Abstract
This paper presents a new technique for recovering continuous distributions of ventilation as a function of ventilation/volume ratio from observed nitrogen washout curves. The expired nitrogen concentration on each breath is modelled as arising from 50 compartments each having a specific ventilation/volume ratio, and described by a set of linear equations, where the number of equations is equal to the number of breaths, and unknown parameters are ventilations of each compartment.
A parameter estimation problem is formulated based on the method of least squares. The sum of the following two terms is minimized:
1) the residual sum of squares: and
2) the difference sum of squares.
The latter term is added in order to smooth differences of neighboring ventilations with respect to ventilation/volume ratio. The optimum weight for the smoothing term can be theoretically defined according to Akaike's ABIC (A Bayesian Information Criterion).
A numerical method for calculation of the optimum weight is presented, and known distributions with gaussian observation noises are more exactly reproduced than conventional empirical methods. Maximum permissible noise levels of nitrogen washout in order to reproduce bimodal or trimodal distributions are estimated by computer simulation.
