title: The Severinghaus square root of time relationship for anesthetic uptake and its implications for the stability of compartmental pharmacokinetics.
abstract: For nitrous oxide, the first anesthetic for which uptake was measured in humans, Severinghaus noted empirically that a plot of the log of uptake against the log of elapsed time produced a straight line with slope -0.5, suggesting that uptake is proportional to the inverse square root of time. This result is something of a black box model, based on empirical curve fitting without regard to physiology. Some authors (e.g., Lowe) repeatedly returned to this inverse square root of time model as a benchmark while others (e.g., Hendrickx) questioned its validity and demanded the relationship be expressed with a physiologic model whose structure matches the known physiology being modeled. Nevertheless, the fact that authors have repeatedly come back to this inverse square root of time model as a benchmark suggests that it might have some underlying validity which has not previously been recognized. We re-explored this mathematically in an attempt to reveal hitherto undiscovered insights or limitations. In this study, we examined the square root of time model (viewed as a power function) and compared it with multi-compartment models. Further, we explored the stability of this relationship to systematic variation in the power value and also to the superimposition of noise-like perturbations, seeking conditions under which it might not work. Based upon this theoretical analysis, we also speculate on the existence of a physiological compartment with a time constant between that of the vessel-rich group (VRG) and muscle, and what the identity of such a compartment might be.
authors.affiliation: Department of Anesthesiology, Perioperative and Pain Medicine, Harvard Medical School, Brigham and Women's Hospital, Boston, MA, USA. cwc@bwh.harvard.edu
authors.forename: Christopher W
authors.initials: CW
authors.lastname: Connor
authors.forename: James H
authors.initials: JH
authors.lastname: Philip
mesh_terms: D000465:Algorithms; D000777:Anesthetics / Q000008:administration & dosage / Q000097:blood* / Q000493:pharmacokinetics*; D003198:Computer Simulation; D004360:Drug Therapy, Computer-Assisted / Q000379:methods*; D006801:Humans; D008657:Metabolic Clearance Rate; D008954:Models, Biological; D009609:Nitrous Oxide / Q000008:administration & dosage / Q000097:blood* / Q000493:pharmacokinetics*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
chemical_list: D000777:Anesthetics; D009609:Nitrous Oxide