A method of determining some non-standard Laplace transformations.

The following paper describes a method whereby awkward mathematical expressions may be manipulated into their respective Laplace transforms. The paper describes several examples and the methods of dealing with such expressions.

A reappraisal of boundary conditions assumed in pulmonary gas transport models.

Solutions of the classic pulmonary gas transport equation are presented in which a true 'no-flux' boundary condition is specified throughout the respiratory cycle. For the particular models studied it is demonstrated that diffusive mixing is incomplete at end expiration, and that such stratified inhomogeneities give rise to a realistic alveolar plateau for a simulated N2 washout test. The reasons for the disparity of the present findings with those obtained by contemporary workers are explained by critically examining the boundary conditions conventionally assumed at the alveolar wall.

Theoretical analysis of independent VA and Q inequalities upon pulmonary gas exchange.

A 10-compartment model is used to study the effects independent regional inequalities in ventilation (VA) and blood flow (Q) upon overall gas exchange in the lung. For the particular distribution considered, it is demonstrated that unequal ventilation always gives rise to a greater degree of hypoxaemia than unequal blood flow, and that these differences become more marked when minute volume is high. In contrast, hypercarbia is more pronounced in situations where blood flow is unequal; however, the differences diminish with increases in minute volume. Increases in cardiac output are found to have a lesser effect upon the gas exchange process. The reasons for the findings are explained by reference to the gas dissociation curves, the spread of VA/Q ratios, and the weighting influence of regional blood flow. The apparent disparity of the present results with those obtained by assuming a log normal distribution of the respiratory parameters (VA and Q) are reconciled.