Optimal Inputs for the Study of Gas Exchange in the Lung

This paper discusses the pulmonary washout tests and some of the considerations involved in applying optimal experimental design theory to these tests. Optimal inputs are described as binary sequences. For a given set of parameters the optimal input is determined by minimizing the determinant of the covariance matrix (J). Optimal inputs for a given set of parameters are determined using a modified random search procedure. The optimal input to deliver in the case where the parameters are unknown is determined by mimimizing a linear combination of the J´s of several parameter sets which to span the range of interest. Individual J´s are weighted by apriori probabilities and by associated costs. For the conditions studied in this work, the optimal inputs involved delivering tracer on breath 7 of a 10 breath test, 12,14,15 and 20 for a 20 breath test, 20,22,23,24 and 30 on a 30 breath test and breaths 23,25,26,32,34,35,40 of a 40 breath test. Implementation of these optimal inputs is also discussed.