Validation and Clinical Application of a First Order Step Response Equation for Nitrogen Clearance During FRC Measurement

Abstract

ObjectiveTo derive a difference equation based on mass conservation and on alveolar tidal volumes for the calculation of Functional Residual Capacity. Derive an equation for the FRC from the difference equation. Furthermore, to derive and validate a step response equation as a solution of the difference equation within the framework of digital signal processing where the FRC is known a priori.MethodsA difference equation for the calculation of Functional Residual Capacity is derived and solved as step response of a first order system. The step response equation calculates endtidal fractions of nitrogen during multiple breath nitrogen clearance. The step response equation contains the eigenvalue defined as the ratio of FRC to the sum of FRC and alveolar tidal ventilation. Agreement of calculated nitrogen fractions with measured fractions is demonstrated with data from a metabolic lung model, measurements from patients in positive pressure ventilation and volunteers breathing spontaneously. Examples of eigenvalue are given and compared between diseased and healthy lungs and between ventilatory settings.ResultsComparison of calculated and measured fractions of endtidal nitrogen demonstrates a high degree of agreement in terms of regression and bias and limits of agreement (precision) in Bland & Altman analysis. Examples illustrate the use of the eigenvalue as a possible discriminator between disease states.ConclusionThe first order step response equation reliably calculates endtidal fractions of nitrogen during washout based on a Functional Residual Capacity. The eigenvalue may be a clinically valuable index alone or in conjunction with other indices in the analysis of respiratory states and may aid in the setting of the ventilator.

Innovations in Mechanical Ventilation

“…The current EELV measurement technique (F IO 2 stepchange then nitrogen washout) was pioneered by Stenqvist and colleagues, 41,42 and several early studies with lung models, animals, and patients found the method accurate and reproducible. [42][43][44] However, the evidence regarding the value of EELV in critically ill patients remains sparse. Bikker et al recently compared EELV in mechanically ventilated patients to reference equations for FRC.…”

Validation and clinical feasibility of nitrogen washin/washout functional residual capacity measurements in children

“…The derivation of the modified washin/washout method for adult patients was detailed in Olegard et al 13 and Choncholas et al 14 Carbon dioxide production () was obtained from the gas analyzer of the monitor (COMVX, S/5, GE Health Care, Helsinki, Finland). The inspiratory minute ventilation () was calculated by Haldane transformation from the measured expiratory minute ventilation ().…”

“…These requirements preclude the use of this approach in pediatric settings. We introduced a multiple breath nitrogen washin/washout (MBNW) method, 13,14 modified from the original method by Darling 15 …”

Measurements of functional residual capacity during intensive care treatment: the technical aspects and its possible clinical applications

“…Despite numerous studies dealing with the methodological and technical aspects of FRC measurements in ventilated adult patients, 10,36,56,58,66–68,70–75,83–85 only a few studies have used FRC measurements during the treatment of patients.…”