Pharmacokinetic Modelling

I wrote this site to make it easier to understand the use of compartmental models, and to see the effect of changing the variables. It is not designed for clinical decision making. As long as your values do not create an error you will see a graph. This does not imply the graph bears any relationship to reality. I have converted all models to be weight adjusted, which may give odd results.

All mistakes are copyright of the author and should not be reproduced without permission. The concept and coding strategy has been derived (somewhat indirectly) from STANPUMP which is freely available from the author here. I also used Dr Shafer's Convert spreadheet to implement the conversion functions in the compartments page.

Some of the t1/2keo values have been calculated from the time to peak effect, rather than coming from the original papers. You can see the effect of changing these values on the Effect Site Concentrations page. NOTE t1/2keo values are model dependent. You will not get the correct result if you use the values from a different model. For alfentanil fentanyl and sufentanil I have used the TTPEs from Scholz.


Context Sensitive Half Times

Hughes MA, Glass SA, Jacobs JR: Context-sensitive Half-time in Multicompartmental Pharmacokinetic Models for Intravenous Anesthetic Drugs. Anesthesiology 76:334-341, 1992
The graph of CSHT in all the textbooks comes from this paper. On the CSHT page you can use their data to reproduce that graph, and also see what happens if you extend the time axis further.


Scott JC, Stanski DR: Decreased Fentanyl and Alfentanil Dose Requirements with Age. Journal of Pharmacology and Experimental Therapeutics 240:159-66, 1987
The constants used in Hughes are slightly different to those calculated by Shafer in STANPUMP


Marathe PH, Dwersteg JF, Pavlin EG, Haschke RH, Heimbach DM, Slattery JT: Effect of Thermal Injury on the Pharmacokinetics and Pharmacodynamics of Atracurium in Humans. Anesthesiology 70:752-755, 1989
I have copied the constants from STANPUMP, which derives them from this paper in 3 males and one female.

Atropine & Glycopyrrolate

Scheinin H, Helminen A, Sakke H, Groönroos P, Bosch JA, Kuusela T, Kanto J, Kaila T: Spectral Analysis of Heart Rate Variability as a Quantitative Measure of Parasympatholytic Effect-Integrated Pharmacokinetics and Pharmacodynamics of Three Anticholinergic Drugs. Therapeutic Drug Monitoring 21:141-151, 1999


Naik BI, Roger C, Ikeda K, Todorovic MS, Wallis SC, Lipman J, Roberts JA: Comparative total and unbound pharmacokinetics of cefazolin administered by bolus versus continuous infusion in patients undergoing major surgery: a randomized controlled trial. British Journal of Anaesthesia 118:876-882, 2017
I have used the data from the 0.1mg/kg dose with the traditional compartmental model. Vc was calculated from the Cp.


Lien CA, Schmith VD, Belmont MR, Abalos A, Kisor DF, Savarese JJ: Pharmacokinetics of Cisatracurium in Patients Receiving Nitrous Oxide/Opioid/Barbiturate Anesthesia. Anesthesiology 84:300-8, 1996
I have used the data from the 0.1mg/kg dose with the traditional compartmental model. Vc was calculated from the Cp.
Tran TV, Fiset P, Varin F: Pharmacokinetics and Pharmacodynamics of Cisatracurium After a Short Infusion in Patients Under Propofol Anesthesia. Anesthesia & Analgesia 87:1158-63, 1998
I have used the microrate constants and the t12ke0. Using the half lives and the keo give slightly different values.


I have used a TTPE of 15 mins, taken from Clinical Anesthesia Cap 15, Barash Ed.

Dyck JB, Maze M, Haack C, Azarnoff DL, Vuorilehto L, Shafer SL: Computer-controlled Infusion of Intravenous Dexmedetomidine Hydrochloride in Adult Human Volunteers. Anesthesiology 78:821-828, 1993
Hannivoort LN, Eleveld DJ, Proost JH, Reyntjens KMEM, Absalom AR, Vereecke HEM, Struys MMRF: Development of an Optimized Pharmacokinetic Model of Dexmedetomidine Using Target-controlled Infusion in Healthy Volunteers. Anesthesiology 123:357-67, 2015
Dutta S, Lal R, Karol MD, Cohen T, Ebert T: Influence of Cardiac Output on Dexmedetomidine Pharmacokinetics. Journal of Pharmaceutical Sciences 89:519-527, 2000
Talke P, Richardson CA, Scheinin M, Fisher DM: Postoperative Pharmacokinetics and Sympatholytic Effects of Dexmedetomidine. Anesthesia & Analgesia 85:1136-42, 1997


Arden JR, Holley FO, Stanski DR: Increased Sensitivity to Etomidate in the Elderly: Initial Distribution versus Altered Brain Response. Anesthesiology 65:19-27, 1986
I have calculated the constants from Vdss, Clearance and half lives.


Scholz J, Steinfath M, Schulz M: Clinical Pharmacokinetics of Alfentanil, Fentanyl and Sufentanil. Clinical Pharmacokinetics 34:275-292, 1996
Shafer SL, Varvel JR, Aziz N, Scott JC: Pharmacokinetics of Fentanyl Administered by Computer-controlled Infusion Pump. Anesthesiology 73:1091-1102, 1990


Hill HF, Coda BA, Tanaka A, Schaffer R: Multiple-Dose Evaluation of Intravenous Hydromorphone Pharmacokinetics in Normal Human Subjects. Anesthesia & Analgesia 72:330-6, 1991
I have divided the Vc by the average weight, and used the microrate constants for the 40µg/kg dose. If you use the Vdss clearance and half life method you get different microrate constants.


Absalom AR, Lee M, Menon DK, Sharar SR, De Smet T, Halliday J, Ogden M, Corlett P, Honey GD, Fletcher PC: Predictive performance of the Domino, Hijazi, and Clements models during low-dose target-controlled ketamine infusions in healthy volunteers. British Journal of Anaesthesia 98:615-23, 2007
Clements JA, Nimmo WS: Pharmacokinetics and Analgesic Effect of Ketamine in Man. British Journal of Anaesthesia 53:27-30, 1981
Domino EF, Zsigmond EK, Domino LE, Domino KE, Kothary SP, Domino SE: Plasma levels of ketamine and two of its metabolites in surgical patients using a gas chromatographic mass fragmento- graphic assay. Anesthesia & Analgesia 61:87-92, 1982
Olofsen E, Noppers I, Niesters M, Kharasche E, Aarts L, Sarton E, Dahan A: Estimation of the Contribution of Norketamine to Ketamine-induced Acute Pain Relief and Neurocognitive Impairment in Healthy Volunteers. Anesthesiology 117:353-364, 2012
This paper uses the parameters from Sigtermans. The t1/2ke0 values depended on the effect with 0 for cognitive flexibility to 11.8 for pain. I have used their average value of 6.1
Persson J, Hasselstroöm J, Maurset A, Öye I, Svensson J-O, Almqvist O, Scheinin H, Gustafsson LL, Almqvist O: Pharmacokinetics and non-analgesic effects of S- and R-ketamines in healthy volunteers with normal and reduced metabolic capacity. European Journal of Clinical Pharmacology 57:869-875, 2002
Sigtermans M, Dahan A, Mooren R, Bauer M, Kest B, Sarton E, Olofson E: S(+􏰖)-ketamine Effect on Experimental Pain and Cardiac Output. Anesthesiology 111:892-903, 2009


Boyes RN, Scott DB, Jebson PJ, Godman MJ, Julian DG: Pharmacokinetics of Lidocaine in Man. Clin Pharmacol Ther 12:105-16 1971
Schnider TW, Gaeta R, Brose W, Minto CF, Gregg KM: Derivation and Cross-validation of Pharmacokinetic Parameters for Computer-controlled Infusion of Lidocaine in Pain Therapy. Anesthesiology 84:1043-1050 1996


Inturrisi CE, Colburn WA, Kaiko RF, Houde RW, Foley KM: Pharmacokinetics and pharmacodynamics of methadone in patients with chronic pain. Clinical Pharmacology & Therapeutics 41:392-401, 1987
Shafer and Flood, P. (2008). The Pharmacology of Opioids. In: J. Silverstein, A. Rooke, J. Reves and C. McLeskey, ed., Geriatric Anesthesiology, 2nd ed. New York: Springer, p.212.
I have used the constants from this table, in combination with the weights from the original paper.


Persson P, Nilsson A, Hartvig P, Tamsen A: Pharmacokinetics of Midazolam in Total I.V. Anaesthesia. British Journal of Anaesthesia 59:548-556, 1987
Hughes' paper derives its midazolam constants from here.
Short TG, Young KK, Tan P, Tam YH, Gin T, Oh TE: Midazolam and flumazenil pharmacokinetics and pharmacodynamics following simultaneous administration to human volunteers. Acta Anaesthesiologica Scandanavica 38:350-356, 1994
Short TG, Tam YH, Tan P, Oh TE: Pharmacokinetic model-controlled infusion of midazolam. Anaesthesia 48:197-191, 1993


Aitkenhead AR, Vater M, Achola K, Cooper, CMS Smith G: Pharmacokinetics of Single Dose I.V. Morphine in Normal Volunteers and Patients with End-Stage Renal Failure. BJA 56:813-18, 1984
I have used the microrate constants from this model, however they are not consistent with the volumes and half lives presented.
Sarton E, Olofsen E, Romberg R, den Hartigh J, Kest B: Sex Differences in Morphine Analgesia: An Experimental Study in Healthy Volunteers. Anesthesiology 90:1245-1254, 2000
ke0 values are for Pain Threshold.


Olkkola KT, Hamunen K, Seppälä T, Maunuksela E-L: Pharmacokinetics and Ventilatory Effects of Intravenous Oxycodone in Postoperative Children. British Journal of Clinical Pharmacology 38:71-76, 1994
Leow KP, Smith MT, Watt JA, Williams BE, Cramond T: Comparative Oxycodone Pharmacokinetics in Humans After Intravenous, Oral and Rectal Administration. Therapeutic Drug Monitoring 14:479-484, 1992
Saari TI, Ihmsen H, Neuvonen PJ, Olkkola KT, Schwilden H: Oxycodone clearance is markedly reduced with advancing age: a population pharmacokinetic study. British Journal of Anaesthesia 3:491-8, 2012
This model calculates the microrate constants with expressions.
I have used the TTPE from Olkkola just to have a figure, so take this with a large dose of salt.


Fung DL, Asling JH, Eisele JH, Martucci R: A Comparison of Alphaprodine and Meperidine Pharmacokinetics. J Clinical Pharmacology 1:37-41, 1980
TTPE is taken from Qiao.
Qiao GL, Fung KF: Pharmacokinetic-pharmacodynamic modelling of meperidine in goats (I): Pharmacokinetics. J Vet Pharmacol Ther 16:426-437, 1993
Qiao GL, Fung KF: Pharmacokinetic-pharmacodynamic modelling of meperidine in goats (II): Modelling. J Vet Pharmacol Ther 17:127-34, 1994
Shafer and Flood, P. (2008). The Pharmacology of Opioids. In: J. Silverstein, A. Rooke, J. Reves and C. McLeskey, ed., Geriatric Anesthesiology, 2nd ed. New York: Springer, p.212.
Original reference is Qiao. This comes from two studies in goats.


Absalom AR, Mani V, De Smet T. Struys MMRF: Pharmacokinetics models for propofol—defining and illuminating the devil in the detail. BJA 103:26-37, 2009
Gepts E, Jonckheer K, Maes V, Sonck W, Camu F: Disposition Kinetics of Propofol During Alfentanil Anaesthesia. Anaesthesia 43:8-13, 1988
Hughes references this paper for his propofol model.
White M, Kenny GNC: Intravenous Propofol Anaesthesia Using a Computerised Infusion System. Anaesthesia 45:204-209, 1990
Hughes also references this paper for his propofol model.


Minto CF, Schnider TW, Egan TD, Youngs E, Lemmens HJ et al: Influence of Age and Gener on the Pharmacokinetics and Pharmacodynamics of Remifentanil: I Model Development. Anesthesiology 86:20-23, 1997
For simiplicity I have used the weight proportional model. The t1/2ke0 increased with age in this study. I have given a middle value here of 1.5 min


Plaud B, Proost JD, Mark J, Wierda KH, Barre J, Debaene B, Meistleman C: Pharmacokinetics and pharmacodynamics of rocuronium at the vocal cords and the adductor pollicis in humans. Clinical Pharmacology & Therapeutics 58:185-191, 1995
Vega EA, Ibacache ME, Anderson BJ, Holford NHG, Nazar CE, Solari S, Allende FA, Cortinez LI: Rocuronium pharmacokinetics and pharmacodynamics in the adductor polycis and masseter muscles. Acta Anaesthesiologica Scandanavica 60:734-756, 2016


Egan TD, Kuramkote S, Gong GQ, Zhang J, McJames SW, Bailey PL: Fentanyl Pharmacokinetics in Hemorrhagic Shock: A Porcine Model. Anesthesiology 91:156-66, 1999
I didn't know the effect of shock on ke0, so I used the same value for both models.
Johnson KB, Kern SE, Hamber EA, McJames SW, Kohnstamm KM, Egan TD: Influence of Hemorrhagic Shock on Remifentanil. Anesthesiology 94:322-32, 2001
I didn't know the effect of shock on ke0, so I used the same value for both models.
Johnson KB, Egan TD, Kern SE, White JL, McJames SW, Syroid N, Whiddon D, Church T: The Influence of Hemorrhagic Shock on Propofol: A Pharmacokinetic and Pharmacodynamic Analysis. Anesthesiology 99:409-20, 2003
This was a study in pigs. You will note that the plasma concentrations in the control group is much lower than what you would expect after the same dose in a human.


Hudson RJ, Bergstrom RG, Thomson IR, Sabourin MA, Rosenbloom M, Strunin L: Pharmacokinetics of Sufentanil in Patients Undergoing Abdominal Aortic Surgery. Anesthesiology 70:426-431, 1989
Constants used by Hughes are slightly different to these.


Ghoneim MM, Van Hamme MJ: Pharmacokinetics of Thiopentone: Effects of Enflurane and Nitrous Oxide Anaesthesia and Surgery. British Journal of Anaesthesia 50:1237-1241, 1978
Hughes uses this paper for his thipoentone simulation. I can't get the figures from this paper to match those used in Hughes
Stanski DR, Maitre PO: Population Pharmacokinetics and Pharmacodynamics of Thiopental: The Effect of Age Revisited. Anesthesiology 72:412-422, 1990
TTPE was calculated as 1.75mins from the ke0 value given in this study, and used to calculate the ke0 for the Hughes model

Vecuronium & Pancuronium

Rupp SM, Castagnoli KP, Fisher DM, Miller RD: Pancuronium and Vecuronium Pharmacokinetics and Pharmacodynamics in Younger and Elderly Adults. Anesthesiology 67:45-49, 1987

Parameter Estimation

Absalom AR, Mani V, De Smet T. Struys MMRF: Pharmacokinetics models for propofol—defining and illuminating the devil in the detail. BJA 103:26-37, 2009
Discusses the use of time to peak effect to estimate the t1/2keo.
Upton RN: Calculating the hybrid (macro) rate constants of a three-compartment mamillary pharmacokinetic model from known micro-rate constants. Journal of Pharmacological and Toxicological Methods 49:65-8, 2004
How to calculate the half lives from the microrate constants.