Uneven distribution of ventilation—perfusion ratios in lungs estimated by a modified Newton method

Abstract

The uneven distribution of ventilation—perfusion ratios ($\dot V_A /\dot Q$) in diseased lungs is the major cause of arterial hypoxemia. Farhi and Yokoyama (1967) and Yokoyama and Farhi (1967) were the first who used physiologically inert gases as indicator gases to assess the uneven distribution of$\dot V_A /\dot Q$ Wagner and his coworkers in San Diego (1977b) extended the method and elaborated the multiple inert gas elimination technique in which blood flows in 50 compartments with different$\dot V_A /\dot Q$ were estimated based on data for 6 indicator gases. They analyzed the indicator gas data through an enforced smoothing technique with the ridge regression. To get smooth distributions, they introduced a weighting function for$\dot V_A /\dot Q$ compartments and an additional treatment for the non-negativity of the blood flow. The weighting function was empirically obtained. We analyzed the data without putting any weights on$\dot V_A /\dot Q$ compartments nor any additional treatment for non-negativity of blood flow. The analytical method in the present study was a modified Newton method, which is one of the enforced smoothing method. Our method was capable of recovering all distribution patterns that were found through the method reported by Wagner et al. (1977b).