Applications of Pick-Nevanlinna interpolation theory to retention- solubility studies in the lungs
Under steady state conditions in a subject receiving an inert test gas in dissolved form by constant intravenous drip the fraction of the gas retained in the blood after a pass through the lungs is called the retention of the gas, and the dependence of this retention on test gas solubility is called the retention-solubility relation. A widely used model for this relation is the parallel ventilation and perfusion model, in which a set number of compartments are assumed to be ventilated and perfused in parallel, with test gas at equilibrium in each compartment and with fluctuations due to cyclical breathing and blood flow averaged out. It is known that such a parallel system may be regarded as an equivalent ''diagonalized'' version of more general compartmental models. In this paper the classical interpolation theory for analytic functions of Pick and Nevanlinna is shown to yield computational techniques of considerable utility in analyzing retention-solubility studies in terms of the above parallel model. At the beginning, a derivation of the retention-solubility relation for parallel lung models is given and this leads to the definition of ''retention functions''. Further, the inverse problem is outlined and the main results of this paper are indicated: computational procedures for determining data feasibility and some properties of lung models compatible with given data. The remaining sections are devoted to the development of basic tools, the classification of data points and proofs. Some new mathematical results, of interest, concerning the class of functions are obtained.
parallel ventilation and perfusion model
scientific article; zbMATH DE number 3843546