A Mathematical Evaluation of the Multiple Breath Nitrogen Washout (MBNW) Technique and the Multiple Inert Gas Elimination Technique (MIGET)

We consider two and 50 compartment lung models for use with two techniques used to investigate the efficiency of the lungs: the Multiple Breath Nitrogen Washout (MBNW) technique used for investigating the ventilation–volume distribution; and the Multiple Inert Gas Elimination Technique (MIGET) used for investigating the ventilation–perfusion distribution. In each of these techniques pulmonary respiratory gas exchange is described by conservation of mass equations which may be written in identical form, and in each the underlying distributions of ventilation to volume and ventilation to perfusion are assumed to be continuous functions (usually assumed to be a linear sum of log-normal distributions). The mathematical models used to describe the lung have predominantly used a collection of discrete compartments to approximate these continuous distributions. The most commonly used models have used one, two or 50 compartments. In this paper, we begin by showing that in the limit as the width of the peaks of the distribution tend to zero, the continuous distributions may be replaced by a single discrete compartment placed at each peak of the distribution. We investigate the various methods used previously for parameter recovery, and show that one commonly used method for the MBNW is not suitable and suggest a modification to this recovery technique. Using simulated error-free data, we show that both the two compartment model and the 50 compartment model contain information about the ventilation–volume (or ventilation–perfusion) distribution, and investigate the extent to which this information can be used to recover the parameters which define these distributions. We go on to use Monte-Carlo methods to investigate the stability of the recovery process.