Combining Propofol and Remifentanil Pharmacokinetic

COMBINING PROPOFOL AND REMIFENTANIL PHARMACOKINETIC

AND PHARMACODYNAMIC MODELS IN THE OPERATING ROOM:

AN OBSERVATIONAL STUDY

Farrant Hiroshi Sakaguchi

A thesis submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of

Master of Science

Department of Bioengineering

The University of Utah

December 2004

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4 ABSTRACT

Remifentanil and propofol are commonly used together for total intravenous anesthesia. Though their synergistic pharmacodynamic interaction has been characterized with surrogate measures in volunteers, the relationship of these surrogate measures to actual surgical stimuli has not been validated prospectively in the operating room. This study combines a set of propofol and remifentanil pharmacokinetic (PK) and pharmacodynamic (PD) models to estimate their PD interaction and predicts the resulting likelihood of sedation and analgesia intraoperatively.

With IRB approval and informed consent, we studied 24 ASA physical status I, II, and III patients scheduled for laproscopic surgery receiving total intravenous anesthesia.

Standard anesthetic practice was not altered for this study. Responses and non- responses to the intraoperative stimuli of laryngoscopy and skin incision were recorded.

The predicted effect-site concentrations at these data points, and at the loss and return of responsiveness, were plotted on response-surface models for corresponding surrogate measures determined in volunteers. Patient observations were compared to pharmacodynamic predictions. Methods to reduce differences between the model predictions and observations in the patients are identified and discussed.

The results of this study suggest that tracheal intubation, a surgical milestone, is more stimulating than the surrogate measure of laryngoscopy alone. The PK-PD

combined models for a surrogate indicator of sedation (OAA/S < 2) predict loss of responsiveness (LOR) and recovery of responsiveness (ROR) for 35% and 87% of the patients above the 50% isobol, respectively. The data also suggest that propofol, rather than remifentanil, is the main contributor to responsiveness in these patients. Clinically, this may mean that a quick recovery of consciousness may be achieved while managing postoperative pain by maintaining opioid levels while propofol levels are reduced.

v TABLE OF CONTENTS

ABSTRACT...... iv

LIST OF FIGURES...... vii

ACKNOWLEDGMENTS...... viii

Chapter

1. INTRODUCTION...... 1

Purpose of Study...... 1 Pharmacological Modeling...... 2 Methods for Preliminary Study...... 10 Conclusion from Preliminary Study ...... 11 References...... 13

2. OBSERVATIONAL STUDY...... 15

Introduction...... 15 Methods...... 16 Results...... 24 Discussion...... 32 References...... 37

3. CONCLUSION ...... 40

Summary...... 40 Comparison of Observational Studies and Clinical Studies ...... 40 Utility and Limitations of Clinical Pharmacological Modeling...... 41 Future Work...... 42 References...... 43

LIST OF FIGURES

Figure Page

1.1. Three compartment model with an effect-site...... 3

1.2. Pharmacodynamic Emax models for sedation and laryngoscopy...... 5

1.3. Isobologram for three pharmacodynamic interactions ...... 6

1.4. Response surface models for surrogate measures from Kern et al...... 9

2.1. Ceff values at loss of responsiveness on the sedation response surface

(OAA/S<2)...... 27

2.2. Ceff values at recovery of responsiveness on the sedation response surface

(OAA/S<2)...... 28

2.2 Ceff values at recovery of responsiveness on the sedation response surface

2.3 Ceff values at laryngoscopy followed by tracheal intubation on the response

surface for laryngoscopy...... 29

2.4 Ceff values at the first skin incision on the response surface for shin algometry

...... 30

2.5 Ceff values at the first skin incision on the response surface for electrical tetany

...... 31

vii ACKNOWLEDGMENTS

I would like to express appreciation to Dr. Dwayne Westenskow for his support and encouragement throughout this project. I am indebted to Dr. Steve Kern for his high expectations and trust in my abilities. I am grateful to Dr. Kenneth Horch for teaching me to think rationally and to expect more of myself while progressing in life. I appreciate Dr. Talmage Egan’s constant enthusiasm and clinical insights. I thank Noah

Syroid for his support in the project, help and patience with my coding. I also acknowledge the support and help of numerous friends who have encouraged, helped, and at times, mocked me through this process. I thank my parents, Maisie and Douglas

Sakaguchi, for their continual love, trust, support, encouragement, and teaching. I especially thank them for their examples of seeking after wisdom and excellence in every area of life while teaching what is of greatest value. I thank my God for being alive and for surrounding me with such fine mentors, colleagues, friends, and family.

This research has been generously funded by the NIH Grant # 1 RO1 HL 64590 and by the NASA Rocky Mountain Space Consortium. Thank you to MedFusion for the use of the Medex 3010a continuous infusion pumps. We appreciate the support of Colin

Corporation for the use of their Colin CBM-7000, a continuous, non-invasive blood pressure monitor. CHAPTER 1

INTRODUCTION

Purpose of Study

Pharmacodynamic studies are often used to characterize the concentration-effect relationship of a single drug. 1,2,3 Predicting the effect of two drugs that have a pharmacodynamic interaction is complex. As a result of this complexity, pharmacodynamic interaction studies are usually performed in volunteers in a controlled environment. 4,5,6,7,8,9 The most significant limitation of these volunteer studies is that responses to surrogate measures of surgical stimuli are used. The relationship between the stimulus induced by a surrogate measure, such as electrical tetany, and by a surgical measure, such as skin incision, remains unclear. A volunteer study also evaluates sedation differently than in the perioperative setting; a volunteer study often describes the depth of sedation using a graded scale such as the observer’s assessment of alertness/sedation (OAA/S). 4,10 In the operating room “unconsciousness” is simply observed when the patient is non-responsive to verbal commands. Additionally, the volunteer study rigorously controls the dosing regimen over wide concentration ranges and allows time for the plasma concentration to equilibrate with the effect-site concentration. 2

This study combines pharmacokinetic and pharmacodynamic models, comparing these predictions with observations in patients. The goal was to assess models developed in volunteers by Kern et al. 4,5 by pharmacodynamically relating surgical stimuli to surrogate measures. An observational study has several limitations.

The first is that the dosing regimen is not strictly controlled, resulting in periods of non- steady-state kinetics and greater uncertainty with respect to drug concentrations in the brain. Secondly, for ethical reasons, surgical stimuli are not attempted at low drug concentrations. Nor are they repeated without clinical expedience. Thus, for each surgical milestone, only a single data point was used from each patient.

Pharmacological Modeling

A pharmacokinetic (PK) model describes the changing concentration of a drug in the body over time after a dose is administered; pharmacokinetics describe what the body does to the drug.11 Figure 1.1 diagrams a three-compartment model with an effect- site compartment used to describe the distribution of drugs through different tissues.11, 12

These theoretical, nonphysical compartments represent different tissues. Once a drug is administered, it is transported in the blood to different compartments, including the biophase or effect site. 12 The biophase consists of the specific tissues, membranes, receptors, and/or enzymes where the drug exerts its pharmacologic effect; the central nervous system is considered the biophase for general anesthetics. 12 Thus, although plasma concentrations of an anesthetic agent are relatively easy to obtain, they are of less direct interest than the effect-site concentrations (Ceff ).13 The transport of drugs

Figure 1.1. Three compartment model with an effect-site. Drug doses given intravenously via infusion or bolus enter the central compartment (roughly the circulatory system). The drug is then distributed to different tissue types or compartments. The effect-site is where the drug exerts its pharmacological effect. Pharmacokinetic models predict the drug concentrations in each compartment.

4 between compartments is generally described by first order differential equations. 14

A pharmacodynamic (PD) model describes the effect of the drug on the patient as the concentration changes; pharmacodynamics describe the drug effects as functions of the drug concentrations at the effect-site.11 The Emax model, Equation 1.1, is a common

PD model for anesthetics and describes a concentration-response relationship that is sigmoidal in shape (Figure 1.2). 15

γ (DrugConcentration/EC ) = 50 NormalizedEffect γ [1.1] (DrugConcentration/EC ) + 1 50

This s-shaped curve is characterized by the EC 50 and by γ (the steepness). At the EC 50 concentration, there is a 50% probability that the patient is “adequately anesthetized.” 4,15

Anesthesia is generally targeted at EC 95 concentrations such that there is a 95% or higher probability that patients will not respond. In most patients, higher anesthetic concentrations will have minimal additional pharmacodynamic benefits.

When more than one anesthetic is used, interactions can produce several positive effects.15,16,17 For example, a certain concentration of either Drug A or Drug B (points J and K in Figure 1.3) may prevent a response to a painful stimulus. The two drugs can also be used in combination to achieve the same drug effect. The curves that connect points j and k and describe combinations of the drugs that predict equal drug effect are termed isoboles. The shape of these isoboles depends on the pharmacodynamic interaction of Drugs A and B. Three potential interactions (synergy, additivity, and

100%

95% Drug Effect 90%

80%

70%

60%

50% Drug Effect 50%

40% Likelihood of Drug Effect ofLikelihood Drug

30%

20%

10% Sedation Laryngoscopy Sedation EC50 EC95 EC50 Laryngoscopy 0% 0 2 4 6 8 10 12 14 16 Drug Concentration

Figure 1.2. Pharmacodynamic Emax models for sedation and laryngoscopy. In this figure, the likelihood of drug effect is a function of drug concentration. The EC 50 and EC 95 describe the drug concentrations necessary to achieve 50% and 95% of drug effect, respectively.

Synergistic Additive Antagonistic Interaction Interaction Interaction

0.5 Normalized Drug B Concentration Drug Normalized

X Y Z

0 0 0.5 1 Normalized Drug A Concentration

Figure 1.3. Isobologram for three pharmacodynamic interactions. The points at J and K represent drug effect when either Drug A or Drug B are given alone (i.e. the 50% likelihood of drug effect). The solid lines represent the combination of drug concentration pairs necessary to achieve the same effect level for different pharmacodynamic interactions. In this figure, the points X, Y, and Z are at equal levels of drug effect, depending on the interaction. Depending on the interaction, for a fixed concentration of Drug B, different concentrations of Drug A are necessary to achieve the same drug effect.

7 antagonism) are shown in Figure 1.3.15,18

Synergism results in reduced individual drug concentrations while providing a targeted effect-level. Additivity means there is no interaction between the two drugs.

Antagonism, in contrast to synergism, requires increased drug concentrations to provide a targeted effect-level. A collection of isoboles, where curves are shown for a range of effect-levels, can be interpolated to create a response surface; a response surface represents the full range of probabilities of a drug effect for different drug concentration pairs.4,6,9,15,18

Pharmacokinetic and pharmacodynamic models can be combined to describe the effect of a drug over time.11 There are several challenges however, due to assumptions made by PK and PD models. PK models assume that a drug distributes homogenously and instantaneously within each compartment. The true complexity of intravascular mixing and drug transport is ignored. 19,20 For example, the predicted Ceff can rise the moment a drug is administered despite that this immediate rise in Ceff does not make physiological sense for anesthetics acting in the CNS. Few anesthetic models consider the effects of temperature, cardiac output, recirculation and the varying distribution volumes over time. 19,20 Anesthetic PD models are also misspecified by using a continuous function to describe logistic observations of “adequate anesthesia” relative to a given stimulus. Most PD models describe the probability of the drug moderating a noxious stimulus instead of the physiological action of the anesthetic. 20 Despite these weaknesses, combined PK-PD models may be useful tools for anesthesiologists to

8 predict the rate of onset of drug effect, the duration of the drug effect, and the minimum effective dose.4,11

Real-time visualization of drug pharmacokinetics and pharmacodynamics may help anesthesiologists more accurately titrate intravenous anesthetics for sedation and analgesia in a critical care setting. 11 There is growing interest in modeling the interactions and effects of two or more anesthetics simultaneously. An increased understanding of drug kinetics and effects will help anesthesiologists gain greater control of their anesthetic. 10 Thus models of these phenomenon may be useful in optimizing the clinical care of patients, potentially offering guidance that may minimize the time between the end of surgery and patient return to consciousness, reduce the amount of anesthetics that are used, or more effectively prevent post-operative pain.

Kern et al. created response surfaces for propofol and remifentanil that describe the drug effect in terms of surrogate measures (OAA/S, laryngoscopy, shin algometry, and electrical tetany), shown in Figures 1.4.4,5 The models were developed using data collected from 24 healthy volunteers. The results show a synergistic pharmacodynamic interaction between remifentanil and propofol over the full clinical concentration range and the stronger the noxious stimulus the stronger the interaction is between the drugs.

A population PD response surface represents the range of probabilities of preventing a response to a stimulus at each drug concentration pair.21 A single isobole represents all the drug concentration pairs that provide a specific probability in a given population of preventing a response to a stimulus. However, it is difficult to assess

Figure 1.4 Response surface models for surrogate measures from Kern et al.. The top left model represents the likelihood of an Observer’s Assessment of Alertness/Sedation (OAA/S) score < 4. The top right model represents the population’s likelihood of not responding to laryngoscopy. The bottom left and right surfaces represents the percentage of maximum stimulus tolerated for shin algometry and electrical tetany, respectively.

10 graded levels of pain for individual patients under general anesthesia. In the operating room, the anesthesiologist assesses surgical pain qualitatively—the patient either responds to pain or does not. Thus, when individual patient data is plotted on the population response surfaces, we are comparing individuals to a population. In other words, a pharmacodynamic estimation does not directly predict whether a specific patient will respond to a stimulus. Rather, if a patient responds to pain at a high probability of anesthetic effect, then the patient can be characterized as being pharmacologically resistant. A resistant patient will require higher dosing throughout the surgery to provide sufficient anesthesia. The same drug regimen in a sensitive patient might result in a prolonged time until recovery of consciousness.

Methods for Preliminary Study

In order to minimize clinical care, this observational study was structured to have minimal impact upon the anesthesiologists’ and surgeons’ standard practice of care. We observed moments of inadequate anesthesia throughout each surgical case, indicated by a 20% rise in heart rate, blood pressure, or another somatic response. The predicted Ceff during patient responses and at surgical landmarks (loss of responsiveness, laryngoscopy, tracheal intubation, skin incisions, intraabdominal manipulations, wound closure, skin closure, recovery of consciousness and extubation) were then be plotted on the response surfaces created by Kern et al. 4,5 The actual patient responses were then compared to the likelihood of anesthesia as estimated by the different response surfaces.

The preliminary study, with institutional review board approval from the

University Hospital and informed consent involved seven patients with ASA physical status I and II scheduled for laparoscopic surgery under total intravenous anesthesia. To minimize experimental intrusiveness, a graduate student observer was the only researcher present in the operating room. To collect dosing data, a laptop interfaced with two Medfusion 3010a infusion pumps (Medex, Dublin, OH, USA) and a DocuJect digital injectable drug monitor (DocuSys, Mobile, AL, USA). All boluses administered through the DocuJect were flushed with a saline bolus to minimize the delay between the recorded drug administration and the actual distribution of the drug to the effect- site. To collect patient monitoring data, an A-2000 BIS EEG monitor (Aspect Medical

Systems, Newton, MA, USA) and CBM-7000, a continuous, non-invasive blood-pressure monitor (Colin Medical Instruments Corp., San Antonio, TX, USA) also interfaced with the laptop.

The digital drug dosing data, collected automatically, was used to run pharmacokinetic simulations. The predicted drug concentrations at the times of surgical landmarks were plotted on the relevant response surfaces of the surrogate measures.

Comparisons of the patient data to the pharmacodynamic predictions were to be used to relate surrogate measures to surgical stimuli.

Conclusion from Preliminary Study

Several problems were initially encountered: logistically, it was difficult for an individual to set up 2 patient monitors and 3 drug delivery systems. Clinically, the

12 anesthesiologists were wary of relying on the Colin continuous non-invasive blood pressure monitor for hemodynamic information and were unfamiliar with the DocuJect bolus monitor combined with the saline flush necessitated by the study. Most significantly, a first-year bioengineering graduate student lacked the clinical expertise to reliably differentiate between patient responses to pain and responses to environmental manipulations (such as when the patient was repositioned). After considering preliminary results, it was decided that only observations of the loss of responsiveness, the first attempt at laryngoscopy and tracheal intubation, the first skin incision, and the recovery of responsiveness were to be compared to the surrogate measure surfaces of sedation, laryngoscopy, shin algometry, and electrical tetany.

We developed a new protocol that involved more researchers, including clinical research nurses, and fewer devices. The data-collecting laptop was interfaced to the standard OR monitor, Datex AS/3 (Datex-Ohmeda Inc., Louisville, CO, USA), an A-2000

BIS, and two Medfusion 3010a infusion pumps. A 20% rise in heart rate (measured by either the ECG or the BP cuff on the Datex AS/3) within one minute of a specific stimulus was the primary indicator of a response to pain. Drug boluses were recorded by hand instead of being digitally collected. Using this protocol, we collected data from 24 patients. This study is fully described in Chapter 2.

References

1. Schnider TW, Minto CF, Shafer SL, Gambus PL, Andresen C, Goodale DB, Youngs EJ: The influence of age on propofol pharmacodynamics. Anesthesiology. 1999 Jun; 90

(6): 1502-16

2. Sheiner LB, Stanski DR, Vozeh S, Miller RD, Ham J: Simultaneous modeling of pharmacokinetics and pharmacodynamics: application to d-tubocurarine. Clin Pharmacol Ther. 1979 Mar; 25 (3): 358-71

3. Scott JC, Cooke JE, Stanski DR.: Electroencephalographic quantitation of opioid effect: comparative pharmacodynamics of fentanyl and sufentanil. Anesthesiology. 1991 Jan; 74 (1): 34-42

4. Kern SE, Xie G, White JL, Egan TE: Opioid-hypnotic synergy. Anesthesiology 2004 Jun; 100: (6): 1373-81

5. Xie G: Computer modeling and visualization of interaction between propofol and remifentanil in volunteers using response surface methodology, Bioengineering. Salt Lake City, University of Utah, 2001

6. Olofsen E, Nieuwenhuijs DJ, Sarton EY, Teppema LJ, Dahan A: Response surface modeling of drug interactions on cardiorespiratory control. Adv Exp Med Biol. 2001; 499: 303-8

7. Struys MM, Vereecke H, Moerman A, Jensen EW, Verhaeghen D, De Neve N, Dumortier FJ, Mortier EP: Ability of the bispectral index, autoregressive modelling with exogenous input-derived auditory evoked potentials, and predicted propofol concentrations to measure patient responsiveness during anesthesia with propofol and remifentanil. Anesthesiology. 2003 Oct; 99 (4): 802-12

8. Bouillon T, Bruhn J, Radu-Radulescu L, Bertaccini E, Park S, Shafer S: Non-steady state analysis of the pharmacokinetic interaction between propofol and remifentanil. Anesthesiology. 2002 Dec; 97 (6): 1350-62

9. Bouillon T, Bruhn J, Radulescu L, Andresen C, Shafer TJ, Cohane C, Shafer S: Pharmacodynamic interaction between propofol and remifentanil regarding hypnosis, tolerance of laryngoscopy, bispectral index, and electroencephalographic approximate entropy. Anesthesiology. 2004 Jun; 100 (6): 1353-72

10. Chernik DA, Gillings D, Laine H, Hendler J, Silver JM, Davidson AB, Schwam EM, Siegel JL: Validity and reliability of the Observer’s Assessment of Alertness/Sedation scale: study with intravenous midazolam. J of Clin Psychopharmacol 1990; 10 (4): 244-251

11. Minto C, Schnider T: Expanding clinical applications of population pharmacodynamic modelling. Br J Clin Pharmacol. 1998 Oct; 46 (4): 321-33

12. Wakeling HG, Zimmerman JB, Howell S, Glass PSA: Targeting effect compartment or central compartment concentration of PROP what predicts loss of consciousness? Anesthesiology 1999; 90 (1): 92-97

13. Nava-Ocampo AA, Shafer SL, Velázquez-Armenta Y, Ruiz-Velazco S, Toni B: Mathematical analysis of a pharmacodynamic model without plasma concentrations to extend its applicability. Medical Hypotheses. 2003 60 (3): 453-57

14. Bailey JM, Shafer SL: A simple analytical solution to the three-compartment pharmacokinetic model suitable for computer-controlled infusion pumps. IEEE Transactions on Biomedical Engineering 1991; 38 (6): 522-25

15. Greco WR, Bravo G, Parsons JC: The search for synergy: a critical review from a response surface perspective. Pharmacological Reviews 1995; 47 (2): 331-85

16. Berenbaum MC: Direct search methods in the optimization of cancer chemotherapy regimens. Br J Cancer 1990 Jan; 61 (1): 101-9

17. Curatolo M, Schnider TW, Petersen-Felix S, Weiss S, Signer C, Scaramozzino P, Zbinden AM: A direct search procedure to optimize combinations of epidural bupivacaine, fentanyl, and clonidine for postoperative analgesia. Anesthesiology 2000 Feb; 92 (2): 325-37

18. Minto CF, Schnider TW, Short TG, Gregg KM, Gentilini A, Shafer SL: Response surface model for anesthetic drug interactions. Anesthesiology 2000 Jun; 92 (6): 1603- 1616

19. Avram MJ, Krejcie TC: Using front-end kinetics to optimize target-controlled drug infusions. Anesthesiology. 2003 Nov; 99 (5): 1078-86

20. Bjorkman S, Wada DR, Stanski DR: Application of physiologic models to predict the influence of changes in body composition and blood flows on the pharmacokinetics of fentanyl and alfentanil. Anesthesiology. 1998 Mar; 88 (3): 657-67

21. Short TG, Ho TY, Minto CF, Schnider TW, Shafer SL: Efficient trial design for eliciting a pharmacokinetic-pharmacodynamic model-based response surface describing the interaction between two intravenous anesthetic drugs. Anesthesiology. 2002 Feb; 96 (2): 400-08

CHAPTER 2

OBSERVATIONAL STUDY

Introduction

Pharmacokinetic (PK) models describe changes in anesthetic concentrations in the body over time following drug administrations.1 Pharmacodynamic (PD) models predict the level of anesthetic effect as a function of drug concentration.1 This observational study combines a set of propofol and remifentanil pharmacokinetic and pharmacodynamic models and evaluates how accurately they predict the level of anesthesia in 24 patients undergoing abdominal laproscopic surgery. Trends to improve differences between the model predictions and observations in the patients are identified and discussed.

Kern et al. and Bouillon et al. created PD response surface models in healthy volunteers using plasma samples, assayed drug concentrations, and surrogate measures of drug effect. 2,3 Mertens et al. created similar PD response surfaces in patients using plasma samples, assayed drug concentrations, and clinical measures of drug effect. 4

This study combines PK and PD models in an attempt to accurately predict patient responses to clinical measures using drug dosing information but without 16 assayed concentrations. Though it is not practical to measure the actual drug concentrations in the brain, propofol and remifentanil effect-site concentrations, which both act primarily in the central nervous system, can be predicted using pharmacokinetic models.5 These models predict the concentrations in generalized compartments as the drug is distributed throughout the body and is metabolized.6

Using these pharmacokinetic estimates, the pharmacodynamic models of Kern et al. were compared to observations in patients for this study.2

We hypothesize that PK-PD combined models can accurately predict when a patient loses and recovers responsiveness in the OR and whether a patient will respond to laryngoscopy followed by tracheal intubation or to the first skin incision of surgery.

Further simulations were used to characterize the sensitivity of individual pharmacokinetic and pharmacodynamic variables for these combined models.

Methods

Study Design

This observational study compares the predictions of combined pharmacokinetic and pharmacodynamic (PK-PD) models in the operating room to observations of the loss and recovery of responsiveness and of adequate anesthesia for two surgical milestones: 1) laryngoscopy followed by tracheal intubation and 2) the first skin incision.

We collected intraoperative drug dosing information, observed the patient loss and recovery of responsiveness, and recorded patient responses and non-responses to surgical stimuli. Comparison of the PK-PD combined model predictions with the

17 patient observations was performed post hoc. Subsequent analyses of the parameters for the PK-PD combined models were also performed.

Subjects and Apparatus

With institutional review board approval from the University of Utah Hospital and informed consent of the patients, we studied 24, ASA physical status I, II, and III, patients (11 males and 13 females) scheduled for abdominal laparoscopic surgery under total intravenous anesthesia. All patients denied having cardiovascular, hepatic, or renal disease or a history of alcohol or drug abuse. The intraoperative anesthetic regimen was limited to propofol, remifentanil and fentanyl.

In the perioperative holding unit, a catheter was placed in the wrist of each patient for fluid and drug administration. Two T-connectors (ET-04T Smallbore T-Port

Extension Set, B. Braun Medical Inc., Bethlehem, PA, USA) were attached to the cannula, in-line with a Baxter IV drip set. Fluids were administered from the IV bag, through IV tubing, through the two T-connectors, and into the patient’s vein.

Propofol and remifentanil syringes were loaded into separate infusion pumps

(Medfusion 3010a, Medex, Inc., Dublin, OH, USA). After the patient entered the OR, the primed remifentanil and propofol infusion lines were attached to the two T-connectors at the patient’s wrist to decrease any potential delays in drug delivery by minimizing the tubing dead-space flushed by the IV drip. The anesthetists administered drug boluses for both induction and maintenance through the second IV access port distal from the patient while the IV was running. An intra-lab software interface collected data from the

18 two infusion pumps. A research nurse and a graduate student observer recorded drug boluses given manually.

Observations at Clinical Milestones

The times of loss of responsiveness (LOR) and recovery of responsiveness (ROR) were recorded by study investigators. LOR during induction was defined as when the patient no longer responded to verbal commands or loudly calling his/her name. ROR at the end of surgery was defined as when the patient responded to loud verbal commands and gentle shaking.

Responses (and non-responses) to surgical stimuli of 1) laryngoscopy followed by tracheal intubation (TI) and 2) the first skin incision (SI) were recorded by the observers. A response to pain was characterized by a 20% increase in heart rate (within

1 minute of the stimulus) subjectively evaluated by the research nurse and the anesthesiologist to be a reaction to a specific stimulus due to relatively light or inadequate anesthesia. Somatic responses to noxious stimuli, such as movement or tearing by the patient, were also considered “responses.”

Pharmacokinetic Modeling

The PK model estimates were calculated post-hoc using the patient and drug dosing data. The pharmacokinetics of each drug were assumed independent of the concentration of the other drugs. Each drug used a three-compartment plus effect-site model.6 The difference equations used to iterate each model are shown in Equations 2.1,

2.2, 2.3, and 2.4.

dC 1/dt=C 2(t)*k 21 +C 3(t)*k 31 +C e(t)*k e0 C 1(t)*(k 10 +k 12 +k 13 +k 1e )+

Input(t) [2.1]

dC 2/dt=C 1(t)*k 12 C 2(t)*k 21 [2.2]

dC 3/dt=C 1(t)*k 13 C 3(t)*k 31 [2.3]

dC e/dt=C 1(t)*k 1e C e(t)*k e0 [2.4]

C1 , C 2, C 3, and C e represent the concentrations in the central compartment, the fast equilibrating peripheral compartment, the slow equilibrating peripheral compartment, and the theoretical effect-site compartment, respectively. All compartment concentrations are functions of time. The k xy represents the microrate constants of the first-order drug transfer from compartment x to compartment y. We used the Minto-

Schnider parameters for remifentanil 7 and an adapted Shafer et al. model for fentanyl 8,9 .

We used the Tackley model for propofol, 10,11 since it had been used in the target- controlled-infusion system used for building the PD models of Kern et al. 2, and adapted it to predict an effect-site concentration 12 . All the pharmacokinetic parameters are shown in Table 2.1.

Pharmacodynamic Modeling

Kern et al. used four surrogate measures to predict anesthetic effects of sedation and analgesia with an Emax model.2,13 They used a single surrogate for sedation; the

Observer’s Assessment of Alertness/Sedation (OAA/S) was used as a measure of the

Table 2.1. Parameters used for pharmacokinetic models. For our PK models, the lean body mass (lbm) for males was defined as 1.1*mass - 128*(mass/height) 2 and for females as 1.07*mass - 148*(mass/height) 2. Age is in years, mass in kilograms, and height in centimeters. Anesthetic Variable Value

Vc 5.10.0201(age40)+0.072(lbm–55) (2.60.0162(age40)+0.0191(lbm–55))/(5.1 k 10 0.0201(age40)+0.072(lbm55)) (2.050.0301(age40))/(5.10.0201(age40)+ k 12 0.072(lbm55)) Remifentanil (0.0760.00113(age40))/(5.10.0201(age40)+ k 13 0.072(lbm55)) (2.050.0301(age40))/(9.820.0811(age40)+ k 21 0.108(lbm55))

k31 (0.0760.00113(age40))/5.42 ke0 0.5950.007(age40) Vc 6.09 k10 0.0827 k12 0.471 Fentanyl k13 0.225 k21 0.102 k31 0.006 ke0 0.112 Vc 0.320 * mass k10 0.0870 k12 0.1050 Propofol k13 0.0220 k21 0.0640 k31 0.00340 ke0 0.250

21 depth of hypnosis.14 Three surrogate measures for analgesia were used; responses to shin algometry, electrical tetany, and laryngoscopy were compared to patient responses to the first skin incision and to laryngoscopy followed by tracheal intubation. The general Emax model of Greco et al. for two synergistic drugs, used by Kern et al., is shown in Equation 2.5 where Drugs A and B are the concentrations of the individual drugs.13

γ  DrugA DrugB DrugA *DrugB   + + α*  =  EC50A EC50B EC50A *EC50B  Effect γ [2.5]  DrugA DrugB DrugA * DrugB   + + α*  + 1  EC50A EC50B EC50A * EC50B 

EC 50A and EC 50B are the drug concentrations necessary to achieve 100% effect in

50% of the population using either drug alone. The α term describes the pharmacodynamic synergism between drugs A and B while the γ term describes the steepness of the surface or the pharmacodynamic variability within the population.

Although the OAA/S follows a discrete scale from 1 to 5, Kern et al. treated

OAA/S scores above and equal to 4 and below 4 as binary states of sedation, because an

OAA/S of 4 represents a sedation level comparable to the conscious sedation desired in some surgeries. Using the raw data of Kern et al., 2,15 we calculated an additional sedation response surface for the transition in OAA/S scores from 2 to 1 because an

OAA/S < 2 is similar to the states “sedated and non-responsive” in the OR for general anesthesia. First EC 50 values for propofol and remifentanil were fit (for each drug alone)

22 to a sigmoid Emax model using WinNonlin (Version 2.1, Pharsight Corp., Mountain

View, CA).2 Those individually solved EC 50 values were plugged into the Greco et al. interaction model to describe the synergistic effects of remifentanil and propofol on sedation. The α and γ terms were solved using the least squares method in Excel (Excel

2000, Microsoft Corp., Redmond, WA). Table 2.2 shows the EC 50 , α, and γ values for the surrogate measures of OAA/S < 2, Laryngoscopy, Shin Algometry, and Electrical Tetany.

The effects of the anesthetics are estimated as functions of a pair of propofol and remifentanil concentrations. Thus, expected PD effects were calculated using the PK estimates of the drug C eff at the time of LOR, ROR, TI, and SI. To account for the analgesic effect of fentanyl we assumed its relative opioid effect to be 1.2.16 To calculate the total opioid concentration, normalized to remifentanil, the predicted concentrations of fentanyl were multiplied by their relative opioid effect (1.2) and were added to the predicted concentration of remifentanil. We estimated the PD effect from the total opioid C eff and the propofol C eff ; the total opioid Ceff values and propofol Ceff values at

LOR, ROR, TI, or SI marked points on the response surfaces.

Data Analysis

We used the estimated Ceff values at the time of LOR, ROR, TI, and SI to calculate the PD prediction of the effects of propofol and total opioid. These predictions were compared to the observations of the patient at these milestones. For LOR and ROR, we also used the observations 30 seconds prior to the recorded change in sedation state. For example, all observations of patients at LOR were “unresponsive” but each of

Table 2.2. Parameters used for pharmacodynamic models. EC 50Prop is in μg/ml, EC 50Remi is in ng/ml, and α and γ terms are both unitless. SurrogateMeasure Variable Value

EC 50Prop 2.60 EC 34.0 OAA/S<2 50Remi α 6.34 γ 5.51

EC 50Prop 5.60 EC 2.20 Laryngoscopy 50Remi α 33.2 γ 2.20

EC 50Prop 4.16 EC 8.84 ShinAlgometry 50Remi α 8.20 γ 8.34

EC 50Prop 4.57 EC 21.3 ElectricalTetany 50Remi α 14.7 γ 6.00

24 those patients were “responsive” 30 seconds earlier. To visualize the PD predictions at the clinical milestones, we used Matlab (The MathWorks, Inc., v 6.5, release 13, Natick,

MA, USA) to plot these values on the PD response surfaces described by Equation 2.5 using parameter sets from Table 2.1.

Combined Model Sensitivity Analysis

To identify the most sensitive parameter of the PK-PD combined models, several simulations were run using individually scaled parameter values. The differences between the initial model predictions (a continuous variable between 0 and 1) and the observations of the patients (where 0 is a response and a non-response is 1) at each stimulus were calculated, squared, and summed.17 As the model parameters were scaled (independently of each other), we summed the square of the differences between these new predictions and the observations. PD changes were based on unchanged PK simulations, and PK changes were compared to unchanged PD simulations. Preliminary analysis identified k 10 and V c as the two most influential PK parameters. An initial set of four different scaling factors ( 1⁄10 , ½, 2, and 10) were applied to k 10 , V c, EC 50Prop , EC 50Remi , α, and γ, individually. A new set of scaling factors were individually chosen for EC 50Prop ,

EC 50Remi , and α to lessen the total squared differences. This process was iterated a total of three times to observe trends in the relative sensitivity of the prediction error to individual parameters.

Results

All patients enrolled completed the study. The 24 patients had a mean age of

38.9 ± 12.4 years, weight of 86.4 ± 22.6 kg, and height of 171.58 ± 8.99 cm. Fifteen of the cases were laproscopic cholecystectomies, 6 were laproscopic hernia repairs, and 3 were laproscopic nissen fundoplications. Sixteen of the anesthetics were delivered by 2 experienced CRNAs, two by two third year residents, three by two second year residents and three by a first year resident.

All but two patients received midazolam (average dose of 1.61 mg, ± 0.49) prior to entering the operating room (OR). (One of the patients declined midazolam and another patient received midazolam after arriving in the OR.) Propofol was the only other intraoperative sedative. Remifentanil and fentanyl were given during the surgial procedure. 10 patients received 30 mg ketorolac tromethamine late in the procedures for maintenance and post-operative pain management, however these pharmacokinetics were not modeled.

Table 2.3 gives the average predicted Ceff values at the observed LOR, ROR, TI, and SI. The table also indicates the number of patients who responded within 1 minute of laryngoscopy followed by tracheal intubation or of the first skin incision.

Figures 2.1, 2.2, 2.3, 2.4, and 2.5 show Ceff values of propofol and remifentanil at

LOR, ROR, TI, and SI plotted on the Kern et al. OAA/S < 2, Laryngoscopy, and Electrical

Tetany PD response surfaces. The response surfaces are shown from a topographical

(top-down) perspective where the darker shading represents lower likelihoods of anesthesia and thus higher likelihoods of patient responses. The 50% and 95% isoboles are also shown on each surface. The figures show Ceff values over 60 seconds; the Ceff prior to the event is the “tail” (triple triangles) and the Ceff 30 seconds following the

Table 2.3. Observations and pharmacokinetic Ceff estimates at surgical milestones.

TotalOpioid Propofol SurgicalStimulus n (ng/ml) (g/ml) ObservedLossofResponsiveness 23 6.83±2.19 1.00±0.91 ObservedReturnofResponsiveness 23 2.83±1.59 1.95±0.42 13NR° 6.96±1.86 2.66±0.86 Laryn.AndTrachealIntub. 11R† 5.81±1.45 2.31±0.64 23NR 5.90±1.94 2.82±0.66 FirstSkinIncision 1R 4.23 1.57 °NRindicatespatientswhodidnotrespondtopainatthesurgicalmilestone. †Rindicatespatientswhorespondedtopainatthesurgicalmilestone.

Figure 2.1. C eff values at loss of responsiveness on the sedation response (OAA/S<2). The large circles represent the remifentanil and propofol C eff values (predicted by the pharmacokinetic models) at LOR when the patients are sedated. The squares represent estimated C eff values 30 seconds prior to LOR when the patients were not sedated. The “arrows” show the PK model-predicted C eff values 30 seconds prior to and after LOR.

Figure 2.2. C eff values at recovery of responsiveness on the sedation response surface (OAA/S<2). The large squares represent the remifentanil and propofol C eff values (predicted by the pharmacokinetic models) at ROR. The circles show estimated C eff values 30 seconds prior to ROR when the patients were sedated. The changes in Ceff from 30 seconds before ROR to 30 seconds after ROR are minimal.

Figure 2.3. C eff values at laryngoscopy followed by tracheal intubation on the response surface for laryngoscopy. Stars represent patient responses and circles represent patient non-responses at the remifentanil and propofol C eff values (predicted by the pharmacokinetic models) at TI. The arrows show the PK model- predicted C eff values for 30 seconds prior to TI and the C eff values 30 seconds after TI.

Figure 2.4. C eff values at the first skin incision on the response surface for shin algometry. The star represents the only patient response to the first skin incision and the circles represent patient non-responses at the remifentanil and propofol C eff values (predicted by the pharmacokinetic models) at SI. The arrows show the PK model-predicted C eff values for 30 seconds prior to SI and the C eff values 30 seconds after SI.

Figure 2.5. C eff values at the first skin incision on the response surface for electrical tetany. The star represents the only patient response to the first skin incision and the circles represent patient non-responses at the C eff values (predicted by the pharmacokinetic models) at SI. The arrows show the PK model-predicted C eff values for 30 seconds prior to SI and the C eff values 30 seconds after SI.

actual observation is marked as the “head” (single triangle).

Table 2.4 shows the summed squared differences between the model predictions and the observations of the patients. To observe the sensitivity of the parameters, they were individually scaled. Some of the scaling factors that resulted in an improved fit between the predictions and observations and the summed squared differences are also shown. Due to a lack of patient responses to the first skin incision, evaluation of the sensitivity of models predicting analgesia for skin incision (shin algometry and electrical tetany) was not performed.

Discussion

We postoperatively used intraoperative dosing data to calculate PK predictions for propofol, remifentanil, and fentanyl at the times of surgical milestones. These PK predictions were then used to create PD predictions of patient responses at these moments. These PD predictions were compared to observations in the patients and were plotted on PD response surface models of surrogate measures. In this observational study, we found great variance in the data from the operating room and were unable to indisputably relate surrogate measures to clinical measures. However, by scaling individual parameters, we recognized several trends that may allow for future improvement of model predictions.

From the LOR plot Figure 2.1, we see that only about 1/3 of the changes from

“responsive” to “unresponsive” occurred at PD prediction levels about the 50% isobole.

Table 2.4. Summed squared differences for scaled PK-PD model parameters. Scaling factors were applied only to the parameter indicated, while original values (Tables 2.1 and 2.2) were used for all other parameters. ImprovingScaling SummedSquared ModelandStimulus Parameter Factor Difference All InitialValues 12.5

k10 0.1 9.46 Vc 0.5 9.13 OAA/S<2andLOR EC 50Prop 0.5 8.18 EC 50Remi 0.5 7.31 α 2.5 7.70 γ 0.15 9.86 All InitialValues 15.8

k10 1 15.8 Vc 1 15.8 OAA/S<2andROR EC 50Prop 1.3 14.6 EC 50Remi 3.0 14.0 α 0.15 13.9 γ 0.05 11.5 All InitialValues 8.72

k10 2.0 7.32 V 2.0 7.35 Laryngoscopy(followedby c EC 2.1 7.25 TrachealIntubation) 50Prop EC 50Remi 3.0 7.01 α 0.25 6.94 γ 0.06 5.96 ShinAlgometryandSkinIncision All InitialValues 24.0 ElectricalTetanyandSkinIncision All InitialValues 23.7

For an ideal fit, half of those points would fall above and half below the 50% isobole. An improved fit occurs when each parameter (EC 50Prop , EC 50Remi , α, γ) is scaled < 1, except for the α term. The low γ scaling factor is most easily interpreted as the large variance within the data.

While this suggests that the “actual” drug effect was greater than predicted by the PD models or that “real” Ceff drug concentrations were higher than those predicted, our data does not let us differentiate between these two possibilities. Other PK errors might arise from a misspecified PK model that eliminates the drug too quickly or that predicts too low of a peak drug concentration. Differences between predicted and real

Ceff may be due to a time lag between the injection of a drug and its distribution to the effect site. Wada and Ward suggested using fixed input and recirculation delays between the infusion and the estimated change in PK model plasma concentration predictions. 18 Had we assumed a 30 second distribution delay, our data points would shift to higher drug concentrations such that ¾ of the changes from “responsive” to

“unresponsive” occurred at PD prediction levels about the 50% isobole. A further limitation of our PK model is that it was designed assuming instantaneous and complete mixing, a fixed V c, and did not account for PK interactions between propofol, remifentanil, or fentanyl, nor the effects of drug recirculation. 19,20,21 Thus studying LOR by bolus induction, as seen in the majority of our study population, is especially difficult.

It is also noteworthy that the average remifentanil C eff at LOR (6.83 ng/ml) is 20% of EC 50Remi (34.0 ng/ml) , while the average propofol C eff at LOR (1.00 μg/ml) is 38% of

EC 50Prop (2.60 μg/ml). This indicates that for these patients and these PD models, propofol contributed more to sedation than did remifentanil.

Though the patient transitions from “unresponsive” to “responsive,” shown in

Figure 2.2, are not evenly distributed above and below the 50% isobole, the majority of these transitions are between the 50% and 95% isoboles. This suggests that the overall combined model predictions are relatively close to matching the patients studied. The simulations for ROR corroborate that at relative steady state, the PK models 7,8,9,10,11 studied are well tuned. This is expected towards the end of surgery when the pharmacokinetics are more stable resulting in Ceff values close to plasma concentrations.

Furthermore, the average remifentanil C eff at ROR (2.83 ng/ml) is 8% of EC 50Remi (34.0 ng/ml) , while the average propofol C eff at ROR (1.95 μg/ml) is 75% of EC 50Prop (2.60

μg/ml). In this study, propofol controlled sedation more than remifentanil. However, for ROR, we observed less synergism or less drug potency than our PD models predicted. Clinically, these data suggest that to achieve quicker wake-ups while managing pain, higher levels of opioid may be acceptable as sedative levels decrease.

Although sedation is treated as a binary state in the operating room, it is actually a continuous measure. In our study, this discrepancy is compounded by our inability to identify the exact moments of LOR and ROR. In a controlled clinical study environment, a typical OAA/S is used in which a volunteer may be asked to repeat a phrase multiple times per minute in order to observe the exact moment of LOR and

ROR.2 Doufas et al. has used another monitor, the automated responsiveness test (ART) or automated responsiveness monitor (ARM), to record the moment of sedation. 22,23,24 In

36 contrast, in the operating room, the moment of LOR was assessed by a research nurse watching the patient and the anesthesiologist but without directly addressing the patient. An automated system that requires a response from the patient may provide a more consistent and precise measure of LOR and ROR.22,23,24

For TI, it appears that the drug effect was less than predicted, or else that higher concentrations are necessary for providing “adequate anesthesia.” Without drug concentration assays, it is impossible to distinguish whether this is due to kinetics or due to dynamics. Clinically, the anesthetists wait until they expect the peak pharmacodynamic effect to be achieved prior to performing laryngoscopy and tracheal intubation. Nonetheless, as shown in Figure 2.3, nearly half the patients responded to tracheal intubation (following laryngoscopy). Tracheal intubation followed laryngoscopy as quickly as possible. As a result, we were unable to separate these two milestones and treated them as a single stimulus. That so many patients responded to laryngoscopy followed by tracheal intubation while at predicted effect levels above the

95% isobole of the laryngoscopy response surface is not surprising; we expect tracheal intubation followed by laryngoscopy is more stimulating than tracheal intubation alone.

Merten et al. found similar results, creating separate response surfaces for laryngoscopy alone and laryngoscopy followed by tracheal intubation.4 However, it appears that less synergism was observed than was predicted by the PD model of Kern et al. for laryngoscopy. Clinically, higher drug concentrations, compared to those targeted for laryngoscopy alone, are necessary for tracheal intubation.

Because only a single patient responded to skin incision, we cannot draw strong

37 conclusions regarding the predictiveness of the PK and PD combined models. However, it is noteworthy that on the electrical tetany response surface, the single response was predicted by the PK and PD models to be near the 50% isobol while the rest of the patients were at or above the 95% isobol at this surgical milestone (see Figure 2.5). The data did not fit the shin algometry response surface as conveniently. Although we observed the first skin incision clearly, the second, third, fourth, etc. incisions were less obvious and were not consistent between the different types of surgery. Furthermore evaluating repeated stimuli in the same patient violates a fundamental assumption of independence, necessary for most statistical tests. However, if repeated measures were used, titration throughout the surgery may result in a better evaluation of intraoperative

PD models of repeated surgical stimuli, such as skin incisions or wound closures. A similar scheme was successfully used by Mertens et al. to create a laryngoscopy response surface directly from patient data.4

A fundamental challenge for this study was the degrees for freedom we allowed while considering numerous variables. The anesthetists were only asked to follow their

(individual) standard practices to provide total intravenous anesthesia (TIVA) using propofol and remifentanil as the primary anesthetic agents. In other words, we did not control the drug concentration ranges. 2,4,25 This lack of control was exasperated by a lack of plasma samples that would be necessary to separate PK from PD errors.

Future protocols should require a slow induction by infusion to minimize the differences between bolus and infusion pharmacokinetics and dynamics. This slower induction may increase the accuracy of the pharmacokinetic predictions by minimizing

38 the bolus kinetics that are particularly hard to predict. Greater control might be accomplished by prescribing an induction scheme and specific dosing changes in response to observations in patients.

Abdominal laproscopic surgeries were chosen because they were appropriate for propofol and opioid TIVAs, and because they were common in the University Hospital.

However, we were unprepared for the subtle stimulation differences between cholecystectomies, hernia repairs, and nissen fundoplications. For example, a bougie was nasally inserted for nissen fundoplications and staples were used for some hernia repairs, and some surgeries were finished within an hour while some required three hours. We chose the four clinical milestones of LOR, ROR, TI, and SI because they were consistently identifiable for all these TIVA-appropriate surgeries. Had we observed more patients for the same types of surgeries, we would expect to have reported on the

PK-PD combined model predictions for other specific surgical stimuli, such as responses to internal sutures or staples for hernia repairs, the incisions and removal of the gall bladder for cholecystectomies, or insertion of a Bougie tube for fundoplications.

In summary, the PK-PD combined models do not predict responsiveness to laryngoscopy followed by tracheal intubation. It is likely that the surgical stimulus is more painful than the surrogate measure. For LOR and ROR, 22% and 65% of the data points from the PK-PD combined models for OAA/S < 2 fall between the 50% and 95% isobols, respectively. That the average propofol C eff for the OR data for LOR and ROR is closer to EC 50Prop than the remifentanil C eff is to EC 50Remi suggests that propofol (rather than remifentanil) was the main contributor to responsiveness in these patients. This

39 suggests that to help manage pain postoperatively while having a quick recovery of consciousness, opioid levels should be maintained while propofol levels should be reduced.

References

1. Minto C, Schnider T: Expanding clinical applications of population pharmacodynamic modelling. Br J Clin Pharmacol. 1998 Oct; 46 (4): 321-33

2. Kern SE, Xie G, White JL, Egan TE: Opioid-hypnotic synergy. Anesthesiology 2004 Jun; 100: (6): 1373-81

3. Bouillon T, Bruhn J, Radulescu L, Andresen C, Shafer TJ, Cohane C, Shafer S: Pharmacodynamic interaction between propofol and remifentanil regarding hypnosis, tolerance of laryngoscopy, bispectral index, and electroencephalographic approximate entropy. Anesthesiology. 2004 Jun; 100 (6): 1353-72

4. Mertens MJ, Olofsen E, Engbers FHM, Burm AGL, Bovill JG, Vuyk J: Propofol reduces perioperative remifentanil requirements in a synergistic manner: response surface modeling of perioperative remifentanil-propofol interactions. Anesthesiology 2003; 99 (2): 347-359

5. Wakeling HG, Zimmerman JB, Howell S, Glass PSA: Targeting effect compartment or central compartment concentration of propofol what predicts loss of consciousness? Anesthesiology 1999; 90 (1): 92-97

6. Bailey JM, Shafer SL: A simple analytical solution to the three-compartment pharmacokinetic model suitable for computer-controlled infusion pumps. IEEE Transactions on Biomedical Engineering 1991; 38 (6): 522-25

7. Minto CF, Schnider TW, Egan TD, Youngs E, Lemmens HJ, Gambus PL, Billard V, Hoke JF, Moore KH, Hermann DJ, Muir KT, Mandema JW, Shafer SL: Influence of age and gender on the pharmacokinetics and pharmacodynamics of remifentanil. I. Model development. Anesthesiology 1997; 86 (1): 10-23

8. Shafer SL, Varvel JR, Aziz N, Scott JC: Pharmacokinetics of fentanyl administered by computer-controlled infusion pump. Anesthesiology 1990; 73 (6): 1091-1102

9. Scott JC, Stanski DR: Decreased fentanyl and alfentanil dose requirements with age. A simultaneous pharmacokinetic and pharmacodynamic evaluation. J Pharmacol Exp Ther. 1987 Jan; 240 (1): 159-66

10. Tackley RM, Lewis GTR, Prys-Roberts C, Boaden RW, Dixon J, Harvey JT: Computer controlled infusion of propofol. Br J Anaesth 1989; 62: 46-53

11. Vuyk J, Engbers FHM, Burm AGL, Vletter AA, Bovill JG: Performance of computer- controlled infusion of propofol: an evaluation of five pharmacokinetic parameter sets. Anesth Analg 1995; 81: 1275-82

12. Gepts E, Claeys MA, Camu F, Smekens L: Infusion of propofol ('Diprivan') as sedative technique for colonoscopies. Postgrad Med J. 1985; 61 Suppl 3: 120-6

13. Greco WR, Bravo G, Parsons JC: The search for synergy: a critical review from a response surface perspective. Pharmacological Reviews 1995; 47 (2): 331-85

14. Chernik DA, Gillings D, Laine H, Hendler J, Silver JM, Davidson AB, Schwam EM, Siegel JL: Validity and reliability of the Observer’s Assessment of Alertness/Sedation scale: study with intravenous midazolam. J of Clin Psychopharmacol 1990; 10 (4): 244-251

15. Xie G: Computer modeling and visualization of interaction between propofol and remifentanil in volunteers using response surface methodology, Bioengineering. Salt Lake City, University of Utah, 2001

16. Egan TD, Muir KT, Hermann DJ, Stanski DR, Shafer SL: The electroencephalogram (EEG) and clinical measures of opioid potency: defining the EEG-clinical potency relationship (‘fingerprint’) with application to remifentanil. International Journal of Pharmaceutical Medicine 2001; 15: 1-9

17. Varvel JR, Donoho DL, Shafer SL: Measuring the predictive performance of computer-controlled infusion pumps. J Pharmacokinet Biopharm. 1992 Feb; 20 (1): 63-94

18. Wada DR, Ward DS: The hybrid model: a new pharmacokinetic model for computer- controlled infusion pumps. IEEE Transactions on Biomedical Engineering 1994 Feb; 41 (2): 134-42

19. Avram MJ, Krejcie TC: Using front-end kinetics to optimize target-controlled drug infusions. Anesthesiology. 2003 Nov; 99 (5): 1078-86

20. Upton RN: The two-compartment recirculatory pharmacokinetic model—an introduction to recirculatory pharmacokinetic concepts. Br J Anaesth. 2004; 92 (4): 475-494

21. Bouillon T, Bruhn J, Radu-Radulescu L, Bertaccini E, Park S, Shafer S: Non-steady state analysis of the pharmacokinetic interaction between propofol and remifentanil. Anesthesiology. 2002 Dec; 97 (6): 1350-62

22. Doufas AG, Bakhshandeh M, Bjorksten AR, Greif R, Sessler DI: Automated responsiveness test (ART) predicts loss of consciousness and adverse physiologic responses during propofol conscious sedation. Anesthesiology. 2001; 94: 585-92

23. Doufas AG, Bakhshandeh M, Bjorksten AR, Greif R, Sessler DI: A new system to target the effect-site during propofol sedation. Acta Anaesthesiol Scand 2003; 47: 944—950

24. Doufas AG, Bakhshandeh M, Bjorksten AR, Shafer SL, Sessler DI: Induction Speed is not a determinant of propofol pharmacodynamics. Anesthesiology. 2004 Nov; 101(5): 1112-1121

25. Short TG, Ho TY, Minto CF, Schnider TW, Shafer SL: Efficient trial design for eliciting a pharmacokinetic-pharmacodynamic model-based response surface describing the interaction between two intravenous anesthetic drugs. Anesthesiology. 2002 Feb; 96 (2): 400-08

CHAPTER 3

CONCLUSION

Summary

The aim of the study was to evaluate how well combined PK and PD models predict the depth of anesthesia in patients by modeling sedation and analgesia to specific stimuli. By study design, observations were made without taking plasma samples and without changing the practice of the surgeon and the anesthesiologist. We hoped to find a clear pharmacodynamic relationship between surgical stimuli and surrogate measures. Ultimately, we identified trends in how to adjust population pharmacological models to provide predictions that better match observations in the study patient population. Clinically these trends suggest how greater analgesia with quicker wake-ups can be achieved with propofol and opioids.

Comparison of Observational Studies and Clinical Studies

It is clear that a clinical research study in which anesthetic regimens are controlled, can validate pharmacokinetic and pharmacodynamic models more robustly than an observational study.1 In this observational study, surgical stimuli occurred at the convenience and discretion of the clinicians, not at specific steady-state 43 concentrations. In contrast, in a clinical research study in volunteers, specific anesthetic concentrations were targeted and maintained before applying a surrogate stimulus.

Thus, in a clinical research study, it is relatively easy to compare consistent stimuli at preset anesthetic concentrations 2,3,4,5 while neither the stimuli nor the concentrations are consistent in an observational study 6. This is one of the reasons that the relationships between surrogate measures and surgical stimuli remain unclear.

Though this observational study ultimately did not define the relationships between surrogate measures and surgical stimuli, the parameters most useful for tuning

PK and PD models were identified by post hoc simulations. However, without assayed anesthetic concentrations, it is impossible to identify “real” PK and PD parameters for the 24 patients studied. Nonetheless, these results help provide a clinical rational for anesthetic recipes: propofol is the key anesthetic in providing sedation while opioids, potentiated even by low propofol concentrations, provide analgesia.

Utility and Limitations of Clinical Pharmacological Modeling

Pharmacological models can be used to calculate the anesthetic path for the shortest wake-up times while avoiding other negative side effects. There are two main obstacles for bringing this information to the operating room for clinical use: 1) there are few tools that provide modeled information to the clinician and 2) models are usually population based. Target-controlled infusion pumps use PK models to achieve and maintain clinician-selected concentrations. However these systems do not truly target the anesthesiologists’ primary interest: appropriate sedation and analgesia for their

44 patients. Future efforts will include the real-time calculation and visualization of both

PK and PD models in the operating room.

Syroid et al. 7 has shown that the visualization of pharmacokinetic and pharmacodynamic models in a simulation scenario allows the anesthesiologist to exert greater control over the anesthetic. This can result in using less drug and achieving quicker wake-ups. In other cases, visualization may help clinicians identify dosing errors. Using models to help titrate the anesthetic may lead to safer anesthesia.

A current limitation for the use of pharmacokinetic and pharmacodynamic models is that they are generally population-based.8 Yet in the operating room, individualized models would provide more accurate predictions for each patient. The use of feedback controllers and microassays may allow future adaptation of population models to an individual patient.

Future Work

Future work will focus on collecting data from surgeries where the surgical stimuli are very consistent. For the current study, we observed several different abdominal laproscopic surgeries but future studies should focus on surgeries where the stimuli and the surgical procedure are more uniform. The anesthetic plan should be defined pre-operatively to include a slow induction and titrating the anesthetic while maintaining patient comfort.3 Plasma samples should be taken to separate pharmacokinetic from pharmacodynamic prediction errors.8,9 Additionally, the interactions between other anesthetics should be studied. Ultimately, the goal will be to

45 visualize pharmacological models in real-time to guide the anesthesiologist to a specific predicted level of anesthesia for a variety of stimuli with a library of anesthetics.

References

1. Fisher DM, Wright PMC: Are plasma concentration values necessary for pharmacodynamic modeling of muscle relaxants? Anesthesiology 1997 Mar; 86 (3): 567-75

2. Bruhn J, Bouillon TW, Radulescu L, Hoeft A, Bertaccini E, Shafer SL: Correlation of approximate entropy, bispectral index, and spectral edge frequency 95 (SEF95) with clinical signs of “anesthetic depth” during coadministration of propofol and remifentanil. Anesthesiology 2003 Mar; 98 (3): 621-7

3. Mertens MJ, Olofsen E, Engbers FHM, Burm AGL, Bovill JG, Vuyk J: Propofol reduces perioperative remifentanil requirements in a synergistic manner: response surface modeling of perioperative remifentanil-propofol interactions. Anesthesiology 2003; 99 (2): 347-359

4. Bouillon T, Bruhn J, Radulescu L, Andresen C, Shafer TJ, Cohane C, Shafer S: Pharmacodynamic interaction between propofol and remifentanil regarding hypnosis, tolerance of laryngoscopy, bispectral index, and electroencephalographic approximate entropy. Anesthesiology 2004 Jun; 100 (6): 1353-72

5. Kern SE, Xie G, White JL, Egan TE: Opioid-hypnotic synergy. Anesthesiology 2004 Jun; 100: (6): 1373-81

6. Vuyk J, Lim T, Engbers FH, Burm AG, Vletter AA, Bovill JG: The pharmacodynamic interaction of propofol and alfentanil during lower abdominal surgery in women. Anesthesiology 1995; 83 (1): 8-22

7. Syroid ND, Agutter J, Drews FA, Westenskow DR, Albert RW, Bermudez JC, Strayer DL, Prenzel H, Loeb RG, Weinger MB: Development and evaluation of a graphical anesthesia drug display. Anesthesiology 2002; 96: 565-575

8. Minto C, Schnider T: Expanding clinical applications of population pharmacodynamic modelling. Br J Clin Pharmacol. 1998 Oct; 46 (4): 321-33

9. Vuyk J, Engbers FHM, Burm AGL, Vletter AA, Bovill JG: Performance of computer- controlled infusion of propofol: an evaluation of five pharmacokinetic parameter sets. Anesth Analg 1995; 81: 1275-82