Some factors of significance for respiratory gas exchange in muscle tissue A mathematical analysis of a capillary model

Morphological dimensions of the Krogh cylinder capillary model were calculated by mathematical simulation of respiratory gas exchange and blood flow in muscle tissue, using experimentally determined values for oxygen consumption (n'O₂), blood flow (Q′), a-V O₂ difference (a-v O₂D) and pressure difference over the capillary (ΔP), for resting and exercise conditions up to maximum performance. In the resting state a capillary radius, r., of 3.5 (3–5) μm a capillary density (CD) of 35 (30–90) capillaries/mm² and a capillary length (L) of 900(400–1000) μm can satisfy experimentally determined values of the physiological variables. During muscular activity a maintained r₁ and L with an increased CD allows higher n'O₂. An increase in capillaries to about 600/mm² can allow an n'O₂ uptake 30 times the resting value (maximum performance). This increase cannot be achieved by an increase only in the r₁. A shift to the right in the O₂Hb dissociation curve during exercise has only a small effect on the O₂ delivering capacity of the model, as has an increase in the diffusion constant for O₂ in tissue. It is remarkable how limited a range of morphological dimensions, particularly of r₁, is compatible with the known range of values for n'O₂, Q′, a-v O₂D and ΔP, at rest and particularly during maximum performance of the muscle.     

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. © 2000 Biomedical Engineering Society. PAC00: 8780-y, 8710+e     

Perfusion,diffusion and their heterogeneities limiting blood–tissue O2 transfer in muscle

The relative roles of blood flow (perfusion) and diffusion in O₂ supply to exercising muscle can be estimated using a simple model consisting of an O₂‐consuming tissue block in contact with blood (perfusion Q˙, slope of O₂ equilibirum curve β) through a resistance to O₂ diffusion (O₂‐diffusing capacity D). The decisive variable is the ‘equilibration index’Y=D/(Q˙β). With decreasing Y, diffusion limitation increases and perfusion limitation decreases (Y > 3 indicates predominant perfusion limitation; 3 > Y > 0.1, combined perfusion and diffusion limitation, Y < 0.1, prevailing diffusion limitation). On the basis of literature data on humans at maximum O₂ uptake, O₂ supply to muscle is shown to be always limited by both perfusion and diffusion. In nomoxia, perfusion limitation is prevalent, but in hypoxia diffusion limitation becomes predominant. The underlying model assumes perfect homogeneity of muscles with respect to O₂ requirement, diffusion conditions and blood flow. In numerous studies on isolated and in situ muscles a pronounced heterogeneity of blood flow has been found, also during exercise and at maximal O₂ uptake. It is shown that with unequal distribution of blood flow and/or O₂‐diffusing capacity the efficiency of O₂ transfer is reduced with reference to the homogeneous model. Therefore, the diffusing capacity value calculated on the basis of the homogeneous model is an underestimate of the true diffusing capacity and diffusion limitation is overestimated.     

Impact of Airway Gas Exchange on the Multiple Inert Gas Elimination Technique: Theory

The multiple inert gas elimination technique (MIGET) provides a method for estimating alveolar gas exchange efficiency. Six soluble inert gases are infused into a peripheral vein. Measurements of these gases in breath, arterial blood, and venous blood are interpreted using a mathematical model of alveolar gas exchange (MIGET model) that neglects airway gas exchange. A mathematical model describing airway and alveolar gas exchange predicts that two of these gases, ether and acetone, exchange primarily within the airways. To determine the effect of airway gas exchange on the MIGET, we selected two additional gases, toluene and m-dichlorobenzene, that have the same blood solubility as ether and acetone and minimize airway gas exchange via their low water solubility. The airway-alveolar gas exchange model simulated the exchange of toluene, m-dichlorobenzene, and the six MIGET gases under multiple conditions of alveolar ventilation-to-perfusion, [(V)\dot]_\textA /[(Q)\dot] \dot{V}_{\text{A}} /\dot{Q} , heterogeneity. We increased the importance of airway gas exchange by changing bronchial blood flow, [(Q)\dot]_\textbr \dot{Q}_{\text{br}} . From these simulations, we calculated the excretion and retention of the eight inert gases and divided the results into two groups: (1) the standard MIGET gases which included acetone and ether and (2) the modified MIGET gases which included toluene and m-dichlorobenzene. The MIGET mathematical model predicted distributions of ventilation and perfusion for each grouping of gases and multiple perturbations of [(V)\dot]_\textA /[(Q)\dot] \dot{V}_{\text{A}} /\dot{Q} and [(Q)\dot]_\textbr \dot{Q}_{\text{br}} . Using the modified MIGET gases, MIGET predicted a smaller dead space fraction, greater mean [(V)\dot]_\textA \dot{V}_{\text{A}} , greater log(SD_VA), and more closely matched the imposed [(V)\dot]_\textA \dot{V}_{\text{A}} distribution than that using the standard MIGET gases. Perfusion distributions were relatively unaffected.     

Hyperoxia does not increase peak muscle oxygen uptake in small muscle group exercise

We examined the influence of hyperoxia on peak oxygen uptake (V˙O _2peak) and peripheral gas exchange during exercise with the quadriceps femoris muscle. Young, trained men (n=5) and women (n=3) performed single-leg knee-extension exercise at 70% and 100% of maximum while inspiring normal air (NOX) or 60% O₂ (HiOX). Blood was sampled from the femoral vein of the exercising limb and from the contralateral artery. In comparison with NOX, hyperoxic arterial O₂ tension (P_aO ₂) increased from 13.5 ± 0.3 (x ± SE) to 41.6 ± 0.3 kPa, O₂ saturation (S_aO ₂) from 98 ± 0.1 to 100 ± 0.1%, and O₂ concentration (C_aO ₂) from 177 ± 4 to 186 ± 4 mL L^–1 (all P < 0.01). Peak exercise femoral venous PO ₂ (P_vO ₂) was also higher in HiOX (3.68 ± 0.06 vs. 3.39 ± 0.7 kPa; P < 0.05), indicating a higher O₂ diffusion driving pressure. HiOX femoral venous O₂ saturation averaged 36.8 ± 2.0% as opposed to 33.4 ± 1.5% in NOX (P < 0.05) and O₂ concentration 63 ± 6 vs. 55 ± 4 mL L^–1 (P < 0.05). Peak exercise quadriceps blood flow (Q˙_leg), measured by the thermo-dilution technique, was lower in HiOX than in NOX, 6.4 ± 0.5 vs. 7.3 ± 0.9 L min^–1 (P < 0.05); mean arterial blood pressure at inguinal height was similar in NOX and HiOX at 144 and 142 mmHg, respectively. O₂ delivery to the limb (Q˙_leq times C_aO ₂) was not significantly different in HiOX and NOX. V˙O _2peak of the exercising limb averaged 890 mL min^–1 in NOX and 801 mL min^–1 in HiOX (n.s.) corresponding to 365 and 330 mL min^–1 per kg active muscle, respectively. The V˙O _2peak-to-P_vO ₂ ratio was lower (P < 0.05) in HiOX than in NOX suggesting a lower O₂ conductance. We conclude that the similar V˙O _2peak values despite higher O₂ driving pressure in HiOX indicates a peripheral limitation for V˙O _2peak. This may relate to saturation of the rate of O₂ turnover in the mitochondria during exercise with a small muscle group but can also be caused by tissue diffusion limitation related to lower O₂ conductance.     

Single breath‐hold measurement of pulmonary gas exchange and diffusion in humans with hyperpolarized 129Xe MR

Pulmonary diseases usually result in changes of the blood‐gas exchange function in the early stages. Gas exchange across the respiratory membrane and gas diffusion in the alveoli can be quantified using hyperpolarized ¹²⁹Xe MR via chemical shift saturation recovery (CSSR) and diffusion‐weighted imaging (DWI), respectively. Generally, CSSR and DWI data have been collected in separate breaths in humans. Unfortunately, the lung inflation level cannot be the exactly same in different breaths, which causes fluctuations in blood‐gas exchange and pulmonary microstructure. Here we combine CSSR and DWI obtained with compressed sensing, to evaluate the gas diffusion and exchange function within a single breath‐hold in humans. A new parameter, namely the perfusion factor of the respiratory membrane (SVR_d/g), is proposed to evaluate the gas exchange function. Hyperpolarized ¹²⁹Xe MR data are compared with pulmonary function tests and computed tomography examinations in healthy young, age‐matched control, and chronic obstructive pulmonary disease human cohorts. SVR_d/g decreases as the ventilation impairment and emphysema index increase. Our results indicate that the proposed method has the potential to detect the extent of lung parenchyma destruction caused by age and pulmonary diseases, and it would be useful in the early diagnosis of pulmonary diseases in clinical practice.     

Oxygen diffusivity in tumor tissue (DS-Carcinosarcoma) under temperature conditions within the range of 20–40°C

Summary The O₂ diffusion constants D and K of tumor tissue (DS-Carcinosarcoma in the rat kidney) were determined at temperatures of 20, 30, 37, and 40°C. The following mean values were obtained for the conditions of 37°C: D=1.75·10^–5 cm²/s and K=1.9·10^–5 mlO₂/cm·min·atm. Within the range of 20–40°C, temperature variations in tumor tissue cause changes in the O₂ diffusion coefficient D of 2.0–2.5%/°C and in the Krogh O₂ diffusion constant K of 0.5–1.5%/°C. The measured O₂ diffusion constants for tumor tissue correspond to values of normal tissue with similar water content. This indicates that the insufficient O₂ supply in DS-Carcinosarcoma is due not to unfavorable O₂ diffusivity of the tumor tissue but rather to a decreased convective O₂ transport and to insufficient capillarization. An analysis of O₂ diffusion in DS-Carcinosarcoma tissue using the determined O₂ diffusion constants lead to the result that, under the conditions of arterial normoxia and normocapnia, critical O₂ supply conditions are to be expected when the intercapillary distance exceeds approximately 120 m.     

Michaelis-Menten kinetics model of oxygen consumption by rat brain slices following hypoxia

In the present study, we have measured partial pressure of oxygen (pO₂) profiles through rat brain slices before and after periods of hypoxia (5 and 10 min) to determine its effect on tissue oxygen demand. Tissue pO₂ profiles were measured through rat cerebral cortex slices superfused with phosphate buffer using oxygen (O₂)-sensitive microelectrodes at different times in controls [40% O₂ balance nitrogen (N₂)], and at different times before and after 5 or 10 min of hypoxia (100% N₂). A one-dimensional, steady-state model of ordinary diffusion with a Michaelis-Menten model of O₂ consumption where the maximal O₂ consumption (V_max) and the rate at half-maximal O₂ consumption (K_m) were allowed to vary was used to determine the kinetics of O₂ consumption. Actual pO₂ profiles through tissue were fitted to theoretical profiles by a least-squares method. V_max varied among penetrations in a control slice and among slices. V_max seemed to decrease after hypoxic insult, but the change was not statistically significant. The K_m value measured before hypoxia was lower than the first K_m value measured after the end of hypoxia, indicating that hypoxia induced a compensatory change in the metabolic state of the tissue. K_m increased immediately after both 5- and 10-min hypoxic insults and returned to normal after recovery for each case. It seems that during and immediately after short periods of hypoxia, K_m increases from near zero but returns to normal values within a few minutes.     

Regulation of erythrocyte function: Multiple evolutionary solutions for respiratory gas transport and its regulation in fish

Gas transport concepts in vertebrates have naturally been formulated based on human blood. However, the first vertebrates were aquatic, and fish and tetrapods diverged hundreds of millions years ago. Water‐breathing vertebrates live in an environment with low and variable O₂ levels, making environmental O₂ an important evolutionary selection pressure in fishes, and various features of their gas transport differ from humans. Erythrocyte function in fish is of current interest, because current environmental changes affect gas transport, and because especially zebrafish is used as a model in biomedical studies, making it important to understand the differences in gas transport between fish and mammals to be able to carry out meaningful studies. Of the close to thirty thousand fish species, teleosts are the most species‐numerous group. However, two additional radiations are discussed: agnathans and elasmobranchs. The gas transport by elasmobranchs may be closest to the ancestors of tetrapods. The major difference in their haemoglobin (Hb) function to humans is their high urea tolerance. Agnathans differ from other vertebrates by having Hbs, where cooperativity is achieved by monomer‐oligomer equilibria. Their erythrocytes also lack the anion exchange pathway with profound effects on CO₂ transport. Teleosts are characterized by highly pH sensitive Hbs, which can fail to become fully O₂‐saturated at low pH. An adrenergically stimulated Na⁺/H⁺ exchanger has evolved in their erythrocyte membrane, and plasma‐accessible carbonic anhydrase can be differentially distributed among their tissues. Together, and differing from other vertebrates, these features can maximize O₂ unloading in muscle while ensuring O₂ loading in gills.     

Enhancement of O2 and CO2 Transfer Through Microporous Hollow Fibers by Pressure Cycling

An intravascular gas exchange device for the treatment of respiratory failure consisted of a multitude of blind-ended hollow fibers glued in a pine-needle arrangement to a central gas supply catheter. It has previously been shown that gas desorption rates can be significantly enhanced by cycling gas pressure between a hypobaric level of 130 and an ambient level of 775 Torr. In this study, influences of the cycling frequency (f) and the cycle fraction during which hypobaric pressure is applied () were investigated. Rates of O₂ desorption from O₂-saturated water and CO₂ desorption from CO₂-saturated water into a manifold containing 198 fibers, 380 m in diameter, were measured over a range of f from 0.2 to 1.0 Hz, from 0.1 to 0.8, and fiber lengths from 4 to 16 cm. Relative to operation at ambient pressure, pressure cycling increased O₂ transfer 3–4 times and CO₂ transfer 4–6 times when the water flowed over the fiber manifold at 2.3 l/min. Transfer rates were relatively insensitive to f and with 80–90% of maximum enhancement obtained when was as low as 0.2. Transfer rates increased continuously with fiber length, implying that pressure cycling reduced the intra-fiber resistance to gas diffusion. A mathematical diffusion model which utilized only two adjustable parameters, a mass transfer coefficient for O₂ and for CO₂, simulated the trends exhibited by desorption data. © 1998 Biomedical Engineering Society. PAC98: 8745Hw, 8790+y     

A Method to Correct for the Influence of Gas Density on Maximal Expiratory Flow Rate

Maximal expiratory flow rate (V?max) was measured at 20, 35, 50, 65, and 80% vital capacity in 4 young healthy subjects breathing air, SF₆/O₂, and He/O₂ mixtures. The flows of SF₆/O₂ and He/O₂ were corrected to normal alveolar gasflow by means of only the density of the gases. The values for normal alveolar gasflow and corrected SF₆/O₂ flow were identical at 35% VC and larger volumes while the values for normal alveolar gasflow and corrected He/O₂ flow were not. The results indicate that in young healthy subjects it is possible to correct Vmax at lung volumes above 359: VC for the changes induced by an increase in density of the gas breathed, provided viscosity is not much changed. Without correction, V?max after O₂-breathing will be underestimated by about 6%, compared with V?max for normal alveolar gas, whereas a change in alveolar CO₂ concentrations between 3 and 9% only causes a 1 % decrease of V? max.     

Evaluation of cardiac output from a tidally ventilated homogeneous lung model

We used the direct Fick measurements to validate a method for estimating cardiac output by iteratively fitting at the mouth to lung model values. This model was run using a series of 50, 30 and 10 breaths to test sensitivity to number of breaths used for fitting. The lung was treated as a catenary two-compartment lung model consisting of a dead space compartment connected with a single alveolar space compartment, perfused with constant pulmonary blood flow. The implemented mathematical modeling described variations in O₂ and CO₂ compartmental fractions and alveolar volume. This model also included pulmonary capillary gas exchange. Experimental data were collected from measurements performed on six healthy subjects at rest and during 20, 40, 60 and 85–90% of peak The correlation between the two methods was highest and the average agreement between the methods was best using 50 breaths The mean difference and lower to upper limits of agreement between measured and estimated data were 0.7 l/min (–2.7 to 4.1 l/min) for cardiac output; –0.9 ml/100 ml (–1.3 to –0.5 ml/100 ml) for arterial O₂ content; –0.8 ml/100 ml (–3.8 to 2.2 ml/100 ml) for mixed venous O₂ content and –0.1 ml/100 ml (–2.9 to 2.7 ml/100 ml) for arteriovenous difference O₂ content. The cardiac output estimated by the lung model was in good agreement with the direct Fick measurements in young healthy subjects.     

Influence of intracellular convection on the oxygen release by human erythrocytes

Summary There is general agreement today that intracellular diffusive transport of HbO₂ and O₂ limits the rate of oxygen uptake or release by the blood in the exchange vessels. Recent hemorheological results have shown that the mammalian erythrocyte exhibits fluidity as its most unique rheological property: it can be deformed continuously and rapidly, shear and normal stresses can be transmitted to the interior of the cell where systems of laminar flow are induced. These mechanical properties lead to the question whether or not intracellular convection does take place in the erythrocyte and to what extent it plays a part in gas exchange. A method was developed which subjects oxygen-saturated solutions and cell suspensions to an artificial but well defined flow (cone-plate-viscosimeter), and allows simulataneous determination of the initial O₂ release indices under standardized conditions (O₂ saturation, temperature, time, diffusion area, and difference of O₂ partial pressure). The results strongly suggest that intracellular flow resulting from the physiological erythrocyte deformation in flow can supplement the O₂ release from intact cells through a convective transport of HbO₂ and O₂ molecules. The example of osmotic shrinking shows that red cell fluidity is not only a precondition for normal flow in the microcirculation, but also for the normal gas exchange of the cells.The experiments were carried out at the Inst. of Physiol. München, supported by the Deutsche Forschungsgemeinschaft.Presented in part at the XXV. Int. Congress of Physiological Sciences, München 1971.     

Hypoxia and hyperoxia both transiently affect distribution of pulmonary perfusion but not ventilation in awake sheep

Despite a remarkable gravity independent heterogeneity in both local pulmonary ventilation and perfusion, the two are closely correlated at rest and during exercise in the normal lung. These observations strongly indicate that there is a mechanism for coupling of the two so that local V˙/Q˙-ratio is kept fairly uniform throughout the lung. This is also necessary to achieve adequate gas exchange in the lung. It was recently suggested that oxygen-induced vasoconstriction has a slow and intense component that might contribute to the matching of ventilation and perfusion also under normal conditions ( 21 ). We therefore simultaneously determined distribution of local (≈ 1½ cm³ lung pieces) ventilation and perfusion in eight sheep at normoxia (FiO₂ 21%) and after 10 min and 2½ h exposure to hypoxia (FiO₂ 12%; four sheep) or hyperoxia (FiO₂ 40%; four sheep). We used a ≈ 1 μm wet fluorescent aerosol and 15 μm radioactive microspheres i.v. to measure local ventilation and perfusion, respectively. Neither hypoxia nor hyperoxia caused changes in the distribution of ventilation. After 10 min exposure to hypoxia or hyperoxia, distribution of perfusion was altered so that the correlation between values for local ventilation and perfusion decreased. After 2½ h exposure to either hypoxia or hyperoxia, distributions of perfusion and v˙/Q˙-ratio had returned to baseline. These results show that distribution of perfusion is influenced by acute changes in oxygen tension, so that local matching of ventilation and perfusion is affected. Apparently, some mechanism restores the matching during extended exposure to the altered oxygen tension.     

Gas transport during high-frequency ventilation: Theoretical model and experimental validation

We present a theoretical model of gas transport through the dead space during high-frequency ventilation (HFV) with volumes less than dead space volume. The analysis is based on the axial distribution of transit times of gas moving through the dead space. The model predicts that for tidal volumes (V) much less than dead space (V_d), gas exchange will be proportional to the product of frequency (f) and V². If gas transport is analyzed in terms of Fick's law, then the effective diffusion coefficient (D_eff) can be shown to be equal to fV² times a constant, whose value equals the square of the coefficient of dispersion of axial transit times through the dead space . Experimental results in straight tubes fit the predictions of this model quite well. A through the entire dead space of about 30% is more than sufficient to account for gas exchange during HFV in physical models or in intact animals. An axial dispersion of this magnitude can be measured directly from a typical Fowler dead space determination in healthy subjects.     

Nitric oxide used to test pulmonary gas exchange in rabbits

 To evaluate whether nitric oxide (NO) is an appropriate test gas for assessing pulmonary gas exchange, we determined the rates of disappearance from the alveolar space (λ) of NO and singly and doubly ¹⁸O-labelled carbon dioxide (C¹⁶O¹⁸O, C¹⁸O₂) by performing single-breath manoeuvres on seven artificially ventilated rabbits. By exploiting unique features of both isotopic species and by analysing pulmonary gas transport and λ values with a commonly used model, we found that diffusion forms 98±6% (mean ± SD) of the overall resistance to alveolar-capillary NO transfer. This means that measurements of pulmonary NO uptake reveal the entire diffusive properties of the alveolar-capillary membrane, because the extremely fast binding of NO to haemoglobin negates the ”reactive” component within red blood cells of pulmonary capillaries. Received: 8 May 1998 / Received after revision: 12 August 1998 / Accepted: 17 August 1998     

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.     

A comprehensive simulator of the human respiratory system: Validation with experimental and simulated data

A comprehensive model of oxygen (O₂) and carbon dioxide (CO₂) exchange, transport, and storage in the adult human is presented, and its ability to provide realistic responses under different physiological conditions is evaluated. The model comprises three compartments (i.e., lung, body tissue, and brain tissue) and incorporates a controller that adjusts alveolar ventilation and cardiac output dynamically integrating stimuli coming from peripheral and central chemoreceptors. A new realistic CO₂ dissociation curve based on a two-buffer model of acid-base chemical regulation is included. In addition, the model explicitly considers relevant physiological factors such as buffer base, the nonlinear interaction between the O₂ and CO₂ chemoreceptor responses, pulmonary shunt, dead space, variable time delays, and Bohr and Haldane effects. Model simulations provide results consistent with both dynamic and steady-state responses measured in subjects undergoing inhalation of high CO₂ (hypercapnia) or low O₂ (hypoxia) and subsequent recovery. An analysis of the results indicates that the proposed model fits the experimental data of ventilation and gas partial pressures as some meaningful simulators now available and in a very large range of gas intake fractions. Moreover, it also provides values of blood concentrations of CO₂, HCO⁻ ₃, and hydrogen ions in good agreement with more complex simulators characterized by an implicit formulation of the CO₂ dissociation curve. In the experimental conditions analyzed, the model seems to represent a single theoretical framework able to appropriately describe the different phenomena involved in the control of respiration.     

CO2 rebreathing model in COPD: blood-to-gas equilibration

Rebreathing in a closed system can be used to estimate mixed venous and cardiac output, but these estimates are affected by heterogeneity. The purpose of this study was to validate a mathematical model of CO₂ exchange during CO₂ rebreathing in 29 patients with chronic obstructive pulmonary disease (COPD), with baseline arterial ranging from 28 to 60 mmHg. Rebreathing increased end-tidal by 20 mmHg over 2.2 min. This model employed baseline values for inspired (bag) estimated distribution of ventilation and blood flow in one high and one low compartment, the ventilation increase and conservation of mass equations to simulate time courses of and Measured and during rebreathing differed by an average (SEM) of 1.4 (0.4) mmHg from simulated values. By end of rebreathing, predicted was lower than measured and predicted indicating gas to blood CO₂ flux. Estimates of the ventilatory response to CO₂, quantified as the slope (S) of the ventilation increase versus were inversely related to gas-to-blood disequilibria due to heterogeneity and buffer capacity (BC), but not airflow limitation. S may be corrected for these artifacts to restore S as a more valid noninvasive index of central CO₂ responsiveness. We conclude that a rebreathing model incorporating baseline heterogeneity and BC can simulate gas and blood in patients with COPD, where variations are large and variable.Laboratory of origin: These experiments were performed at the Lovelace Medical Foundation and at New Mexico Resonance in Albuquerque NM.