An efficient optimization technique for recovering ventilation-perfusion distributions from inert gas data. Effects of random experimental error.

A variable metric optimization method of numerical analysis has been used to recover known distributions of intrapulmonary ventilation-perfusion ratios from inert gas data. Hypothetical lungs were simulated and corresponding inert gas retentions calculated. By using error-free retentions for seven gases and a 50-compartment model, it was possible to recover distributions containing up to three modes accurately and with greater efficiency than with other numerical methods. When random error of a magnitude consistent with present analytical techniques was introduced into retention data, the recovered distributions differed qualitatively from the original ones. This resulted from the ill-conditioned nature of the mathematical problem, which makes a recovered distribution extremely sensitive to small errors in retention. Thus, present levels of measurement error represent an important limitation in current techniques for deriving distributions from inert gas measurements.