The Gradient Perfusion Model Part 2: Substantiation of the GPM with clinical cases.

Introduction: In Part 1 of this three-part series, we provided an explanation as to why and at what sites decompression sickness (DCS) occurs, using the Gradient-Perfusion Model (GPM). In this part, we provide information to substantiate the concept and present clinical cases that were initially labeled as "unexplained DCS," but later disordering events were identified to explain the clinical presentations. Materials and Methods: Among 500 cases of DCS we have managed for over 50 years, a cohort of these patients was initially diagnosed as unexplained DCS. However, some have shown that disordering events are the likely cause of their DCS. Results: By pairing the tissue involved with the patient's dive history, a gradient-perfusion imbalance connection was identified. In all serious (Type 2) presentations of DCS, alterations in perfusion of the fast tissues were able to account for the clinical findings. The consequences demonstrated that the gradients overwhelmed the ability of altered perfusion to offgas/offload the inert gas. Pain-only and peripheral neuropathy presentations involved both intermediate and slowly perfused tissues. Rather than perfusion, gradient limitations were the reasons for the clinical presentations of these patients. Conclusions: The GPM accounts for signs and symptom presentations in DCS. This provides the basis for appropriate treatments and logical recommendations for return to diving. We recommend that the label "unexplained DCS" be discontinued and that the GPM be used to determine the cause. Once the cause is established, "DCS due to disordered decompression" becomes the appropriate term.

Measurement of the distribution of ventilation-perfusion ratios in the human lung with proton MRI: comparison with the multiple inert-gas elimination technique.

We have developed a novel functional proton magnetic resonance imaging (MRI) technique to measure regional ventilation-perfusion (V̇A/Q̇) ratio in the lung. We conducted a comparison study of this technique in healthy subjects (n = 7, age = 42 ± 16 yr, Forced expiratory volume in 1 s = 94% predicted), by comparing data measured using MRI to that obtained from the multiple inert gas elimination technique (MIGET). Regional ventilation measured in a sagittal lung slice using Specific Ventilation Imaging was combined with proton density measured using a fast gradient-echo sequence to calculate regional alveolar ventilation, registered with perfusion images acquired using arterial spin labeling, and divided on a voxel-by-voxel basis to obtain regional V̇A/Q̇ ratio. LogSDV̇ and LogSDQ̇, measures of heterogeneity derived from the standard deviation (log scale) of the ventilation and perfusion vs. V̇A/Q̇ ratio histograms respectively, were calculated. On a separate day, subjects underwent study with MIGET and LogSDV̇ and LogSDQ̇ were calculated from MIGET data using the 50-compartment model. MIGET LogSDV̇ and LogSDQ̇ were normal in all subjects. LogSDQ̇ was highly correlated between MRI and MIGET (R = 0.89, P = 0.007); the intercept was not significantly different from zero (-0.062, P = 0.65) and the slope did not significantly differ from identity (1.29, P = 0.34). MIGET and MRI measures of LogSDV̇ were well correlated (R = 0.83, P = 0.02); the intercept differed from zero (0.20, P = 0.04) and the slope deviated from the line of identity (0.52, P = 0.01). We conclude that in normal subjects, there is a reasonable agreement between MIGET measures of heterogeneity and those from proton MRI measured in a single slice of lung.NEW & NOTEWORTHY We report a comparison of a new proton MRI technique to measure regional V̇A/Q̇ ratio against the multiple inert gas elimination technique (MIGET). The study reports good relationships between measures of heterogeneity derived from MIGET and those derived from MRI. Although currently limited to a single slice acquisition, these data suggest that single sagittal slice measures of V̇A/Q̇ ratio provide an adequate means to assess heterogeneity in the normal lung.

Multiple inert gas elimination technique by micropore membrane inlet mass spectrometry--a comparison with reference gas chromatography.

The mismatching of alveolar ventilation and perfusion (VA/Q) is the major determinant of impaired gas exchange. The gold standard for measuring VA/Q distributions is based on measurements of the elimination and retention of infused inert gases. Conventional multiple inert gas elimination technique (MIGET) uses gas chromatography (GC) to measure the inert gas partial pressures, which requires tonometry of blood samples with a gas that can then be injected into the chromatograph. The method is laborious and requires meticulous care. A new technique based on micropore membrane inlet mass spectrometry (MMIMS) facilitates the handling of blood and gas samples and provides nearly real-time analysis. In this study we compared MIGET by GC and MMIMS in 10 piglets: 1) 3 with healthy lungs; 2) 4 with oleic acid injury; and 3) 3 with isolated left lower lobe ventilation. The different protocols ensured a large range of normal and abnormal VA/Q distributions. Eight inert gases (SF6, krypton, ethane, cyclopropane, desflurane, enflurane, diethyl ether, and acetone) were infused; six of these gases were measured with MMIMS, and six were measured with GC. We found close agreement of retention and excretion of the gases and the constructed VA/Q distributions between GC and MMIMS, and predicted PaO2 from both methods compared well with measured PaO2. VA/Q by GC produced more widely dispersed modes than MMIMS, explained in part by differences in the algorithms used to calculate VA/Q distributions. In conclusion, MMIMS enables faster measurement of VA/Q, is less demanding than GC, and produces comparable results.

Predictions from a mathematical model of decompression compared to Doppler scores.

This paper describes an attempt to calibrate a mathematical model that predicts the extent of bubble formation in both the tissue and blood of subjects experiencing decompression from a hyperbaric exposure. The model combines an inert gas dynamics model for uptake and elimination of inert anesthetic gases with a simple model of bubble dynamics in perfused tissues. The calibration has been carried out using the model prediction for volume of free gas (bubbles) as microl/ml in central venous blood and relating this to Doppler scores recorded at the end of hyperbaric exposures. More than 1,000 Doppler scores have been compared with the model predictions. Discriminant analysis has been used to determine the cut-points between scores below a certain level and all scores at or above that level. This allows each prediction from the model to be equated to a particular pattern of bubble scores. The predictions from the model are thus given a context against the more familiar Doppler scores as a means of evaluating decompression stress. It is thus possible to use the mathematical model to evaluate decompression stress of a hyperbaric exposure in terms of the predicted volume of gas that will form into bubbles and to convert that to a prediction of the most likely pattern of Doppler grades which would be recorded from a group of subjects experiencing that exposure. This model has been used in assisting regulators to set limits to the level decompression risk that should be considered acceptable and in assisting those working with decompression procedures to design effective modifications.

Inert gas transport in blood and tissues.

This article establishes the basic mathematical models and the principles and assumptions used for inert gas transfer within body tissues-first, for a single compartment model and then for a multicompartment model. From these, and other more complex mathematical models, the transport of inert gases between lungs, blood, and other tissues is derived and compared to known experimental studies in both animals and humans. Some aspects of airway and lung transfer are particularly important to the uptake and elimination of inert gases, and these aspects of gas transport in tissues are briefly described. The most frequently used inert gases are those that are administered in anesthesia, and the specific issues relating to the uptake, transport, and elimination of these gases and vapors are dealt with in some detail showing how their transfer depends on various physical and chemical attributes, particularly their solubilities in blood and different tissues. Absorption characteristics of inert gases from within gas cavities or tissue bubbles are described, and the effects other inhaled gas mixtures have on the composition of these gas cavities are discussed. Very brief consideration is given to the effects of hyper- and hypobaric conditions on inert gas transport.

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, VA/Q, heterogeneity. We increased the importance of airway gas exchange by changing bronchial blood flow, Qbr. 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 VA/Q and Qbr. Using the modified MIGET gases, MIGET predicted a smaller dead space fraction, greater mean VA, greater log(SDVA), and more closely matched the imposed VA distribution than that using the standard MIGET gases. Perfusion distributions were relatively unaffected.

Relationship between two different functions derived from diffusion-based decompression theory.

Hempleman's diffusion-based decompression theory yields two different functions; one is expressed by a simple root function and the other by a complex series function. Although both functions predict the same rate of gas uptake for relatively short exposure times, no clear mathematical explanation has been published that describes the relationship between the two functions. We clarified that (1) the root function is the solution of the one-dimensional diffusion equation for a semi-infinite slab, (2) the series function is an applicable solution for a finite slab thickness, (3) the parameter values of the root function can be used to determine the parameter values of the series function, and (4) the predictions of gas kinetics from both functions agree until an adequate amount of diffusing inert gas reaches the boundary at the opposite end of the finite slab. The last point allows the use of the simpler root function for predicting short no-stop decompression limits. Experience dictates that the inert gas accumulation for a 22 min at 100 feet of seawater (fsw) dive is considered safe for no-stop decompression. Although the constraint, Depth square root of Bottom Time = 100 square root of 22, has been applied as an index to determine either the safe depth or bottom time (given the other) for no-stop decompression, it should not be applied more broadly to dives requiring decompression stops.

Soluble gas exchange in the pulmonary airways of sheep.

We studied the airway gas exchange properties of five inert gases with different blood solubilities in the lungs of anesthetized sheep. Animals were ventilated through a bifurcated endobronchial tube to allow independent ventilation and collection of exhaled gases from each lung. An aortic pouch at the origin of the bronchial artery was created to control perfusion and enable infusion of a solution of inert gases into the bronchial circulation. Occlusion of the left pulmonary artery prevented pulmonary perfusion of that lung so that gas exchange occurred predominantly via the bronchial circulation. Excretion from the bronchial circulation (defined as the partial pressure of gas in exhaled gas divided by the partial pressure of gas in bronchial arterial blood) increased with increasing gas solubility (ranging from a mean of 4.2 x 10(-5) for SF6 to 4.8 x 10(-2) for ether) and increasing bronchial blood flow. Excretion was inversely affected by molecular weight (MW), demonstrating a dependence on diffusion. Excretions of the higher MW gases, halothane (MW = 194) and SF6 (MW = 146), were depressed relative to excretion of the lower MW gases ethane, cyclopropane, and ether (MW = 30, 42, 74, respectively). All results were consistent with previous studies of gas exchange in the isolated in situ trachea.

Computation of decompression tables using continuous compartment half-lives.

There is no consensus on the number of compartments and the half-lives (T1/2) used in the calculation of inert gas exchange and decompression sickness (DCS) boundary in existing dive tables and decompression computers. We propose the use of a continuous variable for the tissue half-lives, allowing the simulation of an infinite number of compartments and reducing the discrepancy between different algorithms to a single DCS boundary expression. Our computational method is based on the premise that M-values can be expressed in terms of T1/2 and ambient pressure (D). We combined the surfaces defined by M(D,T1/2) and tissue tension H(t,T1/2) to plan decompression. The efficiency and applicability of the method is investigated with four different DCS boundaries. The first two utilize the M-value relations proposed by Bühlmann and Wienke to derive no-D limits for sea level. The third boundary is defined by a surface fitted to the empirical M-values of US Navy, Bühlmann tables, US Air Force, and our altitude diving data. This expression was used to design the decompression procedure for a multilevel dive at 11,429-ft altitude and was used in six man dives in the Kaçkar Mountains, Turkey. Although precordial bubbles were observed in two dives, there were no cases of DCS. The fourth DCS boundary is constructed with the addition of a constraint that forces calculated M-values to stay below the available M-values. This constraint aims the highest degree of "conservatism". As an application of the new boundary, the method is used to derive decompression stop diving schedules for 11,429-ft altitude. The concept of continuous tissue half-lives is applicable to different types of gas exchange and DCS boundary functions or to a combination of different models with a desired level of conservatism. It has proved to be a useful tool in planning decompression for undocumented modes of diving such as decompression stop diving or multilevel diving at altitude. The algorithm can easily be incorporated into dive computers.

Biomedical imaging using hyperpolarized noble gas MRI: pulse sequence considerations.

Hyperpolarized noble gas MRI is a new technique for imaging of gas spaces and tissues that have been hitherto difficult to image, making it a promising diagnostic tool. The unique properties of hyperpolarized species, particularly the non-renewability of the large non-equilibrium spin polarization, raises questions about the feasibility of hyperpolarized noble gas MRI methods. In this paper, the critical issue of T1 relaxation is discussed and it is shown that a substantial amount of polarization should reach the targets of interest for imaging. We analyse various pulse sequence designs, and point out that total scan times can be decreased so that they are comparable or shorter than tissue T1 values. Pulse sequences can be optimized to effectively utilize the non-renewable hyperpolarization, to enhance the SNR, and to eliminate image artifacts. Hyperpolarized noble gas MRI is concluded to be quite feasible.

Validation of cardiac echocardiography for measuring cardiac output to be applied for the multiple inert gas elimination technique.

The multiple inert gas elimination technique (MIGET) is being increasingly used in respiratory physiology and pathophysiology. Six inert gases are given as an intravenous infusion then measured in samples of expired air and mixed arterial and venous blood. This requires right-sided catheterization, a procedure that is sometimes ethically inappropriate. The present article reports a method in which inert gas levels in mixed venous blood were calculated, rather than measured, using Fick's law. Echocardiography was used to measure arterial inert gas levels and cardiac output. The method was validated in 11 men scheduled to undergo coronary bypass surgery. Cardiac output was either calculated based on biometrical (C) data or measured using four different methods in random order, namely Fick's law with oxygen (FiO2) or the inert gases (FiIG) as the tracers, thermodilution (TH), and echocardiography (E). Cardiac output values in L.min-1 (mean +/- SD) were as follows: C, 4.99 +/- 0.39; FiO2, 5.44 +/- 0.86; FiIG, 5.55 +/- 0.92; TH, 5.77 +/- 0.88; and E, 5.53 +/- 0.64. No significant differences were found among the four measured cardiac output values, of which the mean was 5.57 +/- 0.70 L/min, a value that was significantly higher than the calculated value. This difference is probably ascribable to the use of dopamine, dobutamine, or epinephrine in six of the 11 patients. A 1 L/min-1 cardiac output error, in either direction, was found to have a marked influence on the distribution of alveolar perfusion at various VA/Q ratios. Conversely, as expected, ventilation distribution was not influenced by cardiac output. In conclusion, echocardiography provides satisfactory cardiac output estimations using the MIGET except in patients with septal hypertrophy, subaortic membranes, a mitral valve prosthesis, or a mitral valve ring.

Countercurrent extraction of sparingly soluble gases for membrane introduction mass spectrometry.

Membrane introduction mass spectrometry has been applied to inert gas measurements in blood and tissue, but gases with low blood solubility are associated with reduced sensitivity. Countercurrent extraction of inert gases from a blood sample into a water carrier phase has the potential to extract most of the gas sample while avoiding dependence of signal on blood solubility. We present the design of a membrane countercurrent exchange (CCE) device coupled with a conventional direct insertion membrane probe to measure partial pressure of low solubility inert gases in aqueous samples. A mathematical model of steady-state membrane CCB predicts that countercurrent extraction with appropriate selection of carrier and sample flow rates can provide a mass spectrometer signal nearly independent of variations in solubility over a specified range, while retaining a linear response to changes in gas partial pressure over several orders of magnitude. Experimental data are presented for sulfur hexafluoride and krypton in water samples. Optimal performance is dependent on adequate equilibration between the sample and carrier streams, and the large resistance to diffusion in the aqueous phase for insoluble gases presents a substantial challenge to the application of this principle.

A new method for measuring nitrogen and gases in blood.

The authors developed a new apparatus for extracting nitrogen or other inert gases from blood by flushing (sparging) the specimen with another gas. To investigate the utility of the new methodology, the apparatus was used in conjunction with a mass spectrometer to measure the blood N2 content of healthy normobaric, non-smoking, adult volunteers; the mean was found to be 11.7 microliters/ml +/- 0.9 microliter. This compares closely with values cited in the literature. The within-subject variation for repeat samples taken several weeks apart was significantly (P < 0.003) less than the variation between different subjects, suggesting that there may be true differences in N2 content between different individuals. These data must be considered preliminary, a larger study is needed to investigate population differences in detail. The advantages of the new method are discussed.

Problems in the modelling of inert gas kinetics.

The models used to describe the kinetics of inert gases during underwater diving are inadequate. Medical practitioners and scientists interested in such diving have attempted to quantitatively describe the behaviour of nitrogen in compressed air diving since 1908, with little success. The problems encountered during this diving research are relevant to anaesthesia theory and practice.

Intravascular bubble composition in guinea pigs: a possible explanation for differences in decompression risk among different gases.

Differences in risk of decompression sickness (DCS) that have been observed among inert gases may reflect differences in gas solubility or diffusivity or both. A higher risk gas might generate a larger volume of evolved gas during decompression, thereby increasing the probability of DCS. If this hypothesis is correct, the composition of bubbles that develop during decompression should reflect such gas differences. Unanesthetized guinea pigs were compressed to depths ranging from 250 to 350 fsw with air, He-O2 (21% O2) or one of a number of N2-He-O2 or N2-Ar-O2 mixtures (21% O2). Animals were held at depth from 15 to 60 min, then decompressed slowly (60 fsw/min) or rapidly (less than 15 s) to 5 fsw. If severe DCS developed, as judged by changes in physiologic variables, death usually occurred quickly. Gas/blood samples were then immediately withdrawn from the right atrium or the inferior vena cava, and the gas phase analyzed for He, N2, Ar, O2, and CO2 via gas chromatography. Bubbles from all dives contained 5-9% CO2, 1-4% O2, with the balance inert gas. Bubbles after N2-He-O2 dives contained substantially more N2 than He (up to 1.9 times more) compared to the dive mixture; bubbles after N2-Ar-O2 dives contained more Ar than N2 (up to 1.8 times more). For N2-He-O2 dives, the actual inert gas makeup of bubbles was dependent on the time-at-depth and the decompression profile. Results may reflect differences among He, N2, and Ar in tissue solubility/diffusivity and gas exchange rates, and support the rank order of increasing DCS risk (He less than N2 less than Ar) and rate of gas exchange (N2 less than He) observed previously during rat dives.

Solubility of inert gases in PFC blood substitute, blood plasma, and mixtures.

Measurements are reported of the solubility of nonreactive gases, e.g., hydrogen and xenon, in the following liquids: (a) Oxypherol (FC-43 emulsion) blood substitute, (b) blood plasma, (c) mixtures of Oxypherol and blood plasma, and (d) perfluorotributylamine. Typical results for Ostwald solubility at 25 degrees C for Xe gas in various liquids are 0.118 in H2O, 0.12 in blood plasma, and 1.51 in N(C4F9)3. Observed solubilities for the mixtures can be calculated from the relation: L(mixture) = L(emulsion)xv(emulsion) + L (plasma)xv(plasma), in which the v's are the volume fractions in the mixture. This linear relation implies that the gas dissolves independently in each liquid in the mixture. The effect of the emulsifier (Pluronic F-68, 2.6%), on gas solubility in the mixture, is small. Results for the temperature dependence of Ostwald solubility, L(T), in the range 10-37 degrees C are reported.

How countercurrent blood flow and uneven perfusion affect the motion of inert gas.

Monte Carlo simulations of the passage of inert gas through muscle tissue reveal that countercurrent gas exchange is more important than heterogeneity of flow in determination of the shape of inert gas washout curves. Semilog plots of inert gas washout are usually curved rather than straight. Two explanations often offered are that countercurrent flow may distort the shape and that uneven perfusion of the tissue gives rise to nonuniform washout. The curvature of the semilog plot may be summarized by the relative dispersion (RD), which is the ratio of the standard deviation of transit times to the mean transit time. For straight semilog plots, RD is 1. Semilog plots of data showing xenon washout from dog tissues are curved and have and RD of approximately 2. We have simulated the transit of gas particles through a vascular bed composed of repeating units of 100 mg of tissue perfused by three small vessels 80 microns in diameter and several levels of branching that direct flow through 190,000 capillaries. Geometric distribution of flow is important. Similar degrees of flow heterogeneity affect the curvature of the washout curve more if regions of heterogeneous flow are widely spaced than if they are close together. Diffusion blunts the effects of heterogeneous flow by mixing particles in high-flow regions with particles in low-flow regions. Because of this mixing, alternating regions of high flow and low flow spaced at intervals of less than 0.5 cm are unlikely explanations for the curved semilog plots.(ABSTRACT TRUNCATED AT 250 WORDS)

Effects of SO2 and pH on blood-gas partition coefficients of inert gases.

Potential effects of SO2 and of pH on blood-gas partition coefficients, lambda, for inert gases, including SF6, ethane, cyclopropane, halothane, diethyl ether, acetone and N2, were systematically investigated using human blood. Measurements on lambda were performed at 37 degrees C in conditions of varied SO2 and pH using gas chromatography. Incorporating the experimental data on lambda, multiple inert gas elimination was applied to 18 patients with varied chronic lung diseases, in order to estimate the effects of SO2 and of pH on both inert gas exchange and resultant recovery of VA/Q distribution in the lung. For this purpose, the data obtained by the procedure of multiple inert gas elimination were analyzed with the classical approach but allowance was made for lambda of the indicator gas to vary according to exchange of O2 and of CO2 in the pulmonary capillary. Among the gases studied, ethane, cyclopropane, halothane and diethyl ether showed significantly smaller lambda values in the oxygenated blood than in deoxygenated blood, whereas SF6, acetone and N2 were little dependent on SO2. An increase in lambda was found for ethane and a decrease for halothane with increasing pH in the blood. The other gases were not significantly influenced by pH. In spite of these experimental findings, regional difference of either SO2 or pH in the lung did not exert important influence on the inert gas exchange or on the predicted VA/Q distribution. In conclusion, blood-gas partition coefficients of some inert gases are consistently altered by SO2 and pH, but their possible effects on inert gas exchange seem to be negligible.

Relationships among ventilation-perfusion distribution, multiple inert gas methodology and metabolic blood-gas tensions.

The retention equations upon which the Multiple Inert Gas Method is based are derived from basic principles using elementary algebra. It is shown that widely disparate distributions produce indistinguishable sets of retentions. The limits of resolution of perfused compartments in the VA/Q distribution obtainable by the use of the multiple inert gas method are explored mathematically, and determined to be at most shunt and two alveolar compartments ("tripartite" distribution). Every continuous distribution studied produced retentions indistinguishable from those of its unique "matching" tripartite distribution. When a distribution is minimally specified, it is unique. Any additional specification (increased resolution--more compartments) of the distribution results in the existence of an infinitude of possible distributions characterized by indistinguishable sets of retention values. No further increase in resolution results from the use of more tracers. When sets of retention values were extracted from published multiple inert gas method continuous distributions, and compared with the published "measured" retention sets, substantial differences were found. This illustrates the potential errors incurred in the practical, in vivo application of the multiple inert gas method. In preliminary studies, the tripartite distribution could be determined with at least comparable accuracy by blood-gas (oxygen, carbon dioxide) measurements.