title: Validation and clinical application of a first order step response equation for nitrogen clearance during FRC measurement.
abstract: OBJECTIVE
  To 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.
  
  
  METHODS
  A 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.
  
  
  RESULTS
  Comparison 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.
  
  
  CONCLUSIONS
  The 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.
authors.affiliation: Department of Research & Development, GE Healthcare, Madison, WI, USA.
authors.forename: Gary
authors.initials: G
authors.lastname: Choncholas
authors.forename: Soren
authors.initials: S
authors.lastname: Sondergaard
authors.forename: Erkki
authors.initials: E
authors.lastname: Heinonen
mesh_terms: D000328:Adult; D000368:Aged; D001944:Breath Tests; D005260:Female; D005652:Functional Residual Capacity / Q000502:physiology*; D006801:Humans; D008297:Male; D008875:Middle Aged; D008954:Models, Biological; D008991:Monitoring, Physiologic / Q000379:methods; D009584:Nitrogen / Q000378:metabolism*; D011650:Pulmonary Alveoli / Q000378:metabolism; D012044:Regression Analysis; D012121:Respiration, Artificial; D012815:Signal Processing, Computer-Assisted; D013990:Tidal Volume / Q000502:physiology
chemical_list: D009584:Nitrogen