Corrected formula for rectangular area ratio (RAR), a parameter used to quantify airflow limitation on expiratory flow-volume curves

Published:October 29, 2022DOI:


      Quantification of expiratory flow limitation during exercise has been demonstrated using computerized breath-by-breath analysis of the flow-volume curve. One of the parameters used in quantitation of airflow limitation is the rectangular area ratio (RAR) described in this journal by Ma et al. (2010). Upon closer review of the formula utilized in this paper, it is noted that the formula does not accurately capture the RAR, and the formula may underestimate the true RAR due to errors in various terms contained within the numerator and the denominator. A correct version of the formula is presented in this report. The correct formula does not require re-measurement of new variables but uses the existing variables in the correct mathematical and geometric context. This study has implications for validity of the data contained in the original paper as well as several other studies utilizing the same formula that have been published since the original publication. All future research using the RAR should use the correct formula, as contained in this paper.


      To read this article in full you will need to make a payment

      Purchase one-time access:

      Academic & Personal: 24 hour online accessCorporate R&D Professionals: 24 hour online access
      One-time access price info
      • For academic or personal research use, select 'Academic and Personal'
      • For corporate R&D use, select 'Corporate R&D Professionals'


      Subscribe to Respiratory Medicine
      Already a print subscriber? Claim online access
      Already an online subscriber? Sign in
      Institutional Access: Sign in to ScienceDirect


        • Koulouris N.G.
        • Kaltsakas G.
        • Palamidas A.F.
        • Gennimata S.A.
        Methods for assessing expiratory flow limitation during tidal breathing in COPD patients.
        Pulm Med. 2012; 2012 (Epub 2012 Sep 2. PMID: 23008769; PMCID: PMC3447366)234145
        • Ma S.
        • Hecht A.
        • Varga J.
        • Rambod M.
        • Morford S.
        • Goto S.
        • Casaburi R.
        • Porszasz J.
        Breath-by-breath quantification of progressive airflow limitation during exercise in COPD: a new method.
        Respir. Med. 2010 Mar; 104: 389-396
        • Porszasz J.
        • Carraro N.
        • Cao R.
        • Gore A.
        • Ma S.
        • Jiang T.
        • Maltais F.
        • Ferguson G.T.
        • O'Donnell D.E.
        • Shaikh A.
        • Rossiter H.B.
        • Casaburi R.
        Effect of tiotropium on spontaneous expiratory flow-volume curves during exercise in GOLD 1-2 COPD.
        Respir. Physiol. Neurobiol. 2018 May; 251 (Epub 2018 Feb 10. PMID: 29438808.J.): 8-15
        • Varga J.
        • Casaburi R.
        • Ma S.
        • Hecht A.
        • Hsia D.
        • Somfay A.
        • Porszasz J.
        Relation of concavity in the expiratory flow-volume loop to dynamic hyperinflation during exercise in COPD.
        Respir. Physiol. Neurobiol. 2016 Dec; 234 (Epub 2016 Aug 26. PMID: 27575552): 79-84
        • Erram J.
        • Bari M.
        • Domingo A.
        • Cannon D.T.
        Pulmonary function with expiratory resistive loading in healthy volunteers.
        PLoS One. 2021 Jun 11; 16 (PMID: 34115812; PMCID: PMC8195373)e0252916