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.

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.

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.

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.

Reproducibility of the multiple inert gas elimination technique.

Although measurement errors in the multiple inert gas elimination technique have a coefficient of variation of approximately 3%, small biological fluctuations in ventilation, blood flow, or other variables must contribute additional variance to this method of assessing ventilation-perfusion (VA/Q) mismatch. To determine overall variance of computed indices of VA/Q mismatch, an analysis of variance was carried out using a total of 400 duplicate pairs of inert gas samples obtained from canine (N = 118) and human (N = 282) studies in the past 2 years. In both sets VA/Q mismatch ranged from minimal (2nd moment of ventilation and blood flow distributions, log SDV and log SDQ, respectively approximately equal to 0.3 each) to severe (log SDV and log SDQ approximately equal to 2.0). Differences between duplicate log SD values were computed and found to be a constant fraction of the mean log SD of each duplicate pair, averaging 13% for both canine and human ventilation and blood flow data. The resultant coefficient of variation for a single measurement of log SD about its mean averaged 8.6% for all data combined. This analysis demonstrates excellent reproducibility of these dispersion indices over a wide range of conditions, and if the mean of duplicate values is used, thus reducing variability by square root 2 to 6.1%, log SD can be estimated with an approximately 95% confidence limit of +/- 12%.

Linear programming analysis of VA/Q distributions: limits on central moments.

Linear programming examines the boundaries of infinite sets. We used this method with the multiple-inert gas-elimination technique to examine the central moments and arterial blood gases of the infinite family of ventilation perfusion (VA/Q) distributions that are compatible with a measured inert gas-retention set. A linear program was applied with Monte-Carlo error simulation to theoretical retention data, and 95% confidence intervals were constructed for the first three moments (mean, dispersion, and skew) and the arterial PO2 and PCO2 of all compatible blood flow distributions. Six typical cases were studied. Results demonstrate narrow confidence intervals for both the lower moments and predicted arterial blood gases of all test cases, which widen as moment number or error increase. We conclude that the blood gas composition and basic structure of all compatible VA/Q distributions are tightly constrained and that even subtle changes in this structure, as may occur experimentally, can be identified.

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)

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.

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.

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.

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.

[Mathematical model of the dynamics of transport of inert gases in the microcirculatory system]. / Matematicheskoe modelirovanie dinamiki transporta inertnykh gazov v sisteme mikrotsirkuliatsii.

A mathematical model imitating transport of inert gases in the system of microcirculation under increased pressures was constructed. It has been shown that saturation of microareas nucleus of the brain cortex of average dimensions proceeds in about 90 sec. Effect of the blood flow velocity, gases tension in arterial blood and density of the capillary net on the dynamics of mass transfer of gases in a tissue was investigated.

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.

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.

Inert gas transport in the microcirculation: risk of isobaric supersaturation.

This paper is concerned with the theretical background and implications of isobaric supersaturation and bubble formation in the microcirculation following an abrupt shift from one inspired inert gas to another. The use of more than one inert gas, simultaneously or sequentially, has become common in diving and presents risks as well as potential benefits. A review of microcirculatory model useds, theoretical approaches to decompression, and order of magnitude calculations indicates that present empiricisms are inadequate for predicting such supersaturation phenomena. This is true whether based on the familiar assumption of perfusion-limited behavior or its diffusion-limited counterpart. The "chromatographic" model used here, which considers both perfusion and axial diffusion in tissue cylinders, shows that these combined effects can produce unexpectedly high local supersaturation. The implications include new possibilities for the experimental evaluation of gas transport models as well as practical risks of inert gas shifts in diving and certain diagnostic procedures.

Inert tracer gas washout from mixed venous blood: the sloping alveolar plateau.

The aim of this model study was to investigate the mechanisms underlying the sloping alveolar plateau for inert tracer gases supplied to the lung by mixed venous blood. Transpulmonary gas exchange was simulated in an asymmetric lung model for conditions at rest and in exercise. For highly soluble gases, the calculations show that the varying amount of tracer gas dissolved in superficial parenchymal tissue and capillary blood causes a sustained stratification in the acinus during expiration and that this is mainly responsible for the slope. For this type of tracer gas, the slope is almost independent of variations in the molecular diffusion coefficient (D) of the gases. In contrast, for poorly soluble gases, the contributions of local parallel inhomogeneities of gas concentrations in the acinus and the continued gas exchange across the alveolo-capillary membrane are mainly responsible for the slope. The first factor, which depends on the asymmetric branching pattern of intra-acinar airways, increases with decreasing D values. The contribution of continued gas exchange to the slope is most pronounced under exercise conditions. This contribution is almost independent of the blood/gas partition coefficient, lambda, for lambda values less than 4.0.

Solubility of inert gases in biological fluids and tissues: a review.

Data have been tabulated from more than 150 references on the solubility of inert gases in fluids and tissues of biological interest. Thirty-two gases have been studied in blood with measured solubility ranging from 0.005 to 16 ml of gas at 37 degrees C per ml of blood per ATA (Ostwald coefficient). For most gases, solubility in other tissues such as muscle or brain is between 60% and 300% of blood solubility. Measured solubilities in biological tissues do not correspond well to solubility in water and oil. Most gases decrease in solubility by 1%-6% for each degree C rise in temperature. The effect of pressure on solubility has not been well studied, and only crude estimates can be obtained by using methods of chemical thermodynamics.

[Variations of the sum of the arterial partial pressure of inert gases during changes in the composition of inhaled gas without a variation of the ambient pressure, in a hyperbaric atmosphere]. / Variations de la somme des pressions partielles artérielles des gaz inertes au cours de changements de composition des gaz inhalés sans variation de pression ambiante en atmosphère hyperbare.

In hyperbaric environments, when inhaled inert gas composition is abruptly modified, the sum of the arterial inert gases partial pressures is different to the sum of these same gases in the inhaled mixture. While switching from a helium-oxygen to a nitrogen-oxygen mixture of same P1O2 and total pressure, the sum of the arterial inert gas partial pressure was transiently less than the one in the inspired gases: there was an arterial under-saturation: PaHe + PaN2 = 0.68 (P1He + P1N2). During the opposite switch (from nitrogen to helium), a reversed time course, namely a transient over saturation, was observed: PaHe + PaN2 = 1.31 (P1He + P1N2). Amongst the different possible explanatory hypotheses, the most probable is that inert gas partial pressure equilibrium through the alveolo-capillary membrane is not achieved when the blood leaves the pulmonary capillary.