The arterial, mixed venous, and mixed expired concentrations of six infused inert gases, measured by gas chromatography, are used to calculate the ratio of arterial pressure (Pa) to mixed venous pressure (Pv) (retention) and the ratio of alveolar pressure ( PA) or mixed expired pressure (PE) to mixed venous pressure (excretion).

Retention and excretion are then used to compute multicompartment V^IQ distributions. Six inert gases (sulfur hexafluoride (partition coefficient, 0.005), ethane, cyclopropane, enfluorane or halothane, ether, and acetone (partition coefficient, 300), listed in ascending order of solubility) are used to characterize the distribution ■

of the VktQ ratios in the whole lung (Wagner et al 1974).

The principle modulating inert gas elimination within the lung is based on the simple concept that the uptake (retention or Pa/(Pv) and the elimination (excretion or PE/(Pv) of an inert gas in any ideal homogeneous area of the lung under steady state conditions obey the following equation:

where l defines the solubility (partition coefficient). According to this equation, both the retention and the excretion of an inert gas depend only on the solubility of the

six inert gases and the VpJQ ratio. For each inert gas, the retentions are calculated as the ratio of arterial partial pressure to mixed venous partial pressure and the excretions as the ratio of mixed expired partial pressure to mixed venous partial pressure. By using a multicompartimental approach with enforced smoothing, the

retentions of the six inert gases allow the estimation of a continuous distribution of the pulmonary blood flow against VktQ ratio on a logarithmic scale ( Evans and

Wagner 1977). Similarly, the excretions of the six inert gases provide an estimation of the distribution of the alveolar ventilation against VpJQ ratio. Because the term ■

l/(l + VktQ) is common to both retention and excretion, the blood flow and the ventilation distributions are mathematically interdependent, reflecting the same ■ ■

distribution of the VkIQ ratios seen from opposite sides of the blood-gas barrier. The use of enforced smoothing requires compartments with similar VktQ ratio to

have similar perfusion. In summary, the key variables required for determining VpJQ distributions for real lungs, in either normal subjects or patients with lung disease, are Pv, Pa, and PE for the six inert gases, their partition coefficients, and minute ventilation. If mixed venous and arterial blood samples are available, cardiac output is computed using steady state mass balance equations. The lung is assumed to be composed of a number of homogeneous compartments arranged in parallel, each with constant and continuous ventilation and perfusion. The mathematical model assumes that the ventilation and perfusion distributions have regular contours and do not present sudden irregularities.

Figure 1 shows a typical distribution of VkIQ ratio in a young healthy individual at rest in a semirecumbent position and breathing room air. The amounts

(distributions) of alveolar ventilation and pulmonary perfusion ( y axis) are plotted against 50 V^IQ ratios, ranging from zero to infinity, on a logarithmic scale (x axis).

Each data point represents a specific amount of alveolar ventilation or pulmonary blood flow; the lines are drawn to facilitate visual comprehension. Overall blood flow

or total alveolar ventilation corresponds to the sum of all data points of their respective distributions. The use of a logarithmic rather than a linear axis for V^IQ ratios

is based on established practice in the field of pulmonary gas exchange. The two distributions are characteristically symmetric, positioned around a mean VktQ ratio

of 1.0, and narrow. In healthy individuals, no blood flow is diverted to the left to the zone of low VpJQ ratios (poorly ventilated lung units) nor is ventilation distributed

to the right to the zone of high V^IQ ratios (incompletely perfused, but still finite, lung units). Intrapulmonary shunt is defined as areas with zero VpJQ ratio (less than

0.005), as postpulmonary shunt (bronchial and Thebesian circulations) is insensitive to inert gases. Consequently, intrapulmonary shunt measured by the multiple inert gas elimination technique is lower than the conventional venous admixture ratio (1-2 per cent of cardiac output) when breathing room air as well as the postpulmonary shunt. When breathing 100 per cent O 2 the difference measured by multiple inert gas elimination technique and 100 per cent O 2 is greatly reduced.

The normal value of inert physiological dead-space (infinite VpJQ ratio (> 100); approximately 30 per cent of overall alveolar ventilation) is also slightly less than that computed using the traditional Bohr formula. While the latter variable includes the dead-space-like effects of all lung units whose alveolar PCO2 values are less than

the arterial PC02, the inert gas approach represents only the dead-space-like effects of those alveoli whose VpJQ ratios are greater than 100.

Fig. 1 Representative distributions of VkIQ ratios in a healthy individual breathing spontaneously and in patients needing mechanical ventilation, one with acute

respiratory distress syndrome (ARDS) and one with chronic obstructive pulmonary disease (COPD). Note the different amounts of intrapulmonary shunt and VktQ inequalities in the latter two conditions. Although the main body of each distribution is only slightly broadened in ARDS, shunt is conspicuously increased. In COPD, both distributions are predominantly bimodal but shunt is small. See text for further details.

The first moment of each distribution, namely the mean V~AIQ ratio of each distribution, and the second moment (or dispersion) log SD where SD is the standard

deviation, are commonly used to calculate the degree of V^IQ mismatch. The second moments (square roots) of the pulmonary blood flow and the alveolar ventilation

distributions (log SD Q and log SDV respectively) reflect the variance (standard deviation) of VktQ ratios about the mean. In an ideal homogenous lung, both

dispersions should be zero; in practice, in a normal healthy individual the upper 95 per cent confidence limits are 0.60 and 0.65 ( CgrdusefaA 1997). The degree of V

u a/Q inequality can also be expressed as the total percentage of ventilation and perfusion in defined regions of the VpJQ spectrum. Other approaches, which are equally valid, have used related parameters such as the root mean square of the difference between retention and excretion over the six inert gases, thus giving an

additional quantitative assessment of VpJQ mismatch (Gale et al 1985). Finally, the VpJQ mismatch can be assessed qualitatively by describing the morphological pattern of each distribution, which can be narrowly or broadly unimodal, or clearly bimodal.

The multiple inert gas elimination technique is such a robust tool that it can also be used to assess the potential presence of O 2 diffusion limitation because, in

practice, equilibration of inert gases is not diffusion limited. Accordingly, the technique can be used to compute the Pa02 predicted from the degree of both VpJQ mismatch and shunting and compare it with the measured PaO2. If the measured PaO2 is not significantly different from the estimated value, this indicates that other potential mechanisms of hypoxemia, such as O2 diffusion limitation, increased intrapulmonary parenchymal O2 consumption, or increased postpulmonary shunt, are absent.

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