Parametric estimation of ventilation-perfusion ratio distributions.

We present a model and rigorous statistical approach for recovery of ventilation-perfusion ratio (V/Q) distribution parameters from multiple inert gas elimination data. We model the lung as a parallel combination of shunt, dead space, and one to three log-normal distributions of gas exchange units. This model provides a natural set of parameters for characterizing V/Q distributions. The log-normal terms are adjustable to represent smooth or sharp peaks in the distribution. Since the peak locations and widths are explicit in the model, very few parameters are needed. We select and estimate the significant parameters of the model by use of standard statistical tests and constrained least squares. This method provides two major advances in V/Q distribution estimation: 1) it allows flexible pooling and statistical comparisons of multiple experiments, and 2) it simultaneously gives both point estimates and 95% probability intervals for the V/Q distribution parameters. We present results of our procedure for data from humans in health, stress, and pulmonary disease. A program package, VQPAR, in FORTRAN is available for implementing the procedure.