AnestAssist PK/PD Models

AnestAssist PK/PD Scientific Basis


Introduction

In order to evaluate AnestAssist's results, it is important to understand how those results are produced.

AnestAssist calculates estimates of drug concentrations and probabilities of effects using mathematical models. These models are developed by clinical researchers. The models used by AnestAssist are taken from studies published in prominent peer reviewed journals, by well established researchers. The papers and studies corresponding to each model implemented by AnestAssist are listed in the References section below. These studies are also briefy discussed in the section Discussion of Specific Models Used.

Pharmacokinetic and Pharmacodynamic (PK/PD) model design and development are deep and complex subjects. We present only a very simplified high level overview below. For more detail please refer to the many excellent textbooks and other references that explain PK/PD modeling, and it's usefulness with respect to clinical practice. A highly recommended introduction for students and practicing clinicians can be found in the textbook "Anesthesiology" by Longnecker et al, Chapter 39 - "Principles of Pharmacokinetics and Pharmacodynamics: Applied Clinical Pharmacology for the Practitioner" written by Johnson and Egan.

Pharmacokinetic/Pharmacodynamic Model Overview


PK-PD Diagram

Figure 1

IV Drugs

All IV drugs modeled by AnestAssist are modeled using a mathematical abstraction known as a "compartment model".  The phamacokinetics of many IV anesthetic drugs can be approximated by a 2 or 3 compartment model whose compartment's characteristics (volume and clearances) are empirically derived from pharmacologic studies. Such a model is shown in Figure 1. In this diagram V1, V2, and V3 are the volumes of the compartments, k12, k21, k13, and k31 are drug mass flow rates (clearances) between compartments, k10 is the elimination rate from the body, and ke0 characterizes the time delay for a drug's plasma and effect compartments concentrations to reach equlibrium (sometimes called the "biophase").

In this model a drug is injected or infused into the central (i.e. "plasma") compartment. Conceptually from here the drug then flows to the peripheral compartments, and also after a time delay (ke0) into the effect compartment. Eventually, as the concentration in the central compartment is reduced via elimination (k10) the drug present in the other compartments flows back to the central compartment and is then also removed from the system via elimination (k10). See Figure 3 below to see what the central compartment concentration looks like for a bolus of propofol.

It is important to understand that the compartments in this model do not directly represent any physiological structure. However, the drug concentration in the "central" or "plasma" compartment does represent blood concentration, and this is what is reported by AnestAssist. The "effect site" can be very roughly thought of as corresponding to the brain and central nervous system.  From a clinical point of view it is more useful to know effect site concentrations than blood concentrations because by definition that is where the drug acts (not the blood). Effect site concentrations are also reported by AnestAssist. Finally and most importantly, effect site concentrations are used to estimate a drug's effect (patient response) using effect site concentration vs. patient response curves constructed from observations made in pharmacologic studies.

The volumes and clearances (flow rates)  of compartments in these models are calculated from data obtained in pharmacologic studies where blood concentration vs time in healthy volunteers is measured for differents doses of a drug. The volumes and clearances are mathematically chosen to make the output of the model fit, as closely as possible, the actual observed concentrations. In some studies where where subjects of different ages, weights, or genders are observed it is possible to parameterize compartments based on these patient characteristics (covariates). Thus model output is adjusted to an individual patient's characteristics. A good example of this is the propofol model of Schnider (1) et al. which is parametrized for patient age, weight, and height (height and weight used to calculate lean body mass). See Figure 2.

Schnider Parameters

Figure 2

The output of the Schnider model for different patient weights is shown below in Figure 3. The input dose is constant (150 mcg bolus of propfol), and patient age is constant (50 y/o). Note the substantial patient weight dependent difference in plasma concentrations which is what you would expect from training and intuition. A model which did not take weight into account would not show this difference. Therefore understanding a model's parameterization helps you judge it's strengths (and weaknesses). See specifics for AnestAssist below in the section Discussion of Specific Models Used.


Schnider vs Wt.

Figure 3

Inhaled Agents

Inhaled agents are modeled using a 12 compartment model published by Lerou et al [10]. In this model the compartments represent actual physiologic structures (tissues, organs, blood).

Discussion of Specific Models Used

All IV drug models implemented by AnestAssist are 2 or 3 compartment empirical models.

Propofol

There are several well-known pharmacokinetic models for propofol. A model published by Marsh et al [2] is incorporated in DiprifusorĀ® (Astra-Zeneca), a commercial target controlled infusion system for propofol. Patient weight is the only covariate used by the Marsh model. Later studies, such as by Schnider et al [1] incorporate age and height as well as weight (lean body mass) as covariates. The Schnider model is displayed by General Electric (GE) Healthcare’s Navigator Application SuiteĀ® version 1.0

AnestAssist makes available for educational purposes both the Schnider and Marsh propofol models

Remifentanil

AnestAssist incorporates a remifentanil pharmacokinetic model derived by Minto et al [3]. This model incorporates age and weight (lean body mass) as covariates.

Fentanyl

AnestAssist includes 2 fentanyl pharmacokinetic models.

The first model included was derived in a study by Scott and Stanski [4]. Note that while Scott and Stanski found considerable correlation between age and phamacodynamics (“From age 20 to 85, the IC50 values decreased approximately 50%” [p162]), they did not find important pharmacokinetic changes with age. The parameters of this model include no covariates (i.e. do not account for weight, age, gender, etc.).

The second model included was derived by Schafer et al [5]. This model incorporates weight as a covariate

Alfentanil

AnestAssist includes 2 alfentanil pharmacokinetic models.

The first model was derived in a study by Scott and Stanski [6]. Note that while Scott and Stanski found considerable correlation between age and phamacodynamics (“From age 20 to 85, the IC50 values decreased approximately 50%” [p162]), they did not find important pharmacokinetic changes with age. The parameters of this model include no covariates (i.e. do not account for weight, age, gender, etc.).

The second model included was derived by Maitre et al [7]. This model incorporates weight, age, and gender as covariates.

Sufentanil

AnestAssist includes 2 sufentanil pharmacokinetic models.

The first model was derived in a study by  Gepts et al [8]. The parameters of their model  have no covariates (i.e. do not account for weight, age, gender, etc.).

The second model included was derived by Bovill et al [9]. This model incorporates weight as a covariate.

Dexmedetomidine

AnestAssist incorporates a dexmedetomidine pharmacokinetic model derived by Dyck et al [10]. This model incorporates height as a covariate (note, this study's finding of height instead of weight as a covariate may be a statistical anomoly).

Ketamine

AnestAssist includes 2 ketamine pharmacokinetic models.

The first model was derived in a study by  Clements et al [11]. This model incorporates weight as a covariate.

The second model included was derived by Ihmsen et al [12]. This model incorporates weight as a covariate.

Lidocaine

AnestAssist includes 2 lidocaine pharmacokinetic models.

The first model was derived in a study by  Schnider et al [13]. This model incorporates weight as a covariate.

The second model included was derived by Dyck et al [14]. The parameters of this model include no covariates (i.e. do not account for weight, age, gender, etc.).

Morphine

AnestAssist incorporates a morphine pharmacokinetic model derived by Sarton et al [15]. This model incorporates age and weight as covariates.

Midazolam

AnestAssist incorporates a midazolam pharmacokinetic model derived by Zomorodi et al [16]. This model incorporates weight and height (BSA) as covariates.

Rocuronium

AnestAssist incorporates a rocuronium pharmacokinetic model derived by Cooper et al [25], and a pharmacodynamic model by Plaud et al [25]. The PK model incorporates weight as a covariate.

Vecuronium

AnestAssist incorporates vecuronium pharmacokinetic and pharmacodynamic models derived by Caldwell et al [26]. The PK model incorporates weight as a covariate.

Atracurium

AnestAssist incorporates a atracurium pharmacokinetic model derived by Fahey et al [27], and a pharmacodynamic model by Donoti et al [28]. The PK model incorporates weight as a covariate.

Cisatracurium

AnestAssist incorporates cisatracurium pharmacokinetic and pharmacodynamic models derived by Tran et al [29]. The PK model incorporates weight as a covariate.

Inhaled Agents

Inhaled agents are modeled using a 12 compartment model published by Lerou et al [17]. In this model the compartments represent actual physiologic structures (tissues, organs, blood). This model incorporates total blood volume, tissue volumes, cardiac output, and ventillation rates and volumes as inputs to the system. The only patient specific input available from AnestAssist is patient weight which is used to estimate total blood volume, cardiac  output, tissue volumes, and tidal volume. Respiration rate is assumed to be 10 breaths/minute.

Propofol-Opioid Interactions

Response surface models, using the interaction model of Greco et al [21], were constructed from a study of volunteers by Kern et al [18] to estimate propofol-remifentanil synergistic interactions relative to several surrogate and clinical endpoints. Johnson et al [22] subsequently clinically evaluated these models, and published modified parameters for the sedation model corresponding to an Observer’s Assessment of Alertness and Sedation (OAA/S ) [23] score of less than 2 (loss of response to prodding and shaking). 

AnestAssist uses the Kern-Johnson model for OAA/S < 2 to estimate probability of sedation. This estimate is displayed for propofol. Propofol is the only IV drug modeled by AnestAssist whose effect is primarily sedation. AnestAssist uses the Kern laryngoscopy model for estimating the analgesic effect of remifentanil, and is extended by relative potency relationships to the other opioids modeled (fentanyl, sufentanil, and alfentanil).

Sevoflurane-Opioid Interactions

Response surface models, using a logit interaction model, were constructed from a study of volunteers by Manyam et al [11] to estimate sevoflurane-remifentanil synergistic interactions relative to several surrogate and clinical endpoints.

AnestAssist uses the Manyam model for OAA/S < 2 to estimate probability of sedation. This estimate is displayed for sevoflurane. Inhaled agents modeled by AnestAssist effects are assumed to be primarily sedation. 

AnestAssist uses the Manyam laryngoscopy model for estimating the analgesic effect of remifentanil, and is extended by relative potency relationships to the other opioids modeled (fentanyl, sufentanil, and alfentanil).

Isoflurane-Opioid Interactions

A study by Syroid et al [20] scaled the sevoflurane-remifentanil model of Manyan to isoflurane-fentanyl using relative potency ratios. For a study population of 25 patients scheduled for elective surgery using a isoflurane-fentanyl anesthetic they found similar predictive performance as compared to Manyam's original sevoflurane-remifentanyl study.

AnestAssist uses the Manyam OAA/S < 2 model as scaled by Syroid to estimate the probability of sedation by isoflurane.

Errors and Limitations

Good clinical judgement, training, and experience must always be used in evaluating and interpreting AnestAssist's calculations. Please be aware of the following limitations:

  • As explained above, AnestAssist uses mathematical models to estimate drug concentrations and effects. These models are only simplified approximations, derived from population studies involving small numbers of subjects who are usually relatively healthy. Also, there is an intrinsic performance error between a model's predictions and the the study data it was built from. This error is usually reported with the results of the study, and can vary widely from study to study. An excellent reference explaining model performance error can be in found in the textbook "Miller's Anesthesia", Chaper 12, Intravenous Drug Delivery Systems (authors Peter S.A. Glass, Steven L. Shafer, and J.G. Reves), which also includes a summary table (12-7) listing performance errors for a number of model sets, including several used by AnestAssist.  Because of intrinisic model performance error, and because your patient may be unlike the study population, and finally because of biologic variability among individual patients, AnestAssist's estimates may be significantly different from any individual patient's actual values. 
  • Software, especially complex software such as AnestAssist, may contain errors not identified during testing. AnestAssist was carefully tested, and detailed results published here: AnestAssist Testing. However, no testing can be perfect or exhaustive, so errors may remain that may be obvious or non-obvious.

References

  • [1] Propofol - Schnider, T.W., et al., The influence of method of administration and covariates on the pharmacokinetics of propofol in adult volunteers. Anesthesiology, 1998. 88(5): p. 1170-82.
  • [2] Propofol - Marsh, B., et al., Pharmacokinetic model driven infusion of propofol in children. Br J Anaesth, 1991. 67(1): p. 41-8.
  • [3] Remifentanil - Minto, C.F., et al., Influence of age and gender on the pharmacokinetics and pharmacodynamics of remifentanil. I. Model development. Anesthesiology, 1997. 86(1): p. 10-23.
  • [4] Fentanyl - Scott, J.C. and D.R. Stanski, Decreased fentanyl and alfentanil dose requirements with age. A simultaneous pharmacokinetic and pharmacodynamic evaluation. J Pharmacol Exp Ther, 1987. 240(1): p. 159-66.
  • [5] Fentanyl - Shafer, S.L., et al., Pharmacokinetics of fentanyl administered by computer-controlled infusion pump. Anesthesiology, 1990. 73(6): p. 1091-102.
  • [6] Alfentanil - Scott, J.C. and D.R. Stanski, Decreased fentanyl and alfentanil dose requirements with age. A simultaneous pharmacokinetic and pharmacodynamic evaluation. J Pharmacol Exp Ther, 1987. 240(1): p. 159-66.
  • [7] Alfentanil - Maitre, P.O., et al., Population pharmacokinetics of alfentanil: the average dose-plasma concentration relationship and interindividual variability in patients. Anesthesiology, 1987. 66(1): p. 3-12.
  • [8] Sufentanil - Gepts, E., et al., Linearity of pharmacokinetics and model estimation of sufentanil. Anesthesiology, 1995. 83(6): p. 1194-204.
  • [9] Sufentanil - Bovill, J.G., et al., The pharmacokinetics of sufentanil in surgical patients. Anesthesiology, 1984. 61(5): p. 502-6.
  • [10] Dexmedetomidine - Dyck, J.B., et al., Computer-controlled infusion of intravenous dexmedetomidine hydrochloride in adult human volunteers. Anesthesiology, 1993. 78(5): p. 821-8.
  • [11] Ketamine - Clements, J.A. and W.S. Nimmo, Pharmacokinetics and analgesic effect of ketamine in man. Br J Anaesth, 1981. 53(1): p. 27-30.
  • [12] Ketamine - Ihmsen, H., G. Geisslinger, and J. Schuttler, Stereoselective pharmacokinetics of ketamine: R(-)-ketamine inhibits the elimination of S(+)-ketamine. Clin Pharmacol Ther, 2001. 70(5): p. 431-8.
  • [13] Lidocaine - Schnider, T.W., et al., Derivation and cross-validation of pharmacokinetic parameters for computer-controlled infusion of lidocaine in pain therapy. Anesthesiology, 1996. 84(5): p. 1043-50.
  • [14] Lidocaine - Dyck, J.B., et al., Computer-controlled infusion of intravenous dexmedetomidine hydrochloride in adult human volunteers. Anesthesiology, 1993. 78(5): p. 821-8.
  • [15] Morphine - Sarton, E., et al., Sex differences in morphine analgesia: an experimental study in healthy volunteers. Anesthesiology, 2000. 93(5): p. 1245-54;
  • [16] Midazolam - Zomorodi, K., et al., Population pharmacokinetics of midazolam administered by target controlled infusion for sedation following coronary artery bypass grafting. Anesthesiology, 1998. 89(6): p. 1418-29.
  • [17] Inhaled Agents - Lerou, J.G. and L.H. Booij, Model-based administration of inhalation anaesthesia. 1. Developing a system model. Br J Anaesth, 2001. 86(1): p. 12-28.
  • [18] Propofol-Opioid Interactions - Kern, S.E., et al., A response surface analysis of propofol-remifentanil pharmacodynamic interaction in volunteers. Anesthesiology, 2004. 100(6): p. 1373-81.
  • [19] Sevoflurane-Opioid Interactions - Manyam, S.C., et al., Opioid-volatile anesthetic synergy: a response surface model with remifentanil and sevoflurane as prototypes. Anesthesiology, 2006. 105(2): p. 267-78.
  • [20] Isoflurane-Opioid Interactions - Syroid, N.D., et al., Response Surface Model Predictions of Emergence and Response to Pain in the Recovery Room: An Evaluation of Patients Emerging from an Isoflurane and Fentanyl Anesthetic. Anesth Analg, 2009 (Publish ahead of print)
  • [21] Greco, W.R., G. Bravo, and J.C. Parsons, The search for synergy: a critical review from a response surface perspective. Pharmacol Rev, 1995. 47(2): p. 331-85.
  • [22] Johnson, K.B., et al., An evaluation of remifentanil propofol response surfaces for loss of responsiveness, loss of response to surrogates of painful stimuli and laryngoscopy in patients undergoing elective surgery. Anesth Analg, 2008. 106(2): p. 471-9
  • [23] Chernik, D.A., et al., Validity and reliability of the Observer's Assessment of Alertness/Sedation Scale: study with intravenous midazolam. J Clin Psychopharmacol, 1990. 10(4): p. 244-51.
  • [24] Rocuronium PK - Cooper, R.A., et al., Time course of neuromuscular effects and pharmacokinetics of rocuronium bromide (Org 9426) during isoflurane anaesthesia in patients with and without renal failure. Br J Anaesth, 1993. 71(2): p. 222-6.
  • [25] Rocuronium PD - Plaud, B., et al., Pharmacokinetics and pharmacodynamics of rocuronium at the vocal cords and the adductor pollicis in humans. Clin Pharmacol Ther, 1995. 58(2): p. 185-91.
  • [26] Caldwell, J.E., et al., Temperature-dependent pharmacokinetics and pharmacodynamics of vecuronium. Anesthesiology, 2000. 92(1): p. 84-93.
  • [27] Atricurium PK - Fahey, M.R., et al., The pharmacokinetics and pharmacodynamics of atracurium in patients with and without renal failure. Anesthesiology, 1984. 61(6): p. 699-702.
  • [28] Atracurium PD - Donati, F., et al., Pharmacokinetics and pharmacodynamics of atracurium obtained with arterial and venous blood samples. Clin Pharmacol Ther, 1991. 49(5): p. 515-22.
  • [29] Cisatracurium - Tran, T.V., P. Fiset, and F. Varin, Pharmacokinetics and pharmacodynamics of cisatracurium after a short infusion in patients under propofol anesthesia. Anesth Analg, 1998. 87(5): p. 1158-63.