A computer model was developed to study the relationship between ventilation-to-perfusion (V/Q) mismatch and the development of inert gas arterial-to-alveolar partial pressure differences (a-A differences). Increasing inhomogeneity of V/Q ratio is revealed directly as an increase in the a-A difference of each gas. The quantitative relationships between the Q vs. V/Q distribution and the fractional a-A difference solubility plot (a-A difference plot) were studied and described. These studies demonstrated that for log normally distributed V/Q ratios, the area under the a-A difference plot is linearly related to the log variance of the V/Q distribution and can be estimated directly from the values obtained from six gases. The maximum a-A difference occurs for a gas whose solubility is numerically equal to the mean V/Q. The effects of departure from log normality and multimodality are discussed. We conclude from these studies that quantitative information regarding the degree of inhomogeneity of V/Q for log normal distribution is available from direct calculations of inert gas retention and excretion data. Qualitative information is also available indicating the departure from log normality and the region toward which the distribution is skewed.
