title: An improved equation for correcting slope-intercept measurements of glomerular filtration rate for the single exponential approximation.
abstract: OBJECTIVE
  Glomerular filtration rate (GFR) is commonly assessed by plasma sampling using the slope-intercept technique. This method assumes a single exponential approximation to the plasma curve. To obtain an accurate estimate of GFR it is necessary to correct the slope-intercept value for the approximation. This is commonly done using the Brochner-Mortensen equation. This has been validated for normal and abnormally low GFRs, but there has been some suggestion that it may underestimate supra-normal GFR. This paper investigates this suggestion and aims to produce a new equation based on compartmental analysis, which should extrapolate the correction to higher values of GFR.
  
  
  METHODS
  Compartmental analysis was used to produce the complete expression of the relationship between true GFR and slope-intercept GFR. A simplified analytical equation was then derived. The performance of the new equation was compared to the Brochner-Mortensen and Chantler equations using the true GFR as reference.
  
  
  RESULTS
  The new analytical equation had minimal systematic error compared to true GFR up to 250 ml x min(-1) per 1.73 m(2). The Brochner-Mortensen equation was shown to underestimate high values of GFR. The error increased with GFR with a 10% underestimation at 180 ml x min(-1) per 1.73 m(2). The Chantler equation gave a systematic overestimate of GFR. The error increased with GFR with a 30% overestimate at 180 ml x min(-1) per 1.73 m(2).
  
  
  CONCLUSIONS
  The new equation described in this paper gave considerably improved correction for the single exponential approximation at high GFR compared to previously described equations.
authors.affiliation: Department of Medical Physics and Bioengineering, Southampton University Hospitals NHS Trust, UK. john.fleming@suht.swest.nhs.uk
authors.forename: John S
authors.initials: JS
authors.lastname: Fleming
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D005919:Glomerular Filtration Rate / Q000502:physiology*; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods; D007668:Kidney / Q000000981:diagnostic imaging* / Q000378:metabolism*; D008657:Metabolic Clearance Rate; D008954:Models, Biological; D011866:Radioisotope Renography / Q000379:methods*; D019275:Radiopharmaceuticals / Q000493:pharmacokinetics*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
chemical_list: D019275:Radiopharmaceuticals