For many years physiologists have sought to estimate the distribution of ventilation/perfusion ratios ( $$\dot V_A /\dot Q$$ ) in the lung. While many different procedures have been described, most share two features that limit their usefulness. First, while the lung consists of some 105 separate gas exchange units, $$\dot V_A /\dot Q$$ mismatch is usually analyzed in terms of just two or three hypothetical units sufficient to explain the measured data. Second, no attempts are made to explore alternate $$\dot V_A /\dot Q$$ distributions which could account for the measured data, nor the degree to which these alternate cases differ from each other. The second problem arises from (a) the fact that the lung is numerically complex, while only few data are obtained, and (b) experimental errors. We summarize here our approach to these problems. Methods involving both linear and quadratic programming algorithms are applied to obtain the most reliable and complete information from a set of data. While we focus on the intravenous infusion of several foreign gases as the tool for obtaining data pertinent to $$\dot V_A /\dot Q$$ maldistribution, the proposed scheme is equally applicable to other linear systems in the lung, such as the multibreath N2 washout and the forced expiratory spirogram.