The Severinghaus square root of time relationship for anesthetic uptake and its implications for the stability of compartmental pharmacokinetics.
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.
Connor
Christopher W
CW
Department of Anesthesiology, Perioperative and Pain Medicine, Harvard Medical School, Brigham and Women's Hospital, Boston, MA, USA. cwc@bwh.harvard.edu
Philip
James H
JH
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
D000777:Anesthetics; D009609:Nitrous Oxide