained in normal implementation of the tracer technique can differ from that for the fluid itself within a microvascular network.

Morphometric model for pulmonary diffusing capacity. I. Membrane diffusing capacity

The pulmonary diffusing capacity is related to the quantitative design characteristics of the pulmonary gas exchanger. The current model for estimating DLO2 from morphometric data breaks the diffusion path for O2 into four steps, three of which represent the membrane part of DLO2. A critique of this model on the basis of newer evidence leads to a modification of the model where the path from the alveolar surface to the erythrocyte membrane is considered as a single step. The structural determinant of this model for DMO2 is the ratio of effective diffusion surface to effective total barrier thickness. The effective surface is formulated as a fraction of the alveolar surface area, the most robust measure of lung design, whereas the effective barrier thickness is the harmonic mean distance--or mean proximity--between alveolar surface and erythrocyte surface. The methods for obtaining the morphometric measurements are discussed. The results show that the new morphometric estimates of DMO2 are 33% lower than those obtained with the old model, resulting in a reduction of the estimates of DLO2 by 10-20%.

Influence of bifurcations on forced oscillations in an airway model

Forced oscillations is a technique to determine respiratory input impedance from small amplitude sinusoidal pressure excursions introduced at the airway opening. Models used to predict respiratory input impedance typically ignore the direct effect of bifurcations on the flow, and treat airway branches as individual straight tubes placed appropriately in parallel and series. The flow within the individual tubes is assumed equivalent to that which would occur in infinitely long tubes. In this study we examined the influence of bifurcations on impedance for conditions of the forced oscillatory technique. We measured input impedance using forced oscillations in straight tubes and in an anatomically-relevant, four generation physical model of a human airway network. The input impedance measured experimentally compared well to that obtained theoretically using model predictions. The predictive scheme was based on appropriate parallel and series combinations of theoretically computed individual tube impedances, which were computed from solutions to oscillatory flow of a compressible gas in an infinitely long rigid tube. The agreement between experimental measurements and predictions indicates that bifurcations play a relatively minor direct role on the flow impedance for conditions of the forced oscillations technique. These results are explained in terms of the small tidal volumes used, whereby the axial distance traveled by a fluid particle during an oscillation cycle is appreciably smaller than branch segment lengths. Accordingly, only a small fraction of fluid particles travel through the bifurcation region, and the remainder experience an environment approaching flow in an infinite straight tube. The relevance of the study to the prediction of impedances in the human lung during forced oscillations is discussed.

Use of tracers to measure flow within single microvessels

Most techniques for making quantitative measurements of flow within single microvessels rely on tracers which are injected upstream of the microvessel and monitored noninvasively (e.g., optical densitometry) at selected sites along the microvessel. This study examines theoretically the measurement of average flow velocity (v) within individual microvessels from tracer flow data at monitoring sites. Starting with a fundamental convection-diffusion equation, the theory considers tracers which can distribute across both plasma and red cell phases. An integral analysis indicates that v = delta zeta/delta tau, where delta zeta is the distance between monitoring sites, and delta tau is the tracer transit or "residence" time needed to traverse that distance. The residence time which arises explicitly requires measurement of the flow-weighted average tracer concentration at each monitoring site. Because noninvasive tracer measurements provide indices of the unweighted average tracer concentration, a velocity measurement error, delta(zeta), arises, delta(zeta) is quantified in relation to the axial location of the measurement site, the velocity profile, the tracer Peclet number, and the radial distribution of tracer at the vessel inlet. delta(zeta) does not vanish when tracer enters a microvessel with a radially uniform concentration profile, but does vanish past a critical distance, Lc, from the microvessel entrance. The critical distance can be estimated using Lc/d = 0.05(vd)/D (d. vessel diameter; v, average flow velocity; D, tracer diffusivity). Accordingly, tracer data can be used to quantify flow velocity within a microvessel provided the microvessel length allows for monitoring tracer flow beyond the estimated Lc value. This study serves as a necessary precursor to analyses of plasma-phase tracers used to measure microvascular plasma flow.

Pulmonary diffusing capacity: implications of two-phase blood flow in capillaries

The classical view of oxygen (O2) uptake in pulmonary capillaries assumes implicitly that capillary blood can be regarded as a continuous homogeneous hemoglobin solution. In this study a theoretical model was used to examine the role played by the particulate (two-phase) nature of blood on pulmonary oxygen exchange. Red cells were modelled as discrete hemoglobin (Hb) containing spheres flowing in single file suspension through a cylindrical capillary surrounded by a uniform annulus of alveolar tissue. The model accounted for the free diffusion of O2 from alveolar air space through tissue and plasma, free and Hb facilitated diffusion of O2 inside red cells, and the intracellular kinetics of O2-Hb binding. Oxygen uptake was driven by a specified O2 tension at the alveolar surface. The computed pulmonary diffusing capacity (DLO2) decreased with increasing spacing (Ls) between red cells. The reduction in DLO2 with increasing Ls was marshalled more by a reduction in membrane diffusing capacity (DMO2), than by the reduction in erythrocyte diffusing capacity (DeO2). The dependence of DMO2 on cell spacing stemmed from the manner in which O2 flowed across the alveolar surface into the discrete sinks (red cells) within the capillaries. The degree to which Ls influenced DMO2 was dependent on tissue and plasma layer thickness relative to red cell dimensions. The results indicate that the functional area of the alveolo-capillary membrane for O2 exchange depends on the red cell content of capillaries. Thus, DMO2 is not dictated solely by the morphology of the exchange apparatus (and physical parameters), but has functional determinants as well.

Axial dispersion in respiratory bronchioles and alveolar ducts

The mixing of gases in the pulmonary acinus was characterized by analyzing axial gas dispersion during steady flow in models of respiratory bronchioles and alveolar ducts. An analysis (method of moments) developed for addressing dispersion in porous media was used to derive an integral expression for the axial dispersion coefficient (D*). Evaluation of D* required solving the Navier-Stokes equations for the flow field and a convection-diffusion type equation arising from the analysis. D* was strongly dependent on alveolar volume per central duct volume, the aperture size through which the alveoli communicate with the central duct, and the Péclet number (Pe). At smaller Pe (flow rate) D* was substantially smaller than the molecular diffusion coefficient, whereas at larger Pe (flow rate) D* was much greater than the Taylor-Aris result for flow-enhanced dispersion in straight tubes. Also, flow-enhanced dispersion became appreciable at smaller Pe than indicated by the Taylor-Aris result. These behaviors transcend both the lower and upper limits established previously for gas mixing in the pulmonary acinus.

A theoretical analysis of the effect of the particulate nature of blood on oxygen release in capillaries

A theoretical model is developed to investigate the role played by the particulate (two-phase) nature of blood on oxygen (O2) release in capillary-size vessels. Red cells flowing in single-file suspension through capillaries are modelled as evenly spaced, hemoglobin (Hb)-containing circular particles in a rectangular channel (two-dimensional case) or axisymmetric spheres in a circular tube (three-dimensional case). The model includes the free and Hb-facilitated transport of O2 and Hb-O2 kinetics inside the particles, diffusion of free O2 in the suspending phase, and a specified O2 tension at the capillary wall that drives the release of O2 from the particles as they traverse the capillary. The results are expressed in the form of a capillary mass transfer coefficient, an inverse resistance, that relates the spatial average flux of O2 out of the capillary to a driving force for O2 release. The results indicate that this coefficient depends significantly on particle spacing and clearance (channel size relative to particle size) but not significantly on the O2 tension at the capillary wall nor the eccentricity of the particles in the channel. It is also found that the capillary mass transfer coefficient can be several times smaller (more resistance) than that for a continuous Hb solution releasing O2. As a physiological application of the coefficients obtained, they are combined with a Krogh-type model for tissue, and the resulting analysis suggests that the fraction of total O2 transport resistance that resides inside the capillary is influenced significantly by the discrete nature of blood and can account for 30 to 70% of the total resistance to O2 transport from blood to tissue.

A model study of intracellular oxygen gradients in a myoglobin-containing skeletal muscle fiber

A theoretical two-dimensional model is used to investigate oxygen gradients in a red skeletal muscle fiber. The model describes the steady state, free and myoglobin-facilitated diffusion of oxygen into a respiring cylindrical muscle fiber cross section. The oxygen tension at the sarcolemma is assumed to vary along the sarcolemma as an approximation to the discrete capillary oxygen supply around the fiber. Maximal oxygen gradients are studied by considering parameters relevant to a maximally-respiring red muscle fiber. The model predicts that angular variations in the oxygen tension imposed at the sarcolemma due to the discrete capillary sources do not penetrate deeply into the fiber over a range of physiological values for myoglobin concentration, diffusion coefficients, number of surrounding capillaries, and oxygen tension level at the sarcolemma. Also, the oxygen tension in the core of the fiber is determined by the average oxygen tension at the sarcolemma. The drop in oxygen tension from fiber periphery to core, however, does depend significantly on the myoglobin concentration, the oxygen tension level at the sarcolemma, and the oxygen and myoglobin diffusivities. This dependence is summarized by calculating the minimum average sarcolemmal oxygen tension for maximal respiration without the development of an intracellular anoxic region. For a myoglobin-rich muscle fiber (0.5 mM myoglobin), the model predicts that maximal oxygen consumption can proceed with a relatively flat (less than 5 mm Hg) oxygen tension drop from fiber periphery to core over a large range for diffusion coefficients.

Oxygen delivery from red cells

This paper deals with the theoretical analysis of the unloading of oxygen from a red cell. A scale analysis of the governing transport equations shows that the solutions have a boundary layer structure near the red-cell membrane. The boundary layer is a region of chemical nonequilibrium, and it owes its existence to the fact that the kinetic time scales are shorter than the diffusion time scales in the red cell. The presence of the boundary layer allows an analytical solution to be obtained by the method of matched asymptotic expansions. A very useful result from the analysis is a simple, lumped-parameter description of the oxygen delivery from a red cell. The accuracy of the lumped-parameter description has been verified by comparing its predictions with results obtained by numerical integration of the full equations for a one-dimensional slab. As an application, we calculate minimum oxygen unloading times for red cells.

An examination of the contribution of red cell spacing to the uniformity of oxygen flux at the capillary wall

It is generally assumed that capillary blood is homogeneous for O2 supply and that red cells can provide a constant, uniform flux of O2 out of the capillary regardless of the spacing between cells. Using a simplified model of red cells moving through a capillary in skeletal muscle, an approximate analysis is developed to study the effect of red cell spacing on the ability of erythrocytes to provide a constant, uniform flux of O2 at the capillary wall. The results suggest the existence of a critical red cell separation distance above which the flux of O2 at the capillary wall between red cells cannot remain uniform and the capillary blood is no longer homogeneous for O2 supply. In resting muscle the predicted critical separation distance is greater than four cell lengths. During maximal O2 consumption, the critical separation distance predicted by the model is one cell length. These predictions agree closely with in vivo observations of red cell spacing. The total red cell flux through a capillary is determined not only by red cell spacing (hematocrit) but also by erythrocyte velocity; a simple example is given which suggests that changes in each of these variables are not equivalent in maintaining a constant and uniform flux of O2 at the capillary wall.